Diffusion tensor imaging fiber tracking with reliable tracking orientation and flexible step size☆

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Yao, Xufeng; Wang, Manning; Chen, Xinrong; Nie, Shengdong; Li, Zhexu; Xu, Xiaoping; Zhang, Xuelong; Song, Zhijian

2013-01-01

We propose a method of reliable tracking orientation and flexible step size fiber tracking. A new directional strategy was defined to select one optimal tracking orientation from each directional set, which was based on the single-tensor model and the two-tensor model. The directional set of planar voxels contained three tracking directions: two from the two-tensor model and one from the single-tensor model. The directional set of linear voxels contained only one principal vector. In addition, a flexible step size, rather than fixable step sizes, was implemented to improve the accuracy of fiber tracking. We used two sets of human data to assess the performance of our method; one was from a healthy volunteer and the other from a patient with low-grade glioma. Results verified that our method was superior to the single-tensor Fiber Assignment by Continuous Tracking and the two-tensor eXtended Streamline Tractography for showing detailed images of fiber bundles. PMID:25206444

Novel diffusion tensor imaging technique reveals developmental streamline volume changes in the corticospinal tract associated with leg motor control.

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Kamson, David O; Juhász, Csaba; Chugani, Harry T; Jeong, Jeong-Won

2015-04-01

Diffusion tensor imaging (DTI) has expanded our knowledge of corticospinal tract (CST) anatomy and development. However, previous developmental DTI studies assessed the CST as a whole, overlooking potential differences in development of its components related to control of the upper and lower extremities. The present cross-sectional study investigated age-related changes, side and gender differences in streamline volume of the leg- and hand-related segments of the CST in children. DTI data of 31 children (1-14 years; mean age: 6±4 years; 17 girls) with normal conventional MRI were analyzed. Leg- and hand-related CST streamline volumes were quantified separately, using a recently validated novel tractography approach. CST streamline volumes on both sides were compared between genders and correlated with age. Higher absolute streamline volumes were found in the left leg-related CST compared to the right (p=0.001) without a gender effect (p=0.4), whereas no differences were found in the absolute hand-related CST volumes (p>0.4). CST leg-related streamline volumes, normalized to hemispheric white matter volumes, declined with age in the right hemisphere only (R=-.51; p=0.004). Absolute leg-related CST streamline volumes showed similar, but slightly weaker correlations. Hand-related absolute or normalized CST streamline volumes showed no age-related variations on either side. These results suggest differential development of CST segments controlling hand vs. leg movements. Asymmetric volume changes in the lower limb motor pathway may be secondary to gradually strengthening left hemispheric dominance and is consistent with previous data suggesting that footedness is a better predictor of hemispheric lateralization than handedness. Copyright © 2014 The Japanese Society of Child Neurology. Published by Elsevier B.V. All rights reserved.

A higher-order tensor vessel tractography for segmentation of vascular structures.

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Cetin, Suheyla; Unal, Gozde

2015-10-01

A new vascular structure segmentation method, which is based on a cylindrical flux-based higher order tensor (HOT), is presented. On a vessel structure, the HOT naturally models branching points, which create challenges for vessel segmentation algorithms. In a general linear HOT model embedded in 3D, one has to work with an even order tensor due to an enforced antipodal-symmetry on the unit sphere. However, in scenarios such as in a bifurcation, the antipodally-symmetric tensor embedded in 3D will not be useful. In order to overcome that limitation, we embed the tensor in 4D and obtain a structure that can model asymmetric junction scenarios. During construction of a higher order tensor (e.g. third or fourth order) in 4D, the orientation vectors lie on the unit 3-sphere, in contrast to the unit 2-sphere in 3D tensor modeling. This 4D tensor is exploited in a seed-based vessel segmentation algorithm, where the principal directions of the 4D HOT is obtained by decomposition, and used in a HOT tractography approach. We demonstrate quantitative validation of the proposed algorithm on both synthetic complex tubular structures as well as real cerebral vasculature in Magnetic Resonance Angiography (MRA) datasets and coronary arteries from Computed Tomography Angiography (CTA) volumes.

AxTract: Toward microstructure informed tractography.

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Girard, Gabriel; Daducci, Alessandro; Petit, Laurent; Thiran, Jean-Philippe; Whittingstall, Kevin; Deriche, Rachid; Wassermann, Demian; Descoteaux, Maxime

2017-11-01

Diffusion-weighted (DW) magnetic resonance imaging (MRI) tractography has become the tool of choice to probe the human brain's white matter in vivo. However, tractography algorithms produce a large number of erroneous streamlines (false positives), largely due to complex ambiguous tissue configurations. Moreover, the relationship between the resulting streamlines and the underlying white matter microstructure characteristics remains poorly understood. In this work, we introduce a new approach to simultaneously reconstruct white matter fascicles and characterize the apparent distribution of axon diameters within fascicles. To achieve this, our method, AxTract, takes full advantage of the recent development DW-MRI microstructure acquisition, modeling, and reconstruction techniques. This enables AxTract to separate parallel fascicles with different microstructure characteristics, hence reducing ambiguities in areas of complex tissue configuration. We report a decrease in the incidence of erroneous streamlines compared to the conventional deterministic tractography algorithms on simulated data. We also report an average increase in streamline density over 15 known fascicles of the 34 healthy subjects. Our results suggest that microstructure information improves tractography in crossing areas of the white matter. Moreover, AxTract provides additional microstructure information along the fascicle that can be studied alongside other streamline-based indices. Overall, AxTract provides the means to distinguish and follow white matter fascicles using their microstructure characteristics, bringing new insights into the white matter organization. This is a step forward in microstructure informed tractography, paving the way to a new generation of algorithms able to deal with intricate configurations of white matter fibers and providing quantitative brain connectivity analysis. Hum Brain Mapp 38:5485-5500, 2017. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Visualizing whole-brain DTI tractography with GPU-based Tuboids and LoD management.

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Petrovic, Vid; Fallon, James; Kuester, Falko

2007-01-01

Diffusion Tensor Imaging (DTI) of the human brain, coupled with tractography techniques, enable the extraction of large-collections of three-dimensional tract pathways per subject. These pathways and pathway bundles represent the connectivity between different brain regions and are critical for the understanding of brain related diseases. A flexible and efficient GPU-based rendering technique for DTI tractography data is presented that addresses common performance bottlenecks and image-quality issues, allowing interactive render rates to be achieved on commodity hardware. An occlusion query-based pathway LoD management system for streamlines/streamtubes/tuboids is introduced that optimizes input geometry, vertex processing, and fragment processing loads, and helps reduce overdraw. The tuboid, a fully-shaded streamtube impostor constructed entirely on the GPU from streamline vertices, is also introduced. Unlike full streamtubes and other impostor constructs, tuboids require little to no preprocessing or extra space over the original streamline data. The supported fragment processing levels of detail range from texture-based draft shading to full raycast normal computation, Phong shading, environment mapping, and curvature-correct text labeling. The presented text labeling technique for tuboids provides adaptive, aesthetically pleasing labels that appear attached to the surface of the tubes. Furthermore, an occlusion query aggregating and scheduling scheme for tuboids is described that reduces the query overhead. Results for a tractography dataset are presented, and demonstrate that LoD-managed tuboids offer benefits over traditional streamtubes both in performance and appearance.

Comparing a diffusion tensor and non-tensor approach to white matter fiber tractography in chronic stroke.

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Auriat, A M; Borich, M R; Snow, N J; Wadden, K P; Boyd, L A

2015-01-01

Diffusion tensor imaging (DTI)-based tractography has been used to demonstrate functionally relevant differences in white matter pathway status after stroke. However, it is now known that the tensor model is insensitive to the complex fiber architectures found in the vast majority of voxels in the human brain. The inability to resolve intra-voxel fiber orientations may have important implications for the utility of standard DTI-based tract reconstruction methods. Intra-voxel fiber orientations can now be identified using novel, tensor-free approaches. Constrained spherical deconvolution (CSD) is one approach to characterize intra-voxel diffusion behavior. In the current study, we performed DTI- and CSD-based tract reconstruction of the corticospinal tract (CST) and corpus callosum (CC) to test the hypothesis that characterization of complex fiber orientations may improve the robustness of fiber tract reconstruction and increase the sensitivity to identify functionally relevant white matter abnormalities in individuals with chronic stroke. Diffusion weighted magnetic resonance imaging was performed in 27 chronic post-stroke participants and 12 healthy controls. Transcallosal pathways and the CST bilaterally were reconstructed using DTI- and CSD-based tractography. Mean fractional anisotropy (FA), apparent diffusion coefficient (ADC), axial diffusivity (AD), and radial diffusivity (RD) were calculated across the tracts of interest. The total number and volume of reconstructed tracts was also determined. Diffusion measures were compared between groups (Stroke, Control) and methods (CSD, DTI). The relationship between post-stroke motor behavior and diffusion measures was evaluated. Overall, CSD methods identified more tracts than the DTI-based approach for both CC and CST pathways. Mean FA, ADC, and RD differed between DTI and CSD for CC-mediated tracts. In these tracts, we discovered a difference in FA for the CC between stroke and healthy control groups using CSD but

Comparing a diffusion tensor and non-tensor approach to white matter fiber tractography in chronic stroke

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A.M. Auriat

2015-01-01

Full Text Available Diffusion tensor imaging (DTI-based tractography has been used to demonstrate functionally relevant differences in white matter pathway status after stroke. However, it is now known that the tensor model is insensitive to the complex fiber architectures found in the vast majority of voxels in the human brain. The inability to resolve intra-voxel fiber orientations may have important implications for the utility of standard DTI-based tract reconstruction methods. Intra-voxel fiber orientations can now be identified using novel, tensor-free approaches. Constrained spherical deconvolution (CSD is one approach to characterize intra-voxel diffusion behavior. In the current study, we performed DTI- and CSD-based tract reconstruction of the corticospinal tract (CST and corpus callosum (CC to test the hypothesis that characterization of complex fiber orientations may improve the robustness of fiber tract reconstruction and increase the sensitivity to identify functionally relevant white matter abnormalities in individuals with chronic stroke. Diffusion weighted magnetic resonance imaging was performed in 27 chronic post-stroke participants and 12 healthy controls. Transcallosal pathways and the CST bilaterally were reconstructed using DTI- and CSD-based tractography. Mean fractional anisotropy (FA, apparent diffusion coefficient (ADC, axial diffusivity (AD, and radial diffusivity (RD were calculated across the tracts of interest. The total number and volume of reconstructed tracts was also determined. Diffusion measures were compared between groups (Stroke, Control and methods (CSD, DTI. The relationship between post-stroke motor behavior and diffusion measures was evaluated. Overall, CSD methods identified more tracts than the DTI-based approach for both CC and CST pathways. Mean FA, ADC, and RD differed between DTI and CSD for CC-mediated tracts. In these tracts, we discovered a difference in FA for the CC between stroke and healthy control groups

BootGraph: probabilistic fiber tractography using bootstrap algorithms and graph theory.

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Vorburger, Robert S; Reischauer, Carolin; Boesiger, Peter

2013-02-01

Bootstrap methods have recently been introduced to diffusion-weighted magnetic resonance imaging to estimate the measurement uncertainty of ensuing diffusion parameters directly from the acquired data without the necessity to assume a noise model. These methods have been previously combined with deterministic streamline tractography algorithms to allow for the assessment of connection probabilities in the human brain. Thereby, the local noise induced disturbance in the diffusion data is accumulated additively due to the incremental progression of streamline tractography algorithms. Graph based approaches have been proposed to overcome this drawback of streamline techniques. For this reason, the bootstrap method is in the present work incorporated into a graph setup to derive a new probabilistic fiber tractography method, called BootGraph. The acquired data set is thereby converted into a weighted, undirected graph by defining a vertex in each voxel and edges between adjacent vertices. By means of the cone of uncertainty, which is derived using the wild bootstrap, a weight is thereafter assigned to each edge. Two path finding algorithms are subsequently applied to derive connection probabilities. While the first algorithm is based on the shortest path approach, the second algorithm takes all existing paths between two vertices into consideration. Tracking results are compared to an established algorithm based on the bootstrap method in combination with streamline fiber tractography and to another graph based algorithm. The BootGraph shows a very good performance in crossing situations with respect to false negatives and permits incorporating additional constraints, such as a curvature threshold. By inheriting the advantages of the bootstrap method and graph theory, the BootGraph method provides a computationally efficient and flexible probabilistic tractography setup to compute connection probability maps and virtual fiber pathways without the drawbacks of

Impact of Gradient Number and Voxel Size on Diffusion Tensor Imaging Tractography for Resective Brain Surgery

NARCIS (Netherlands)

Hoefnagels, Friso W. A.; de Witt Hamer, Philip C.; Pouwels, Petra J. W.; Barkhof, Frederik; Vandertop, W. Peter

2017-01-01

To explore quantitatively and qualitatively how the number of gradient directions (NGD) and spatial resolution (SR) affect diffusion tensor imaging (DTI) tractography in patients planned for brain tumor surgery, using routine clinical magnetic resonance imaging protocols. Of 67 patients with

Tracking errors in tractography of the gastrocnemius muscle. A comparison between the transverse and sagittal planes

International Nuclear Information System (INIS)

Aoki, Takako; Tohdoh, Yukihiro; Tawara, Noriyuki; Okuwaki, Toru; Horiuchi, Akira; Itagaki, Takuma; Niitsu, Mamoru

2010-01-01

In scans taken in conventional direction, tracking errors may occur when using a streamline-based algorithm for the tractography of the gastrocnemius muscle. To solve errors in tracking, we applied tractography to the musculotendinous junction and performed fiber tracking on the gastrocnemius muscle of 10 healthy subjects with their written informed consent. We employed a spin-echo diffusion tensor imaging (SE-DTI) sequence with 6-direction diffusion gradient sensitization and acquired DTI images at 1.5 tesla using a body array coil with parallel imaging. We compared tractography obtained in the transverse and sagittal planes using anatomical reference and found that the gastrocnemius muscle and musculotendinous junction were significantly better visualized on sagittal scans and in 3 regions of interest. We utilized Mann-Whitney U-test to determine significant differences between rates of concordance (P 2 value of skeletal muscle is around 50 ms, and TE should be as short as possible. A streamline-based algorithm is based on the continuity of a vector. It is easy to take running of the muscle fiber in sagittal scan. Therefore, tracking error is hard to occur. In conclusion, sagittal scanning may be one way to eliminate tracking errors in the tractography of the gastrocnemius muscle. Tracking errors were smaller with sagittal scans than transverse scans, and sagittal scans allow better fiber tracking. (author)

Prediction of motor outcomes and activities of daily living function using diffusion tensor tractography in acute hemiparetic stroke patients.

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Imura, Takeshi; Nagasawa, Yuki; Inagawa, Tetsuji; Imada, Naoki; Izumi, Hiroaki; Emoto, Katsuya; Tani, Itaru; Yamasaki, Hiroyuki; Ota, Yuichiro; Oki, Shuichi; Maeda, Tadanori; Araki, Osamu

2015-05-01

[Purpose] The efficacy of diffusion tensor imaging in the prediction of motor outcomes and activities of daily living function remains unclear. We evaluated the most appropriate diffusion tensor parameters and methodology to determine whether the region of interest- or tractography-based method was more useful for predicting motor outcomes and activities of daily living function in stroke patients. [Subjects and Methods] Diffusion tensor imaging data within 10 days after stroke onset were collected and analyzed for 25 patients. The corticospinal tract was analyzed. Fractional anisotropy, number of fibers, and apparent diffusion coefficient were used as diffusion tensor parameters. Motor outcomes and activities of daily living function were evaluated on the same day as diffusion tensor imaging and at 1 month post-onset. [Results] The fractional anisotropy value of the affected corticospinal tract significantly correlated with the motor outcome and activities of daily living function within 10 days post-onset and at 1 month post-onset. Tthere were no significant correlations between other diffusion tensor parameters and motor outcomes or activities of daily living function. [Conclusion] The fractional anisotropy value of the affected corticospinal tract obtained using the tractography-based method was useful for predicting motor outcomes and activities of daily living function in stroke patients.

Diffusion tensor tractography of the mammillothalamic tract in the human brain using a high spatial resolution DTI technique.

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Kamali, Arash; Zhang, Caroline C; Riascos, Roy F; Tandon, Nitin; Bonafante-Mejia, Eliana E; Patel, Rajan; Lincoln, John A; Rabiei, Pejman; Ocasio, Laura; Younes, Kyan; Hasan, Khader M

2018-03-27

The mammillary bodies as part of the hypothalamic nuclei are in the central limbic circuitry of the human brain. The mammillary bodies are shown to be directly or indirectly connected to the amygdala, hippocampus, and thalami as the major gray matter structures of the human limbic system. Although it is not primarily considered as part of the human limbic system, the thalamus is shown to be involved in many limbic functions of the human brain. The major direct connection of the thalami with the hypothalamic nuclei is known to be through the mammillothalamic tract. Given the crucial role of the mammillothalamic tracts in memory functions, diffusion tensor imaging may be helpful in better visualizing the surgical anatomy of this pathway noninvasively. This study aimed to investigate the utility of high spatial resolution diffusion tensor tractography for mapping the trajectory of the mammillothalamic tract in the human brain. Fifteen healthy adults were studied after obtaining written informed consent. We used high spatial resolution diffusion tensor imaging data at 3.0 T. We delineated, for the first time, the detailed trajectory of the mammillothalamic tract of the human brain using deterministic diffusion tensor tractography.

Flexible ex vivo phantoms for validation of diffusion tensor tractography on a clinical scanner.

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Watanabe, Makoto; Aoki, Shigeki; Masutani, Yoshitaka; Abe, Osamu; Hayashi, Naoto; Masumoto, Tomohiko; Mori, Harushi; Kabasawa, Hiroyuki; Ohtomo, Kuni

2006-11-01

The aim of this study was to develop ex vivo diffusion tensor (DT) flexible phantoms. Materials were bundles of textile threads of cotton, monofilament nylon, rayon, and polyester bunched with spiral wrapping bands and immersed in water. DT images were acquired on a 1.5-Tesla clinical magnetic resonance scanner using echo planar imaging sequences with 15 motion probing gradient directions. DT tractography with seeding and a line-tracking method was carried out by software originally developed on a PC-based workstation. We observed relatively high fractional anisotropy on the polyester phantom and were able to reconstruct tractography. Straight tracts along the bundle were displayed when it was arranged linearly. It was easy to bend arcuately or bifurcate at one end; and tracts followed the course of the bundle, whether it was curved or branched and had good agreement with direct visual observation. Tractography with the other fibers was unsuccessful. The polyester phantom revealed a diffusion anisotropic structure according to its shape and would be utilizable repeatedly under the same conditions, differently from living central neuronal system. It would be useful to validate DT sequences and to optimize an algorithm or parameters of DT tractography software. Additionally, the flexibility of the phantom would enable us to model human axonal projections.

Flexible ex vivo phantoms for validation of diffusion tensor tractography on a clinical scanner

International Nuclear Information System (INIS)

Watanabe, Makoto; Aoki, Shigeki; Masutani, Yoshitaka; Abe, Osamu; Hayashi, Naoto; Masumoto, Tomohiko; Mori, Harushi; Kabasawa, Hiroyuki; Ohtomo, Kuni

2006-01-01

The aim of this study was to develop ex vivo diffusion tensor (DT) flexible phantoms. Materials were bundles of textile threads of cotton, monofilament nylon, rayon, and polyester bunched with spiral wrapping bands and immersed in water. DT images were acquired on a 1.5-Tesla clinical magnetic resonance scanner using echo planar imaging sequences with 15 motion probing gradient directions. DT tractography with seeding and a line-tracking method was carried out by software originally developed on a PC-based workstation. We observed relatively high fractional anisotropy on the polyester phantom and were able to reconstruct tractography. Straight tracts along the bundle were displayed when it was arranged linearly. It was easy to bend arcuately or bifurcate at one end; and tracts followed the course of the bundle, whether it was curved or branched and had good agreement with direct visual observation. Tractography with the other fibers was unsuccessful. The polyester phantom revealed a diffusion anisotropic structure according to its shape and would be utilizable repeatedly under the same conditions, differently from living central neuronal system. It would be useful to validate DT sequences and to optimize an algorithm or parameters of DT tractography software. Additionally, the flexibility of the phantom would enable us to model human axonal projections. (author)

Diffusion tensor imaging and fiber tractography in cervical compressive myelopathy: preliminary results

International Nuclear Information System (INIS)

Lee, Joon Woo; Kim, Jae Hyoung; Park, Jong Bin; Lee, Guen Young; Kang, Heung Sik; Park, Kun Woo; Yeom, Jin S.

2011-01-01

To assess diffusion tensor imaging (DTI) parameters in cervical compressive myelopathy (CCM) patients compared to normal volunteers, to relate them with myelopathy severity, and to relate tractography patterns with postoperative neurologic improvement. Twenty patients suffering from CCM were prospectively enrolled (M:F = 13:7, mean age, 49.6 years; range 22-67 years) from September 2009 to March 2010. Sensitivity encoding (SENSE) single-shot echo-planar imaging (EPI) was used for the sagittal DTI. Twenty sex- and age-matched normal volunteers underwent the same scanning procedure. Fractional anisotropy (FA) and apparent diffusion coefficient (ADC) values in the spinal cord were compared between the patients and normal volunteers and were related to myelopathy severity based on Japanese Orthopedic Association (JOA) scores. Tractography patterns were related to myelopathy severity and postoperative improvement. There were significant differences between patients and normal volunteers in terms of FA (0.498 ± 0.114 vs. 0.604 ± 0.057; p = 0.001) and ADC (1.442 ± 0.389 vs. 1.169 ± 0.098; p = 0.001). DTI parameters and tractography patterns were not related to myelopathy severity. In ten patients in the neurologically worse group, postoperative neurologic improvement was seen in four of five patients with intact fiber tracts, but only one of five patients with interrupted fiber tracts exhibited neurologic improvement. DTI parameters in CCM patients were significantly different from those in normal volunteers but were not significantly related to myelopathy severity. The patterns of tractography appear to correlate with postoperative neurologic improvement. (orig.)

Preoperative Identification of Facial Nerve in Vestibular Schwannomas Surgery Using Diffusion Tensor Tractography

OpenAIRE

Choi, Kyung-Sik; Kim, Min-Su; Kwon, Hyeok-Gyu; Jang, Sung-Ho; Kim, Oh-Lyong

2014-01-01

Objective Facial nerve palsy is a common complication of treatment for vestibular schwannoma (VS), so preserving facial nerve function is important. The preoperative visualization of the course of facial nerve in relation to VS could help prevent injury to the nerve during the surgery. In this study, we evaluate the accuracy of diffusion tensor tractography (DTT) for preoperative identification of facial nerve. Methods We prospectively collected data from 11 patients with VS, who underwent pr...

Diffusion tensor imaging (DTI) and tractography of the brachial plexus: feasibility and initial experience in neoplastic conditions

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Vargas, Maria Isabel; Nguyen, Duy; Delavelle, Jacqueline [Geneva University Hospital, Department of Neuroradiology, DISIM, Geneve 14 (Switzerland); Viallon, Magalie [Geneva University Hospital and University of Geneva, Radiology, Geneva (Switzerland); Becker, Minerva [Geneva University Hospital and University of Geneva, Unit of Head and Neck Radiology, Geneva (Switzerland)

2010-03-15

The objective of this study was to assess the feasibility and potential clinical applications of diffusion tensor imaging (DTI) and tractography in the normal and pathologic brachial plexus prospectively. Six asymptomatic volunteers and 12 patients with symptoms related to the brachial plexus underwent DTI on a 1.5T system in addition to the routine anatomic plexus imaging protocol. Maps of the apparent diffusion coefficient (ADC) and of fractional anisotropy (FA), as well as tractography of the brachial plexus were obtained. Images were evaluated by two experienced neuroradiologists in a prospective fashion. Three patients underwent surgery, and nine patients underwent conservative medical treatment. Reconstructed DTI (17/18) were of good quality (one case could not be reconstructed due to artifacts). In all volunteers and in 11 patients, the roots and the trunks were clearly delineated with tractography. Mean FA and mean ADC values were as follows: 0.30{+-}0.079 and 1.70{+-}0.35 mm{sup 2}/s in normal fibers, 0.22{+-}0.04 and 1.49{+-}0.49 mm{sup 2}/s in benign neurogenic tumors, and 0.24{+-}0.08 and 1.51{+-}0.52 mm{sup 2}/s in malignant tumors, respectively. Although there was no statistically significant difference in FA and ADC values of normal fibers and fibers at the level of pathology, tractography revealed major differences regarding fiber architecture. In benign neurogenic tumors (n=4), tractography revealed fiber displacement alone (n=2) or fiber displacement and encasement by the tumor (n=2), whereas in the malignant tumors, either fiber disruption/destruction with complete disorganization (n=6) or fiber displacement (n=1) were seen. In patients with fiber displacement alone, surgery confirmed the tractography findings, and excision was successful without sequelae. Our preliminary data suggest that DTI with tractography is feasible in a clinical routine setting. DTI may demonstrate normal tracts, tract displacement, deformation, infiltration, disruption

Diffusion tensor imaging (DTI) and tractography of the brachial plexus: feasibility and initial experience in neoplastic conditions

International Nuclear Information System (INIS)

Vargas, Maria Isabel; Nguyen, Duy; Delavelle, Jacqueline; Viallon, Magalie; Becker, Minerva

2010-01-01

The objective of this study was to assess the feasibility and potential clinical applications of diffusion tensor imaging (DTI) and tractography in the normal and pathologic brachial plexus prospectively. Six asymptomatic volunteers and 12 patients with symptoms related to the brachial plexus underwent DTI on a 1.5T system in addition to the routine anatomic plexus imaging protocol. Maps of the apparent diffusion coefficient (ADC) and of fractional anisotropy (FA), as well as tractography of the brachial plexus were obtained. Images were evaluated by two experienced neuroradiologists in a prospective fashion. Three patients underwent surgery, and nine patients underwent conservative medical treatment. Reconstructed DTI (17/18) were of good quality (one case could not be reconstructed due to artifacts). In all volunteers and in 11 patients, the roots and the trunks were clearly delineated with tractography. Mean FA and mean ADC values were as follows: 0.30±0.079 and 1.70±0.35 mm 2 /s in normal fibers, 0.22±0.04 and 1.49±0.49 mm 2 /s in benign neurogenic tumors, and 0.24±0.08 and 1.51±0.52 mm 2 /s in malignant tumors, respectively. Although there was no statistically significant difference in FA and ADC values of normal fibers and fibers at the level of pathology, tractography revealed major differences regarding fiber architecture. In benign neurogenic tumors (n=4), tractography revealed fiber displacement alone (n=2) or fiber displacement and encasement by the tumor (n=2), whereas in the malignant tumors, either fiber disruption/destruction with complete disorganization (n=6) or fiber displacement (n=1) were seen. In patients with fiber displacement alone, surgery confirmed the tractography findings, and excision was successful without sequelae. Our preliminary data suggest that DTI with tractography is feasible in a clinical routine setting. DTI may demonstrate normal tracts, tract displacement, deformation, infiltration, disruption, and disorganization of

Diffusion tensor tractography of normal and compressed spinal cord: a preliminary study at 3.0 T MR

International Nuclear Information System (INIS)

Wang Wei; Chang Shixin; Hao Nanxin; Du Yushan; Wang Yibin; Zong Genlin; Cao Kaiming; Lu Jianping; Zhao Cheng; Qin Wen

2007-01-01

Objective: To study the feasibility and clinical values of diffusion tensor tractography (DTT) in the spinal cord at 3.0 T MR. Methods: Forty patients with spinal cord compression including cervical cord herniation and cervical spondylosis (30 cases), tumors in spinal canal (9 cases) and old injury in cervical vertebrae (1 cases) and 20 healthy volunteers participated in this study. Single-shot spin- echo echo-planar diffusion tensor sequence for tractography of the spinal cord was performed. The fibers of spinal cord were visualized by using fiber tracking software. Results: On the DTT maps, the normal spinal cord was depicted as a fiber tract showing color-encoded cephalocaudally, which indicated anisotropy in the cephalocaudal direction. By setting two ROI, the main spinal cord fiber tracts, such as corticospinal or spinothalamic tract, were visualized. The tracts from two sides of the brain did not completely cross. It was asymmetric in the number of tracts on the two sides in most normal subjects (8/10). The tracts of all patients with cord compression were seen oppressed or damaged in different degrees. The DTT in patients with cervical spondylosis and extramedullary-intradural neurolemmoma demonstrated that tracts were oppressed but not damaged. The DTT in one ependymoma showed that tract was markedly compressed and slightly damaged. Conclusion: DTT is a promising tool for demonstrating the spinal cord tracts and abnormalities, can provide useful information for the localization of compression and evaluation of the impairment extent on the white matter tracts of the spinal cord. (authors)

Evaluation of the female pelvic floor in pelvic organ prolapse using 3.0-Tesla diffusion tensor imaging and fibre tractography

Energy Technology Data Exchange (ETDEWEB)

Zijta, F.M. [University of Amsterdam, Department of Radiology, Academic Medical Centre, Amsterdam (Netherlands); Onze Lieve Vrouwe Gasthuis, Amsterdam and Department of Radiology, Amsterdam (Netherlands); Academic Medical Center, Department of Radiology, Amsterdam, AZ (Netherlands); Lakeman, M.M.E.; Roovers, J.P. [University of Amsterdam the Netherlands and Biomedical NMR, Amsterdam and Department of Gynaecology, Academic Medical Centre, Amsterdam (Netherlands); Froeling, M. [University of Amsterdam, Department of Radiology, Academic Medical Centre, Amsterdam (Netherlands); Eindhoven University of Technology, Department of Biomedical Engineering, Eindhoven (Netherlands); Paardt, M.P. van der; Borstlap, C.S.V.; Bipat, S.; Nederveen, A.J.; Stoker, J. [University of Amsterdam, Department of Radiology, Academic Medical Centre, Amsterdam (Netherlands); Montauban van Swijndregt, A.D. [Onze Lieve Vrouwe Gasthuis, Amsterdam and Department of Radiology, Amsterdam (Netherlands); Strijkers, G.J. [Eindhoven University of Technology, Department of Biomedical Engineering, Eindhoven (Netherlands)

2012-12-15

To prospectively explore the clinical application of diffusion tensor imaging (DTI) and fibre tractography in evaluating the pelvic floor. Ten patients with pelvic organ prolapse, ten with pelvic floor symptoms and ten asymptomatic women were included. A two-dimensional (2D) spin-echo (SE) echo-planar imaging (EPI) sequence of the pelvic floor was acquired. Offline fibre tractography and morphological analysis of pelvic magnetic resonance imaging (MRI) were performed. Inter-rater agreement for quality assessment of fibre tracking results was evaluated using weighted kappa ({kappa}). From agreed tracking results, eigen values ({lambda}1, {lambda}2, {lambda}3), mean diffusivity (MD) and fractional anisotropy (FA) were calculated. MD and FA values were compared using ANOVA. Inter-rater reliability of DTI parameters was interpreted using the intra-class correlation coefficient (ICC). Substantial inter-rater agreement was found ({kappa} = 0.71 [95% CI 0.63-0.78]). Four anatomical structures were reliably identified. Substantial inter-rater agreement was found for MD and FA (ICC 0.60-0.91). No significant differences between groups were observed for anal sphincter, perineal body and puboperineal muscle. A significant difference in FA was found for internal obturator muscle between the prolapse group and the asymptomatic group (0.27 {+-} 0.05 vs 0.22 {+-} 0.03; P = 0.015). DTI with fibre tractography permits identification of part of the clinically relevant pelvic structures. Overall, no significant differences in DTI parameters were found between groups. circle Diffusion tensor MRI offers new insights into female pelvic floor problems. (orig.)

Diffusion tensor tractography of the arcuate fasciculus in patients with brain tumors: Comparison between deterministic and probabilistic models.

Science.gov (United States)

Li, Zhixi; Peck, Kyung K; Brennan, Nicole P; Jenabi, Mehrnaz; Hsu, Meier; Zhang, Zhigang; Holodny, Andrei I; Young, Robert J

2013-02-01

The purpose of this study was to compare the deterministic and probabilistic tracking methods of diffusion tensor white matter fiber tractography in patients with brain tumors. We identified 29 patients with left brain tumors probabilistic method based on an extended Monte Carlo Random Walk algorithm. Tracking was controlled using two ROIs corresponding to Broca's and Wernicke's areas. Tracts in tumoraffected hemispheres were examined for extension between Broca's and Wernicke's areas, anterior-posterior length and volume, and compared with the normal contralateral tracts. Probabilistic tracts displayed more complete anterior extension to Broca's area than did FACT tracts on the tumor-affected and normal sides (p probabilistic tracts than FACT tracts (p probabilistic tracts than FACT tracts (p = 0.01). Probabilistic tractography reconstructs the arcuate fasciculus more completely and performs better through areas of tumor and/or edema. The FACT algorithm tends to underestimate the anterior-most fibers of the arcuate fasciculus, which are crossed by primary motor fibers.

Investigating the effects of streamline-based fiber tractography on matrix scaling in brain connective network.

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Jan, Hengtai; Chao, Yi-Ping; Cho, Kuan-Hung; Kuo, Li-Wei

2013-01-01

Investigating the brain connective network using the modern graph theory has been widely applied in cognitive and clinical neuroscience research. In this study, we aimed to investigate the effects of streamline-based fiber tractography on the change of network properties and established a systematic framework to understand how an adequate network matrix scaling can be determined. The network properties, including degree, efficiency and betweenness centrality, show similar tendency in both left and right hemispheres. By employing the curve-fitting process with exponential law and measuring the residuals, the association between changes of network properties and threshold of track numbers is found and an adequate range of investigating the lateralization of brain network is suggested. The proposed approach can be further applied in clinical applications to improve the diagnostic sensitivity using network analysis with graph theory.

Three-dimensional white matter tractography by diffusion tensor imaging in ischaemic stroke involving the corticospinal tract

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Kunimatsu, A.; Aoki, S.; Masutani, Y.; Abe, O.; Mori, H.; Ohtomo, K.

2003-01-01

Diffusion tensor MR imaging (DTI) provides information on diffusion anisotropy, which can be expressed with three-dimensional (3D) white matter tractography. We used 3D white matter tractography to show the corticospinal tract in eight patients with acute or early subacute ischaemic stroke involving the posterior limb of the internal capsule or corona radiata and to assess involvement of the tract. Infarcts and the tract were shown simultaneously, providing information on their spatial relationships. In five of the eight patients, 3D fibre tract maps showed the corticospinal tract in close proximity to the infarct but not to pass through it. All these patients recovered well, with maximum improvement from the lowest score on manual muscle testing (MMT) up to the full score through rehabilitation. In the other three patients the corticospinal tract was shown running through the infarct; reduction in MMT did not necessarily improve favourably or last longer, other than in one patient. As 3D white matter tractography can show spatial relationships between the corticospinal tract and an infarct, it might be helpful in prognosis of gross motor function. (orig.)

Three-dimensional white matter tractography by diffusion tensor imaging in ischaemic stroke involving the corticospinal tract

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Kunimatsu, A.; Aoki, S.; Masutani, Y.; Abe, O.; Mori, H.; Ohtomo, K. [Department of Radiology, Graduate School of Medicine, Tokyo University, 7-3-1 Hongo, Bunkyo-ku, 113-8655, Tokyo (Japan)

2003-08-01

Diffusion tensor MR imaging (DTI) provides information on diffusion anisotropy, which can be expressed with three-dimensional (3D) white matter tractography. We used 3D white matter tractography to show the corticospinal tract in eight patients with acute or early subacute ischaemic stroke involving the posterior limb of the internal capsule or corona radiata and to assess involvement of the tract. Infarcts and the tract were shown simultaneously, providing information on their spatial relationships. In five of the eight patients, 3D fibre tract maps showed the corticospinal tract in close proximity to the infarct but not to pass through it. All these patients recovered well, with maximum improvement from the lowest score on manual muscle testing (MMT) up to the full score through rehabilitation. In the other three patients the corticospinal tract was shown running through the infarct; reduction in MMT did not necessarily improve favourably or last longer, other than in one patient. As 3D white matter tractography can show spatial relationships between the corticospinal tract and an infarct, it might be helpful in prognosis of gross motor function. (orig.)

The Safe Area in the Parieto-Occipital Lobe in the Human Brain: Diffusion Tensor Tractography.

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Jang, Sung Ho; Kim, Seong Ho; Kwon, Hyeok Gyu

2015-06-01

A recent study reported on the relatively safe area in the frontal lobe for performance of neurological interventions; however, no study on the posterior safe area has been reported. In this study, using diffusion tensor tractography, we attempted to identify the safe area in the parieto-occipital lobe in healthy subjects. A total of 47 healthy subjects were recruited for this study. Eleven neural tracts were reconstructed in and around the parieto-occipital area of the brain using diffusion tensor tractography. The safe area, which is free from any trajectory of 10 neural tracts, was measured anteriorly and medially from the line of the most posterior and lateral margin of the brain at 5 axial levels (from the cerebral cortex to the corona radiata). The anterior boundaries of the safe area in the upper cerebral cortex, lower cerebral cortex, centrum semiovale, upper corona radiata, and lower corona radiata levels were located at 31.0, 32.6, 32.7, 35.1, and 35.2 mm anteriorly from the line of the most posterior margin of the brain, respectively, and the medial boundaries were located at an average of 34.7, 38.1, 39.2, 36.1, and 33.6 mm medially from the line of the most lateral margin of the brain, respectively. According to our findings, the safe area was located in the posterolateral portion of the parieto-occipital lobe in the shape of a triangle. However, we found no safe area in the deep white matter around the lateral ventricle. Copyright © 2015 Elsevier Inc. All rights reserved.

Impact of Gradient Number and Voxel Size on Diffusion Tensor Imaging Tractography for Resective Brain Surgery.

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Hoefnagels, Friso W A; de Witt Hamer, Philip C; Pouwels, Petra J W; Barkhof, Frederik; Vandertop, W Peter

2017-09-01

To explore quantitatively and qualitatively how the number of gradient directions (NGD) and spatial resolution (SR) affect diffusion tensor imaging (DTI) tractography in patients planned for brain tumor surgery, using routine clinical magnetic resonance imaging protocols. Of 67 patients with intracerebral lesions who had 2 different DTI scans, 3 DTI series were reconstructed to compare the effects of NGD and SR. Tractographies for 4 clinically relevant tracts (corticospinal tract, superior longitudinal fasciculus, optic radiation, and inferior fronto-occipital fasciculus) were constructed with a probabilistic tracking algorithm and automated region of interest placement and compared for 3 quantitative measurements: tract volume, median fiber density, and mean fractional anisotropy, using linear mixed-effects models. The mean tractography volume and intersubject reliability were visually compared across scanning protocols, to assess the clinical relevance of the quantitative differences. Both NGD and SR significantly influenced tract volume, median fiber density, and mean fractional anisotropy, but not to the same extent. In particular, higher NGD increased tract volume and median fiber density. More importantly, these effects further increased when tracts were affected by disease. The effects were tract specific, but not dependent on threshold. The superior longitudinal fasciculus and inferior fronto-occipital fasciculus showed the most significant differences. Qualitative assessment showed larger tract volumes given a fixed confidence level, and better intersubject reliability for the higher NGD protocol. SR in the range we considered seemed less relevant than NGD. This study indicates that, under time constraints of clinical imaging, a higher number of diffusion gradients is more important than spatial resolution for superior DTI probabilistic tractography in patients undergoing brain tumor surgery. Copyright © 2017 Elsevier Inc. All rights reserved.

Correlation between language function and the left arcuate fasciculus detected by diffusion tensor imaging tractography after brain tumor surgery.

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Hayashi, Yutaka; Kinoshita, Masashi; Nakada, Mitsutoshi; Hamada, Jun-ichiro

2012-11-01

Disturbance of the arcuate fasciculus in the dominant hemisphere is thought to be associated with language-processing disorders, including conduction aphasia. Although the arcuate fasciculus can be visualized in vivo with diffusion tensor imaging (DTI) tractography, its involvement in functional processes associated with language has not been shown dynamically using DTI tractography. In the present study, to clarify the participation of the arcuate fasciculus in language functions, postoperative changes in the arcuate fasciculus detected by DTI tractography were evaluated chronologically in relation to postoperative changes in language function after brain tumor surgery. Preoperative and postoperative arcuate fasciculus area and language function were examined in 7 right-handed patients with a brain tumor in the left hemisphere located in proximity to part of the arcuate fasciculus. The arcuate fasciculus was depicted, and its area was calculated using DTI tractography. Language functions were measured using the Western Aphasia Battery (WAB). After tumor resection, visualization of the arcuate fasciculus was increased in 5 of the 7 patients, and the total WAB score improved in 6 of the 7 patients. The relative ratio of postoperative visualized area of the arcuate fasciculus to preoperative visualized area of the arcuate fasciculus was increased in association with an improvement in postoperative language function (p = 0.0039). The role of the left arcuate fasciculus in language functions can be evaluated chronologically in vivo by DTI tractography after brain tumor surgery. Because increased postoperative visualization of the fasciculus was significantly associated with postoperative improvement in language functions, the arcuate fasciculus may play an important role in language function, as previously thought. In addition, postoperative changes in the arcuate fasciculus detected by DTI tractography could represent a predicting factor for postoperative language

The Value of Neurosurgical and Intraoperative Magnetic Resonance Imaging and Diffusion Tensor Imaging Tractography in Clinically Integrated Neuroanatomy Modules: A Cross-Sectional Study

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Familiari, Giuseppe; Relucenti, Michela; Heyn, Rosemarie; Baldini, Rossella; D'Andrea, Giancarlo; Familiari, Pietro; Bozzao, Alessandro; Raco, Antonino

2013-01-01

Neuroanatomy is considered to be one of the most difficult anatomical subjects for students. To provide motivation and improve learning outcomes in this area, clinical cases and neurosurgical images from diffusion tensor imaging (DTI) tractographies produced using an intraoperative magnetic resonance imaging apparatus (MRI/DTI) were presented and…

Correlation between pennation angle and image quality of skeletal muscle fibre tractography using deterministic diffusion tensor imaging.

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Okamoto, Yoshikazu; Okamoto, Toru; Yuka, Kujiraoka; Hirano, Yuji; Isobe, Tomonori; Minami, Manabu

2012-12-01

The aim of this study was to ascertain whether a correlation existed between muscle pennation angle and the ability to successfully perform tractography of the lower leg muscle fibres with deterministic diffusion tensor imaging (DTI) in normal volunteers. Fourteen volunteers aged 20-39 (mean 28.2 years old) were recruited. All volunteers were scanned using DTI, and six fibre tractographs were constructed from one lower leg of each volunteer, and the 'fibre density' was calculated in each of the tractographs. The pennation angle is the angle formed by the muscle fibre and the aponeurosis. The average pennation angle (AVPA) and standard deviation of the pennation angle (SDPA) were also measured for each muscle by ultrasonography in the same region as the MRI scan. For all 84 tractography images, the correlation coefficient between the fibre density and AVPA or SDPA was calculated. Fibre density and AVPA showed a moderate negative correlation (R = -0.72), and fibre density and SDPA showed a weak negative correlation (R = -0.47). With respect to comparisons within each muscle, AVPA and fibre density showed a moderate negative correlation in the gastrocnemius lateralis muscle (R = -0.57). Our data suggest that a larger, more variable pennation angle resulted in worse skeletal muscle tractography using deterministic DTI. © 2012 The Authors. Journal of Medical Imaging and Radiation Oncology © 2012 The Royal Australian and New Zealand College of Radiologists.

Real-time multi-peak tractography for instantaneous connectivity display

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Maxime eChamberland

2014-05-01

Full Text Available The computerized process of reconstructing white matter tracts from diffusion MRI (dMRI data is often referred to as tractography. Tractography is nowadays central in structural connectivity since it is the only non-invasive technique to obtain information about brain wiring. Most publicly available tractography techniques and most studies are based on a fixed set of tractography parameters. However, the scale and curvature of fiber bundles can vary from region to region in the brain. Therefore, depending on the area of interest or subject (e.g. healthy control vs. tumor patient, optimal tracking parameters can be dramatically different. As a result, a slight change in tracking parameters may return different connectivity profiles and complicate the interpretation of the results. Having access to tractography parameters can thus be advantageous, as it will help in better isolating those which are sensitive to certain streamline features and potentially converge on optimal settings which are area-specific. In this work, we propose a real-time fiber tracking (RTT tool which can instantaneously compute and display streamlines. To achieve such real-time performance, we propose a novel evolution equation based on the upsampled principal directions, also called peaks, extracted at each voxel of the dMRI dataset. The technique runs on a single Computer Processing Unit (CPU without the need for Graphical Unit Processing (GPU programming. We qualitatively illustrate and quantitatively evaluate our novel multi-peak RTT technique on phantom and human datasets in comparison with the state of the art offline tractography from MRtrix, which is robust to fiber crossings. Finally, we show how our RTT tool facilitates neurosurgical planning and allows one to find fibers that infiltrate tumor areas, otherwise missing when using the standard default tracking parameters.

Connectivity between the superior colliculus and the amygdala in humans and macaque monkeys: virtual dissection with probabilistic DTI tractography

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Koller, Kristin; Bultitude, Janet H.; Mullins, Paul; Ward, Robert; Mitchell, Anna S.; Bell, Andrew H.

2015-01-01

It has been suggested that some cortically blind patients can process the emotional valence of visual stimuli via a fast, subcortical pathway from the superior colliculus (SC) that reaches the amygdala via the pulvinar. We provide in vivo evidence for connectivity between the SC and the amygdala via the pulvinar in both humans and rhesus macaques. Probabilistic diffusion tensor imaging tractography revealed a streamlined path that passes dorsolaterally through the pulvinar before arcing rostrally to traverse above the temporal horn of the lateral ventricle and connect to the lateral amygdala. To obviate artifactual connectivity with crossing fibers of the stria terminalis, the stria was also dissected. The putative streamline between the SC and amygdala traverses above the temporal horn dorsal to the stria terminalis and is positioned medial to it in humans and lateral to it in monkeys. The topography of the streamline was examined in relation to lesion anatomy in five patients who had previously participated in behavioral experiments studying the processing of emotionally valenced visual stimuli. The pulvinar lesion interrupted the streamline in two patients who had exhibited contralesional processing deficits and spared the streamline in three patients who had no deficit. Although not definitive, this evidence supports the existence of a subcortical pathway linking the SC with the amygdala in primates. It also provides a necessary bridge between behavioral data obtained in future studies of neurological patients, and any forthcoming evidence from more invasive techniques, such as anatomical tracing studies and electrophysiological investigations only possible in nonhuman species. PMID:26224780

[Assessment of motor and sensory pathways of the brain using diffusion-tensor tractography in children with cerebral palsy].

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Memedyarov, A M; Namazova-Baranova, L S; Ermolina, Y V; Anikin, A V; Maslova, O I; Karkashadze, M Z; Klochkova, O A

2014-01-01

Diffusion tensor tractography--a new method of magnetic resonance imaging, that allows to visualize the pathways of the brain and to study their structural-functional state. The authors investigated the changes in motor and sensory pathways of brain in children with cerebral palsy using routine magnetic resonance imaging and diffusion-tensor tractography. The main group consisted of 26 patients with various forms of cerebral palsy and the comparison group was 25 people with normal psychomotor development (aged 2 to 6 years) and MR-picture of the brain. Magnetic resonance imaging was performed on the scanner with the induction of a magnetic field of 1,5 Tesla. Coefficients of fractional anisotropy and average diffusion coefficient estimated in regions of the brain containing the motor and sensory pathways: precentral gyrus, posterior limb of the internal capsule, thalamus, posterior thalamic radiation and corpus callosum. Statistically significant differences (p cerebral palsy in relation to the comparison group. All investigated regions, the coefficients of fractional anisotropy in children with cerebral palsy were significantly lower, and the average diffusion coefficient, respectively, higher. These changes indicate a lower degree of ordering of the white matter tracts associated with damage and subsequent development of gliosis of varying severity in children with cerebral palsy. It is shown that microstructural damage localized in both motor and sensory tracts that plays a leading role in the development of the clinical picture of cerebral palsy.

Glioma surgery using intraoperative tractography and MEP monitoring

International Nuclear Information System (INIS)

Maesawa, Satoshi; Nakahara, Norimoto; Watanabe, Tadashi; Fujii, Masazumi; Yoshida, Jun

2009-01-01

In surgery of gliomas in motor-eloquent locations, it is essential to maximize resection while minimizing motor deficits. We attempted to identify the cortico-spinal tract (CST) by intraoperative-diffusion tensor imaging (DTI) tractography, combined with electrophysiological mapping using direct subcortical stimulation during tumor resection. Our techniques and preliminary results are reported. Tumors were removed from twelve patients with gliomas in and around the CST using high-field intraoperative MRI and neuronavigation system (BrainSUITE). DTI-based tractography was implemented for navigation of CST pre-and intraoperatively. When the CST was close to the manipulating area, direct subcortical stimulation was performed, and motor evoked potential (MEP)-responses were examined. Locations of CST indicated by pre- and intraoperative tractography (pre- or intra-CST-tractography), and locations identified by subcortical stimulation were recorded, and those correlations were examined. Imaging and functional outcomes were reviewed. Total resections were achieved in 10 patients (83.4%). Two patients developed transient deterioration of motor function (16.6%), and permanent paresis was seen in one (8.3%). The distance from intra-CST-tractography to corresponding sites by subcortical stimulation was 4.5 mm in average (standard deviation (SD)=4.2), and significantly shorter than from pre-CST-tractography. That distance correlated significantly with the intensity of subcortical stimulation. We observed that intraoperative DTI-tractography demonstrated the location of the pyramidal tract more accurately than preoperative one. The combination of intraoperative tractgraphy and MEP monitoring enhanced the quality of surgery for gliomas in motor-eloquent area. (author)

Diffusion tensor tractography-based analysis of the cingulum: clinical utility and findings in traumatic brain injury with chronic sequels

International Nuclear Information System (INIS)

Kurki, Timo; Himanen, Leena; Vuorinen, Elina; Myllyniemi, Anna; Saarenketo, Anna-Riitta; Kauko, Tommi; Brandstack, Nina; Tenovuo, Olli

2014-01-01

To evaluate the clinical utility of quantitative diffusion tensor tractography (DTT) and tractography-based core analysis (TBCA) of the cingulum by defining the reproducibility, normal values, and findings in traumatic brain injury (TBI). Eighty patients with TBI and normal routine MRI and 78 controls underwent MRI at 3T. To determine reproducibility, 12 subjects were scanned twice. Superior (SC) and inferior (IC) cingulum were analyzed separately by DTT (fractional anisotropy (FA) thresholds 0.15 and 0.30). TBCA was performed from volumes defined by tractography with gradually changed FA thresholds. FA values were correlated with clinical and neuropsychological data. The lowest coefficient of variation was obtained at DTT threshold 0.30 (2.0 and 2.4 % for SC and IC, respectively), but in proportion to standard deviations of normal controls, the reproducibility of TBCA was better in SC and similar to that of DTT in IC. In patients with TBI, volume reduction with loss of peripheral fibers was relatively common; mean FA was mostly normal in these tractograms. The frequency of FA reductions (>2 SD) was in DTT smaller than in TBCA, in which FA decrease was present in 42 (13.1 %) of the 320 measurements. Central FA values in SC predicted visuoperceptual ability, and those in left IC predicted cognitive speed, language, and communication ability (p < 0.05). Tractography-based measurements have sufficient reproducibility for demonstration of severe abnormalities of the cingulum. TBCA is preferential for clinical FA analysis, because it measures corresponding areas in patients and controls without inaccuracies due to trauma-induced structural changes. (orig.)

Diffusion tensor tractography-based analysis of the cingulum: clinical utility and findings in traumatic brain injury with chronic sequels

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Kurki, Timo [Turku University Hospital, Department of Radiology, Turku (Finland); MRI Unit, Terveystalo Pulssi Medical Centre, Turku (Finland); Himanen, Leena; Vuorinen, Elina; Myllyniemi, Anna; Saarenketo, Anna-Riitta [NeuTera Neuropsychologist Centre, Turku (Finland); Kauko, Tommi [University of Turku, Department of Biostatistics, Turku (Finland); Brandstack, Nina [Turku University Hospital, Department of Radiology, Turku (Finland); Helsinki University Hospital, Department of Radiology, Helsinki (Finland); Tenovuo, Olli [Turku University Hospital and University of Turku, Department of Rehabilitation and Brain Trauma, Turku (Finland)

2014-10-15

To evaluate the clinical utility of quantitative diffusion tensor tractography (DTT) and tractography-based core analysis (TBCA) of the cingulum by defining the reproducibility, normal values, and findings in traumatic brain injury (TBI). Eighty patients with TBI and normal routine MRI and 78 controls underwent MRI at 3T. To determine reproducibility, 12 subjects were scanned twice. Superior (SC) and inferior (IC) cingulum were analyzed separately by DTT (fractional anisotropy (FA) thresholds 0.15 and 0.30). TBCA was performed from volumes defined by tractography with gradually changed FA thresholds. FA values were correlated with clinical and neuropsychological data. The lowest coefficient of variation was obtained at DTT threshold 0.30 (2.0 and 2.4 % for SC and IC, respectively), but in proportion to standard deviations of normal controls, the reproducibility of TBCA was better in SC and similar to that of DTT in IC. In patients with TBI, volume reduction with loss of peripheral fibers was relatively common; mean FA was mostly normal in these tractograms. The frequency of FA reductions (>2 SD) was in DTT smaller than in TBCA, in which FA decrease was present in 42 (13.1 %) of the 320 measurements. Central FA values in SC predicted visuoperceptual ability, and those in left IC predicted cognitive speed, language, and communication ability (p < 0.05). Tractography-based measurements have sufficient reproducibility for demonstration of severe abnormalities of the cingulum. TBCA is preferential for clinical FA analysis, because it measures corresponding areas in patients and controls without inaccuracies due to trauma-induced structural changes. (orig.)

Traumatic brain injury and the post-concussion syndrome: A diffusion tensor tractography study

International Nuclear Information System (INIS)

D’souza, Maria M; Trivedi, Richa; Singh, Kavita; Grover, Hemal; Choudhury, Ajay; Kaur, Prabhjot; Kumar, Pawan; Tripathi, Rajendra Prashad

2015-01-01

The aim of the present study is to evaluate diffusion tensor tractography (DTT) as a tool for detecting diffuse axonal injury in patients of acute, mild, and moderate traumatic brain injury (TBI), using two diffusion variables: Fractional anisotropy (FA) and mean diffusivity (MD). The correlation of these indices with the severity of post-concussive symptoms was also assessed. Nineteen patients with acute, mild, or moderate TBI and twelve age- and sex-matched healthy controls were recruited. Following Magnetic Resonance Imaging (MRI) on a 3.0-T scanner, DTT was performed using the ‘fiber assignment by continuous tracking’ (FACT) algorithm for fiber reconstruction. Appropriate statistical tools were used to see the difference in FA and MD values between the control and patient groups. In the latter group, the severity of post-concussive symptoms was assessed six months following trauma, using the Rivermead Postconcussion Symptoms Questionnaire (RPSQ). The patients displayed significant reduction in FA compared to the controls (P < 0.05) in several tracts, notably the corpus callosum, fornix, bilateral uncinate fasciculus, and bilateral superior thalamic radiations. Changes in MD were statistically significant in the left uncinate, inferior longitudinal fasciculus, and left posterior thalamic radiation. A strong correlation between these indices and the RPSQ scores was observed in several white matter tracts. Diffusion tensor imaging (DTI)-based quantitative analysis in acute, mild, and moderate TBI can identify axonal injury neuropathology, over and above that visualized on conventional MRI scans. Furthermore, the significant correlation observed between FA and MD indices and the severity of post-concussive symptoms could make it a useful predictor of the long-term outcome

Utility of diffusion tensor imaging tractography in decision making for extratemporal resective epilepsy surgery.

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Radhakrishnan, Ashalatha; James, Jija S; Kesavadas, Chandrasekharan; Thomas, Bejoy; Bahuleyan, Biji; Abraham, Mathew; Radhakrishnan, Kurupath

2011-11-01

To assess the utility of diffusion tensor imaging tractography (DTIT) in decision making in patients considered for extratemporal resective epilepsy surgery. We subjected 49 patients with drug-resistant focal seizures due to lesions located in frontal, parietal and occipital lobes to DTIT to map the white matter fiber anatomy in relation to the planned resection zone, in addition to routine presurgical evaluation. We stratified our patients preoperatively into different grades of risk for anticipated neurological deficits as judged by the distance of the white matter tracts from the resection zones and functional cortical areas. Thirty-seven patients underwent surgery; surgery was abandoned in 12 (24.5%) patients because of the high risk of postoperative neurological deficit. DTIT helped us to modify the surgical procedures in one-fourth of occipital, one-third of frontal, and two-thirds of parietal and multilobar resections. Overall, DTIT assisted us in surgical decision making in two-thirds of our patients. DTIT is a noninvasive imaging strategy that can be used effectively in planning resection of epileptogenic lesions at or close to eloquent cortical areas. DTIT helps in predicting postoperative neurological outcome and thereby assists in surgical decision making and in preoperative counseling of patients with extratemporal focal epilepsies. Copyright © 2011 Elsevier B.V. All rights reserved.

Diffusion tensor tractography reveals muscle reconnection during axolotl limb regeneration.

Directory of Open Access Journals (Sweden)

Cheng-Han Wu

Full Text Available Axolotls have amazing ability to regenerate their lost limbs. Our previous works showed that after amputation the remnant muscle ends remained at their original location whilst sending satellite cells into the regenerating parts to develop into early muscle fibers in the late differentiation stage. The parental and the newly formed muscle fibers were not connected until very late stage. The present study used non-invasive diffusion tensor imaging (DTI to monitor weekly axolotl upper arm muscles after amputation of their upper arms. DTI tractography showed that the regenerating muscle fibers became visible at 9-wpa (weeks post amputation, but a gap was observed between the regenerating and parental muscles. The gap was filled at 10-wpa, indicating reconnection of the fibers of both muscles. This was confirmed by histology. The DTI results indicate that 23% of the muscle fibers were reconnected at 10-wpa. In conclusion, DTI can be used to visualize axolotls' skeletal muscles and the results of muscle reconnection were in accordance with our previous findings. This non-invasive technique will allow researchers to identify the timeframe in which muscle fiber reconnection takes place and thus enable the study of the mechanisms underlying this reconnection.

Joint eigenvector estimation from mutually anisotropic tensors improves susceptibility tensor imaging of the brain, kidney, and heart.

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Dibb, Russell; Liu, Chunlei

2017-06-01

To develop a susceptibility-based MRI technique for probing microstructure and fiber architecture of magnetically anisotropic tissues-such as central nervous system white matter, renal tubules, and myocardial fibers-in three dimensions using susceptibility tensor imaging (STI) tools. STI can probe tissue microstructure, but is limited by reconstruction artifacts because of absent phase information outside the tissue and noise. STI accuracy may be improved by estimating a joint eigenvector from mutually anisotropic susceptibility and relaxation tensors. Gradient-recalled echo image data were simulated using a numerical phantom and acquired from the ex vivo mouse brain, kidney, and heart. Susceptibility tensor data were reconstructed using STI, regularized STI, and the proposed algorithm of mutually anisotropic and joint eigenvector STI (MAJESTI). Fiber map and tractography results from each technique were compared with diffusion tensor data. MAJESTI reduced the estimated susceptibility tensor orientation error by 30% in the phantom, 36% in brain white matter, 40% in the inner medulla of the kidney, and 45% in myocardium. This improved the continuity and consistency of susceptibility-based fiber tractography in each tissue. MAJESTI estimation of the susceptibility tensors yields lower orientation errors for susceptibility-based fiber mapping and tractography in the intact brain, kidney, and heart. Magn Reson Med 77:2331-2346, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Injury of the inferior cerebellar peduncle in patients with mild traumatic brain injury: A diffusion tensor tractography study.

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Jang, Sung Ho; Yi, Ji Hyun; Kwon, Hyeok Gyu

2016-01-01

No study on injury of the inferior cerebellar peduncle (ICP) in patients with mild traumatic brain injury (mTBI) has been reported. This study, using diffusion tensor tractography (DTT), attempted to demonstrate injury of the ICP in patients with mTBI. Three patients with mTBI resulting from a car accident and 18 normal healthy control subjects were enrolled in this study. Diffusion tensor imaging data were acquired at 2 months (patient 1) and 3 months (patients 2 and 3) after onset and the ICP was reconstructed. The Balance Error Scoring System was used for evaluation of balance at the same time diffusion tensor imaging scanning was performed. The ICPs were discontinued at the upper portion of the vertical cerebellar branch and the transverse cerebellar branch (patient 1) and the proximal portion of the transverse cerebellar branch (patients 2 and 3) compared to the normal control subjects. Regarding DTT parameters, in the three patients, the fibre number of the ICPs was decreased by more than 2 SD compared with those of subjects in the control group. Evaluation of the ICP using DTT would be useful in patients with a balance problem after mTBI.

Reproducibility of corticospinal diffusion tensor tractography in normal subjects and hemiparetic stroke patients

International Nuclear Information System (INIS)

Lin, Chao-Chun; Tsai, Miao-Yu; Lo, Yu-Chien; Liu, Yi-Jui; Tsai, Po-Pang; Wu, Chiao-Ying; Lin, Chia-Wei; Shen, Wu-Chung; Chung, Hsiao-Wen

2013-01-01

Purpose: The reproducibility of corticospinal diffusion tensor tractography (DTT) for a guideline is important before longitudinal monitoring of the therapy effects in stroke patients. This study aimed to establish the reproducibility of corticospinal DTT indices in healthy subjects and chronic hemiparetic stroke patients. Materials and methods: Written informed consents were obtained from 10 healthy subjects (mean age 25.8 ± 6.8 years), who underwent two scans in one session plus the third scan one week later, and from 15 patients (mean age 47.5 ± 9.1 years, 6–60 months after the onset of stroke, NIHSS scores between 9 and 20) who were scanned thrice on separate days within one month. Diffusion-tensor imaging was performed at 3 T with 25 diffusion directions. Corticospinal tracts were reconstructed using fiber assignment by continuous tracking without and with motion/eddy-current corrections. Intra- and inter-rater as well as intra- and inter-session variations of the DTT derived indices (fiber number, apparent diffusion coefficient (ADC), and fractional anisotropy (FA)) were assessed. Results: Intra-session and inter-session coefficients of variations (CVs) are small for FA (1.13–2.09%) and ADC (0.45–1.64%), but much larger for fiber number (8.05–22.4%). Inter-session CVs in the stroke side of patients (22.4%) are higher than those in the normal sides (18.0%) and in the normal subjects (14.7%). Motion/eddy-current correction improved inter-session reproducibility only for the fiber number of the infarcted corticospinal tract (CV reduced from 22.4% to 14.1%). Conclusion: The fiber number derived from corticospinal DTT shows substantially lower precision than ADC and FA, with infarcted tracts showing lower reproducibility than the healthy tissues

Longitudinal study on diffusion tensor imaging and diffusion tensor tractography following spinal cord contusion injury in rats.

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Zhao, Can; Rao, Jia-Sheng; Pei, Xiao-Jiao; Lei, Jian-Feng; Wang, Zhan-Jing; Yang, Zhao-Yang; Li, Xiao-Guang

2016-06-01

Diffusion tensor imaging (DTI) as a potential technology has been used in spinal cord injury (SCI) studies, but the longitudinal evaluation of DTI parameters after SCI, and the correlation between DTI parameters and locomotor outcomes need to be defined. Adult Wistar rats (n = 6) underwent traumatic thoracic cord contusion by an NYU impactor. DTI and Basso-Beattie-Bresnahan datasets were collected pre-SCI and 1, 3, 7, 14, and 84 days post-SCI. Diffusion tensor tractography (DTT) of the spinal cord was also generated. Fractional anisotropy (FA) and connection rate of fibers at the injury epicenter and at 5 mm rostral/caudal to the epicenter were calculated. The variations of these parameters after SCI were observed by one-way analysis of variance and the correlations between these parameters and motor function were explored by Pearson's correlation. FA at the epicenter decreased most remarkably on day 1 post-SCI (from 0.780 ± 0.012 to 0.330 ± 0.015), and continued to decrease slightly by day 3 post-SCI (0.313 ± 0.015), while other parameters decreased significantly over the first 3 days after SCI. DTT showed residual fibers concentrated on ventral and ventrolateral sides of the cord. Moreover, FA at the epicenter exhibited the strongest correlation (r = 0.887, p = 0.000) with the locomotion performance. FA was sensitive to degeneration in white matter and DTT could directly reflect the distribution of the residual white matter. Moreover, days 1 to 3 post-SCI may be the optimal time window for SCI examination and therapy.

Diffusion tensor imaging in spinal cord compression

International Nuclear Information System (INIS)

Wang, Wei; Qin, Wen; Hao, Nanxin; Wang, Yibin; Zong, Genlin

2012-01-01

Background Although diffusion tensor imaging has been successfully applied in brain research for decades, several main difficulties have hindered its extended utilization in spinal cord imaging. Purpose To assess the feasibility and clinical value of diffusion tensor imaging and tractography for evaluating chronic spinal cord compression. Material and Methods Single-shot spin-echo echo-planar DT sequences were scanned in 42 spinal cord compression patients and 49 healthy volunteers. The mean values of the apparent diffusion coefficient and fractional anisotropy were measured in region of interest at the cervical and lower thoracic spinal cord. The patients were divided into two groups according to the high signal on T2WI (the SCC-HI group and the SCC-nHI group for with or without high signal). A one-way ANOVA was used. Diffusion tensor tractography was used to visualize the morphological features of normal and impaired white matter. Results There were no statistically significant differences in the apparent diffusion coefficient and fractional anisotropy values between the different spinal cord segments of the normal subjects. All of the patients in the SCC-HI group had increased apparent diffusion coefficient values and decreased fractional anisotropy values at the lesion level compared to the normal controls. However, there were no statistically significant diffusion index differences between the SCC-nHI group and the normal controls. In the diffusion tensor imaging maps, the normal spinal cord sections were depicted as fiber tracts that were color-encoded to a cephalocaudal orientation. The diffusion tensor images were compressed to different degrees in all of the patients. Conclusion Diffusion tensor imaging and tractography are promising methods for visualizing spinal cord tracts and can provide additional information in clinical studies in spinal cord compression

Assessment of arcuate fasciculus with diffusion-tensor tractography may predict the prognosis of aphasia in patients with left middle cerebral artery infarcts

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Hosomi, Akiko; Nagakane, Yoshinari; Kuriyama, Nagato; Mizuno, Toshiki; Nakagawa, Masanori [Kyoto Prefectural University of Medicine, Department of Neurology, Graduate School of Medical Science, Kyoto (Japan); Yamada, Kei; Nishimura, Tsunehiko [Kyoto Prefectural University of Medicine, Department of Radiology, Graduate School of Medical Science, Kyoto (Japan)

2009-09-15

It is often clinically difficult to assess the severity of aphasia in the earliest stage of cerebral infarction. A method enabling objective assessment of verbal function is needed for this purpose. We examined whether diffusion tensor (DT) tractography is of clinical value in assessing aphasia. Thirteen right-handed patients with left middle cerebral artery infarcts who were scanned within 2 days after stroke onset were enrolled in this study. Magnetic resonance data of ten control subjects were also examined by DT tractography. Based on the severity of aphasia at discharge, patients were divided into two groups: six patients in the aphasic group and seven in the nonaphasic group. Fractional anisotropy (FA) and number of arcuate fasciculus fibers were evaluated. Asymmetry index was calculated for both FA and number of fibers. FA values for the arcuate fasciculus fibers did not differ between hemispheres in either the patient groups or the controls. Number of arcuate fasciculus fibers exhibited a significant leftward asymmetry in the controls and the nonaphasic group but not in the aphasic group. Asymmetry index of number of fibers was significantly lower (rightward) in the aphasic group than in the nonaphasic (P = 0.015) and control (P = 0.005) groups. Loss of leftward asymmetry in number of AF fibers predicted aphasia at discharge with a sensitivity of 0.83 and specificity of 0.86. Asymmetry of arcuate fasciculus fibers by DT tractography may deserve to be assessed in acute infarction for predicting the fate of vascular aphasia. (orig.)

Assessment of arcuate fasciculus with diffusion-tensor tractography may predict the prognosis of aphasia in patients with left middle cerebral artery infarcts

International Nuclear Information System (INIS)

Hosomi, Akiko; Nagakane, Yoshinari; Kuriyama, Nagato; Mizuno, Toshiki; Nakagawa, Masanori; Yamada, Kei; Nishimura, Tsunehiko

2009-01-01

It is often clinically difficult to assess the severity of aphasia in the earliest stage of cerebral infarction. A method enabling objective assessment of verbal function is needed for this purpose. We examined whether diffusion tensor (DT) tractography is of clinical value in assessing aphasia. Thirteen right-handed patients with left middle cerebral artery infarcts who were scanned within 2 days after stroke onset were enrolled in this study. Magnetic resonance data of ten control subjects were also examined by DT tractography. Based on the severity of aphasia at discharge, patients were divided into two groups: six patients in the aphasic group and seven in the nonaphasic group. Fractional anisotropy (FA) and number of arcuate fasciculus fibers were evaluated. Asymmetry index was calculated for both FA and number of fibers. FA values for the arcuate fasciculus fibers did not differ between hemispheres in either the patient groups or the controls. Number of arcuate fasciculus fibers exhibited a significant leftward asymmetry in the controls and the nonaphasic group but not in the aphasic group. Asymmetry index of number of fibers was significantly lower (rightward) in the aphasic group than in the nonaphasic (P = 0.015) and control (P = 0.005) groups. Loss of leftward asymmetry in number of AF fibers predicted aphasia at discharge with a sensitivity of 0.83 and specificity of 0.86. Asymmetry of arcuate fasciculus fibers by DT tractography may deserve to be assessed in acute infarction for predicting the fate of vascular aphasia. (orig.)

Measuring Connectivity in the Primary Visual Pathway in Human Albinism Using Diffusion Tensor Imaging and Tractography.

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Grigorian, Anahit; McKetton, Larissa; Schneider, Keith A

2016-08-11

In albinism, the number of ipsilaterally projecting retinal ganglion cells (RGCs) is significantly reduced. The retina and optic chiasm have been proposed as candidate sites for misrouting. Since a correlation between the number of lateral geniculate nucleus (LGN) relay neurons and LGN size has been shown, and based on previously reported reductions in LGN volumes in human albinism, we suggest that fiber projections from LGN to the primary visual cortex (V1) are also reduced. Studying structural differences in the visual system of albinism can improve the understanding of the mechanism of misrouting and subsequent clinical applications. Diffusion data and tractography are useful for mapping the OR (optic radiation). This manuscript describes two algorithms for OR reconstruction in order to compare brain connectivity in albinism and controls.An MRI scanner with a 32-channel head coil was used to acquire structural scans. A T1-weighted 3D-MPRAGE sequence with 1 mm(3) isotropic voxel size was used to generate high-resolution images for V1 segmentation. Multiple proton density (PD) weighted images were acquired coronally for right and left LGN localization. Diffusion tensor imaging (DTI) scans were acquired with 64 diffusion directions. Both deterministic and probabilistic tracking methods were run and compared, with LGN as the seed mask and V1 as the target mask. Though DTI provides relatively poor spatial resolution, and accurate delineation of OR may be challenging due to its low fiber density, tractography has been shown to be advantageous both in research and clinically. Tract based spatial statistics (TBSS) revealed areas of significantly reduced white matter integrity within the OR in patients with albinism compared to controls. Pairwise comparisons revealed a significant reduction in LGN to V1 connectivity in albinism compared to controls. Comparing both tracking algorithms revealed common findings, strengthening the reliability of the technique.

Limb apraxia in a patient with cerebral infarct: diffusion tensor tractography study.

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Hong, Ji Heon; Lee, Jun; Cho, Yoon Woo; Byun, Woo Mok; Cho, Hee Kyung; Son, Su Min; Jang, Sung Ho

2012-01-01

We report on a patient with ideomotor apraxia (IMA) and limb-kinetic apraxia (LKA) following cerebral infarct, which demonstrated neural tract injuries by diffusion tensor tractography (DTT). A 67-year-old male was diagnosed as cerebral infarct in the left frontal cortex (anterior portion of the precentral gyrus and prefrontal cortex) and centrum semiovale. The patient presented with severe paralysis of the right upper extremity and mild weakness of the right lower extremity at onset. At the time of DTT scanning (5 months after onset), the patient was able to move all joint muscles of the right upper extremity against gravity, except for the finger extensors, which he could extend partially against gravity. The patient showed intact ideational plan for motor performance; however, his movements were slow, clumsy, and mutilated when executing grasp-release movements of his affected hand. The patient's score on the ideomotor apraxia test was 20 (cut-off score < 32). DTTs for premotor cortex fibers, supplementary motor area fibers, and superior longitudinal fasciculus of the left hemisphere showed partial injuries, compared with those of the right side, and these injuries appeared to be responsible for IMA and LKA in this patient.

Tractography of the brainstem in major depressive disorder using diffusion tensor imaging.

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Yun Ju C Song

Full Text Available BACKGROUND: The brainstem is the main region that innervates neurotransmitter release to the Hypothalamic-Pituitary Adrenal (HPA axis and fronto-limbic circuits, two key brain circuits found to be dysfunctional in Major Depressive Disorder (MDD. However, the brainstem's role in MDD has only been evaluated in limited reports. Using Diffusion Tensor Imaging (DTI, we investigated whether major brainstem white matter tracts that relate to these two circuits differ in MDD patients compared to healthy controls. METHODS: MDD patients (n = 95 and age- and gender-matched controls (n = 34 were assessed using probabilistic tractography of DTI to delineate three distinct brainstem tracts: the nigrostriatal tract (connecting brainstem to striatum, solitary tract (connecting brainstem to amygdala and corticospinal tract (connecting brainstem to precentral cortex. Fractional anisotropy (FA was used to measure the white matter integrity of these tracts, and measures were compared between MDD and control participants. RESULTS: MDD participants were characterized by a significant and specific decrease in white matter integrity of the right solitary tract (p<0.009 using independent t-test, which is a "bottom up" afferent pathway that connects the brainstem to the amygdala. This decrease was not related to symptom severity. CONCLUSIONS: The results provide new evidence to suggest that structural connectivity between the brainstem and the amygdala is altered in MDD. These results are interesting in light of predominant theories regarding amygdala-mediated emotional reactivity observed in functional imaging studies of MDD. The characterization of altered white matter integrity in the solitary tract in MDD supports the possibility of dysfunctional brainstem-amygdala connectivity impacting vulnerable circuits in MDD.

Introduction to tractography-guided navigation: using 3-tesla magnetic resonance tractography in surgery for cerebral arteriovenous malformations.

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Kikuta, K; Takagi, Y; Nozaki, K; Hashimoto, N

2008-01-01

To examine the effectiveness of magnetic resonance (MR) tractography in surgery for cerebral arteriovenous malformations (AVMs). A preoperative evaluation of major neural tracts around the nidus was carried out with 3-tesla (3 T) MR tractography in 25 consecutive patients with cerebral AVMs. The patients were 12 men and 13 women ranging in age from 4 to 60 years of age (mean age: 31.2 +/- 14.1 years). Twelve presented with hemorrhage. Images were obtained with T2-weighted turbo spin echo sequences, axial T1-weighted three-dimensional magnetization-prepared rapid acquisition gradient-echo (MPRAGE) sequences, three-dimensional time-of-flight MR angiography (3D TOF MRA), and thin-section diffusion-tensor imaging (DTI). The AVMs were obliterated in 22 of the 25 patients. A postoperative study of the MR tractography was carried out in 24 patients. In 21 patients, tracts were preserved and no postoperative neurological worsening was observed. Disruption of the tracts was found in 3 patients, and postoperative worsening was observed in 2 patients. However, no deterioration occurred in 1 patient with cerebellar AVM. Notwithstanding the limitations of this method, MR tractography can be considered useful for confirming the integrity of deviated tracts, for localizing deviated tracts, and for evaluating surgical risk, especially in cases of non-hemorrhagic AVM.

Diffusion Tensor Imaging Tractography in Pure Neuritic Leprosy: First Experience Report and Review of the Literature

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Michele R. Colonna

2016-01-01

Full Text Available Five years after both right ulnar and median nerve decompression for paraesthesias and palsy, a patient, coming from Nigeria but living in Italy, came to our unit claiming to have persistent pain and combined median and ulnar palsy. Under suspicion of leprosy, skin and left sural nerve biopsy were performed. Skin tests were negative, but Schwann cells resulted as positive for acid-fast bacilli (AFB, leading to the diagnosis of Pure Neuritic Leprosy (PNL. The patient was given PB multidrug therapy and recovered from pain in two months. After nine months both High Resolution Ultrasonography (HRUS and Magnetic Resonance Imaging (MRI were performed, revealing thickening of the nerves. Since demyelination is common in PNL, the Authors started to use Diffusion Tensor Imaging Tractography (DTIT to get better morphological and functional data about myelination than does the traditional imaging. DTIT proved successful in showing myelin discontinuity, reorganization, and myelination, and the Authors suggest that it can give more information about the evolution of the disease, as well as further indications for surgery (nerve decompression, nerve transfers, and babysitting for distal effector protection, and should be added to traditional imaging tools in leprosy.

Spinal diffusion tensor imaging: a comprehensive review with emphasis on spinal cord anatomy and clinical applications.

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Hendrix, Philipp; Griessenauer, Christoph J; Cohen-Adad, Julien; Rajasekaran, Shanmuganathan; Cauley, Keith A; Shoja, Mohammadali M; Pezeshk, Parham; Tubbs, R Shane

2015-01-01

Magnetic resonance imaging technology allows for in vivo visualization of fiber tracts of the central nervous system using diffusion-weighted imaging sequences and data processing referred to as "diffusion tensor imaging" and "diffusion tensor tractography." While protocols for high-fidelity diffusion tensor imaging of the brain are well established, the spinal cord has proven a more difficult target for diffusion tensor methods. Here, we review the current literature on spinal diffusion tensor imaging and tractography with special emphasis on neuroanatomical correlations and clinical applications. © 2014 Wiley Periodicals, Inc.

Predicting pituitary stalk position by in vivo visualization of the hypothalamo-hypophyseal tract in craniopharyngioma using diffusion tensor imaging tractography.

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Wang, Fuyu; Jiang, Jinli; Zhang, Jiashu; Wang, Qun

2018-07-01

The pituitary stalk (PS) is crucial to endocrine function and water-electrolyte equilibrium. Preservation of the PS during craniopharyngioma (CP) surgery is critical; however, in a pathological state, it is difficult to identify. The hypothalamo-hypophyseal tract (HHT) connects the hypothalamus and the posterior pituitary gland and projects through the PS. Thus, visualization of the HHT can help locate the PS. Preoperative visualization of the neural fasciculus has been widely achieved using diffusion tensor imaging (DTI) tractography. Therefore, this study evaluated the use of DTI tractography to identify and characterize the human HHT. We used DTI tractography to track the HHT in 10 patients with CP and compared the location of the tract with the intraoperative view of the PS in these patients. We successfully tracked the HHT in nine patients, indicating that delineating and quantifying the tracked HHT using this method is feasible. In addition, we found that the tract was consistent with the intraoperative view of the PS in seven out of eight patients (87.50%). Finally, we found that the mean number of tracts was 7.11 ± 12.28, the mean fractional anisotropy (FA) was 0.11 ± 0.04, and the mean tract length was 24.22 ± 9.39 mm. Taken together, our results demonstrate that the HHT can be visualized and characterized with DTI even in a clinical application, which may aid in preoperative identification of the PS. Characterization of the tracked HHT with this technique could also be used to advance our understanding of the HHT.

Hemispheric Asymmetry of Human Brain Anatomical Network Revealed by Diffusion Tensor Tractography

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Ni Shu

2015-01-01

Full Text Available The topological architecture of the cerebral anatomical network reflects the structural organization of the human brain. Recently, topological measures based on graph theory have provided new approaches for quantifying large-scale anatomical networks. However, few studies have investigated the hemispheric asymmetries of the human brain from the perspective of the network model, and little is known about the asymmetries of the connection patterns of brain regions, which may reflect the functional integration and interaction between different regions. Here, we utilized diffusion tensor imaging to construct binary anatomical networks for 72 right-handed healthy adult subjects. We established the existence of structural connections between any pair of the 90 cortical and subcortical regions using deterministic tractography. To investigate the hemispheric asymmetries of the brain, statistical analyses were performed to reveal the brain regions with significant differences between bilateral topological properties, such as degree of connectivity, characteristic path length, and betweenness centrality. Furthermore, local structural connections were also investigated to examine the local asymmetries of some specific white matter tracts. From the perspective of both the global and local connection patterns, we identified the brain regions with hemispheric asymmetries. Combined with the previous studies, we suggested that the topological asymmetries in the anatomical network may reflect the functional lateralization of the human brain.

A Review of Traumatic Axonal Injury following Whiplash Injury As Demonstrated by Diffusion Tensor Tractography

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Sung Ho Jang

2018-02-01

Full Text Available Whiplash is a bony or soft tissue injury resulting from an acceleration–deceleration energy transfer in the neck. Although patients with whiplash injury often complain of cerebral symptoms, and previous studies have reported evidence indicating brain injury, such an association has not been clearly elucidated. Traumatic axonal injury (TAI is tearing of axons due to indirect shearing forces during acceleration, deceleration, and rotation of the brain or to direct head trauma. Diffusion tensor imaging (DTI has a unique advantage to detect TAI in patients whose conventional brain CT or magnetic resonance imaging (MRI results were negative following head trauma. Since the introduction of DTI, six studies using diffusion tensor tractography (DTT based on DTI data have reported TAI in patients with whiplash injury, even though conventional brain CT or MRI results were negative. A precise TAI diagnosis in whiplash patients is clinically important for proper management and prognosis. Among the methods employed to diagnose TAI in the six previous studies, the common diagnostic approach for neural tract TAI in individual patients with whiplash injury were (1 whiplash injury history due to car accident; (2 development of new clinical symptoms and signs after whiplash injury; (3 evidence of neural tract TAI in DTT results, mainly via configurational analysis; and (4 coincidence of newly developed clinical manifestations and the function of injured neural tracts. All six studies were individual patient case studies; therefore, further prospective studies involving larger number of subjects should be encouraged.

Probabilistic shortest path tractography in DTI using Gaussian Process ODE solvers

DEFF Research Database (Denmark)

Schober, Michael; Kasenburg, Niklas; Feragen, Aasa

2014-01-01

Tractography in diffusion tensor imaging estimates connectivity in the brain through observations of local diffusivity. These observations are noisy and of low resolution and, as a consequence, connections cannot be found with high precision. We use probabilistic numerics to estimate connectivity...

Abnormal topological organization in white matter structural networks revealed by diffusion tensor tractography in unmedicated patients with obsessive-compulsive disorder.

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Zhong, Zhaoxi; Zhao, Tengda; Luo, Jia; Guo, Zhihua; Guo, Meng; Li, Ping; Sun, Jing; He, Yong; Li, Zhanjiang

2014-06-03

Obsessive-compulsive disorder (OCD) is a chronic psychiatric disorder defined by recurrent thoughts, intrusive and distressing impulses, or images and ritualistic behaviors. Although focal diverse regional abnormalities white matter integrity in specific brain regions have been widely studied in populations with OCD, alterations in the structural connectivities among them remain poorly understood. The aim was to investigate the abnormalities in the topological efficiency of the white matter networks and the correlation between the network metrics and Yale-Brown Obsessive-Compulsive Scale scores in unmedicated OCD patients, using diffusion tensor tractography and graph theoretical approaches. This study used diffusion tensor imaging and deterministic tractography to map the white matter structural networks in 26 OCD patients and 39 age- and gender-matched healthy controls; and then applied graph theoretical methods to investigate abnormalities in the global and regional properties of the white matter network in these patients. The patients and control participants both showed small-world organization of the white matter networks. However, the OCD patients exhibited significant abnormal global topology, including decreases in global efficiency (t = -2.32, p = 0.02) and increases in shortest path length, Lp (t = 2.30, p = 0.02), the normalized weighted shortest path length, λ (t = 2.08, p=0.04), and the normalized clustering coefficient, γ (t = 2.26, p = 0.03), of their white matter structural networks compared with healthy controls. Further, the OCD patients showed a reduction in nodal efficiency predominately in the frontal regions, the parietal regions and caudate nucleus. The normalized weighted shortest path length of the network metrics was significantly negatively correlated with obsessive subscale of the Yale-Brown Obsessive-Compulsive Scale (r = -0.57, p = 0.0058). These findings demonstrate the abnormal topological efficiency in the white matter networks

Diffusion tensor imaging and tractography for assessment of renal allograft dysfunction - initial results

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Hueper, Katja; Gutberlet, M.; Rodt, T.; Wacker, F.; Galanski, M.; Hartung, D. [Institute for Diagnostic and Interventional Radiology, Hannover Medical School - Germany, Hannover (Germany); Gwinner, W. [Clinic for Nephrology, Hannover Medical School - Germany, Hannover (Germany); Lehner, F. [Clinic for General, Abdominal and Transplant Surgery, Hannover Medical School - Germany, Hannover (Germany)

2011-11-15

To evaluate MR diffusion tensor imaging (DTI) as non-invasive diagnostic tool for detection of acute and chronic allograft dysfunction and changes of organ microstructure. 15 kidney transplanted patients with allograft dysfunction and 14 healthy volunteers were examined using a fat-saturated echo-planar DTI-sequence at 1.5 T (6 diffusion directions, b = 0, 600 s/mm{sup 2}). Mean apparent diffusion coefficient (ADC) and mean fractional anisotropy (FA) were calculated separately for the cortex and for the medulla and compared between healthy and transplanted kidneys. Furthermore, the correlation between diffusion parameters and estimated GFR was determined. The ADC in the cortex and in the medulla were lower in transplanted than in healthy kidneys (p < 0.01). Differences were more distinct for FA, especially in the renal medulla, with a significant reduction in allografts (p < 0.001). Furthermore, in transplanted patients a correlation between mean FA in the medulla and estimated GFR was observed (r = 0.72, p < 0.01). Tractography visualized changes in renal microstructure in patients with impaired allograft function. Changes in allograft function and microstructure can be detected and quantified using DTI. However, to prove the value of DTI for standard clinical application especially correlation of imaging findings and biopsy results is necessary. (orig.)

The optimal trackability threshold of fractional anisotropy for diffusion tensor tractography of the corticospinal tract

International Nuclear Information System (INIS)

Kunimatsu, Akira; Aoki, Shigeki; Masutani, Yoshitaka; Abe, Osamu; Hayashi, Naoto; Mori, Harushi; Masumoto, Tomohiko; Ohtomo, Kuni

2004-01-01

In order to ensure that three-dimensional diffusion tensor tractography (3D-DTT) of the corticospinal tract (CST), is performed accurately and efficiently, we set out to find the optimal lower threshold of fractional anisotropy (FA) below which tract elongation is terminated (trackability threshold). Thirteen patients with acute or early subacute ischemic stroke causing motor deficits were enrolled in this study. We performed 3D-DTT of the CST with diffusion tensor MR (magnetic resonance) imaging. We segmented the CST and established a cross-section of the CST in a transaxial plane as a region of interest. Thus, we selectively measured the FA values of the right and left corticospinal tracts at the level of the cerebral peduncle, the posterior limb of the internal capsule, and the centrum semiovale. The FA values of the CST were also measured on the affected side at the level where the clinically relevant infarction was present in isotropic diffusion-weighted imaging. 3D-DTT allowed us to selectively measure the FA values of the CST. Among the 267 regions of interest we measured, the minimum FA value was 0.22. The FA values of the CST were smaller and more variable in the centrum semiovale than in the other regions. The mean minus twice the standard deviation of the FA values of the CST in the centrum semiovale was calculated at 0.22 on the normal unaffected side and 0.16 on the affected side. An FA value of about 0.20 was found to be the optimal trackability threshold. (author)

Multimodality 3D Superposition and Automated Whole Brain Tractography: Comprehensive Printing of the Functional Brain.

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Konakondla, Sanjay; Brimley, Cameron J; Sublett, Jesna Mathew; Stefanowicz, Edward; Flora, Sarah; Mongelluzzo, Gino; Schirmer, Clemens M

2017-09-29

Whole brain tractography using diffusion tensor imaging (DTI) sequences can be used to map cerebral connectivity; however, this can be time-consuming due to the manual component of image manipulation required, calling for the need for a standardized, automated, and accurate fiber tracking protocol with automatic whole brain tractography (AWBT). Interpreting conventional two-dimensional (2D) images, such as computed tomography (CT) and magnetic resonance imaging (MRI), as an intraoperative three-dimensional (3D) environment is a difficult task with recognized inter-operator variability. Three-dimensional printing in neurosurgery has gained significant traction in the past decade, and as software, equipment, and practices become more refined, trainee education, surgical skills, research endeavors, innovation, patient education, and outcomes via valued care is projected to improve. We describe a novel multimodality 3D superposition (MMTS) technique, which fuses multiple imaging sequences alongside cerebral tractography into one patient-specific 3D printed model. Inferences on cost and improved outcomes fueled by encouraging patient engagement are explored.

Segmentation of the canine corpus callosum using diffusion-tensor imaging tractography.

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Pierce, Theodore T; Calabrese, Evan; White, Leonard E; Chen, Steven D; Platt, Simon R; Provenzale, James M

2014-01-01

We set out to determine functional white matter (WM) connections passing through the canine corpus callosum; these WM connections would be useful for subsequent studies of canine brains that serve as models for human WM pathway disease. Based on prior studies, we anticipated that the anterior corpus callosum would send projections to the anterior cerebral cortex whereas progressively posterior segments would send projections to more posterior cortex. A postmortem canine brain was imaged using a 7-T MRI system producing 100-μm-isotropic-resolution diffusion-tensor imaging analyzed by tractography. Using regions of interest (ROIs) within cortical locations, which were confirmed by a Nissl stain that identified distinct cortical architecture, we successfully identified six important WM pathways. We also compared fractional anisotropy (FA), apparent diffusion coefficient (ADC), radial diffusivity, and axial diffusivity in tracts passing through the genu and splenium. Callosal fibers were organized on the basis of cortical destination (e.g., fibers from the genu project to the frontal cortex). Histologic results identified the motor cortex on the basis of cytoarchitectonic criteria that allowed placement of ROIs to discriminate between frontal and parietal lobes. We also identified cytoarchitecture typical of the orbital frontal, anterior frontal, and occipital regions and placed ROIs accordingly. FA, ADC, radial diffusivity, and axial diffusivity values were all higher in posterior corpus callosum fiber tracts. Using six cortical ROIs, we identified six major WM tracts that reflect major functional divisions of the cerebral hemispheres, and we derived quantitative values that can be used for study of canine models of human WM pathologic states.

Tractography of lumbar nerve roots: initial results

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Balbi, Vincent; Budzik, Jean-Francois; Thuc, Vianney le; Cotten, Anne [Hopital Roger Salengro, Service de Radiologie et d' Imagerie musculo-squelettique, Lille Cedex (France); Duhamel, Alain [Universite de Lille 2, UDSL, Lille (France); Bera-Louville, Anne [Service de Rhumatologie, Hopital Roger Salengro, Lille (France)

2011-06-15

The aims of this preliminary study were to demonstrate the feasibility of in vivo diffusion tensor imaging (DTI) and fibre tracking (FT) of the lumbar nerve roots, and to assess potential differences in the DTI parameters of the lumbar nerves between healthy volunteers and patients suffering from disc herniation. Nineteen patients with unilateral sciatica related to posterolateral or foraminal disc herniation and 19 healthy volunteers were enrolled in this study. DTI with tractography of the L5 or S1 nerves was performed. Mean fractional anisotropy (FA) and mean diffusivity (MD) values were calculated from tractography images. FA and MD values could be obtained from DTI-FT images in all controls and patients. The mean FA value of the compressed lumbar nerve roots was significantly lower than the FA of the contralateral nerve roots (p=0.0001) and of the nerve roots of volunteers (p=0.0001). MD was significantly higher in compressed nerve roots than in the contralateral nerve root (p=0.0002) and in the nerve roots of volunteers (p=0.04). DTI with tractography of the lumbar nerves is possible. Significant changes in diffusion parameters were found in the compressed lumbar nerves. (orig.)

Tractography of lumbar nerve roots: initial results

International Nuclear Information System (INIS)

Balbi, Vincent; Budzik, Jean-Francois; Thuc, Vianney le; Cotten, Anne; Duhamel, Alain; Bera-Louville, Anne

2011-01-01

The aims of this preliminary study were to demonstrate the feasibility of in vivo diffusion tensor imaging (DTI) and fibre tracking (FT) of the lumbar nerve roots, and to assess potential differences in the DTI parameters of the lumbar nerves between healthy volunteers and patients suffering from disc herniation. Nineteen patients with unilateral sciatica related to posterolateral or foraminal disc herniation and 19 healthy volunteers were enrolled in this study. DTI with tractography of the L5 or S1 nerves was performed. Mean fractional anisotropy (FA) and mean diffusivity (MD) values were calculated from tractography images. FA and MD values could be obtained from DTI-FT images in all controls and patients. The mean FA value of the compressed lumbar nerve roots was significantly lower than the FA of the contralateral nerve roots (p=0.0001) and of the nerve roots of volunteers (p=0.0001). MD was significantly higher in compressed nerve roots than in the contralateral nerve root (p=0.0002) and in the nerve roots of volunteers (p=0.04). DTI with tractography of the lumbar nerves is possible. Significant changes in diffusion parameters were found in the compressed lumbar nerves. (orig.)

Diffusion Tensor Imaging Tractography Reveals Disrupted White Matter Structural Connectivity Network in Healthy Adults with Insomnia Symptoms

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Feng-Mei Lu

2017-11-01

Full Text Available Neuroimaging studies have revealed that insomnia is characterized by aberrant neuronal connectivity in specific brain regions, but the topological disruptions in the white matter (WM structural connectivity networks remain largely unknown in insomnia. The current study uses diffusion tensor imaging (DTI tractography to construct the WM structural networks and graph theory analysis to detect alterations of the brain structural networks. The study participants comprised 30 healthy subjects with insomnia symptoms (IS and 62 healthy subjects without IS. Both the two groups showed small-world properties regarding their WM structural connectivity networks. By contrast, increased local efficiency and decreased global efficiency were identified in the IS group, indicating an insomnia-related shift in topology away from regular networks. In addition, the IS group exhibited disrupted nodal topological characteristics in regions involving the fronto-limbic and the default-mode systems. To our knowledge, this is the first study to explore the topological organization of WM structural network connectivity in insomnia. More importantly, the dysfunctions of large-scale brain systems including the fronto-limbic pathways, salience network and default-mode network in insomnia were identified, which provides new insights into the insomnia connectome. Topology-based brain network analysis thus could be a potential biomarker for IS.

MR neurography of the median nerve at 3.0 T: Optimization of diffusion tensor imaging and fiber tractography

International Nuclear Information System (INIS)

Guggenberger, Roman; Eppenberger, Patrick; Markovic, Daniel; Nanz, Daniel; Chhabra, Avneesh; Pruessmann, Klaas P.; Andreisek, Gustav

2012-01-01

Objectives: The purpose of this study was to systematically assess the optimal b-value and reconstruction parameters for DTI and fiber tractography of the median nerve at 3.0 T. Methods: Local ethical board approved study with 45 healthy volunteers (15 men, 30 women; mean age, 41 ± 3.4 years) who underwent DTI of the right wrist at 3.0 T. A single-shot echo-planar-imaging sequence (TR/TE 10123/40 ms) was acquired at four different b-values (800, 1000, 1200, and 1400 s/mm 2 ). Two independent readers performed post processing and fiber-tractography. Fractional anisotropy (FA) maps were calculated. Fiber tracts of the median nerve were generated using four different algorithms containing different FA thresholds and different angulation tolerances. Data were evaluated quantitatively and qualitatively. Results: Tracking algorithms using a minimum FA threshold of 0.2 and a maximum angulation of 10° were significantly better than other algorithms. Fiber tractography generated significantly longer fibers in DTI acquisitions with higher b-values (1200 and 1400 s/mm 2 versus 800 s/mm 2 ; p 2 (p 2 for DTI of the median nerve at 3.0 T. Optimal reconstruction parameters for fiber tractography should encompass a minimum FA threshold of 0.2 and a maximum angulation tolerance of 10.

Somatotopic location of corticospinal tract at pons in human brain: a diffusion tensor tractography study.

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Hong, Ji Heon; Son, Su Min; Jang, Sung Ho

2010-07-01

No diffusion tensor tractography (DTT) study has yet investigated the somatotopic location of the corticospinal tract (CST) at the pons. In the current study, we used DTT to investigate the somatotopic location of the CST at the pons in the human brain. We recruited 25 healthy volunteers for this study. Diffusion tensor images (DTIs) were scanned using 1.5-T; CSTs for the hand and leg were obtained using FMRIB software. Normalized DTT was reconstructed using the Montreal Neurological Institute echo-planar imaging template supplied with the SPM. Individual DTI data were calculated as a pixel unit at the upper and lower pons. Relative average location of the highest probability point of the CST for the hand was 47.70%, with the standard from the midline to the most lateral point of the upper pons, and 35.87% at the lower pons. For the leg, the CST was located at 56.82% at the upper pons and 40.63% at the lower pons. For the anteroposterior direction from the most anterior point of the pons to the most anterior point of the fourth ventricle, the CST for the hand was located at 42.30% at the upper pons and 36.18% at the lower pons. For the leg, the CST was located at 45.68% and 39.01%, respectively. We found that the hand somatotopy of the CST was located at the antero-medial portion at the pons and that the leg somatotopy of the CST was located postero-laterally to the hand somatotopy of the CST. Copyright (c) 2010 Elsevier Inc. All rights reserved.

Age related diffusion and tractography changes in typically developing pediatric cervical and thoracic spinal cord

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Mahdi Alizadeh

Full Text Available Background and objective: Diffusion tensor imaging (DTI and diffusion tensor tractography (DTT are two techniques that can measure white matter integrity of the spinal cord. Recently, DTI indices have been shown to change with age. The purpose of this study is (a to evaluate the maturational states of the entire pediatric spinal cord using DTI and DTT indices including fractional anisotropy (FA, mean diffusivity (MD, mean length of white matter fiber tracts and tract density and (b to analyze the DTI and DTT parameters along the entire spinal cord as a function of spinal cord levels and age. Method: A total of 23 typically developing (TD pediatric subjects ranging in age from 6 to 16 years old (11.94 ± 3.26 (mean ± standard deviation, 13 females and 10 males were recruited, and scanned using 3.0 T MR scanner. Reduced FOV diffusion tensor images were acquired axially in the same anatomical location prescribed for the T2-weighted images to cover the entire spinal cord (C1-mid L1 levels. To mitigate motion induced artifacts, diffusion directional images were aligned with the reference image (b0 using a rigid body registration algorithm performed by in-house software developed in Matlab (MathWorks, Natick, Massachusetts. Diffusion tensor maps (FA and MD and streamline deterministic tractography were then generated from the motion corrected DTI dataset. DTI and DTT parameters were calculated by using ROIs drawn to encapsulate the whole cord along the entire spinal cord by an independent board certified neuroradiologist. These indices then were compared between two age groups (age group A = 6–11 years (n = 11 and age group B = 12–16 years (n = 12 based on similar standards and age definitions used for reporting spinal cord injury in the pediatric population. Standard least squared linear regression based on a restricted maximum likelihood (REML method was used to evaluate the relationship between age and DTI and

Diffusion tensor tractography of the brainstem pyramidal tract; A study on the optimal reduction factor in parallel imaging

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Bae, Yun Jung; Park, Jong Bin; Kim, Jae Hyoung; Choi, Byung Se; Jung, Cheol Kyu [Dept. of of Radiology, Seoul National University College of Medicine, Seoul National University Bundang Hospital, Seongnam (Korea, Republic of)

2016-08-15

Parallel imaging mitigates susceptibility artifacts that can adversely affect diffusion tensor tractography (DTT) of the pons depending on the reduction (R) factor. We aimed to find the optimal R factor for DTT of the pons that would allow us to visualize the largest possible number of pyramidal tract fibers. Diffusion tensor imaging was performed on 10 healthy subjects at 3 Tesla based on single-shot echo-planar imaging using the following parameters: b value, 1000 s/mm{sup 2}; gradient direction, 15; voxel size, 2 × 2 × 2 mm{sup 3}; and R factors, 1, 2, 3, 4, and 5. DTT of the right and left pyramidal tracts in the pons was conducted in all subjects. Signal-to-noise ratio (SNR), image distortion, and the number of fibers in the tracts were compared across R factors. SNR, image distortion, and fiber number were significantly different according to R factor. Maximal SNR was achieved with an R factor of 2. Image distortion was minimal with an R factor of 5. The number of visible fibers was greatest with an R factor of 3. R factor 3 is optimal for DTT of the pontine pyramidal tract. A balanced consideration of SNR and image distortion, which do not have the same dependence on the R factor, is necessary for DTT of the pons.

The Emerging Role of Tractography in Deep Brain Stimulation: Basic Principles and Current Applications

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Nelson B. Rodrigues

2018-01-01

Full Text Available Diffusion tensor imaging (DTI is an MRI-based technique that delineates white matter tracts in the brain by tracking the diffusion of water in neural tissue. This methodology, known as “tractography”, has been extensively applied in clinical neuroscience to explore nervous system architecture and diseases. More recently, tractography has been used to assist with neurosurgical targeting in functional neurosurgery. This review provides an overview of DTI principles, and discusses current applications of tractography for improving and helping develop novel deep brain stimulation (DBS targets.

Diffusion tensor imaging of the nigrostriatal fibers in Parkinson's disease.

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Zhang, Yu; Wu, I-Wei; Buckley, Shannon; Coffey, Christopher S; Foster, Eric; Mendick, Susan; Seibyl, John; Schuff, Norbert

2015-08-01

Parkinson's disease (PD) is histopathologically characterized by the loss of dopamine neurons in the substantia nigra pars compacta. The depletion of these neurons is thought to reduce the dopaminergic function of the nigrostriatal pathway, as well as the neural fibers that link the substantia nigra to the striatum (putamen and caudate), causing a dysregulation in striatal activity that ultimately leads to lack of movement control. Based on diffusion tensor imaging, visualizing this pathway and measuring alterations of the fiber integrity remain challenging. The objectives were to 1) develop a diffusion tensor tractography protocol for reliably tracking the nigrostriatal fibers on multicenter data; 2) test whether the integrities measured by diffusion tensor imaging of the nigrostriatal fibers are abnormal in PD; and 3) test whether abnormal integrities of the nigrostriatal fibers in PD patients are associated with the severity of motor disability and putaminal dopamine binding ratios. Diffusion tensor tractography was performed on 50 drug-naïve PD patients and 27 healthy control subjects from the international multicenter Parkinson's Progression Marker Initiative. Tractography consistently detected the nigrostriatal fibers, yielding reliable diffusion measures. Fractional anisotropy, along with radial and axial diffusivity of the nigrostriatal tract, showed systematic abnormalities in patients. In addition, variations in fractional anisotropy and radial diffusivity of the nigrostriatal tract were associated with the degree of motor deficits in PD patients. Taken together, the findings imply that the diffusion tensor imaging characteristic of the nigrostriatal tract is potentially an index for detecting and staging of early PD. © 2015 International Parkinson and Movement Disorder Society.

MARCHIAFAVA-BIGNAMI DISEASE (MBD AND DIFFUSION TENSOR IMAGE (DTI TRACTOGRAPHY

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Priscilla Chukwueke

2015-06-01

Full Text Available Marchiafava-Bignami Disease (MBD is a rare central nervous system (CNS disease characterized by demyelination of the corpus callosum. It is mostly found in men with alcohol use disorder and malnutrition with cases reported worldwide across all races. The onset of the disease may be sudden presenting with stupor, coma or seizures while some may present with gait abnormality (spasticity, psychiatric problems, hemiparesis, aphasia, apraxia and incontinence with a resultant high morbidity and mortality rates. Case description: patient is a 30 year old left handed African-American, who presented with c/o altered mental status, urinary incontinence, slurred speech and left-sided weakness. The diagnosis of MBD was confirmed with DTI Tractography which showed significantly diminished commissural fibers extending to the right central semiovale lesion, near absent or significantly diminished commissural fiber extending through the corpus callosum indicating demyelination. Discussion: MBD is often an incidental diagnosis with high morbidity and mortality. This is different from previous casas because of earlier onset as opposed to onset around age 45, rapid recovery and minimal disability as he could walk independently before discharge from hospital. This case also shows added benefit of the DTI tractography in the diagnosis of MBD.

Corticospinal MRI tractography in space-occupying brain lesions by diffusion tensor and kurtosis imaging methods

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Leote, Joao [epartment of Neurosurgery, Hospital Garcia de Orta, Almada (Portugal); Institute of Biophysics and Biomedical Engineering, Faculty of Sciences of the University of Lisbon, Lisboa (Portugal); Nunes, Rita; Cerqueira, Luis; Ferreira, Hugo Alexandre [Institute of Biophysics and Biomedical Engineering, Faculty of Sciences of the University of Lisbon, Lisboa (Portugal)

2015-05-18

Recently, DKI-based tractography has been developed, showing improved crossing-fiber resolution in comparison to deterministic DTI-based tractography in healthy subjects. In this work, DTI and DKI-based tractography methods were compared regarding the assessment of the corticospinal tract in patients presenting space-occupying brain lesions near cortical motor areas. Nine patients (4 males) aged 23 to 62 years old, with space-occupying brain lesions (e.g. tumors) were studied for pre-surgical planning using a 1.5T MRI scanner and a 12-channel head coil. In 5 patients diffusion data was acquired along 64 directions and in 4 patients along 32 directions both with b-values 0, 1000 and 2000 s/mm2. Corticospinal tracts were estimated using deterministic DTI and DKI methods and also using probabilistic DTI. The superior cerebellar peduncles and the motor cortical areas, ipsilateral and contralateral to the lesions, were used as seed regions-of-interest for fiber tracking. Tracts courses and volumes were documented and compared between methods. Results showed that it was possible to estimate fiber tracts using deterministic DTI and DKI methods in 8/9 patients, and using the probabilistic DTI method in all patients. Overall, it was observed that DKI-based tractography showed more voluminous fiber tracts than when using deterministic DTI. The DKI method also showed curvilinear fibers mainly above lesions margins, which were not visible with deterministic DTI in 5 patients. Similar tracts were observed when using probabilistic DTI in 3 of those patients. Results suggest that the DKI method contribute with additional information about the corticospinal tract course in comparison with the DTI method, especially with subcortical lesions and near lesions’ margins. Therefore, this study suggests that DKI-based tractography could be useful in MRI and hybrid PET-MRI pre-surgical planning protocols for improved corticospinal tract evaluation.

Activation of less affected corticospinal tract and poor motor outcome in hemiplegic pediatric patients: a diffusion tensor tractography imaging study

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Jin Hyun Kim

2015-01-01

Full Text Available The less affected hemisphere is important in motor recovery in mature brains. However, in terms of motor outcome in immature brains, no study has been reported on the less affected corticospinal tract in hemiplegic pediatric patients. Therefore, we examined the relationship between the condition of the less affected corticospinal tract and motor function in hemiplegic pediatric patients. Forty patients with hemiplegia due to perinatal or prenatal injury (13.7 ± 3.0 months and 40 age-matched typically developing controls were recruited. These patients were divided into two age-matched groups, the high functioning group (20 patients and the low functioning group (20 patients using functional level of hemiplegia scale. Diffusion tensor tractography images showed that compared with the control group, the patient group of the less affected corticospinal tract showed significantly increased fiber number and significantly decreased fractional anisotropy value. Significantly increased fiber number and significantly decreased fractional anisotropy value in the low functioning group were observed than in the high functioning group. These findings suggest that activation of the less affected hemisphere presenting as increased fiber number and decreased fractional anisotropy value is related to poor motor function in pediatric hemiplegic patients.

Comparison of Magnetic Susceptibility Tensor and Diffusion Tensor of the Brain.

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Li, Wei; Liu, Chunlei

2013-10-01

Susceptibility tensor imaging (STI) provides a novel approach for noninvasive assessment of the white matter pathways of the brain. Using mouse brain ex vivo , we compared STI with diffusion tensor imaging (DTI), in terms of tensor values, principal tensor values, anisotropy values, and tensor orientations. Despite the completely different biophysical underpinnings, magnetic susceptibility tensors and diffusion tensors show many similarities in the tensor and principal tensor images, for example, the tensors perpendicular to the fiber direction have the highest gray-white matter contrast, and the largest principal tensor is along the fiber direction. Comparison to DTI fractional anisotropy, the susceptibility anisotropy provides much higher sensitivity to the chemical composition of the white matter, especially myelin. The high sensitivity can be further enhanced with the perfusion of ProHance, a gadolinium-based contrast agent. Regarding the tensor orientations, the direction of the largest principal susceptibility tensor agrees with that of diffusion tensors in major white matter fiber bundles. The STI fiber tractography can reconstruct the fiber pathways for the whole corpus callosum and for white matter fiber bundles that are in close contact but in different orientations. There are some differences between susceptibility and diffusion tensor orientations, which are likely due to the limitations in the current STI reconstruction. With the development of more accurate reconstruction methods, STI holds the promise for probing the white matter micro-architectures with more anatomical details and higher chemical sensitivity.

MR tractography

International Nuclear Information System (INIS)

Kinosada, Yasutomi; Okuda, Yasuyuki; Ono, Mototsugu

1993-01-01

We developed a new noninvasive technique to visualize the anatomical structure of the nerve fiber system in vivo, and named this technique magnetic resonance (MR) tractography and the acquired image an MR tractogram. MR tractography has two steps. One is to obtain diffusion-weighted images sensitized along axes appropriate for depicting the intended nerve fibers with anisotropic water diffusion MR imaging. The other is to extract the anatomical structure of the nerve fiber system from a series of diffusion-weighted images by the maximum intensity projection method. To examine the clinical usefulness of the proposed technique, many contiguous, thin (3 mm) coronal two-dimensional sections of the brain were acquired sequentially in normal volunteers and selected patients with paralyses, on a 1.5 Tesla MR system (Signa, GE) with an ECG-gated Stejskal-Tanner pulse sequence. The structure of the nerve fiber system of normal volunteers was almost the same as the anatomy. The tractograms of patients with paralyses clearly showed the degeneration of nerve fibers and were correlated with clinical symptoms. MR tractography showed great promise for the study of neuroanatomy and neuroradiology. (author)

Quantitative evaluation of the white matter tracts of the limbic system segmented by diffusion tensor tractography with schizophrenia. A preliminary study

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Aoki, Shigeki; Yamada, Haruyasu; Abe, Osamu

2005-01-01

In this study, the clinical feasibility of combined technique with diffusion tensor tractography (DTT) and fractional anisotropy (FA) analysis in patients with schizophrenia is evaluated. Fourteen patients with schizophrenia and 15 age-matched volunteers were studied on a 1.5 T MR imager. DTT of the fornix, anterior and posterior cingulum, and uncinate fasciculus were visualized by dTV (free software by Masutani Y, URL: http://www.ut-radiology.umin.jp/people/masutani/dTV.htm) and VOLUME-ONE. Region of interest (ROIs) were semi-automatically placed on the tracts and FA values were calculated. FA values on the anterior cingulum, fornix and uncinate fasciculus of the schizophrenia patients were significantly lower than those of the volunteers. This combined method may be useful in evaluating subtle changes in the white matter tracts in patients with schizophrenia. (author)

Characterization of short white matter fiber bundles in the central area from diffusion tensor MRI

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Magro, Elsa [INSERM U 1099/Universite de Rennes 1, Equipe MediCIS, Faculte de Medecine, Rennes Cedex (France); CHU Cavale Blanche, Service de Neurochirurgie, Pole Neurolocomoteur, Brest (France); Moreau, Tristan; Gibaud, Bernard [INSERM U 1099/Universite de Rennes 1, Equipe MediCIS, Faculte de Medecine, Rennes Cedex (France); Seizeur, Romuald [INSERM U 1099/Universite de Rennes 1, Equipe MediCIS, Faculte de Medecine, Rennes Cedex (France); CHU Cavale Blanche, Service de Neurochirurgie, Pole Neurolocomoteur, Brest (France); INSERM UMR 1101 LaTIM, Brest (France); Morandi, Xavier [INSERM U 1099/Universite de Rennes 1, Equipe MediCIS, Faculte de Medecine, Rennes Cedex (France); CHU Pontchaillou, Service de Neurochirurgie, Rennes (France)

2012-11-15

Diffusion tensor imaging and tractography allow studying white matter fiber bundles in the human brain in vivo. Electrophysiological studies and postmortem dissections permit improving our knowledge about the short association fibers connecting the pre- and postcentral gyri. The aim of this study was first to extract and analyze the features of these short fiber bundles and secondly to analyze their asymmetry according to the subjects' handedness. Ten right-handed and ten left-handed healthy subjects were included. White matter fiber bundles were extracted using a streamline tractography approach, with two seed regions of interest (ROI) taken from a parcellation of the pre- and postcentral gyri. This parcellation was achieved using T1 magnetic resonance images (MRI) and semi-automatically generated three ROIs within each gyrus. MRI tracks were reconstructed between all pairs of ROIs connecting the adjacent pre- and postcentral gyri. A quantitative analysis was performed on the number of tracks connecting each ROI pair. A statistical analysis studied the repartition of these MRI tracks in the right and left hemispheres and as a function of the subjects' handedness. The quantitative analysis showed an increased density of MRI tracks in the middle part of the central area in each hemisphere of the 20 subjects. The statistical analysis showed significantly more MRI tracks for the left hemisphere, when we consider the whole population, and this difference was presumably driven by the left-handers. These results raise questions about the functional role of these MRI tracks and their relation with laterality. (orig.)

Characterization of short white matter fiber bundles in the central area from diffusion tensor MRI

International Nuclear Information System (INIS)

Magro, Elsa; Moreau, Tristan; Gibaud, Bernard; Seizeur, Romuald; Morandi, Xavier

2012-01-01

Diffusion tensor imaging and tractography allow studying white matter fiber bundles in the human brain in vivo. Electrophysiological studies and postmortem dissections permit improving our knowledge about the short association fibers connecting the pre- and postcentral gyri. The aim of this study was first to extract and analyze the features of these short fiber bundles and secondly to analyze their asymmetry according to the subjects' handedness. Ten right-handed and ten left-handed healthy subjects were included. White matter fiber bundles were extracted using a streamline tractography approach, with two seed regions of interest (ROI) taken from a parcellation of the pre- and postcentral gyri. This parcellation was achieved using T1 magnetic resonance images (MRI) and semi-automatically generated three ROIs within each gyrus. MRI tracks were reconstructed between all pairs of ROIs connecting the adjacent pre- and postcentral gyri. A quantitative analysis was performed on the number of tracks connecting each ROI pair. A statistical analysis studied the repartition of these MRI tracks in the right and left hemispheres and as a function of the subjects' handedness. The quantitative analysis showed an increased density of MRI tracks in the middle part of the central area in each hemisphere of the 20 subjects. The statistical analysis showed significantly more MRI tracks for the left hemisphere, when we consider the whole population, and this difference was presumably driven by the left-handers. These results raise questions about the functional role of these MRI tracks and their relation with laterality. (orig.)

The value of 3 T MR diffusion tensor fiber tractography study of association fasciculus of normative human in vivo primarily

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Sun Xuejin; Dai Jianping; Gao Peiyi; Li Shaowu; Ai Lin; Chen Hongyan; Tian Shengyong; Pang Ruilin

2006-01-01

Objective: To exhibit the fibers of association fascicules, aims at demonstrating the association fibers of brain with diffusion tensor fiber tracking technique. Methods: Conventionality MRI, diffusion tensor imaging (DTI) and diffusion tensor fiber tractography (DT-FT) were performed in twenty healthy subjects, including eighteen right-handed (sixteen men and four women) and two left-handed (one male and one female) by 3 T Siemens Trio 2003 T MRI. To select arcuate fascicules, inferior longitudinal fascicules, frontalwoceipital fascicules, corpus callosum, posterior limb of internal capsule and external capsule as seeds used to track fibers. Results: Diffusion tensor fiber tracking exhibited bundles of external capsule left mean fibers were 308 bundles, right fibers were 307 bundles (t=0.138, P>0.05), frontal-occipital tracks left mean fibers were 115 bundles, right fibers were 110 bundles(t=1.174, P>0.05), and their fractional anisotropy (FA) valueexternal capsule mean FA left was 0.361, the right was 0.362 (t=-0.184, P>0.05). Frontal-occipital tracks mean fractional anisotropy left was 0.352, the right was 0.351 (t=-0.816, P>0.05). The difference between both sides were statistically insignificant (P>0.05). The posterior limb of internal capsule left mean fibers were 249 bundles, right fibers were 257 bundles (t=-0.818, P>0.05), arcuate fascietfiesleft mean fibers were 198 bundles, right fibers were 204 bundles (t=-0.465, P>0.05 ) fibers difference between both sides were statistically insignificant (P>0.05), but the individual difference was significant, and their fractional anisotropy difference between both sides (posterior limb of internal capsule mean FA left was 0.450, the right was 0.444 (t=2.771, P 0.05). Mean FA left was 0.369, the right was 0.370(t=-0.178, P>0.05) ,difference between both sides was statistically insignificant (P>0.05). But the individual difference was significant. Some of them were the left larger than the right side. The frontal

White matter mapping by DTI-based tractography for neurosurgery

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Kamada, Kyousuke

2009-01-01

To validate the corticospinal tract (CST) and arcuate fasciculus (AF) illustrated by diffusion tensor imaging (DTI), we used CST- and AF-tractography integrated neuronavigation and monopolar and bipolar direct fiber stimulation. Forty seven patients with brain lesions adjacent to the CST and AF were studied. During lesion resection, direct fiber stimulation was applied to the CST and AF to elicit motor responses (fiber-motor evoked potential (MEP)) and the impairment of language-related functions to identify the CST and AF. The minimum distance between the resection border and illustrated CST was measured on postoperative images. Direct fiber stimulation demonstrated that CST- and AF-tractography accurately reflected anatomical CST functioning. The cortical stimulation to the gyrus, including the language-functional MRI (fMRI) activation, evoked speech arrest, while the subcortical stimulation close to the AF reproducibly caused 'paranomia' without speech arrest. There were strong correlations between stimulus intensity for the fiber-MEP and the distance between eloquent fibers and the stimulus points. The convergent calculation formulated 1.8 mA as the electrical threshold of CST for the fiber-MEP, which was much smaller than that of the hand motor area. Validated tractography demonstrated the mean distance and intersection angle between CST and AF were 5 mm and 107 deg, respectively. In addition, the anisotropic diffusion-weighted image (ADWI) and CST-tractography clearly indicated the locations of the primary motor area (PMA) and the central sulcus and well reflected the anatomical characteristics of the corticospinal tract in the human brain. DTI-based tractography is a reliable way to map the white matter connections in the entire brain in clinical and basic neuroscience. By combining these techniques, investigating the cortico-subcortical connections in the human central nervous system could contribute to elucidating the neural networks of the human brain and

White matter mapping by DTI-based tractography for neurosurgery

International Nuclear Information System (INIS)

Kamada, Kyousuke

2011-01-01

The purpose of this study was to validate the corticospinal tract (CST) and arcuate fasciculus (AF) illustrated by diffusion tensor imaging (DTI), we used CST- and AF-tractography integrated neuronavigation and monopolar and bipolar direct fiber stimulation. Forty seven patients with brain lesions adjacent to the CST and AF were studied. During lesion resection, direct fiber stimulation was applied to the CST and AF to elicit motor responses (fiber-MEP) and the impairment of language-related functions to identify the CST and AF. The minimum distance between the resection border and illustrated CST was measured on postoperative images. Direct fiber stimulation demonstrated that CST- and AF-tractography accurately reflected anatomical CST functioning. The cortical stimulation to the gyrus, including the language-fMRI activation, evoked speech arrest, while the subcortical stimulation close to the AF reproducibly caused 'paranomia' without speech arrest. There were strong correlations between stimulus intensity for the fiber-MEP and the distance between eloquent fibers and the stimulus points. The convergent calculation formulated 1.8 mA as the electrical threshold of CST for the fiber-MEP, which was much smaller than that of the hand motor area. Validated tractography demonstrated the mean distance and intersection angle between CST and AF were 5 mm and 107 deg, respectively. In addition, the anisotropic diffusion-weighted image (ADWI) and CST-tractography clearly indicated the locations of the primary motor area (PMA) and the central sulcus and well reflected the anatomical characteristics of the corticospinal tract in the human brain. DTI-based tractography is a reliable way to map the white matter connections in the entire brain in clinical and basic neuroscience. By combining these techniques, investigating the cortico-subcortical connections in the human central nervous system could contribute to elucidating the neural networks of the human brain and shed light

Reconstruction of white matter fibre tracts using diffusion kurtosis tensor imaging at 1.5T: Pre-surgical planning in patients with gliomas.

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Leote, Joao; Nunes, Rita G; Cerqueira, Luis; Loução, Ricardo; Ferreira, Hugo A

2018-01-01

Tractography studies for pre-surgical planning of primary brain tumors is typically done using diffusion tensor imaging (DTI), which cannot resolve crossing, kissing or highly angulated fibres. Tractography based on the estimation of the diffusion kurtosis (DK) tensor was recently demonstrated to enable tackling these limitations. However, its use in the clinical context at low 1.5T field has not yet been reported. To evaluate if the estimation of whole-brain tractography using the DK tensor is feasible for pre-surgical investigation of patients with brain tumors at 1.5T. Eight healthy subjects and 3 patients with brain tumors were scanned at 1.5T using a 12-channel head coil. Diffusion-weighted images were acquired with repetition/echo times of 5800/107 ms, 82 × 82 resolution, 3 × 3 × 3 mm 3 voxel size, b-values of 0, 1000, 2000 s/mm 2 and 64 gradient sensitising directions. Whole-brain tractography was estimated using the DK tensor and corticospinal tracts (CST) were isolated using regions-of-interest placed at the cerebral peduncles and motor gyrus. Tract size, DK metrics and CST deviation index (highest curvature point) were compared between healthy subjects and patients. Tract sizes did not differ between groups. The CST deviation index was significantly higher in patients compared to healthy subjects. Fractional anisotropy was significantly lower in patients, with higher mean kurtosis asymmetry index at the highest curvature point in patients. Corticospinal fibre bundles estimated using DK tensor in a 1.5T scanner presented similar properties in patients with brain gliomas as those reported in the literature using DTI-based tractography.

Imaging Arterial Fibres Using Diffusion Tensor Imaging—Feasibility Study and Preliminary Results

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Kerskens Christian

2010-01-01

Full Text Available Abstract MR diffusion tensor imaging (DTI was used to analyze the fibrous structure of aortic tissue. A fresh porcine aorta was imaged at 7T using a spin echo sequence with the following parameters: matrix 128 128 pixel; slice thickness 0.5 mm; interslice spacing 0.1 mm; number of slices 16; echo time 20.3 s; field of view 28 mm 28 mm. Eigenvectors from the diffusion tensor images were calculated for the central image slice and the averaged tensors and the eigenvector corresponding to the largest eigenvalue showed two distinct angles corresponding to near and to the transverse plane of the aorta. Fibre tractography within the aortic volume imaged confirmed that fibre angles were oriented helically with lead angles of and . The findings correspond to current histological and microscopy data on the fibrous structure of aortic tissue, and therefore the eigenvector maps and fibre tractography appear to reflect the alignment of the fibers in the aorta. In view of current efforts to develop noninvasive diagnostic tools for cardiovascular diseases, DTI may offer a technique to assess the structural properties of arterial tissue and hence any changes or degradation in arterial tissue.

Preoperative DTI and probabilistic tractography in an amputee with deep brain stimulation for lower limb stump pain.

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Owen, S L F; Heath, J; Kringelbach, M L; Stein, J F; Aziz, T Z

2007-10-01

This study aimed to find out whether preoperative diffusion tensor imaging (DTI) and probabilistic tractography could help with surgical planning for deep brain stimulation in the periaqueductal/periventricular grey area (PAG/PVG) in a patient with lower leg stump pain. A preoperative DTI was obtained from the patient, who then received DBS surgery in the PAG/PVG area with good pain relief. The postoperative MRI scan showing electrode placement was used to calculate four seed areas to represent the contacts on the Medtronic 3387 electrode. Probabilistic tractography was then performed from the pre-operative DTI image. Tracts were seen to connect to many areas within the pain network from the four different contacts. These initial findings suggest that preoperative DTI scanning and probabilistic tractography may be able to assist surgical planning in the future.

Application of fiber tractography for neurosurgery

International Nuclear Information System (INIS)

Hashimoto, Naoya; Yoshimine, Toshiki

2007-01-01

This review describes about the fiber tractography (FT) for its basic principle, method, and application to neurosurgery involving usefulness, pitfall, validation needed and future perspective. MR diffusion weighted image exhibits the diffusion (Brownian movement) of water molecules and its multiple images taken by different angles of magnetic field can also give information of their diffusion anisotropy, whereby diffusion tensor image is yielded as FT owing to their high anisotropy, with use of appropriate softwares assuming an ellipsoid of anisotropic water (single tensor model). FT thus presents an image of a specific and functional neurofiber bundle. Recently, FT in neurosurgery has been recognized to have pitfalls in tracing the bundle at its crossing and branch, e.g., suggested avoidance of surgery of eloquent area navigated with FT alone. For this, developed and considered are the multi-tensor models based on multiple ellipsoids and on probabilistic one on probability, and combination of electrophysiological mapping is thought necessary as well. Application of FT is also actively in progress to understand neurological diseases like cerebral vascular lesion, hemiplegia, epilepsy, injury and many others. FT navigation without other validation is thus limited in neurosurgery, but FT is surely one of means to improve patients' prognosis and quality of life (QOL). (R.T.)

Using Tractography to Distinguish SWEDD from Parkinson’s Disease Patients Based on Connectivity

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Mansu Kim

2016-01-01

Full Text Available Background. It is critical to distinguish between Parkinson’s disease (PD and scans without evidence of dopaminergic deficit (SWEDD, because the two groups are different and require different therapeutic approaches. Objective. The aim of this study was to distinguish SWEDD patients from PD patients using connectivity information derived from diffusion tensor imaging tractography. Methods. Diffusion magnetic resonance images of SWEDD (n=37 and PD (n=40 were obtained from a research database. Tractography, the process of obtaining neural fiber information, was performed using custom software. Group-wise differences between PD and SWEDD patients were quantified using the number of connected fibers between two regions, and correlation analyses were performed based on clinical scores. A support vector machine classifier (SVM was applied to distinguish PD and SWEDD based on group-wise differences. Results. Four connections showed significant group-wise differences and correlated with the Unified Parkinson’s Disease Rating Scale sponsored by the Movement Disorder Society. The SVM classifier attained 77.92% accuracy in distinguishing between SWEDD and PD using these identified connections. Conclusions. The connections and regions identified represent candidates for future research investigations.

The tensor rank of tensor product of two three-qubit W states is eight

OpenAIRE

Chen, Lin; Friedland, Shmuel

2017-01-01

We show that the tensor rank of tensor product of two three-qubit W states is not less than eight. Combining this result with the recent result of M. Christandl, A. K. Jensen, and J. Zuiddam that the tensor rank of tensor product of two three-qubit W states is at most eight, we deduce that the tensor rank of tensor product of two three-qubit W states is eight. We also construct the upper bound of the tensor rank of tensor product of many three-qubit W states.

Diffusion tensor MRI tractography reveals increased fractional anisotropy (FA) in arcuate fasciculus following music-cued motor training.

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Moore, Emma; Schaefer, Rebecca S; Bastin, Mark E; Roberts, Neil; Overy, Katie

2017-08-01

Auditory cues are frequently used to support movement learning and rehabilitation, but the neural basis of this behavioural effect is not yet clear. We investigated the microstructural neuroplasticity effects of adding musical cues to a motor learning task. We hypothesised that music-cued, left-handed motor training would increase fractional anisotropy (FA) in the contralateral arcuate fasciculus, a fibre tract connecting auditory, pre-motor and motor regions. Thirty right-handed participants were assigned to a motor learning condition either with (Music Group) or without (Control Group) musical cues. Participants completed 20minutes of training three times per week over four weeks. Diffusion tensor MRI and probabilistic neighbourhood tractography identified FA, axial (AD) and radial (RD) diffusivity before and after training. Results revealed that FA increased significantly in the right arcuate fasciculus of the Music group only, as hypothesised, with trends for AD to increase and RD to decrease, a pattern of results consistent with activity-dependent increases in myelination. No significant changes were found in the left ipsilateral arcuate fasciculus of either group. This is the first evidence that adding musical cues to movement learning can induce rapid microstructural change in white matter pathways in adults, with potential implications for therapeutic clinical practice. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

Altered brain structural connectivity in post-traumatic stress disorder: a diffusion tensor imaging tractography study.

Science.gov (United States)

Long, Zhiliang; Duan, Xujun; Xie, Bing; Du, Handan; Li, Rong; Xu, Qiang; Wei, Luqing; Zhang, Shao-xiang; Wu, Yi; Gao, Qing; Chen, Huafu

2013-09-25

Post-traumatic stress disorder (PTSD) is characterized by dysfunction of several discrete brain regions such as medial prefrontal gyrus with hypoactivation and amygdala with hyperactivation. However, alterations of large-scale whole brain topological organization of structural networks remain unclear. Seventeen patients with PTSD in motor vehicle accident survivors and 15 normal controls were enrolled in our study. Large-scale structural connectivity network (SCN) was constructed using diffusion tensor tractography, followed by thresholding the mean factional anisotropy matrix of 90 brain regions. Graph theory analysis was then employed to investigate their aberrant topological properties. Both patient and control group showed small-world topology in their SCNs. However, patients with PTSD exhibited abnormal global properties characterized by significantly decreased characteristic shortest path length and normalized characteristic shortest path length. Furthermore, the patient group showed enhanced nodal centralities predominately in salience network including bilateral anterior cingulate and pallidum, and hippocampus/parahippocamus gyrus, and decreased nodal centralities mainly in medial orbital part of superior frontal gyrus. The main limitation of this study is the small sample of PTSD patients, which may lead to decrease the statistic power. Consequently, this study should be considered an exploratory analysis. These results are consistent with the notion that PTSD can be understood by investigating the dysfunction of large-scale, spatially distributed neural networks, and also provide structural evidences for further exploration of neurocircuitry models in PTSD. © 2013 Elsevier B.V. All rights reserved.

The 1/ N Expansion of Tensor Models with Two Symmetric Tensors

Science.gov (United States)

Gurau, Razvan

2018-06-01

It is well known that tensor models for a tensor with no symmetry admit a 1/ N expansion dominated by melonic graphs. This result relies crucially on identifying jackets, which are globally defined ribbon graphs embedded in the tensor graph. In contrast, no result of this kind has so far been established for symmetric tensors because global jackets do not exist. In this paper we introduce a new approach to the 1/ N expansion in tensor models adapted to symmetric tensors. In particular we do not use any global structure like the jackets. We prove that, for any rank D, a tensor model with two symmetric tensors and interactions the complete graph K D+1 admits a 1/ N expansion dominated by melonic graphs.

Time-optimized high-resolution readout-segmented diffusion tensor imaging.

Directory of Open Access Journals (Sweden)

Gernot Reishofer

Full Text Available Readout-segmented echo planar imaging with 2D navigator-based reacquisition is an uprising technique enabling the sampling of high-resolution diffusion images with reduced susceptibility artifacts. However, low signal from the small voxels and long scan times hamper the clinical applicability. Therefore, we introduce a regularization algorithm based on total variation that is applied directly on the entire diffusion tensor. The spatially varying regularization parameter is determined automatically dependent on spatial variations in signal-to-noise ratio thus, avoiding over- or under-regularization. Information about the noise distribution in the diffusion tensor is extracted from the diffusion weighted images by means of complex independent component analysis. Moreover, the combination of those features enables processing of the diffusion data absolutely user independent. Tractography from in vivo data and from a software phantom demonstrate the advantage of the spatially varying regularization compared to un-regularized data with respect to parameters relevant for fiber-tracking such as Mean Fiber Length, Track Count, Volume and Voxel Count. Specifically, for in vivo data findings suggest that tractography results from the regularized diffusion tensor based on one measurement (16 min generates results comparable to the un-regularized data with three averages (48 min. This significant reduction in scan time renders high resolution (1 × 1 × 2.5 mm(3 diffusion tensor imaging of the entire brain applicable in a clinical context.

Imaging Arterial Fibres Using Diffusion Tensor Imaging—Feasibility Study and Preliminary Results

Directory of Open Access Journals (Sweden)

Ciaran K. Simms

2010-01-01

Full Text Available MR diffusion tensor imaging (DTI was used to analyze the fibrous structure of aortic tissue. A fresh porcine aorta was imaged at 7T using a spin echo sequence with the following parameters: matrix 128 × 128 pixel; slice thickness 0.5 mm; interslice spacing 0.1 mm; number of slices 16; echo time 20.3 s; field of view 28 mm × 28 mm. Eigenvectors from the diffusion tensor images were calculated for the central image slice and the averaged tensors and the eigenvector corresponding to the largest eigenvalue showed two distinct angles corresponding to near 0∘ and 180∘ to the transverse plane of the aorta. Fibre tractography within the aortic volume imaged confirmed that fibre angles were oriented helically with lead angles of 15±2.5∘ and 175±2.5∘. The findings correspond to current histological and microscopy data on the fibrous structure of aortic tissue, and therefore the eigenvector maps and fibre tractography appear to reflect the alignment of the fibers in the aorta. In view of current efforts to develop noninvasive diagnostic tools for cardiovascular diseases, DTI may offer a technique to assess the structural properties of arterial tissue and hence any changes or degradation in arterial tissue.

Diffusion imaging and tractography of congenital brain malformations

International Nuclear Information System (INIS)

Wahl, Michael; Barkovich, A.J.; Mukherjee, Pratik

2010-01-01

Diffusion imaging is an MRI modality that measures the microscopic molecular motion of water in order to investigate white matter microstructure. The modality has been used extensively in recent years to investigate the neuroanatomical basis of congenital brain malformations. We review the basic principles of diffusion imaging and of specific techniques, including diffusion tensor imaging (DTI) and high angular resolution diffusion imaging (HARDI). We show how DTI and HARDI, and their application to fiber tractography, has elucidated the aberrant connectivity underlying a number of congenital brain malformations. Finally, we discuss potential uses for diffusion imaging of developmental disorders in the clinical and research realms. (orig.)

Shape anisotropy: tensor distance to anisotropy measure

Science.gov (United States)

Weldeselassie, Yonas T.; El-Hilo, Saba; Atkins, M. S.

2011-03-01

Fractional anisotropy, defined as the distance of a diffusion tensor from its closest isotropic tensor, has been extensively studied as quantitative anisotropy measure for diffusion tensor magnetic resonance images (DT-MRI). It has been used to reveal the white matter profile of brain images, as guiding feature for seeding and stopping in fiber tractography and for the diagnosis and assessment of degenerative brain diseases. Despite its extensive use in DT-MRI community, however, not much attention has been given to the mathematical correctness of its derivation from diffusion tensors which is achieved using Euclidean dot product in 9D space. But, recent progress in DT-MRI has shown that the space of diffusion tensors does not form a Euclidean vector space and thus Euclidean dot product is not appropriate for tensors. In this paper, we propose a novel and robust rotationally invariant diffusion anisotropy measure derived using the recently proposed Log-Euclidean and J-divergence tensor distance measures. An interesting finding of our work is that given a diffusion tensor, its closest isotropic tensor is different for different tensor distance metrics used. We demonstrate qualitatively that our new anisotropy measure reveals superior white matter profile of DT-MR brain images and analytically show that it has a higher signal to noise ratio than fractional anisotropy.

Evaluation of left-right asymmetry of pyramidal tracts in preterm neonates by diffusion tensor imaging and tractography

International Nuclear Information System (INIS)

Ogita, Kaori

2010-01-01

Diffusion Tensor Tractography (DTT) is a new noninvasive brain imaging technique to detect the neural tract and is expected to be instrumental in diagnosing diseases with white matter involvement. Assessing the pyramidal tract with DTT will be useful in diagnosing motor dysfunction. However, the pyramidal tract (PT) has not been fully investigated with this technique especially in neonates. The aim of this study is to clarify the normal characteristics, especially the latevility, of the PT in healthy neonates. Fourteen preterm neonates were examined with DTT before being discharged from the neonatal intensive care unit (NICU). Free software dTV and Volume-One were used to depict the PT and analyze the fractional anisotrophy (FA) value, a parameter used in Diffusion Tensor Imaging (DTI). In the beginning, the FA at the medulla oblongata as the initial region of interest was determined to be 0.18 or more to depict the PT by DTT. The FA values at the level of the posterior limb of the Internal Capsule (IC), the Corona Radiate (CR), and the Centrum Semiovale (CS) of the depicted PT were measured and compared with the contralateral. The upper limit of the level of the FA at the medulla oblongata value capable of depicting the PT was measured and compared with the contralateral. All data was analyzed using the Mann-Whitney test. A p-value of less than 0.05 was considered to indicate significant difference. The FA value of the left CS was higher than that of the right in all 14 cases, and the FA value of the left CA was higher than that of the right in 13 cases. The upper limit of the FA value of the medulla oblongata as the initial region of interest to depict the left side of the PT was higher than for the right side of the PT in all 14 cases. We clarified the laterality of the PT in healthy neonates using DTT. This laterality must be taken into consideration when involvement of the PT is diagnosed using this technique. (author)

Diffusion Tensor Imaging-Based Research on Human White Matter Anatomy

Directory of Open Access Journals (Sweden)

Ming-guo Qiu

2012-01-01

Full Text Available The aim of this study is to investigate the white matter by the diffusion tensor imaging and the Chinese visible human dataset and to provide the 3D anatomical data of the corticospinal tract for the neurosurgical planning by studying the probabilistic maps and the reproducibility of the corticospinal tract. Diffusion tensor images and high-resolution T1-weighted images of 15 healthy volunteers were acquired; the DTI data were processed using DtiStudio and FSL software. The FA and color FA maps were compared with the sectional images of the Chinese visible human dataset. The probability maps of the corticospinal tract were generated as a quantitative measure of reproducibility for each voxel of the stereotaxic space. The fibers displayed by the diffusion tensor imaging were well consistent with the sectional images of the Chinese visible human dataset and the existing anatomical knowledge. The three-dimensional architecture of the white matter fibers could be clearly visualized on the diffusion tensor tractography. The diffusion tensor tractography can establish the 3D probability maps of the corticospinal tract, in which the degree of intersubject reproducibility of the corticospinal tract is consistent with the previous architectonic report. DTI is a reliable method of studying the fiber connectivity in human brain, but it is difficult to identify the tiny fibers. The probability maps are useful for evaluating and identifying the corticospinal tract in the DTI, providing anatomical information for the preoperative planning and improving the accuracy of surgical risk assessments preoperatively.

Quantitative evaluation of normal lumbosacral plexus nerve by using diffusion tensor imaging

International Nuclear Information System (INIS)

Shi Yin; Wang Chuanbing; Liu Wei; Zong Min; Sa Rina; Shi Haibin; Wang Dehang

2014-01-01

Objective: To observe the lumbosacral plexus nerves by diffusion tensor tractography (DTT) and quantitatively evaluate them by using diffusion tensor imaging (DTI) in healthy volunteers. Methods: A total of 60 healthy volunteers (30 males and 30 females) underwent DTI scanning. Mean FA values of the lumbosacral plexus nerves (both sides of lumbar roots L3 to S1, proximal and distal to the lumbar foraminal zone) were quantified. Differences among various segments of lumbar nerve roots were compared with ANOVA test and SNK test. Differences between two sides of the lumbar nerve roots at the same lumbar segment were compared with paired-samples t test. Differences between the proximal and the distal nerve to the the lumbar foraminal zone at the same lumbar segment were compared with paired-samples t test. The lumbosacral plexus nerve was visualized with tractography. Results: (1) The lumbosacral plexus nerve was clearly visualized with tractography. (2) Mean FA values of the lumbar nerve roots L3 to S1 were as followings: proximal to the left lumbar foraminal zone 0.202 ± 0.021, 0.201 ± 0.026, 0.201 ± 0.027, 0.191 ±0.016, distal to the left lumbar foraminal zone 0.222 ± 0.034, 0.250 ± 0.028, 0.203 ± 0.026, 0.183 ± 0.020, proximal to the right lumbar foraminal zone 0.200 ± 0.023, 0.202 ± 0.023, 0.205 ± 0.027, 0.191 ± 0.017, distal to the right lumbar foraminal zone 0.225 ± 0.032, 0.247 ± 0.027, 0.205 ± 0.033, 0.183 ± 0.021. Mean FA values were significantly different between the proximal nerve to the distal nerve in lumbar nerve roots L3, L4, S1 (t=-9.114-2.366, P<0.05), but not significantly different in L5 (P>0.05). Differences were not found between the right and left side nerves at the same lumbar segment (P>0.05). (3) The whole length of the lumbar roots nerve L3 to S1 can be visualized clearly by using DTT. Conclusions: Diffusion tensor imaging and tractography can show and provide quantitative information of human lumbosacral plexus nerves. DTI

Assessment of Brain Damage and Plasticity in the Visual System Due to Early Occipital Lesion: Comparison of FDG-PET with Diffusion MRI Tractography

Science.gov (United States)

Jeong, Jeong-won; Tiwari, Vijay N.; Shin, Joseph; Chugani, Harry T.; Juhász, Csaba

2015-01-01

Purpose To determine the relation between glucose metabolic changes of the primary visual cortex, structural abnormalities of the corresponding visual tracts, and visual symptoms in children with Sturge-Weber syndrome (SWS). Materials and Methods In 10 children with unilateral SWS (ages 1.5–5.5 years), a region-of-interest analysis was applied in the bilateral medial occipital cortex on positron emission tomography (PET) and used to track diffusion-weighted imaging (DWI) streamlines corresponding to the central visual pathway. Normalized streamline volumes of individual SWS patients were compared with values from age-matched control groups as well as correlated with normalized glucose uptakes and visual field deficit. Results Lower glucose uptake and lower corresponding streamline volumes were detected in the affected occipital lobe in 9/10 patients, as compared to the contralateral side. Seven of these 9 patients had visual field deficit and normal or decreased streamline volumes on the unaffected side. The two other children had no visual symptoms and showed high contralateral visual streamline volumes. There was a positive correlation between the normalized ratios on DWI and PET, indicating that lower glucose metabolism was associated with lower streamline volume in the affected hemisphere (R = 0.70, P = 0.024). Conclusion We demonstrated that 18F-flurodeoxyglucose (FDG)-PET combined with DWI tractography can detect both brain damage on the side of the lesion and contralateral plasticity in children with early occipital lesions. PMID:24391057

MR neurography of ulnar nerve entrapment at the cubital tunnel: a diffusion tensor imaging study

International Nuclear Information System (INIS)

Breitenseher, Julia B.; Berzaczy, Dominik; Nemec, Stefan F.; Weber, Michael; Prayer, Daniela; Kasprian, Gregor; Kranz, Gottfried; Sycha, Thomas; Hold, Alina

2015-01-01

MR neurography, diffusion tensor imaging (DTI) and tractography at 3 Tesla were evaluated for the assessment of patients with ulnar neuropathy at the elbow (UNE). Axial T2-weighted and single-shot DTI sequences (16 gradient encoding directions) were acquired, covering the cubital tunnel of 46 patients with clinically and electrodiagnostically confirmed UNE and 20 healthy controls. Cross-sectional area (CSA) was measured at the retrocondylar sulcus and FA and ADC values on each section along the ulnar nerve. Three-dimensional nerve tractography and T2-weighted neurography results were independently assessed by two raters. Patients showed a significant reduction of ulnar nerve FA values at the retrocondylar sulcus (p = 0.002) and the deep flexor fascia (p = 0.005). At tractography, a complete or partial discontinuity of the ulnar nerve was found in 26/40 (65 %) of patients. Assessment of T2 neurography was most sensitive in detecting UNE (sensitivity, 91 %; specificity, 79 %), followed by tractography (88 %/69 %). CSA and FA measurements were less effective in detecting UNE. T2-weighted neurography remains the most sensitive MR technique in the imaging evaluation of clinically manifest UNE. DTI-based neurography at 3 Tesla supports the MR imaging assessment of UNE patients by adding quantitative and 3D imaging data. (orig.)

MR neurography of ulnar nerve entrapment at the cubital tunnel: a diffusion tensor imaging study

Energy Technology Data Exchange (ETDEWEB)

Breitenseher, Julia B.; Berzaczy, Dominik; Nemec, Stefan F.; Weber, Michael; Prayer, Daniela; Kasprian, Gregor [Medical University of Vienna, Department of Biomedical Imaging and Image-guided Therapy, Vienna (Austria); Kranz, Gottfried; Sycha, Thomas [Medical University of Vienna, Department of Neurology, Vienna (Austria); Hold, Alina [Medical University of Vienna, Department of Plastic and Reconstructive Surgery, Vienna (Austria)

2015-07-15

MR neurography, diffusion tensor imaging (DTI) and tractography at 3 Tesla were evaluated for the assessment of patients with ulnar neuropathy at the elbow (UNE). Axial T2-weighted and single-shot DTI sequences (16 gradient encoding directions) were acquired, covering the cubital tunnel of 46 patients with clinically and electrodiagnostically confirmed UNE and 20 healthy controls. Cross-sectional area (CSA) was measured at the retrocondylar sulcus and FA and ADC values on each section along the ulnar nerve. Three-dimensional nerve tractography and T2-weighted neurography results were independently assessed by two raters. Patients showed a significant reduction of ulnar nerve FA values at the retrocondylar sulcus (p = 0.002) and the deep flexor fascia (p = 0.005). At tractography, a complete or partial discontinuity of the ulnar nerve was found in 26/40 (65 %) of patients. Assessment of T2 neurography was most sensitive in detecting UNE (sensitivity, 91 %; specificity, 79 %), followed by tractography (88 %/69 %). CSA and FA measurements were less effective in detecting UNE. T2-weighted neurography remains the most sensitive MR technique in the imaging evaluation of clinically manifest UNE. DTI-based neurography at 3 Tesla supports the MR imaging assessment of UNE patients by adding quantitative and 3D imaging data. (orig.)

Preoperative Quantitative MR Tractography Compared with Visual Tract Evaluation in Patients with Neuropathologically Confirmed Gliomas Grades II and III: A Prospective Cohort Study

International Nuclear Information System (INIS)

Delgado, Anna F.; Nilsson, Markus; Latini, Francesco; Mårtensson, Johanna; Zetterling, Maria; Berntsson, Shala G.; Alafuzoff, Irina; Lätt, Jimmy; Larsson, Elna-Marie

2016-01-01

Background and Purpose. Low-grade gliomas show infiltrative growth in white matter tracts. Diffusion tensor tractography can noninvasively assess white matter tracts. The aim was to preoperatively assess tumor growth in white matter tracts using quantitative MR tractography (3T). The hypothesis was that suspected infiltrated tracts would have altered diffusional properties in infiltrated tract segments compared to noninfiltrated tracts. Materials and Methods. Forty-eight patients with suspected low-grade glioma were included after written informed consent and underwent preoperative diffusion tensor imaging in this prospective review-board approved study. Major white matter tracts in both hemispheres were tracked, segmented, and visually assessed for tumor involvement in thirty-four patients with gliomas grade II or III (astrocytomas or oligodendrogliomas) on postoperative neuropathological evaluation. Relative fractional anisotropy (rFA) and mean diffusivity (rMD) in tract segments were calculated and compared with visual evaluation and neuropathological diagnosis. Results. Tract segment infiltration on visual evaluation was associated with a lower rFA and high rMD in a majority of evaluated tract segments (89% and 78%, resp.). Grade II and grade III gliomas had similar infiltrating behavior. Conclusion. Quantitative MR tractography corresponds to visual evaluation of suspected tract infiltration. It may be useful for an objective preoperative evaluation of tract segment involvement

An improved Bayesian tensor regularization and sampling algorithm to track neuronal fiber pathways in the language circuit.

Science.gov (United States)

Mishra, Arabinda; Anderson, Adam W; Wu, Xi; Gore, John C; Ding, Zhaohua

2010-08-01

The purpose of this work is to design a neuronal fiber tracking algorithm, which will be more suitable for reconstruction of fibers associated with functionally important regions in the human brain. The functional activations in the brain normally occur in the gray matter regions. Hence the fibers bordering these regions are weakly myelinated, resulting in poor performance of conventional tractography methods to trace the fiber links between them. A lower fractional anisotropy in this region makes it even difficult to track the fibers in the presence of noise. In this work, the authors focused on a stochastic approach to reconstruct these fiber pathways based on a Bayesian regularization framework. To estimate the true fiber direction (propagation vector), the a priori and conditional probability density functions are calculated in advance and are modeled as multivariate normal. The variance of the estimated tensor element vector is associated with the uncertainty due to noise and partial volume averaging (PVA). An adaptive and multiple sampling of the estimated tensor element vector, which is a function of the pre-estimated variance, overcomes the effect of noise and PVA in this work. The algorithm has been rigorously tested using a variety of synthetic data sets. The quantitative comparison of the results to standard algorithms motivated the authors to implement it for in vivo DTI data analysis. The algorithm has been implemented to delineate fibers in two major language pathways (Broca's to SMA and Broca's to Wernicke's) across 12 healthy subjects. Though the mean of standard deviation was marginally bigger than conventional (Euler's) approach [P. J. Basser et al., "In vivo fiber tractography using DT-MRI data," Magn. Reson. Med. 44(4), 625-632 (2000)], the number of extracted fibers in this approach was significantly higher. The authors also compared the performance of the proposed method to Lu's method [Y. Lu et al., "Improved fiber tractography with Bayesian

Contrasting Connectivity of the Vim and Vop Nuclei of the Motor Thalamus Demonstrated by Probabilistic Tractography

DEFF Research Database (Denmark)

Hyam, Jonathan A; Owen, Sarah L F; Kringelbach, Morten L.

2011-01-01

BACKGROUND:: Targeting of the motor thalamus for the treatment of tremor has traditionally been achieved by a combination of anatomical atlases and neuro-imaging, intra-operative clinical assessment, and physiological recordings. OBJECTIVE:: To evaluate whether thalamic nuclei targeted in tremor...... surgery could be identified by virtue of their differing connections using non-invasive neuro-imaging, thereby providing an extra factor to aid successful targeting. METHODS:: Diffusion tensor tractography was performed in seventeen healthy control subjects using diffusion data acquired at 1.5T magnetic...... resonance imaging (60 directions, b-value=1000 s/mm, 2x2x2 mm voxels). The ventralis intermedius (Vim) and ventralis oralis posterior (Vop) nuclei were identified by a stereotactic neurosurgeon and these sites were used as seeds for probabilistic tractography. The expected cortical connections...

Homogeneity based segmentation and enhancement of Diffusion Tensor Images : a white matter processing framework

OpenAIRE

Rodrigues, P.R.

2011-01-01

In diffusion magnetic resonance imaging (DMRI) the Brownian motion of the water molecules, within biological tissue, is measured through a series of images. In diffusion tensor imaging (DTI) this diffusion is represented using tensors. DTI describes, in a non-invasive way, the local anisotropy pattern enabling the reconstruction of the nervous fibers - dubbed tractography. DMRI constitutes a powerful tool to analyse the structure of the white matter within a voxel, but also to investigate the...

Comparative assessment of therapeutic response to physiotherapy with or without botulinum toxin injection using diffusion tensor tractography and clinical scores in term diplegic cerebral palsy children.

Science.gov (United States)

Chaturvedi, Saurabh K; Rai, Yogita; Chourasia, Ankita; Goel, Puneet; Paliwal, Vimal K; Garg, Ravindra K; Rathore, Ram Kishore S; Pandey, Chandra M; Gupta, Rakesh K

2013-08-01

The present study was to compare the effects of combined therapy [botulinum (BTX) plus physiotherapy] with physiotherapy alone using diffusion tensor imaging (DTI) derived fractional anisotropy (FA) values of motor and sensory fiber bundles and clinical grade of the disability to see the value of BTX in term children with spastic diplegic cerebral palsy (CP). Clinically diagnosed 36 children participated in the study. All these children were born at term, and had no history of seizures. The study was randomly categorized into two groups: group I (n=18) - physiotherapy alone and group II (n=18) - physiotherapy plus BTX injection. Quantitative diffusion tensor tractography on all these children was performed on motor and sensory fiber bundles on baseline as well as after 6months of therapy. Motor function and clinical grades were also measured by gross motor function measures (GMFM) scale on both occasions. We observed significant change in FA value in motor and sensory fiber bundle as well as in GMFM scores at 6months compared to baseline study in both the groups. However, delta change and relative delta change in FA values of sensory and motor fiber bundle as well as GMFM score between group I and group II was statistically insignificant. We conclude that addition of BTX to physiotherapy regimen does not influence the outcome at 6months with similar insult in children with term diplegic spastic CP. This information may influence management of diplegic CP especially in developing countries, where BTX is beyond the reach of these children. Copyright © 2012 The Japanese Society of Child Neurology. Published by Elsevier B.V. All rights reserved.

Diffusion tensor imaging using multiple coils for mouse brain connectomics.

Science.gov (United States)

Nouls, John C; Badea, Alexandra; Anderson, Robert B J; Cofer, Gary P; Allan Johnson, G

2018-04-19

The correlation between brain connectivity and psychiatric or neurological diseases has intensified efforts to develop brain connectivity mapping techniques on mouse models of human disease. The neural architecture of mouse brain specimens can be shown non-destructively and three-dimensionally by diffusion tensor imaging, which enables tractography, the establishment of a connectivity matrix and connectomics. However, experiments on cohorts of animals can be prohibitively long. To improve throughput in a 7-T preclinical scanner, we present a novel two-coil system in which each coil is shielded, placed off-isocenter along the axis of the magnet and connected to a receiver circuit of the scanner. Preservation of the quality factor of each coil is essential to signal-to-noise ratio (SNR) performance and throughput, because mouse brain specimen imaging at 7 T takes place in the coil-dominated noise regime. In that regime, we show a shielding configuration causing no SNR degradation in the two-coil system. To acquire data from several coils simultaneously, the coils are placed in the magnet bore, around the isocenter, in which gradient field distortions can bias diffusion tensor imaging metrics, affect tractography and contaminate measurements of the connectivity matrix. We quantified the experimental alterations in fractional anisotropy and eigenvector direction occurring in each coil. We showed that, when the coils were placed 12 mm away from the isocenter, measurements of the brain connectivity matrix appeared to be minimally altered by gradient field distortions. Simultaneous measurements on two mouse brain specimens demonstrated a full doubling of the diffusion tensor imaging throughput in practice. Each coil produced images devoid of shading or artifact. To further improve the throughput of mouse brain connectomics, we suggested a future expansion of the system to four coils. To better understand acceptable trade-offs between imaging throughput and connectivity

Cognitive Function and 3-Tesla Magnetic Resonance Imaging Tractography of White Matter Hyperintensities in Elderly Persons

OpenAIRE

Reginold, William; Luedke, Angela C.; Tam, Angela; Itorralba, Justine; Fernandez-Ruiz, Juan; Reginold, Jennifer; Islam, Omar; Garcia, Angeles

2015-01-01

Background/Aims: This study used 3-Tesla magnetic resonance imaging (MRI) tractography to determine if there was an association between tracts crossing white matter hyperintensities (WMH) and cognitive function in elderly persons. Methods: Brain T2-weighted fluid-attenuated inversion recovery (FLAIR) and diffusion tensor MRI scans were acquired in participants above the age of 60 years. Twenty-six persons had WMH identified on T2 FLAIR scans. They completed a battery of neuropsychological tes...

Learning from Tractography

DEFF Research Database (Denmark)

Kasenburg, Niklas

Analysis of structural connections between brain regions enables us to gain insight into the structural architecture of the human brain and into how connections are affected by age or pathology. Tractography is the standard tool for automatic delineation of structural connections or tracts. Post......-processing of tractography results using expert prior knowledge is often performed to ensure a robust delineation. In this thesis, I present a shortest-path tractography (SPT) framework that can automatically incorporate any prior knowledge about the location of a tract. Furthermore, I show how such a prior can be learned...... of a connection and demonstrate their application in connectivity-based parcellation. Network models are a common way to represent structural connections of the whole brain. With supervised learning methods, features are extracted from these networks and are associated with a parameter of interest. Dimensionality...

Piriformis muscle syndrome with assessment of sciatic nerve using diffusion tensor imaging and tractography: a case report

Energy Technology Data Exchange (ETDEWEB)

Wada, Keizo; Goto, Tomohiro; Takasago, Tomoya; Hamada, Daisuke; Sairyo, Koichi [The University of Tokushima Graduate School, Department of Orthopedics, Institute of Health Biosciences, Tokushima (Japan)

2017-10-15

Piriformis muscle syndrome (PMS) is difficult to diagnose by objective evaluation of sciatic nerve injury. Here we report a case of PMS diagnosed by diffusion tensor imaging (DTI) and tractography of the sciatic nerve, which can assess and visualize the extent of nerve injury. The patient was a 53-year-old man with a 2-year history of continuous pain and numbness in the left leg. His symptoms worsened when sitting. Physical examination, including sensorimotor neurologic tests, the deep tendon reflex test, and the straight leg raise test, revealed no specific findings. The hip flexion adduction and internal rotation test and resisted contraction maneuvers for the piriformis muscle were positive. There were no abnormal findings on magnetic resonance imaging (MRI) of the lumbar spine. The transverse diameter of piriformis muscle was slightly thicker in affected side on MRI of the pelvis. A single DTI sequence was performed during MRI of the pelvis. Fractional anisotropy (FA) and the apparent diffusion coefficient (ADC) of the sciatic nerve were quantified at three levels using the fiber-tracking method. FA values were significantly lower and ADC values were significantly higher distal to the piriformis muscle. We performed endoscopic-assisted resection of the piriformis tendon. Intraoperatively, the motor-evoked potentials in the left gastrocnemius were improved by resection of the piriformis tendon. The patient's symptoms improved immediately after surgery. There was no significant difference in FA or ADC at any level between the affected side and the unaffected side 3 months postoperatively. MRI-DTI may aid the diagnosis of PMS. (orig.)

Piriformis muscle syndrome with assessment of sciatic nerve using diffusion tensor imaging and tractography: a case report.

Science.gov (United States)

Wada, Keizo; Goto, Tomohiro; Takasago, Tomoya; Hamada, Daisuke; Sairyo, Koichi

2017-10-01

Piriformis muscle syndrome (PMS) is difficult to diagnose by objective evaluation of sciatic nerve injury. Here we report a case of PMS diagnosed by diffusion tensor imaging (DTI) and tractography of the sciatic nerve, which can assess and visualize the extent of nerve injury. The patient was a 53-year-old man with a 2-year history of continuous pain and numbness in the left leg. His symptoms worsened when sitting. Physical examination, including sensorimotor neurologic tests, the deep tendon reflex test, and the straight leg raise test, revealed no specific findings. The hip flexion adduction and internal rotation test and resisted contraction maneuvers for the piriformis muscle were positive. There were no abnormal findings on magnetic resonance imaging (MRI) of the lumbar spine. The transverse diameter of piriformis muscle was slightly thicker in affected side on MRI of the pelvis. A single DTI sequence was performed during MRI of the pelvis. Fractional anisotropy (FA) and the apparent diffusion coefficient (ADC) of the sciatic nerve were quantified at three levels using the fiber-tracking method. FA values were significantly lower and ADC values were significantly higher distal to the piriformis muscle. We performed endoscopic-assisted resection of the piriformis tendon. Intraoperatively, the motor-evoked potentials in the left gastrocnemius were improved by resection of the piriformis tendon. The patient's symptoms improved immediately after surgery. There was no significant difference in FA or ADC at any level between the affected side and the unaffected side 3 months postoperatively. MRI-DTI may aid the diagnosis of PMS.

Piriformis muscle syndrome with assessment of sciatic nerve using diffusion tensor imaging and tractography: a case report

International Nuclear Information System (INIS)

Wada, Keizo; Goto, Tomohiro; Takasago, Tomoya; Hamada, Daisuke; Sairyo, Koichi

2017-01-01

Piriformis muscle syndrome (PMS) is difficult to diagnose by objective evaluation of sciatic nerve injury. Here we report a case of PMS diagnosed by diffusion tensor imaging (DTI) and tractography of the sciatic nerve, which can assess and visualize the extent of nerve injury. The patient was a 53-year-old man with a 2-year history of continuous pain and numbness in the left leg. His symptoms worsened when sitting. Physical examination, including sensorimotor neurologic tests, the deep tendon reflex test, and the straight leg raise test, revealed no specific findings. The hip flexion adduction and internal rotation test and resisted contraction maneuvers for the piriformis muscle were positive. There were no abnormal findings on magnetic resonance imaging (MRI) of the lumbar spine. The transverse diameter of piriformis muscle was slightly thicker in affected side on MRI of the pelvis. A single DTI sequence was performed during MRI of the pelvis. Fractional anisotropy (FA) and the apparent diffusion coefficient (ADC) of the sciatic nerve were quantified at three levels using the fiber-tracking method. FA values were significantly lower and ADC values were significantly higher distal to the piriformis muscle. We performed endoscopic-assisted resection of the piriformis tendon. Intraoperatively, the motor-evoked potentials in the left gastrocnemius were improved by resection of the piriformis tendon. The patient's symptoms improved immediately after surgery. There was no significant difference in FA or ADC at any level between the affected side and the unaffected side 3 months postoperatively. MRI-DTI may aid the diagnosis of PMS. (orig.)

Tractography of the corticospinal tracts in infants with focal perinatal injury: comparison with normal controls and to motor development

International Nuclear Information System (INIS)

Roze, Elise; Harris, Polly A.; Ball, Gareth; Braga, Rodrigo M.; Allsop, Joanna M.; Counsell, Serena J.; Elorza, Leire Zubiaurre; Merchant, Nazakat; Arichi, Tomoki; Edwards, A.D.; Cowan, Frances M.; Porter, Emma; Rutherford, Mary A.

2012-01-01

Our aims were to (1) assess the corticospinal tracts (CSTs) in infants with focal injury and healthy term controls using probabilistic tractography and (2) to correlate the conventional magnetic resonance imaging (MRI) and tractography findings in infants with focal injury with their later motor function. We studied 20 infants with focal lesions and 23 controls using MRI and diffusion tensor imaging. Tract volume, fractional anisotropy (FA), apparent diffusion coefficient (ADC) values, axial diffusivity and radial diffusivity (RD) of the CSTs were determined. Asymmetry indices (AIs) were calculated by comparing ipsilateral to contralateral CSTs. Motor outcome was assessed using a standardized neurological examination. Conventional MRI was able to predict normal motor development (n = 9) or hemiplegia (n = 6). In children who developed a mild motor asymmetry (n = 5), conventional MRI predicted a hemiplegia in two and normal motor development in three infants. The AIs for tract volume, FA, ADC and RD showed a significant difference between controls and infants who developed a hemiplegia, and RD also showed a significant difference in AI between controls and infants who developed a mild asymmetry. Conventional MRI was able to predict subsequent normal motor development or hemiplegia following focal injury in newborn infants. Measures of RD obtained from diffusion tractography may offer additional information for predicting a subsequent asymmetry in motor function. (orig.)

Diffusion tensor imaging with quantitative evaluation and fiber tractography of lumbar nerve roots in sciatica.

Science.gov (United States)

Shi, Yin; Zong, Min; Xu, Xiaoquan; Zou, Yuefen; Feng, Yang; Liu, Wei; Wang, Chuanbing; Wang, Dehang

2015-04-01

To quantitatively evaluate nerve roots by measuring fractional anisotropy (FA) values in healthy volunteers and sciatica patients, visualize nerve roots by tractography, and compare the diagnostic efficacy between conventional magnetic resonance imaging (MRI) and DTI. Seventy-five sciatica patients and thirty-six healthy volunteers underwent MR imaging using DTI. FA values for L5-S1 lumbar nerve roots were calculated at three levels from DTI images. Tractography was performed on L3-S1 nerve roots. ROC analysis was performed for FA values. The lumbar nerve roots were visualized and FA values were calculated in all subjects. FA values decreased in compressed nerve roots and declined from proximal to distal along the compressed nerve tracts. Mean FA values were more sensitive and specific than MR imaging for differentiating compressed nerve roots, especially in the far lateral zone at distal nerves. DTI can quantitatively evaluate compressed nerve roots, and DTT enables visualization of abnormal nerve tracts, providing vivid anatomic information and localization of probable nerve compression. DTI has great potential utility for evaluating lumbar nerve compression in sciatica. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Two-perfect fluid interpretation of an energy tensor

International Nuclear Information System (INIS)

Ferrando, J.J.; Morales, J.A.; Portilla, M.

1990-01-01

There are many topics in General Relativity where matter is represented by a mixture of two fluids. In fact, some astrophysical and cosmological situations need to be described by an energy tensor made up of the sum of two or more perfect fluids rather than that with only one. The paper contains the necessary and sufficient conditions for a given energy tensor to be interpreted as a sum of two perfect fluids. Given a tensor of this class, the decomposition in two perfect fluids (which is determined up to a couple of real functions) is obtained

New insights into the developing rabbit brain using diffusion tensor tractography and generalized q-sampling MRI.

Directory of Open Access Journals (Sweden)

Seong Yong Lim

Full Text Available The use of modern neuroimaging methods to characterize the complex anatomy of brain development at different stages reveals an enormous wealth of information in understanding this highly ordered process and provides clues to detect neurological and neurobehavioral disorders that have their origin in early structural and functional cerebral maturation. Non-invasive diffusion tensor magnetic resonance imaging (DTI is able to distinguish cerebral microscopic structures, especially in the white matter regions. However, DTI is unable to resolve the complicated neural structure, i.e., the fiber crossing that is frequently observed during the maturation process. To overcome this limitation, several methods have been proposed. One such method, generalized q-sampling imaging (GQI, can be applied to a variety of datasets, including the single shell, multi-shell or grid sampling schemes that are believed to be able to resolve the complicated crossing fibers. Rabbits have been widely used for neurodevelopment research because they exhibit human-like timing of perinatal brain white matter maturation. Here, we present a longitudinal study using both DTI and GQI to demonstrate the changes in cerebral maturation of in vivo developing rabbit brains over a period of 40 weeks. Fractional anisotropy (FA of DTI and generalized fractional anisotropy (GFA of GQI indices demonstrated that the white matter anisotropy increased with age, with GFA exhibiting an increase in the hippocampus as well. Normalized quantitative anisotropy (NQA of GQI also revealed an increase in the hippocampus, allowing us to observe the changes in gray matter as well. Regional and whole brain DTI tractography also demonstrated refinement in fiber pathway architecture with maturation. We concluded that DTI and GQI results were able to characterize the white matter anisotropy changes, whereas GQI provided further information about the gray matter hippocampus area. This developing rabbit brain

Cognitive Function and 3-Tesla Magnetic Resonance Imaging Tractography of White Matter Hyperintensities in Elderly Persons.

Science.gov (United States)

Reginold, William; Luedke, Angela C; Tam, Angela; Itorralba, Justine; Fernandez-Ruiz, Juan; Reginold, Jennifer; Islam, Omar; Garcia, Angeles

2015-01-01

This study used 3-Tesla magnetic resonance imaging (MRI) tractography to determine if there was an association between tracts crossing white matter hyperintensities (WMH) and cognitive function in elderly persons. Brain T2-weighted fluid-attenuated inversion recovery (FLAIR) and diffusion tensor MRI scans were acquired in participants above the age of 60 years. Twenty-six persons had WMH identified on T2 FLAIR scans. They completed a battery of neuropsychological tests and were classified as normal controls (n = 15) or with Alzheimer's dementia (n = 11). Tractography was generated by the Fiber Assignment by Continuous Tracking method. All tracts that crossed WMH were segmented. The average fractional anisotropy and average mean diffusivity of these tracts were quantified. We studied the association between cognitive test scores with the average mean diffusivity and average fractional anisotropy of tracts while controlling for age, total WMH volume and diagnosis. An increased mean diffusivity of tracts crossing WMH was associated with worse performance on the Wechsler Memory Scale-III Longest Span Forward (p = 0.02). There was no association between the fractional anisotropy of tracts and performance on cognitive testing. The mean diffusivity of tracts crossing WMH measured by tractography is a novel correlate of performance on the Wechsler Memory Scale-III Longest Span Forward in elderly persons.

Determining injuries from posterior and flank stab wounds using computed tomography tractography.

Science.gov (United States)

Bansal, Vishal; Reid, Chris M; Fortlage, Dale; Lee, Jeanne; Kobayashi, Leslie; Doucet, Jay; Coimbra, Raul

2014-04-01

Unlike anterior stab wounds (SW), in which local exploration may direct management, posterior SW can be challenging to evaluate. Traditional triple contrast computed tomography (CT) imaging is cumbersome and technician-dependent. The present study examines the role of CT tractography as a strategy to manage select patients with back and flank SW. Hemodynamically stable patients with back and flank SW were studied. After resuscitation, Betadine- or Visipaque®-soaked sterile sponges were inserted into each SW for the estimated depth of the wound. Patients underwent abdominal helical CT scanning, including intravenous contrast, as the sole abdominal imaging study. Images were reviewed by an attending radiologist and trauma surgeon. The tractogram was evaluated to determine SW trajectory and injury to intra- or retroperitoneal organs, vascular structures, the diaphragm, and the urinary tract. Complete patient demographics including operative management and injuries were collected. Forty-one patients underwent CT tractography. In 11 patients, tractography detected violation of the intra- or retroperitoneal cavity leading to operative exploration. Injuries detected included: the spleen (two), colon (one), colonic mesentery (one), kidney (kidney), diaphragm (kidney), pneumothorax (seven), hemothorax (two), iliac artery (one), and traumatic abdominal wall hernia (two). In all patients, none had negative CT findings that failed observation. In this series, CT tractography is a safe and effective imaging strategy to evaluate posterior torso SW. It is unknown whether CT tractography is superior to traditional imaging modalities. Other uses for CT tractography may include determining trajectory from missile wounds and tangential penetrating injuries.

A novel approach of fMRI-guided tractography analysis within a group: construction of an fMRI-guided tractographic atlas.

Science.gov (United States)

Preti, Maria Giulia; Makris, Nikos; Laganà, Maria Marcella; Papadimitriou, George; Baglio, Francesca; Griffanti, Ludovica; Nemni, Raffaello; Cecconi, Pietro; Westin, Carl-Fredrik; Baselli, Giuseppe

2012-01-01

Diffusion Tensor Imaging (DTI) tractography and functional Magnetic Resonance Imaging (fMRI) investigate two complementary aspects of brain networks: white matter (WM) anatomical connectivity and gray matter (GM) function. However, integration standards have yet to be defined; namely, individual fMRI-driven tractography is usually applied and only few studies address group analysis. This work proposes an efficient method of fMRI-driven tractography at group level through the creation of a tractographic atlas starting from the GM areas activated by a verbal fluency task in 11 healthy subjects. The individual tracts were registered to the MNI space. Selection ROIs derived by GM masking and dilation of group activated areas were applied to obtain the fMRI-driven subsets within tracts. An atlas of the tracts recruited among the population was obtained by selecting for each subject the fMRI-guided tracts passing through the high probability voxels (the voxels recruited by the 90% of the subjects) and merging them together. The reliability of this approach was assessed by comparing it with the probabilistic atlas previously introduced in literature. The introduced method allowed to successfully reconstruct activated tracts, which comprehended corpus callosum, left cingulum and arcuate, a small portion of the right arcuate, both cortico-spinal tracts and inferior fronto-occipital fasciculi. Moreover, it proved to give results concordant with the previously introduced probabilistic approach, allowing in addition to reconstruct 3D trajectories of the activated fibers, which appear particularly helpful in the detection of WM connections.

Validation of in vitro probabilistic tractography

DEFF Research Database (Denmark)

Dyrby, Tim B.; Sogaard, L.V.; Parker, G.J.

2007-01-01

assessed the anatomical validity and reproducibility of in vitro multi-fiber probabilistic tractography against two invasive tracers: the histochemically detectable biotinylated dextran amine and manganese enhanced magnetic resonance imaging. Post mortern DWI was used to ensure that most of the sources...

Cognitive Function and 3-Tesla Magnetic Resonance Imaging Tractography of White Matter Hyperintensities in Elderly Persons

Directory of Open Access Journals (Sweden)

William Reginold

2015-10-01

Full Text Available Background/Aims: This study used 3-Tesla magnetic resonance imaging (MRI tractography to determine if there was an association between tracts crossing white matter hyperintensities (WMH and cognitive function in elderly persons. Methods: Brain T2-weighted fluid-attenuated inversion recovery (FLAIR and diffusion tensor MRI scans were acquired in participants above the age of 60 years. Twenty-six persons had WMH identified on T2 FLAIR scans. They completed a battery of neuropsychological tests and were classified as normal controls (n = 15 or with Alzheimer's dementia (n = 11. Tractography was generated by the Fiber Assignment by Continuous Tracking method. All tracts that crossed WMH were segmented. The average fractional anisotropy and average mean diffusivity of these tracts were quantified. We studied the association between cognitive test scores with the average mean diffusivity and average fractional anisotropy of tracts while controlling for age, total WMH volume and diagnosis. Results: An increased mean diffusivity of tracts crossing WMH was associated with worse performance on the Wechsler Memory Scale-III Longest Span Forward (p = 0.02. There was no association between the fractional anisotropy of tracts and performance on cognitive testing. Conclusion: The mean diffusivity of tracts crossing WMH measured by tractography is a novel correlate of performance on the Wechsler Memory Scale-III Longest Span Forward in elderly persons.

[Tractography of the uncinate fasciculus and the posterior cingulate fasciculus in patients with mild cognitive impairment and Alzheimer disease].

Science.gov (United States)

Larroza, A; Moratal, D; D'ocón Alcañiz, V; Arana, E

2014-01-01

Brain tractography is a non-invasive medical imaging technique which enables in vivo visualisation and various types of quantitative studies of white matter fibre tracts connecting different parts of the brain. We completed a quantitative study using brain tractography with diffusion tensor imaging in patients with mild cognitive impairment, patients with Alzheimer disease, and normal controls, in order to analyse the reproducibility and validity of the results. Fractional anisotropy (FA) and mean diffusivity (MD) were measured across the uncinate fasciculus and the posterior cingulate fasciculus in images, obtained from a database and a research centre, representing 52 subjects distributed among the 3 study groups. Two observers took the measurements twice in order to evaluate intra- and inter-observer reproducibility. Measurements of FA and MD of the uncinate fasciculus delivered an intraclass correlation coefficient above 0.9; ICC was above 0.68 for the posterior cingulate fasciculus. Patients with Alzheimer disease showed lower values of FA and higher MD values in the right uncinate fasciculus in images from the research centre. A comparison of the measurements from the 2 centres revealed significant differences. We established a reproducible methodology for performing tractography of the tracts in question. FA and MD indexes may serve as early indicators of Alzheimer disease. The type of equipment and the method used to acquire images must be considered because they may alter results as shown by comparing the 2 data sets in this study. Copyright © 2012 Sociedad Española de Neurología. Published by Elsevier Espana. All rights reserved.

Diffusion tensor imaging in spinal cord injury

International Nuclear Information System (INIS)

Kamble, Ravindra B; Venkataramana, Neelam K; Naik, Arun L; Rao, Shailesh V

2011-01-01

To assess the feasibility of spinal tractography in patients of spinal cord injury vs a control group and to compare fractional anisotropy (FA) values between the groups. Diffusion tensor imaging (DTI) was performed in the spinal cord of 29 patients (18 patients and 11 controls). DTI was done in the cervical region if the cord injury was at the dorsal or lumbar region and in the conus region if cord injury was in the cervical or dorsal region. FA was calculated for the patients and the controls and the values were compared. The mean FA value was 0.550±0.09 in the control group and 0.367±0.14 in the patients; this difference was statistically significant (P=0.001). Spinal tractography is a feasible technique to assess the extent of spinal cord injury by FA, which is reduced in patients of spinal cord injury, suggesting possible Wallerian degeneration. In future, this technique may become a useful tool for assessing cord injury patients after stem cell therapy, with improvement in FA values indicating axonal regeneration

Anatomical parcellation of the brainstem and cerebellar white matter: a preliminary probabilistic tractography study at 3 T

Energy Technology Data Exchange (ETDEWEB)

Habas, Christophe; Cabanis, Emmanuel A. [UPMC Paris 6, Service de NeuroImagerie, Hopital des Quinze-Vingts, Paris (France)

2007-10-15

The aims of this study were: (1) to test whether higher spatial resolution diffusion tensor images and a higher field strength (3 T) enable a more accurate delineation of the anatomical tract within the brainstem, and, in particular, (2) to try to distinguish the different components of the corticopontocerebellar paths in terms of their cortical origins. The main tracts of the brainstem of four volunteers were studied at 3 T using a probabilistic diffusion tensor imaging (DTI) axonal tracking. The resulting tractograms enabled anatomical well-delineated structures to be identified on the diffusion tensor coloured images. We tracked corticopontine, corticospinal, central tegmental, inferior and superior cerebellopeduncular, transverse, medial lemniscal and, possibly, longitudinal medial fibres. Moreover, DTI tracking allowed a broad delineation of the corticopontocerebellar paths. Diffusion tensor coloured images allow a rapid and reliable access to the white matter broad parcellation of the brainstem and of the cerebellum, which can be completed by fibre tracking. However, a more accurate and exhaustive depiction of the anatomical connectivity within the brainstem requires the application of more sophisticated techniques and tractography algorithms, such as diffusion spectrum imaging. (orig.)

Anatomical parcellation of the brainstem and cerebellar white matter: a preliminary probabilistic tractography study at 3 T

International Nuclear Information System (INIS)

Habas, Christophe; Cabanis, Emmanuel A.

2007-01-01

The aims of this study were: (1) to test whether higher spatial resolution diffusion tensor images and a higher field strength (3 T) enable a more accurate delineation of the anatomical tract within the brainstem, and, in particular, (2) to try to distinguish the different components of the corticopontocerebellar paths in terms of their cortical origins. The main tracts of the brainstem of four volunteers were studied at 3 T using a probabilistic diffusion tensor imaging (DTI) axonal tracking. The resulting tractograms enabled anatomical well-delineated structures to be identified on the diffusion tensor coloured images. We tracked corticopontine, corticospinal, central tegmental, inferior and superior cerebellopeduncular, transverse, medial lemniscal and, possibly, longitudinal medial fibres. Moreover, DTI tracking allowed a broad delineation of the corticopontocerebellar paths. Diffusion tensor coloured images allow a rapid and reliable access to the white matter broad parcellation of the brainstem and of the cerebellum, which can be completed by fibre tracking. However, a more accurate and exhaustive depiction of the anatomical connectivity within the brainstem requires the application of more sophisticated techniques and tractography algorithms, such as diffusion spectrum imaging. (orig.)

Using Diffusion Tractography to Predict Cortical Connection Strength and Distance: A Quantitative Comparison with Tracers in the Monkey

DEFF Research Database (Denmark)

Donahue, Chad J.; Sotiropoulos, Stamatios N.; Jbabdi, Saad

2016-01-01

of tractography for analyzing interareal corticocortical connectivity in nonhuman primates and a framework for assessing future tractography methodological refinements objectively. SIGNIFICANCE STATEMENT Tractography based on diffusion MRI has great potential for a variety of applications, including estimation......Tractography based on diffusion MRI offers the promise of characterizing many aspects of long-distance connectivity in the brain, but requires quantitative validation to assess its strengths and limitations. Here, we evaluate tractography's ability to estimate the presence and strength...... of connections between areas of macaque neocortex by comparing its results with published data from retrograde tracer injections. Probabilistic tractography was performed on high-quality postmortem diffusion imaging scans from two Old World monkey brains. Tractography connection weights were estimated using...

Evaluation of two streamlined life cycle assessment methods

International Nuclear Information System (INIS)

Hochschomer, Elisabeth; Finnveden, Goeran; Johansson, Jessica

2002-02-01

Two different methods for streamlined life cycle assessment (LCA) are described: the MECO-method and SLCA. Both methods are tested on an already made case-study on cars fuelled with petrol or ethanol, and electric cars with electricity produced from hydro power or coal. The report also contains some background information on LCA and streamlined LCA, and a deschption of the case study used. The evaluation of the MECO and SLCA-methods are based on a comparison of the results from the case study as well as practical aspects. One conclusion is that the SLCA-method has some limitations. Among the limitations are that the whole life-cycle is not covered, it requires quite a lot of information and there is room for arbitrariness. It is not very flexible instead it difficult to develop further. We are therefore not recommending the SLCA-method. The MECO-method does in comparison show several attractive features. It is also interesting to note that the MECO-method produces information that is complementary compared to a more traditional quantitative LCA. We suggest that the MECO method needs some further development and adjustment to Swedish conditions

A DTI-based tractography study of effects on brain structure associated with prenatal alcohol exposure in newborns

Science.gov (United States)

Taylor, Paul A.; Jacobson, Sandra W.; van der Kouwe, André; Molteno, Christopher D.; Chen, Gang; Wintermark, Pia; Alhamud, Alkathafi; Jacobson, Joseph L.; Meintjes, Ernesta M.

2014-01-01

Prenatal alcohol exposure is known to have severe, long-term consequences for brain and behavioral development already detectable in infancy and childhood. Resulting features of fetal alcohol spectrum disorders (FASD) include cognitive and behavioral effects, as well as facial anomalies and growth deficits. Diffusion tensor imaging (DTI) and tractography were used to analyze white matter development in 11 newborns (age since conception <45 weeks) whose mothers were recruited during pregnancy. Comparisons were made with 9 age-matched controls born to abstainers or light drinkers from the same Cape Coloured (mixed ancestry) community near Cape Town, South Africa. DTI parameters, T1 relaxation time, proton density and volumes were used to quantify and investigate group differences in white matter (WM) in the newborn brains. Probabilistic tractography was used to estimate and to delineate similar tract locations among the subjects for transcallosal pathways, cortico-spinal projection fibers and cortico-cortical association fibers. In each of these WM networks, the axial diffusivity AD was the parameter that showed the strongest association with maternal drinking. The strongest relations were observed in medial and inferior WM, regions in which the myelination process typically begins. In contrast to studies of older individuals with prenatal alcohol exposure, FA did not exhibit a consistent and significant relation with alcohol exposure. To our knowledge, this is the first DTI-tractography study of prenatally alcohol exposed newborns. PMID:25182535

Abscess of the medulla oblongata in a toddler: case report and technical considerations based on magnetic resonance imaging tractography.

Science.gov (United States)

Arzoglou, Vasileios; D'Angelo, Luca; Koutzoglou, Michael; Di Rocco, Concezio

2011-08-01

We report a unique case of a toddler (the only one reported) successfully operated on for a medulla oblongata abscess and comment on the influence of neuroimaging modalities in the preoperative planning of the surgical approach. We report a case of a 20-month-old child with a solitary medulla oblongata abscess. The abscess appeared to be in close proximity to the anterior medulla oblongata, but preoperative planning based on diffusion tensor imaging (DTI) tractography motivated us to try to remove this lesion through a midline suboccipital approach. The ventral medulla oblongata abscess was surgically removed via a telovelar approach. At the anterior wall of the 4th ventricle, a fenestration was made with pus release and evacuation of the cavity. The child was discharged 1 week later with an uneventful and full recovery. Modern imaging modalities of the nervous system can be very helpful in preoperative planning. Functional visualization of the nervous system provided by modern imaging techniques, such as the DTI tractography, can alter the classic topographic concept of surgical approach. In the case presented, approaching an anterior medulla oblongata abscess based on DTI tractography data, through a suboccipital midline transventricular approach, proved to be an effective and safe technique.

Principles and implementation of diffusion-weighted and diffusion tensor imaging

International Nuclear Information System (INIS)

Roberts, Timothy P.L.; Schwartz, E.S.

2007-01-01

We review the physiological basis of diffusion-weighted imaging and discuss the implementation of diffusion-weighted imaging pulse sequences and the subsequent postprocessing to yield quantitative estimations of diffusion parameters. We also introduce the concept of directionality of ''apparent'' diffusion in vivo and the means of assessing such anisotropy quantitatively. This in turn leads to the methodological application of diffusion tensor imaging and the subsequent postprocessing, known as tractography. The following articles deal with the clinical applications enabled by such methodologies. (orig.)

Correlation of quantitative sensorimotor tractography with clinical grade of cerebral palsy

International Nuclear Information System (INIS)

Trivedi, Richa; Gupta, Rakesh K.; Agarwal, Shruti; Rathore, Ram K.S.; Shah, Vipul; Goyel, Puneet; Paliwal, Vimal K.

2010-01-01

The purpose of this study was to determine whether tract-specific diffusion tensor imaging measures in somatosensory and motor pathways correlate with clinical grades as defined using the Gross Motor Function Classification System (GMFCS) in cerebral palsy (CP) children. Quantitative diffusion tensor tractography was performed on 39 patients with spastic quadriparesis (mean age = 8 years) and 14 age/sex-matched controls. All patients were graded on the basis of GMFCS scale into grade II (n = 12), grade IV (n = 22), and grade V (n = 5) CP and quantitative analysis reconstruction of somatosensory and motor tracts performed. Significant inverse correlation between clinical grade and fractional anisotropy (FA) was observed in both right and left motor and sensory tracts. A significant direct correlation of mean diffusivity values from both motor and sensory tracts was also observed with clinical grades. Successive decrease in FA values was observed in all tracts except for left motor tracts moving from age/sex-matched controls to grade V through grades II and IV. We conclude that white matter tracts from both the somatosensory and the motor cortex play an important role in the pathophysiology of motor disability in patients with CP. (orig.)

Correlation of quantitative sensorimotor tractography with clinical grade of cerebral palsy

Energy Technology Data Exchange (ETDEWEB)

Trivedi, Richa; Gupta, Rakesh K. [Sanjay Gandhi Postgraduate Institute of Medical Sciences, Department of Radiodiagnosis, Lucknow (India); Agarwal, Shruti; Rathore, Ram K.S. [Indian Institute of Technology, Department of Mathematics and Statistics, Kanpur (India); Shah, Vipul [Bhargava Nursing Home, Pediatric Orthopedic Surgery unit, Lucknow (India); Goyel, Puneet [Sanjay Gandhi Postgraduate Institute of Medical Sciences, Department of Anesthesiology, Lucknow (India); Paliwal, Vimal K. [Sanjay Gandhi Postgraduate Institute of Medical Sciences, Department of Neurology, Lucknow (India)

2010-08-15

The purpose of this study was to determine whether tract-specific diffusion tensor imaging measures in somatosensory and motor pathways correlate with clinical grades as defined using the Gross Motor Function Classification System (GMFCS) in cerebral palsy (CP) children. Quantitative diffusion tensor tractography was performed on 39 patients with spastic quadriparesis (mean age = 8 years) and 14 age/sex-matched controls. All patients were graded on the basis of GMFCS scale into grade II (n = 12), grade IV (n = 22), and grade V (n = 5) CP and quantitative analysis reconstruction of somatosensory and motor tracts performed. Significant inverse correlation between clinical grade and fractional anisotropy (FA) was observed in both right and left motor and sensory tracts. A significant direct correlation of mean diffusivity values from both motor and sensory tracts was also observed with clinical grades. Successive decrease in FA values was observed in all tracts except for left motor tracts moving from age/sex-matched controls to grade V through grades II and IV. We conclude that white matter tracts from both the somatosensory and the motor cortex play an important role in the pathophysiology of motor disability in patients with CP. (orig.)

Streamlets for visualisation and data exploration

DEFF Research Database (Denmark)

Liptrot, Matthew George

Streamlets for visualisation and data exploration Matthew Liptrot, Image Group, Department of Computer Science, University of Copenhagen, Denmark Target Audience Anyone using streamlines for interpreting tractography from diffusion-weighted MRI Purpose The purpose of streamline tractography...

Diffusion tensor imaging of the human skeletal muscle: contributions and applications

International Nuclear Information System (INIS)

Neji, Radhouene

2010-01-01

In this thesis, we present several techniques for the processing of diffusion tensor images. They span a wide range of tasks such as estimation and regularization, clustering and segmentation, as well as registration. The variational framework proposed for recovering a tensor field from noisy diffusion weighted images exploits the fact that diffusion data represent populations of fibers and therefore each tensor can be reconstructed using a weighted combination of tensors lying in its neighborhood. The segmentation approach operates both at the voxel and the fiber tract levels. It is based on the use of Mercer kernels over Gaussian diffusion probabilities to model tensor similarity and spatial interactions, allowing the definition of fiber metrics that combine information from spatial localization and diffusion tensors. Several clustering techniques can be subsequently used to segment tensor fields and fiber tractographies. Moreover, we show how to develop supervised extensions of these algorithms. The registration algorithm uses probability kernels in order to match moving and target images. The deformation consistency is assessed using the distortion induced in the distances between neighboring probabilities. Discrete optimization is used to seek an optimum of the defined objective function. The experimental validation is done over a dataset of manually segmented diffusion images of the lower leg muscle for healthy and diseased subjects. The results of the techniques developed throughout this thesis are promising. (author)

Entanglement and tensor product decomposition for two fermions

International Nuclear Information System (INIS)

Caban, P; Podlaski, K; Rembielinski, J; Smolinski, K A; Walczak, Z

2005-01-01

The problem of the choice of tensor product decomposition in a system of two fermions with the help of Bogoliubov transformations of creation and annihilation operators is discussed. The set of physical states of the composite system is restricted by the superselection rule forbidding the superposition of fermions and bosons. It is shown that the Wootters concurrence is not the proper entanglement measure in this case. The explicit formula for the entanglement of formation is found. This formula shows that the entanglement of a given state depends on the tensor product decomposition of a Hilbert space. It is shown that the set of separable states is narrower than in the two-qubit case. Moreover, there exist states which are separable with respect to all tensor product decompositions of the Hilbert space. (letter to the editor)

Brain diffusion tensor MRI in systematic lupus erythematosus: A systematic review.

Science.gov (United States)

Costallat, Beatriz Lavras; Ferreira, Daniel Miranda; Lapa, Aline Tamires; Rittner, Letícia; Costallat, Lilian Tereza Lavras; Appenzeller, Simone

2018-01-01

Diffusion tensor imaging (DTI) maps the brain's microstructure by measuring fractional anisotropy (FA) and mean diffusivity (MD). This systematic review describes brain diffusion tensor Magnetic resonance imaging (MRI) studies in systemic lupus erythematosus (SLE).The literature was reviewed following the PRISMA guidelines and using the terms "lupus", "systemic lupus erythematosus", "SLE", "diffusion tensor imaging", "DTI", "white matter" (WM), "microstructural damage", "tractography", and "fractional anisotropy"; the search included articles published in English from January 2007 to April 2017. The subjects included in the study were selected according to the ACR criteria and included 195 SLE patients with neuropsychiatric manifestation (NPSLE), 299 without neuropsychiatric manifestation (non-NPSLE), and 423 healthy controls (HC). Most studies identified significantly reduced FA and increased MD values in several WM regions of both NPSLE and non-NPSLE patients compared to HC. Subclinical microstructural changes were observed in either regional areas or the entire brain in both the non-NPSLE and NPSLE groups. Copyright © 2017 Elsevier B.V. All rights reserved.

Fiber tractography of the axonal pathways linking the basal ganglia and cerebellum in Parkinson disease: implications for targeting in deep brain stimulation.

Science.gov (United States)

Sweet, Jennifer A; Walter, Benjamin L; Gunalan, Kabilar; Chaturvedi, Ashutosh; McIntyre, Cameron C; Miller, Jonathan P

2014-04-01

Stimulation of white matter pathways near targeted structures may contribute to therapeutic effects of deep brain stimulation (DBS) for patients with Parkinson disease (PD). Two tracts linking the basal ganglia and cerebellum have been described in primates: the subthalamopontocerebellar tract (SPCT) and the dentatothalamic tract (DTT). The authors used fiber tractography to evaluate white matter tracts that connect the cerebellum to the region of the basal ganglia in patients with PD who were candidates for DBS. Fourteen patients with advanced PD underwent 3-T MRI, including 30-directional diffusion-weighted imaging sequences. Diffusion tensor tractography was performed using 2 regions of interest: ipsilateral subthalamic and red nuclei, and contralateral cerebellar hemisphere. Nine patients underwent subthalamic DBS, and the course of each tract was observed relative to the location of the most effective stimulation contact and the volume of tissue activated. In all patients 2 distinct tracts were identified that corresponded closely to the described anatomical features of the SPCT and DTT, respectively. The mean overall distance from the active contact to the DTT was 2.18 ± 0.35 mm, and the mean proportional distance relative to the volume of tissue activated was 1.35 ± 0.48. There was a nonsignificant trend toward better postoperative tremor control in patients with electrodes closer to the DTT. The SPCT and the DTT may be related to the expression of symptoms in PD, and this may have implications for DBS targeting. The use of tractography to identify the DTT might assist with DBS targeting in the future.

Diffusion tensor imaging with quantitative evaluation and fiber tractography of lumbar nerve roots in sciatica

International Nuclear Information System (INIS)

Shi, Yin; Zong, Min; Xu, Xiaoquan; Zou, Yuefen; Feng, Yang; Liu, Wei; Wang, Chuanbing; Wang, Dehang

2015-01-01

Highlights: •In the present study, we first elected ROIs corresponding to the proximal, medial, and distal levels of the lumbar foraminal zone. •The ROC analysis for FA values of distal nerves indicated a high level of reliability in the diagnosis of sciatica. •The declining trend of FA values from proximal to distal along the nerve tract may correlate with the disparity of axonal regeneration at different levels. •DTI is able to quantitatively evaluate compressed nerve roots and has a higher sensitivity and specificity for diagnosing sciatica than conventional MR imaging. •DTT enables visualization of abnormal nerve tracts, providing vivid anatomic information and probable localization of nerve compression. -- Abstract: Objective: To quantitatively evaluate nerve roots by measuring fractional anisotropy (FA) values in healthy volunteers and sciatica patients, visualize nerve roots by tractography, and compare the diagnostic efficacy between conventional magnetic resonance imaging (MRI) and DTI. Materials and methods: Seventy-five sciatica patients and thirty-six healthy volunteers underwent MR imaging using DTI. FA values for L5–S1 lumbar nerve roots were calculated at three levels from DTI images. Tractography was performed on L3–S1 nerve roots. ROC analysis was performed for FA values. Results: The lumbar nerve roots were visualized and FA values were calculated in all subjects. FA values decreased in compressed nerve roots and declined from proximal to distal along the compressed nerve tracts. Mean FA values were more sensitive and specific than MR imaging for differentiating compressed nerve roots, especially in the far lateral zone at distal nerves. Conclusions: DTI can quantitatively evaluate compressed nerve roots, and DTT enables visualization of abnormal nerve tracts, providing vivid anatomic information and localization of probable nerve compression. DTI has great potential utility for evaluating lumbar nerve compression in sciatica

Diffusion tensor imaging with quantitative evaluation and fiber tractography of lumbar nerve roots in sciatica

Energy Technology Data Exchange (ETDEWEB)

Shi, Yin; Zong, Min; Xu, Xiaoquan; Zou, Yuefen; Feng, Yang; Liu, Wei; Wang, Chuanbing; Wang, Dehang, E-mail: njmu_wangdehang@126.com

2015-04-15

Highlights: •In the present study, we first elected ROIs corresponding to the proximal, medial, and distal levels of the lumbar foraminal zone. •The ROC analysis for FA values of distal nerves indicated a high level of reliability in the diagnosis of sciatica. •The declining trend of FA values from proximal to distal along the nerve tract may correlate with the disparity of axonal regeneration at different levels. •DTI is able to quantitatively evaluate compressed nerve roots and has a higher sensitivity and specificity for diagnosing sciatica than conventional MR imaging. •DTT enables visualization of abnormal nerve tracts, providing vivid anatomic information and probable localization of nerve compression. -- Abstract: Objective: To quantitatively evaluate nerve roots by measuring fractional anisotropy (FA) values in healthy volunteers and sciatica patients, visualize nerve roots by tractography, and compare the diagnostic efficacy between conventional magnetic resonance imaging (MRI) and DTI. Materials and methods: Seventy-five sciatica patients and thirty-six healthy volunteers underwent MR imaging using DTI. FA values for L5–S1 lumbar nerve roots were calculated at three levels from DTI images. Tractography was performed on L3–S1 nerve roots. ROC analysis was performed for FA values. Results: The lumbar nerve roots were visualized and FA values were calculated in all subjects. FA values decreased in compressed nerve roots and declined from proximal to distal along the compressed nerve tracts. Mean FA values were more sensitive and specific than MR imaging for differentiating compressed nerve roots, especially in the far lateral zone at distal nerves. Conclusions: DTI can quantitatively evaluate compressed nerve roots, and DTT enables visualization of abnormal nerve tracts, providing vivid anatomic information and localization of probable nerve compression. DTI has great potential utility for evaluating lumbar nerve compression in sciatica.

Abnormal Corpus Callosum Connectivity, Socio-Communicative Deficits, and Motor Deficits in Children with Autism Spectrum Disorder: A Diffusion Tensor Imaging Study

Science.gov (United States)

Hanaie, Ryuzo; Mohri, Ikuko; Kagitani-Shimono, Kuriko; Tachibana, Masaya; Matsuzaki, Junko; Watanabe, Yoshiyuki; Fujita, Norihiko; Taniike, Masako

2014-01-01

In addition to social and communicative deficits, many studies have reported motor deficits in autism spectrum disorder (ASD). This study investigated the macro and microstructural properties of the corpus callosum (CC) of 18 children with ASD and 12 typically developing controls using diffusion tensor imaging tractography. We aimed to explore…

Gender differences in MR muscle tractography

International Nuclear Information System (INIS)

Okamoto, Yoshikazu; Minami, Manabu; Kunimatsu, Akira; Kono, Tatsuo; Sonobe, Jyunichi; Kujiraoka, Yuka

2010-01-01

Tractography of skeletal muscle can clearly reveal the 3-dimensional course of muscle fibers, and the procedure has great potential and could open new fields for diagnostic imaging. Studying this technique for clinical application, we noticed differences in the number of visualized tracts among volunteers and among muscles in the same volunteer. To comprehend why the number of visualized tracts varied so that we could acquire consistently high quality tractography of muscle fiber, we started to examine whether differences in individual parameters affected tractography visualization. The purpose of this study was to determine whether there are gender- and age-specific differences that differentiate the muscles by gender and age in MR tractography of skeletal muscle fiber. We divided 33 healthy volunteers by gender and age among 3 groups, A (13 younger men, aged 20 to 36 years), B (11 younger women, 25 to 39 years), and C (9 older men, 50 to 69), and we obtained from each volunteer tractographs of 8 fibers, including the bilateral gastrocnemius medialis (GCM), gastrocnemius lateralis (GCL), soleus (SOL), and anterior tibialis (AT) muscles. We classified the fibers into 5 grades depending on the extent of visualized tracts and used Mann-Whitney U-test to compare scores by gender (Group A versus B) and age (Group A versus C). Muscle tracts were significantly better visualized in women than men (median total visual score, 34 versus 24, P<0.05). In particular, the SOL muscles showed better visualization in the right (4.0 in women, 1.0 in men, P<0.05) and left (3.0 in women, 1.0 in men, P<0.05). Difference by age was not significant. The GCL was the highest scored muscle in all groups. Our results suggest that group differences, especially by gender, affected visualization of tractography of muscle fiber of the calf. (author)

Diffusion tensor tract-specific analysis of the uncinate fasciculus in patients with amyotrophic lateral sclerosis

Energy Technology Data Exchange (ETDEWEB)

Sato, Kanako; Masutani, Yoshitaka; Watadani, Takeyuki; Nakata, Yasuhiro; Yoshida, Mariko; Abe, Osamu; Ohtomo, Kuni [University of Tokyo, Department of Radiology, Graduate School of Medicine, Bunkyo, Tokyo (Japan); Aoki, Shigeki [Juntendo University, Department of Radiology, Bunkyo, Tokyo (Japan); Iwata, Nobue K.; Terao, Yasuo; Tsuji, Shoji [University of Tokyo, Department of Neurology, Graduate School of Medicine, Bunkyo, Tokyo (Japan)

2010-08-15

The uncinate fasciculus (UF) consists of core fibers connecting the frontal and temporal lobes and is considered to be related to cognitive/behavioral function. Using diffusion tensor tractography, we quantitatively evaluated changes in fractional anisotropy (FA) and the apparent diffusion coefficient (ADC) of the UF by tract-specific analysis to evaluate the damage of the UF in patients with amyotrophic lateral sclerosis (ALS). We obtained diffusion tensor images of 15 patients with ALS and 9 age-matched volunteers. Patients with ALS showed significantly lower mean FA (P = 0.029) compared with controls. No significant difference was seen in mean ADC. The results suggest that damage of the UF in patients with ALS can be quantitatively evaluated with FA. (orig.)

Comparison of two global digital algorithms for Minkowski tensor estimation

DEFF Research Database (Denmark)

The geometry of real world objects can be described by Minkowski tensors. Algorithms have been suggested to approximate Minkowski tensors if only a binary image of the object is available. This paper presents implementations of two such algorithms. The theoretical convergence properties...... are confirmed by simulations on test sets, and recommendations for input arguments of the algorithms are given. For increasing resolutions, we obtain more accurate estimators for the Minkowski tensors. Digitisations of more complicated objects are shown to require higher resolutions....

Training shortest-path tractography: Automatic learning of spatial priors

DEFF Research Database (Denmark)

Kasenburg, Niklas; Liptrot, Matthew George; Reislev, Nina Linde

2016-01-01

Tractography is the standard tool for automatic delineation of white matter tracts from diffusion weighted images. However, the output of tractography often requires post-processing to remove false positives and ensure a robust delineation of the studied tract, and this demands expert prior...... knowledge. Here we demonstrate how such prior knowledge, or indeed any prior spatial information, can be automatically incorporated into a shortest-path tractography approach to produce more robust results. We describe how such a prior can be automatically generated (learned) from a population, and we...

Topology of streamlines and vorticity contours for two - dimensional flows

DEFF Research Database (Denmark)

Andersen, Morten

on the vortex filament by the localised induction approximation the stream function is slightly modified and an extra parameter is introduced. In this setting two new flow topologies arise, but not more than two critical points occur for any combination of the parameters. The analysis of the closed form show...... by a point vortex above a wall in inviscid fluid. There is no reason to a priori expect equivalent results of the three vortex definitions. However, the study is mainly motivated by the findings of Kudela & Malecha (Fluid Dyn. Res. 41, 2009) who find good agreement between the vorticity and streamlines...

Segmentation of the Canine Corpus Callosum using Diffusion Tensor Imaging Tractography

Science.gov (United States)

Pierce, T.T.; Calabrese, E.; White, L.E.; Chen, S.D.; Platt, S.R.; Provenzale, J.M.

2014-01-01

Background We set out to determine functional white matter (WM) connections passing through the canine corpus callosum useful for subsequent studies of canine brains that serve as models for human WM pathway disease. Based on prior studies, we anticipated that the anterior corpus callosum would send projections to the anterior cerebral cortex while progressively posterior segments would send projections to more posterior cortex. Methods A post mortem canine brain was imaged using a 7T MRI producing 100 micron isotropic resolution DTI analyzed by tractography. Using ROIs within cortical locations, which were confirmed by a Nissl stain that identified distinct cortical architecture, we successfully identified 6 important WM pathways. We also compared fractional anisotropy (FA), apparent diffusion coefficient (ADC), radial diffusivity (RD), and axial diffusivity (AD) in tracts passing through the genu and splenium. Results Callosal fibers were organized based upon cortical destination, i.e. fibers from the genu project to the frontal cortex. Histologic results identified the motor cortex based on cytoarchitectonic criteria that allowed placement of ROIs to discriminate between frontal and parietal lobes. We also identified cytoarchitecture typical of the orbital frontal, anterior frontal, and occipital regions and placed ROIs accordingly. FA, ADC, RD and AD values were all higher in posterior corpus callosum fiber tracts. Conclusions Using 6 cortical ROIs, we identified 6 major white matter tracts that reflect major functional divisions of the cerebral hemispheres and we derived quantitative values that can be used for study of canine models of human WM pathological states. PMID:24370161

Structural equations for Killing tensors of order two. II

International Nuclear Information System (INIS)

Hauser, I.; Malhiot, R.J.

1975-01-01

In a preceding paper, a new form of the structural equations for any Killing tensor of order two have been derived; these equations constitute a system analogous to the Killing vector equations Nabla/sub alpha/ K/sub beta/ = ω/sub alpha beta/ = -ω/sub beta alpha/ and Nabla/sub gamma/ ω/sub alpha beta = R/sub alpha beta gamma delta/ K/sup delta/. The first integrability condition for the Killing tensor structural equations is now derived. The structural equations and the integrability condition have forms which can readily be expressed in terms of a null tetrad to furnish a Killing tensor parallel of the Newman--Penrose equations; this is briefly described. The integrability condition implies the new result, for any given space--time, that the dimension of the set of second-order Killing tensors attains its maximum possible value of 50 only if the space--time is of constant curvature. Potential applications of the structural equations are discussed

Addressing the path-length-dependency confound in white matter tract segmentation

DEFF Research Database (Denmark)

Liptrot, Matthew George; Sidaros, Karam; Dyrby, Tim B.

2014-01-01

of streamlines emitted per voxel, and a threshold applied at each iteration. As few as 20 streamlines per seed-voxel, and a robust range of ICE-T thresholds, were shown to sufficiently segment the desired tract network. Outside this range, the tract network either approximated the complete white-matter...... complexity, and therefore cannot be handled using linear correction methods. ICE-T is an easy-to-implement framework that acts as a wrapper around most probabilistic streamline tractography methods, iteratively growing the tractography seed regions. Tract networks segmented with ICE-T can subsequently...... consider this or a similar approach when using tractography to provide tract segmentations for tract based analysis, or for brain network analysis....

Tensor Factorization for Low-Rank Tensor Completion.

Science.gov (United States)

Zhou, Pan; Lu, Canyi; Lin, Zhouchen; Zhang, Chao

2018-03-01

Recently, a tensor nuclear norm (TNN) based method was proposed to solve the tensor completion problem, which has achieved state-of-the-art performance on image and video inpainting tasks. However, it requires computing tensor singular value decomposition (t-SVD), which costs much computation and thus cannot efficiently handle tensor data, due to its natural large scale. Motivated by TNN, we propose a novel low-rank tensor factorization method for efficiently solving the 3-way tensor completion problem. Our method preserves the low-rank structure of a tensor by factorizing it into the product of two tensors of smaller sizes. In the optimization process, our method only needs to update two smaller tensors, which can be more efficiently conducted than computing t-SVD. Furthermore, we prove that the proposed alternating minimization algorithm can converge to a Karush-Kuhn-Tucker point. Experimental results on the synthetic data recovery, image and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state-of-the-arts including the TNN and matricization methods.

Neutrino stress tensor regularization in two-dimensional space-time

International Nuclear Information System (INIS)

Davies, P.C.W.; Unruh, W.G.

1977-01-01

The method of covariant point-splitting is used to regularize the stress tensor for a massless spin 1/2 (neutrino) quantum field in an arbitrary two-dimensional space-time. A thermodynamic argument is used as a consistency check. The result shows that the physical part of the stress tensor is identical with that of the massless scalar field (in the absence of Casimir-type terms) even though the formally divergent expression is equal to the negative of the scalar case. (author)

Diffusion Tensor Tractography Reveals Disrupted Structural Connectivity during Brain Aging

Science.gov (United States)

Lin, Lan; Tian, Miao; Wang, Qi; Wu, Shuicai

2017-10-01

Brain aging is one of the most crucial biological processes that entail many physical, biological, chemical, and psychological changes, and also a major risk factor for most common neurodegenerative diseases. To improve the quality of life for the elderly, it is important to understand how the brain is changed during the normal aging process. We compared diffusion tensor imaging (DTI)-based brain networks in a cohort of 75 healthy old subjects by using graph theory metrics to describe the anatomical networks and connectivity patterns, and network-based statistic (NBS) analysis was used to identify pairs of regions with altered structural connectivity. The NBS analysis revealed a significant network comprising nine distinct fiber bundles linking 10 different brain regions showed altered white matter structures in young-old group compare with middle-aged group (p < .05, family-wise error-corrected). Our results might guide future studies and help to gain a better understanding of brain aging.

Streamline topologies near simple degenerate critical points in two-dimensional flow away from boundaries

DEFF Research Database (Denmark)

Brøns, Morten; Hartnack, Johan Nicolai

1998-01-01

Streamline patterns and their bifurcations in two-dimensional incompressible flow are investigated from a topological point of view. The velocity field is expanded at a point in the fluid, and the expansion coefficients are considered as bifurcation parameters. A series of non-linear coordinate c...

Streamline topologies near simple degenerate critical points in two-dimensional flow away from boundaries

DEFF Research Database (Denmark)

Brøns, Morten; Hartnack, Johan Nicolai

1999-01-01

Streamline patterns and their bifurcations in two-dimensional incompressible flow are investigated from a topological point of view. The velocity field is expanded at a point in the fluid, and the expansion coefficients are considered as bifurcation parameters. A series of nonlinear coordinate ch...

4.7-T diffusion tensor imaging of acute traumatic peripheral nerve injury.

Science.gov (United States)

Boyer, Richard B; Kelm, Nathaniel D; Riley, D Colton; Sexton, Kevin W; Pollins, Alonda C; Shack, R Bruce; Dortch, Richard D; Nanney, Lillian B; Does, Mark D; Thayer, Wesley P

2015-09-01

Diagnosis and management of peripheral nerve injury is complicated by the inability to assess microstructural features of injured nerve fibers via clinical examination and electrophysiology. Diffusion tensor imaging (DTI) has been shown to accurately detect nerve injury and regeneration in crush models of peripheral nerve injury, but no prior studies have been conducted on nerve transection, a surgical emergency that can lead to permanent weakness or paralysis. Acute sciatic nerve injuries were performed microsurgically to produce multiple grades of nerve transection in rats that were harvested 1 hour after surgery. High-resolution diffusion tensor images from ex vivo sciatic nerves were obtained using diffusion-weighted spin-echo acquisitions at 4.7 T. Fractional anisotropy was significantly reduced at the injury sites of transected rats compared with sham rats. Additionally, minor eigenvalues and radial diffusivity were profoundly elevated at all injury sites and were negatively correlated to the degree of injury. Diffusion tensor tractography showed discontinuities at all injury sites and significantly reduced continuous tract counts. These findings demonstrate that high-resolution DTI is a promising tool for acute diagnosis and grading of traumatic peripheral nerve injuries.

Testing the connections within face processing circuitry in Capgras delusion with diffusion imaging tractography

Directory of Open Access Journals (Sweden)

Maria A. Bobes

2016-01-01

Full Text Available Although Capgras delusion (CD patients are capable of recognizing familiar faces, they present a delusional belief that some relatives have been replaced by impostors. CD has been explained as a selective disruption of a pathway processing affective values of familiar faces. To test the integrity of connections within face processing circuitry, diffusion tensor imaging was performed in a CD patient and 10 age-matched controls. Voxel-based morphometry indicated gray matter damage in right frontal areas. Tractography was used to examine two important tracts of the face processing circuitry: the inferior fronto-occipital fasciculus (IFOF and the inferior longitudinal (ILF. The superior longitudinal fasciculus (SLF and commissural tracts were also assessed. CD patient did not differ from controls in the commissural fibers, or the SLF. Right and left ILF, and right IFOF were also equivalent to those of controls. However, the left IFOF was significantly reduced respect to controls, also showing a significant dissociation with the ILF, which represents a selective impairment in the fiber-tract connecting occipital and frontal areas. This suggests a possible involvement of the IFOF in affective processing of faces in typical observers and in covert recognition in some cases with prosopagnosia.

The Disruption of Geniculocalcarine Tract in Occipital Neoplasm: A Diffusion Tensor Imaging Study

Directory of Open Access Journals (Sweden)

Yan Zhang

2016-01-01

Full Text Available Aim. Investigate the disruption of geniculocalcarine tract (GCT in different occipital neoplasm by diffusion tensor imaging (DTI. Methods. Thirty-two subjects (44.1 ± 3.6 years who had single occipital neoplasm (9 gliomas, 6 meningiomas, and 17 metastatic tumors with ipsilateral GCT involved and thirty healthy subjects (39.2 ± 3.3 years underwent conventional sequences scanning and diffusion tensor imaging by a 1.5T MR scanner. The diffusion-sensitive gradient direction is 13. Compare the fractional anisotropy (FA and mean diffusivity (MD values of healthy GCT with the corresponding values of GCT in peritumoral edema area. Perform diffusion tensor tractography (DTT on GCT by the line propagation technique in all subjects. Results. The FA values of GCT in peritumoral edema area decreased (P=0.001 while the MD values increased (P=0.002 when compared with healthy subjects. There was no difference in the FA values across tumor types (P=0.114 while the MD values of GCT in the metastatic tumor group were higher than the other groups (P=0.001. GCTs were infiltrated in all the 9 gliomas cases, with displacement in 2 cases and disruption in 7 cases. GCTs were displaced in 6 meningiomas cases. GCTs were displaced in all the 7 metastatic cases, with disruption in 7 cases. Conclusions. DTI represents valid markers for evaluating GCT’s disruption in occipital neoplasm. The disruption of GCT varies according to the properties of neoplasm.

TensorLy: Tensor Learning in Python

NARCIS (Netherlands)

Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja

2016-01-01

Tensor methods are gaining increasing traction in machine learning. However, there are scant to no resources available to perform tensor learning and decomposition in Python. To answer this need we developed TensorLy. TensorLy is a state of the art general purpose library for tensor learning.

A continuous tensor field approximation of discrete DT-MRI data for extracting microstructural and architectural features of tissue.

Science.gov (United States)

Pajevic, Sinisa; Aldroubi, Akram; Basser, Peter J

2002-01-01

The effective diffusion tensor of water, D, measured by diffusion tensor MRI (DT-MRI), is inherently a discrete, noisy, voxel-averaged sample of an underlying macroscopic effective diffusion tensor field, D(x). Within fibrous tissues this field is presumed to be continuous and smooth at a gross anatomical length scale. Here a new, general mathematical framework is proposed that uses measured DT-MRI data to produce a continuous approximation to D(x). One essential finding is that the continuous tensor field representation can be constructed by repeatedly performing one-dimensional B-spline transforms of the DT-MRI data. The fidelity and noise-immunity of this approximation are tested using a set of synthetically generated tensor fields to which background noise is added via Monte Carlo methods. Generally, these tensor field templates are reproduced faithfully except at boundaries where diffusion properties change discontinuously or where the tensor field is not microscopically homogeneous. Away from such regions, the tensor field approximation does not introduce bias in useful DT-MRI parameters, such as Trace(D(x)). It also facilitates the calculation of several new parameters, particularly differential quantities obtained from the tensor of spatial gradients of D(x). As an example, we show that they can identify tissue boundaries across which diffusion properties change rapidly using in vivo human brain data. One important application of this methodology is to improve the reliability and robustness of DT-MRI fiber tractography.

TensorLy: Tensor Learning in Python

OpenAIRE

Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja

2016-01-01

Tensors are higher-order extensions of matrices. While matrix methods form the cornerstone of machine learning and data analysis, tensor methods have been gaining increasing traction. However, software support for tensor operations is not on the same footing. In order to bridge this gap, we have developed \\emph{TensorLy}, a high-level API for tensor methods and deep tensorized neural networks in Python. TensorLy aims to follow the same standards adopted by the main projects of the Python scie...

Numerical evaluation of the tensor bispectrum in two field inflation

Energy Technology Data Exchange (ETDEWEB)

Raveendran, Rathul Nath [The Institute of Mathematical Sciences, HBNI, CIT Campus, Chennai, 600113 India (India); Sriramkumar, L., E-mail: rathulnr@imsc.res.in, E-mail: sriram@physics.iitm.ac.in [Department of Physics, Indian Institute of Technology Madras, Chennai, 600036 India (India)

2017-07-01

We evaluate the dimensionless non-Gaussianity parameter h {sub NL}, that characterizes the amplitude of the tensor bispectrum, numerically for a class of two field inflationary models such as double inflation, hybrid inflation and aligned natural inflation. We compare the numerical results with the slow roll results which can be obtained analytically. In the context of double inflation, we also investigate the effects on h {sub NL} due to curved trajectories in the field space. We explicitly examine the validity of the consistency relation governing the tensor bispectrum in the squeezed limit. Lastly, we discuss the contribution to h {sub NL} due to the epoch of preheating in two field models.

Numerical evaluation of the tensor bispectrum in two field inflation

International Nuclear Information System (INIS)

Raveendran, Rathul Nath; Sriramkumar, L.

2017-01-01

We evaluate the dimensionless non-Gaussianity parameter h NL , that characterizes the amplitude of the tensor bispectrum, numerically for a class of two field inflationary models such as double inflation, hybrid inflation and aligned natural inflation. We compare the numerical results with the slow roll results which can be obtained analytically. In the context of double inflation, we also investigate the effects on h NL due to curved trajectories in the field space. We explicitly examine the validity of the consistency relation governing the tensor bispectrum in the squeezed limit. Lastly, we discuss the contribution to h NL due to the epoch of preheating in two field models.

The challenge of mapping the human connectome based on diffusion tractography.

Science.gov (United States)

Maier-Hein, Klaus H; Neher, Peter F; Houde, Jean-Christophe; Côté, Marc-Alexandre; Garyfallidis, Eleftherios; Zhong, Jidan; Chamberland, Maxime; Yeh, Fang-Cheng; Lin, Ying-Chia; Ji, Qing; Reddick, Wilburn E; Glass, John O; Chen, David Qixiang; Feng, Yuanjing; Gao, Chengfeng; Wu, Ye; Ma, Jieyan; Renjie, H; Li, Qiang; Westin, Carl-Fredrik; Deslauriers-Gauthier, Samuel; González, J Omar Ocegueda; Paquette, Michael; St-Jean, Samuel; Girard, Gabriel; Rheault, François; Sidhu, Jasmeen; Tax, Chantal M W; Guo, Fenghua; Mesri, Hamed Y; Dávid, Szabolcs; Froeling, Martijn; Heemskerk, Anneriet M; Leemans, Alexander; Boré, Arnaud; Pinsard, Basile; Bedetti, Christophe; Desrosiers, Matthieu; Brambati, Simona; Doyon, Julien; Sarica, Alessia; Vasta, Roberta; Cerasa, Antonio; Quattrone, Aldo; Yeatman, Jason; Khan, Ali R; Hodges, Wes; Alexander, Simon; Romascano, David; Barakovic, Muhamed; Auría, Anna; Esteban, Oscar; Lemkaddem, Alia; Thiran, Jean-Philippe; Cetingul, H Ertan; Odry, Benjamin L; Mailhe, Boris; Nadar, Mariappan S; Pizzagalli, Fabrizio; Prasad, Gautam; Villalon-Reina, Julio E; Galvis, Justin; Thompson, Paul M; Requejo, Francisco De Santiago; Laguna, Pedro Luque; Lacerda, Luis Miguel; Barrett, Rachel; Dell'Acqua, Flavio; Catani, Marco; Petit, Laurent; Caruyer, Emmanuel; Daducci, Alessandro; Dyrby, Tim B; Holland-Letz, Tim; Hilgetag, Claus C; Stieltjes, Bram; Descoteaux, Maxime

2017-11-07

Tractography based on non-invasive diffusion imaging is central to the study of human brain connectivity. To date, the approach has not been systematically validated in ground truth studies. Based on a simulated human brain data set with ground truth tracts, we organized an open international tractography challenge, which resulted in 96 distinct submissions from 20 research groups. Here, we report the encouraging finding that most state-of-the-art algorithms produce tractograms containing 90% of the ground truth bundles (to at least some extent). However, the same tractograms contain many more invalid than valid bundles, and half of these invalid bundles occur systematically across research groups. Taken together, our results demonstrate and confirm fundamental ambiguities inherent in tract reconstruction based on orientation information alone, which need to be considered when interpreting tractography and connectivity results. Our approach provides a novel framework for estimating reliability of tractography and encourages innovation to address its current limitations.

Anti-symmetric rank-two tensor matter field on superspace for NT=2

International Nuclear Information System (INIS)

Spalenza, Wesley; Ney, Wander G.; Helayel-Neto, J.A.

2004-01-01

In this work, we discuss the interaction between anti-symmetric rank-two tensor matter and topological Yang-Mills fields. The matter field considered here is the rank-2 Avdeev-Chizhov tensor matter field in a suitably extended N T =2 SUSY. We start off from the N T =2, D=4 superspace formulation and we go over to Riemannian manifolds. The matter field is coupled to the topological Yang-Mills field. We show that both actions are obtained as Q-exact forms, which allows us to express the energy-momentum tensor as Q-exact observables

When tractography meets tracer injections: a systematic study of trends and variation sources of diffusion-based connectivity.

Science.gov (United States)

Aydogan, Dogu Baran; Jacobs, Russell; Dulawa, Stephanie; Thompson, Summer L; Francois, Maite Christi; Toga, Arthur W; Dong, Hongwei; Knowles, James A; Shi, Yonggang

2018-04-16

Tractography is a powerful technique capable of non-invasively reconstructing the structural connections in the brain using diffusion MRI images, but the validation of tractograms is challenging due to lack of ground truth. Owing to recent developments in mapping the mouse brain connectome, high-resolution tracer injection-based axonal projection maps have been created and quickly adopted for the validation of tractography. Previous studies using tracer injections mainly focused on investigating the match in projections and optimal tractography protocols. Being a complicated technique, however, tractography relies on multiple stages of operations and parameters. These factors introduce large variabilities in tractograms, hindering the optimization of protocols and making the interpretation of results difficult. Based on this observation, in contrast to previous studies, in this work we focused on quantifying and ranking the amount of performance variation introduced by these factors. For this purpose, we performed over a million tractography experiments and studied the variability across different subjects, injections, anatomical constraints and tractography parameters. By using N-way ANOVA analysis, we show that all tractography parameters are significant and importantly performance variations with respect to the differences in subjects are comparable to the variations due to tractography parameters, which strongly underlines the importance of fully documenting the tractography protocols in scientific experiments. We also quantitatively show that inclusion of anatomical constraints is the most significant factor for improving tractography performance. Although this critical factor helps reduce false positives, our analysis indicates that anatomy-informed tractography still fails to capture a large portion of axonal projections.

Diffusion Properties and 3D Architecture of Human Lower Leg Muscles Assessed with Ultra-High-Field-Strength Diffusion-Tensor MR Imaging and Tractography: Reproducibility and Sensitivity to Sex Difference and Intramuscular Variability.

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Fouré, Alexandre; Ogier, Augustin C; Le Troter, Arnaud; Vilmen, Christophe; Feiweier, Thorsten; Guye, Maxime; Gondin, Julien; Besson, Pierre; Bendahan, David

2018-05-01

Purpose To demonstrate the reproducibility of the diffusion properties and three-dimensional structural organization measurements of the lower leg muscles by using diffusion-tensor imaging (DTI) assessed with ultra-high-field-strength (7.0-T) magnetic resonance (MR) imaging and tractography of skeletal muscle fibers. On the basis of robust statistical mapping analyses, this study also aimed at determining the sensitivity of the measurements to sex difference and intramuscular variability. Materials and Methods All examinations were performed with ethical review board approval; written informed consent was obtained from all volunteers. Reproducibility of diffusion tensor indexes assessment including eigenvalues, mean diffusivity, and fractional anisotropy (FA) as well as muscle volume and architecture (ie, fiber length and pennation angle) were characterized in lower leg muscles (n = 8). Intramuscular variability and sex differences were characterized in young healthy men and women (n = 10 in each group). Student t test, statistical parametric mapping, correlation coefficients (Spearman rho and Pearson product-moment) and coefficient of variation (CV) were used for statistical data analysis. Results High reproducibility of measurements (mean CV ± standard deviation, 4.6% ± 3.8) was determined in diffusion properties and architectural parameters. Significant sex differences were detected in FA (4.2% in women for the entire lower leg; P = .001) and muscle volume (21.7% in men for the entire lower leg; P = .008), whereas architecture parameters were almost identical across sex. Additional differences were found independently of sex in diffusion properties and architecture along several muscles of the lower leg. Conclusion The high-spatial-resolution DTI assessed with 7.0-T MR imaging allows a reproducible assessment of structural organization of superficial and deep muscles, giving indirect information on muscle function. © RSNA, 2018 Online supplemental material is

Fiber architecture in remodeled myocardium revealed with a quantitative diffusion CMR tractography framework and histological validation.

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Mekkaoui, Choukri; Huang, Shuning; Chen, Howard H; Dai, Guangping; Reese, Timothy G; Kostis, William J; Thiagalingam, Aravinda; Maurovich-Horvat, Pal; Ruskin, Jeremy N; Hoffmann, Udo; Jackowski, Marcel P; Sosnovik, David E

2012-10-12

The study of myofiber reorganization in the remote zone after myocardial infarction has been performed in 2D. Microstructural reorganization in remodeled hearts, however, can only be fully appreciated by considering myofibers as continuous 3D entities. The aim of this study was therefore to develop a technique for quantitative 3D diffusion CMR tractography of the heart, and to apply this method to quantify fiber architecture in the remote zone of remodeled hearts. Diffusion Tensor CMR of normal human, sheep, and rat hearts, as well as infarcted sheep hearts was performed ex vivo. Fiber tracts were generated with a fourth-order Runge-Kutta integration technique and classified statistically by the median, mean, maximum, or minimum helix angle (HA) along the tract. An index of tract coherence was derived from the relationship between these HA statistics. Histological validation was performed using phase-contrast microscopy. In normal hearts, the subendocardial and subepicardial myofibers had a positive and negative HA, respectively, forming a symmetric distribution around the midmyocardium. However, in the remote zone of the infarcted hearts, a significant positive shift in HA was observed. The ratio between negative and positive HA variance was reduced from 0.96 ± 0.16 in normal hearts to 0.22 ± 0.08 in the remote zone of the remodeled hearts (p layers of the myocardium. Tractography-based quantification, performed here for the first time in remodeled hearts, may provide a framework for assessing regional changes in the left ventricle following infarction.

Middle longitudinal fasciculus delineation within language pathways: A diffusion tensor imaging study in human

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Menjot de Champfleur, Nicolas, E-mail: nicolasdechampfleur@orange.fr [Department of Neuroradiology, University Hospital Center, Gui de Chauliac Hospital, Montpellier (France); Team “Plasticity of Central Nervous System, Stem Cells and Glial Tumors,” Institut National de la Santé et de la Recherche Médicale Unité 1051, Institut of Neurosciences of Montpellier, Saint Eloi Hospital, Montpellier (France); Lima Maldonado, Igor [Department of Neuroradiology, University Hospital Center, Gui de Chauliac Hospital, Montpellier (France); Team “Plasticity of Central Nervous System, Stem Cells and Glial Tumors,” Institut National de la Santé et de la Recherche Médicale Unité 1051, Institut of Neurosciences of Montpellier, Saint Eloi Hospital, Montpellier (France); Divisão de Neurologia e Epidemiologia (CPPHO), Complexo Hospital Universitário Professor Edgard Santos, Universidade Federal da Bahia, Salvador-Bahia (Brazil); Moritz-Gasser, Sylvie [Department of Neuroradiology, University Hospital Center, Gui de Chauliac Hospital, Montpellier (France); Department of Neurology, University Hospital Center, Gui de Chauliac Hospital, Montpellier (France); Machi, Paolo [Department of Neuroradiology, University Hospital Center, Gui de Chauliac Hospital, Montpellier (France); and others

2013-01-15

Introduction: The existence in the human brain of the middle longitudinal fasciculus (MdLF), initially described in the macaque monkey, is supported by diffusion tensor imaging studies. In the present work, we aim (1) to confirm that this fascicle is found constantly in control subjects with the use of DTI techniques and (2) to delineate the MdLF from the other fiber bundles that constitute the language pathways. Materials and methods: Tractography was realized in four right-handed healthy volunteers for the arcuate fascicle, uncinate fascicle, inferior fronto-occipital fascicle, inferior longitudinal fascicle and the middle longitudinal fascicle. The fiber tracts were characterized for their size, mean fractional anisotropy (FA), for their length, number of streamlines, and lateralization indices were calculated. Results: The MdLF is found constantly and it is clearly delineated from the other fascicles that constitute the language pathways, especially the ventral pathway. It runs within the superior temporal gyrus white matter from the temporal pole, then it extends caudally in the upper part of the sagittal stratum and the posterior part of the corona radiata, to reach the inferior parietal lobule (angular gyrus). We found a leftward asymmetry for all fiber tracts when considering the mean FA. Discussion: Using DTI methods, we confirm that the MdLF connects the angular gyrus and the superior temporal gyrus. On the basis of these findings, the role of the MdLF is discussed. Conclusion: The middle longitudinal fasciculus, connects the angular gyrus and the superior temporal gyrus and its course can be systematically differenciated from those of other fascicles composing both ventral and dorsal routes (IFOF, IFL, AF and UF)

Middle longitudinal fasciculus delineation within language pathways: A diffusion tensor imaging study in human

International Nuclear Information System (INIS)

Menjot de Champfleur, Nicolas; Lima Maldonado, Igor; Moritz-Gasser, Sylvie; Machi, Paolo

2013-01-01

Introduction: The existence in the human brain of the middle longitudinal fasciculus (MdLF), initially described in the macaque monkey, is supported by diffusion tensor imaging studies. In the present work, we aim (1) to confirm that this fascicle is found constantly in control subjects with the use of DTI techniques and (2) to delineate the MdLF from the other fiber bundles that constitute the language pathways. Materials and methods: Tractography was realized in four right-handed healthy volunteers for the arcuate fascicle, uncinate fascicle, inferior fronto-occipital fascicle, inferior longitudinal fascicle and the middle longitudinal fascicle. The fiber tracts were characterized for their size, mean fractional anisotropy (FA), for their length, number of streamlines, and lateralization indices were calculated. Results: The MdLF is found constantly and it is clearly delineated from the other fascicles that constitute the language pathways, especially the ventral pathway. It runs within the superior temporal gyrus white matter from the temporal pole, then it extends caudally in the upper part of the sagittal stratum and the posterior part of the corona radiata, to reach the inferior parietal lobule (angular gyrus). We found a leftward asymmetry for all fiber tracts when considering the mean FA. Discussion: Using DTI methods, we confirm that the MdLF connects the angular gyrus and the superior temporal gyrus. On the basis of these findings, the role of the MdLF is discussed. Conclusion: The middle longitudinal fasciculus, connects the angular gyrus and the superior temporal gyrus and its course can be systematically differenciated from those of other fascicles composing both ventral and dorsal routes (IFOF, IFL, AF and UF)

Region-specific connectivity in patients with periventricular nodular heterotopia and epilepsy: A study combining diffusion tensor imaging and functional MRI.

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Liu, Wenyu; An, Dongmei; Tong, Xin; Niu, Running; Gong, Qiyong; Zhou, Dong

2017-10-01

Periventricular nodular heterotopia (PNH) is an important cause of chronic epilepsy. The purpose of this study was to evaluate region-specific connectivity in PNH patients with epilepsy and assess correlation between connectivity strength and clinical factors including duration and prognosis. Diffusion tensor imaging (DTI) and resting state functional MRI (fMRI) were performed in 28 subjects (mean age 27.4years; range 9-56years). The structural connectivity of fiber bundles passing through the manually-selected segmented nodules and other brain regions were analyzed by tractography. Cortical lobes showing functional correlations to nodules were also determined. For all heterotopic gray matter nodules, including at least one in each subject, the most frequent segments to which nodular heterotopia showed structural (132/151) and functional (146/151) connectivity were discrete regions of the ipsilateral overlying cortex. Agreement between diffusion tensor tractography and functional connectivity analyses was conserved in 81% of all nodules (122/151). In patients with longer duration or refractory epilepsy, the connectivity was significantly stronger, particularly to the frontal and temporal lobes (P<0.05). Nodules in PNH were structurally and functionally connected to the cortex. The extent is stronger in patients with longstanding or intractable epilepsy. These findings suggest the region-specific interactions may help better evaluate prognosis and seek medical or surgical interventions of PNH-related epilepsy. Copyright © 2017 Elsevier B.V. All rights reserved.

A Review of Tensors and Tensor Signal Processing

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Cammoun, L.; Castaño-Moraga, C. A.; Muñoz-Moreno, E.; Sosa-Cabrera, D.; Acar, B.; Rodriguez-Florido, M. A.; Brun, A.; Knutsson, H.; Thiran, J. P.

Tensors have been broadly used in mathematics and physics, since they are a generalization of scalars or vectors and allow to represent more complex properties. In this chapter we present an overview of some tensor applications, especially those focused on the image processing field. From a mathematical point of view, a lot of work has been developed about tensor calculus, which obviously is more complex than scalar or vectorial calculus. Moreover, tensors can represent the metric of a vector space, which is very useful in the field of differential geometry. In physics, tensors have been used to describe several magnitudes, such as the strain or stress of materials. In solid mechanics, tensors are used to define the generalized Hooke’s law, where a fourth order tensor relates the strain and stress tensors. In fluid dynamics, the velocity gradient tensor provides information about the vorticity and the strain of the fluids. Also an electromagnetic tensor is defined, that simplifies the notation of the Maxwell equations. But tensors are not constrained to physics and mathematics. They have been used, for instance, in medical imaging, where we can highlight two applications: the diffusion tensor image, which represents how molecules diffuse inside the tissues and is broadly used for brain imaging; and the tensorial elastography, which computes the strain and vorticity tensor to analyze the tissues properties. Tensors have also been used in computer vision to provide information about the local structure or to define anisotropic image filters.

Atomic-batched tensor decomposed two-electron repulsion integrals

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Schmitz, Gunnar; Madsen, Niels Kristian; Christiansen, Ove

2017-04-01

We present a new integral format for 4-index electron repulsion integrals, in which several strategies like the Resolution-of-the-Identity (RI) approximation and other more general tensor-decomposition techniques are combined with an atomic batching scheme. The 3-index RI integral tensor is divided into sub-tensors defined by atom pairs on which we perform an accelerated decomposition to the canonical product (CP) format. In a first step, the RI integrals are decomposed to a high-rank CP-like format by repeated singular value decompositions followed by a rank reduction, which uses a Tucker decomposition as an intermediate step to lower the prefactor of the algorithm. After decomposing the RI sub-tensors (within the Coulomb metric), they can be reassembled to the full decomposed tensor (RC approach) or the atomic batched format can be maintained (ABC approach). In the first case, the integrals are very similar to the well-known tensor hypercontraction integral format, which gained some attraction in recent years since it allows for quartic scaling implementations of MP2 and some coupled cluster methods. On the MP2 level, the RC and ABC approaches are compared concerning efficiency and storage requirements. Furthermore, the overall accuracy of this approach is assessed. Initial test calculations show a good accuracy and that it is not limited to small systems.

Diffusion tensor tractography of language functional areas and fiber pathways in normal human brain

International Nuclear Information System (INIS)

Sun Xuejin; Dai Jianping; Chen Hongyan; Gao Peiyi; Ai Lin; Tian Shengyong; Pang Ruilin

2007-01-01

Objective: To demonstrate the fiber pathways of Broca area to the other functional brain areas with diffusion tensor imaging and fiber tracking. Methods: Conventionality MRI, diffusion tensor imaging (DTI) and fiber tracking were performed using 3.0 T MRI in 20 healthy person. The fiber bundles and tracts were analyzed in Broca area and contralateral normal area. Results: The left-side fiber bundles were 428 and the right-side were 416 in B45 area, there were no statistically significant differences between both sides (t=0.216, P>0.05). The left-side fiber bundles were 432 and the right-side were 344 in B44 area,there were statistically significant (t=2.314, P 0.05). Differences of the arcuate fascicule between both sides were not statistically significant (t=-0.465, P>0.05), the mean FA on the left was higher than the right (t=1.912, P<0.05). DTI and fiber tracking exhibited that the fiber bundles from Broca area were distributed superoanteriorly to the lateral foreside of the frontal lobe, lateroinferiorly to the occipital lobe through external capsule, and went down through globus pallidus and internal capsule. Conclusion: The fiber tracts bewteen Broca area and other brain areas were the fundamental structures for performing language function of the human brain. (authors)

Diffusion tensor tractography as a supplementary tool to conventional MRI for evaluating patients with myelopathy

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Amal Amin A. El Maati

2014-12-01

Conclusion: Diffusion tensor imaging is a reliable method for the evaluation of the diffusion properties of normal and compressed spinal cords. Furthermore, this technique can be used as an important supplementary tool to conventional MRI for the quantification of fiber damage in spinal cord compression, thus has the potential to be of great utility for treatment planning and follow up.

MR diffusion histology and micro-tractography reveal mesoscale features of the human cerebellum.

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Dell'Acqua, Flavio; Bodi, Istvan; Slater, David; Catani, Marco; Modo, Michel

2013-12-01

After 140 years from the discovery of Golgi's black reaction, the study of connectivity of the cerebellum remains a fascinating yet challenging task. Current histological techniques provide powerful methods for unravelling local axonal architecture, but the relatively low volume of data that can be acquired in a reasonable amount of time limits their application to small samples. State-of-the-art in vivo magnetic resonance imaging (MRI) methods, such as diffusion tractography techniques, can reveal trajectories of the major white matter pathways, but their correspondence with underlying anatomy is yet to be established. Hence, a significant gap exists between these two approaches as neither of them can adequately describe the three-dimensional complexity of fibre architecture at the level of the mesoscale (from a few millimetres to micrometres). In this study, we report the application of MR diffusion histology and micro-tractography methods to reveal the combined cytoarchitectural organisation and connectivity of the human cerebellum at a resolution of 100-μm (2 nl/voxel volume). Results show that the diffusion characteristics for each layer of the cerebellar cortex correctly reflect the known cellular composition and its architectural pattern. Micro-tractography also reveals details of the axonal connectivity of individual cerebellar folia and the intra-cortical organisation of the different cerebellar layers. The direct correspondence between MR diffusion histology and micro-tractography with immunohistochemistry indicates that these approaches have the potential to complement traditional histology techniques by providing a non-destructive, quantitative and three-dimensional description of the microstructural organisation of the healthy and pathological tissue.

Automatic target validation based on neuroscientific literature mining for tractography

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Xavier eVasques

2015-05-01

Full Text Available Target identification for tractography studies requires solid anatomical knowledge validated by an extensive literature review across species for each seed structure to be studied. Manual literature review to identify targets for a given seed region is tedious and potentially subjective. Therefore, complementary approaches would be useful. We propose to use text-mining models to automatically suggest potential targets from the neuroscientific literature, full-text articles and abstracts, so that they can be used for anatomical connection studies and more specifically for tractography. We applied text-mining models to three structures: two well studied structures, since validated deep brain stimulation targets, the internal globus pallidus and the subthalamic nucleus and, the nucleus accumbens, an exploratory target for treating psychiatric disorders. We performed a systematic review of the literature to document the projections of the three selected structures and compared it with the targets proposed by text-mining models, both in rat and primate (including human. We ran probabilistic tractography on the nucleus accumbens and compared the output with the results of the text-mining models and literature review. Overall, text-mining the literature could find three times as many targets as two man-weeks of curation could. The overall efficiency of the text-mining against literature review in our study was 98% recall (at 36% precision, meaning that over all the targets for the three selected seeds, only one target has been missed by text-mining. We demonstrate that connectivity for a structure of interest can be extracted from a very large amount of publications and abstracts. We believe this tool will be useful in helping the neuroscience community to facilitate connectivity studies of particular brain regions. The text mining tools used for the study are part of the HBP Neuroinformatics Platform, publicly available at http://connectivity-brainer.rhcloud.com/.

Properties of the stress tensor in more than two dimensions

International Nuclear Information System (INIS)

Cappelli, A.

1988-03-01

Some aspects of conformal invariance in more than two dimensions are analysed. In this case conformal (Weyl) transformations of the metric are not realized in general by coordinate transformations. The operator product expansion of the stress tensor is investigated by means of examples in the free bosonic and fermionic theories. The effective action for the general form of the trace anomaly is built in four dimensions and the Wess-Zumino consistency conditions are discussed. This gives the anomalous transformation law of the stress tensor and the relation to the Casimir effect in the geometry R x S 3 . The explicit computation of the bosonic partition function provides a check

Evaluation of 3D tensor tractography of pyramidal tract depicted by 3T MRI in patients with lacunar infarcts. For prediction of motor function outcome

International Nuclear Information System (INIS)

Igase, Keiji; Arai, Masamori; Matsubara, Ichiro; Goishi, Jyunji; Sadamoto, Kazuhiko; Kumon, Yoshiaki; Nagato, Shigeyuki; Seno, Toshimoto; Ohnishi, Takanori

2007-01-01

3D tensor tractography (DTT) has been applied to central nervous system (CNS) diseases to depict neuronal fibers. In this study with 3 tesla MRI, we have evaluated DTT to predict outcome of motor function in patients with lacunar infarcts. Fifteen patients with New lacunar infarcts, underwent DTTs with at least one in the acute (mean 1.4 days) and another in the subacute phase (mean 18.7 days). Patients were separated to 2 groups, recovery and non-recovery. Patients in former group had almost complete recovery in motor function 3 month later, while those to latter had a residual hemiparesis. Motor function was assessed with MMT score, which was uniquely stratefied into 12 levels by a modified MMT (manual muscle testing) protocol. DTT was implemented with 3 tesla MRI (Signa Excite; GE) and analyzed with dTV. IISR which was produced by the Department of Radiology, Tokyo University. The pyramidal tract was delineated by setting each region of interest (ROI), with the cerebral peduncle as the seed point and the motor cortex as the target point. The number of pyramidal fibers was identified as drawn lines obtained from a result display. The ratio of the number of fibers (RF) was calculated based on the number of fibers in the injured side relative to the number of fibers in the intact side x 100. In acute phase mean RFs the recovery (70.8±21.6%) and non-recovery (63.5±23.4%) groups were not significantly different. RF of recovery group in subacute phase was 100.5±28.3%, which was significantly higher with that in acute phase, meanwhile there was no significance difference between RFs of non-recovery group in two phases. In addition there was a significant correlation (R 2 =0.89) between MMT score 3 month later and RF in subacute phase in all patients group. There seems to be a correlation between long-term recovery of motor function and increased numbers in pyramidal fibers defected by DTT. Therefore, DTT may have a potential use in predicting the outcome of patients

Target identification for stereotactic thalamotomy using diffusion tractography.

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Zsigmond Tamás Kincses

Full Text Available BACKGROUND: Stereotactic targets for thalamotomy are usually derived from population-based coordinates. Individual anatomy is used only to scale the coordinates based on the location of some internal guide points. While on conventional MR imaging the thalamic nuclei are indistinguishable, recently it has become possible to identify individual thalamic nuclei using different connectivity profiles, as defined by MR diffusion tractography. METHODOLOGY AND PRINCIPAL FINDINGS: Here we investigated the inter-individual variation of the location of target nuclei for thalamotomy: the putative ventralis oralis posterior (Vop and the ventral intermedius (Vim nucleus as defined by probabilistic tractography. We showed that the mean inter-individual distance of the peak Vop location is 7.33 mm and 7.42 mm for Vim. The mean overlap between individual Vop nuclei was 40.2% and it was 31.8% for Vim nuclei. As a proof of concept, we also present a patient who underwent Vop thalamotomy for untreatable tremor caused by traumatic brain injury and another patient who underwent Vim thalamotomy for essential tremor. The probabilistic tractography indicated that the successful tremor control was achieved with lesions in the Vop and Vim respectively. CONCLUSIONS: Our data call attention to the need for a better appreciation of the individual anatomy when planning stereotactic functional neurosurgery.

Efficient tensor completion for color image and video recovery: Low-rank tensor train

OpenAIRE

Bengua, Johann A.; Phien, Ho N.; Tuan, Hoang D.; Do, Minh N.

2016-01-01

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via tensor tra...

Investigating the tradeoffs between spatial resolution and diffusion sampling for brain mapping with diffusion tractography: time well spent?

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Calabrese, Evan; Badea, Alexandra; Coe, Christopher L; Lubach, Gabriele R; Styner, Martin A; Johnson, G Allan

2014-11-01

Interest in mapping white matter pathways in the brain has peaked with the recognition that altered brain connectivity may contribute to a variety of neurologic and psychiatric diseases. Diffusion tractography has emerged as a popular method for postmortem brain mapping initiatives, including the ex-vivo component of the human connectome project, yet it remains unclear to what extent computer-generated tracks fully reflect the actual underlying anatomy. Of particular concern is the fact that diffusion tractography results vary widely depending on the choice of acquisition protocol. The two major acquisition variables that consume scan time, spatial resolution, and diffusion sampling, can each have profound effects on the resulting tractography. In this analysis, we determined the effects of the temporal tradeoff between spatial resolution and diffusion sampling on tractography in the ex-vivo rhesus macaque brain, a close primate model for the human brain. We used the wealth of autoradiography-based connectivity data available for the rhesus macaque brain to assess the anatomic accuracy of six time-matched diffusion acquisition protocols with varying balance between spatial and diffusion sampling. We show that tractography results vary greatly, even when the subject and the total acquisition time are held constant. Further, we found that focusing on either spatial resolution or diffusion sampling at the expense of the other is counterproductive. A balanced consideration of both sampling domains produces the most anatomically accurate and consistent results. Copyright © 2014 Wiley Periodicals, Inc.

Does the use of hormonal contraceptives cause microstructural changes in cerebral white matter? Preliminary results of a DTI and tractography study.

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De Bondt, Timo; Van Hecke, Wim; Veraart, Jelle; Leemans, Alexander; Sijbers, Jan; Sunaert, Stefan; Jacquemyn, Yves; Parizel, Paul M

2013-01-01

To evaluate the effect of monophasic combined oral contraceptive pill (COCP) and menstrual cycle phase in healthy young women on white matter (WM) organization using diffusion tensor imaging (DTI). Thirty young women were included in the study; 15 women used COCP and 15 women had a natural cycle. All subjects underwent DTI magnetic resonance imaging during the follicular and luteal phase of their cycle, or in different COCP cycle phases. DTI parameters were obtained in different WM structures by performing diffusion tensor fibre tractography. Fractional anisotropy and mean diffusivity were calculated for different WM structures. Hormonal plasma concentrations were measured in peripheral venous blood samples and correlated with the DTI findings. We found a significant difference in mean diffusivity in the fornix between the COCP and the natural cycle group. Mean diffusivity values in the fornix were negatively correlated with luteinizing hormone and estradiol blood concentrations. An important part in the limbic system, the fornix, regulates emotional processes. Differences in diffusion parameters in the fornix may contribute to behavioural alternations related to COCP use. This finding also suggests that the use of oral contraceptives needs to be taken into account when designing DTI group studies.

Killing-Yano tensors and Nambu mechanics

International Nuclear Information System (INIS)

Baleanu, D.

1998-01-01

Killing-Yano tensors were introduced in 1952 by Kentaro-Yano from mathematical point of view. The physical interpretation of Killing-Yano tensors of rank higher than two was unclear. We found that all Killing-Yano tensors η i 1 i 2 . .. i n with covariant derivative zero are Nambu tensors. We found that in the case of flat space case all Killing-Yano tensors are Nambu tensors. In the case of Taub-NUT and Kerr-Newmann metric Killing-Yano tensors of order two generate Nambu tensors of rank 3

Diagnosis of Lumbar Foraminal Stenosis using Diffusion Tensor Imaging.

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Eguchi, Yawara; Ohtori, Seiji; Suzuki, Munetaka; Oikawa, Yasuhiro; Yamanaka, Hajime; Tamai, Hiroshi; Kobayashi, Tatsuya; Orita, Sumihisa; Yamauchi, Kazuyo; Suzuki, Miyako; Aoki, Yasuchika; Watanabe, Atsuya; Kanamoto, Hirohito; Takahashi, Kazuhisa

2016-02-01

Diagnosis of lumbar foraminal stenosis remains difficult. Here, we report on a case in which bilateral lumbar foraminal stenosis was difficult to diagnose, and in which diffusion tensor imaging (DTI) was useful. The patient was a 52-year-old woman with low back pain and pain in both legs that was dominant on the right. Right lumbosacral nerve compression due to a massive uterine myoma was apparent, but the leg pain continued after a myomectomy was performed. No abnormalities were observed during nerve conduction studies. Computed tomography and magnetic resonance imaging indicated bilateral L5 lumbar foraminal stenosis. DTI imaging was done. The extraforaminal values were decreased and tractography was interrupted in the foraminal region. Bilateral L5 vertebral foraminal stenosis was treated by transforaminal lumbar interbody fusion and the pain in both legs disappeared. The case indicates the value of DTI for diagnosing vertebral foraminal stenosis.

Anti-symmetric rank-two tensor matter field on superspace for N{sub T}=2

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Spalenza, Wesley; Ney, Wander G; Helayel-Neto, J A

2004-05-06

In this work, we discuss the interaction between anti-symmetric rank-two tensor matter and topological Yang-Mills fields. The matter field considered here is the rank-2 Avdeev-Chizhov tensor matter field in a suitably extended N{sub T}=2 SUSY. We start off from the N{sub T}=2, D=4 superspace formulation and we go over to Riemannian manifolds. The matter field is coupled to the topological Yang-Mills field. We show that both actions are obtained as Q-exact forms, which allows us to express the energy-momentum tensor as Q-exact observables.

Diffusion tensor imaging of occult injury of optic radiation following optic neuritis in multiple sclerosis.

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Chen, Jiafeng; Zhu, Lijun; Li, He; Lu, Ziwen; Chen, Xin; Fang, Shaokuan

2016-10-01

Multiple sclerosis (MS) is easily detected by routine magnetic resonance imaging (MRI). However, it is not possible to detect early or occult lesions in MS by routine MRI, and this may explain the inconsistency between the severity of the lesions found by MRI and the degree of clinical disability of patients with MS. The present study included 10 patients with relapsing-remitting MS and 10 healthy volunteers. Each patient underwent routine 3.0 T MRI, diffusion tensor imaging (DTI), and diffusion tensor tractography (DTT). Optic nerve and optic radiation were analyzed by DTI and DTT. The fractional anisotropy (FA), mean diffusivity (MD), λ // , and λ ┴ values were measured. In the 10 patients with MS, 7 optic nerves were affected, and 13 optic nerves were not affected. Cranial MRI showed that optic nerve thickening and hyperintensity occurred in 2 patients with MS. In the directionally encoded color maps, a hypointensive green signal in the optic nerve was observed in 3 patients with MS. The FA values were significantly lower and the MD, λ // , and λ ┴ values were significantly higher in the affected and unaffected optic nerves and optic radiations in patients with MS in comparison with controls (P0.05). Diffusion tensor imaging is sensitive in the detection of occult injury of the optic nerve and optic radiation following optic neuritis. Diffusion tensor imaging may be a useful tool for the early diagnosis, treatment and management of MS.

Trade-off between angular and spatial resolutions in in vivo fiber tractography

OpenAIRE

Vos, Sjoerd B.; Aksoy, Murat; Han, Zhaoying; Holdsworth, Samantha J.; Maclaren, Julian; Viergever, Max A.; Leemans, Alexander; Bammer, Roland

2016-01-01

Tractography is becoming an increasingly popular method to reconstruct white matter connections in vivo. The diffusion MRI data that tractography is based on requires a high angular resolution to resolve crossing fibers whereas high spatial resolution is required to distinguish kissing from crossing fibers. However, scan time increases with increasing spatial and angular resolutions, which can become infeasible in clinical settings. Here we investigated the trade-off between spatial and angul...

Global tractography with embedded anatomical priors for quantitative connectivity analysis

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Alia eLemkaddem

2014-11-01

Full Text Available The main assumption of fiber-tracking algorithms is that fiber trajectories are represented by paths of highest diffusion, which is usually accomplished by following the principal diffusion directions estimated in every voxel from the measured diffusion MRI data. The state-of-the-art approaches, known as global tractography, reconstruct all the fiber tracts of the whole brain simultaneously by solving a global energy minimization problem. The tractograms obtained with these algorithms outperform any previous technique but, unfortunately, the price to pay is an increased computational cost which is not suitable in many practical settings, both in terms of time and memory requirements. Furthermore, existing global tractography algorithms suffer from an important shortcoming that is crucial in the context of brain connectivity analyses. As no anatomical priors are used during in the reconstruction process, the recovered fiber tracts are not guaranteed to connect cortical regions and, as a matter of fact, most of them stop prematurely in the white matter. This does not only unnecessarily slow down the estimation procedure and potentially biases any subsequent analysis but also, most importantly, prevents the de facto quantification of brain connectivity. In this work, we propose a novel approach for global tractography that is specifically designed for connectivity analysis applications by explicitly enforcing anatomical priors of the tracts in the optimization and considering the effective contribution of each of them, i.e. volume, to the acquired diffusion MRI image. We evaluated our approach on both a realistic diffusion MRI phantom and in-vivo data, and also compared its performance to existing tractography aloprithms.

Automated Whole Brain Tractography Affects Preoperative Surgical Decision Making.

Science.gov (United States)

Zakaria, Hesham; Haider, Sameah; Lee, Ian

2017-09-06

Surgery in and around eloquent brain structures poses a technical challenge when the goal of surgery is maximal safe resection. Magnetic resonance imaging (MRI) has revolutionized the diagnosis and treatment of neurological disorders, but tractography still remains limited in terms of utility because of the requisite manual labor and time required combined with the high risk of bias and inaccuracy. Automated whole brain tractography (AWBT) has simplified this workflow, overcoming historical barriers, and allowing for integration into modern neuronavigation. However, current literature showing the usefulness of this new technology is limited. In this study, we aimed to illustrate the utility of AWBT during cranial surgery and its ability to affect presurgical and intraoperative clinical decision making. We performed a retrospective chart review of cases that underwent AWBT for one year from July 2016 to July 2017. All patients underwent conventional anatomic MRI with and without contrast sequences, in addition to diffusion tensor imaging (DTI) on a 3 Tesla MRI scanner (Ingenia 3.0T, Philips, Amsterdam NL). Post-hoc AWBT processing was performed on a separate workstation. Patients were subsequently grouped into those that had undergone either language or motor mapping and those that did not. We compared both sets of patients to see any differences in patient age, sex, laterality of surgery, depth of resection from cortical surface, and smallest distance between the lesion and adjacent eloquent white matter tracts. We identified illustrative cases which demonstrated the ability of AWBT to affect surgical decision making. In this single-center series, we identified 73 total patients who underwent AWBT for intracranial surgery, of which 28 patients underwent either speech or language mapping. When comparing mapping to non-mapping patients, we found no difference with respect to age, gender, laterality of surgery, or whether the surgery was a revision. The distance

Streamline segment statistics of premixed flames with nonunity Lewis numbers

Science.gov (United States)

Chakraborty, Nilanjan; Wang, Lipo; Klein, Markus

2014-03-01

The interaction of flame and surrounding fluid motion is of central importance in the fundamental understanding of turbulent combustion. It is demonstrated here that this interaction can be represented using streamline segment analysis, which was previously applied in nonreactive turbulence. The present work focuses on the effects of the global Lewis number (Le) on streamline segment statistics in premixed flames in the thin-reaction-zones regime. A direct numerical simulation database of freely propagating thin-reaction-zones regime flames with Le ranging from 0.34 to 1.2 is used to demonstrate that Le has significant influences on the characteristic features of the streamline segment, such as the curve length, the difference in the velocity magnitude at two extremal points, and their correlations with the local flame curvature. The strengthenings of the dilatation rate, flame normal acceleration, and flame-generated turbulence with decreasing Le are principally responsible for these observed effects. An expression for the probability density function (pdf) of the streamline segment length, originally developed for nonreacting turbulent flows, captures the qualitative behavior for turbulent premixed flames in the thin-reaction-zones regime for a wide range of Le values. The joint pdfs between the streamline length and the difference in the velocity magnitude at two extremal points for both unweighted and density-weighted velocity vectors are analyzed and compared. Detailed explanations are provided for the observed differences in the topological behaviors of the streamline segment in response to the global Le.

Diffusion tensor imaging of the anterior cruciate ligament graft.

Science.gov (United States)

Van Dyck, Pieter; Froeling, Martijn; De Smet, Eline; Pullens, Pim; Torfs, Michaël; Verdonk, Peter; Sijbers, Jan; Parizel, Paul M; Jeurissen, Ben

2017-11-01

A great need exists for objective biomarkers to assess graft healing following ACL reconstruction to guide the time of return to sports. The purpose of this study was to evaluate the feasibility and reliability of diffusion tensor imaging (DTI) to delineate the anterior cruciate ligament (ACL) graft and to investigate its diffusion properties using a clinical 3T scanner. DTI of the knee (b = 0, 400, and 800 s/mm 2 , 10 diffusion directions, repeated 16 times for a total of 336 diffusion-weighted volumes) was performed at 3T in 17 patients between 3 and 7 months (mean, 4 months) following ACL reconstruction. Tractography was performed by two independent observers to delineate the ACL graft. Fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD), and radial diffusivity (RD) were calculated within the graft. Interrater reliability was assessed using the intraclass correlation coefficient (ICC) and the scan-rescan reproducibility was evaluated based on the percentage coefficient of variance (%CV) across 20 repetition bootknife samples. In all subjects, tractography of the ACL graft was feasible. Quantitative evaluation of the diffusion properties of the ACL graft yielded the following mean ± SD values: FA = 0.23 ± 0.04; MD = 1.30 ± 0.11 × 10 -3 mm 2 /s; AD = 1.61 ± 0.12 × 10 -3 mm 2 /s, and RD = 1.15 ± 0.11 × 10 -3 mm 2 /s. Interrater reliability for the DTI parameters was excellent (ICC = 0.91-0.98). Mean %CVs for FA, MD, AD, and RD were 4.6%, 3.5%, 3.7%, and 4.4%, respectively. We demonstrated the feasibility and reliability of DTI for the visualization and quantitative evaluation of the ACL graft at 3T. 3 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2017;46:1423-1432. © 2017 International Society for Magnetic Resonance in Medicine.

MR tractography; Visualization of structure of nerve fiber system from diffusion weighted images with maximum intensity projection method

Energy Technology Data Exchange (ETDEWEB)

Kinosada, Yasutomi; Okuda, Yasuyuki (Mie Univ., Tsu (Japan). School of Medicine); Ono, Mototsugu (and others)

1993-02-01

We developed a new noninvasive technique to visualize the anatomical structure of the nerve fiber system in vivo, and named this technique magnetic resonance (MR) tractography and the acquired image an MR tractogram. MR tractography has two steps. One is to obtain diffusion-weighted images sensitized along axes appropriate for depicting the intended nerve fibers with anisotropic water diffusion MR imaging. The other is to extract the anatomical structure of the nerve fiber system from a series of diffusion-weighted images by the maximum intensity projection method. To examine the clinical usefulness of the proposed technique, many contiguous, thin (3 mm) coronal two-dimensional sections of the brain were acquired sequentially in normal volunteers and selected patients with paralyses, on a 1.5 Tesla MR system (Signa, GE) with an ECG-gated Stejskal-Tanner pulse sequence. The structure of the nerve fiber system of normal volunteers was almost the same as the anatomy. The tractograms of patients with paralyses clearly showed the degeneration of nerve fibers and were correlated with clinical symptoms. MR tractography showed great promise for the study of neuroanatomy and neuroradiology. (author).

Two new eigenvalue localization sets for tensors and theirs applications

Directory of Open Access Journals (Sweden)

Zhao Jianxing

2017-10-01

Full Text Available A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Qi (J. Symbolic Comput., 2005, 40, 1302-1324 and Li et al. (Numer. Linear Algebra Appl., 2014, 21, 39-50. As an application, a weaker checkable sufficient condition for the positive (semi-definiteness of an even-order real symmetric tensor is obtained. Meanwhile, an S-type E-eigenvalue localization set for tensors is given and proved to be tighter than that presented by Wang et al. (Discrete Cont. Dyn.-B, 2017, 22(1, 187-198. As an application, an S-type upper bound for the Z-spectral radius of weakly symmetric nonnegative tensors is obtained. Finally, numerical examples are given to verify the theoretical results.

Altered structural connectivity of pain-related brain network in burning mouth syndrome-investigation by graph analysis of probabilistic tractography.

Science.gov (United States)

Wada, Akihiko; Shizukuishi, Takashi; Kikuta, Junko; Yamada, Haruyasu; Watanabe, Yusuke; Imamura, Yoshiki; Shinozaki, Takahiro; Dezawa, Ko; Haradome, Hiroki; Abe, Osamu

2017-05-01

Burning mouth syndrome (BMS) is a chronic intraoral pain syndrome featuring idiopathic oral pain and burning discomfort despite clinically normal oral mucosa. The etiology of chronic pain syndrome is unclear, but preliminary neuroimaging research has suggested the alteration of volume, metabolism, blood flow, and diffusion at multiple brain regions. According to the neuromatrix theory of Melzack, pain sense is generated in the brain by the network of multiple pain-related brain regions. Therefore, the alteration of pain-related network is also assumed as an etiology of chronic pain. In this study, we investigated the brain network of BMS brain by using probabilistic tractography and graph analysis. Fourteen BMS patients and 14 age-matched healthy controls underwent 1.5T MRI. Structural connectivity was calculated in 83 anatomically defined regions with probabilistic tractography of 60-axis diffusion tensor imaging and 3D T1-weighted imaging. Graph theory network analysis was used to evaluate the brain network at local and global connectivity. In BMS brain, a significant difference of local brain connectivity was recognized at the bilateral rostral anterior cingulate cortex, right medial orbitofrontal cortex, and left pars orbitalis which belong to the medial pain system; however, no significant difference was recognized at the lateral system including the somatic sensory cortex. A strengthened connection of the anterior cingulate cortex and medial prefrontal cortex with the basal ganglia, thalamus, and brain stem was revealed. Structural brain network analysis revealed the alteration of the medial system of the pain-related brain network in chronic pain syndrome.

Seeing More by Showing Less: Orientation-Dependent Transparency Rendering for Fiber Tractography Visualization

OpenAIRE

Tax, Chantal M. W.; Chamberland, Maxime; van Stralen, Marijn; Viergever, Max A.; Whittingstall, Kevin; Fortin, David; Descoteaux, Maxime; Leemans, Alexander

2015-01-01

Fiber tractography plays an important role in exploring the architectural organization of fiber trajectories, both in fundamental neuroscience and in clinical applications. With the advent of diffusion MRI (dMRI) approaches that can also model "crossing fibers", the complexity of the fiber network as reconstructed with tractography has increased tremendously. Many pathways interdigitate and overlap, which hampers an unequivocal 3D visualization of the network and impedes an efficient study of...

Connectomic disturbances in attention-deficit/hyperactivity disorder: a whole-brain tractography analysis.

Science.gov (United States)

Hong, Soon-Beom; Zalesky, Andrew; Fornito, Alex; Park, Subin; Yang, Young-Hui; Park, Min-Hyeon; Song, In-Chan; Sohn, Chul-Ho; Shin, Min-Sup; Kim, Bung-Nyun; Cho, Soo-Churl; Han, Doug Hyun; Cheong, Jae Hoon; Kim, Jae-Won

2014-10-15

Few studies have sought to identify, in a regionally unbiased way, the precise cortical and subcortical regions that are affected by white matter abnormalities in attention-deficit/hyperactivity disorder (ADHD). This study aimed to derive a comprehensive, whole-brain characterization of connectomic disturbances in ADHD. Using diffusion tensor imaging, whole-brain tractography, and an imaging connectomics approach, we characterized altered white matter connectivity in 71 children and adolescents with ADHD compared with 26 healthy control subjects. White matter differences were further delineated between patients with (n = 40) and without (n = 26) the predominantly hyperactive/impulsive subtype of ADHD. A significant network comprising 25 distinct fiber bundles linking 23 different brain regions spanning frontal, striatal, and cerebellar brain regions showed altered white matter structure in ADHD patients (p attentional disturbances. Attention-deficit/hyperactivity disorder subtypes were differentiated by a right-lateralized network (p attentional performance underscore the functional importance of these connectomic disturbances for the clinical phenotype of ADHD. A distributed pattern of white matter microstructural integrity separately involving frontal, striatal, and cerebellar brain regions, rather than direct frontostriatal connectivity, appears to be disrupted in children and adolescents with ADHD. Copyright © 2014 Society of Biological Psychiatry. Published by Elsevier Inc. All rights reserved.

Fiber architecture in remodeled myocardium revealed with a quantitative diffusion CMR tractography framework and histological validation

Directory of Open Access Journals (Sweden)

Mekkaoui Choukri

2012-10-01

Full Text Available Abstract Background The study of myofiber reorganization in the remote zone after myocardial infarction has been performed in 2D. Microstructural reorganization in remodeled hearts, however, can only be fully appreciated by considering myofibers as continuous 3D entities. The aim of this study was therefore to develop a technique for quantitative 3D diffusion CMR tractography of the heart, and to apply this method to quantify fiber architecture in the remote zone of remodeled hearts. Methods Diffusion Tensor CMR of normal human, sheep, and rat hearts, as well as infarcted sheep hearts was performed ex vivo. Fiber tracts were generated with a fourth-order Runge-Kutta integration technique and classified statistically by the median, mean, maximum, or minimum helix angle (HA along the tract. An index of tract coherence was derived from the relationship between these HA statistics. Histological validation was performed using phase-contrast microscopy. Results In normal hearts, the subendocardial and subepicardial myofibers had a positive and negative HA, respectively, forming a symmetric distribution around the midmyocardium. However, in the remote zone of the infarcted hearts, a significant positive shift in HA was observed. The ratio between negative and positive HA variance was reduced from 0.96 ± 0.16 in normal hearts to 0.22 ± 0.08 in the remote zone of the remodeled hearts (p Conclusions A significant reorganization of the 3D fiber continuum is observed in the remote zone of remodeled hearts. The positive (rightward shift in HA in the remote zone is greatest in the subepicardium, but involves all layers of the myocardium. Tractography-based quantification, performed here for the first time in remodeled hearts, may provide a framework for assessing regional changes in the left ventricle following infarction.

Multiple sclerosis: changes in microarchitecture of white matter tracts after training with a video game balance board.

Science.gov (United States)

Prosperini, Luca; Fanelli, Fulvia; Petsas, Nikolaos; Sbardella, Emilia; Tona, Francesca; Raz, Eytan; Fortuna, Deborah; De Angelis, Floriana; Pozzilli, Carlo; Pantano, Patrizia

2014-11-01

To determine if high-intensity, task-oriented, visual feedback training with a video game balance board (Nintendo Wii) induces significant changes in diffusion-tensor imaging ( DTI diffusion-tensor imaging ) parameters of cerebellar connections and other supratentorial associative bundles and if these changes are related to clinical improvement in patients with multiple sclerosis. The protocol was approved by local ethical committee; each participant provided written informed consent. In this 24-week, randomized, two-period crossover pilot study, 27 patients underwent static posturography and brain magnetic resonance (MR) imaging at study entry, after the first 12-week period, and at study termination. Thirteen patients started a 12-week training program followed by a 12-week period without any intervention, while 14 patients received the intervention in reverse order. Fifteen healthy subjects also underwent MR imaging once and underwent static posturography. Virtual dissection of white matter tracts was performed with streamline tractography; values of DTI diffusion-tensor imaging parameters were then obtained for each dissected tract. Repeated measures analyses of variance were performed to evaluate whether DTI diffusion-tensor imaging parameters significantly changed after intervention, with false discovery rate correction for multiple hypothesis testing. There were relevant differences between patients and healthy control subjects in postural sway and DTI diffusion-tensor imaging parameters (P balance improvement detected at static posturography (r = -0.381 to 0.401, P balance board system modified the microstructure of superior cerebellar peduncles. The clinical improvement observed after training might be mediated by enhanced myelination-related processes, suggesting that high-intensity, task-oriented exercises could induce favorable microstructural changes in the brains of patients with multiple sclerosis.

Efficient Tensor Completion for Color Image and Video Recovery: Low-Rank Tensor Train.

Science.gov (United States)

Bengua, Johann A; Phien, Ho N; Tuan, Hoang Duong; Do, Minh N

2017-05-01

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via TT (SiLRTC-TT) is intimately related to minimizing a nuclear norm based on TT rank. The second one is from a multilinear matrix factorization model to approximate the TT rank of a tensor, and is called tensor completion by parallel matrix factorization via TT (TMac-TT). A tensor augmentation scheme of transforming a low-order tensor to higher orders is also proposed to enhance the effectiveness of SiLRTC-TT and TMac-TT. Simulation results for color image and video recovery show the clear advantage of our method over all other methods.

Migration transformation of two-dimensional magnetic vector and tensor fields

DEFF Research Database (Denmark)

Zhdanov, Michael; Cai, Hongzhu; Wilson, Glenn

2012-01-01

We introduce a new method of rapid interpretation of magnetic vector and tensor field data, based on ideas of potential field migration which extends the general principles of seismic and electromagnetic migration to potential fields. 2-D potential field migration represents a direct integral...... to the downward continuation of a well-behaved analytical function. We present case studies for imaging of SQUID-based magnetic tensor data acquired over a magnetite skarn at Tallawang, Australia. The results obtained from magnetic tensor field migration agree very well with both Euler deconvolution and the known...

Predictability of motor outcome according to the time of diffusion tensor imaging in patients with cerebral infarct

Energy Technology Data Exchange (ETDEWEB)

Kwon, Yong Hyun [Yeungnam College of Science and Technology, Department of Physical Therapy, Taegu (Korea, Republic of); Jeoung, Yong Jae [Yeungnam University, Department of Physical Medicine and Rehabilitation, College of Medicine, Taegu (Korea, Republic of); Lee, Jun [Yeungnam University, Department of Neurology, College of Medicine, Taegu (Korea, Republic of); Son, Su Min; Jang, Sung Ho [Yeungnam University 317-1, Department of Physical Medicine and Rehabilitation, College of Medicine, Taegu (Korea, Republic of); Kim, Saeyoon [Yeungnam University, Department of Pediatrics, College of Medicine, Taegu (Korea, Republic of); Kim, Chulseung [Medical Devices Clinical Trial Center of Yeungnam University Hospital, Taegu (Korea, Republic of)

2012-07-15

Predictability of diffusion tensor imaging tractography (DTT) for motor outcome can differ according to the time of DTT. We attempted to compare the predictability for motor outcome according to the time of diffusion tensor imaging (DTI) by analyzing the corticospinal tract (CST) integrity on DTT in patients with corona radiata (CR) infarct. Seventy-one consecutive hemiparetic patients with CR infarct were recruited. Motor function of the affected extremities was measured twice: at onset and at 6 months from onset. According to the time of DTI, patients were classified into two groups: the early scanning group (ES group) within 14 days since stroke onset; and the late scanning group (LS group) 15-28 days. Motor outcome was compared with the CST integrity on DTT. Motor prognosis was predicted from scan time of DTI and the CST integrity on DTT in the logistic regression model. According to separate regression analysis, the CST integrity of the late group was found to predict MI score (OR = 14.000, 95% CI = 3.194-61.362, p < 0.05), whereas the CST integrity of the early group was not found to predict MI score. In terms of both positive and negative predictabilities, we found that predictability of DTT for motor outcome was better in patients who were scanned later (15-28 days after onset) than in patients who were scanned earlier (1-14 days after onset). (orig.)

Predictability of motor outcome according to the time of diffusion tensor imaging in patients with cerebral infarct

International Nuclear Information System (INIS)

Kwon, Yong Hyun; Jeoung, Yong Jae; Lee, Jun; Son, Su Min; Jang, Sung Ho; Kim, Saeyoon; Kim, Chulseung

2012-01-01

Predictability of diffusion tensor imaging tractography (DTT) for motor outcome can differ according to the time of DTT. We attempted to compare the predictability for motor outcome according to the time of diffusion tensor imaging (DTI) by analyzing the corticospinal tract (CST) integrity on DTT in patients with corona radiata (CR) infarct. Seventy-one consecutive hemiparetic patients with CR infarct were recruited. Motor function of the affected extremities was measured twice: at onset and at 6 months from onset. According to the time of DTI, patients were classified into two groups: the early scanning group (ES group) within 14 days since stroke onset; and the late scanning group (LS group) 15-28 days. Motor outcome was compared with the CST integrity on DTT. Motor prognosis was predicted from scan time of DTI and the CST integrity on DTT in the logistic regression model. According to separate regression analysis, the CST integrity of the late group was found to predict MI score (OR = 14.000, 95% CI = 3.194-61.362, p < 0.05), whereas the CST integrity of the early group was not found to predict MI score. In terms of both positive and negative predictabilities, we found that predictability of DTT for motor outcome was better in patients who were scanned later (15-28 days after onset) than in patients who were scanned earlier (1-14 days after onset). (orig.)

Identification of the pyramidal tract by neuronavigation based on intraoperative magnetic resonance tractography: correlation with subcortical stimulation

Energy Technology Data Exchange (ETDEWEB)

Bozzao, Alessandro; Romano, Andrea; Calabria, Luigi Fausto; Coppola, Valeria; Fantozzi, Luigi Maria [University of Rome Sapienza, Department of Neuroradiology, Rome (Italy); Angelini, Albina; D' Andrea, Giancarlo; Mastronardi, Luciano; Ferrante, Luigi [University of Rome Sapienza, Department of Neurosurgery, Rome (Italy)

2010-10-15

To demonstrate the accuracy of magnetic resonance tractography (MRT) in localizing the cortical spinal tract (CST) close to brain tumours by using intraoperative electric subcortical stimulation. Nine patients with intra-axial brain tumours underwent neurosurgery. Planning was based on analysis of the course of streamlines compatible with the CST. After tumour removal, intraoperative MRT was reacquired. Sites at various distance from the CST were repeatedly stimulated to assess whether registered motor evoked potential (MEP) could be elicited. All patients were assessed clinically both pre- and postoperatively. The motor function was preserved in all patients. In all patients intraoperative MRT demonstrated shift of the bundle position caused by the surgical procedure. The distance between the estimated intraoperative CST and the point of elicited MEP was 1 cm or less in all nine patients. At distances greater than 2 cm, no patient reported positive MEP. Intraoperative MRT is a reliable technique for localization of CST. In all patients MEP were elicited by direct subcortical electrical stimulation at a distance below 1 cm from the CST as represented by MRT. Brain shifting might impact this evaluation since CST position may change during surgery in the range of 8 mm. (orig.)

Identification of the pyramidal tract by neuronavigation based on intraoperative magnetic resonance tractography: correlation with subcortical stimulation

International Nuclear Information System (INIS)

Bozzao, Alessandro; Romano, Andrea; Calabria, Luigi Fausto; Coppola, Valeria; Fantozzi, Luigi Maria; Angelini, Albina; D'Andrea, Giancarlo; Mastronardi, Luciano; Ferrante, Luigi

2010-01-01

To demonstrate the accuracy of magnetic resonance tractography (MRT) in localizing the cortical spinal tract (CST) close to brain tumours by using intraoperative electric subcortical stimulation. Nine patients with intra-axial brain tumours underwent neurosurgery. Planning was based on analysis of the course of streamlines compatible with the CST. After tumour removal, intraoperative MRT was reacquired. Sites at various distance from the CST were repeatedly stimulated to assess whether registered motor evoked potential (MEP) could be elicited. All patients were assessed clinically both pre- and postoperatively. The motor function was preserved in all patients. In all patients intraoperative MRT demonstrated shift of the bundle position caused by the surgical procedure. The distance between the estimated intraoperative CST and the point of elicited MEP was 1 cm or less in all nine patients. At distances greater than 2 cm, no patient reported positive MEP. Intraoperative MRT is a reliable technique for localization of CST. In all patients MEP were elicited by direct subcortical electrical stimulation at a distance below 1 cm from the CST as represented by MRT. Brain shifting might impact this evaluation since CST position may change during surgery in the range of 8 mm. (orig.)

Probabilistic Tractography Recovers a Rostrocaudal Trajectory of Connectivity Variability in the Human Insular Cortex

Science.gov (United States)

Cerliani, Leonardo; Thomas, Rajat M; Jbabdi, Saad; Siero, Jeroen CW; Nanetti, Luca; Crippa, Alessandro; Gazzola, Valeria; D'Arceuil, Helen; Keysers, Christian

2012-01-01

The insular cortex of macaques has a wide spectrum of anatomical connections whose distribution is related to its heterogeneous cytoarchitecture. Although there is evidence of a similar cytoarchitectural arrangement in humans, the anatomical connectivity of the insula in the human brain has not yet been investigated in vivo. In the present work, we used in vivo probabilistic white-matter tractography and Laplacian eigenmaps (LE) to study the variation of connectivity patterns across insular territories in humans. In each subject and hemisphere, we recovered a rostrocaudal trajectory of connectivity variation ranging from the anterior dorsal and ventral insula to the dorsal caudal part of the long insular gyri. LE suggested that regional transitions among tractography patterns in the insula occur more gradually than in other brain regions. In particular, the change in tractography patterns was more gradual in the insula than in the medial premotor region, where a sharp transition between different tractography patterns was found. The recovered trajectory of connectivity variation in the insula suggests a relation between connectivity and cytoarchitecture in humans resembling that previously found in macaques: tractography seeds from the anterior insula were mainly found in limbic and paralimbic regions and in anterior parts of the inferior frontal gyrus, while seeds from caudal insular territories mostly reached parietal and posterior temporal cortices. Regions in the putative dysgranular insula displayed more heterogeneous connectivity patterns, with regional differences related to the proximity with either putative granular or agranular regions. Hum Brain Mapp 33:2005–2034, 2012. © 2011 Wiley Periodicals, Inc. PMID:21761507

Accelerated Logistics: Streamlining the Army's Supply Chain

National Research Council Canada - National Science Library

Wang, Mark

2000-01-01

...) initiative, the Army has dramatically streamlined its supply chain, cutting order and ship times for repair parts by nearly two-thirds nationwide and over 75 percent at several of the major Forces Command (FORSCOM) installations...

Mapping population-based structural connectomes.

Science.gov (United States)

Zhang, Zhengwu; Descoteaux, Maxime; Zhang, Jingwen; Girard, Gabriel; Chamberland, Maxime; Dunson, David; Srivastava, Anuj; Zhu, Hongtu

2018-05-15

Advances in understanding the structural connectomes of human brain require improved approaches for the construction, comparison and integration of high-dimensional whole-brain tractography data from a large number of individuals. This article develops a population-based structural connectome (PSC) mapping framework to address these challenges. PSC simultaneously characterizes a large number of white matter bundles within and across different subjects by registering different subjects' brains based on coarse cortical parcellations, compressing the bundles of each connection, and extracting novel connection weights. A robust tractography algorithm and streamline post-processing techniques, including dilation of gray matter regions, streamline cutting, and outlier streamline removal are applied to improve the robustness of the extracted structural connectomes. The developed PSC framework can be used to reproducibly extract binary networks, weighted networks and streamline-based brain connectomes. We apply the PSC to Human Connectome Project data to illustrate its application in characterizing normal variations and heritability of structural connectomes in healthy subjects. Copyright © 2018 Elsevier Inc. All rights reserved.

Diffusion abnormalities of the uncinate fasciculus in Alzheimer's disease: diffusion tensor tract-specific analysis using a new method to measure the core of the tract

International Nuclear Information System (INIS)

Yasmin, Hasina; Nakata, Yasuhiro; Abe, Osamu; Masutani, Yoshitaka; Ohtomo, Kuni; Aoki, Shigeki; Sato, Noriko; Nemoto, Kiyotaka; Arima, Kunimasa; Furuta, Nobuo; Uno, Masatake; Hirai, Shigeo

2008-01-01

Our aim was to determine diffusion abnormalities in the uncinate fasciculus (UF) in Alzheimer's disease (AD) by diffusion tensor tractography (DTT) using a new method for measuring the core of the tract. We studied 19 patients with AD and 19 age-matched control subjects who underwent MRI using diffusion tensor imaging (DTI). DTT of the UF was generated. The mean diffusivity (MD) and fractional anisotropy (FA) of the core of the tract were measured after voxelized tract shape processing. Student's t-test was used to compare results between patients with AD and controls. Intraobserver correlation tests were also performed. FA was significantly lower (P 0.93 for measured FA and r > 0.92 for measured MD. Our results suggest that FA reflects progression of AD-related histopathological changes in the UF of the white matter and may represent a useful biological index in monitoring AD. Diffusion tensor tract-specific analysis with voxelized tract shape processing to measure the core of the tract may be a sensitive tool for evaluation of diffusion abnormalities of white matter tracts in AD. (orig.)

Gogny interactions with tensor terms

Energy Technology Data Exchange (ETDEWEB)

Anguiano, M.; Lallena, A.M.; Bernard, R.N. [Universidad de Granada, Departamento de Fisica Atomica, Molecular y Nuclear, Granada (Spain); Co' , G. [INFN, Lecce (Italy); De Donno, V. [Universita del Salento, Dipartimento di Matematica e Fisica ' ' E. De Giorgi' ' , Lecce (Italy); Grasso, M. [Universite Paris-Sud, Institut de Physique Nucleaire, IN2P3-CNRS, Orsay (France)

2016-07-15

We present a perturbative approach to include tensor terms in the Gogny interaction. We do not change the values of the usual parameterisations, with the only exception of the spin-orbit term, and we add tensor terms whose only free parameters are the strengths of the interactions. We identify observables sensitive to the presence of the tensor force in Hartree-Fock, Hartree-Fock-Bogoliubov and random phase approximation calculations. We show the need of including two tensor contributions, at least: a pure tensor term and a tensor-isospin term. We show results relevant for the inclusion of the tensor term for single-particle energies, charge-conserving magnetic excitations and Gamow-Teller excitations. (orig.)

Feasibility of Diffusion Tensor Imaging for Assessing Functional Recovery in Rats with Olfactory Ensheathing Cell Transplantation After Contusive Spinal Cord Injury (SCI).

Science.gov (United States)

Gu, Mengchao; Gao, Zhengchao; Li, Xiaohui; Zhao, Feng; Guo, Lei; Liu, Jiantao; He, Xijing

2017-06-17

BACKGROUND Olfactory ensheathing cell transplantation is a promising treatment for spinal cord injury. Diffusion tensor imaging has been applied to assess various kinds of spinal cord injury. However, it has rarely been used to evaluate the beneficial effects of olfactory ensheathing cell transplantation. This study aimed to explore the feasibility of diffusion tensor imaging in the evaluation of functional recovery in rats with olfactory ensheathing cell transplantation after contusive spinal cord injury. MATERIAL AND METHODS Immunofluorescence staining was performed to determine the purity of olfactory ensheathing cells. Rats received cell transplantation at week 1 after injury. Basso, Beattie, and Bresnahan score was used to assess the functional recovery. Magnetic resonance imaging was applied weekly, including diffusion tensor imaging. Diffusion tensor tractography was reconstructed to visualize the repair process. RESULTS The results showed that olfactory ensheathing cell transplantation increased the functional and histological recovery and restrained the secondary injury process after the initial spinal cord injury. The fractional anisotropy values in rats with cell transplantation were significantly higher than those in the control group, while the apparent diffusion coefficient values were significantly lower. Basso, Beattie, and Bresnahan score was positively and linearly correlated with fractional anisotropy value, and it was negatively and linearly correlated with apparent diffusion coefficient value. CONCLUSIONS These findings suggest that diffusion tensor imaging parameters are sensitive biomarker indices for olfactory ensheathing cell transplantation interventions, and diffusion tensor imaging scan can reflect the functional recovery promoted by the olfactory ensheathing cell transplantation after contusive spinal cord injury.

Energy-momentum tensor in theories with scalar fields and two coupling constants. I. Non-Abelian case

International Nuclear Information System (INIS)

Joglekar, S.D.; Misra, A.

1989-01-01

In this paper, we generalize our earlier discussion of renormalization of the energy-momentum tensor in scalar QED to that in non-Abelian gauge theories involving scalar fields. We show the need for adding an improvement term to the conventional energy-momentum tensor. We consider two possible forms for the improvement term: (i) one in which the improvement coefficient is a finite function of bare parameters of the theory (so that the energy-momentum tensor can be derived from an action that is a finite function of bare quantities); (ii) one in which the improvement coefficient is a finite quantity, i.e., a finite function of renormalized parameters. We establish a negative result; viz., neither form leads to a finite energy-momentum tensor to O(e 2 λ/sup n/)

Two-body tensor interactions in the nuclear matter response function

International Nuclear Information System (INIS)

Besprosvany, J.

1997-01-01

The inclusive scattering response of nuclear matter is studied in the regime of large momentum transfer q, and around the quasielastic peak. We review interaction corrections to free propagation as embodied in the impulse approximation. Calculations of the two-body and many-body corrections within an eikonal approach are presented. These use an approximated two-body density matrix which takes account of spin and isospin degrees of freedom. Both calculations give similar and sizable corrections at q = 550 MeV and reproduce data extrapolated from finite nuclei; this indicates the relevance of two-body tensor contributions in this regime. (Author)

Tensor spaces and exterior algebra

CERN Document Server

Yokonuma, Takeo

1992-01-01

This book explains, as clearly as possible, tensors and such related topics as tensor products of vector spaces, tensor algebras, and exterior algebras. You will appreciate Yokonuma's lucid and methodical treatment of the subject. This book is useful in undergraduate and graduate courses in multilinear algebra. Tensor Spaces and Exterior Algebra begins with basic notions associated with tensors. To facilitate understanding of the definitions, Yokonuma often presents two or more different ways of describing one object. Next, the properties and applications of tensors are developed, including the classical definition of tensors and the description of relative tensors. Also discussed are the algebraic foundations of tensor calculus and applications of exterior algebra to determinants and to geometry. This book closes with an examination of algebraic systems with bilinear multiplication. In particular, Yokonuma discusses the theory of replicas of Chevalley and several properties of Lie algebras deduced from them.

Probabilistic Tractography of the Cranial Nerves in Vestibular Schwannoma.

Science.gov (United States)

Zolal, Amir; Juratli, Tareq A; Podlesek, Dino; Rieger, Bernhard; Kitzler, Hagen H; Linn, Jennifer; Schackert, Gabriele; Sobottka, Stephan B

2017-11-01

Multiple recent studies have reported on diffusion tensor-based fiber tracking of cranial nerves in vestibular schwannoma, with conflicting results as to the accuracy of the method and the occurrence of cochlear nerve depiction. Probabilistic nontensor-based tractography might offer advantages in terms of better extraction of directional information from the underlying data in cranial nerves, which are of subvoxel size. Twenty-one patients with large vestibular schwannomas were recruited. The probabilistic tracking was run preoperatively and the position of the potential depictions of the facial and cochlear nerves was estimated postoperatively by 3 independent observers in a blinded fashion. The true position of the nerve was determined intraoperatively by the surgeon. Thereafter, the imaging-based estimated position was compared with the intraoperatively determined position. Tumor size, cystic appearance, and postoperative House-Brackmann score were analyzed with regard to the accuracy of the depiction of the nerves. The probabilistic tracking showed a connection that correlated to the position of the facial nerve in 81% of the cases and to the position of the cochlear nerve in 33% of the cases. Altogether, the resulting depiction did not correspond to the intraoperative position of any of the nerves in 3 cases. In a majority of cases, the position of the facial nerve, but not of the cochlear nerve, could be estimated by evaluation of the probabilistic tracking results. However, false depictions not corresponding to any nerve do occur and cannot be discerned as such from the image only. Copyright © 2017 Elsevier Inc. All rights reserved.

Diffusion abnormalities of the uncinate fasciculus in Alzheimer's disease: diffusion tensor tract-specific analysis using a new method to measure the core of the tract

Energy Technology Data Exchange (ETDEWEB)

Yasmin, Hasina; Nakata, Yasuhiro; Abe, Osamu; Masutani, Yoshitaka; Ohtomo, Kuni [University of Tokyo, Department of Radiology, Tokyo (Japan); Aoki, Shigeki [University of Tokyo, Department of Radiology, Tokyo (Japan); Sato, Noriko [National Center of Neurology and Psychiatry, Department of Radiology, National Center Hospital for Mental, Nervous and Muscular Disorders, Tokyo (Japan); Nemoto, Kiyotaka [Ibaraki Prefectural Tomobe Hospital, Department of Psychiatry, Ibaraki (Japan); Arima, Kunimasa; Furuta, Nobuo [National Center of Neurology and Psychiatry, Department of Psychiatry, National Center Hospital for Mental, Nervous and Muscular Disorders, Tokyo (Japan); Uno, Masatake [Yoshioka Rehabilitation Clinic, Department of Psychiatry, Tokyo (Japan); Hirai, Shigeo [Iruma Hirai Clinic, Department of Psychiatry, Saitama (Japan)

2008-04-15

Our aim was to determine diffusion abnormalities in the uncinate fasciculus (UF) in Alzheimer's disease (AD) by diffusion tensor tractography (DTT) using a new method for measuring the core of the tract. We studied 19 patients with AD and 19 age-matched control subjects who underwent MRI using diffusion tensor imaging (DTI). DTT of the UF was generated. The mean diffusivity (MD) and fractional anisotropy (FA) of the core of the tract were measured after voxelized tract shape processing. Student's t-test was used to compare results between patients with AD and controls. Intraobserver correlation tests were also performed. FA was significantly lower (P < 0.0001) in the UF of patients with AD than of controls. There was no significant difference in MD along the UF between the two groups. Intraobserver reliability (intraclass correlation coefficient) for the first and second measurement was r > 0.93 for measured FA and r > 0.92 for measured MD. Our results suggest that FA reflects progression of AD-related histopathological changes in the UF of the white matter and may represent a useful biological index in monitoring AD. Diffusion tensor tract-specific analysis with voxelized tract shape processing to measure the core of the tract may be a sensitive tool for evaluation of diffusion abnormalities of white matter tracts in AD. (orig.)

Identification of Stria Medullaris Fibers in the Massa Intermedia Using Diffusion Tensor Imaging.

Science.gov (United States)

Kochanski, Ryan B; Dawe, Robert; Kocak, Mehmet; Sani, Sepehr

2018-04-01

The massa intermedia (MI) or interthalamic adhesion is an inconsistent band spanning between bilateral medial thalami that is absent in up to 20%-30% of individuals. Little is known of its significance, especially in regard to functional pathways. Probabilistic diffusion tensor imaging (DTI) has recently been used to seed the lateral habenula and define its afferent white matter pathway, the stria medullaris thalami (SM). We sought to determine whether the MI serves as a conduit for crossing of limbic fibers such as the SM. Probabilistic DTI was performed on 10 subjects who had presence of a MI as visualized on magnetic resonance imaging. Tractography was also performed on 2 subjects without MI. Manual identification of the lateral habenula on axial T1-weighted magnetic resonance imaging was used for the initial seed region for tractography. In all subjects, the SM was reliably visualized. In 7 of the 10 subjects with MI, there was evidence of SM fibers that crossed to the ipsilateral hemisphere. Three subjects with small diameter MI did not have tractographic evidence of crossing SM fibers. Of the 7 subjects with crossing SM fibers within the MI, 5 showed predilection toward the right orbitofrontal cortex from both the left and right seed regions. Probabilistic DTI provides evidence of SM fibers within the MI. Given its anatomic location as a bridging pathway between thalami, further studies are necessary to assess its role within the limbic functional network. Copyright © 2018 Elsevier Inc. All rights reserved.

Delineating Neural Structures of Developmental Human Brains with Diffusion Tensor Imaging

Directory of Open Access Journals (Sweden)

Hao Huang

2010-01-01

Full Text Available The human brain anatomy is characterized by dramatic structural changes during fetal development. It is extraordinarily complex and yet its origin is a simple tubular structure. Revealing detailed anatomy at different stages of brain development not only aids in understanding this highly ordered process, but also provides clues to detect abnormalities caused by genetic or environmental factors. However, anatomical studies of human brain development during the fetal period are surprisingly scarce and histology-based atlases have become available only recently. Diffusion tensor imaging (DTI measures water diffusion to delineate the underlying neural structures. The high contrasts derived from DTI can be used to establish the brain atlas. With DTI tractography, coherent neural structures, such as white matter tracts, can be three-dimensionally reconstructed. The primary eigenvector of the diffusion tensor can be further explored to characterize microstructures in the cerebral wall of the developmental brains. In this mini-review, the application of DTI in order to reveal the structures of developmental fetal brains has been reviewed in the above-mentioned aspects. The fetal brain DTI provides a unique insight for delineating the neural structures in both macroscopic and microscopic levels. The resultant DTI database will provide structural guidance for the developmental study of human fetal brains in basic neuroscience, and reference standards for diagnostic radiology of premature newborns.

Joint Multi-Fiber NODDI Parameter Estimation and Tractography using the Unscented Information Filter

Directory of Open Access Journals (Sweden)

Yogesh eRathi

2016-04-01

Full Text Available Tracing white matter fiber bundles is an integral part of analyzing brain connectivity. An accurate estimate of the underlying tissue parameters is also paramount in several neuroscience applications. In this work, we propose to use a joint fiber model estimation and tractography algorithm that uses the NODDI (neurite orientation dispersion diffusion imaging model to estimate fiber orientation dispersion consistently and smoothly along the fiber tracts along with estimating the intracellular and extracellular volume fractions from the diffusion signal. While the NODDI model has been used in earlier works to estimate the microstructural parameters at each voxel independently, for the first time, we propose to integrate it into a tractography framework. We extend this framework to estimate the NODDI parameters for two crossing fibers, which is imperative to trace fiber bundles through crossings as well as to estimate the microstructural parameters for each fiber bundle separately. We propose to use the unscented information filter (UIF to accurately estimate the model parameters and perform tractography. The proposed approach has significant computational performance improvements as well as numerical robustness over the unscented Kalman filter (UKF. Our method not only estimates the confidence in the estimated parameters via the covariance matrix, but also provides the Fisher-information matrix of the state variables (model parameters, which can be quite useful to measure model complexity. Results from in-vivo human brain data sets demonstrate the ability of our algorithm to trace through crossing fiber regions, while estimating orientation dispersion and other biophysical model parameters in a consistent manner along the tracts.

Tensor rank is not multiplicative under the tensor product

NARCIS (Netherlands)

M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)

2018-01-01

textabstractThe tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the

Tensor rank is not multiplicative under the tensor product

NARCIS (Netherlands)

M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)

2017-01-01

textabstractThe tensor rank of a tensor is the smallest number r such that the tensor can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor (not to be confused with the "tensor Kronecker product" used in

Tensor rank is not multiplicative under the tensor product

OpenAIRE

Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen

2017-01-01

The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection between restrictions and degenerations. A result of our study is that tensor rank is not in general multiplicative under the tensor product. This answers a question of Draisma and Saptharishi. Specif...

Parotid gland tumours: MR tractography to assess contact with the facial nerve.

Science.gov (United States)

Attyé, Arnaud; Karkas, Alexandre; Troprès, Irène; Roustit, Matthieu; Kastler, Adrian; Bettega, Georges; Lamalle, Laurent; Renard, Félix; Righini, Christian; Krainik, Alexandre

2016-07-01

To assess the feasibility of intraparotid facial nerve (VIIn) tractographic reconstructions in estimating the presence of a contact between the VIIn and the tumour, in patients requiring surgical resection of parotid tumours. Patients underwent MR scans with VIIn tractography calculated with the constrained spherical deconvolution model. The parameters of the diffusion sequence were: b-value of 1000 s/mm(2); 32 directions; voxel size: 2 mm isotropic; scan time: 9'31'. The potential contacts between VIIn branches and tumours were estimated with different initial fractional anisotropy (iFA) cut-offs compared to surgical data. Surgeons were blinded to the tractography reconstructions and identified both nerves and contact with tumours using nerve stimulation and reference photographs. Twenty-six patients were included in this study and the mean patient age was 55.2 years. Surgical direct assessment of VIIn allowed identifying 0.1 as the iFA threshold with the best sensitivity to detect tumour contact. In all patients with successful VIIn identification by tractography, surgeons confirmed nerve courses as well as lesion location in parotid glands. Mean VIIn branch FA values were significantly lower in cases with tumour contact (t-test; p ≤ 0.01). This study showed the feasibility of intraparotid VIIn tractography to identify nerve contact with parotid tumours. • Diffusion imaging is an efficient method for highlighting the intraparotid VIIn. • Visualization of the VIIn may help to better manage patients before surgery. • We bring new insights to future trials for patients with VIIn dysfunction. • We aimed to provide radio-anatomical references for further studies.

Tensor surgery and tensor rank

NARCIS (Netherlands)

M. Christandl (Matthias); J. Zuiddam (Jeroen)

2018-01-01

textabstractWe introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new vertices

Tensor surgery and tensor rank

NARCIS (Netherlands)

M. Christandl (Matthias); J. Zuiddam (Jeroen)

2016-01-01

textabstractWe introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new

Tensor rank is not multiplicative under the tensor product

DEFF Research Database (Denmark)

Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen

2018-01-01

The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection b...

High-definition fiber tractography for the evaluation of perilesional white matter tracts in high-grade glioma surgery.

Science.gov (United States)

Abhinav, Kumar; Yeh, Fang-Cheng; Mansouri, Alireza; Zadeh, Gelareh; Fernandez-Miranda, Juan C

2015-09-01

Conventional white matter (WM) imaging approaches, such as diffusion tensor imaging (DTI), have been used to preoperatively identify the location of affected WM tracts in patients with intracranial tumors in order to maximize the extent of resection and potentially reduce postoperative morbidity. DTI, however, has limitations that include its inability to resolve multiple crossing fibers and its susceptibility to partial volume effects. Therefore, recent focus has shifted to more advanced WM imaging techniques such as high-definition fiber tractography (HDFT). In this paper, we illustrate the application of HDFT, which in our preliminary experience has enabled accurate depiction of perilesional tracts in a 3-dimensional manner in multiple anatomical compartments including edematous zones around high-grade gliomas. This has facilitated accurate surgical planning. This is illustrated by using case examples of patients with glioblastoma multiforme. We also discuss future directions in the role of these techniques in surgery for gliomas. © The Author(s) 2015. Published by Oxford University Press on behalf of the Society for Neuro-Oncology. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

TractoR: Magnetic Resonance Imaging and Tractography with R

Directory of Open Access Journals (Sweden)

Chris A. Clark

2011-10-01

Full Text Available Statistical techniques play a major role in contemporary methods for analyzing magnetic resonance imaging (MRI data. In addition to the central role that classical statistical methods play in research using MRI, statistical modeling and machine learning techniques are key to many modern data analysis pipelines. Applications for these techniques cover a broad spectrum of research, including many preclinical and clinical studies, and in some cases these methods are working their way into widespread routine use. In this manuscript we describe a software tool called TractoR (for “Tractography with R”, a collection of packages for the R language and environment, along with additional infrastructure for straightforwardly performing common image processing tasks. TractoR provides general purpose functions for reading, writing and manipulating MR images, as well as more specific code for fitting signal models to diffusion MRI data and performing tractography, a technique for visualizing neural connectivity.

Clinical feasibility of simultaneous multi-slice imaging with blipped-CAIPI for diffusion-weighted imaging and diffusion-tensor imaging of the brain.

Science.gov (United States)

Yokota, Hajime; Sakai, Koji; Tazoe, Jun; Goto, Mariko; Imai, Hiroshi; Teramukai, Satoshi; Yamada, Kei

2017-12-01

Background Simultaneous multi-slice (SMS) imaging is starting to be used in clinical situation, although evidence of clinical feasibility is scanty. Purpose To prospectively assess the clinical feasibility of SMS diffusion-weighted imaging (DWI) and diffusion-tensor imaging (DTI) with blipped-controlled aliasing in parallel imaging for brain lesions. Material and Methods The institutional review board approved this study. This study included 156 hyperintense lesions on DWI from 32 patients. A slice acceleration factor of 2 was applied for SMS scans, which allowed shortening of the scan time by 41.3%. The signal-to-noise ratio (SNR) was calculated for brain tissue of a selected slice. The contrast-to-noise ratio (CNR), apparent diffusion coefficient (ADC), and fractional anisotropy (FA) were calculated in 36 hyperintense lesions with a diameter of three pixels or more. Visual assessment was performed for all 156 lesions. Tractography of the corticospinal tract of 29 patients was evaluated. The number of tracts and averaged tract length were used for quantitative analysis, and visual assessment was evaluated by grading. Results The SMS scan showed no bias and acceptable 95% limits of agreement compared to conventional scans in SNR, CNR, and ADC on Bland-Altman analyses. Only FA of the lesions was higher in the SMS scan by 9% ( P = 0.016), whereas FA of the surrounding tissues was similar. Quantitative analysis of tractography showed similar values. Visual assessment of DWI hyperintense lesions and tractography also resulted in comparable evaluation. Conclusion SMS imaging was clinically feasible for imaging quality and quantitative values compared with conventional DWI and DTI.

Stream-lined Gating Systems with Improved Yield - Dimensioning and Experimental Validation

DEFF Research Database (Denmark)

Tiedje, Niels Skat; Skov-Hansen, Søren Peter

the two types of lay-outs are cast in production. It is shown that flow in the stream-lined lay-out is well controlled and that the quality of the castings is as at least equal to that of castings produced with a traditional lay-out. Further, the yield is improved by 4 % relative to a traditional lay-out.......The paper describes how a stream-lined gating system where the melt is confined and controlled during filling can be designed. Commercial numerical modelling software has been used to compare the stream-lined design with a traditional gating system. These results are confirmed by experiments where...

MR muscle tractography study on VX2 soft-tissue tumor in rabbits

International Nuclear Information System (INIS)

Li Yonggang; Guo Liang; Xie Daohai; Hu Chunhogn; Guo Maofeng; Zhu Wei; Chen Jianhua; Xing Jianming; Wang Renfa

2008-01-01

Objective: To determine if diffusion tensor imaging (DTI) and muscle fiber tracts of muscle disease are feasible. Methods: Twenty Newzealand white rabbits were implanted with 0.2 ml VX 2 tumor tissue suspension in the right proximal thighs. MRI and DTI were performed on these rabbits and DTI of muscle fiber tracts in the muscles around the lesions were reconstructed. The fractional anisotropy(FA) and volume ratio anisotropy(VrA) of the tumor and the normal muscle were analyzed. The correlation study between MRI and pathological findings was done. Results: All experimental animal models of rabbit VX 2 soft tissue tumors were successfully established. The difference of FA between the central parenchyma area and the necrosis area, the peripheral area of the tumor, the adjacent and contralateral normal muscle was statistically significant (P 0.05). The difference of FA and VrA between the adjacent and contralateral normal muscle was not statistically significant (P>0.05). The arrangement of normal muscle was regular on DTI of muscle tract. The muscle around the tumor lesions was infiltrated and destructed, which demonstrated irregular and interrupted muscle fiber on muscle tractography. Conclusion: DTI is advantageous to demonstrate the structure of soft tissue tumors and its border, which should be helpful in the structure and function research of muscle, as well as in the diagnosis of muscle diseases. (authors)

Tensoral for post-processing users and simulation authors

Science.gov (United States)

Dresselhaus, Eliot

1993-01-01

The CTR post-processing effort aims to make turbulence simulations and data more readily and usefully available to the research and industrial communities. The Tensoral language, which provides the foundation for this effort, is introduced here in the form of a user's guide. The Tensoral user's guide is presented in two main sections. Section one acts as a general introduction and guides database users who wish to post-process simulation databases. Section two gives a brief description of how database authors and other advanced users can make simulation codes and/or the databases they generate available to the user community via Tensoral database back ends. The two-part structure of this document conforms to the two-level design structure of the Tensoral language. Tensoral has been designed to be a general computer language for performing tensor calculus and statistics on numerical data. Tensoral's generality allows it to be used for stand-alone native coding of high-level post-processing tasks (as described in section one of this guide). At the same time, Tensoral's specialization to a minute task (namely, to numerical tensor calculus and statistics) allows it to be easily embedded into applications written partly in Tensoral and partly in other computer languages (here, C and Vectoral). Embedded Tensoral, aimed at advanced users for more general coding (e.g. of efficient simulations, for interfacing with pre-existing software, for visualization, etc.), is described in section two of this guide.

DTI fiber tractography of cerebro-cerebellar pathways and clinical evaluation of ataxia in childhood posterior fossa tumor survivors.

Science.gov (United States)

Oh, Myung Eun; Driever, Pablo Hernáiz; Khajuria, Rajiv K; Rueckriegel, Stefan Mark; Koustenis, Elisabeth; Bruhn, Harald; Thomale, Ulrich-Wilhelm

2017-01-01

Pediatric posterior fossa (PF) tumor survivors experience long-term motor deficits. Specific cerebrocerebellar connections may be involved in incidence and severity of motor dysfunction. We examined the relationship between long-term ataxia as well as fine motor function and alteration of differential cerebellar efferent and afferent pathways using diffusion tensor imaging (DTI) and tractography. DTI-based tractography was performed in 19 patients (10 pilocytic astrocytoma (PA) and 9 medulloblastoma patients (MB)) and 20 healthy peers. Efferent Cerebello-Thalamo-Cerebral (CTC) and afferent Cerebro-Ponto-Cerebellar (CPC) tracts were reconstructed and analyzed concerning fractional anisotropy (FA) and volumetric measurements. Clinical outcome was assessed with the International Cooperative Ataxia Rating Scale (ICARS). Kinematic parameters of fine motor function (speed, automation, variability, and pressure) were obtained by employing a digitizing graphic tablet. ICARS scores were significantly higher in MB patients than in PA patients. Poorer ICARS scores and impaired fine motor function correlated significantly with volume loss of CTC pathway in MB patients, but not in PA patients. Patients with pediatric post-operative cerebellar mutism syndrome showed higher loss of CTC pathway volume and were more atactic. CPC pathway volume was significantly reduced in PA patients, but not in MB patients. Neither relationship was observed between the CPC pathway and ICARS or fine motor function. There was no group difference of FA values between the patients and healthy peers. Reduced CTC pathway volumes in our cohorts were associated with severity of long-term ataxia and impaired fine motor function in survivors of MBs. We suggest that the CTC pathway seems to play a role in extent of ataxia and fine motor dysfunction after childhood cerebellar tumor treatment. DTI may be a useful tool to identify relevant structures of the CTC pathway and possibly avoid surgically induced long

Symmetric Tensor Decomposition

DEFF Research Database (Denmark)

Brachat, Jerome; Comon, Pierre; Mourrain, Bernard

2010-01-01

We present an algorithm for decomposing a symmetric tensor, of dimension n and order d, as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables...... of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on this characterization and on linear algebra computations with Hankel matrices. The impact of this contribution is two-fold. First it permits an efficient computation...... of the decomposition of any tensor of sub-generic rank, as opposed to widely used iterative algorithms with unproved global convergence (e.g. Alternate Least Squares or gradient descents). Second, it gives tools for understanding uniqueness conditions and for detecting the rank....

Diffusion tensor imaging of spinal cord parenchyma lesion in rat with chronic spinal cord injury.

Science.gov (United States)

Zhao, Can; Rao, Jia-Sheng; Pei, Xiao-Jiao; Lei, Jian-Feng; Wang, Zhan-Jing; Zhao, Wen; Wei, Rui-Han; Yang, Zhao-Yang; Li, Xiao-Guang

2018-04-01

Adequate evaluation of spinal cord parenchyma and accurate identification of injury range are considered two premises for the research and treatment of chronic spinal cord injury (SCI). Diffusion tensor imaging (DTI) provides information about water diffusion in spinal cord, and thus makes it possible to realize these premises. In this study, we conducted magnetic resonance imaging (MRI) for Wistar rats 84days after spinal cord contusion. DTI metrics including fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD), and radial diffusivity (RD) from different positions of the injured cord were collected, analyzed, and compared with the histological results and locomotor outcomes. Moreover, we performed fiber tractography, and examined the difference in cavity percentage obtained respectively via conventional MRI, DTI and histology. Results showed that the chronic SCI rats had the largest changes of all DTI metrics at the epicenter; the farther away from the epicenter, the smaller the variation. FA, AD and RD were all influenced by SCI in a greater space range than MD. The good consistency of FA values and histological results in specific regions evidenced FA's capability of reflecting Wallerian degeneration after SCI. DTI metrics at the epicenter in ventral funiculus also showed a close correlation with the BBB scores. Additionally, supported by the histological results, DTI enables a more accurate measurement of cavity percentage compared to the conventional MRI. DTI parameters might comprehensively reflect the post-SCI pathological status of spinal cord parenchyma at the epicenter and distal parts during the chronic stage, while showing good consistency with locomotor performance. DTI combined with tractography could intuitively display the distribution of spared fibers after SCI and accurately provide information such as cavity area. This may shed light on the research and treatment of chronic SCI. Copyright © 2017 Elsevier Inc. All rights

Diffusion tensor imaging of the human calf: Variation of inter- and intramuscle-specific diffusion parameters.

Science.gov (United States)

Schlaffke, Lara; Rehmann, Robert; Froeling, Martijn; Kley, Rudolf; Tegenthoff, Martin; Vorgerd, Matthias; Schmidt-Wilcke, Tobias

2017-10-01

To investigate to what extent inter- and intramuscular variations of diffusion parameters of human calf muscles can be explained by age, gender, muscle location, and body mass index (BMI) in a specific age group (20-35 years). Whole calf muscles of 18 healthy volunteers were evaluated. Magnetic resonance imaging (MRI) was performed using a 3T scanner and a 16-channel Torso XL coil. Diffusion-weighted images were acquired to perform fiber tractography and diffusion tensor imaging (DTI) analysis for each muscle of both legs. Fiber tractography was used to separate seven lower leg muscles. Associations between DTI parameters and confounds were evaluated. All muscles were additionally separated in seven identical segments along the z-axis to evaluate intramuscular differences in diffusion parameters. Fractional anisotropy (FA) and mean diffusivity (MD) were obtained for each muscle with low standard deviations (SDs) (SD FA : 0.01-0.02; SD MD : 0.07-0.14(10 -3 )). We found significant differences in FA values of the tibialis anterior muscle (AT) and extensor digitorum longus (EDL) muscles between men and women for whole muscle FA (two-sample t-tests; AT: P = 0.0014; EDL: P = 0.0004). We showed significant intramuscular differences in diffusion parameters between adjacent segments in most calf muscles (P < 0.001). Whereas muscle insertions showed higher (SD 0.03-0.06) than muscle bellies (SD 0.01-0.03), no relationships between FA or MD with age or BMI were found. Inter- and intramuscular variations in diffusion parameters of the calf were shown, which are not related to age or BMI in this age group. Differences between muscle belly and insertion should be considered when interpreting datasets not including whole muscles. 3 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2017;46:1137-1148. © 2017 International Society for Magnetic Resonance in Medicine.

MATLAB tensor classes for fast algorithm prototyping.

Energy Technology Data Exchange (ETDEWEB)

Bader, Brett William; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)

2004-10-01

Tensors (also known as mutidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. We describe four MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLAB's multidimensional arrays by supporting additional operations such as tensor multiplication. The tensor as matrix class supports the 'matricization' of a tensor, i.e., the conversion of a tensor to a matrix (and vice versa), a commonly used operation in many algorithms. Two additional classes represent tensors stored in decomposed formats: cp tensor and tucker tensor. We descibe all of these classes and then demonstrate their use by showing how to implement several tensor algorithms that have appeared in the literature.

Streamline-concentration balance model for in-situ uranium leaching and site restoration

International Nuclear Information System (INIS)

Bommer, P.M.; Schechter, R.S.; Humenick, M.J.

1981-03-01

This work presents two computer models. One describes in-situ uranium leaching and the other describes post leaching site restoration. Both models use a streamline generator to set up the flow field over the reservoir. The leaching model then uses the flow data in a concentration balance along each streamline coupled with the appropriate reaction kinetics to calculate uranium production. The restoration model uses the same procedure except that binary cation exchange is used as the restoring mechanism along each streamline and leaching cation clean up is simulated. The mathematical basis for each model is shown in detail along with the computational schemes used. Finally, the two models have been used with several data sets to point out their capabilities and to illustrate important leaching and restoration parameters and schemes

Streamline-concentration balance model for in situ uranium leaching and site restoration

International Nuclear Information System (INIS)

Bommer, P.M.

1979-01-01

This work presents two computer models. One describes in situ uranium leaching and the other describes post leaching site restoration. Both models use a streamline generator to set up the flow field over the reservoir. The leaching model then uses the flow data in a concentration balance along each streamline coupled with the appropriate reaction kinetics to calculate uranium production. The restoration model uses the same procedure ecept that binary cation exchange is used as the restoring mechanism along each streamline and leaching cation clean up is stimulated. The mathematical basis for each model is shown in detail along with the computational schemes used. Finally, the two models have been used with several data sets to point out their capabilities and to illustrate important leaching and restoration parameters and schemes

Diffusion tensor MRI: clinical applications

International Nuclear Information System (INIS)

Meli, Francisco; Romero, Carlos; Carpintiero, Silvina; Salvatico, Rosana; Lambre, Hector; Vila, Jose

2005-01-01

Purpose: To evaluate the usefulness of diffusion-tensor imaging (DTI) on different neurological diseases, and to know if this technique shows additional information than conventional Magnetic Resonance Imaging (MRI). Materials and method: Eight patients, with neurological diseases (five patients with brain tumors, one with multiple sclerosis (MS), one with variant Creutzfeldt-Jakob disease (vCJD) and the other with delayed CO intoxication were evaluated. A MR scanner of 1.5 T was used and conventional sequences and DTI with twenty-five directions were done. Quantitative maps were gotten, where the fractional anisotropy (FA) through regions of interest (ROIs) in specific anatomic area were quantified (i.e.: internal and external capsules, frontal and temporal bundles, corpus fibers). Results: In the patients with brain tumors, there was a decrease of FA on intra and peritumoral fibers. Some of them had a disruption in their pattern. In patients with MS and CO intoxication, partial interruption along white matter bundles was demonstrated. However, a 'mismatch' between the findings of FLAIR, Diffusion-weighted images (DWI) and DTI, in the case of CO intoxication, was seen. Conclusions: DTI gave more information compared to conventional sequences about ultrastructural brain tissue in almost all the diseases above mentioned. Therefore, there is a work in progress about DTI acquisition, to evaluate a new technique, called tractography. (author)

Beyond Low Rank: A Data-Adaptive Tensor Completion Method

OpenAIRE

Zhang, Lei; Wei, Wei; Shi, Qinfeng; Shen, Chunhua; Hengel, Anton van den; Zhang, Yanning

2017-01-01

Low rank tensor representation underpins much of recent progress in tensor completion. In real applications, however, this approach is confronted with two challenging problems, namely (1) tensor rank determination; (2) handling real tensor data which only approximately fulfils the low-rank requirement. To address these two issues, we develop a data-adaptive tensor completion model which explicitly represents both the low-rank and non-low-rank structures in a latent tensor. Representing the no...

Dividing Streamline Formation Channel Confluences by Physical Modeling

Directory of Open Access Journals (Sweden)

Minarni Nur Trilita

2010-02-01

Full Text Available Confluence channels are often found in open channel network system and is the most important element. The incoming flow from the branch channel to the main cause various forms and cause vortex flow. Phenomenon can cause erosion of the side wall of the channel, the bed channel scour and sedimentation in the downstream confluence channel. To control these problems needed research into the current width of the branch channel. The incoming flow from the branch channel to the main channel flow bounded by a line distributors (dividing streamline. In this paper, the wide dividing streamline observed in the laboratory using a physical model of two open channels, a square that formed an angle of 30º. Observations were made with a variety of flow coming from each channel. The results obtained in the laboratory observation that the width of dividing streamline flow is influenced by the discharge ratio between the channel branch with the main channel. While the results of a comparison with previous studies showing that the observation in the laboratory is smaller than the results of previous research.

Highly Efficient and Scalable Compound Decomposition of Two-Electron Integral Tensor and Its Application in Coupled Cluster Calculations

Energy Technology Data Exchange (ETDEWEB)

Peng, Bo [William R. Wiley Environmental; Kowalski, Karol [William R. Wiley Environmental

2017-08-11

The representation and storage of two-electron integral tensors are vital in large- scale applications of accurate electronic structure methods. Low-rank representation and efficient storage strategy of integral tensors can significantly reduce the numerical overhead and consequently time-to-solution of these methods. In this paper, by combining pivoted incomplete Cholesky decomposition (CD) with a follow-up truncated singular vector decomposition (SVD), we develop a decomposition strategy to approximately represent the two-electron integral tensor in terms of low-rank vectors. A systematic benchmark test on a series of 1-D, 2-D, and 3-D carbon-hydrogen systems demonstrates high efficiency and scalability of the compound two-step decomposition of the two-electron integral tensor in our implementation. For the size of atomic basis set N_b ranging from ~ 100 up to ~ 2, 000, the observed numerical scaling of our implementation shows O(N_b^{2.5~3}) versus O(N_b^{3~4}) of single CD in most of other implementations. More importantly, this decomposition strategy can significantly reduce the storage requirement of the atomic-orbital (AO) two-electron integral tensor from O(N_b^4) to O(N_b^2 log_{10}(N_b)) with moderate decomposition thresholds. The accuracy tests have been performed using ground- and excited-state formulations of coupled- cluster formalism employing single and double excitations (CCSD) on several bench- mark systems including the C_{60} molecule described by nearly 1,400 basis functions. The results show that the decomposition thresholds can be generally set to 10^{-4} to 10^{-3} to give acceptable compromise between efficiency and accuracy.

Detection of hand and leg motor tract injury using novel diffusion tensor MRI tractography in children with central motor dysfunction.

Science.gov (United States)

Jeong, Jeong-Won; Lee, Jessica; Kamson, David O; Chugani, Harry T; Juhász, Csaba

2015-09-01

To examine whether an objective segmenation of corticospinal tract (CST) associated with hand and leg movements can be used to detect central motor weakness in the corresponding extremities in a pediatric population. This retrospective study included diffusion tensor imaging (DTI) of 25 children with central paresis affecting at least one limb (age: 9.0±4.2years, 15 boys, 5/13/7 children with left/right/both hemispheric lesions including ischemia, cyst, and gliosis), as well as 42 pediatric control subjects with no motor dysfunction (age: 9.0±5.5years, 21 boys, 31 healthy/11 non-lesional epilepsy children). Leg- and hand-related CST pathways were segmented using DTI-maximum a posteriori (DTI-MAP) classification. The resulting CST volumes were then divided by total supratentorial white matter volume, resulting in a marker called "normalized streamline volume ratio (NSVR)" to quantify the degree of axonal loss in separate CST pathways associated with leg and hand motor functions. A receiver operating characteristic curve was applied to measure the accuracy of this marker to identify extremities with motor weakness. NSVR values of hand/leg CST selectively achieved the following values of accuracy/sensitivity/specificity: 0.84/0.84/0.57, 0.82/0.81/0.55, 0.78/0.75/0.55, 0.79/0.81/0.54 at a cut-off of 0.03/0.03/0.03/0.02 for right hand CST, left hand CST, right leg CST, and left leg CST, respectively. Motor weakness of hand and leg was most likely present at the cut-off values of hand and leg NSVR (i.e., 0.029/0.028/0.025/0.020 for left-hand/right-hand/left-leg/right-leg). The control group showed a moderate age-related increase in absolute CST volumes and a biphasic age-related variation of the normalized CST volumes, which were lacking in the paretic children. This study demonstrates that DTI-MAP classification may provide a new imaging tool to quantify axonal loss in children with central motor dysfunction. Using this technique, we found that early-life brain

Quantifying diffusion MRI tractography of the corticospinal tract in brain tumors with deterministic and probabilistic methods.

Science.gov (United States)

Bucci, Monica; Mandelli, Maria Luisa; Berman, Jeffrey I; Amirbekian, Bagrat; Nguyen, Christopher; Berger, Mitchel S; Henry, Roland G

2013-01-01

Diffusion MRI tractography has been increasingly used to delineate white matter pathways in vivo for which the leading clinical application is presurgical mapping of eloquent regions. However, there is rare opportunity to quantify the accuracy or sensitivity of these approaches to delineate white matter fiber pathways in vivo due to the lack of a gold standard. Intraoperative electrical stimulation (IES) provides a gold standard for the location and existence of functional motor pathways that can be used to determine the accuracy and sensitivity of fiber tracking algorithms. In this study we used intraoperative stimulation from brain tumor patients as a gold standard to estimate the sensitivity and accuracy of diffusion tensor MRI (DTI) and q-ball models of diffusion with deterministic and probabilistic fiber tracking algorithms for delineation of motor pathways. We used preoperative high angular resolution diffusion MRI (HARDI) data (55 directions, b = 2000 s/mm(2)) acquired in a clinically feasible time frame from 12 patients who underwent a craniotomy for resection of a cerebral glioma. The corticospinal fiber tracts were delineated with DTI and q-ball models using deterministic and probabilistic algorithms. We used cortical and white matter IES sites as a gold standard for the presence and location of functional motor pathways. Sensitivity was defined as the true positive rate of delineating fiber pathways based on cortical IES stimulation sites. For accuracy and precision of the course of the fiber tracts, we measured the distance between the subcortical stimulation sites and the tractography result. Positive predictive rate of the delineated tracts was assessed by comparison of subcortical IES motor function (upper extremity, lower extremity, face) with the connection of the tractography pathway in the motor cortex. We obtained 21 cortical and 8 subcortical IES sites from intraoperative mapping of motor pathways. Probabilistic q-ball had the best

Tensor gauge condition and tensor field decomposition

Science.gov (United States)

Zhu, Ben-Chao; Chen, Xiang-Song

2015-10-01

We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin ≥ 2. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.

Tensor spherical harmonics and tensor multipoles. II. Minkowski space

International Nuclear Information System (INIS)

Daumens, M.; Minnaert, P.

1976-01-01

The bases of tensor spherical harmonics and of tensor multipoles discussed in the preceding paper are generalized in the Hilbert space of Minkowski tensor fields. The transformation properties of the tensor multipoles under Lorentz transformation lead to the notion of irreducible tensor multipoles. We show that the usual 4-vector multipoles are themselves irreducible, and we build the irreducible tensor multipoles of the second order. We also give their relations with the symmetric tensor multipoles defined by Zerilli for application to the gravitational radiation

Early diagnosis of Balo's concentric sclerosis by diffusion tensor tractography: a case report and literature review

Directory of Open Access Journals (Sweden)

Juan Alberto Nader Kawachi

2016-03-01

Full Text Available La esclerosis concéntrica de Baló es una variante infrecuente de enfermedad desmielinizante relacionada con la esclerosis múltiple, inicialmente considerada de progresión fatal. En estudios recientes se reportan variantes no fatales de esclerosis concéntrica de Baló en los que se enfatiza la importancia del diagnóstico por medio de la imagen por resonancia magnética, utilizando además la espectroscopia y las secuencias de difusión y perfusión. En los últimos años se ha logrado reproducir la imagen tridimensional de un fascículo en particular y observar la presencia de lesiones por medio de la tractografía por imagen por resonancia magnética mediante la técnica de tensor de difusión. Presentamos el caso de una mujer joven con síntomas neurológicos focales agudos, incluyendo paresia de extremidades derechas, cuyo diagnóstico por biopsia fue de esclerosis concéntrica de Baló, confirmando el resultado de los estudios de imagen. La paciente recibió tratamiento con bolos de metilprednisolona, obteniendo remisión clínica completa a largo plazo. A nuestro entender, este es el primer reporte que describe los hallazgos de la esclerosis concéntrica de Baló utilizando la técnica de tensor de difusión. Consideramos que dicha técnica permitirá en el futuro la detección temprana de la enfermedad, su tratamiento oportuno y permitirá establecer nuevos criterios de clasificación y estratificación. Este caso demuestra la existencia de variantes benignas de esclerosis concéntrica de Baló, que tienen buena respuesta a la terapia con glucocorticoides y donde se logra la recuperación funcional.

Linear Invariant Tensor Interpolation Applied to Cardiac Diffusion Tensor MRI

Science.gov (United States)

Gahm, Jin Kyu; Wisniewski, Nicholas; Kindlmann, Gordon; Kung, Geoffrey L.; Klug, William S.; Garfinkel, Alan; Ennis, Daniel B.

2015-01-01

Purpose Various methods exist for interpolating diffusion tensor fields, but none of them linearly interpolate tensor shape attributes. Linear interpolation is expected not to introduce spurious changes in tensor shape. Methods Herein we define a new linear invariant (LI) tensor interpolation method that linearly interpolates components of tensor shape (tensor invariants) and recapitulates the interpolated tensor from the linearly interpolated tensor invariants and the eigenvectors of a linearly interpolated tensor. The LI tensor interpolation method is compared to the Euclidean (EU), affine-invariant Riemannian (AI), log-Euclidean (LE) and geodesic-loxodrome (GL) interpolation methods using both a synthetic tensor field and three experimentally measured cardiac DT-MRI datasets. Results EU, AI, and LE introduce significant microstructural bias, which can be avoided through the use of GL or LI. Conclusion GL introduces the least microstructural bias, but LI tensor interpolation performs very similarly and at substantially reduced computational cost. PMID:23286085

Impact assessment: Eroding benefits through streamlining?

Energy Technology Data Exchange (ETDEWEB)

Bond, Alan, E-mail: alan.bond@uea.ac.uk [School of Environmental Sciences, University of East Anglia (United Kingdom); School of Geo and Spatial Sciences, North-West University (South Africa); Pope, Jenny, E-mail: jenny@integral-sustainability.net [Integral Sustainability (Australia); Curtin University Sustainability Policy Institute (Australia); Morrison-Saunders, Angus, E-mail: A.Morrison-Saunders@murdoch.edu.au [School of Geo and Spatial Sciences, North-West University (South Africa); Environmental Science, Murdoch University (Australia); Retief, Francois, E-mail: francois.retief@nwu.ac.za [School of Geo and Spatial Sciences, North-West University (South Africa); Gunn, Jill A.E., E-mail: jill.gunn@usask.ca [Department of Geography and Planning and School of Environment and Sustainability, University of Saskatchewan (Canada)

2014-02-15

This paper argues that Governments have sought to streamline impact assessment in recent years (defined as the last five years) to counter concerns over the costs and potential for delays to economic development. We hypothesise that this has had some adverse consequences on the benefits that subsequently accrue from the assessments. This hypothesis is tested using a framework developed from arguments for the benefits brought by Environmental Impact Assessment made in 1982 in the face of the UK Government opposition to its implementation in a time of economic recession. The particular benefits investigated are ‘consistency and fairness’, ‘early warning’, ‘environment and development’, and ‘public involvement’. Canada, South Africa, the United Kingdom and Western Australia are the jurisdictions tested using this framework. The conclusions indicate that significant streamlining has been undertaken which has had direct adverse effects on some of the benefits that impact assessment should deliver, particularly in Canada and the UK. The research has not examined whether streamlining has had implications for the effectiveness of impact assessment, but the causal link between streamlining and benefits does sound warning bells that merit further investigation. -- Highlights: • Investigation of the extent to which government has streamlined IA. • Evaluation framework was developed based on benefits of impact assessment. • Canada, South Africa, the United Kingdom, and Western Australia were examined. • Trajectory in last five years is attrition of benefits of impact assessment.

Impact assessment: Eroding benefits through streamlining?

International Nuclear Information System (INIS)

Bond, Alan; Pope, Jenny; Morrison-Saunders, Angus; Retief, Francois; Gunn, Jill A.E.

2014-01-01

This paper argues that Governments have sought to streamline impact assessment in recent years (defined as the last five years) to counter concerns over the costs and potential for delays to economic development. We hypothesise that this has had some adverse consequences on the benefits that subsequently accrue from the assessments. This hypothesis is tested using a framework developed from arguments for the benefits brought by Environmental Impact Assessment made in 1982 in the face of the UK Government opposition to its implementation in a time of economic recession. The particular benefits investigated are ‘consistency and fairness’, ‘early warning’, ‘environment and development’, and ‘public involvement’. Canada, South Africa, the United Kingdom and Western Australia are the jurisdictions tested using this framework. The conclusions indicate that significant streamlining has been undertaken which has had direct adverse effects on some of the benefits that impact assessment should deliver, particularly in Canada and the UK. The research has not examined whether streamlining has had implications for the effectiveness of impact assessment, but the causal link between streamlining and benefits does sound warning bells that merit further investigation. -- Highlights: • Investigation of the extent to which government has streamlined IA. • Evaluation framework was developed based on benefits of impact assessment. • Canada, South Africa, the United Kingdom, and Western Australia were examined. • Trajectory in last five years is attrition of benefits of impact assessment

Seeing More by Showing Less: Orientation-Dependent Transparency Rendering for Fiber Tractography Visualization.

Directory of Open Access Journals (Sweden)

Chantal M W Tax

Full Text Available Fiber tractography plays an important role in exploring the architectural organization of fiber trajectories, both in fundamental neuroscience and in clinical applications. With the advent of diffusion MRI (dMRI approaches that can also model "crossing fibers", the complexity of the fiber network as reconstructed with tractography has increased tremendously. Many pathways interdigitate and overlap, which hampers an unequivocal 3D visualization of the network and impedes an efficient study of its organization. We propose a novel fiber tractography visualization approach that interactively and selectively adapts the transparency rendering of fiber trajectories as a function of their orientation to enhance the visibility of the spatial context. More specifically, pathways that are oriented (locally or globally along a user-specified opacity axis can be made more transparent or opaque. This substantially improves the 3D visualization of the fiber network and the exploration of tissue configurations that would otherwise be largely covered by other pathways. We present examples of fiber bundle extraction and neurosurgical planning cases where the added benefit of our new visualization scheme is demonstrated over conventional fiber visualization approaches.

Preoperative Navigated Transcranial Magnetic Stimulation and Tractography to Guide Endoscopic Cystoventriculostomy: A Technical Note and Case Report.

Science.gov (United States)

Hendrix, Philipp; Senger, Sebastian; Griessenauer, Christoph J; Simgen, Andreas; Linsler, Stefan; Oertel, Joachim

2018-01-01

To report a technique for endoscopic cystoventriculostomy guided by preoperative navigated transcranial magnetic stimulation (nTMS) and tractography in a patient with a large speech eloquent arachnoid cyst. A 74-year old woman presented with a seizure and subsequent persistent anomic aphasia from a progressive left-sided parietal arachnoid cyst. An endoscopic cystoventriculostomy and endoscope-assisted ventricle catheter placement were performed. Surgery was guided by preoperative nTMS and tractography to avoid eloquent language, motor, and visual pathways. Preoperative nTMS motor and language mapping were used to guide tractography of motor and language white matter tracts. The ideal locations of entry point and cystoventriculostomy as well as trajectory for stent-placement were determined preoperatively with a pseudo-3-dimensional model visualizing eloquent language, motor, and visual cortical and subcortical information. The early postoperative course was uneventful. At her 3-month follow-up visit, her language impairments had completely recovered. Additionally, magnetic resonance imaging demonstrated complete collapse of the arachnoid cyst. The combination of nTMS and tractography supports the identification of a safe trajectory for cystoventriculostomy in eloquent arachnoid cysts. Copyright © 2017 Elsevier Inc. All rights reserved.

Development of a web-based graphical user interface to design brain fiber models for tractography validation

OpenAIRE

González Vela, Guillem

2017-01-01

Diffusion Magnetic Resonance Imaging (MRI) is an advanced MRI technique which can provide brain white matter tissue microscopic information. From this information, the connectivity map of axons in the brain can be obtained using tractography algorithms. However, this cartography of the brain wiring is known to suffer from several biases. Phantomas is an open source library created with the aim of evaluating tractography. It allows the creation of in silico brain phantoms and simulates i...

Scale-free crystallization of two-dimensional complex plasmas: Domain analysis using Minkowski tensors

Science.gov (United States)

Böbel, A.; Knapek, C. A.; Räth, C.

2018-05-01

Experiments of the recrystallization processes in two-dimensional complex plasmas are analyzed to rigorously test a recently developed scale-free phase transition theory. The "fractal-domain-structure" (FDS) theory is based on the kinetic theory of Frenkel. It assumes the formation of homogeneous domains, separated by defect lines, during crystallization and a fractal relationship between domain area and boundary length. For the defect number fraction and system energy a scale-free power-law relation is predicted. The long-range scaling behavior of the bond-order correlation function shows clearly that the complex plasma phase transitions are not of the Kosterlitz, Thouless, Halperin, Nelson, and Young type. Previous preliminary results obtained by counting the number of dislocations and applying a bond-order metric for structural analysis are reproduced. These findings are supplemented by extending the use of the bond-order metric to measure the defect number fraction and furthermore applying state-of-the-art analysis methods, allowing a systematic testing of the FDS theory with unprecedented scrutiny: A morphological analysis of lattice structure is performed via Minkowski tensor methods. Minkowski tensors form a complete family of additive, motion covariant and continuous morphological measures that are sensitive to nonlinear properties. The FDS theory is rigorously confirmed and predictions of the theory are reproduced extremely well. The predicted scale-free power-law relation between defect fraction number and system energy is verified for one more order of magnitude at high energies compared to the inherently discontinuous bond-order metric. It is found that the fractal relation between crystalline domain area and circumference is independent of the experiment, the particular Minkowski tensor method, and the particular choice of parameters. Thus, the fractal relationship seems to be inherent to two-dimensional phase transitions in complex plasmas. Minkowski

On improving the efficiency of tensor voting.

Science.gov (United States)

Moreno, Rodrigo; Garcia, Miguel Angel; Puig, Domenec; Pizarro, Luis; Burgeth, Bernhard; Weickert, Joachim

2011-11-01

This paper proposes two alternative formulations to reduce the high computational complexity of tensor voting, a robust perceptual grouping technique used to extract salient information from noisy data. The first scheme consists of numerical approximations of the votes, which have been derived from an in-depth analysis of the plate and ball voting processes. The second scheme simplifies the formulation while keeping the same perceptual meaning of the original tensor voting: The stick tensor voting and the stick component of the plate tensor voting must reinforce surfaceness, the plate components of both the plate and ball tensor voting must boost curveness, whereas junctionness must be strengthened by the ball component of the ball tensor voting. Two new parameters have been proposed for the second formulation in order to control the potentially conflictive influence of the stick component of the plate vote and the ball component of the ball vote. Results show that the proposed formulations can be used in applications where efficiency is an issue since they have a complexity of order O(1). Moreover, the second proposed formulation has been shown to be more appropriate than the original tensor voting for estimating saliencies by appropriately setting the two new parameters.

Streamlining Research by Using Existing Tools

OpenAIRE

Greene, Sarah M.; Baldwin, Laura-Mae; Dolor, Rowena J.; Thompson, Ella; Neale, Anne Victoria

2011-01-01

Over the past two decades, the health research enterprise has matured rapidly, and many recognize an urgent need to translate pertinent research results into practice, to help improve the quality, accessibility, and affordability of U.S. health care. Streamlining research operations would speed translation, particularly for multi-site collaborations. However, the culture of research discourages reusing or adapting existing resources or study materials. Too often, researchers start studies and...

Two-dimensional NMR measurement and point dipole model prediction of paramagnetic shift tensors in solids

Energy Technology Data Exchange (ETDEWEB)

Walder, Brennan J.; Davis, Michael C.; Grandinetti, Philip J. [Department of Chemistry, Ohio State University, 100 West 18th Avenue, Columbus, Ohio 43210 (United States); Dey, Krishna K. [Department of Physics, Dr. H. S. Gour University, Sagar, Madhya Pradesh 470003 (India); Baltisberger, Jay H. [Division of Natural Science, Mathematics, and Nursing, Berea College, Berea, Kentucky 40403 (United States)

2015-01-07

A new two-dimensional Nuclear Magnetic Resonance (NMR) experiment to separate and correlate the first-order quadrupolar and chemical/paramagnetic shift interactions is described. This experiment, which we call the shifting-d echo experiment, allows a more precise determination of tensor principal components values and their relative orientation. It is designed using the recently introduced symmetry pathway concept. A comparison of the shifting-d experiment with earlier proposed methods is presented and experimentally illustrated in the case of {sup 2}H (I = 1) paramagnetic shift and quadrupolar tensors of CuCl{sub 2}⋅2D{sub 2}O. The benefits of the shifting-d echo experiment over other methods are a factor of two improvement in sensitivity and the suppression of major artifacts. From the 2D lineshape analysis of the shifting-d spectrum, the {sup 2}H quadrupolar coupling parameters are 〈C{sub q}〉 = 118.1 kHz and 〈η{sub q}〉 = 0.88, and the {sup 2}H paramagnetic shift tensor anisotropy parameters are 〈ζ{sub P}〉 = − 152.5 ppm and 〈η{sub P}〉 = 0.91. The orientation of the quadrupolar coupling principal axis system (PAS) relative to the paramagnetic shift anisotropy principal axis system is given by (α,β,γ)=((π)/2 ,(π)/2 ,0). Using a simple ligand hopping model, the tensor parameters in the absence of exchange are estimated. On the basis of this analysis, the instantaneous principal components and orientation of the quadrupolar coupling are found to be in excellent agreement with previous measurements. A new point dipole model for predicting the paramagnetic shift tensor is proposed yielding significantly better agreement than previously used models. In the new model, the dipoles are displaced from nuclei at positions associated with high electron density in the singly occupied molecular orbital predicted from ligand field theory.

Neuroanatomical correlates of developmental dyscalculia: combined evidence from morphometry and tractography

Directory of Open Access Journals (Sweden)

Elena Rykhlevskaia

2009-11-01

Full Text Available Poor mathematical abilities adversely affect academic and career opportunities. The neuroanatomical basis of developmental dyscalculia (DD, a specific learning deficit with prevalence rates exceeding 5%, is poorly understood. We used structural MRI and diffusion tensor imaging (DTI to examine macro- and micro-structural impairments in 7-9 year old children with DD, compared to a group of typically developing (TD children matched on age, gender, intelligence, reading abilities and working memory capacity. Voxel-based morphometry (VBM revealed reduced grey matter (GM bilaterally in superior parietal lobule, intra-parietal sulcus, fusiform gyrus, parahippocampal gyrus and right anterior temporal cortex in children with DD. VBM analysis also showed reduced white matter (WM volume in right temporal-parietal cortex. DTI revealed reduced fractional anisotropy (FA in this WM region, pointing to significant right hemisphere micro-structural impairments. Furthermore, FA in this region was correlated with numerical operations but not verbal mathematical reasoning or word reading. Atlas-based tract mapping identified the inferior longitudinal fasciculus, inferior fronto-occipital fasciculus and caudal forceps major as key pathways impaired in DD. DTI tractography suggests that long-range WM projection fibers linking the right fusiform gyrus with temporal-parietal WM are a specific source of vulnerability in DD. Network and classification analysis suggest that DD in children may be characterized by multiple dysfunctional circuits arising from a core WM deficit. Our findings link GM and WM abnormalities in children with DD and they point to macro- and micro-structural abnormalities in right hemisphere temporal-parietal WM, and pathways associated with it, as key neuroanatomical correlates of DD.

Multi-tensor investigation of orbitofrontal cortex tracts affected in subcaudate tractotomy.

Science.gov (United States)

Yang, Jimmy C; Papadimitriou, George; Eckbo, Ryan; Yeterian, Edward H; Liang, Lichen; Dougherty, Darin D; Bouix, Sylvain; Rathi, Yogesh; Shenton, Martha; Kubicki, Marek; Eskandar, Emad N; Makris, Nikos

2015-06-01

Subcaudate tractotomy (SCT) is a neurosurgical lesioning procedure that can reduce symptoms in medically intractable obsessive compulsive disorder (OCD). Due to the putative importance of the orbitofrontal cortex (OFC) in symptomatology, fibers that connect the OFC, SCT lesion, and either the thalamus or brainstem were investigated with two-tensor tractography using an unscented Kalman filter approach. From this dataset, fibers were warped to Montreal Neurological Institute space, and probability maps with center-of-mass analysis were subsequently generated. In comparing fibers from the same OFC region, including medial OFC (mOFC), central OFC (cOFC), and lateral OFC (lOFC), the area of divergence for fibers connected with the thalamus versus the brainstem is posterior to the anterior commissure. At the anterior commissure, fibers connected with the thalamus run dorsal to those connected with the brainstem. As OFC fibers travel through the ventral aspect of the internal capsule, lOFC fibers are dorsal to cOFC and mOFC fibers. Using neuroanatomical comparison, tracts coursing between the OFC and thalamus are likely part of the anterior thalamic radiations, while those between the OFC and brainstem likely belong to the medial forebrain bundle. These data support the involvement of the OFC in OCD and may be relevant to creating differential lesional procedures of specific tracts or to developing deep brain stimulation programming paradigms.

Tensor voting for robust color edge detection

OpenAIRE

Moreno, Rodrigo; García, Miguel Ángel; Puig, Domenec

2014-01-01

The final publication is available at Springer via http://dx.doi.org/10.1007/978-94-007-7584-8_9 This chapter proposes two robust color edge detection methods based on tensor voting. The first method is a direct adaptation of the classical tensor voting to color images where tensors are initialized with either the gradient or the local color structure tensor. The second method is based on an extension of tensor voting in which the encoding and voting processes are specifically tailored to ...

Streamline Patterns and their Bifurcations near a wall with Navier slip Boundary Conditions

DEFF Research Database (Denmark)

Tophøj, Laust; Møller, Søren; Brøns, Morten

2006-01-01

We consider the two-dimensional topology of streamlines near a surface where the Navier slip boundary condition applies. Using transformations to bring the streamfunction in a simple normal form, we obtain bifurcation diagrams of streamline patterns under variation of one or two external parameters....... Topologically, these are identical with the ones previously found for no-slip surfaces. We use the theory to analyze the Stokes flow inside a circle, and show how it can be used to predict new bifurcation phenomena. ©2006 American Institute of Physics...

Colored Tensor Models - a Review

Directory of Open Access Journals (Sweden)

Razvan Gurau

2012-04-01

Full Text Available Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this rapidly expanding research field. Colored tensor models have been shown to share many of the properties of their direct ancestor, matrix models, which encode a theory of fluctuating two-dimensional surfaces. These features include the possession of Feynman graphs encoding topological spaces, a 1/N expansion of graph amplitudes, embedded matrix models inside the tensor structure, a resumable leading order with critical behavior and a continuum large volume limit, Schwinger-Dyson equations satisfying a Lie algebra (akin to the Virasoro algebra in two dimensions, non-trivial classical solutions and so on. In this review, we give a detailed introduction of colored tensor models and pointers to current and future research directions.

Diffusion tensor image registration using hybrid connectivity and tensor features.

Science.gov (United States)

Wang, Qian; Yap, Pew-Thian; Wu, Guorong; Shen, Dinggang

2014-07-01

Most existing diffusion tensor imaging (DTI) registration methods estimate structural correspondences based on voxelwise matching of tensors. The rich connectivity information that is given by DTI, however, is often neglected. In this article, we propose to integrate complementary information given by connectivity features and tensor features for improved registration accuracy. To utilize connectivity information, we place multiple anchors representing different brain anatomies in the image space, and define the connectivity features for each voxel as the geodesic distances from all anchors to the voxel under consideration. The geodesic distance, which is computed in relation to the tensor field, encapsulates information of brain connectivity. We also extract tensor features for every voxel to reflect the local statistics of tensors in its neighborhood. We then combine both connectivity features and tensor features for registration of tensor images. From the images, landmarks are selected automatically and their correspondences are determined based on their connectivity and tensor feature vectors. The deformation field that deforms one tensor image to the other is iteratively estimated and optimized according to the landmarks and their associated correspondences. Experimental results show that, by using connectivity features and tensor features simultaneously, registration accuracy is increased substantially compared with the cases using either type of features alone. Copyright © 2013 Wiley Periodicals, Inc.

Potentials for transverse trace-free tensors

International Nuclear Information System (INIS)

Conboye, Rory; Murchadha, Niall Ó

2014-01-01

In constructing and understanding initial conditions in the 3 + 1 formalism for numerical relativity, the transverse and trace-free (TT) part of the extrinsic curvature plays a key role. We know that TT tensors possess two degrees of freedom per space point. However, finding an expression for a TT tensor depending on only two scalar functions is a non-trivial task. Assuming either axial or translational symmetry, expressions depending on two scalar potentials alone are derived here for all TT tensors in flat 3-space. In a more general spatial slice, only one of these potentials is found, the same potential given in (Baker and Puzio 1999 Phys. Rev. D 59 044030) and (Dain 2001 Phys. Rev. D 64 124002), with the remaining equations reduced to a partial differential equation, depending on boundary conditions for a solution. As an exercise, we also derive the potentials which give the Bowen-York curvature tensor in flat space. (paper)

Mapping topographic structure in white matter pathways with level set trees.

Directory of Open Access Journals (Sweden)

Brian P Kent

Full Text Available Fiber tractography on diffusion imaging data offers rich potential for describing white matter pathways in the human brain, but characterizing the spatial organization in these large and complex data sets remains a challenge. We show that level set trees--which provide a concise representation of the hierarchical mode structure of probability density functions--offer a statistically-principled framework for visualizing and analyzing topography in fiber streamlines. Using diffusion spectrum imaging data collected on neurologically healthy controls (N = 30, we mapped white matter pathways from the cortex into the striatum using a deterministic tractography algorithm that estimates fiber bundles as dimensionless streamlines. Level set trees were used for interactive exploration of patterns in the endpoint distributions of the mapped fiber pathways and an efficient segmentation of the pathways that had empirical accuracy comparable to standard nonparametric clustering techniques. We show that level set trees can also be generalized to model pseudo-density functions in order to analyze a broader array of data types, including entire fiber streamlines. Finally, resampling methods show the reliability of the level set tree as a descriptive measure of topographic structure, illustrating its potential as a statistical descriptor in brain imaging analysis. These results highlight the broad applicability of level set trees for visualizing and analyzing high-dimensional data like fiber tractography output.

Regularization of DT-MRI Using 3D Median Filtering Methods

Directory of Open Access Journals (Sweden)

Soondong Kwon

2014-01-01

Full Text Available DT-MRI (diffusion tensor magnetic resonance imaging tractography is a method to determine the architecture of axonal fibers in the central nervous system by computing the direction of the principal eigenvectors obtained from tensor matrix, which is different from the conventional isotropic MRI. Tractography based on DT-MRI is known to need many computations and is highly sensitive to noise. Hence, adequate regularization methods, such as image processing techniques, are in demand. Among many regularization methods we are interested in the median filtering method. In this paper, we extended two-dimensional median filters already developed to three-dimensional median filters. We compared four median filtering methods which are two-dimensional simple median method (SM2D, two-dimensional successive Fermat method (SF2D, three-dimensional simple median method (SM3D, and three-dimensional successive Fermat method (SF3D. Three kinds of synthetic data with different altitude angles from axial slices and one kind of human data from MR scanner are considered for numerical implementation by the four filtering methods.

Killing tensors and conformal Killing tensors from conformal Killing vectors

International Nuclear Information System (INIS)

Rani, Raffaele; Edgar, S Brian; Barnes, Alan

2003-01-01

Koutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the completely general result demonstrating that this severe restriction of orthogonality is unnecessary. In addition, we correct and extend some results concerning Killing tensors constructed from a single conformal Killing vector. A number of examples demonstrate that it is possible to construct a much larger class of reducible proper conformal Killing tensors and Killing tensors than permitted by the Koutras algorithms. In particular, by showing that all conformal Killing tensors are reducible in conformally flat spaces, we have a method of constructing all conformal Killing tensors, and hence all the Killing tensors (which will in general be irreducible) of conformally flat spaces using their conformal Killing vectors

Tensors for physics

CERN Document Server

Hess, Siegfried

2015-01-01

This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics,  at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to  tensors of any rank, at graduate level.  Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-...

ACHP | News | ACHP Issues Program Comment to Streamline Communication

Science.gov (United States)

Program Comment to Streamline Communication Facilities Construction and Modification ACHP Issues Program Comment to Streamline Communication Facilities Construction and Modification The Advisory Council on

Joint statistics and conditional mean strain rates of streamline segments

International Nuclear Information System (INIS)

Schaefer, P; Gampert, M; Peters, N

2013-01-01

Based on four different direct numerical simulations of turbulent flows with Taylor-based Reynolds numbers ranging from Re λ = 50 to 300 among which are two homogeneous isotropic decaying, one forced and one homogeneous shear flow, streamlines are identified and the obtained space curves are parameterized with the pseudo-time as well as the arclength. Based on local extrema of the absolute value of the velocity along the streamlines, the latter are partitioned into segments following Wang (2010 J. Fluid Mech. 648 183–203). Streamline segments are then statistically analyzed based on both parameterizations using the joint probability density function of the pseudo-time lag τ (arclength l, respectively) between and the velocity difference Δu at the extrema: P(τ,Δu), (P(l,Δu)). We distinguish positive and negative streamline segments depending on the sign of the velocity difference Δu. Differences as well as similarities in the statistical description for both parameterizations are discussed. In particular, it turns out that the normalized probability distribution functions (pdfs) (of both parameterizations) of the length of positive, negative and all segments assume a universal shape for all Reynolds numbers and flow types and are well described by a model derived in Schaefer P et al (2012 Phys. Fluids 24 045104). Particular attention is given to the conditional mean velocity difference at the ending points of the segments, which can be understood as a first-order structure function in the context of streamline segment analysis. It determines to a large extent the stretching (compression) of positive (negative) streamline segments and corresponds to the convective velocity in phase space in the transport model equation for the pdf. While based on the random sweeping hypothesis a scaling ∝ (u rms ετ) 1/3 is found for the parameterization based on the pseudo-time, the parameterization with the arclength l yields a much larger than expected l 1/3 scaling. A

Regularization of DT-MR images using a successive Fermat median filtering method.

Science.gov (United States)

Kwon, Kiwoon; Kim, Dongyoun; Kim, Sunghee; Park, Insung; Jeong, Jaewon; Kim, Taehwan; Hong, Cheolpyo; Han, Bongsoo

2008-05-21

Tractography using diffusion tensor magnetic resonance imaging (DT-MRI) is a method to determine the architecture of axonal fibers in the central nervous system by computing the direction of greatest diffusion in the white matter of the brain. To reduce the noise in DT-MRI measurements, a tensor-valued median filter, which is reported to be denoising and structure preserving in the tractography, is applied. In this paper, we proposed the successive Fermat (SF) method, successively using Fermat point theory for a triangle contained in the two-dimensional plane, as a median filtering method. We discussed the error analysis and numerical study about the SF method for phantom and experimental data. By considering the computing time and the image quality aspects of the numerical study simultaneously, we showed that the SF method is much more efficient than the simple median (SM) and gradient descents (GD) methods.

Regularization of DT-MR images using a successive Fermat median filtering method

International Nuclear Information System (INIS)

Kwon, Kiwoon; Kim, Dongyoun; Kim, Sunghee; Park, Insung; Jeong, Jaewon; Kim, Taehwan; Hong, Cheolpyo; Han, Bongsoo

2008-01-01

Tractography using diffusion tensor magnetic resonance imaging (DT-MRI) is a method to determine the architecture of axonal fibers in the central nervous system by computing the direction of greatest diffusion in the white matter of the brain. To reduce the noise in DT-MRI measurements, a tensor-valued median filter, which is reported to be denoising and structure preserving in the tractography, is applied. In this paper, we proposed the successive Fermat (SF) method, successively using Fermat point theory for a triangle contained in the two-dimensional plane, as a median filtering method. We discussed the error analysis and numerical study about the SF method for phantom and experimental data. By considering the computing time and the image quality aspects of the numerical study simultaneously, we showed that the SF method is much more efficient than the simple median (SM) and gradient descents (GD) methods

Regularization of DT-MR images using a successive Fermat median filtering method

Energy Technology Data Exchange (ETDEWEB)

Kwon, Kiwoon; Kim, Dongyoun; Kim, Sunghee; Park, Insung; Jeong, Jaewon; Kim, Taehwan [Department of Biomedical Engineering, Yonsei University, Wonju, 220-710 (Korea, Republic of); Hong, Cheolpyo; Han, Bongsoo [Department of Radiological Science, Yonsei University, Wonju, 220-710 (Korea, Republic of)], E-mail: bshan@yonsei.ac.kr

2008-05-21

Tractography using diffusion tensor magnetic resonance imaging (DT-MRI) is a method to determine the architecture of axonal fibers in the central nervous system by computing the direction of greatest diffusion in the white matter of the brain. To reduce the noise in DT-MRI measurements, a tensor-valued median filter, which is reported to be denoising and structure preserving in the tractography, is applied. In this paper, we proposed the successive Fermat (SF) method, successively using Fermat point theory for a triangle contained in the two-dimensional plane, as a median filtering method. We discussed the error analysis and numerical study about the SF method for phantom and experimental data. By considering the computing time and the image quality aspects of the numerical study simultaneously, we showed that the SF method is much more efficient than the simple median (SM) and gradient descents (GD) methods.

Glyph-Based Comparative Visualization for Diffusion Tensor Fields.

Science.gov (United States)

Zhang, Changgong; Schultz, Thomas; Lawonn, Kai; Eisemann, Elmar; Vilanova, Anna

2016-01-01

Diffusion Tensor Imaging (DTI) is a magnetic resonance imaging modality that enables the in-vivo reconstruction and visualization of fibrous structures. To inspect the local and individual diffusion tensors, glyph-based visualizations are commonly used since they are able to effectively convey full aspects of the diffusion tensor. For several applications it is necessary to compare tensor fields, e.g., to study the effects of acquisition parameters, or to investigate the influence of pathologies on white matter structures. This comparison is commonly done by extracting scalar information out of the tensor fields and then comparing these scalar fields, which leads to a loss of information. If the glyph representation is kept, simple juxtaposition or superposition can be used. However, neither facilitates the identification and interpretation of the differences between the tensor fields. Inspired by the checkerboard style visualization and the superquadric tensor glyph, we design a new glyph to locally visualize differences between two diffusion tensors by combining juxtaposition and explicit encoding. Because tensor scale, anisotropy type, and orientation are related to anatomical information relevant for DTI applications, we focus on visualizing tensor differences in these three aspects. As demonstrated in a user study, our new glyph design allows users to efficiently and effectively identify the tensor differences. We also apply our new glyphs to investigate the differences between DTI datasets of the human brain in two different contexts using different b-values, and to compare datasets from a healthy and HIV-infected subject.

The challenge of mapping the human connectome based on diffusion tractography

DEFF Research Database (Denmark)

Maier-Hein, Klaus H.; Neher, Peter F.; Houde, Jean-Christophe

2017-01-01

Tractography based on non-invasive diffusion imaging is central to the study of human brain connectivity. To date, the approach has not been systematically validated in ground truth studies. Based on a simulated human brain data set with ground truth tracts, we organized an open international tra...

The challenge of mapping the human connectome based on diffusion tractography

NARCIS (Netherlands)

Maier-Hein, Klaus H; Neher, Peter F; Houde, Jean-Christophe; Côté, Marc-Alexandre; Garyfallidis, Eleftherios; Zhong, Jidan; Chamberland, Maxime; Yeh, Fang-Cheng; Lin, Ying-Chia; Ji, Qing; Reddick, Wilburn E; Glass, John O; Chen, David Qixiang; Feng, Yuanjing; Gao, Chengfeng; Wu, Ye; Ma, Jieyan; Renjie, H; Li, Qiang; Westin, Carl Fredrik; Deslauriers-Gauthier, Samuel; González, J Omar Ocegueda; Paquette, Michael; St-Jean, Samuel; Girard, Gabriel; Rheault, François; Sidhu, Jasmeen; Tax, Chantal M.W.; Guo, Fenghua; Mesri, Hamed Y.; Dávid, Szabolcs; Froeling, Martijn; Heemskerk, Anneriet M.; Leemans, Alexander; Boré, Arnaud; Pinsard, Basile; Bedetti, Christophe; Desrosiers, Matthieu; Brambati, Simona; Doyon, Julien; Sarica, Alessia; Vasta, Roberta; Cerasa, Antonio; Quattrone, Aldo; Yeatman, Jason; Khan, Ali R.; Hodges, Wes; Alexander, Simon; Romascano, David; Barakovic, Muhamed; Auría, Anna; Esteban, Oscar; Lemkaddem, Alia; Thiran, Jean-Philippe; Cetingul, H Ertan; Odry, Benjamin L; Mailhe, Boris; Nadar, Mariappan S; Pizzagalli, Fabrizio; Prasad, Gautam; Villalon-Reina, Julio E; Galvis, Justin; Thompson, Paul M.; Requejo, Francisco De Santiago; Laguna, Pedro Luque; Lacerda, Luis Miguel; Barrett, Rachel; Dell'Acqua, Flavio; Catani, Marco; Petit, Laurent; Caruyer, Emmanuel; Daducci, Alessandro; Dyrby, Tim B; Holland-Letz, Tim; Hilgetag, Claus C.; Stieltjes, Bram; Descoteaux, Maxime

2017-01-01

Tractography based on non-invasive diffusion imaging is central to the study of human brain connectivity. To date, the approach has not been systematically validated in ground truth studies. Based on a simulated human brain data set with ground truth tracts, we organized an open international

Comparative Analysis of Wolbachia Genomes Reveals Streamlining and Divergence of Minimalist Two-Component Systems

Science.gov (United States)

Christensen, Steen; Serbus, Laura Renee

2015-01-01

Two-component regulatory systems are commonly used by bacteria to coordinate intracellular responses with environmental cues. These systems are composed of functional protein pairs consisting of a sensor histidine kinase and cognate response regulator. In contrast to the well-studied Caulobacter crescentus system, which carries dozens of these pairs, the streamlined bacterial endosymbiont Wolbachia pipientis encodes only two pairs: CckA/CtrA and PleC/PleD. Here, we used bioinformatic tools to compare characterized two-component system relays from C. crescentus, the related Anaplasmataceae species Anaplasma phagocytophilum and Ehrlichia chaffeensis, and 12 sequenced Wolbachia strains. We found the core protein pairs and a subset of interacting partners to be highly conserved within Wolbachia and these other Anaplasmataceae. Genes involved in two-component signaling were positioned differently within the various Wolbachia genomes, whereas the local context of each gene was conserved. Unlike Anaplasma and Ehrlichia, Wolbachia two-component genes were more consistently found clustered with metabolic genes. The domain architecture and key functional residues standard for two-component system proteins were well-conserved in Wolbachia, although residues that specify cognate pairing diverged substantially from other Anaplasmataceae. These findings indicate that Wolbachia two-component signaling pairs share considerable functional overlap with other α-proteobacterial systems, whereas their divergence suggests the potential for regulatory differences and cross-talk. PMID:25809075

Three-dimensional corticospinal tractography for brain tumor surgery

International Nuclear Information System (INIS)

Kamada, Kyousuke

2009-01-01

Maximal resection of the intracranial lesion like a brain tumor and concomitant identification of the unresectable region for avoiding the loss of motor and language functions are important before and during the operation. For these purposes, corticospinal tract (CST)-tractography (TG) based on diffusion tensor imaging (DTI) is widely used for nerve fiber tracking but it is conceivably essential to examine if the CST image in problem reflects the actually valid anatomical, functional CST. For the problem, in author's department, the intraoperative local relationship between the lesion and CST is monitored by a neuronavigation (NNA) system combined with CST-TG in case of patients who have the lesion close to CST and, when the resection site approaches CST, its surrounding white matter is electrically stimulated to evoke the myoelectric potential at upper and lower limbs. Here are reported examinations of the reliability of CST-TG by analysis of the positional relation of CST with the electric stimulating point and current value, and of the expansion of the subcortical stimulation current in the white matter. MRI data of such 40 patients as above by 1.5 or 3T machine were obtained with spin-echo/echo planer imaging and subsequent DTI data were processed by authors' VOLUME-ONE/dTV (http://volume-one.org). CST-TG-fused functional NNA was conducted by NNA system where 3D reconstructed image of CST-TG DTI and 3DMRI using digital imaging and communication medicine (DICOM) and the evoked functional myoelectric potential had been combined. This fusion was found useful for rapid decision of the position and timing of the electric stimulation at surgery, and highly reliable as CST-TG. Further, the stimulating threshold in the white matter was found lower than in the cortex. Future progress in imaging technology and separating algorithm of crossing fibers was expected for improved image of more complex central nervous system (CNS) structures. (K.T.)

Linear associations between clinically assessed upper motor neuron disease and diffusion tensor imaging metrics in amyotrophic lateral sclerosis.

Science.gov (United States)

Woo, John H; Wang, Sumei; Melhem, Elias R; Gee, James C; Cucchiara, Andrew; McCluskey, Leo; Elman, Lauren

2014-01-01

To assess the relationship between clinically assessed Upper Motor Neuron (UMN) disease in Amyotrophic Lateral Sclerosis (ALS) and local diffusion alterations measured in the brain corticospinal tract (CST) by a tractography-driven template-space region-of-interest (ROI) analysis of Diffusion Tensor Imaging (DTI). This cross-sectional study included 34 patients with ALS, on whom DTI was performed. Clinical measures were separately obtained including the Penn UMN Score, a summary metric based upon standard clinical methods. After normalizing all DTI data to a population-specific template, tractography was performed to determine a region-of-interest (ROI) outlining the CST, in which average Mean Diffusivity (MD) and Fractional Anisotropy (FA) were estimated. Linear regression analyses were used to investigate associations of DTI metrics (MD, FA) with clinical measures (Penn UMN Score, ALSFRS-R, duration-of-disease), along with age, sex, handedness, and El Escorial category as covariates. For MD, the regression model was significant (p = 0.02), and the only significant predictors were the Penn UMN Score (p = 0.005) and age (p = 0.03). The FA regression model was also significant (p = 0.02); the only significant predictor was the Penn UMN Score (p = 0.003). Measured by the template-space ROI method, both MD and FA were linearly associated with the Penn UMN Score, supporting the hypothesis that DTI alterations reflect UMN pathology as assessed by the clinical examination.

Spherical Tensor Calculus for Local Adaptive Filtering

Science.gov (United States)

Reisert, Marco; Burkhardt, Hans

In 3D image processing tensors play an important role. While rank-1 and rank-2 tensors are well understood and commonly used, higher rank tensors are rare. This is probably due to their cumbersome rotation behavior which prevents a computationally efficient use. In this chapter we want to introduce the notion of a spherical tensor which is based on the irreducible representations of the 3D rotation group. In fact, any ordinary cartesian tensor can be decomposed into a sum of spherical tensors, while each spherical tensor has a quite simple rotation behavior. We introduce so called tensorial harmonics that provide an orthogonal basis for spherical tensor fields of any rank. It is just a generalization of the well known spherical harmonics. Additionally we propose a spherical derivative which connects spherical tensor fields of different degree by differentiation. Based on the proposed theory we present two applications. We propose an efficient algorithm for dense tensor voting in 3D, which makes use of tensorial harmonics decomposition of the tensor-valued voting field. In this way it is possible to perform tensor voting by linear-combinations of convolutions in an efficient way. Secondly, we propose an anisotropic smoothing filter that uses a local shape and orientation adaptive filter kernel which can be computed efficiently by the use spherical derivatives.

Simultaneous two-view epipolar geometry estimation and motion segmentation by 4D tensor voting.

Science.gov (United States)

Tong, Wai-Shun; Tang, Chi-Keung; Medioni, Gérard

2004-09-01

We address the problem of simultaneous two-view epipolar geometry estimation and motion segmentation from nonstatic scenes. Given a set of noisy image pairs containing matches of n objects, we propose an unconventional, efficient, and robust method, 4D tensor voting, for estimating the unknown n epipolar geometries, and segmenting the static and motion matching pairs into n independent motions. By considering the 4D isotropic and orthogonal joint image space, only two tensor voting passes are needed, and a very high noise to signal ratio (up to five) can be tolerated. Epipolar geometries corresponding to multiple, rigid motions are extracted in succession. Only two uncalibrated frames are needed, and no simplifying assumption (such as affine camera model or homographic model between images) other than the pin-hole camera model is made. Our novel approach consists of propagating a local geometric smoothness constraint in the 4D joint image space, followed by global consistency enforcement for extracting the fundamental matrices corresponding to independent motions. We have performed extensive experiments to compare our method with some representative algorithms to show that better performance on nonstatic scenes are achieved. Results on challenging data sets are presented.

Tensor network state correspondence and holography

Science.gov (United States)

Singh, Sukhwinder

2018-01-01

In recent years, tensor network states have emerged as a very useful conceptual and simulation framework to study quantum many-body systems at low energies. In this paper, we describe a particular way in which any given tensor network can be viewed as a representation of two different quantum many-body states. The two quantum many-body states are said to correspond to each other by means of the tensor network. We apply this "tensor network state correspondence"—a correspondence between quantum many-body states mediated by tensor networks as we describe—to the multi-scale entanglement renormalization ansatz (MERA) representation of ground states of one dimensional (1D) quantum many-body systems. Since the MERA is a 2D hyperbolic tensor network (the extra dimension is identified as the length scale of the 1D system), the two quantum many-body states obtained from the MERA, via tensor network state correspondence, are seen to live in the bulk and on the boundary of a discrete hyperbolic geometry. The bulk state so obtained from a MERA exhibits interesting features, some of which caricature known features of the holographic correspondence of String theory. We show how (i) the bulk state admits a description in terms of "holographic screens", (ii) the conformal field theory data associated with a critical ground state can be obtained from the corresponding bulk state, in particular, how pointlike boundary operators are identified with extended bulk operators. (iii) We also present numerical results to illustrate that bulk states, dual to ground states of several critical spin chains, have exponentially decaying correlations, and that the bulk correlation length generally decreases with increase in central charge for these spin chains.

弥散张量成像的脑神经示踪重建及临床应用研究%Three-dimensional reconstruction of cranial nerves and clinical exploration based on diffusion tensor tractography

Institute of Scientific and Technical Information of China (English)

马峻; 苏少波; 赵岩; 李勇刚; 岳树源

2014-01-01

目的 探讨应用弥散张量成像进行脑神经(CNs)纤维束示踪、可视化重建的可行性,并尝试将其应用于颅底肿瘤术前规划.方法 利用3.0T磁共振对10例健康志愿者,10例颅底肿瘤患者进行稳态采集快速成像、弥散张量成像扫描,3D Slicer软件完成脑神经纤维示踪、重建,病变患者重建肿瘤三维影像,通过手术观察及神经电生理监测确认脑神经的位置.结果 CNⅡ、Ⅲ、Ⅴ、Ⅵ、Ⅶ～Ⅷ、Ⅹ、Ⅻ成像良好,肿瘤、水肿与相关脑神经的三维空间关系通过纤维示踪与三维重建得以呈现,经过手术验证准确无误.结论联合应用弥散张量成像及3D Slicer软件是正常及病理状态下脑神经可视化重建切实可行的方案,具有良好的临床应用前景.%Objective To investigate the feasibility of 3-dimensional reconstruction of cranial nerves (CNs) via diffusion imaging tractography,and attempt to apply in the preoperative plan of skull base tumor.Methods 3-Tesla magnetic resonance imaging scans,including 3D-FSPGR,FIESTA and DTI,were used to collect information of 10 healthy subjects and 10 skull base tumor patients.DTI data were integrated into the 3D-Slicer for fiber tracking,overlapped anatomic images to determine course of nerves.3D reconstructions of tumors were achieved to perform neighbor,encasing,invading relationship between lesion and nerves whose location was then recorded during surgery by surgical observation and neurophysiological monitoring.Results Detailed fibers of the cranialnerves were depicted.Optic pathway showed perfect 3D streamline body,especially the posterior of optic chiasm.Oculomotor nerve coursed from the brainstem to the cavernous sinus distally,which also had high fidelity.Trigeminal nerve allowed visualization of gasserian ganglion as cisternal segment.Cisternal parts of abducent nerve,facial/ vestibulocochlear nerve,vagus nerve,hypoglossal nerve were also imaged well.Moreover,the 3D

Efficient MATLAB computations with sparse and factored tensors.

Energy Technology Data Exchange (ETDEWEB)

Bader, Brett William; Kolda, Tamara Gibson (Sandia National Lab, Livermore, CA)

2006-12-01

In this paper, the term tensor refers simply to a multidimensional or N-way array, and we consider how specially structured tensors allow for efficient storage and computation. First, we study sparse tensors, which have the property that the vast majority of the elements are zero. We propose storing sparse tensors using coordinate format and describe the computational efficiency of this scheme for various mathematical operations, including those typical to tensor decomposition algorithms. Second, we study factored tensors, which have the property that they can be assembled from more basic components. We consider two specific types: a Tucker tensor can be expressed as the product of a core tensor (which itself may be dense, sparse, or factored) and a matrix along each mode, and a Kruskal tensor can be expressed as the sum of rank-1 tensors. We are interested in the case where the storage of the components is less than the storage of the full tensor, and we demonstrate that many elementary operations can be computed using only the components. All of the efficiencies described in this paper are implemented in the Tensor Toolbox for MATLAB.

Tensor network decompositions in the presence of a global symmetry

International Nuclear Information System (INIS)

Singh, Sukhwinder; Pfeifer, Robert N. C.; Vidal, Guifre

2010-01-01

Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a compact, completely reducible group G, in tensor network decompositions and algorithms. This is achieved by considering tensors that are invariant under the action of the group G. Each symmetric tensor decomposes into two types of tensors: degeneracy tensors, containing all the degrees of freedom, and structural tensors, which only depend on the symmetry group. In numerical calculations, the use of symmetric tensors ensures the preservation of the symmetry, allows selection of a specific symmetry sector, and significantly reduces computational costs. On the other hand, the resulting tensor network can be interpreted as a superposition of exponentially many spin networks. Spin networks are used extensively in loop quantum gravity, where they represent states of quantum geometry. Our work highlights their importance in the context of tensor network algorithms as well, thus setting the stage for cross-fertilization between these two areas of research.

Contemporary imaging of mild TBI: the journey toward diffusion tensor imaging to assess neuronal damage.

Science.gov (United States)

Fox, W Christopher; Park, Min S; Belverud, Shawn; Klugh, Arnett; Rivet, Dennis; Tomlin, Jeffrey M

2013-04-01

To follow the progression of neuroimaging as a means of non-invasive evaluation of mild traumatic brain injury (mTBI) in order to provide recommendations based on reproducible, defined imaging findings. A comprehensive literature review and analysis of contemporary published articles was performed to study the progression of neuroimaging findings as a non-invasive 'biomarker' for mTBI. Multiple imaging modalities exist to support the evaluation of patients with mTBI, including ultrasound (US), computed tomography (CT), single photon emission computed tomography (SPECT), positron emission tomography (PET), and magnetic resonance imaging (MRI). These techniques continue to evolve with the development of fractional anisotropy (FA), fiber tractography (FT), and diffusion tensor imaging (DTI). Modern imaging techniques, when applied in the appropriate clinical setting, may serve as a valuable tool for diagnosis and management of patients with mTBI. An understanding of modern neuroanatomical imaging will enhance our ability to analyse injury and recognize the manifestations of mTBI.

The Topology of Symmetric Tensor Fields

Science.gov (United States)

Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval

1997-01-01

Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.

On Lovelock analogs of the Riemann tensor

Science.gov (United States)

Camanho, Xián O.; Dadhich, Naresh

2016-03-01

It is possible to define an analog of the Riemann tensor for Nth order Lovelock gravity, its characterizing property being that the trace of its Bianchi derivative yields the corresponding analog of the Einstein tensor. Interestingly there exist two parallel but distinct such analogs and the main purpose of this note is to reconcile both formulations. In addition we will introduce a simple tensor identity and use it to show that any pure Lovelock vacuum in odd d=2N+1 dimensions is Lovelock flat, i.e. any vacuum solution of the theory has vanishing Lovelock-Riemann tensor. Further, in the presence of cosmological constant it is the Lovelock-Weyl tensor that vanishes.

Mean streamline analysis for performance prediction of cross-flow fans

International Nuclear Information System (INIS)

Kim, Jae Won; Oh, Hyoung Woo

2004-01-01

This paper presents the mean streamline analysis using the empirical loss correlations for performance prediction of cross-flow fans. Comparison of overall performance predictions with test data of a cross-flow fan system with a simplified vortex wall scroll casing and with the published experimental characteristics for a cross-flow fan has been carried out to demonstrate the accuracy of the proposed method. Predicted performance curves by the present mean streamline analysis agree well with experimental data for two different cross-flow fans over the normal operating conditions. The prediction method presented herein can be used efficiently as a tool for the preliminary design and performance analysis of general-purpose cross-flow fans

Q-creation and annihilation tensors for the two parameters deformation of U(SU(2))

International Nuclear Information System (INIS)

Wehrhahn, R.F.; Vraceanu, D.

1993-03-01

The Jordan-Schwinger construction for the Hopf algebra U qp (su(2)) is realized. The creation and annihilation tensor operators together with their tensor products including the Casimir operators are calculated. (orig.)

Reconstruction of convex bodies from surface tensors

DEFF Research Database (Denmark)

Kousholt, Astrid; Kiderlen, Markus

2016-01-01

We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. When only measurements subject to noise...... of surface tensors are available for reconstruction, we recommend to use certain values of the surface tensors, namely harmonic intrinsic volumes instead of the surface tensors evaluated at the standard basis. The second algorithm we present is based on harmonic intrinsic volumes and allows for noisy...... measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based on measurements subject to noise is established under certain assumptions on the noise...

Energy-momentum tensor in scalar QED

International Nuclear Information System (INIS)

Joglekar, S.D.; Misra, A.

1988-01-01

We consider the renormalization of the energy-momentum tensor in scalar quantum electrodynamics. We show the need for adding an improvement term to the conventional energy-momentum tensor. We consider two possible forms for the improvement term: (i) one in which the improvement coefficient is a finite function of bare parameters of the theory (so that the energy-momentum tensor can be obtained from an action that is a finite function of bare quantities); (ii) one in which the improvement coefficient is a finite quantity, i.e., a finite function of renormalized parameters. We establish a negative result; viz., neither form leads to a finite energy-momentum tensor to O(e 2 λ/sup n/). .AE

MRI and MR tractography in bilateral hypertrophic olivary degeneration.

Science.gov (United States)

Sen, Debraj; Gulati, Yoginder S; Malik, Virender; Mohimen, Aneesh; Sibi, Eranki; Reddy, Deepak Chandra

2014-10-01

Hypertrophic olivary degeneration is a trans-synaptic neuronal degeneration associated with hypertrophy of the inferior olivary nucleus due to a lesion in the triangle of Guillain-Mollaret. Familiarity with this entity on magnetic resonance imaging (MRI) is essential to avoid other erroneous ominous diagnoses. We present a case of bilateral hypertrophic olivary degeneration and discuss the etiopathogenesis and MRI findings in this entity. The contributory role of MR tractography in the diagnosis is also highlighted.

MRI and MR tractography in bilateral hypertrophic olivary degeneration

International Nuclear Information System (INIS)

Sen, Debraj; Gulati, Yoginder S.; Malik, Virender; Mohimen, Aneesh; Sibi, Eranki; Reddy, Deepak Chandra

2014-01-01

Hypertrophic olivary degeneration is a trans-synaptic neuronal degeneration associated with hypertrophy of the inferior olivary nucleus due to a lesion in the triangle of Guillain-Mollaret. Familiarity with this entity on magnetic resonance imaging (MRI) is essential to avoid other erroneous ominous diagnoses. We present a case of bilateral hypertrophic olivary degeneration and discuss the etiopathogenesis and MRI findings in this entity. The contributory role of MR tractography in the diagnosis is also highlighted

Probing white-matter microstructure with higher-order diffusion tensors and susceptibility tensor MRI

Science.gov (United States)

Liu, Chunlei; Murphy, Nicole E.; Li, Wei

2012-01-01

Diffusion MRI has become an invaluable tool for studying white matter microstructure and brain connectivity. The emergence of quantitative susceptibility mapping and susceptibility tensor imaging (STI) has provided another unique tool for assessing the structure of white matter. In the highly ordered white matter structure, diffusion MRI measures hindered water mobility induced by various tissue and cell membranes, while susceptibility sensitizes to the molecular composition and axonal arrangement. Integrating these two methods may produce new insights into the complex physiology of white matter. In this study, we investigated the relationship between diffusion and magnetic susceptibility in the white matter. Experiments were conducted on phantoms and human brains in vivo. Diffusion properties were quantified with the diffusion tensor model and also with the higher order tensor model based on the cumulant expansion. Frequency shift and susceptibility tensor were measured with quantitative susceptibility mapping and susceptibility tensor imaging. These diffusion and susceptibility quantities were compared and correlated in regions of single fiber bundles and regions of multiple fiber orientations. Relationships were established with similarities and differences identified. It is believed that diffusion MRI and susceptibility MRI provide complementary information of the microstructure of white matter. Together, they allow a more complete assessment of healthy and diseased brains. PMID:23507987

The energy–momentum tensor(s in classical gauge theories

Directory of Open Access Journals (Sweden)

Daniel N. Blaschke

2016-11-01

Full Text Available We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.

Industrial Compositional Streamline Simulation for Efficient and Accurate Prediction of Gas Injection and WAG Processes

Energy Technology Data Exchange (ETDEWEB)

Margot Gerritsen

2008-10-31

the redundant work generally done in the near-well regions. We improved the accuracy of the streamline simulator with a higher order mapping from pressure grid to streamlines that significantly reduces smoothing errors, and a Kriging algorithm is used to map from the streamlines to the background grid. The higher accuracy of the Kriging mapping means that it is not essential for grid blocks to be crossed by one or more streamlines. The higher accuracy comes at the price of increased computational costs, but allows coarser coverage and so does not generally increase the overall costs of the computations. To reduce errors associated with fixing the pressure field between pressure updates, we developed a higher order global time-stepping method that allows the use of larger global time steps. Third-order ENO schemes are suggested to propagate components along streamlines. Both in the two-phase and three-phase experiments these ENO schemes outperform other (higher order) upwind schemes. Application of the third order ENO scheme leads to overall computational savings because the computational grid used can be coarsened. Grid adaptivity along streamlines is implemented to allow sharp but efficient resolution of solution fronts at reduced computational costs when displacement fronts are sufficiently separated. A correction for Volume Change On Mixing (VCOM) is implemented that is very effective at handling this effect. Finally, a specialized gravity operator splitting method is proposed for use in compositional streamline methods that gives an effective correction of gravity segregation. A significant part of our effort went into the development of a parallelization strategy for streamline solvers on the next generation shared memory machines. We found in this work that the built-in dynamic scheduling strategies of OpenMP lead to parallel efficiencies that are comparable to optimal schedules obtained with customized explicit load balancing strategies as long as the ratio of

Applications of tensor functions in creep mechanics

International Nuclear Information System (INIS)

Betten, J.

1991-01-01

Within this contribution a short survey is given of some recent advances in the mathematical modelling of materials behaviour under creep conditions. The mechanical behaviour of anisotropic solids requires a suitable mathematical modelling. The properties of tensor functions with several argument tensors constitute a rational basis for a consistent mathematical modelling of complex material behaviour. This paper presents certain principles, methods, and recent successfull applications of tensor functions in solid mechanics. The rules for specifying irreducible sets of tensor invariants and tensor generators for material tensors of rank two and four are also discussed. Furthermore, it is very important that the scalar coefficients in constitutive and evolutional equations are determined as functions of the integrity basis and experimental data. It is explained in detail that these coefficients can be determined by using tensorial interpolation methods. Some examples for practical use are discussed. (orig./RHM)

Tensor Galileons and gravity

Energy Technology Data Exchange (ETDEWEB)

Chatzistavrakidis, Athanasios [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Khoo, Fech Scen [Department of Physics and Earth Sciences, Jacobs University Bremen,Campus Ring 1, 28759 Bremen (Germany); Roest, Diederik [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Schupp, Peter [Department of Physics and Earth Sciences, Jacobs University Bremen,Campus Ring 1, 28759 Bremen (Germany)

2017-03-13

The particular structure of Galileon interactions allows for higher-derivative terms while retaining second order field equations for scalar fields and Abelian p-forms. In this work we introduce an index-free formulation of these interactions in terms of two sets of Grassmannian variables. We employ this to construct Galileon interactions for mixed-symmetry tensor fields and coupled systems thereof. We argue that these tensors are the natural generalization of scalars with Galileon symmetry, similar to p-forms and scalars with a shift-symmetry. The simplest case corresponds to linearised gravity with Lovelock invariants, relating the Galileon symmetry to diffeomorphisms. Finally, we examine the coupling of a mixed-symmetry tensor to gravity, and demonstrate in an explicit example that the inclusion of appropriate counterterms retains second order field equations.

Tensor completion and low-n-rank tensor recovery via convex optimization

International Nuclear Information System (INIS)

Gandy, Silvia; Yamada, Isao; Recht, Benjamin

2011-01-01

In this paper we consider sparsity on a tensor level, as given by the n-rank of a tensor. In an important sparse-vector approximation problem (compressed sensing) and the low-rank matrix recovery problem, using a convex relaxation technique proved to be a valuable solution strategy. Here, we will adapt these techniques to the tensor setting. We use the n-rank of a tensor as a sparsity measure and consider the low-n-rank tensor recovery problem, i.e. the problem of finding the tensor of the lowest n-rank that fulfills some linear constraints. We introduce a tractable convex relaxation of the n-rank and propose efficient algorithms to solve the low-n-rank tensor recovery problem numerically. The algorithms are based on the Douglas–Rachford splitting technique and its dual variant, the alternating direction method of multipliers

Tensor eigenvalues and their applications

CERN Document Server

Qi, Liqun; Chen, Yannan

2018-01-01

This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues.

Loop optimization for tensor network renormalization

Science.gov (United States)

Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang

We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network, which can be successfully applied to both classical and quantum systems on and off criticality. The key idea of our scheme is to deform a 2D tensor network into small loops and then optimize tensors on each loop. In this way we remove short-range entanglement at each iteration step, and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model. NSF Grant No. DMR-1005541 and NSFC 11274192, BMO Financial Group, John Templeton Foundation, Government of Canada through Industry Canada, Province of Ontario through the Ministry of Economic Development & Innovation.

Algebraic Rainich conditions for the fourth rank tensor V

International Nuclear Information System (INIS)

So, Lau Loi

2011-01-01

Algebraic conditions on the Ricci tensor in the Rainich-Misner-Wheeler unified field theory are known as the Rainich conditions. Penrose and more recently Bergqvist and Lankinen made an analogy from the Ricci tensor to the Bel-Robinson tensor B αβμν , a certain fourth rank tensor quadratic in the Weyl curvature, which also satisfies algebraic Rainich-like conditions. However, we found that not only does the tensor B αβμν fulfill these conditions, but so also does our recently proposed tensor V αβμν , which has many of the desirable properties of B αβμν . For the quasilocal small sphere limit restriction, we found that there are only two fourth rank tensors, B αβμν and V αβμν , which form a basis for good energy expressions. Both of them have the completely trace free and causal properties, these two form necessary and sufficient conditions. Surprisingly either completely traceless or causal is enough to fulfill the algebraic Rainich conditions.

Tensor network method for reversible classical computation

Science.gov (United States)

Yang, Zhi-Cheng; Kourtis, Stefanos; Chamon, Claudio; Mucciolo, Eduardo R.; Ruckenstein, Andrei E.

2018-03-01

We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017), 10.1038/ncomms15303]. By encoding the truth table of each vertex constraint in a tensor, the total number of solutions compatible with partial inputs and outputs at the boundary can be represented as the full contraction of a tensor network. We introduce an iterative compression-decimation (ICD) scheme that performs this contraction efficiently. The ICD algorithm first propagates local constraints to longer ranges via repeated contraction-decomposition sweeps over all lattice bonds, thus achieving compression on a given length scale. It then decimates the lattice via coarse-graining tensor contractions. Repeated iterations of these two steps gradually collapse the tensor network and ultimately yield the exact tensor trace for large systems, without the need for manual control of tensor dimensions. Our protocol allows us to obtain the exact number of solutions for computations where a naive enumeration would take astronomically long times.

Robust estimation of adaptive tensors of curvature by tensor voting.

Science.gov (United States)

Tong, Wai-Shun; Tang, Chi-Keung

2005-03-01

Although curvature estimation from a given mesh or regularly sampled point set is a well-studied problem, it is still challenging when the input consists of a cloud of unstructured points corrupted by misalignment error and outlier noise. Such input is ubiquitous in computer vision. In this paper, we propose a three-pass tensor voting algorithm to robustly estimate curvature tensors, from which accurate principal curvatures and directions can be calculated. Our quantitative estimation is an improvement over the previous two-pass algorithm, where only qualitative curvature estimation (sign of Gaussian curvature) is performed. To overcome misalignment errors, our improved method automatically corrects input point locations at subvoxel precision, which also rejects outliers that are uncorrectable. To adapt to different scales locally, we define the RadiusHit of a curvature tensor to quantify estimation accuracy and applicability. Our curvature estimation algorithm has been proven with detailed quantitative experiments, performing better in a variety of standard error metrics (percentage error in curvature magnitudes, absolute angle difference in curvature direction) in the presence of a large amount of misalignment noise.

On improving the efficiency of tensor voting

OpenAIRE

Moreno, Rodrigo; Garcia, Miguel Angel; Puig, Domenec; Pizarro, Luis; Burgeth, Bernhard; Weickert, Joachim

2011-01-01

This paper proposes two alternative formulations to reduce the high computational complexity of tensor voting, a robust perceptual grouping technique used to extract salient information from noisy data. The first scheme consists of numerical approximations of the votes, which have been derived from an in-depth analysis of the plate and ball voting processes. The second scheme simplifies the formulation while keeping the same perceptual meaning of the original tensor voting: The stick tensor v...

Tensor Transpose and Its Properties

OpenAIRE

Pan, Ran

2014-01-01

Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes. Properties of tensor transpose are studied in relation to tensor multiplication, tensor eigenvalues, tensor decompositions and tensor rank.

MRI and MR tractography in bilateral hypertrophic olivary degeneration

Directory of Open Access Journals (Sweden)

Debraj Sen

2014-01-01

Full Text Available Hypertrophic olivary degeneration is a trans-synaptic neuronal degeneration associated with hypertrophy of the inferior olivary nucleus due to a lesion in the triangle of Guillain-Mollaret. Familiarity with this entity on magnetic resonance imaging (MRI is essential to avoid other erroneous ominous diagnoses. We present a case of bilateral hypertrophic olivary degeneration and discuss the etiopathogenesis and MRI findings in this entity. The contributory role of MR tractography in the diagnosis is also highlighted.

Periventricular Nodular Heterotopia: Detection of Abnormal Microanatomic Fiber Structures with Whole-Brain Diffusion MR Imaging Tractography.

Science.gov (United States)

Farquharson, Shawna; Tournier, J-Donald; Calamante, Fernando; Mandelstam, Simone; Burgess, Rosemary; Schneider, Michal E; Berkovic, Samuel F; Scheffer, Ingrid E; Jackson, Graeme D; Connelly, Alan

2016-12-01

Purpose To investigate whether it is possible in patients with periventricular nodular heterotopia (PVNH) to detect abnormal fiber projections that have only previously been reported in the histopathology literature. Materials and Methods Whole-brain diffusion-weighted (DW) imaging data from 14 patients with bilateral PVNH and 14 age- and sex-matched healthy control subjects were prospectively acquired by using 3.0-T magnetic resonance (MR) imaging between August 1, 2008, and December 5, 2012. All participants provided written informed consent. The DW imaging data were processed to generate whole-brain constrained spherical deconvolution (CSD)-based tractography data and super-resolution track-density imaging (TDI) maps. The tractography data were overlaid on coregistered three-dimensional T1-weighted images to visually assess regions of heterotopia. A panel of MR imaging researchers independently assessed each case and indicated numerically (no = 1, yes = 2) as to the presence of abnormal fiber tracks in nodular tissue. The Fleiss κ statistical measure was applied to assess the reader agreement. Results Abnormal fiber tracks emanating from one or more regions of heterotopia were reported by all four readers in all 14 patients with PVNH (Fleiss κ = 1). These abnormal structures were not visible on the tractography data from any of the control subjects and were not discernable on the conventional T1-weighted images of the patients with PVNH. Conclusion Whole-brain CSD-based fiber tractography and super-resolution TDI mapping reveals abnormal fiber projections in nodular tissue suggestive of abnormal organization of white matter (with abnormal fibers both within nodules and projecting to the surrounding white matter) in patients with bilateral PVNH. © RSNA, 2016.

Creating customer value by streamlining business processes.

Science.gov (United States)

Vantrappen, H

1992-02-01

Much of the strategic preoccupation of senior managers in the 1990s is focusing on the creation of customer value. Companies are seeking competitive advantage by streamlining the three processes through which they interact with their customers: product creation, order handling and service assurance. 'Micro-strategy' is a term which has been coined for the trade-offs and decisions on where and how to streamline these three processes. The article discusses micro-strategies applied by successful companies.

Hydrodynamic Drag on Streamlined Projectiles and Cavities

KAUST Repository

Jetly, Aditya

2016-04-19

The air cavity formation resulting from the water-entry of solid objects has been the subject of extensive research due to its application in various fields such as biology, marine vehicles, sports and oil and gas industries. Recently we demonstrated that at certain conditions following the closing of the air cavity formed by the initial impact of a superhydrophobic sphere on a free water surface a stable streamlined shape air cavity can remain attached to the sphere. The formation of superhydrophobic sphere and attached air cavity reaches a steady state during the free fall. In this thesis we further explore this novel phenomenon to quantify the drag on streamlined shape cavities. The drag on the sphere-cavity formation is then compared with the drag on solid projectile which were designed to have self-similar shape to that of the cavity. The solid projectiles of adjustable weight were produced using 3D printing technique. In a set of experiments on the free fall of projectile we determined the variation of projectiles drag coefficient as a function of the projectiles length to diameter ratio and the projectiles specific weight, covering a range of intermediate Reynolds number, Re ~ 104 – 105 which are characteristic for our streamlined cavity experiments. Parallel free fall experiment with sphere attached streamlined air cavity and projectile of the same shape and effective weight clearly demonstrated the drag reduction effect due to the stress-free boundary condition at cavity liquid interface. The streamlined cavity experiments can be used as the upper bound estimate of the drag reduction by air layers naturally sustained on superhydrophobic surfaces in contact with water. In the final part of the thesis we design an experiment to test the drag reduction capacity of robust superhydrophobic coatings deposited on the surface of various model vessels.

Regional differences in fiber tractography predict neurodevelopmental outcomes in neonates with infantile Krabbe disease

Directory of Open Access Journals (Sweden)

A. Gupta

2015-01-01

Interpretation: Neonatal microstructural abnormalities correlate with neurodevelopmental treatment outcomes in patients treated for infantile Krabbe disease. DTI with quantitative tractography is an excellent biomarker for evaluating infants with Krabbe disease identified through newborn screening.

Coordinate independent expression for transverse trace-free tensors

International Nuclear Information System (INIS)

Conboye, Rory

2016-01-01

The transverse and trace-free (TT) part of the extrinsic curvature represents half of the dynamical degrees of freedom of the gravitational field in the 3 + 1 formalism. As such, it is part of the freely specifiable initial data for numerical relativity. Though TT tensors in three-space possess only two component degrees of freedom, they cannot ordinarily be given solely by two scalar potentials. Such expressions have been derived, however, in coordinate form, for all TT tensors in flat space which are also translationally or axially symmetric (Conboye and Murchadha 2014 Class. Quantum Grav. 31 085019). Since TT tensors are conformally covariant, these also give TT tensors in conformally flat space. In this article, the work above has been extended by giving a coordinate-independent expression for these TT tensors. The translational and axial symmetry conditions have also been generalized to invariance along any hypersurface orthogonal Killing vector. (paper)

Seeing More by Showing Less : Orientation-Dependent Transparency Rendering for Fiber Tractography Visualization

NARCIS (Netherlands)

Tax, Chantal M. W.; Chamberland, Maxime; van Stralen, Marijn; Viergever, Max A.; Whittingstall, Kevin; Fortin, David; Descoteaux, Maxime; Leemans, Alexander

2015-01-01

Fiber tractography plays an important role in exploring the architectural organization of fiber trajectories, both in fundamental neuroscience and in clinical applications. With the advent of diffusion MRI (dMRI) approaches that can also model "crossing fibers", the complexity of the fiber network

White matter tracts in first-episode psychosis: A DTI tractography study of the uncinate fasciculus

Science.gov (United States)

Price, Gary; Cercignani, Mara; Parker, Geoffrey J.M.; Altmann, Daniel R.; Barnes, Thomas R.E.; Barker, Gareth J.; Joyce, Eileen M.; Ron, Maria A.

2008-01-01

A model of disconnectivity involving abnormalities in the cortex and connecting white matter pathways may explain the symptoms and cognitive abnormalities of schizophrenia. Recently, diffusion imaging tractography has made it possible to study white matter pathways in detail, and we present here a study of patients with first-episode psychosis using this technique. We studied the uncinate fasciculus (UF), the largest white matter tract that connects the frontal and temporal lobes, two brain regions significantly implicated in schizophrenia. Nineteen patients with first-episode schizophrenia and 23 controls were studied using a probabilistic tractography algorithm (PICo). Fractional anisotropy (FA) and probability of connection were obtained for every voxel in the tract, and the group means and distributions of these variables were compared. The spread of the FA distribution in the upper tail, as measured by the squared coefficient of variance (SCV), was reduced in the left UF in the patient group, indicating that the number of voxels with high FA values was reduced in the core of the tract and suggesting the presence of changes in fibre alignment and tract coherence in the patient group. The SCV of FA was lower in females across both groups and there was no correlation between the SCV of FA and clinical ratings. PMID:17988894

Abnormal anatomical connectivity between the amygdala and orbitofrontal cortex in conduct disorder.

Directory of Open Access Journals (Sweden)

Luca Passamonti

Full Text Available Previous research suggested that structural and functional abnormalities within the amygdala and orbitofrontal cortex contribute to the pathophysiology of Conduct Disorder (CD. Here, we investigated whether the integrity of the white-matter pathways connecting these regions is abnormal and thus may represent a putative neurobiological marker for CD.Diffusion Tensor Imaging (DTI was used to investigate white-matter microstructural integrity in male adolescents with childhood-onset CD, compared with healthy controls matched in age, sex, intelligence, and socioeconomic status. Two approaches were employed to analyze DTI data: voxel-based morphometry of fractional anisotropy (FA, an index of white-matter integrity, and virtual dissection of white-matter pathways using tractography.Adolescents with CD displayed higher FA within the right external capsule relative to controls (T = 6.08, P<0.05, Family-Wise Error, whole-brain correction. Tractography analyses showed that FA values within the uncinate fascicle (connecting the amygdala and orbitofrontal cortex were abnormally increased in individuals with CD relative to controls. This was in contrast with the inferior frontal-occipital fascicle, which showed no significant group differences in FA. The finding of increased FA in the uncinate fascicle remained significant when factoring out the contribution of attention-deficit/hyperactivity disorder symptoms. There were no group differences in the number of streamlines in either of these anatomical tracts.These results provide evidence that CD is associated with white-matter microstructural abnormalities in the anatomical tract that connects the amygdala and orbitofrontal cortex, the uncinate fascicle. These results implicate abnormal maturation of white-matter pathways which are fundamental in the regulation of emotional behavior in CD.

Bowen-York tensors

International Nuclear Information System (INIS)

Beig, Robert; Krammer, Werner

2004-01-01

For a conformally flat 3-space, we derive a family of linear second-order partial differential operators which sends vectors into trace-free, symmetric 2-tensors. These maps, which are parametrized by conformal Killing vectors on the 3-space, are such that the divergence of the resulting tensor field depends only on the divergence of the original vector field. In particular, these maps send source-free electric fields into TT tensors. Moreover, if the original vector field is the Coulomb field on R 3 {0}, the resulting tensor fields on R 3 {0} are nothing but the family of TT tensors originally written by Bowen and York

Diffusion tensor imaging of the cervical spinal cord in healthy adult population: normative values and measurement reproducibility at 3T MRI.

Science.gov (United States)

Brander, Antti; Koskinen, Eerika; Luoto, Teemu M; Hakulinen, Ullamari; Helminen, Mika; Savilahti, Sirpa; Ryymin, Pertti; Dastidar, Prasun; Ohman, Juha

2014-05-01

Compared to diffusion tensor imaging (DTI) of the brain, there is a paucity of reports addressing the applicability of DTI in the evaluation of the spinal cord. Most normative data of cervical spinal cord DTI consist of relatively small and arbitrarily collected populations. Comprehensive normative data are necessary for clinical decision-making. To establish normal values for cervical spinal cord DTI metrics with region of interest (ROI)- and fiber tractography (FT)-based measurements and to assess the reproducibility of both measurement methods. Forty healthy adults underwent cervical spinal cord 3T MRI. Sagittal and axial conventional T2 sequences and DTI in the axial plane were performed. Whole cord fractional anisotropy (FA) and apparent diffusion coefficient (ADC) values were determined at different cervical levels from C2 to C7 using the ROI method. DTI metrics (FA, axial, and radial diffusivities based on eigenvalues λ1, λ2, and λ3, and ADC) of the lateral and posterior funicles were measured at C3 level. FA and ADC of the whole cord and the lateral and posterior funicles were also measured using quantitative tractography. Intra- and inter-observer variation of the measurement methods were assessed. Whole cord FA values decreased and ADC values increased in the rostral to caudal direction from C2 to C7. Between the individual white matter funicles no statistically significant difference for FA or ADC values was found. Both axial diffusivity and radial diffusivity of both lateral funicles differed significantly from those of the posterior funicle. Neither gender nor age correlated with any of the DTI metrics. Intra-observer variation of the measurements for whole cord FA and ADC showed almost perfect agreement with both ROI and tractography-based measurements. There was more variation in measurements of individual columns. Inter-observer agreement varied from moderate to strong for whole cord FA and ADC. Both ROI- and FT-based measurements are applicable

Diffusion tensor imaging tensor shape analysis for assessment of regional white matter differences.

Science.gov (United States)

Middleton, Dana M; Li, Jonathan Y; Lee, Hui J; Chen, Steven; Dickson, Patricia I; Ellinwood, N Matthew; White, Leonard E; Provenzale, James M

2017-08-01

Purpose The purpose of this study was to investigate a novel tensor shape plot analysis technique of diffusion tensor imaging data as a means to assess microstructural differences in brain tissue. We hypothesized that this technique could distinguish white matter regions with different microstructural compositions. Methods Three normal canines were euthanized at seven weeks old. Their brains were imaged using identical diffusion tensor imaging protocols on a 7T small-animal magnetic resonance imaging system. We examined two white matter regions, the internal capsule and the centrum semiovale, each subdivided into an anterior and posterior region. We placed 100 regions of interest in each of the four brain regions. Eigenvalues for each region of interest triangulated onto tensor shape plots as the weighted average of three shape metrics at the plot's vertices: CS, CL, and CP. Results The distribution of data on the plots for the internal capsule differed markedly from the centrum semiovale data, thus confirming our hypothesis. Furthermore, data for the internal capsule were distributed in a relatively tight cluster, possibly reflecting the compact and parallel nature of its fibers, while data for the centrum semiovale were more widely distributed, consistent with the less compact and often crossing pattern of its fibers. This indicates that the tensor shape plot technique can depict data in similar regions as being alike. Conclusion Tensor shape plots successfully depicted differences in tissue microstructure and reflected the microstructure of individual brain regions. This proof of principle study suggests that if our findings are reproduced in larger samples, including abnormal white matter states, the technique may be useful in assessment of white matter diseases.

Detection of the arcuate fasciculus in congenital amusia depends on the tractography algorithm

Directory of Open Access Journals (Sweden)

Joyce L Chen

2015-01-01

Full Text Available The advent of diffusion magnetic resonance imaging allows researchers to virtually dissect white matter fibre pathways in the brain in vivo. This, for example, allows us to characterize and quantify how fibre tracts differ across populations in health and disease, and change as a function of training. Based on diffusion MRI, prior literature reports the absence of the arcuate fasciculus (AF in some control individuals and as well in those with congenital amusia. The complete absence of such a major anatomical tract is surprising given the subtle impairments that characterize amusia. Thus, we hypothesize that failure to detect the AF in this population may relate to the tracking algorithm used, and is not necessarily reflective of their phenotype. Diffusion data in control and amusic individuals were analyzed using three different tracking algorithms: deterministic and probabilistic, the latter either modeling two or one fibre populations. Across the three algorithms, we replicate prior findings of a left greater than right AF volume, but do not find group differences or an interaction. We detect the AF in all individuals using the probabilistic 2-fibre model, however, tracking failed in some control and amusic individuals when deterministic tractography was applied. These findings show that the ability to detect the AF in our sample is dependent on the type of tractography algorithm. This raises the question of whether failure to detect the AF in prior studies may be unrelated to the underlying anatomy or phenotype.

Detection of the arcuate fasciculus in congenital amusia depends on the tractography algorithm.

Science.gov (United States)

Chen, Joyce L; Kumar, Sukhbinder; Williamson, Victoria J; Scholz, Jan; Griffiths, Timothy D; Stewart, Lauren

2015-01-01

The advent of diffusion magnetic resonance imaging (MRI) allows researchers to virtually dissect white matter fiber pathways in the brain in vivo. This, for example, allows us to characterize and quantify how fiber tracts differ across populations in health and disease, and change as a function of training. Based on diffusion MRI, prior literature reports the absence of the arcuate fasciculus (AF) in some control individuals and as well in those with congenital amusia. The complete absence of such a major anatomical tract is surprising given the subtle impairments that characterize amusia. Thus, we hypothesize that failure to detect the AF in this population may relate to the tracking algorithm used, and is not necessarily reflective of their phenotype. Diffusion data in control and amusic individuals were analyzed using three different tracking algorithms: deterministic and probabilistic, the latter either modeling two or one fiber populations. Across the three algorithms, we replicate prior findings of a left greater than right AF volume, but do not find group differences or an interaction. We detect the AF in all individuals using the probabilistic 2-fiber model, however, tracking failed in some control and amusic individuals when deterministic tractography was applied. These findings show that the ability to detect the AF in our sample is dependent on the type of tractography algorithm. This raises the question of whether failure to detect the AF in prior studies may be unrelated to the underlying anatomy or phenotype.

Sensitivity analysis of human brain structural network construction

Directory of Open Access Journals (Sweden)

Kuang Wei

2017-12-01

Full Text Available Network neuroscience leverages diffusion-weighted magnetic resonance imaging and tractography to quantify structural connectivity of the human brain. However, scientists and practitioners lack a clear understanding of the effects of varying tractography parameters on the constructed structural networks. With diffusion images from the Human Connectome Project (HCP, we characterize how structural networks are impacted by the spatial resolution of brain atlases, total number of tractography streamlines, and grey matter dilation with various graph metrics. We demonstrate how injudicious combinations of highly refined brain parcellations and low numbers of streamlines may inadvertently lead to disconnected network models with isolated nodes. Furthermore, we provide solutions to significantly reduce the likelihood of generating disconnected networks. In addition, for different tractography parameters, we investigate the distributions of values taken by various graph metrics across the population of HCP subjects. Analyzing the ranks of individual subjects within the graph metric distributions, we find that the ranks of individuals are affected differently by atlas scale changes. Our work serves as a guideline for researchers to optimize the selection of tractography parameters and illustrates how biological characteristics of the brain derived in network neuroscience studies can be affected by the choice of atlas parcellation schemes. Diffusion tractography has been proven to be a promising noninvasive technique to study the network properties of the human brain. However, how various tractography and network construction parameters affect network properties has not been studied using a large cohort of high-quality data. We utilize data provided by the Human Connectome Project to characterize the changes to network properties induced by varying the brain parcellation atlas scales, the number of reconstructed tractography tracks, and the degree of grey

Off-shell N = 2 tensor supermultiplets

International Nuclear Information System (INIS)

Wit, Bernard de; Saueressig, Frank

2006-01-01

A multiplet calculus is presented for an arbitrary number n of N = 2 tensor supermultiplets. For rigid supersymmetry the known couplings are reproduced. In the superconformal case the target spaces parametrized by the scalar fields are cones over (3n-1)-dimensional spaces encoded in homogeneous SU(2) invariant potentials, subject to certain constraints. The coupling to conformal supergravity enables the derivation of a large class of supergravity Lagrangians with vector and tensor multiplets and hypermultiplets. Dualizing the tensor fields into scalars leads to hypermultiplets with hyperkaehler or quaternion-Kaehler target spaces with at least n abelian isometries. It is demonstrated how to use the calculus for the construction of Lagrangians containing higher-derivative couplings of tensor multiplets. For the application of the c-map between vector and tensor supermultiplets to Lagrangians with higher-order derivatives, an off-shell version of this map is proposed. Various other implications of the results are discussed. As an example an elegant derivation of the classification of 4-dimensional quaternion-Kaehler manifolds with two commuting isometries is given

Harmonic d-tensors

Energy Technology Data Exchange (ETDEWEB)

Hohmann, Manuel [Physikalisches Institut, Universitaet Tartu (Estonia)

2016-07-01

Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group SO(3). In order to make use of this tool also in the setting of Finsler geometry, where the objects of relevance are d-tensors instead of tensors, we construct a set of d-tensor harmonics for both SO(3) and SO(4) symmetries and show how these can be used for calculations in Finsler geometry and gravity.

Exploring the tensor networks/AdS correspondence

Energy Technology Data Exchange (ETDEWEB)

Bhattacharyya, Arpan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Centre For High Energy Physics, Indian Institute of Science,560012 Bangalore (India); Gao, Zhe-Shen [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Hung, Ling-Yan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); State Key Laboratory of Surface Physics and Department of Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Collaborative Innovation Center of Advanced Microstructures, Nanjing University,Nanjing, 210093 (China); Liu, Si-Nong [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China)

2016-08-11

In this paper we study the recently proposed tensor networks/AdS correspondence. We found that the Coxeter group is a useful tool to describe tensor networks in a negatively curved space. Studying generic tensor network populated by perfect tensors, we find that the physical wave function generically do not admit any connected correlation functions of local operators. To remedy the problem, we assume that wavefunctions admitting such semi-classical gravitational interpretation are composed of tensors close to, but not exactly perfect tensors. Computing corrections to the connected two point correlation functions, we find that the leading contribution is given by structures related to geodesics connecting the operators inserted at the boundary physical dofs. Such considerations admit generalizations at least to three point functions. This is highly suggestive of the emergence of the analogues of Witten diagrams in the tensor network. The perturbations alone however do not give the right entanglement spectrum. Using the Coxeter construction, we also constructed the tensor network counterpart of the BTZ black hole, by orbifolding the discrete lattice on which the network resides. We found that the construction naturally reproduces some of the salient features of the BTZ black hole, such as the appearance of RT surfaces that could wrap the horizon, depending on the size of the entanglement region A.

Current density tensors

Science.gov (United States)

Lazzeretti, Paolo

2018-04-01

It is shown that nonsymmetric second-rank current density tensors, related to the current densities induced by magnetic fields and nuclear magnetic dipole moments, are fundamental properties of a molecule. Together with magnetizability, nuclear magnetic shielding, and nuclear spin-spin coupling, they completely characterize its response to magnetic perturbations. Gauge invariance, resolution into isotropic, deviatoric, and antisymmetric parts, and contributions of current density tensors to magnetic properties are discussed. The components of the second-rank tensor properties are rationalized via relationships explicitly connecting them to the direction of the induced current density vectors and to the components of the current density tensors. The contribution of the deviatoric part to the average value of magnetizability, nuclear shielding, and nuclear spin-spin coupling, uniquely determined by the antisymmetric part of current density tensors, vanishes identically. The physical meaning of isotropic and anisotropic invariants of current density tensors has been investigated, and the connection between anisotropy magnitude and electron delocalization has been discussed.

Recovery of an injured fornix in a stroke patient.

Science.gov (United States)

Yeo, Sang Seok; Jang, Sung Ho

2013-11-01

Knowledge about recovery of an injured fornix following brain injury is limited. We describe here a patient who showed recovery of an injured fornix following stroke. A 57-year-old female patient underwent coiling for a ruptured anterior communicating cerebral artery aneurysm, and conservative management for subarachnoid and intraventricular haemorrhage. The patient showed severe cognitive impairment 6 weeks after onset. However, her cognition showed continuous improvement with time; based on the Mini-Mental State Examination and the Memory Assessment Scale, her cognition was within the normal range 7 months after onset. Findings from diffusion tensor tractography at 6 weeks and 7 months showed discontinuations in both columns of the fornix. The proximal portion of both crus also showed discontinuation on diffusion tensor tractography at 6 weeks and 7 months; however, on 7-month diffusion tensor tractography, the end of the fornical body was shown to be connected to the splenium of the corpus callosum and then branched to the right medial temporal lobe and right thalamus. The unusual neural connection between the injured fornix and the thalamus appears to be a recovery phenomenon, which allows the injured fornix and the medial temporal lobe to obtain cholinergic innervation from cholinergic nuclei in the brainstem rather than from cholinergic nuclei in the basal forebrain.

Multidimensional supersymmetric quantum mechanics: spurious states for the tensor sector two Hamiltonian.

Science.gov (United States)

Chou, Chia-Chun; Kouri, Donald J

2013-04-25

We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum mechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantum mechanics, there exist normalizable spurious states for the sector two Hamiltonian with energy equal to the ground state energy of the sector one. These spurious states are annihilated by the adjoint charge operator, and hence, they do not correspond to physical states for the original Hamiltonian. The Hermitian property of the sector two Hamiltonian implies the orthogonality between spurious and physical states. In addition, we develop a method for construction of a specific form of the spurious states for any quantum system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom.

Reconstruction of convex bodies from surface tensors

DEFF Research Database (Denmark)

Kousholt, Astrid; Kiderlen, Markus

. The output of the reconstruction algorithm is a polytope P, where the surface tensors of P and K are identical up to rank s. We establish a stability result based on a generalization of Wirtinger’s inequality that shows that for large s, two convex bodies are close in shape when they have identical surface...... that are translates of each other. An algorithm for reconstructing an unknown convex body in R 2 from its surface tensors up to a certain rank is presented. Using the reconstruction algorithm, the shape of an unknown convex body can be approximated when only a finite number s of surface tensors are available...... tensors up to rank s. This is used to establish consistency of the developed reconstruction algorithm....

Identification of the Occipito-Pontine Tract Using Diffusion-Tensor Fiber Tracking in Adult-Onset Adrenoleukodystrophy with Topographic Disorientation

Directory of Open Access Journals (Sweden)

Yuji Uchida

2011-05-01

Full Text Available X-linked adrenoleukodystrophy is a severe and progressive neurodegenerative disease caused by the peroxisomal transporter ATP-binding cassette, subfamily D, member 1 gene mutations. The defect of this gene product results in accumulation of very-long-chain fatty acids in organs and serum, central demyelination, and peripheral axonopathy. Although there are different magnetic resonance (MR findings which reflect various phenotypes in adrenoleukodystrophy, some cases present with specific symmetrical occipital white-matter lesions. We describe a patient with adult-onset X-linked adrenoleukodystrophy with topographic disorientation, whose brain MR images revealed T2-signal hyperintensity along the occipito-pontine tract and lateral lemnisci, but not in the cortico-spinal tract in the brainstem. The occipito-pontine tract and lateral lemnisci were clearly detected using diffusion-tensor fiber tracking, suggesting that the topographic disorientation of this patient might be related to the occipito-pontine tract. MR tractography can effectively identify the occipito-pontine tract and may help to localize the fibers associated with clinical symptoms.

Pre-surgical evaluation of the cerebral tumor in the left language related areas by functional MRI

International Nuclear Information System (INIS)

Zou Zhitong; Ma Lin; Weng Xuchu

2010-01-01

Objective: To evaluate the application of combination of BOLD-fMRI and diffusion tensor tractography (DTT) in pre-operative evaluation of cerebral tumors located at the left language related areas. Methods: A non-vocal button pressing semantic judging paradigm was developed and validated in 10 right-handed volunteers at 3 T. After validation, this protocol combined with DTI were applied to 15 patients with left cerebral tumor prior to surgical resection, and 3 of them had aphasia. fMRI data analysis was on subject-specific basis by one-sampled t-test. The distance from the tumor to Broca area and pre-central 'hand-knot' area were measured separately. Functional language laterality index (LI) was calculated by taking out Broca area and Wernicke area. Three dimensional architecture of frontal lobe white matter fibers, especially arcuate fasciculus, were visualized using diffusion tensor tractography on Volume-one software. The images demonstrating relationship among tumor, language activation areas and white matter fibers were reviewed by neurosurgeons as part of pre-operative planning. One year after the operation, patients were followed up with MRI and language function test. Results: The non-vocal semantic judging paradigm successfully detect Broca area, Wernicke area and pre-central 'hand-knot' area. In 12 of 15 patients, the relationship of Broca area and pre-central motor area to the left brain tumor in language related areas was identified, which make the pre-operative neurosurgical plan applicable to minimize the disruption of language and motor. 8 patients had the left language dominant hemisphere, 3 patients with the right language dominant hemisphere and 1 patient with bilateral dominance. The other 3 patients' fMRI data were corrupted by patients' motion. Diffusion tensor images were corrupted by motion in 1 patient but demonstrated the impact of tumor on left accouter fasciculus in 14 patients. Diffusion tensor tractography showed disruption of left

Diffusion Capillary Phantom vs. Human Data: Outcomes for Reconstruction Methods Depend on Evaluation Medium

Directory of Open Access Journals (Sweden)

Sarah D. Lichenstein

2016-09-01

Full Text Available Purpose: Diffusion MRI provides a non-invasive way of estimating structural connectivity in the brain. Many studies have used diffusion phantoms as benchmarks to assess the performance of different tractography reconstruction algorithms and assumed that the results can be applied to in vivo studies. Here we examined whether quality metrics derived from a common, publically available, diffusion phantom can reliably predict tractography performance in human white matter tissue. Material and Methods: We compared estimates of fiber length and fiber crossing among a simple tensor model (diffusion tensor imaging, a more complicated model (ball-and-sticks and model-free (diffusion spectrum imaging, generalized q-sampling imaging reconstruction methods using a capillary phantom and in vivo human data (N=14. Results: Our analysis showed that evaluation outcomes differ depending on whether they were obtained from phantom or human data. Specifically, the diffusion phantom favored a more complicated model over a simple tensor model or model-free methods for resolving crossing fibers. On the other hand, the human studies showed the opposite pattern of results, with the model-free methods being more advantageous than model-based methods or simple tensor models. This performance difference was consistent across several metrics, including estimating fiber length and resolving fiber crossings in established white matter pathways. Conclusions: These findings indicate that the construction of current capillary diffusion phantoms tends to favor complicated reconstruction models over a simple tensor model or model-free methods, whereas the in vivo data tends to produce opposite results. This brings into question the previous phantom-based evaluation approaches and suggests that a more realistic phantom or simulation is necessary to accurately predict the relative performance of different tractography reconstruction methods. Acronyms: BSM: ball-and-sticks model; d

Southern Ocean overturning across streamlines in an eddying simulation of the Antarctic Circumpolar Current

Directory of Open Access Journals (Sweden)

A. M. Treguier

2007-12-01

Full Text Available An eddying global model is used to study the characteristics of the Antarctic Circumpolar Current (ACC in a streamline-following framework. Previous model-based estimates of the meridional circulation were calculated using zonal averages: this method leads to a counter-intuitive poleward circulation of the less dense waters, and underestimates the eddy effects. We show that on the contrary, the upper ocean circulation across streamlines agrees with the theoretical view: an equatorward mean flow partially cancelled by a poleward eddy mass flux. Two model simulations, in which the buoyancy forcing above the ACC changes from positive to negative, suggest that the relationship between the residual meridional circulation and the surface buoyancy flux is not as straightforward as assumed by the simplest theoretical models: the sign of the residual circulation cannot be inferred from the surface buoyancy forcing only. Among the other processes that likely play a part in setting the meridional circulation, our model results emphasize the complex three-dimensional structure of the ACC (probably not well accounted for in streamline-averaged, two-dimensional models and the distinct role of temperature and salinity in the definition of the density field. Heat and salt transports by the time-mean flow are important even across time-mean streamlines. Heat and salt are balanced in the ACC, the model drift being small, but the nonlinearity of the equation of state cannot be ignored in the density balance.

On energy-momentum tensors of gravitational field

International Nuclear Information System (INIS)

Nikishov, A.I.

2001-01-01

The phenomenological approach to gravitation is discussed in which the 3-graviton interaction is reduced to the interaction of each graviton with the energy-momentum tensor of two others. If this is so, (and in general relativity this is not so), then the problem of choosing the correct energy-momentum tensor comes to finding the right 3-graviton vertex. Several energy-momentum tensors od gravitational field are considered and compared in the lowest approximation. Each of them together with the energy-momentum tensor of point-like particles satisfies the conservation laws when equations of motion of particles are the same as in general relativity. It is shown that in Newtonian approximation the considered tensors differ one from other in the way their energy density is distributed between energy density of interaction (nonzero only at locations of particles) and energy density of gravitational field. Stating from Lorentz invariance, the Lagrangians for spin-2, mass-0 field are considered [ru

Single-shot full strain tensor determination with microbeam X-ray Laue diffraction and a two-dimensional energy-dispersive detector.

Science.gov (United States)

Abboud, A; Kirchlechner, C; Keckes, J; Conka Nurdan, T; Send, S; Micha, J S; Ulrich, O; Hartmann, R; Strüder, L; Pietsch, U

2017-06-01

The full strain and stress tensor determination in a triaxially stressed single crystal using X-ray diffraction requires a series of lattice spacing measurements at different crystal orientations. This can be achieved using a tunable X-ray source. This article reports on a novel experimental procedure for single-shot full strain tensor determination using polychromatic synchrotron radiation with an energy range from 5 to 23 keV. Microbeam X-ray Laue diffraction patterns were collected from a copper micro-bending beam along the central axis (centroid of the cross section). Taking advantage of a two-dimensional energy-dispersive X-ray detector (pnCCD), the position and energy of the collected Laue spots were measured for multiple positions on the sample, allowing the measurement of variations in the local microstructure. At the same time, both the deviatoric and hydrostatic components of the elastic strain and stress tensors were calculated.

The Topology of Three-Dimensional Symmetric Tensor Fields

Science.gov (United States)

Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus

1994-01-01

We study the topology of 3-D symmetric tensor fields. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector field topology. The basic constituents of tensor topology are the degenerate points, or points where eigenvalues are equal to each other. First, we introduce a new method for locating 3-D degenerate points. We then extract the topological skeletons of the eigenvector fields and use them for a compact, comprehensive description of the tensor field. Finally, we demonstrate the use of tensor field topology for the interpretation of the two-force Boussinesq problem.

Accelerated magnetic resonance diffusion tensor imaging of the median nerve using simultaneous multi-slice echo planar imaging with blipped CAIPIRINHA

Energy Technology Data Exchange (ETDEWEB)

Filli, Lukas; Kenkel, David; Boss, Andreas; Manoliu, Andrei; Andreisek, Gustav; Runge, Val M.; Guggenberger, Roman [University Hospital of Zurich, University of Zurich, Institute of Diagnostic and Interventional Radiology, Zurich (Switzerland); Piccirelli, Marco [University Hospital of Zurich, Department of Neuroradiology, Zurich (Switzerland); Bhat, Himanshu [Siemens Medical Solutions USA Inc, Charlestown, MA (United States)

2016-06-15

To investigate the feasibility of MR diffusion tensor imaging (DTI) of the median nerve using simultaneous multi-slice echo planar imaging (EPI) with blipped CAIPIRINHA. After federal ethics board approval, MR imaging of the median nerves of eight healthy volunteers (mean age, 29.4 years; range, 25-32) was performed at 3 T using a 16-channel hand/wrist coil. An EPI sequence (b-value, 1,000 s/mm{sup 2}; 20 gradient directions) was acquired without acceleration as well as with twofold and threefold slice acceleration. Fractional anisotropy (FA), mean diffusivity (MD) and quality of nerve tractography (number of tracks, average track length, track homogeneity, anatomical accuracy) were compared between the acquisitions using multivariate ANOVA and the Kruskal-Wallis test. Acquisition time was 6:08 min for standard DTI, 3:38 min for twofold and 2:31 min for threefold acceleration. No differences were found regarding FA (standard DTI: 0.620 ± 0.058; twofold acceleration: 0.642 ± 0.058; threefold acceleration: 0.644 ± 0.061; p ≥ 0.217) and MD (standard DTI: 1.076 ± 0.080 mm{sup 2}/s; twofold acceleration: 1.016 ± 0.123 mm{sup 2}/s; threefold acceleration: 0.979 ± 0.153 mm{sup 2}/s; p ≥ 0.074). Twofold acceleration yielded similar tractography quality compared to standard DTI (p > 0.05). With threefold acceleration, however, average track length and track homogeneity decreased (p = 0.004-0.021). Accelerated DTI of the median nerve is feasible. Twofold acceleration yields similar results to standard DTI. (orig.)

Unique encoding for streamline topologies of incompressible and inviscid flows in multiply connected domains

Energy Technology Data Exchange (ETDEWEB)

Sakajo, T [Department of Mathematics, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502 (Japan); Sawamura, Y; Yokoyama, T, E-mail: sakajo@math.kyoto-u.ac.jp [JST CREST, Kawaguchi, Saitama 332-0012 (Japan)

2014-06-01

This study considers the flow of incompressible and inviscid fluid in two-dimensional multiply connected domains. For such flows, encoding algorithms to assign a unique sequence of words to any structurally stable streamline topology based on the theory presented by Yokoyama and Sakajo (2013 Proc. R. Soc. A 469 20120558) are proposed. As an application, we utilize the algorithms to characterize the evolution of an incompressible and viscid flow around a flat plate inclined to the uniform flow in terms of the change of the word representations for their instantaneous streamline topologies. (papers)

TensorFlow Agents: Efficient Batched Reinforcement Learning in TensorFlow

OpenAIRE

Hafner, Danijar; Davidson, James; Vanhoucke, Vincent

2017-01-01

We introduce TensorFlow Agents, an efficient infrastructure paradigm for building parallel reinforcement learning algorithms in TensorFlow. We simulate multiple environments in parallel, and group them to perform the neural network computation on a batch rather than individual observations. This allows the TensorFlow execution engine to parallelize computation, without the need for manual synchronization. Environments are stepped in separate Python processes to progress them in parallel witho...

Analyzing functional, structural, and anatomical correlation of hemispheric language lateralization in healthy subjects using functional MRI, diffusion tensor imaging, and voxel-based morphometry.

Science.gov (United States)

James, Jija S; Kumari, Sheela R; Sreedharan, Ruma Madhu; Thomas, Bejoy; Radhkrishnan, Ashalatha; Kesavadas, Chandrasekharan

2015-01-01

To evaluate the efficacy of diffusion fiber tractography (DFT) and voxel-based morphometry (VBM) for lateralizing language in comparison with functional magnetic resonance imaging (fMRI) to noninvasively assess hemispheric language lateralization in normal healthy volunteers. The aim of the present study is to evaluate the concordance of language lateralization obtained by diffusion tensor imaging (DTI) and VBM to fMRI, and thus to see whether there exists an anatomical correlate for language lateralization result obtained using fMRI. This is an advanced neuroimaging study conducted in normal healthy volunteers. Fifty-seven normal healthy subjects (39 males and 18 females; age range: 15-40 years) underwent language fMRI and 30 underwent direction DTI. fMRI language laterality index (LI), fiber tract asymmetry index (AI), and tract-based statistics of dorsal and ventral language pathways were calculated. The combined results were correlated with VBM-based volumetry of Heschl's gyrus (HG), planum temporale (PT), and insula for lateralization of language function. A linear regression analysis was done to study the correlation between fMRI, DTI, and VBM measurements. A good agreement was found between language fMRI LI and fiber tract AI, more specifically for arcuate fasciculus (ArcF) and inferior longitudinal fasciculus (ILF). The study demonstrated significant correlations (P based statistics, and PT and HG volumetry for determining language lateralization. A strong one-to-one correlation between fMRI, laterality index, DTI tractography measures, and VBM-based volumetry measures for determining language lateralization exists.

A RENORMALIZATION PROCEDURE FOR TENSOR MODELS AND SCALAR-TENSOR THEORIES OF GRAVITY

OpenAIRE

SASAKURA, NAOKI

2010-01-01

Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian config...

Superconformal tensor calculus in five dimensions

International Nuclear Information System (INIS)

Fujita, Tomoyuki; Ohashi, Keisuke

2001-01-01

We present a full superconformal tensor calculus in five spacetime dimensions in which the Weyl multiplet has 32 Bose plus 32 Fermi degrees of freedom. It is derived using dimensional reduction from the 6D superconformal tensor calculus. We present two types of 32+32 Weyl multiplets, a vector multiplet, linear multiplet, hypermultiplet and nonlinear multiplet. Their superconformal transformation laws and the embedding and invariant action formulas are given. (author)

A similarity hypothesis for the two-point correlation tensor in a temporally evolving plane wake

Science.gov (United States)

Ewing, D. W.; George, W. K.; Moser, R. D.; Rogers, M. M.

1995-01-01

The analysis demonstrated that the governing equations for the two-point velocity correlation tensor in the temporally evolving wake admit similarity solutions, which include the similarity solutions for the single-point moment as a special case. The resulting equations for the similarity solutions include two constants, beta and Re(sub sigma), that are ratios of three characteristic time scales of processes in the flow: a viscous time scale, a time scale characteristic of the spread rate of the flow, and a characteristic time scale of the mean strain rate. The values of these ratios depend on the initial conditions of the flow and are most likely measures of the coherent structures in the initial conditions. The occurrences of these constants in the governing equations for the similarity solutions indicates that these solutions, in general, will only be the same for two flows if these two constants are equal (and hence the coherent structures in the flows are related). The comparisons between the predictions of the similarity hypothesis and the data presented here and elsewhere indicate that the similarity solutions for the two-point correlation tensors provide a good approximation of the measures of those motions that are not significantly affected by the boundary conditions caused by the finite extent of real flows. Thus, the two-point similarity hypothesis provides a useful tool for both numerical and physical experimentalist that can be used to examine how the finite extent of real flows affect the evolution of the different scales of motion in the flow.

Time integration of tensor trains

OpenAIRE

Lubich, Christian; Oseledets, Ivan; Vandereycken, Bart

2014-01-01

A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the projector onto the tangent space of the tensor manifold. The algorithm can be used for updating time-dependent tensors in the given data-sparse tensor train / matrix product state format and for computing an approximate solution to high-dimensional tensor differential equations within this data-sparse format. The formul...

The impact of groundwater velocity fields on streamlines in an aquifer system with a discontinuous aquitard (Inner Mongolia, China)

Science.gov (United States)

Wu, Qiang; Zhao, Yingwang; Xu, Hua

2018-04-01

Many numerical methods that simulate groundwater flow, particularly the continuous Galerkin finite element method, do not produce velocity information directly. Many algorithms have been proposed to improve the accuracy of velocity fields computed from hydraulic potentials. The differences in the streamlines generated from velocity fields obtained using different algorithms are presented in this report. The superconvergence method employed by FEFLOW, a popular commercial code, and some dual-mesh methods proposed in recent years are selected for comparison. The applications to depict hydrogeologic conditions using streamlines are used, and errors in streamlines are shown to lead to notable errors in boundary conditions, the locations of material interfaces, fluxes and conductivities. Furthermore, the effects of the procedures used in these two types of methods, including velocity integration and local conservation, are analyzed. The method of interpolating velocities across edges using fluxes is shown to be able to eliminate errors associated with refraction points that are not located along material interfaces and streamline ends at no-flow boundaries. Local conservation is shown to be a crucial property of velocity fields and can result in more accurate streamline densities. A case study involving both three-dimensional and two-dimensional cross-sectional models of a coal mine in Inner Mongolia, China, are used to support the conclusions presented.

The direct tensor solution and higher-order acquisition schemes for generalized diffusion tensor imaging

NARCIS (Netherlands)

Akkerman, Erik M.

2010-01-01

Both in diffusion tensor imaging (DTI) and in generalized diffusion tensor imaging (GDTI) the relation between the diffusion tensor and the measured apparent diffusion coefficients is given by a tensorial equation, which needs to be inverted in order to solve the diffusion tensor. The traditional

Scalar-tensor linear inflation

Energy Technology Data Exchange (ETDEWEB)

Artymowski, Michał [Institute of Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków (Poland); Racioppi, Antonio, E-mail: Michal.Artymowski@uj.edu.pl, E-mail: Antonio.Racioppi@kbfi.ee [National Institute of Chemical Physics and Biophysics, Rävala 10, 10143 Tallinn (Estonia)

2017-04-01

We investigate two approaches to non-minimally coupled gravity theories which present linear inflation as attractor solution: a) the scalar-tensor theory approach, where we look for a scalar-tensor theory that would restore results of linear inflation in the strong coupling limit for a non-minimal coupling to gravity of the form of f (φ) R /2; b) the particle physics approach, where we motivate the form of the Jordan frame potential by loop corrections to the inflaton field. In both cases the Jordan frame potentials are modifications of the induced gravity inflationary scenario, but instead of the Starobinsky attractor they lead to linear inflation in the strong coupling limit.

Composite antisymmetric tensor bosons in a four-fermion interaction model

International Nuclear Information System (INIS)

Dmitrasinovic, V.

2000-01-01

We discuss the phenomenological consequences of the U A (1) symmetry-breaking two-flavour four-fermion antisymmetric (AS) Lorentz tensor interaction Lagrangians. We use the recently developed methods that respect the 'duality' symmetry of this interaction. Starting from the Fierz transform of the two-flavour 't Hooft interaction (a four-fermion Lagrangian with AS tensor interaction terms augmented by Nambu and Jona-Lasinio (NJL)-type Lorentz scalar interaction responsible for dynamical symmetry breaking and quark mass generation), we find the following. (a) Four antisymmetric tensor and four AS pseudotensor bosons exist which satisfy a mass relation previously derived for scalar and pseudoscalar mesons from the 't Hooft interaction. (b) Antisymmetric tensor bosons mix with vector bosons via one-fermion-loop effective couplings so that both kinds of bosons have their masses shifted and the fermions (quarks) acquire anomalous magnetic moment form factors that explicitly violate chiral symmetry. (c) The mixing of massive AS tensor fields with vector fields leads to two sets of spin-1 states. The second set of spin-1 mesons is heavy and has not been observed. Moreover, at least one member of this second set is tachyonic, under standard assumptions about the source and strength of the AS tensor interaction. The tachyonic state also shows up as a pole in the space-like region of the electromagnetic form factors. (d) The mixing of axial-vector fields with antisymmetric tensor bosons is proportional to the (small) isospin-breaking up-down quark mass difference, so the mixing-induced mass shift is negligible. (e) The AS tensor version of the Veneziano-Witten U A (1) symmetry-breaking interaction does not lead to tachyons, or any AS tensor field propagation to leading order in N C . (author)

Extended vector-tensor theories

Energy Technology Data Exchange (ETDEWEB)

Kimura, Rampei; Naruko, Atsushi; Yoshida, Daisuke, E-mail: rampei@th.phys.titech.ac.jp, E-mail: naruko@th.phys.titech.ac.jp, E-mail: yoshida@th.phys.titech.ac.jp [Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551 (Japan)

2017-01-01

Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-tensor theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless tensor modes. We find that the generalized Proca and the beyond generalized Proca theories up to the quartic Lagrangian, which should be included in this formulation, are degenerate theories even in curved space-time. Finally, introducing new metric and vector field transformations, we investigate the properties of thus obtained theories under such transformations.

Mapping remodeling of thalamocortical projections in the living reeler mouse brain by diffusion tractography

Science.gov (United States)

Harsan, Laura-Adela; Dávid, Csaba; Reisert, Marco; Schnell, Susanne; Hennig, Jürgen; von Elverfeldt, Dominik; Staiger, Jochen F.

2013-01-01

A major challenge in neuroscience is to accurately decipher in vivo the entire brain circuitry (connectome) at a microscopic level. Currently, the only methodology providing a global noninvasive window into structural brain connectivity is diffusion tractography. The extent to which the reconstructed pathways reflect realistic neuronal networks depends, however, on data acquisition and postprocessing factors. Through a unique combination of approaches, we designed and evaluated herein a framework for reliable fiber tracking and mapping of the living mouse brain connectome. One important wiring scheme, connecting gray matter regions and passing fiber-crossing areas, was closely examined: the lemniscal thalamocortical (TC) pathway. We quantitatively validated the TC projections inferred from in vivo tractography with correlative histological axonal tracing in the same wild-type and reeler mutant mice. We demonstrated noninvasively that changes in patterning of the cortical sheet, such as highly disorganized cortical lamination in reeler, led to spectacular compensatory remodeling of the TC pathway. PMID:23610438

SU-F-J-160: Clinical Evaluation of Targeting Accuracy in Radiosurgery Using Tractography

Energy Technology Data Exchange (ETDEWEB)

Juh, R; Han, J; Kim, C; Oh, C [Seoul National University Bundang Hospital, Seongnamsi, GyeonggiDo (Korea, Republic of); Suh, T [The catholic university of Korea, Seoul (Korea, Republic of)

2016-06-15

Purpose: Focal radiosurgery is a common treatment modality for trigeminal neuralgia (TN), a neuropathic facial pain condition. Assessment of treatment effectiveness is primarily clinical, given the paucity of investigational tools to assess trigeminal nerve changes. The efficiency of radiosurgery is related to its highly precise targeting. We assessed clinically the targeting accuracy of radiosurgery with Gamma knife. We hypothesized that trigeminal tractography provides more information than 2D-MR imaging, allowing detection of unique, focal changes in the target area after radiosurgery. Methods: Sixteen TN patients (2 females, 4 males, average age 65.3 years) treated with Gamma Knife radiosurgery, 40 Gy/50% isodose line underwent 1.5Tesla MR trigeminal nerve. Target accuracy was assessed from deviation of the coordinates of the target compared with the center of enhancement on post MRI. Radiation dose delivered at the borders of contrast enhancement was evaluated. Results: The median deviation of the coordinates between the intended target and the center of contrast enhancement was within 1mm. The radiation doses fitting within the borders of the contrast enhancement the target ranged from 37.5 to 40 Gy. Trigeminal tractography accurately detected the radiosurgical target. Radiosurgery resulted in 47% drop in FA values at the target with no significant change in FA outside the target, suggesting that radiosurgery primarily affects myelin. Tractography was more sensitive, since FA changes were detected regardless of trigeminal nerve enhancement. Conclusion: The median deviation found in clinical assessment of gamma knife treatment for TN Is low and compatible with its high rate of efficiency. DTI parameters accurately detect the effects of focal radiosurgery on the trigeminal nerve, serving as an in vivo imaging tool to study TN. This study is a proof of principle for further assessment of DTI parameters to understand the pathophysiology of TN and treatment

Tensor structure for Nori motives

OpenAIRE

Barbieri-Viale, Luca; Huber, Annette; Prest, Mike

2018-01-01

We construct a tensor product on Freyd's universal abelian category attached to an additive tensor category or a tensor quiver and establish a universal property. This is used to give an alternative construction for the tensor product on Nori motives.

Massless and massive quanta resulting from a mediumlike metric tensor

International Nuclear Information System (INIS)

Soln, J.

1985-01-01

A simple model of the ''primordial'' scalar field theory is presented in which the metric tensor is a generalization of the metric tensor from electrodynamics in a medium. The radiation signal corresponding to the scalar field propagates with a velocity that is generally less than c. This signal can be associated simultaneously with imaginary and real effective (momentum-dependent) masses. The requirement that the imaginary effective mass vanishes, which we take to be the prerequisite for the vacuumlike signal propagation, leads to the ''spontaneous'' splitting of the metric tensor into two distinct metric tensors: one metric tensor gives rise to masslesslike radiation and the other to a massive particle. (author)

Tensor SOM and tensor GTM: Nonlinear tensor analysis by topographic mappings.

Science.gov (United States)

Iwasaki, Tohru; Furukawa, Tetsuo

2016-05-01

In this paper, we propose nonlinear tensor analysis methods: the tensor self-organizing map (TSOM) and the tensor generative topographic mapping (TGTM). TSOM is a straightforward extension of the self-organizing map from high-dimensional data to tensorial data, and TGTM is an extension of the generative topographic map, which provides a theoretical background for TSOM using a probabilistic generative model. These methods are useful tools for analyzing and visualizing tensorial data, especially multimodal relational data. For given n-mode relational data, TSOM and TGTM can simultaneously organize a set of n-topographic maps. Furthermore, they can be used to explore the tensorial data space by interactively visualizing the relationships between modes. We present the TSOM algorithm and a theoretical description from the viewpoint of TGTM. Various TSOM variations and visualization techniques are also described, along with some applications to real relational datasets. Additionally, we attempt to build a comprehensive description of the TSOM family by adapting various data structures. Copyright © 2016 Elsevier Ltd. All rights reserved.

Study of streamline flow in the portal system

International Nuclear Information System (INIS)

Atkins, H.L.; Deitch, J.S.; Oster, Z.H.; Perkes, E.A.

1985-01-01

The study was undertaken to determine if streamline flow occurs in the portal vein, thus separating inflow from the superior mesenteric artery (SMA) and the inferior mesenteric artery. Previously published data on this subject is inconsistent. Patients undergoing abdominal angiography received two administrations of Tc-99m sulfur colloid, first via the SMA during angiography and, after completion of the angiographic procedure, via a peripheral vein (IV). Anterior images of the liver were recorded over a three minute acquisition before and after the IV injection without moving the patient. The image from the SMA injection was subtracted from the SMA and IV image to provide a pure IV image. Analysis of R to L ratios for selected regions of interest as well as whole lobes was carried out and the shift of R to L (SMA to IV) determined. Six patients had liver metastases from the colon, four had cirrhosis and four had no known liver disease. The shift in the ratio was highly variable without a consistent pattern. Large changes in some patients could be attributed to hepatic artery flow directed to metastases. No consistent evidence for streamlining of portal flow was discerned

Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature

OpenAIRE

Loveridge, Lee C.

2004-01-01

Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity from Einstein's Equations is given.

Generalized tensor-based morphometry of HIV/AIDS using multivariate statistics on deformation tensors.

Science.gov (United States)

Lepore, N; Brun, C; Chou, Y Y; Chiang, M C; Dutton, R A; Hayashi, K M; Luders, E; Lopez, O L; Aizenstein, H J; Toga, A W; Becker, J T; Thompson, P M

2008-01-01

This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor) of these deformations, as is common, we retain the full deformation tensors and apply a manifold version of Hotelling's $T(2) test to them, in a Log-Euclidean domain. In 2-D and 3-D magnetic resonance imaging (MRI) data from 26 HIV/AIDS patients and 14 matched healthy subjects, we compared multivariate tensor analysis versus univariate tests of simpler tensor-derived indices: the Jacobian determinant, the trace, geodesic anisotropy, and eigenvalues of the deformation tensor, and the angle of rotation of its eigenvectors. We detected consistent, but more extensive patterns of structural abnormalities, with multivariate tests on the full tensor manifold. Their improved power was established by analyzing cumulative p-value plots using false discovery rate (FDR) methods, appropriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studies of disease that use tensor-based morphometry.

Development of the Tensoral Computer Language

Science.gov (United States)

Ferziger, Joel; Dresselhaus, Eliot

1996-01-01

The research scientist or engineer wishing to perform large scale simulations or to extract useful information from existing databases is required to have expertise in the details of the particular database, the numerical methods and the computer architecture to be used. This poses a significant practical barrier to the use of simulation data. The goal of this research was to develop a high-level computer language called Tensoral, designed to remove this barrier. The Tensoral language provides a framework in which efficient generic data manipulations can be easily coded and implemented. First of all, Tensoral is general. The fundamental objects in Tensoral represent tensor fields and the operators that act on them. The numerical implementation of these tensors and operators is completely and flexibly programmable. New mathematical constructs and operators can be easily added to the Tensoral system. Tensoral is compatible with existing languages. Tensoral tensor operations co-exist in a natural way with a host language, which may be any sufficiently powerful computer language such as Fortran, C, or Vectoral. Tensoral is very-high-level. Tensor operations in Tensoral typically act on entire databases (i.e., arrays) at one time and may, therefore, correspond to many lines of code in a conventional language. Tensoral is efficient. Tensoral is a compiled language. Database manipulations are simplified optimized and scheduled by the compiler eventually resulting in efficient machine code to implement them.

Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery.

Science.gov (United States)

Xie, Qi; Zhao, Qian; Meng, Deyu; Xu, Zongben

2017-08-02

It is well known that the sparsity/low-rank of a vector/matrix can be rationally measured by nonzero-entries-number ($l_0$ norm)/nonzero- singular-values-number (rank), respectively. However, data from real applications are often generated by the interaction of multiple factors, which obviously cannot be sufficiently represented by a vector/matrix, while a high order tensor is expected to provide more faithful representation to deliver the intrinsic structure underlying such data ensembles. Unlike the vector/matrix case, constructing a rational high order sparsity measure for tensor is a relatively harder task. To this aim, in this paper we propose a measure for tensor sparsity, called Kronecker-basis-representation based tensor sparsity measure (KBR briefly), which encodes both sparsity insights delivered by Tucker and CANDECOMP/PARAFAC (CP) low-rank decompositions for a general tensor. Then we study the KBR regularization minimization (KBRM) problem, and design an effective ADMM algorithm for solving it, where each involved parameter can be updated with closed-form equations. Such an efficient solver makes it possible to extend KBR to various tasks like tensor completion and tensor robust principal component analysis. A series of experiments, including multispectral image (MSI) denoising, MSI completion and background subtraction, substantiate the superiority of the proposed methods beyond state-of-the-arts.

Tensor Rank Preserving Discriminant Analysis for Facial Recognition.

Science.gov (United States)

Tao, Dapeng; Guo, Yanan; Li, Yaotang; Gao, Xinbo

2017-10-12

Facial recognition, one of the basic topics in computer vision and pattern recognition, has received substantial attention in recent years. However, for those traditional facial recognition algorithms, the facial images are reshaped to a long vector, thereby losing part of the original spatial constraints of each pixel. In this paper, a new tensor-based feature extraction algorithm termed tensor rank preserving discriminant analysis (TRPDA) for facial image recognition is proposed; the proposed method involves two stages: in the first stage, the low-dimensional tensor subspace of the original input tensor samples was obtained; in the second stage, discriminative locality alignment was utilized to obtain the ultimate vector feature representation for subsequent facial recognition. On the one hand, the proposed TRPDA algorithm fully utilizes the natural structure of the input samples, and it applies an optimization criterion that can directly handle the tensor spectral analysis problem, thereby decreasing the computation cost compared those traditional tensor-based feature selection algorithms. On the other hand, the proposed TRPDA algorithm extracts feature by finding a tensor subspace that preserves most of the rank order information of the intra-class input samples. Experiments on the three facial databases are performed here to determine the effectiveness of the proposed TRPDA algorithm.

A tensor-based dictionary learning approach to tomographic image reconstruction

DEFF Research Database (Denmark)

Soltani, Sara; Kilmer, Misha E.; Hansen, Per Christian

2016-01-01

We consider tomographic reconstruction using priors in the form of a dictionary learned from training images. The reconstruction has two stages: first we construct a tensor dictionary prior from our training data, and then we pose the reconstruction problem in terms of recovering the expansion...... coefficients in that dictionary. Our approach differs from past approaches in that (a) we use a third-order tensor representation for our images and (b) we recast the reconstruction problem using the tensor formulation. The dictionary learning problem is presented as a non-negative tensor factorization problem...... with sparsity constraints. The reconstruction problem is formulated in a convex optimization framework by looking for a solution with a sparse representation in the tensor dictionary. Numerical results show that our tensor formulation leads to very sparse representations of both the training images...

Non-Abelian tensor gauge fields and higher-spin extension of standard model

International Nuclear Information System (INIS)

Savvidy, G.

2006-01-01

We suggest an extension of the gauge principle which includes non-Abelian tensor gauge fields. The invariant Lagrangian is quadratic in the field strength tensors and describes interaction of charged tensor gauge bosons of arbitrary large integer spin 1,2,l. Non-Abelian tensor gauge fields can be viewed as a unique gauge field with values in the infinite-dimensional current algebra associated with compact Lie group. The full Lagrangian exhibits also enhanced local gauge invariance with double number of gauge parameters which allows to eliminate all negative norm states of the nonsymmetric second-rank tensor gauge field, which describes therefore two polarizations of helicity-two massless charged tensor gauge boson and the helicity-zero ''axion'' The geometrical interpretation of the enhanced gauge symmetry with double number of gauge parameters is not yet known. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

Tensor force and debye screening in quarkonium-type mesons

International Nuclear Information System (INIS)

Kovacs, L.B.; Kovacs, T.G.; Lovas, I.

1990-01-01

We use a non-relativistic quantum-mechanical model to investigate the effect of a screening plasma on two quarkonium-type mesons: the charmonium and bottonium. The stability of these mesons in the plasma is estimated in two cases: including the tensor and spin-orbit term in the potential and without these terms. It turns out that while the bottonium is somewhat stabilized by the tensor force, the charmonium becomes less stabil due to this modification of the potential. Thus the charmonium seems to be a more sensitive probe of the quark-gluon plasma formation than it was thought to be without including the tensor force. (Authors)

On the energy-momentum tensor in Moyal space

International Nuclear Information System (INIS)

Balasin, Herbert; Schweda, Manfred; Blaschke, Daniel N.; Gieres, Francois

2015-01-01

We study the properties of the energy-momentum tensor of gauge fields coupled to matter in non-commutative (Moyal) space. In general, the non-commutativity affects the usual conservation law of the tensor as well as its transformation properties (gauge covariance instead of gauge invariance). It is well known that the conservation of the energy-momentum tensor can be achieved by a redefinition involving another star-product. Furthermore, for a pure gauge theory it is always possible to define a gauge invariant energy-momentum tensor by means of a Wilson line. We show that the last two procedures are incompatible with each other if couplings of gauge fields to matter fields (scalars or fermions) are considered: The gauge invariant tensor (constructed via Wilson line) does not allow for a redefinition assuring its conservation, and vice versa the introduction of another star-product does not allow for gauge invariance by means of a Wilson line. (orig.)

Reconstruction of convex bodies from surface tensors

DEFF Research Database (Denmark)

Kousholt, Astrid; Kiderlen, Markus

We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. The second algorithm uses harmonic intrinsic...... volumes which are certain values of the surface tensors and allows for noisy measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based...

The Superior Fronto-Occipital Fasciculus in the Human Brain Revealed by Diffusion Spectrum Imaging Tractography: An Anatomical Reality or a Methodological Artifact?

Science.gov (United States)

Bao, Yue; Wang, Yong; Wang, Wei; Wang, Yibao

2017-01-01

The existence of the superior fronto-occipital fasciculus (SFOF) in the human brain remains controversial. The aim of the present study was to clarify the existence, course, and terminations of the SFOF. High angular diffusion spectrum imaging (DSI) analysis was performed on six healthy adults and on a template of 842 subjects from the Human Connectome Project. To verify tractography results, we performed fiber microdissections of four post-mortem human brains. Based on DSI tractography, we reconstructed the SFOF in the subjects and the template from the Human Connectome Project that originated from the rostral and medial parts of the superior and middle frontal gyri. By tractography, we found that the fibers formed a compact fascicle at the level of the anterior horn of the lateral ventricle coursing above the head of caudate nucleus, medial to the corona radiate and under the corpus callosum (CC), and terminated at the parietal region via the lower part of the caudate nucleus. We consider that this fiber bundle observed by tractography is the SFOF, although it terminates mainly at the parietal region, rather than occipital lobe. By contrast, we were unable to identify a fiber bundle corresponding to the SFOF in our fiber dissection study. Although we did not provide definite evidence of the SFOF in the human brain, these findings may be useful for future studies in this field. PMID:29321729

The Superior Fronto-Occipital Fasciculus in the Human Brain Revealed by Diffusion Spectrum Imaging Tractography: An Anatomical Reality or a Methodological Artifact?

Directory of Open Access Journals (Sweden)

Yue Bao

2017-12-01

Full Text Available The existence of the superior fronto-occipital fasciculus (SFOF in the human brain remains controversial. The aim of the present study was to clarify the existence, course, and terminations of the SFOF. High angular diffusion spectrum imaging (DSI analysis was performed on six healthy adults and on a template of 842 subjects from the Human Connectome Project. To verify tractography results, we performed fiber microdissections of four post-mortem human brains. Based on DSI tractography, we reconstructed the SFOF in the subjects and the template from the Human Connectome Project that originated from the rostral and medial parts of the superior and middle frontal gyri. By tractography, we found that the fibers formed a compact fascicle at the level of the anterior horn of the lateral ventricle coursing above the head of caudate nucleus, medial to the corona radiate and under the corpus callosum (CC, and terminated at the parietal region via the lower part of the caudate nucleus. We consider that this fiber bundle observed by tractography is the SFOF, although it terminates mainly at the parietal region, rather than occipital lobe. By contrast, we were unable to identify a fiber bundle corresponding to the SFOF in our fiber dissection study. Although we did not provide definite evidence of the SFOF in the human brain, these findings may be useful for future studies in this field.

Categorical Tensor Network States

Directory of Open Access Journals (Sweden)

Jacob D. Biamonte

2011-12-01

Full Text Available We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not previously appeared in either side of the literature. Our approach enabled the development of a tensor network framework allowing a solution to the quantum decomposition problem which has several appealing features. Specifically, given an n-body quantum state |ψ〉, we present a new and general method to factor |ψ〉 into a tensor network of clearly defined building blocks. We use the solution to expose a previously unknown and large class of quantum states which we prove can be sampled efficiently and exactly. This general framework of categorical tensor network states, where a combination of generic and algebraically defined tensors appear, enhances the theory of tensor network states.

Holographic stress tensor for non-relativistic theories

International Nuclear Information System (INIS)

Ross, Simon F.; Saremi, Omid

2009-01-01

We discuss the calculation of the field theory stress tensor from the dual geometry for two recent proposals for gravity duals of non-relativistic conformal field theories. The first of these has a Schroedinger symmetry including Galilean boosts, while the second has just an anisotropic scale invariance (the Lifshitz case). For the Lifshitz case, we construct an appropriate action principle. We propose a definition of the non-relativistic stress tensor complex for the field theory as an appropriate variation of the action in both cases. In the Schroedinger case, we show that this gives physically reasonable results for a simple black hole solution and agrees with an earlier proposal to determine the stress tensor from the familiar AdS prescription. In the Lifshitz case, we solve the linearised equations of motion for a general perturbation around the background, showing that our stress tensor is finite on-shell.

Assessment of Rotationally-Invariant Clustering Using Streamlet Tractography

DEFF Research Database (Denmark)

Liptrot, Matthew George; Lauze, François

2016-01-01

We present a novel visualisation-based strategy for the assessment of a recently proposed clustering technique for raw DWI volumes which derives rotationally-invariant metrics to classify voxels. The validity of the division of all brain tissue voxels into such classes was assessed using the rece......We present a novel visualisation-based strategy for the assessment of a recently proposed clustering technique for raw DWI volumes which derives rotationally-invariant metrics to classify voxels. The validity of the division of all brain tissue voxels into such classes was assessed using...... the recently developed streamlets visualisation technique, which aims to represent brain fibres by collections of many short streamlines. Under the assumption that streamlines seeded in a cluster should stay within it, we were able to assess how well perceptual tracing could occur across the boundaries...... of the clusters....

Tensor Permutation Matrices in Finite Dimensions

OpenAIRE

Christian, Rakotonirina

2005-01-01

We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows us to construct a tensor permutation matrix, which is a generalisation of tensor commutation matrix, has been established. The expression of an element of a tensor commutation matrix has been generalised in the case of any element of a tensor permutation ma...

Study of the tensor correlation in oxygen isotopes using mean-field-type and shell model methods

International Nuclear Information System (INIS)

Sugimoto, Satoru

2007-01-01

The tensor force plays important roles in nuclear structure. Recently, we have developed a mean-field-type model which can treat the two-particle-two-hole correlation induced by the tensor force. We applied the model to sub-closed-shell oxygen isotopes and found that an sizable attractive energy comes from the tensor force. We also studied the tensor correlation in 16O using a shell model including two-particle-two-hole configurations. In this case, quite a large attractive energy is obtained for the correlation energy from the tensor force

Diffusion tensor imaging for target volume definition in glioblastoma multiforme

Energy Technology Data Exchange (ETDEWEB)

Berberat, Jatta; Remonda, Luca [Cantonal Hospital, Department of Neuro-radiology, Aarau (Switzerland); McNamara, Jane; Rogers, Susanne [Cantonal Hospital, Department of Radiation Oncology, Aarau (Switzerland); Bodis, Stephan [Cantonal Hospital, Department of Radiation Oncology, Aarau (Switzerland); University Hospital, Department of Radiation Oncology, Zurich (Switzerland)

2014-10-15

Diffusion tensor imaging (DTI) is an MR-based technique that may better detect the peritumoural region than MRI. Our aim was to explore the feasibility of using DTI for target volume delineation in glioblastoma patients. MR tensor tracts and maps of the isotropic (p) and anisotropic (q) components of water diffusion were coregistered with CT in 13 glioblastoma patients. An in-house image processing program was used to analyse water diffusion in each voxel of interest in the region of the tumour. Tumour infiltration was mapped according to validated criteria and contralateral normal brain was used as an internal control. A clinical target volume (CTV) was generated based on the T{sub 1}-weighted image obtained using contrast agent (T{sub 1Gd}), tractography and the infiltration map. This was compared to a conventional T{sub 2}-weighted CTV (T{sub 2}-w CTV). Definition of a diffusion-based CTV that included the adjacent white matter tracts proved highly feasible. A statistically significant difference was detected between the DTI-CTV and T{sub 2}-w CTV volumes (p < 0.005, t = 3.480). As the DTI-CTVs were smaller than the T{sub 2}-w CTVs (tumour plus peritumoural oedema), the pq maps were not simply detecting oedema. Compared to the clinical planning target volume (PTV), the DTI-PTV showed a trend towards volume reduction. These diffusion-based volumes were smaller than conventional volumes, yet still included sites of tumour recurrence. Extending the CTV along the abnormal tensor tracts in order to preserve coverage of the likely routes of dissemination, whilst sparing uninvolved brain, is a rational approach to individualising radiotherapy planning for glioblastoma patients. (orig.) [German] Die Diffusions-Tensor-Bildgebung (DTI) ist eine MR-Technik, die dank der Erfassung des peritumoralen Bereichs eine Verbesserung bezueglich MRI bringt. Unser Ziel war die Pruefung der Machbarkeit der Verwendung der DTI fuer die Zielvolumenabgrenzung fuer Patienten mit

Confinement through tensor gauge fields

International Nuclear Information System (INIS)

Salam, A.; Strathdee, J.

1977-12-01

Using the 0(3,2)-symmetric de Sitter solution of Einstein's equation describing a strongly interacting tensor field it is shown that hadronic bags confining quarks can be represented as de Sitter ''micro-universes'' with radii given 1/R 2 =lambdak 2 /6. Here k 2 and lambda are the strong coupling and the ''cosmological'' constant which apear in the Einstein equation used. Surprisingly the energy spectrum for the two-body hadronic states is the same as that for a harmonic oscillator potential, though the wave functions are completely different. The Einstein equation can be extended to include colour for the tensor fields

Migration Pathways of Thalamic Neurons and Development of Thalamocortical Connections in Humans Revealed by Diffusion MR Tractography.

Science.gov (United States)

Wilkinson, Molly; Kane, Tara; Wang, Rongpin; Takahashi, Emi

2017-12-01

The thalamus plays an important role in signal relays in the brain, with thalamocortical (TC) neuronal pathways linked to various sensory/cognitive functions. In this study, we aimed to see fetal and postnatal development of the thalamus including neuronal migration to the thalamus and the emergence/maturation of the TC pathways. Pathways from/to the thalami of human postmortem fetuses and in vivo subjects ranging from newborns to adults with no neurological histories were studied using high angular resolution diffusion MR imaging (HARDI) tractography. Pathways likely linked to neuronal migration from the ventricular zone and ganglionic eminence (GE) to the thalami were both successfully detected. Between the ventricular zone and thalami, more tractography pathways were found in anterior compared with posterior regions, which was well in agreement with postnatal observations that the anterior TC segment had more tract count and volume than the posterior segment. Three different pathways likely linked to neuronal migration from the GE to the thalami were detected. No hemispheric asymmetry of the TC pathways was quantitatively observed during development. These results suggest that HARDI tractography is useful to identify multiple differential neuronal migration pathways in human brains, and regional differences in brain development in fetal ages persisted in postnatal development. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

The geomagnetic field gradient tensor

DEFF Research Database (Denmark)

Kotsiaros, Stavros; Olsen, Nils

2012-01-01

We develop the general mathematical basis for space magnetic gradiometry in spherical coordinates. The magnetic gradient tensor is a second rank tensor consisting of 3 × 3 = 9 spatial derivatives. Since the geomagnetic field vector B is always solenoidal (∇ · B = 0) there are only eight independent...... tensor elements. Furthermore, in current free regions the magnetic gradient tensor becomes symmetric, further reducing the number of independent elements to five. In that case B is a Laplacian potential field and the gradient tensor can be expressed in series of spherical harmonics. We present properties...... of the magnetic gradient tensor and provide explicit expressions of its elements in terms of spherical harmonics. Finally we discuss the benefit of using gradient measurements for exploring the Earth’s magnetic field from space, in particular the advantage of the various tensor elements for a better determination...

Streamlining environmental product declarations: a stage model

Science.gov (United States)

Lefebvre, Elisabeth; Lefebvre, Louis A.; Talbot, Stephane; Le Hen, Gael

2001-02-01

General public environmental awareness and education is increasing, therefore stimulating the demand for reliable, objective and comparable information about products' environmental performances. The recently published standard series ISO 14040 and ISO 14025 are normalizing the preparation of Environmental Product Declarations (EPDs) containing comprehensive information relevant to a product's environmental impact during its life cycle. So far, only a few environmentally leading manufacturing organizations have experimented the preparation of EPDs (mostly from Europe), demonstrating its great potential as a marketing weapon. However the preparation of EPDs is a complex process, requiring collection and analysis of massive amounts of information coming from disparate sources (suppliers, sub-contractors, etc.). In a foreseeable future, the streamlining of the EPD preparation process will require product manufacturers to adapt their information systems (ERP, MES, SCADA) in order to make them capable of gathering, and transmitting the appropriate environmental information. It also requires strong functional integration all along the product supply chain in order to ensure that all the information is made available in a standardized and timely manner. The goal of the present paper is two fold: first to propose a transitional model towards green supply chain management and EPD preparation; second to identify key technologies and methodologies allowing to streamline the EPD process and subsequently the transition toward sustainable product development

Algebraic classification of the Weyl tensor in higher dimensions based on its 'superenergy' tensor

International Nuclear Information System (INIS)

Senovilla, Jose M M

2010-01-01

The algebraic classification of the Weyl tensor in the arbitrary dimension n is recovered by means of the principal directions of its 'superenergy' tensor. This point of view can be helpful in order to compute the Weyl aligned null directions explicitly, and permits one to obtain the algebraic type of the Weyl tensor by computing the principal eigenvalue of rank-2 symmetric future tensors. The algebraic types compatible with states of intrinsic gravitational radiation can then be explored. The underlying ideas are general, so that a classification of arbitrary tensors in the general dimension can be achieved. (fast track communication)

The light-front gauge-invariant energy-momentum tensor

International Nuclear Information System (INIS)

Lorce, Cedric

2015-01-01

In this study, we provide for the first time a complete parametrization for the matrix elements of the generic asymmetric, non-local and gauge-invariant canonical energy-momentum tensor, generalizing therefore former works on the symmetric, local and gauge-invariant kinetic energy-momentum tensor also known as the Belinfante-Rosenfeld energy-momentum tensor. We discuss in detail the various constraints imposed by non-locality, linear and angular momentum conservation. We also derive the relations with two-parton generalized and transverse-momentum dependent distributions, clarifying what can be learned from the latter. In particular, we show explicitly that two-parton transverse-momentum dependent distributions cannot provide any model-independent information about the parton orbital angular momentum. On the way, we recover the Burkardt sum rule and obtain similar new sum rules for higher-twist distributions

Physical states in the canonical tensor model from the perspective of random tensor networks

Energy Technology Data Exchange (ETDEWEB)

Narain, Gaurav [The Institute for Fundamental Study “The Tah Poe Academia Institute”,Naresuan University, Phitsanulok 65000 (Thailand); Sasakura, Naoki [Yukawa Institute for Theoretical Physics,Kyoto University, Kyoto 606-8502 (Japan); Sato, Yuki [National Institute for Theoretical Physics,School of Physics and Centre for Theoretical Physics,University of the Witwartersrand, WITS 2050 (South Africa)

2015-01-07

Tensor models, generalization of matrix models, are studied aiming for quantum gravity in dimensions larger than two. Among them, the canonical tensor model is formulated as a totally constrained system with first-class constraints, the algebra of which resembles the Dirac algebra of general relativity. When quantized, the physical states are defined to be vanished by the quantized constraints. In explicit representations, the constraint equations are a set of partial differential equations for the physical wave-functions, which do not seem straightforward to be solved due to their non-linear character. In this paper, after providing some explicit solutions for N=2,3, we show that certain scale-free integration of partition functions of statistical systems on random networks (or random tensor networks more generally) provides a series of solutions for general N. Then, by generalizing this form, we also obtain various solutions for general N. Moreover, we show that the solutions for the cases with a cosmological constant can be obtained from those with no cosmological constant for increased N. This would imply the interesting possibility that a cosmological constant can always be absorbed into the dynamics and is not an input parameter in the canonical tensor model. We also observe the possibility of symmetry enhancement in N=3, and comment on an extension of Airy function related to the solutions.

Polarization dependence of two-photon absorption coefficient and nonlinear susceptibility tensor in InP

International Nuclear Information System (INIS)

Matsusue, Toshio; Bando, Hiroyuki; Fujita, Shoichi; Takayama, Yusuke

2011-01-01

Two-photon absorption (TPA) effect in (001) InP is investigated using fs laser. Its dependences on wavelength and polarization are clarified by single and double beam methods with linearly polarized lights. Characteristic features are revealed and discussed with scaling law, crystal bonding and mutual relation of polarizations for double beams. The results are successfully analyzed on the basis of the third-order susceptibility tensor for comprehensive understanding of TPA effect at any polarization geometry. (copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

Tensor squeezed limits and the Higuchi bound

Energy Technology Data Exchange (ETDEWEB)

Bordin, Lorenzo [SISSA, via Bonomea 265, 34136, Trieste (Italy); Creminelli, Paolo [Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste (Italy); Mirbabayi, Mehrdad [Institute for Advanced Study, Princeton, NJ 08540 (United States); Noreña, Jorge, E-mail: lbordin@sissa.it, E-mail: creminel@ictp.it, E-mail: mehrdadm@ias.edu, E-mail: jorge.norena@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Avenida Universidad 330, Curauma, Valparaíso (Chile)

2016-09-01

We point out that tensor consistency relations—i.e. the behavior of primordial correlation functions in the limit a tensor mode has a small momentum—are more universal than scalar consistency relations. They hold in the presence of multiple scalar fields and as long as anisotropies are diluted exponentially fast. When de Sitter isometries are approximately respected during inflation this is guaranteed by the Higuchi bound, which forbids the existence of light particles with spin: de Sitter space can support scalar hair but no curly hair. We discuss two indirect ways to look for the violation of tensor consistency relations in observations, as a signature of models in which inflation is not a strong isotropic attractor, such as solid inflation: (a) graviton exchange contribution to the scalar four-point function; (b) quadrupolar anisotropy of the scalar power spectrum due to super-horizon tensor modes. This anisotropy has a well-defined statistics which can be distinguished from cases in which the background has a privileged direction.

Monograph On Tensor Notations

Science.gov (United States)

Sirlin, Samuel W.

1993-01-01

Eight-page report describes systems of notation used most commonly to represent tensors of various ranks, with emphasis on tensors in Cartesian coordinate systems. Serves as introductory or refresher text for scientists, engineers, and others familiar with basic concepts of coordinate systems, vectors, and partial derivatives. Indicial tensor, vector, dyadic, and matrix notations, and relationships among them described.

Cartesian tensors an introduction

CERN Document Server

Temple, G

2004-01-01

This undergraduate text provides an introduction to the theory of Cartesian tensors, defining tensors as multilinear functions of direction, and simplifying many theorems in a manner that lends unity to the subject. The author notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. He therefore provides an elementary discussion of the subject, in addition to a view of isotropic tensors and spinor analysis within the confines of Euclidean space. The text concludes with an examination of t

Visualizing Tensor Normal Distributions at Multiple Levels of Detail.

Science.gov (United States)

Abbasloo, Amin; Wiens, Vitalis; Hermann, Max; Schultz, Thomas

2016-01-01

Despite the widely recognized importance of symmetric second order tensor fields in medicine and engineering, the visualization of data uncertainty in tensor fields is still in its infancy. A recently proposed tensorial normal distribution, involving a fourth order covariance tensor, provides a mathematical description of how different aspects of the tensor field, such as trace, anisotropy, or orientation, vary and covary at each point. However, this wealth of information is far too rich for a human analyst to take in at a single glance, and no suitable visualization tools are available. We propose a novel approach that facilitates visual analysis of tensor covariance at multiple levels of detail. We start with a visual abstraction that uses slice views and direct volume rendering to indicate large-scale changes in the covariance structure, and locations with high overall variance. We then provide tools for interactive exploration, making it possible to drill down into different types of variability, such as in shape or orientation. Finally, we allow the analyst to focus on specific locations of the field, and provide tensor glyph animations and overlays that intuitively depict confidence intervals at those points. Our system is demonstrated by investigating the effects of measurement noise on diffusion tensor MRI, and by analyzing two ensembles of stress tensor fields from solid mechanics.

Structure of the Einstein tensor for class-1 embedded space time

Energy Technology Data Exchange (ETDEWEB)

Krause, J [Universidad Central de Venezuela, Caracas

1976-04-11

Continuing previous work, some features of the flat embedding theory of class-1 curved space-time are further discussed. In the two-metric formalism provided by the embedding approach the Gauss tensor obtains as the flat-covariant gradient of a fundamental vector potential. The Einstein tensor is then examined in terms of the Gauss tensor. It is proved that the Einstein tensor is divergence free in flat space-time, i.e. a true Lorentz-covariant conservation law for the Einstein tensor is shown to hold. The form of the Einstein tensor in flat space-time also appears as a canonical energy-momentum tensor of the vector potential. The corresponding Lagrangian density, however, does not provide us with a set of field equations for the fundamental vector potential; indeed, the Euler-Lagrange ''equations'' collapse to a useless identity, while the Lagrangian density has the form of a flat divergence.

Application-Tailored I/O with Streamline

NARCIS (Netherlands)

de Bruijn, W.J.; Bos, H.J.; Bal, H.E.

2011-01-01

Streamline is a stream-based OS communication subsystem that spans from peripheral hardware to userspace processes. It improves performance of I/O-bound applications (such as webservers and streaming media applications) by constructing tailor-made I/O paths through the operating system for each

Mesh Denoising based on Normal Voting Tensor and Binary Optimization

OpenAIRE

Yadav, S. K.; Reitebuch, U.; Polthier, K.

2016-01-01

This paper presents a tensor multiplication based smoothing algorithm that follows a two step denoising method. Unlike other traditional averaging approaches, our approach uses an element based normal voting tensor to compute smooth surfaces. By introducing a binary optimization on the proposed tensor together with a local binary neighborhood concept, our algorithm better retains sharp features and produces smoother umbilical regions than previous approaches. On top of that, we provide a stoc...

Dark energy in scalar-tensor theories

International Nuclear Information System (INIS)

Moeller, J.

2007-12-01

We investigate several aspects of dynamical dark energy in the framework of scalar-tensor theories of gravity. We provide a classification of scalar-tensor coupling functions admitting cosmological scaling solutions. In particular, we recover that Brans-Dicke theory with inverse power-law potential allows for a sequence of background dominated scaling regime and scalar field dominated, accelerated expansion. Furthermore, we compare minimally and non-minimally coupled models, with respect to the small redshift evolution of the dark energy equation of state. We discuss the possibility to discriminate between different models by a reconstruction of the equation-of-state parameter from available observational data. The non-minimal coupling characterizing scalar-tensor models can - in specific cases - alleviate fine tuning problems, which appear if (minimally coupled) quintessence is required to mimic a cosmological constant. Finally, we perform a phase-space analysis of a family of biscalar-tensor models characterized by a specific type of σ-model metric, including two examples from recent literature. In particular, we generalize an axion-dilaton model of Sonner and Townsend, incorporating a perfect fluid background consisting of (dark) matter and radiation. (orig.)

Dark energy in scalar-tensor theories

Energy Technology Data Exchange (ETDEWEB)

Moeller, J.

2007-12-15

We investigate several aspects of dynamical dark energy in the framework of scalar-tensor theories of gravity. We provide a classification of scalar-tensor coupling functions admitting cosmological scaling solutions. In particular, we recover that Brans-Dicke theory with inverse power-law potential allows for a sequence of background dominated scaling regime and scalar field dominated, accelerated expansion. Furthermore, we compare minimally and non-minimally coupled models, with respect to the small redshift evolution of the dark energy equation of state. We discuss the possibility to discriminate between different models by a reconstruction of the equation-of-state parameter from available observational data. The non-minimal coupling characterizing scalar-tensor models can - in specific cases - alleviate fine tuning problems, which appear if (minimally coupled) quintessence is required to mimic a cosmological constant. Finally, we perform a phase-space analysis of a family of biscalar-tensor models characterized by a specific type of {sigma}-model metric, including two examples from recent literature. In particular, we generalize an axion-dilaton model of Sonner and Townsend, incorporating a perfect fluid background consisting of (dark) matter and radiation. (orig.)

Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions

Energy Technology Data Exchange (ETDEWEB)

Krtous, Pavel [Institute of Theoretical Physics, Charles University, V Holesovickach 2, Prague (Czech Republic); Kubiznak, David [Institute of Theoretical Physics, Charles University, V Holesovickach 2, Prague (Czech Republic); Page, Don N. [Theoretical Physics Institute, University of Alberta, Edmonton T6G 2G7, Alberta (Canada); Frolov, Valeri P. [Theoretical Physics Institute, University of Alberta, Edmonton T6G 2G7, Alberta (Canada)

2007-02-15

From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k = [(D+1)/2] Killing-Yano tensors, of rank D-2j for all 0 {<=} j {<=} k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245)

Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions

International Nuclear Information System (INIS)

Krtous, Pavel; Kubiznak, David; Page, Don N.; Frolov, Valeri P.

2007-01-01

From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k = [(D+1)/2] Killing-Yano tensors, of rank D-2j for all 0 ≤ j ≤ k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245)

Low-grade intraventricular hemorrhage disrupts cerebellar white matter in preterm infants: evidence from diffusion tensor imaging

Energy Technology Data Exchange (ETDEWEB)

Morita, Takashi; Morimoto, Masafumi; Hasegawa, Tatsuji; Morioka, Shigemi; Kidowaki, Satoshi; Moroto, Masaharu; Yamashita, Satoshi; Maeda, Hiroshi; Chiyonobu, Tomohiro; Tokuda, Sachiko; Hosoi, Hajime [Kyoto Prefectural University of Medicine, Department of Pediatrics, Graduate School of Medical Science, Kyoto (Japan); Yamada, Kei [Kyoto Prefectural University of Medicine, Department of Radiology, Graduate School of Medical Science, Kyoto (Japan)

2015-05-01

Recent diffusion tensor imaging (DTI) studies have demonstrated that leakage of hemosiderin into cerebrospinal fluid (CSF), which is caused by high-grade intraventricular hemorrhage (IVH), can affect cerebellar development in preterm born infants. However, a direct effect of low-grade IVH on cerebellar development is unknown. Thus, we evaluated the cerebellar and cerebral white matter (WM) of preterm infants with low-grade IVH. Using DTI tractography performed at term-equivalent age, we analyzed 42 infants who were born less than 30 weeks gestational age (GA) at birth (22 with low-grade IVH, 20 without). These infants were divided into two birth groups depending on GA, and we then compared the presence and absence of IVH which was diagnosed by cerebral ultrasound (CUS) within 10 days after birth or conventional magnetic resonance imaging (MRI) at term-equivalent age in each group. Fractional anisotropy (FA) and apparent diffusion coefficient (ADC) at the superior cerebellar peduncle (SCP), middle cerebellar peduncle (MCP), motor tract, and sensory tract were measured. In the SCP, preterm born infants with IVH had lower FA values compared with infants without IVH. In particular, younger preterm birth with IVH had lower FA values in the SCP and motor tract and higher ADC values in the MCP. Low-grade IVH impaired cerebellar and cerebral WM, especially in the SCP. Moreover, younger preterm infants exhibited greater disruptions to cerebellar WM and the motor tract than infants of older preterm birth. (orig.)

Inference of segmented color and texture description by tensor voting.

Science.gov (United States)

Jia, Jiaya; Tang, Chi-Keung

2004-06-01

A robust synthesis method is proposed to automatically infer missing color and texture information from a damaged 2D image by (N)D tensor voting (N > 3). The same approach is generalized to range and 3D data in the presence of occlusion, missing data and noise. Our method translates texture information into an adaptive (N)D tensor, followed by a voting process that infers noniteratively the optimal color values in the (N)D texture space. A two-step method is proposed. First, we perform segmentation based on insufficient geometry, color, and texture information in the input, and extrapolate partitioning boundaries by either 2D or 3D tensor voting to generate a complete segmentation for the input. Missing colors are synthesized using (N)D tensor voting in each segment. Different feature scales in the input are automatically adapted by our tensor scale analysis. Results on a variety of difficult inputs demonstrate the effectiveness of our tensor voting approach.

Exact tensor network ansatz for strongly interacting systems

Science.gov (United States)

Zaletel, Michael P.

It appears that the tensor network ansatz, while not quite complete, is an efficient coordinate system for the tiny subset of a many-body Hilbert space which can be realized as a low energy state of a local Hamiltonian. However, we don't fully understand precisely which phases are captured by the tensor network ansatz, how to compute their physical observables (even numerically), or how to compute a tensor network representation for a ground state given a microscopic Hamiltonian. These questions are algorithmic in nature, but their resolution is intimately related to understanding the nature of quantum entanglement in many-body systems. For this reason it is useful to compute the tensor network representation of various `model' wavefunctions representative of different phases of matter; this allows us to understand how the entanglement properties of each phase are expressed in the tensor network ansatz, and can serve as test cases for algorithm development. Condensed matter physics has many illuminating model wavefunctions, such as Laughlin's celebrated wave function for the fractional quantum Hall effect, the Bardeen-Cooper-Schrieffer wave function for superconductivity, and Anderson's resonating valence bond ansatz for spin liquids. This thesis presents some results on exact tensor network representations of these model wavefunctions. In addition, a tensor network representation is given for the time evolution operator of a long-range one-dimensional Hamiltonian, which allows one to numerically simulate the time evolution of power-law interacting spin chains as well as two-dimensional strips and cylinders.

Classification of the Ricci and Plebanski tensors in general relativity using Newman--Penrose formalism

International Nuclear Information System (INIS)

McIntosh, C.B.G.; Foyster, J.M.; Lun, A.W.h.

1981-01-01

A list is given of a canonical set of the Newman--Penrose quantities Phi/sub A/B, the tetrad components of the trace-free Ricci tensor, for each Plebanski class according to Plebanski's classification of this tensor. This comparative list can easily be extended to cover the classification in tetrad language of any second-order, trace-free, symmetric tensor in a space-time. A fourth-order tensor which is the product of two such tensors was defined by Plebanski and used in his classification. This has the same symmetries as the Weyl tensor. The Petrov classification of this tensor, here called the Plebanski tensor, is discussed along with the classification of the Ricci tensor. The use of the Plebanski tensor in a couple of areas of general relativity is also briefly discussed

Estimation of Uncertainties of Full Moment Tensors

Science.gov (United States)

2017-10-06

For our moment tensor inversions, we use the ‘cut-and-paste’ ( CAP ) code of Zhu and Helmberger (1996) and Zhu and Ben-Zion (2013), with some...modifications. For the misfit function we use an L1 norm Silwal and Tape (2016), and we incorporate the number of misfitting polarities into the waveform... norm of the eigenvalue triple provides the magnitude of the moment tensor, leaving two free parameters to define the source type. In the same year

Abnormal brain connectivity in first-episode psychosis: A diffusion MRI tractography study of the corpus callosum

Science.gov (United States)

Price, Gary; Cercignani, Mara; Parker, Geoffrey J.M.; Altmann, Daniel R.; Barnes, Thomas R.E.; Barker, Gareth J.; Joyce, Eileen M.; Ron, Maria A.

2007-01-01

A model of disconnectivity involving abnormalities in the cortex and connecting white matter pathways may explain the clinical manifestations of schizophrenia. Recently, diffusion imaging tractography has made it possible to study white matter pathways in detail and we present here a study of patients with first-episode psychosis using this technique. We selected the corpus callosum for this study because there is evidence that it is abnormal in schizophrenia. In addition, the topographical organization of its fibers makes it possible to relate focal abnormalities to specific cortical regions. Eighteen patients with first-episode psychosis and 21 healthy subjects took part in the study. A probabilistic tractography algorithm (PICo) was used to study fractional anisotropy (FA). Seed regions were placed in the genu and splenium to track fiber tracts traversing these regions, and a multi-threshold approach to study the probability of connection was used. Multiple linear regressions were used to explore group differences. FA, a measure of tract coherence, was reduced in tracts crossing the genu, and to a lesser degree the splenium, in patients compared with controls. FA was also lower in the genu in females across both groups, but there was no gender-by-group interaction. The FA reduction in patients may be due to aberrant myelination or axonal abnormalities, but the similar tract volumes in the two groups suggest that severe axonal loss is unlikely at this stage of the illness. PMID:17275337

CONSTRAINTS ON SCALAR AND TENSOR PERTURBATIONS IN PHENOMENOLOGICAL AND TWO-FIELD INFLATION MODELS: BAYESIAN EVIDENCES FOR PRIMORDIAL ISOCURVATURE AND TENSOR MODES

Energy Technology Data Exchange (ETDEWEB)

Vaeliviita, Jussi [Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029, Blindern, N-0315 Oslo (Norway); Savelainen, Matti; Talvitie, Marianne; Kurki-Suonio, Hannu; Rusak, Stanislav, E-mail: jussi.valiviita@astro.uio.no [Department of Physics and Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, FIN-00014 University of Helsinki (Finland)

2012-07-10

We constrain cosmological models where the primordial perturbations have an adiabatic and a (possibly correlated) cold dark matter (CDM) or baryon isocurvature component. We use both a phenomenological approach, where the power spectra of primordial perturbations are parameterized with amplitudes and spectral indices, and a slow-roll two-field inflation approach where slow-roll parameters are used as primary parameters, determining the spectral indices and the tensor-to-scalar ratio. In the phenomenological case, with CMB data, the upper limit to the CDM isocurvature fraction is {alpha} < 6.4% at k = 0.002 Mpc{sup -1} and 15.4% at k = 0.01 Mpc{sup -1}. The non-adiabatic contribution to the CMB temperature variance is -0.030 < {alpha}{sub T} < 0.049 at the 95% confidence level. Including the supernova (SN) (or large-scale structure) data, these limits become {alpha} < 7.0%, 13.7%, and -0.048 < {alpha}{sub T} < 0.042 (or {alpha} < 10.2%, 16.0%, and -0.071 < {alpha}{sub T} < 0.024). The CMB constraint on the tensor-to-scalar ratio, r < 0.26 at k = 0.01 Mpc{sup -1}, is not affected by the non-adiabatic modes. In the slow-roll two-field inflation approach, the spectral indices are constrained close to 1. This leads to tighter limits on the isocurvature fraction; with the CMB data {alpha} < 2.6% at k = 0.01 Mpc{sup -1}, but the constraint on {alpha}{sub T} is not much affected, -0.058 < {alpha}{sub T} < 0.045. Including SN (or LSS) data, these limits become {alpha} < 3.2% and -0.056 < {alpha}{sub T} < 0.030 (or {alpha} < 3.4% and -0.063 < {alpha}{sub T} < -0.008). In addition to the generally correlated models, we study also special cases where the adiabatic and isocurvature modes are uncorrelated or fully (anti)correlated. We calculate Bayesian evidences (model probabilities) in 21 different non-adiabatic cases and compare them to the corresponding adiabatic models, and find that in all cases the data support the pure adiabatic model.

Tensor-based spatiotemporal saliency detection

Science.gov (United States)

Dou, Hao; Li, Bin; Deng, Qianqian; Zhang, LiRui; Pan, Zhihong; Tian, Jinwen

2018-03-01

This paper proposes an effective tensor-based spatiotemporal saliency computation model for saliency detection in videos. First, we construct the tensor representation of video frames. Then, the spatiotemporal saliency can be directly computed by the tensor distance between different tensors, which can preserve the complete temporal and spatial structure information of object in the spatiotemporal domain. Experimental results demonstrate that our method can achieve encouraging performance in comparison with the state-of-the-art methods.

TensorFlow Distributions

OpenAIRE

Dillon, Joshua V.; Langmore, Ian; Tran, Dustin; Brevdo, Eugene; Vasudevan, Srinivas; Moore, Dave; Patton, Brian; Alemi, Alex; Hoffman, Matt; Saurous, Rif A.

2017-01-01

The TensorFlow Distributions library implements a vision of probability theory adapted to the modern deep-learning paradigm of end-to-end differentiable computation. Building on two basic abstractions, it offers flexible building blocks for probabilistic computation. Distributions provide fast, numerically stable methods for generating samples and computing statistics, e.g., log density. Bijectors provide composable volume-tracking transformations with automatic caching. Together these enable...

Relativistic interpretation of the nature of the nuclear tensor force

Science.gov (United States)

Zong, Yao-Yao; Sun, Bao-Yuan

2018-02-01

The spin-dependent nature of the nuclear tensor force is studied in detail within the relativistic Hartree-Fock approach. The relativistic formalism for the tensor force is supplemented with an additional Lorentz-invariant tensor formalism in the σ-scalar channel, so as to take into account almost fully the nature of the tensor force brought about by the Fock diagrams in realistic nuclei. Specifically, the tensor sum rules are tested for the spin and pseudo-spin partners with and without nodes, to further understand the nature of the tensor force within the relativistic model. It is shown that the interference between the two components of nucleon spinors causes distinct violations of the tensor sum rules in realistic nuclei, mainly due to the opposite signs on the κ quantities of the upper and lower components, as well as the nodal difference. However, the sum rules can be precisely reproduced if the same radial wave functions are taken for the spin/pseudo-spin partners in addition to neglecting the lower/upper components, revealing clearly the nature of the tensor force. Supported by National Natural Science Foundation of China (11375076, 11675065) and the Fundamental Research Funds for the Central Universities (lzujbky-2016-30)

Generalized dielectric permittivity tensor

International Nuclear Information System (INIS)

Borzdov, G.N.; Barkovskii, L.M.; Fedorov, F.I.

1986-01-01

The authors deal with the question of what is to be done with the formalism of the electrodynamics of dispersive media based on the introduction of dielectric-permittivity tensors for purely harmonic fields when Voigt waves and waves of more general form exist. An attempt is made to broaden and generalize the formalism to take into account dispersion of waves of the given type. In dispersive media, the polarization, magnetization, and conduction current-density vectors of point and time are determined by the values of the electromagnetic field vectors in the vicinity of this point (spatial dispersion) in the preceding instants of time (time dispersion). The dielectric-permittivity tensor and other tensors of electrodynamic parameters of the medium are introduced in terms of a set of evolution operators and not the set of harmonic function. It is noted that a magnetic-permeability tensor and an elastic-modulus tensor may be introduced for an acoustic field in dispersive anisotropic media with coupling equations of general form

Tensor analysis for physicists

CERN Document Server

Schouten, J A

1989-01-01

This brilliant study by a famed mathematical scholar and former professor of mathematics at the University of Amsterdam integrates a concise exposition of the mathematical basis of tensor analysis with admirably chosen physical examples of the theory. The first five chapters incisively set out the mathematical theory underlying the use of tensors. The tensor algebra in EN and RN is developed in Chapters I and II. Chapter II introduces a sub-group of the affine group, then deals with the identification of quantities in EN. The tensor analysis in XN is developed in Chapter IV. In chapters VI through IX, Professor Schouten presents applications of the theory that are both intrinsically interesting and good examples of the use and advantages of the calculus. Chapter VI, intimately connected with Chapter III, shows that the dimensions of physical quantities depend upon the choice of the underlying group, and that tensor calculus is the best instrument for dealing with the properties of anisotropic media. In Chapte...

Sparse alignment for robust tensor learning.

Science.gov (United States)

Lai, Zhihui; Wong, Wai Keung; Xu, Yong; Zhao, Cairong; Sun, Mingming

2014-10-01

Multilinear/tensor extensions of manifold learning based algorithms have been widely used in computer vision and pattern recognition. This paper first provides a systematic analysis of the multilinear extensions for the most popular methods by using alignment techniques, thereby obtaining a general tensor alignment framework. From this framework, it is easy to show that the manifold learning based tensor learning methods are intrinsically different from the alignment techniques. Based on the alignment framework, a robust tensor learning method called sparse tensor alignment (STA) is then proposed for unsupervised tensor feature extraction. Different from the existing tensor learning methods, L1- and L2-norms are introduced to enhance the robustness in the alignment step of the STA. The advantage of the proposed technique is that the difficulty in selecting the size of the local neighborhood can be avoided in the manifold learning based tensor feature extraction algorithms. Although STA is an unsupervised learning method, the sparsity encodes the discriminative information in the alignment step and provides the robustness of STA. Extensive experiments on the well-known image databases as well as action and hand gesture databases by encoding object images as tensors demonstrate that the proposed STA algorithm gives the most competitive performance when compared with the tensor-based unsupervised learning methods.

TensorPack: a Maple-based software package for the manipulation of algebraic expressions of tensors in general relativity

International Nuclear Information System (INIS)

Huf, P A; Carminati, J

2015-01-01

In this paper we: (1) introduce TensorPack, a software package for the algebraic manipulation of tensors in covariant index format in Maple; (2) briefly demonstrate the use of the package with an orthonormal tensor proof of the shearfree conjecture for dust. TensorPack is based on the Riemann and Canon tensor software packages and uses their functions to express tensors in an indexed covariant format. TensorPack uses a string representation as input and provides functions for output in index form. It extends the functionality to basic algebra of tensors, substitution, covariant differentiation, contraction, raising/lowering indices, symmetry functions and other accessory functions. The output can be merged with text in the Maple environment to create a full working document with embedded dynamic functionality. The package offers potential for manipulation of indexed algebraic tensor expressions in a flexible software environment. (paper)

Tensor fields on orbits of quantum states and applications

Energy Technology Data Exchange (ETDEWEB)

Volkert, Georg Friedrich

2010-07-19

On classical Lie groups, which act by means of a unitary representation on finite dimensional Hilbert spaces H, we identify two classes of tensor field constructions. First, as pull-back tensor fields of order two from modified Hermitian tensor fields, constructed on Hilbert spaces by means of the property of having the vertical distributions of the C{sub 0}-principal bundle H{sub 0} {yields} P(H) over the projective Hilbert space P(H) in the kernel. And second, directly constructed on the Lie group, as left-invariant representation-dependent operator-valued tensor fields (LIROVTs) of arbitrary order being evaluated on a quantum state. Within the NP-hard problem of deciding whether a given state in a n-level bi-partite quantum system is entangled or separable (Gurvits, 2003), we show that both tensor field constructions admit a geometric approach to this problem, which evades the traditional ambiguity on defining metrical structures on the convex set of mixed states. In particular by considering manifolds associated to orbits passing through a selected state when acted upon by the local unitary group U(n) x U(n) of Schmidt coefficient decomposition inducing transformations, we find the following results: In the case of pure states we show that Schmidt-equivalence classes which are Lagrangian submanifolds define maximal entangled states. This implies a stronger statement as the one proposed by Bengtsson (2007). Moreover, Riemannian pull-back tensor fields split on orbits of separable states and provide a quantitative characterization of entanglement which recover the entanglement measure proposed by Schlienz and Mahler (1995). In the case of mixed states we highlight a relation between LIROVTs of order two and a class of computable separability criteria based on the Bloch-representation (de Vicente, 2007). (orig.)

Tensor fields on orbits of quantum states and applications

International Nuclear Information System (INIS)

Volkert, Georg Friedrich

2010-01-01

On classical Lie groups, which act by means of a unitary representation on finite dimensional Hilbert spaces H, we identify two classes of tensor field constructions. First, as pull-back tensor fields of order two from modified Hermitian tensor fields, constructed on Hilbert spaces by means of the property of having the vertical distributions of the C 0 -principal bundle H 0 → P(H) over the projective Hilbert space P(H) in the kernel. And second, directly constructed on the Lie group, as left-invariant representation-dependent operator-valued tensor fields (LIROVTs) of arbitrary order being evaluated on a quantum state. Within the NP-hard problem of deciding whether a given state in a n-level bi-partite quantum system is entangled or separable (Gurvits, 2003), we show that both tensor field constructions admit a geometric approach to this problem, which evades the traditional ambiguity on defining metrical structures on the convex set of mixed states. In particular by considering manifolds associated to orbits passing through a selected state when acted upon by the local unitary group U(n) x U(n) of Schmidt coefficient decomposition inducing transformations, we find the following results: In the case of pure states we show that Schmidt-equivalence classes which are Lagrangian submanifolds define maximal entangled states. This implies a stronger statement as the one proposed by Bengtsson (2007). Moreover, Riemannian pull-back tensor fields split on orbits of separable states and provide a quantitative characterization of entanglement which recover the entanglement measure proposed by Schlienz and Mahler (1995). In the case of mixed states we highlight a relation between LIROVTs of order two and a class of computable separability criteria based on the Bloch-representation (de Vicente, 2007). (orig.)

Tensor hypercontraction. II. Least-squares renormalization

Science.gov (United States)

Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David

2012-12-01

The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)], 10.1063/1.4732310. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1/r12 operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N^5) effort if exact integrals are decomposed, or O(N^4) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N^4) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.

Positivity of linear maps under tensor powers

Energy Technology Data Exchange (ETDEWEB)

Müller-Hermes, Alexander, E-mail: muellerh@ma.tum.de; Wolf, Michael M., E-mail: m.wolf@tum.de [Zentrum Mathematik, Technische Universität München, 85748 Garching (Germany); Reeb, David, E-mail: reeb.qit@gmail.com [Zentrum Mathematik, Technische Universität München, 85748 Garching (Germany); Institute for Theoretical Physics, Leibniz Universität Hannover, 30167 Hannover (Germany)

2016-01-15

We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with n copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show that for every n ∈ ℕ, there exist non-trivial maps with this property and that for two-dimensional Hilbert spaces there is no non-trivial map for which this holds for all n. For higher dimensions, we reduce the existence question of such non-trivial “tensor-stable positive maps” to a one-parameter family of maps and show that an affirmative answer would imply the existence of non-positive partial transpose bound entanglement. As an application, we show that any tensor-stable positive map that is not completely positive yields an upper bound on the quantum channel capacity, which for the transposition map gives the well-known cb-norm bound. We, furthermore, show that the latter is an upper bound even for the local operations and classical communications-assisted quantum capacity, and that moreover it is a strong converse rate for this task.

Positivity of linear maps under tensor powers

International Nuclear Information System (INIS)

Müller-Hermes, Alexander; Wolf, Michael M.; Reeb, David

2016-01-01

We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with n copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show that for every n ∈ ℕ, there exist non-trivial maps with this property and that for two-dimensional Hilbert spaces there is no non-trivial map for which this holds for all n. For higher dimensions, we reduce the existence question of such non-trivial “tensor-stable positive maps” to a one-parameter family of maps and show that an affirmative answer would imply the existence of non-positive partial transpose bound entanglement. As an application, we show that any tensor-stable positive map that is not completely positive yields an upper bound on the quantum channel capacity, which for the transposition map gives the well-known cb-norm bound. We, furthermore, show that the latter is an upper bound even for the local operations and classical communications-assisted quantum capacity, and that moreover it is a strong converse rate for this task

Unique characterization of the Bel-Robinson tensor

International Nuclear Information System (INIS)

Bergqvist, G; Lankinen, P

2004-01-01

We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel-Robinson-type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors

Tensor Product of Polygonal Cell Complexes

OpenAIRE

Chien, Yu-Yen

2017-01-01

We introduce the tensor product of polygonal cell complexes, which interacts nicely with the tensor product of link graphs of complexes. We also develop the unique factorization property of polygonal cell complexes with respect to the tensor product, and study the symmetries of tensor products of polygonal cell complexes.

Mean template for tensor-based morphometry using deformation tensors.

Science.gov (United States)

Leporé, Natasha; Brun, Caroline; Pennec, Xavier; Chou, Yi-Yu; Lopez, Oscar L; Aizenstein, Howard J; Becker, James T; Toga, Arthur W; Thompson, Paul M

2007-01-01

Tensor-based morphometry (TBM) studies anatomical differences between brain images statistically, to identify regions that differ between groups, over time, or correlate with cognitive or clinical measures. Using a nonlinear registration algorithm, all images are mapped to a common space, and statistics are most commonly performed on the Jacobian determinant (local expansion factor) of the deformation fields. In, it was shown that the detection sensitivity of the standard TBM approach could be increased by using the full deformation tensors in a multivariate statistical analysis. Here we set out to improve the common space itself, by choosing the shape that minimizes a natural metric on the deformation tensors from that space to the population of control subjects. This method avoids statistical bias and should ease nonlinear registration of new subjects data to a template that is 'closest' to all subjects' anatomies. As deformation tensors are symmetric positive-definite matrices and do not form a vector space, all computations are performed in the log-Euclidean framework. The control brain B that is already the closest to 'average' is found. A gradient descent algorithm is then used to perform the minimization that iteratively deforms this template and obtains the mean shape. We apply our method to map the profile of anatomical differences in a dataset of 26 HIV/AIDS patients and 14 controls, via a log-Euclidean Hotelling's T2 test on the deformation tensors. These results are compared to the ones found using the 'best' control, B. Statistics on both shapes are evaluated using cumulative distribution functions of the p-values in maps of inter-group differences.

Stress-energy tensor near a charged, rotating, evaporating black hole

International Nuclear Information System (INIS)

Hiscock, W.A.

1977-01-01

The recently developed two-dimensional stress-energy regularization techniques are applied to the two-dimensional analog of the Reissner-Nordstroem family of black-hole metrics. The calculated stress-energy tensor in all cases contains the thermal radiation discovered by Hawking. Implications for the evolution of the interior of a charged black hole are considered. The calculated stress-energy tensor is found to diverge on the inner, Cauchy, horizon. Thus the effect of quantum mechanics is to cause the Cauchy horizon to become singular. The stress-energy tensor is also calculated for the ''most reasonable'' two-dimensional analog of the Kerr-Newman family of black-hole metrics. Although the analysis is not as rigorous as in the Reissner-Nordstroem case, it appears that the correct value for the Hawking radiation also appears in this model

TENSOR DECOMPOSITIONS AND SPARSE LOG-LINEAR MODELS

Science.gov (United States)

Johndrow, James E.; Bhattacharya, Anirban; Dunson, David B.

2017-01-01

Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. We derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions. PMID:29332971

Streamline-based microfluidic device

Science.gov (United States)

Tai, Yu-Chong (Inventor); Zheng, Siyang (Inventor); Kasdan, Harvey (Inventor)

2013-01-01

The present invention provides a streamline-based device and a method for using the device for continuous separation of particles including cells in biological fluids. The device includes a main microchannel and an array of side microchannels disposed on a substrate. The main microchannel has a plurality of stagnation points with a predetermined geometric design, for example, each of the stagnation points has a predetermined distance from the upstream edge of each of the side microchannels. The particles are separated and collected in the side microchannels.

Multivariate Tensor-based Brain Anatomical Surface Morphometry via Holomorphic One-Forms

OpenAIRE

Wang, Yalin; Chan, Tony F.; Toga, Arthur W.; Thompson, Paul M.

2009-01-01

Here we introduce multivariate tensor-based surface morphometry using holomorphic one-forms to study brain anatomy. We computed new statistics from the Riemannian metric tensors that retain the full information in the deformation tensor fields. We introduce two different holomorphic one-forms that induce different surface conformal parameterizations. We applied this framework to 3D MRI data to analyze hippocampal surface morphometry in Alzheimer’s Disease (AD; 26 subjects), lateral ventricula...

Notes on super Killing tensors

Energy Technology Data Exchange (ETDEWEB)

Howe, P.S. [Department of Mathematics, King’s College London,The Strand, London WC2R 2LS (United Kingdom); Lindström, University [Department of Physics and Astronomy, Theoretical Physics, Uppsala University,SE-751 20 Uppsala (Sweden); Theoretical Physics, Imperial College London,Prince Consort Road, London SW7 2AZ (United Kingdom)

2016-03-14

The notion of a Killing tensor is generalised to a superspace setting. Conserved quantities associated with these are defined for superparticles and Poisson brackets are used to define a supersymmetric version of the even Schouten-Nijenhuis bracket. Superconformal Killing tensors in flat superspaces are studied for spacetime dimensions 3,4,5,6 and 10. These tensors are also presented in analytic superspaces and super-twistor spaces for 3,4 and 6 dimensions. Algebraic structures associated with superconformal Killing tensors are also briefly discussed.

Simultaneous analysis and quality assurance for diffusion tensor imaging.

Directory of Open Access Journals (Sweden)

Carolyn B Lauzon

Full Text Available Diffusion tensor imaging (DTI enables non-invasive, cyto-architectural mapping of in vivo tissue microarchitecture through voxel-wise mathematical modeling of multiple magnetic resonance imaging (MRI acquisitions, each differently sensitized to water diffusion. DTI computations are fundamentally estimation processes and are sensitive to noise and artifacts. Despite widespread adoption in the neuroimaging community, maintaining consistent DTI data quality remains challenging given the propensity for patient motion, artifacts associated with fast imaging techniques, and the possibility of hardware changes/failures. Furthermore, the quantity of data acquired per voxel, the non-linear estimation process, and numerous potential use cases complicate traditional visual data inspection approaches. Currently, quality inspection of DTI data has relied on visual inspection and individual processing in DTI analysis software programs (e.g. DTIPrep, DTI-studio. However, recent advances in applied statistical methods have yielded several different metrics to assess noise level, artifact propensity, quality of tensor fit, variance of estimated measures, and bias in estimated measures. To date, these metrics have been largely studied in isolation. Herein, we select complementary metrics for integration into an automatic DTI analysis and quality assurance pipeline. The pipeline completes in 24 hours, stores statistical outputs, and produces a graphical summary quality analysis (QA report. We assess the utility of this streamlined approach for empirical quality assessment on 608 DTI datasets from pediatric neuroimaging studies. The efficiency and accuracy of quality analysis using the proposed pipeline is compared with quality analysis based on visual inspection. The unified pipeline is found to save a statistically significant amount of time (over 70% while improving the consistency of QA between a DTI expert and a pool of research associates. Projection of QA

Streamlining: Reducing costs and increasing STS operations effectiveness

Science.gov (United States)

Petersburg, R. K.

1985-01-01

The development of streamlining as a concept, its inclusion in the space transportation system engineering and operations support (STSEOS) contract, and how it serves as an incentive to management and technical support personnel is discussed. The mechanics of encouraging and processing streamlining suggestions, reviews, feedback to submitters, recognition, and how individual employee performance evaluations are used to motivation are discussed. Several items that were implemented are mentioned. Information reported and the methodology of determining estimated dollar savings are outlined. The overall effect of this activity on the ability of the McDonnell Douglas flight preparation and mission operations team to support a rapidly increasing flight rate without a proportional increase in cost is illustrated.

Electrical tensor Green functions for cylindrical waveguides

International Nuclear Information System (INIS)

Prijmenko, S.D.; Papkovich, V.G.; Khizhnyak, N.A.

1988-01-01

Formation of electrical tensor Green functions for cylindrical waveguides is considered. Behaviour of these functions in the source region is studied. Cases of electrical tensor Green functions for vector potential G E (r-vector, r'-vector) and electric field G e (r-vector, r'-vector) are analysed. When forming G E (r-vector, r'-vector), its dependence on lateral coordinates is taken into account by means of two-dimensional fundamental vector Hansen functions, several methods are used to take into account the dependence on transverse coordinate. When forming G e (r-vector, r'-vector) we use the fact that G E (r-vector, r'-vector) and G e (r-vector, r'-vector) are the generalized functions. It is shown that G e (r-vector, r'-vector) behaviour in the source region is defined by a singular term, which properties are described by the delta-function. Two variants of solving the problem of defining singular and regular sides of tensor function G E (r-vector, r'-vector) are presented. 23 refs

Tensor Train Neighborhood Preserving Embedding

Science.gov (United States)

Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin

2018-05-01

In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior trade-off in classification, computation, and dimensionality reduction in MNIST handwritten digits and Weizmann face datasets.

Curvature tensors and unified field equations on SEX/sub n/

International Nuclear Information System (INIS)

Chung, K.T.; Lee, I.L.

1988-01-01

We study the curvature tensors and field equations in the n-dimensional SE manifold SEX/sub n/. We obtain several basic properties of the vectors S/subλ/ and U/sub λ/ and then of the SE curvature tensor and its contractions, such as a generalized Ricci identity, a generalized Bianchi identity, and two variations of the Bianchi identity satisfied by the SE Einstein tensor. Finally, a system of field equations is discussed in SEX/sub n/ an done of its particular solutions is constructed and displayed

Fractional Killing-Yano Tensors and Killing Vectors Using the Caputo Derivative in Some One- and Two-Dimensional Curved Space

Directory of Open Access Journals (Sweden)

Ehab Malkawi

2014-01-01

Full Text Available The classical free Lagrangian admitting a constant of motion, in one- and two-dimensional space, is generalized using the Caputo derivative of fractional calculus. The corresponding metric is obtained and the fractional Christoffel symbols, Killing vectors, and Killing-Yano tensors are derived. Some exact solutions of these quantities are reported.

Random SU(2) invariant tensors

Science.gov (United States)

Li, Youning; Han, Muxin; Ruan, Dong; Zeng, Bei

2018-04-01

SU(2) invariant tensors are states in the (local) SU(2) tensor product representation but invariant under the global group action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An average over the ensemble is carried out when computing any physical quantities. The random tensor exhibits a phenomenon known as ‘concentration of measure’, which states that for any bipartition the average value of entanglement entropy of its reduced density matrix is asymptotically the maximal possible as the local dimensions go to infinity. We show that this phenomenon is also true when the average is over the SU(2) invariant subspace instead of the entire space for rank-n tensors in general. It is shown in our earlier work Li et al (2017 New J. Phys. 19 063029) that the subleading correction of the entanglement entropy has a mild logarithmic divergence when n  =  4. In this paper, we show that for n  >  4 the subleading correction is not divergent but a finite number. In some special situation, the number could be even smaller than 1/2, which is the subleading correction of random state over the entire Hilbert space of tensors.

Black holes with surrounding matter in scalar-tensor theories.

Science.gov (United States)

Cardoso, Vitor; Carucci, Isabella P; Pani, Paolo; Sotiriou, Thomas P

2013-09-13

We uncover two mechanisms that can render Kerr black holes unstable in scalar-tensor gravity, both associated with the presence of matter in the vicinity of the black hole and the fact that this introduces an effective mass for the scalar. Our results highlight the importance of understanding the structure of spacetime in realistic, astrophysical black holes in scalar-tensor theories.

Nonperturbative loop quantization of scalar-tensor theories of gravity

International Nuclear Information System (INIS)

Zhang Xiangdong; Ma Yongge

2011-01-01

The Hamiltonian formulation of scalar-tensor theories of gravity is derived from their Lagrangian formulation by Hamiltonian analysis. The Hamiltonian formalism marks off two sectors of the theories by the coupling parameter ω(φ). In the sector of ω(φ)=-(3/2), the feasible theories are restricted and a new primary constraint generating conformal transformations of spacetime is obtained, while in the other sector of ω(φ)≠-(3/2), the canonical structure and constraint algebra of the theories are similar to those of general relativity coupled with a scalar field. By canonical transformations, we further obtain the connection-dynamical formalism of the scalar-tensor theories with real su(2) connections as configuration variables in both sectors. This formalism enables us to extend the scheme of nonperturbative loop quantum gravity to the scalar-tensor theories. The quantum kinematical framework for the scalar-tensor theories is rigorously constructed. Both the Hamiltonian constraint operator and master constraint operator are well defined and proposed to represent quantum dynamics. Thus the loop quantum gravity method is also valid for general scalar-tensor theories.

Improved tensor multiplets

International Nuclear Information System (INIS)

Wit, B. de; Rocek, M.

1982-01-01

We construct a conformally invariant theory of the N = 1 supersymmetric tensor gauge multiplet and discuss the situation in N = 2. We show that our results give rise to the recently proposed variant of Poincare supergravity, and provide the complete tensor calculus for the theory. Finally, we argue that this theory cannot be quantized sensibly. (orig.)

The evolution of tensor polarization

International Nuclear Information System (INIS)

Huang, H.; Lee, S.Y.; Ratner, L.

1993-01-01

By using the equation of motion for the vector polarization, the spin transfer matrix for spin tensor polarization, the spin transfer matrix for spin tensor polarization is derived. The evolution equation for the tensor polarization is studied in the presence of an isolate spin resonance and in the presence of a spin rotor, or snake

Tri-Clustered Tensor Completion for Social-Aware Image Tag Refinement.

Science.gov (United States)

Tang, Jinhui; Shu, Xiangbo; Qi, Guo-Jun; Li, Zechao; Wang, Meng; Yan, Shuicheng; Jain, Ramesh

2017-08-01

Social image tag refinement, which aims to improve tag quality by automatically completing the missing tags and rectifying the noise-corrupted ones, is an essential component for social image search. Conventional approaches mainly focus on exploring the visual and tag information, without considering the user information, which often reveals important hints on the (in)correct tags of social images. Towards this end, we propose a novel tri-clustered tensor completion framework to collaboratively explore these three kinds of information to improve the performance of social image tag refinement. Specifically, the inter-relations among users, images and tags are modeled by a tensor, and the intra-relations between users, images and tags are explored by three regularizations respectively. To address the challenges of the super-sparse and large-scale tensor factorization that demands expensive computing and memory cost, we propose a novel tri-clustering method to divide the tensor into a certain number of sub-tensors by simultaneously clustering users, images and tags into a bunch of tri-clusters. And then we investigate two strategies to complete these sub-tensors by considering (in)dependence between the sub-tensors. Experimental results on a real-world social image database demonstrate the superiority of the proposed method compared with the state-of-the-art methods.

Tensor algebra and tensor analysis for engineers with applications to continuum mechanics

CERN Document Server

Itskov, Mikhail

2015-01-01

This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side. In accordance with the contemporary way of scientific publications, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this monograph addresses graduate students as well as scientists working in this field. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.

Effect of thyroxine on brain microstructure in extremely premature babies: magnetic resonance imaging findings in the TIPIT study.

Science.gov (United States)

Ng, Sze May; Turner, Mark A; Gamble, Carrol; Didi, Mohammed; Victor, Suresh; Atkinson, Jessica; Sluming, Vanessa; Parkes, Laura M; Tietze, Anna; Abernethy, Laurence J; Weindling, Alan Michael

2014-08-01

In order to assess relationships between thyroid hormone status and findings on brain MRI, a subset of babies was recruited to a multi-centre randomised, placebo-controlled trial of levothyroxine (LT4) supplementation for babies born before 28 weeks' gestation (known as the TIPIT study, for Thyroxine supplementation In Preterm InfanTs). These infants were imaged at term-equivalence. Forty-five TIPIT participants had brain MRI using diffusion tensor imaging (DTI) to estimate white matter development by apparent diffusion coefficient (ADC), fractional anisotropy (FA) and tractography metrics of number and length of streamlines. We made comparisons between babies with the lowest and highest plasma FT4 concentrations during the initial 4 weeks after birth. There were no differences in DTI metrics between babies who had received LT4 supplementation and those who had received a placebo. Among recipients of a placebo, babies in the lowest quartile of plasma-free thyroxine (FT4) concentrations had significantly higher apparent diffusion coefficient measurements in the posterior corpus callosum and streamlines that were shorter and less numerous in the right internal capsule. Among LT4-supplemented babies, those who had plasma FT4 concentrations in the highest quartile had significantly lower apparent diffusion coefficient values in the left occipital lobe, higher fractional anisotropy in the anterior corpus callosum and longer and more numerous streamlines in the anterior corpus callosum. DTI variables were not associated with allocation of placebo or thyroid supplementation. Markers of poorly organised brain microstructure were associated with low plasma FT4 concentrations after birth. The findings suggest that plasma FT4 concentrations affect brain development in very immature infants and that the effect of LT4 supplementation for immature babies with low FT4 plasma concentrations warrants further study.

Inflationary tensor fossils in large-scale structure

Energy Technology Data Exchange (ETDEWEB)

Dimastrogiovanni, Emanuela [School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455 (United States); Fasiello, Matteo [Department of Physics, Case Western Reserve University, Cleveland, OH 44106 (United States); Jeong, Donghui [Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, PA 16802 (United States); Kamionkowski, Marc, E-mail: ema@physics.umn.edu, E-mail: mrf65@case.edu, E-mail: duj13@psu.edu, E-mail: kamion@jhu.edu [Department of Physics and Astronomy, 3400 N. Charles St., Johns Hopkins University, Baltimore, MD 21218 (United States)

2014-12-01

Inflation models make specific predictions for a tensor-scalar-scalar three-point correlation, or bispectrum, between one gravitational-wave (tensor) mode and two density-perturbation (scalar) modes. This tensor-scalar-scalar correlation leads to a local power quadrupole, an apparent departure from statistical isotropy in our Universe, as well as characteristic four-point correlations in the current mass distribution in the Universe. So far, the predictions for these observables have been worked out only for single-clock models in which certain consistency conditions between the tensor-scalar-scalar correlation and tensor and scalar power spectra are satisfied. Here we review the requirements on inflation models for these consistency conditions to be satisfied. We then consider several examples of inflation models, such as non-attractor and solid-inflation models, in which these conditions are put to the test. In solid inflation the simplest consistency conditions are already violated whilst in the non-attractor model we find that, contrary to the standard scenario, the tensor-scalar-scalar correlator probes directly relevant model-dependent information. We work out the predictions for observables in these models. For non-attractor inflation we find an apparent local quadrupolar departure from statistical isotropy in large-scale structure but that this power quadrupole decreases very rapidly at smaller scales. The consistency of the CMB quadrupole with statistical isotropy then constrains the distance scale that corresponds to the transition from the non-attractor to attractor phase of inflation to be larger than the currently observable horizon. Solid inflation predicts clustering fossils signatures in the current galaxy distribution that may be large enough to be detectable with forthcoming, and possibly even current, galaxy surveys.

A streamlined failure mode and effects analysis

International Nuclear Information System (INIS)

Ford, Eric C.; Smith, Koren; Terezakis, Stephanie; Croog, Victoria; Gollamudi, Smitha; Gage, Irene; Keck, Jordie; DeWeese, Theodore; Sibley, Greg

2014-01-01

Purpose: Explore the feasibility and impact of a streamlined failure mode and effects analysis (FMEA) using a structured process that is designed to minimize staff effort. Methods: FMEA for the external beam process was conducted at an affiliate radiation oncology center that treats approximately 60 patients per day. A structured FMEA process was developed which included clearly defined roles and goals for each phase. A core group of seven people was identified and a facilitator was chosen to lead the effort. Failure modes were identified and scored according to the FMEA formalism. A risk priority number,RPN, was calculated and used to rank failure modes. Failure modes with RPN > 150 received safety improvement interventions. Staff effort was carefully tracked throughout the project. Results: Fifty-two failure modes were identified, 22 collected during meetings, and 30 from take-home worksheets. The four top-ranked failure modes were: delay in film check, missing pacemaker protocol/consent, critical structures not contoured, and pregnant patient simulated without the team's knowledge of the pregnancy. These four failure modes hadRPN > 150 and received safety interventions. The FMEA was completed in one month in four 1-h meetings. A total of 55 staff hours were required and, additionally, 20 h by the facilitator. Conclusions: Streamlined FMEA provides a means of accomplishing a relatively large-scale analysis with modest effort. One potential value of FMEA is that it potentially provides a means of measuring the impact of quality improvement efforts through a reduction in risk scores. Future study of this possibility is needed

A streamlined failure mode and effects analysis.

Science.gov (United States)

Ford, Eric C; Smith, Koren; Terezakis, Stephanie; Croog, Victoria; Gollamudi, Smitha; Gage, Irene; Keck, Jordie; DeWeese, Theodore; Sibley, Greg

2014-06-01

Explore the feasibility and impact of a streamlined failure mode and effects analysis (FMEA) using a structured process that is designed to minimize staff effort. FMEA for the external beam process was conducted at an affiliate radiation oncology center that treats approximately 60 patients per day. A structured FMEA process was developed which included clearly defined roles and goals for each phase. A core group of seven people was identified and a facilitator was chosen to lead the effort. Failure modes were identified and scored according to the FMEA formalism. A risk priority number,RPN, was calculated and used to rank failure modes. Failure modes with RPN > 150 received safety improvement interventions. Staff effort was carefully tracked throughout the project. Fifty-two failure modes were identified, 22 collected during meetings, and 30 from take-home worksheets. The four top-ranked failure modes were: delay in film check, missing pacemaker protocol/consent, critical structures not contoured, and pregnant patient simulated without the team's knowledge of the pregnancy. These four failure modes had RPN > 150 and received safety interventions. The FMEA was completed in one month in four 1-h meetings. A total of 55 staff hours were required and, additionally, 20 h by the facilitator. Streamlined FMEA provides a means of accomplishing a relatively large-scale analysis with modest effort. One potential value of FMEA is that it potentially provides a means of measuring the impact of quality improvement efforts through a reduction in risk scores. Future study of this possibility is needed.

A streamlined failure mode and effects analysis

Energy Technology Data Exchange (ETDEWEB)

Ford, Eric C., E-mail: eford@uw.edu; Smith, Koren; Terezakis, Stephanie; Croog, Victoria; Gollamudi, Smitha; Gage, Irene; Keck, Jordie; DeWeese, Theodore; Sibley, Greg [Department of Radiation Oncology and Molecular Radiation Sciences, Johns Hopkins University, Baltimore, MD 21287 (United States)

2014-06-15

Purpose: Explore the feasibility and impact of a streamlined failure mode and effects analysis (FMEA) using a structured process that is designed to minimize staff effort. Methods: FMEA for the external beam process was conducted at an affiliate radiation oncology center that treats approximately 60 patients per day. A structured FMEA process was developed which included clearly defined roles and goals for each phase. A core group of seven people was identified and a facilitator was chosen to lead the effort. Failure modes were identified and scored according to the FMEA formalism. A risk priority number,RPN, was calculated and used to rank failure modes. Failure modes with RPN > 150 received safety improvement interventions. Staff effort was carefully tracked throughout the project. Results: Fifty-two failure modes were identified, 22 collected during meetings, and 30 from take-home worksheets. The four top-ranked failure modes were: delay in film check, missing pacemaker protocol/consent, critical structures not contoured, and pregnant patient simulated without the team's knowledge of the pregnancy. These four failure modes hadRPN > 150 and received safety interventions. The FMEA was completed in one month in four 1-h meetings. A total of 55 staff hours were required and, additionally, 20 h by the facilitator. Conclusions: Streamlined FMEA provides a means of accomplishing a relatively large-scale analysis with modest effort. One potential value of FMEA is that it potentially provides a means of measuring the impact of quality improvement efforts through a reduction in risk scores. Future study of this possibility is needed.

Tensor Calculus: Unlearning Vector Calculus

Science.gov (United States)

Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita

2018-01-01

Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…

Spatial Mapping of Structural and Connectional Imaging Data for the Developing Human Brain with Diffusion Tensor Imaging

Science.gov (United States)

Ouyang, Austin; Jeon, Tina; Sunkin, Susan M.; Pletikos, Mihovil; Sedmak, Goran; Sestan, Nenad; Lein, Ed S.; Huang, Hao

2014-01-01

During human brain development from fetal stage to adulthood, the white matter (WM) tracts undergo dramatic changes. Diffusion tensor imaging (DTI), a widely used magnetic resonance imaging (MRI) modality, offers insight into the dynamic changes of WM fibers as these fibers can be noninvasively traced and three-dimensionally (3D) reconstructed with DTI tractography. The DTI and conventional T1 weighted MRI images also provide sufficient cortical anatomical details for mapping the cortical regions of interests (ROIs). In this paper, we described basic concepts and methods of DTI techniques that can be used to trace major WM tracts noninvasively from fetal brain of 14 postconceptional weeks (pcw) to adult brain. We applied these techniques to acquire DTI data and trace, reconstruct and visualize major WM tracts during development. After categorizing major WM fiber bundles into five unique functional tract groups, namely limbic, brain stem, projection, commissural and association tracts, we revealed formation and maturation of these 3D reconstructed WM tracts of the developing human brain. The structural and connectional imaging data offered by DTI provides the anatomical backbone of transcriptional atlas of the developing human brain. PMID:25448302

Spatial mapping of structural and connectional imaging data for the developing human brain with diffusion tensor imaging.

Science.gov (United States)

Ouyang, Austin; Jeon, Tina; Sunkin, Susan M; Pletikos, Mihovil; Sedmak, Goran; Sestan, Nenad; Lein, Ed S; Huang, Hao

2015-02-01

During human brain development from fetal stage to adulthood, the white matter (WM) tracts undergo dramatic changes. Diffusion tensor imaging (DTI), a widely used magnetic resonance imaging (MRI) modality, offers insight into the dynamic changes of WM fibers as these fibers can be noninvasively traced and three-dimensionally (3D) reconstructed with DTI tractography. The DTI and conventional T1 weighted MRI images also provide sufficient cortical anatomical details for mapping the cortical regions of interests (ROIs). In this paper, we described basic concepts and methods of DTI techniques that can be used to trace major WM tracts noninvasively from fetal brain of 14 postconceptional weeks (pcw) to adult brain. We applied these techniques to acquire DTI data and trace, reconstruct and visualize major WM tracts during development. After categorizing major WM fiber bundles into five unique functional tract groups, namely limbic, brain stem, projection, commissural and association tracts, we revealed formation and maturation of these 3D reconstructed WM tracts of the developing human brain. The structural and connectional imaging data offered by DTI provides the anatomical backbone of transcriptional atlas of the developing human brain. Copyright © 2014 Elsevier Inc. All rights reserved.

Numerical evaluation of tensor Feynman integrals in Euclidean kinematics

Energy Technology Data Exchange (ETDEWEB)

Gluza, J.; Kajda [Silesia Univ., Katowice (Poland). Inst. of Physics; Riemann, T.; Yundin, V. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

2010-10-15

For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently 'simple' numerical approaches. We elaborate two algorithms for this purpose which may be applied in the Euclidean kinematical region and in d=4-2{epsilon} dimensions. One method uses Mellin-Barnes representations for the Feynman parameter representation of multi-loop Feynman integrals with arbitrary tensor rank. Our Mathematica package AMBRE has been extended for that purpose, and together with the packages MB (M. Czakon) or MBresolve (A. V. Smirnov and V. A. Smirnov) one may perform automatically a numerical evaluation of planar tensor Feynman integrals. Alternatively, one may apply sector decomposition to planar and non-planar multi-loop {epsilon}-expanded Feynman integrals with arbitrary tensor rank. We automatized the preparations of Feynman integrals for an immediate application of the package sectordecomposition (C. Bogner and S. Weinzierl) so that one has to give only a proper definition of propagators and numerators. The efficiency of the two implementations, based on Mellin-Barnes representations and sector decompositions, is compared. The computational packages are publicly available. (orig.)

Link prediction via generalized coupled tensor factorisation

DEFF Research Database (Denmark)

Ermiş, Beyza; Evrim, Acar Ataman; Taylan Cemgil, A.

2012-01-01

and higher-order tensors. We propose to use an approach based on probabilistic interpretation of tensor factorisation models, i.e., Generalised Coupled Tensor Factorisation, which can simultaneously fit a large class of tensor models to higher-order tensors/matrices with com- mon latent factors using...... different loss functions. Numerical experiments demonstrate that joint analysis of data from multiple sources via coupled factorisation improves the link prediction performance and the selection of right loss function and tensor model is crucial for accurately predicting missing links....

Role of magnetic resonance tractography in the preoperative planning and intraoperative assessment of patients with intra-axial brain tumours.

Science.gov (United States)

Romano, A; Ferrante, M; Cipriani, V; Fasoli, F; Ferrante, L; D'Andrea, G; Fantozzi, L M; Bozzao, A

2007-09-01

This study was conducted to assess the possibility of identifying precise white matter tracts situated in proximity to intracranial tumours, to define the anatomical and topographical relations between the same white matter tracts and the tumour, to verify the possibility of integrating tractographic images in the context of a package of three-dimensional anatomical images to send to the neuronavigation system, to assess the impact of this information on surgical planning, and to analyse, both pre-and postoperatively, the patient's clinical conditions as an index of the functional integrity of the fibres themselves. Twenty-five patients underwent diffusion tensor study prior to neurosurgery. With the use of dedicated software, relative colour maps were obtained and the trajectories of the white matter tracts adjacent to the tumour were reconstructed in three dimensions. These were then processed for preoperative planning. Planning, which was performed with the neuronavigator, was based on analysis of the location of the course of the main white matter tracts adjacent to the lesion (pyramidal tract, optic radiation and arcuate fasciculus). Two neurosurgeons were asked whether the tractography images had modified the access and/or intraoperative approach to the tumour. All patients were clinically assessed both pre-and postoperatively 1 month after the procedure to define the presence of symptoms related to the involvement of the white matter tracts studied and therefore to assess the integrity of the fibres after the operation. In one patient, the tumour was situated away from all the tracts studied and did not compress them in any way. Overall, 40/75 tracts studied had no anatomical relation with the tumour, were not displaced by the tumour or could not be visualised in their entire course. Analysis of the remaining 35 white matter tracts led to an a priori change in the surgical approach for corticotomy in four patients (16%), with no disagreement between the two