Linear Invariant Tensor Interpolation Applied to Cardiac Diffusion Tensor MRI
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
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)
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
Analytical performance bounds for multi-tensor diffusion-MRI.
Ahmed Sid, Farid; Abed-Meraim, Karim; Harba, Rachid; Oulebsir-Boumghar, Fatima
2017-02-01
To examine the effects of MR acquisition parameters on brain white matter fiber orientation estimation and parameter of clinical interest in crossing fiber areas based on the Multi-Tensor Model (MTM). We compute the Cramér-Rao Bound (CRB) for the MTM and the parameter of clinical interest such as the Fractional Anisotropy (FA) and the dominant fiber orientations, assuming that the diffusion MRI data are recorded by a multi-coil, multi-shell acquisition system. Considering the sum-of-squares method for the reconstructed magnitude image, we introduce an approximate closed-form formula for Fisher Information Matrix that has the simplicity and easy interpretation advantages. In addition, we propose to generalize the FA and the mean diffusivity to the multi-tensor model. We show the application of the CRB to reduce the scan time while preserving a good estimation precision. We provide results showing how the increase of the number of acquisition coils compensates the decrease of the number of diffusion gradient directions. We analyze the impact of the b-value and the Signal-to-Noise Ratio (SNR). The analysis shows that the estimation error variance decreases with a quadratic rate with the SNR, and that the optimum b-values are not unique but depend on the target parameter, the context, and eventually the target cost function. In this study we highlight the importance of choosing the appropriate acquisition parameters especially when dealing with crossing fiber areas. We also provide a methodology for the optimal tuning of these parameters using the CRB. Copyright © 2016 Elsevier Inc. All rights reserved.
MRI-negative refractory partial epilepsy: role for diffusion tensor imaging in high field MRI.
Chen, Qin; Lui, Su; Li, Chun-Xiao; Jiang, Li-Jun; Ou-Yang, Luo; Tang, He-Han; Shang, Hui-Fang; Huang, Xiao-Qi; Gong, Qi-Yong; Zhou, Dong
2008-07-01
Our aim is to use the high field MR scanner (3T) to verify whether diffusion tensor imaging (DTI) could help in locating the epileptogenic zone in patients with MRI-negative refractory partial epilepsy. Fifteen patients with refractory partial epilepsy who had normal conventional MRI, and 40 healthy volunteers were recruited for the study. DTI was performed on a 3T MR scanner, individual maps of mean diffusivity (MD) and fractional anisotropy (FA) were calculated, and Voxel-Based Analysis (VBA) was performed for individual comparison between patients and controls. Voxel-based analysis revealed significant MD increase in variant regions in 13 patients. The electroclinical seizure localization was concurred to seven patients. No patient exhibited regions of significant decreased MD. Regions of significant reduced FA were observed in five patients, with two of these concurring with electroclinical seizure localization. Two patients had regions of significant increase in FA, which were distinct from electroclinical seizure localization. Our study's results revealed that DTI is a responsive neuroradiologic technique that provides information about the epileptogenic areas in patients with MRI-negative refractory partial epilepsy. This technique may also helpful in pre-surgical evaluation.
3D structure tensor analysis of light microscopy data for validating diffusion MRI.
Khan, Ahmad Raza; Cornea, Anda; Leigland, Lindsey A; Kohama, Steven G; Jespersen, Sune Nørhøj; Kroenke, Christopher D
2015-05-01
Diffusion magnetic resonance imaging (d-MRI) is a powerful non-invasive and non-destructive technique for characterizing brain tissue on the microscopic scale. However, the lack of validation of d-MRI by independent experimental means poses an obstacle to accurate interpretation of data acquired using this method. Recently, structure tensor analysis has been applied to light microscopy images, and this technique holds promise to be a powerful validation strategy for d-MRI. Advantages of this approach include its similarity to d-MRI in terms of averaging the effects of a large number of cellular structures, and its simplicity, which enables it to be implemented in a high-throughput manner. However, a drawback of previous implementations of this technique arises from it being restricted to 2D. As a result, structure tensor analyses have been limited to tissue sectioned in a direction orthogonal to the direction of interest. Here we describe the analytical framework for extending structure tensor analysis to 3D, and utilize the results to analyze serial image "stacks" acquired with confocal microscopy of rhesus macaque hippocampal tissue. Implementation of 3D structure tensor procedures requires removal of sources of anisotropy introduced in tissue preparation and confocal imaging. This is accomplished with image processing steps to mitigate the effects of anisotropic tissue shrinkage, and the effects of anisotropy in the point spread function (PSF). In order to address the latter confound, we describe procedures for measuring the dependence of PSF anisotropy on distance from the microscope objective within tissue. Prior to microscopy, ex vivo d-MRI measurements performed on the hippocampal tissue revealed three regions of tissue with mutually orthogonal directions of least restricted diffusion that correspond to CA1, alveus and inferior longitudinal fasciculus. We demonstrate the ability of 3D structure tensor analysis to identify structure tensor orientations that
On the Averaging of Cardiac Diffusion Tensor MRI Data: The Effect of Distance Function Selection
Giannakidis, Archontis; Melkus, Gerd; Yang, Guang; Gullberg, Grant T.
2016-01-01
Diffusion tensor magnetic resonance imaging (DT-MRI) allows a unique insight into the microstructure of highly-directional tissues. The selection of the most proper distance function for the space of diffusion tensors is crucial in enhancing the clinical application of this imaging modality. Both linear and nonlinear metrics have been proposed in the literature over the years. The debate on the most appropriate DT-MRI distance function is still ongoing. In this paper, we presented a framework to compare the Euclidean, affine-invariant Riemannian and log-Euclidean metrics using actual high-resolution DT-MRI rat heart data. We employed temporal averaging at the diffusion tensor level of three consecutive and identically-acquired DT-MRI datasets from each of five rat hearts as a means to rectify the background noise-induced loss of myocyte directional regularity. This procedure is applied here for the first time in the context of tensor distance function selection. When compared with previous studies that used a different concrete application to juxtapose the various DT-MRI distance functions, this work is unique in that it combined the following: (i) Metrics were judged by quantitative –rather than qualitative– criteria, (ii) the comparison tools were non-biased, (iii) a longitudinal comparison operation was used on a same-voxel basis. The statistical analyses of the comparison showed that the three DT-MRI distance functions tend to provide equivalent results. Hence, we came to the conclusion that the tensor manifold for cardiac DT-MRI studies is a curved space of almost zero curvature. The signal to noise ratio dependence of the operations was investigated through simulations. Finally, the “swelling effect” occurrence following Euclidean averaging was found to be too unimportant to be worth consideration. PMID:27754986
On the averaging of cardiac diffusion tensor MRI data: the effect of distance function selection
Giannakidis, Archontis; Melkus, Gerd; Yang, Guang; Gullberg, Grant T.
2016-11-01
Diffusion tensor magnetic resonance imaging (DT-MRI) allows a unique insight into the microstructure of highly-directional tissues. The selection of the most proper distance function for the space of diffusion tensors is crucial in enhancing the clinical application of this imaging modality. Both linear and nonlinear metrics have been proposed in the literature over the years. The debate on the most appropriate DT-MRI distance function is still ongoing. In this paper, we presented a framework to compare the Euclidean, affine-invariant Riemannian and log-Euclidean metrics using actual high-resolution DT-MRI rat heart data. We employed temporal averaging at the diffusion tensor level of three consecutive and identically-acquired DT-MRI datasets from each of five rat hearts as a means to rectify the background noise-induced loss of myocyte directional regularity. This procedure is applied here for the first time in the context of tensor distance function selection. When compared with previous studies that used a different concrete application to juxtapose the various DT-MRI distance functions, this work is unique in that it combined the following: (i) metrics were judged by quantitative—rather than qualitative—criteria, (ii) the comparison tools were non-biased, (iii) a longitudinal comparison operation was used on a same-voxel basis. The statistical analyses of the comparison showed that the three DT-MRI distance functions tend to provide equivalent results. Hence, we came to the conclusion that the tensor manifold for cardiac DT-MRI studies is a curved space of almost zero curvature. The signal to noise ratio dependence of the operations was investigated through simulations. Finally, the ‘swelling effect’ occurrence following Euclidean averaging was found to be too unimportant to be worth consideration.
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.
Directory of Open Access Journals (Sweden)
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.
In vivo reconstruction of lumbar erector spinae architecture using diffusion tensor MRI
Sieben, Judith M.; Van Otten, Ilse; Lataster, Arno; Froeling, Martijn; Nederveen, Aart J.; Strijkers, Gustav J.; Drost, Maarten R.
2016-01-01
Study Design: Diffusion tensor magnetic resonance imaging (DTMRI) reconstruction of lumbar erector spinae (ES) compared with cadaver dissection. Objective: The aim of this study was to reconstruct the human lumbar ES from in vivo DT-MRI measurements and to compare the results with literature and
Teh, Irvin; McClymont, Darryl; Zdora, Marie-Christine; Whittington, Hannah J; Davidoiu, Valentina; Lee, Jack; Lygate, Craig A; Rau, Christoph; Zanette, Irene; Schneider, Jürgen E
2017-03-10
Diffusion tensor imaging (DTI) is widely used to assess tissue microstructure non-invasively. Cardiac DTI enables inference of cell and sheetlet orientations, which are altered under pathological conditions. However, DTI is affected by many factors, therefore robust validation is critical. Existing histological validation is intrinsically flawed, since it requires further tissue processing leading to sample distortion, is routinely limited in field-of-view and requires reconstruction of three-dimensional volumes from two-dimensional images. In contrast, synchrotron radiation imaging (SRI) data enables imaging of the heart in 3D without further preparation following DTI. The objective of the study was to validate DTI measurements based on structure tensor analysis of SRI data. One isolated, fixed rat heart was imaged ex vivo with DTI and X-ray phase contrast SRI, and reconstructed at 100 μm and 3.6 μm isotropic resolution respectively. Structure tensors were determined from the SRI data and registered to the DTI data. Excellent agreement in helix angles (HA) and transverse angles (TA) was observed between the DTI and structure tensor synchrotron radiation imaging (STSRI) data, where HA DTI-STSRI = -1.4° ± 23.2° and TA DTI-STSRI = -1.4° ± 35.0° (mean ± 1.96 standard deviation across all voxels in the left ventricle). STSRI confirmed that the primary eigenvector of the diffusion tensor corresponds with the cardiomyocyte long-axis across the whole myocardium. We have used STSRI as a novel and high-resolution gold standard for the validation of DTI, allowing like-with-like comparison of three-dimensional tissue structures in the same intact heart free of distortion. This represents a critical step forward in independently verifying the structural basis and informing the interpretation of cardiac DTI data, thereby supporting the further development and adoption of DTI in structure-based electro-mechanical modelling and routine clinical
Brody, David L; Mac Donald, Christine L; Shimony, Joshua S
2015-01-01
Brain imaging plays a key role in the assessment of traumatic brain injury. In this review, we present our perspectives on the use of computed tomography (CT), conventional magnetic resonance imaging (MRI), and newer advanced modalities such as diffusion tensor imaging. Specifically, we address assessment for immediately life-threatening intracranial lesions (noncontrast head CT), assessment of progression of intracranial lesions (noncontrast head CT), documenting intracranial abnormalities for medicolegal reasons (conventional MRI with blood-sensitive sequences), presurgical planning for post-traumatic epilepsy (high spatial resolution conventional MRI), early prognostic decision making (conventional MRI with diffusion-weighted imaging), prognostic assessment for rehabilitative planning (conventional MRI and possibly diffusion tensor imaging in the future), stratification of subjects and pharmacodynamic tracking of targeted therapies in clinical trials (specific MRI sequences or positron emission tomography (PET) ligands, e.g., diffusion tensor imaging for traumatic axonal injury). We would like to emphasize that all of these methods, especially the newer research approaches, require careful radiologic-pathologic validation for optimal interpretation. We have taken this approach in a mouse model of pericontusional traumatic axonal injury. We found that the extent of reduction in the diffusion tensor imaging parameter relative anisotropy directly correlated with the number of amyloid precursor protein (APP)-stained axonal varicosities (r(2)=0.81, p<0.0001, n=20 injured mice). Interestingly, however, the least severe contusional injuries did not result in APP-stained axonal varicosities, but did cause reduction in relative anisotropy. Clearly, both the imaging assessments and the pathologic assessments will require iterative refinement. © 2015 Elsevier B.V. All rights reserved.
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Stahl, R. [Institut fuer Klinische Radiologie - Grosshadern, Klinikum der Universitaet Muenchen (Germany); Institut fuer Klinische Radiologie - Grosshadern, Klinikum der Universitaet Muenchen, Marchioninistr. 15, 81377, Muenchen (Germany); Dietrich, O.; Reiser, M.F.; Schoenberg, S.O. [Institut fuer Klinische Radiologie - Grosshadern, Klinikum der Universitaet Muenchen (Germany); Teipel, S.; Hampel, H. [Klinik fuer Psychiatrie und Psychotherapie, Klinikum der Universitaet Muenchen (Germany)
2003-07-01
Alzheimer disease (AD) causes cortical degeneration with subsequent degenerative changes of the white matter. The aim of this study was to investigate the extent of white matter tissue damage of patients with Alzheimer's disease in comparison with healthy subjects using diffusion tensor MRI (DTI). The value of integrated parallel imaging techniques (iPAT) for reduction of image distortion was assessed. We studied 9 patients with mild AD and 10 age and gender matched healthy controls. DTI brain scans were obtained on a 1.5 tesla system (Siemens Magnetom Sonata) using parallel imaging (iPAT) and an EPI diffusion sequence with TE/TR 71 ms/6000 ms. We used an 8-element head coil and a GRAPPA reconstruction algorithm with an acceleration factor of 2. From the tensor, the mean diffusivity (D), the fractional anisotropy (FA), and the relative anisotropy (RA) of several white matter regions were determined. FA was significantly lower (p <0,05) in the white matter of the genu of corpus callosum from patients with AD than in the corresponding regions from healthy controls. There was a trend observed for slightly higher ADC values in the AD group (p=0,06). No significant changes were observed in the regions of the splenium, internal capsule, pericallosal areas, frontal, temporal, parietal, and occipital lobe. The images obtained with iPAT contained substantially less susceptibility artefacts and were less distorted than images acquired with non-parallel imaging technique. DTI is a method with potential to assess early stages of white matter damage in vivo. The altered FA and ADC values in the genu of corpus callosum of patients with AD presumably reflect the microscopic white matter degeneration. Acquisition time can be reduced by iPAT methods with less image distortion from susceptibility artefacts resulting in a more accurate calculation of the diffusion tensor. (orig.) [German] Bei der Alzheimer-Erkrankung (AD) kommt es zur kortikalen Degeneration und sekundaer zu
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.)
Assessment of axonal degeneration in Alzheimer's disease with diffusion tensor MRI
International Nuclear Information System (INIS)
Stahl, R.; Dietrich, O.; Reiser, M.F.; Schoenberg, S.O.; Teipel, S.; Hampel, H.
2003-01-01
Alzheimer disease (AD) causes cortical degeneration with subsequent degenerative changes of the white matter. The aim of this study was to investigate the extent of white matter tissue damage of patients with Alzheimer's disease in comparison with healthy subjects using diffusion tensor MRI (DTI). The value of integrated parallel imaging techniques (iPAT) for reduction of image distortion was assessed. We studied 9 patients with mild AD and 10 age and gender matched healthy controls. DTI brain scans were obtained on a 1.5 tesla system (Siemens Magnetom Sonata) using parallel imaging (iPAT) and an EPI diffusion sequence with TE/TR 71 ms/6000 ms. We used an 8-element head coil and a GRAPPA reconstruction algorithm with an acceleration factor of 2. From the tensor, the mean diffusivity (D), the fractional anisotropy (FA), and the relative anisotropy (RA) of several white matter regions were determined. FA was significantly lower (p [de
Directory of Open Access Journals (Sweden)
Swarupa Kancherla
Full Text Available Visual function has been shown to deteriorate prior to the onset of retinopathy in some diabetic patients and experimental animal models. This suggests the involvement of the brain's visual system in the early stages of diabetes. In this study, we tested this hypothesis by examining the integrity of the visual pathway in a diabetic rat model using in vivo multi-modal magnetic resonance imaging (MRI. Ten-week-old Sprague-Dawley rats were divided into an experimental diabetic group by intraperitoneal injection of 65 mg/kg streptozotocin in 0.01 M citric acid, and a sham control group by intraperitoneal injection of citric acid only. One month later, diffusion tensor MRI (DTI was performed to examine the white matter integrity in the brain, followed by chromium-enhanced MRI of retinal integrity and manganese-enhanced MRI of anterograde manganese transport along the visual pathway. Prior to MRI experiments, the streptozotocin-induced diabetic rats showed significantly smaller weight gain and higher blood glucose level than the control rats. DTI revealed significantly lower fractional anisotropy and higher radial diffusivity in the prechiasmatic optic nerve of the diabetic rats compared to the control rats. No apparent difference was observed in the axial diffusivity of the optic nerve, the chromium enhancement in the retina, or the manganese enhancement in the lateral geniculate nucleus and superior colliculus between groups. Our results suggest that streptozotocin-induced diabetes leads to early injury in the optic nerve when no substantial change in retinal integrity or anterograde transport along the visual pathways was observed in MRI using contrast agent enhancement. DTI may be a useful tool for detecting and monitoring early pathophysiological changes in the visual system of experimental diabetes non-invasively.
Brain diffusion tensor MRI in systematic lupus erythematosus: A systematic review.
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.
Sreedharan, Ruma Madhu; Menon, Amitha C; James, Jija S; Kesavadas, Chandrasekharan; Thomas, Sanjeev V
2015-03-01
Language lateralization is unique to humans. Functional MRI (fMRI) and diffusion tensor imaging (DTI) enable the study of language areas and white matter fibers involved in language, respectively. The objective of this study was to correlate arcuate fasciculus (AF) laterality by diffusion tensor imaging with that by fMRI in preadolescent children which has not yet been reported. Ten children between 8 and 12 years were subjected to fMRI and DTI imaging using Siemens 1.5 T MRI. Two language fMRI paradigms--visual verb generation and word pair task--were used. Analysis was done using SPM8 software. In DTI, the fiber volume of the arcuate fasciculus (AFV) and fractional anisotropy (FA) was measured. The fMRI Laterality Index (fMRI-LI) and DTI Laterality Index (DTI-LI) were calculated and their correlation assessed using the Pearson Correlation Index. Of ten children, mean age 10.6 years, eight showed left lateralization while bilateral language lateralization was seen in two. AFV by DTI was more on the left side in seven of the eight children who had left lateralization by fMRI. DTI could not trace the AF in one child. Of the two with bilateral language lateralization on fMRI, one showed larger AFV on the right side while the other did not show any asymmetry. There was a significant correlation (p laterality in children with a high degree of correlation between the two imaging modalities.
Applying tensor-based morphometry to parametric surfaces can improve MRI-based disease diagnosis.
Wang, Yalin; Yuan, Lei; Shi, Jie; Greve, Alexander; Ye, Jieping; Toga, Arthur W; Reiss, Allan L; Thompson, Paul M
2013-07-01
Many methods have been proposed for computer-assisted diagnostic classification. Full tensor information and machine learning with 3D maps derived from brain images may help detect subtle differences or classify subjects into different groups. Here we develop a new approach to apply tensor-based morphometry to parametric surface models for diagnostic classification. We use this approach to identify cortical surface features for use in diagnostic classifiers. First, with holomorphic 1-forms, we compute an efficient and accurate conformal mapping from a multiply connected mesh to the so-called slit domain. Next, the surface parameterization approach provides a natural way to register anatomical surfaces across subjects using a constrained harmonic map. To analyze anatomical differences, we then analyze the full Riemannian surface metric tensors, which retain multivariate information on local surface geometry. As the number of voxels in a 3D image is large, sparse learning is a promising method to select a subset of imaging features and to improve classification accuracy. Focusing on vertices with greatest effect sizes, we train a diagnostic classifier using the surface features selected by an L1-norm based sparse learning method. Stability selection is applied to validate the selected feature sets. We tested the algorithm on MRI-derived cortical surfaces from 42 subjects with genetically confirmed Williams syndrome and 40 age-matched controls, multivariate statistics on the local tensors gave greater effect sizes for detecting group differences relative to other TBM-based statistics including analysis of the Jacobian determinant and the largest eigenvalue of the surface metric. Our method also gave reasonable classification results relative to the Jacobian determinant, the pair of eigenvalues of the Jacobian matrix and volume features. This analysis pipeline may boost the power of morphometry studies, and may assist with image-based classification. Copyright © 2013
Characterization of short white matter fiber bundles in the central area from diffusion tensor MRI
Energy Technology Data Exchange (ETDEWEB)
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.)
Can musical training influence brain connectivity? Evidence from diffusion tensor MRI.
Moore, Emma; Schaefer, Rebecca S; Bastin, Mark E; Roberts, Neil; Overy, Katie
2014-06-10
In recent years, musicians have been increasingly recruited to investigate grey and white matter neuroplasticity induced by skill acquisition. The development of Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) has allowed more detailed investigation of white matter connections within the brain, addressing questions about the effect of musical training on connectivity between specific brain regions. Here, current DT-MRI analysis techniques are discussed and the available evidence from DT-MRI studies into differences in white matter architecture between musicians and non-musicians is reviewed. Collectively, the existing literature tends to support the hypothesis that musical training can induce changes in cross-hemispheric connections, with significant differences frequently reported in various regions of the corpus callosum of musicians compared with non-musicians. However, differences found in intra-hemispheric fibres have not always been replicated, while findings regarding the internal capsule and corticospinal tracts appear to be contradictory. There is also recent evidence to suggest that variances in white matter structure in non-musicians may correlate with their ability to learn musical skills, offering an alternative explanation for the structural differences observed between musicians and non-musicians. Considering the inconsistencies in the current literature, possible reasons for conflicting results are offered, along with suggestions for future research in this area.
Effect of cocaine on structural changes in brain: MRI volumetry using tensor-based morphometry.
Narayana, Ponnada A; Datta, Sushmita; Tao, Guozhi; Steinberg, Joel L; Moeller, F Gerard
2010-10-01
Magnetic resonance imaging (MRI) was performed in cocaine-dependent subjects to determine the structural changes in brain compared to non-drug using controls. Cocaine-dependent subjects and controls were carefully screened to rule out brain pathology of undetermined origin. Magnetic resonance images were analyzed using tensor-based morphometry (TBM) and voxel-based morphometry (VBM) without and with modulation to adjust for volume changes during normalization. For TBM analysis, unbiased atlases were generated using two different inverse consistent and diffeomorphic nonlinear registration techniques. Two different control groups were used for generating unbiased atlases. Independent of the nonlinear registration technique and normal cohorts used for creating the unbiased atlases, our analysis failed to detect any statistically significant effect of cocaine on brain volumes. These results show that cocaine-dependent subjects do not show differences in regional brain volumes compared to non-drug using controls. Copyright © 2010 Elsevier Ireland Ltd. All rights reserved.
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Sreedharan, Ruma Madhu; Menon, Amitha C.; Thomas, Sanjeev V.; James, Jija S.; Kesavadas, Chandrasekharan
2015-01-01
Language lateralization is unique to humans. Functional MRI (fMRI) and diffusion tensor imaging (DTI) enable the study of language areas and white matter fibers involved in language, respectively. The objective of this study was to correlate arcuate fasciculus (AF) laterality by diffusion tensor imaging with that by fMRI in preadolescent children which has not yet been reported. Ten children between 8 and 12 years were subjected to fMRI and DTI imaging using Siemens 1.5 T MRI. Two language fMRI paradigms - visual verb generation and word pair task - were used. Analysis was done using SPM8 software. In DTI, the fiber volume of the arcuate fasciculus (AFV) and fractional anisotropy (FA) was measured. The fMRI Laterality Index (fMRI-LI) and DTI Laterality Index (DTI-LI) were calculated and their correlation assessed using the Pearson Correlation Index. Of ten children, mean age 10.6 years, eight showed left lateralization while bilateral language lateralization was seen in two. AFV by DTI was more on the left side in seven of the eight children who had left lateralization by fMRI. DTI could not trace the AF in one child. Of the two with bilateral language lateralization on fMRI, one showed larger AFV on the right side while the other did not show any asymmetry. There was a significant correlation (p < 0.02) between fMRI-LI and DTI-LI. Group mean of AFV by DTI was higher on the left side (2659.89 ± 654.75 mm 3 ) as compared to the right (1824.11 ± 582.81 mm 3 ) (p < 0.01). Like fMRI, DTI also reveals language laterality in children with a high degree of correlation between the two imaging modalities. (orig.)
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Sreedharan, Ruma Madhu [Government Medical College Hospital, Department of Radiology, Trivandrum, Kerala (India); Menon, Amitha C.; Thomas, Sanjeev V. [Sree Chitra, Thirunal Institute for Medical Sciences and Technology, Department of Neurology, Thiruvananthapuram, Kerala (India); James, Jija S.; Kesavadas, Chandrasekharan [SCTIMST, Department of Imaging Science and Interventional Radiology, Trivandrum, Kerala (India)
2015-03-01
Language lateralization is unique to humans. Functional MRI (fMRI) and diffusion tensor imaging (DTI) enable the study of language areas and white matter fibers involved in language, respectively. The objective of this study was to correlate arcuate fasciculus (AF) laterality by diffusion tensor imaging with that by fMRI in preadolescent children which has not yet been reported. Ten children between 8 and 12 years were subjected to fMRI and DTI imaging using Siemens 1.5 T MRI. Two language fMRI paradigms - visual verb generation and word pair task - were used. Analysis was done using SPM8 software. In DTI, the fiber volume of the arcuate fasciculus (AFV) and fractional anisotropy (FA) was measured. The fMRI Laterality Index (fMRI-LI) and DTI Laterality Index (DTI-LI) were calculated and their correlation assessed using the Pearson Correlation Index. Of ten children, mean age 10.6 years, eight showed left lateralization while bilateral language lateralization was seen in two. AFV by DTI was more on the left side in seven of the eight children who had left lateralization by fMRI. DTI could not trace the AF in one child. Of the two with bilateral language lateralization on fMRI, one showed larger AFV on the right side while the other did not show any asymmetry. There was a significant correlation (p < 0.02) between fMRI-LI and DTI-LI. Group mean of AFV by DTI was higher on the left side (2659.89 ± 654.75 mm{sup 3}) as compared to the right (1824.11 ± 582.81 mm{sup 3}) (p < 0.01). Like fMRI, DTI also reveals language laterality in children with a high degree of correlation between the two imaging modalities. (orig.)
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Reinges, Marcus H.T.; Schoth, Felix; Coenen, Volker A.; Krings, Timo
2004-01-01
Diffusion weighted MRI offers the possibility to study the course of the cerebral white matter tracts. In the present manuscript, the basics, the technique and the limitations of diffusion tensor imaging and anisotropic diffusion weighted MRI are presented and their applications in various neurological and neurosurgical diseases are discussed with special emphasis on the visual system. A special focus is laid on the combination of fiber tract imaging, anatomical imaging and functional MRI for presurgical planning and intraoperative neuronavigation of lesions near the visual system
Short-term evolution of spinal cord damage in multiple sclerosis: a diffusion tensor MRI study
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Theaudin, M.; Denier, C.; Adams, D. [AP-HP, CHU Bicetre, Service de Neurologie Adultes, Le Kremlin-Bicetre (France); INSERM, UMR788, Faculte de Medecine Paris Sud, Le Kremlin-Bicetre (France); Saliou, G. [AP-HP, CHU Bicetre, Service de Neuroradiologie, Le Kremlin-Bicetre (France); Ducot, B. [INSERM, U1018, CESP Centre for Research in Epidemiology and Population Health, Faculte de Medecine Paris Sud, Le Kremlin-Bicetre (France); Deiva, K. [Service de Neuropediatrie, Le Kremlin-Bicetre (France); Ducreux, D. [INSERM, UMR788, Faculte de Medecine Paris Sud, Le Kremlin-Bicetre (France); AP-HP, CHU Bicetre, Service de Neuroradiologie, Le Kremlin-Bicetre (France)
2012-10-15
The potential of diffusion tensor imaging (DTI) to detect spinal cord abnormalities in patients with multiple sclerosis has already been demonstrated. The objective of this study was to apply DTI techniques to multiple sclerosis patients with a recently diagnosed spinal cord lesion, in order to demonstrate a correlation between variations of DTI parameters and clinical outcome, and to try to identify DTI parameters predictive of outcome. A prospective single-centre study of patients with spinal cord relapse treated by intravenous steroid therapy was made. Patients were assessed clinically and by conventional MRI with DTI sequences at baseline and at 3 months. Sixteen patients were recruited. At 3 months, 12 patients were clinically improved. All but one patient had lower fractional anisotropy (FA) and apparent diffusion coefficient (ADC) values than normal subjects in either inflammatory lesions or normal-appearing spinal cord. Patients who improved at 3 months presented a significant reduction in the radial diffusivity (p = 0.05) in lesions during the follow-up period. They also had a significant reduction in the mean ADC (p = 0.002), axial diffusivity (p = 0.02), radial diffusivity (p = 0.02) and a significant increase in FA values (p = 0.02) in normal-appearing spinal cord. Patients in whom the American Spinal Injury Association sensory score improved at 3 months showed a significantly higher FA (p = 0.009) and lower radial diffusivity (p = 0.04) in inflammatory lesion at baseline compared to patients with no improvement. DTI MRI detects more extensive abnormalities than conventional T2 MRI. A less marked decrease in FA value and more marked decreased in radial diffusivity inside the inflammatory lesion were associated with better outcome. (orig.)
Short-term evolution of spinal cord damage in multiple sclerosis: a diffusion tensor MRI study
International Nuclear Information System (INIS)
Theaudin, M.; Denier, C.; Adams, D.; Saliou, G.; Ducot, B.; Deiva, K.; Ducreux, D.
2012-01-01
The potential of diffusion tensor imaging (DTI) to detect spinal cord abnormalities in patients with multiple sclerosis has already been demonstrated. The objective of this study was to apply DTI techniques to multiple sclerosis patients with a recently diagnosed spinal cord lesion, in order to demonstrate a correlation between variations of DTI parameters and clinical outcome, and to try to identify DTI parameters predictive of outcome. A prospective single-centre study of patients with spinal cord relapse treated by intravenous steroid therapy was made. Patients were assessed clinically and by conventional MRI with DTI sequences at baseline and at 3 months. Sixteen patients were recruited. At 3 months, 12 patients were clinically improved. All but one patient had lower fractional anisotropy (FA) and apparent diffusion coefficient (ADC) values than normal subjects in either inflammatory lesions or normal-appearing spinal cord. Patients who improved at 3 months presented a significant reduction in the radial diffusivity (p = 0.05) in lesions during the follow-up period. They also had a significant reduction in the mean ADC (p = 0.002), axial diffusivity (p = 0.02), radial diffusivity (p = 0.02) and a significant increase in FA values (p = 0.02) in normal-appearing spinal cord. Patients in whom the American Spinal Injury Association sensory score improved at 3 months showed a significantly higher FA (p = 0.009) and lower radial diffusivity (p = 0.04) in inflammatory lesion at baseline compared to patients with no improvement. DTI MRI detects more extensive abnormalities than conventional T2 MRI. A less marked decrease in FA value and more marked decreased in radial diffusivity inside the inflammatory lesion were associated with better outcome. (orig.)
Longitudinal stability of MRI for mapping brain change using tensor-based morphometry
Leow, Alex D.; Klunder, Andrea D.; Jack, Clifford R.; Toga, Arthur W.; Dale, Anders M.; Bernstein, Matt A.; Britson, Paula J.; Gunter, Jeffrey L.; Ward, Chadwick P.; Whitwell, Jennifer L.; Borowski, Bret J.; Fleisher, Adam S.; Fox, Nick C.; Harvey, Danielle; Kornak, John; Schuff, Norbert; Studholme, Colin; Alexander, Gene E.; Weiner, Michael W.; Thompson, Paul M.
2007-01-01
Measures of brain change can be computed from sequential MRI scans, providing valuable information on disease progression, e.g., for patient monitoring and drug trials. Tensor-based morphometry (TBM) creates maps of these brain changes, visualizing the 3D profile and rates of tissue growth or atrophy, but its sensitivity depends on the contrast and geometric stability of the images. A s part of the Alzheimer’s Disease Neuroimaging Initiative (ADNI), 17 normal elderly subjects were scanned twice (at a 2-week interval) with several 3D 1.5 T MRI pulse sequences: high and low flip angle SPGR/FLASH (from which Synthetic T1 images were generated), MP-RAGE, IR-SPGR (N = 10) and MEDIC (N = 7) scans. For each subject and scan type, a 3D deformation map aligned baseline and follow-up scans, computed with a nonlinear, inverse-consistent elastic registration algorithm. Voxelwise statistics, in ICBM stereotaxic space, visualized the profile of mean absolute change and its cross-subject variance; these maps were then compared using permutation testing. Image stability depended on: (1) the pulse sequence; (2) the transmit/receive coil type (birdcage versus phased array); (3) spatial distortion corrections (using MEDIC sequence information); (4) B1-field intensity inhomogeneity correction (using N3). SPGR/FLASH images acquired using a birdcage coil had least overall deviation. N3 correction reduced coil type and pulse sequence differences and improved scan reproducibility, except for Synthetic T1 images (which were intrinsically corrected for B1-inhomogeneity). No strong evidence favored B0 correction. Although SPGR/FLASH images showed least deviation here, pulse sequence selection for the ADNI project was based on multiple additional image analyses, to be reported elsewhere. PMID:16480900
Accurate measurement of brain changes in longitudinal MRI scans using tensor-based morphometry.
Hua, Xue; Gutman, Boris; Boyle, Christina P; Rajagopalan, Priya; Leow, Alex D; Yanovsky, Igor; Kumar, Anand R; Toga, Arthur W; Jack, Clifford R; Schuff, Norbert; Alexander, Gene E; Chen, Kewei; Reiman, Eric M; Weiner, Michael W; Thompson, Paul M
2011-07-01
This paper responds to Thompson and Holland (2011), who challenged our tensor-based morphometry (TBM) method for estimating rates of brain changes in serial MRI from 431 subjects scanned every 6 months, for 2 years. Thompson and Holland noted an unexplained jump in our atrophy rate estimates: an offset between 0 and 6 months that may bias clinical trial power calculations. We identified why this jump occurs and propose a solution. By enforcing inverse-consistency in our TBM method, the offset dropped from 1.4% to 0.28%, giving plausible anatomical trajectories. Transitivity error accounted for the minimal remaining offset. Drug trial sample size estimates with the revised TBM-derived metrics are highly competitive with other methods, though higher than previously reported sample size estimates by a factor of 1.6 to 2.4. Importantly, estimates are far below those given in the critique. To demonstrate a 25% slowing of atrophic rates with 80% power, 62 AD and 129 MCI subjects would be required for a 2-year trial, and 91 AD and 192 MCI subjects for a 1-year trial. Copyright © 2011 Elsevier Inc. All rights reserved.
Potential of diffusion tensor MRI in the assessment of periventricular leukomalacia
International Nuclear Information System (INIS)
Fan, G.G.; Yu, B.; Quan, S.M.; Sun, B.H.; Guo, Q.Y.
2006-01-01
AIM: To investigate magnetic resonance (MR) diffusion tensor imaging (DTI) and fibre tractography in the assessment of altered major white matter (WM) fibre tracts in periventricular leukomalacia (PVL). MATERIALS AND METHODS: Twelve children (male:female=7:5, age range 3-10 years; mean age=6.5 years) who had suffered PVL were included in this study. Meanwhile, Twelve age-matched normal controls (male:female=6:6, age range 4-12 years; mean age=7.3 years) with normal MRI findings and no neurological abnormalities were recruited for comparison. DTI was performed with 15 different diffusion gradient directions and DTI colour maps were created from fractional anisotropy (FA) values and the three vector elements. To identify alteration of WM fibre tracts in patient of PVL quantitatively, FA values on diffusion tensor colour maps were compared between the patients and controls. Quantitative analysis was performed using the regions of interest (ROI) method settled on the central part of all identifiable WM fibres, including the corticospinal tract (CST) in the brainstem, middle cerebellar peduncle (MCP), medial lemniscus (ML), anterior/posterior limb of internal capsule (ICAL/ICPL), arcuate fasciculus (AF), posterior thalamic radiation (PTR), genu of corpus callosum (GCC), splenium of corpus callosum (SCC), corona radiata (CR), cingulum (CG), and superior longitudinal fasciculus (SLF). The averaged FA value of each WM fibre was measured and summarized as the mean±standard deviation (SD). All data were analysed by paired Student's t-test. A p-value of less than 0.05 was considered to indicate statistical significance. RESULTS: Visual investigation of WM fibre tracts showed that the ICAL, brainstem CST, ML, MCP, and external capsule (EC) was similar in controls and subjects. However, the ICPL, AF, PTR, CR, CG, SLF and corpus callosum, were all attenuated in size. All 12 cases of PVL showed a significant mean FA reduction in the ICPL, AF, PTR, CR, CG, SLF, SCC, and GCC in
Directory of Open Access Journals (Sweden)
Zoë A. Englander
2015-01-01
Full Text Available Cerebral Palsy (CP refers to a heterogeneous group of permanent but non-progressive movement disorders caused by injury to the developing fetal or infant brain (Bax et al., 2005. Because of its serious long-term consequences, effective interventions that can help improve motor function, independence, and quality of life are critically needed. Our ongoing longitudinal clinical trial to treat children with CP is specifically designed to meet this challenge. To maximize the potential for functional improvement, all children in this trial received autologous cord blood transfusions (with order randomized with a placebo administration over 2 years in conjunction with more standard physical and occupational therapies. As a part of this trial, magnetic resonance imaging (MRI is used to improve our understanding of how these interventions affect brain development, and to develop biomarkers of treatment efficacy. In this report, diffusion tensor imaging (DTI and subsequent brain connectome analyses were performed in a subset of children enrolled in the clinical trial (n = 17, who all exhibited positive but varying degrees of functional improvement over the first 2-year period of the study. Strong correlations between increases in white matter (WM connectivity and functional improvement were demonstrated; however no significant relationships between either of these factors with the age of the child at time of enrollment were identified. Thus, our data indicate that increases in brain connectivity reflect improved functional abilities in children with CP. In future work, this potential biomarker can be used to help differentiate the underlying mechanisms of functional improvement, as well as to identify treatments that can best facilitate functional improvement upon un-blinding of the timing of autologous cord blood transfusions at the completion of this study.
Englander, Zoë A; Sun, Jessica; Laura Case; Mikati, Mohamad A; Kurtzberg, Joanne; Song, Allen W
2015-01-01
Cerebral Palsy (CP) refers to a heterogeneous group of permanent but non-progressive movement disorders caused by injury to the developing fetal or infant brain (Bax et al., 2005). Because of its serious long-term consequences, effective interventions that can help improve motor function, independence, and quality of life are critically needed. Our ongoing longitudinal clinical trial to treat children with CP is specifically designed to meet this challenge. To maximize the potential for functional improvement, all children in this trial received autologous cord blood transfusions (with order randomized with a placebo administration over 2 years) in conjunction with more standard physical and occupational therapies. As a part of this trial, magnetic resonance imaging (MRI) is used to improve our understanding of how these interventions affect brain development, and to develop biomarkers of treatment efficacy. In this report, diffusion tensor imaging (DTI) and subsequent brain connectome analyses were performed in a subset of children enrolled in the clinical trial (n = 17), who all exhibited positive but varying degrees of functional improvement over the first 2-year period of the study. Strong correlations between increases in white matter (WM) connectivity and functional improvement were demonstrated; however no significant relationships between either of these factors with the age of the child at time of enrollment were identified. Thus, our data indicate that increases in brain connectivity reflect improved functional abilities in children with CP. In future work, this potential biomarker can be used to help differentiate the underlying mechanisms of functional improvement, as well as to identify treatments that can best facilitate functional improvement upon un-blinding of the timing of autologous cord blood transfusions at the completion of this study.
Lampinen, Björn; Szczepankiewicz, Filip; Mårtensson, Johan; van Westen, Danielle; Sundgren, Pia C; Nilsson, Markus
2017-02-15
In diffusion MRI (dMRI), microscopic diffusion anisotropy can be obscured by orientation dispersion. Separation of these properties is of high importance, since it could allow dMRI to non-invasively probe elongated structures such as neurites (axons and dendrites). However, conventional dMRI, based on single diffusion encoding (SDE), entangles microscopic anisotropy and orientation dispersion with intra-voxel variance in isotropic diffusivity. SDE-based methods for estimating microscopic anisotropy, such as the neurite orientation dispersion and density imaging (NODDI) method, must thus rely on model assumptions to disentangle these features. An alternative approach is to directly quantify microscopic anisotropy by the use of variable shape of the b-tensor. Along those lines, we here present the 'constrained diffusional variance decomposition' (CODIVIDE) method, which jointly analyzes data acquired with diffusion encoding applied in a single direction at a time (linear tensor encoding, LTE) and in all directions (spherical tensor encoding, STE). We then contrast the two approaches by comparing neurite density estimated using NODDI with microscopic anisotropy estimated using CODIVIDE. Data were acquired in healthy volunteers and in glioma patients. NODDI and CODIVIDE differed the most in gray matter and in gliomas, where NODDI detected a neurite fraction higher than expected from the level of microscopic diffusion anisotropy found with CODIVIDE. The discrepancies could be explained by the NODDI tortuosity assumption, which enforces a connection between the neurite density and the mean diffusivity of tissue. Our results suggest that this assumption is invalid, which leads to a NODDI neurite density that is inconsistent between LTE and STE data. Using simulations, we demonstrate that the NODDI assumptions result in parameter bias that precludes the use of NODDI to map neurite density. With CODIVIDE, we found high levels of microscopic anisotropy in white matter
Diffusion tensor MRI and fiber tractography of the sacral plexus in children with spina bifida
DEFF Research Database (Denmark)
Haakma, Wieke; Dik, Pieter; ten Haken, Bennie
2014-01-01
anatomical and microstructural properties of the sacral plexus of patients with spina bifida using diffusion tensor imaging and fiber tractography. MATERIALS AND METHODS: Ten patients 8 to 16 years old with spina bifida underwent diffusion tensor imaging on a 3 Tesla magnetic resonance imaging system...... diffusivity values at S1-S3 were significantly lower in patients. CONCLUSIONS: To our knowledge this 3 Tesla magnetic resonance imaging study showed for the first time sacral plexus asymmetry and disorganization in 10 patients with spina bifida using diffusion tensor imaging and fiber tractography...
International Nuclear Information System (INIS)
Meijer, Frederick J.A.; Rumund, Anouke van; Tuladhar, Anil M.; Aerts, Marjolein B.; Titulaer, Imke; Esselink, Rianne A.J.; Bloem, Bastiaan R.; Verbeek, Marcel M.; Goraj, Bozena
2015-01-01
The aim of this study is to evaluate whether the diagnostic accuracy of 3 T brain MRI is improved by region of interest (ROI) measures of diffusion tensor imaging (DTI), to differentiate between neurodegenerative atypical parkinsonism (AP) and Parkinson's disease (PD) in early stage parkinsonism. We performed a prospective observational cohort study of 60 patients presenting with early stage parkinsonism and initial uncertain diagnosis. At baseline, patients underwent a 3 T brain MRI including DTI. After clinical follow-up (mean 28.3 months), diagnoses could be made in 49 patients (30 PD and 19 AP). Conventional brain MRI was evaluated for regions of atrophy and signal intensity changes. Tract-based spatial statistics and ROI analyses of DTI were performed to analyze group differences in mean diffusivity (MD) and fractional anisotropy (FA), and diagnostic thresholds were determined. Diagnostic accuracy of conventional brain MRI and DTI was assessed with the receiver operating characteristic (ROC). Significantly higher MD of the centrum semiovale, body corpus callosum, putamen, external capsule, midbrain, superior cerebellum, and superior cerebellar peduncles was found in AP. Significantly increased MD of the putamen was found in multiple system atrophy-parkinsonian form (MSA-P) and increased MD in the midbrain and superior cerebellar peduncles in progressive supranuclear palsy (PSP). The diagnostic accuracy of brain MRI to identify AP as a group was not improved by ROI measures of MD, though the diagnostic accuracy to identify MSA-P was slightly increased (AUC 0.82 to 0.85). The diagnostic accuracy of brain MRI to identify AP as a group was not improved by the current analysis approach to DTI, though DTI measures could be of added value to identify AP subgroups. (orig.)
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Meijer, Frederick J.A. [Radboud University Nijmegen Medical Center, Department of Radiology and Nuclear Medicine, Nijmegen (Netherlands); Rumund, Anouke van; Tuladhar, Anil M.; Aerts, Marjolein B.; Titulaer, Imke; Esselink, Rianne A.J.; Bloem, Bastiaan R. [Radboud University Nijmegen Medical Center, Department of Neurology, Donders Institute for Brain, Cognition and Behaviour, Nijmegen (Netherlands); Verbeek, Marcel M. [Radboud University Nijmegen Medical Center, Department of Neurology, Donders Institute for Brain, Cognition and Behaviour, Nijmegen (Netherlands); Radboud University Nijmegen Medical Center, Department of Laboratory Medicine, Nijmegen (Netherlands); Goraj, Bozena [Radboud University Nijmegen Medical Center, Department of Radiology and Nuclear Medicine, Nijmegen (Netherlands); Medical Center of Postgraduate Education, Department of Diagnostic Imaging, Warsaw (Poland)
2015-07-15
The aim of this study is to evaluate whether the diagnostic accuracy of 3 T brain MRI is improved by region of interest (ROI) measures of diffusion tensor imaging (DTI), to differentiate between neurodegenerative atypical parkinsonism (AP) and Parkinson's disease (PD) in early stage parkinsonism. We performed a prospective observational cohort study of 60 patients presenting with early stage parkinsonism and initial uncertain diagnosis. At baseline, patients underwent a 3 T brain MRI including DTI. After clinical follow-up (mean 28.3 months), diagnoses could be made in 49 patients (30 PD and 19 AP). Conventional brain MRI was evaluated for regions of atrophy and signal intensity changes. Tract-based spatial statistics and ROI analyses of DTI were performed to analyze group differences in mean diffusivity (MD) and fractional anisotropy (FA), and diagnostic thresholds were determined. Diagnostic accuracy of conventional brain MRI and DTI was assessed with the receiver operating characteristic (ROC). Significantly higher MD of the centrum semiovale, body corpus callosum, putamen, external capsule, midbrain, superior cerebellum, and superior cerebellar peduncles was found in AP. Significantly increased MD of the putamen was found in multiple system atrophy-parkinsonian form (MSA-P) and increased MD in the midbrain and superior cerebellar peduncles in progressive supranuclear palsy (PSP). The diagnostic accuracy of brain MRI to identify AP as a group was not improved by ROI measures of MD, though the diagnostic accuracy to identify MSA-P was slightly increased (AUC 0.82 to 0.85). The diagnostic accuracy of brain MRI to identify AP as a group was not improved by the current analysis approach to DTI, though DTI measures could be of added value to identify AP subgroups. (orig.)
International Nuclear Information System (INIS)
Montet, Xavier; Mauget, Denis; Sandoz, Alain; Martinoli, Carlo; Bianchi, Stefano
2002-01-01
A 20-year-old white man presented with a localized unilateral swelling in the popliteal fossa. Ultrasound (US) showed the presence of an accessory muscle, the tensor fasciae suralis. The muscle was located in the proximal portion of the popliteal fossa, superficial to the medial head of the gastrocnemius. Its long tendon extended inferiorly to join the Achilles tendon. Magnetic resonance images correlated well with the US findings, confirming the diagnosis. Tensor fasciae suralis muscle is a rare cause of popliteal swelling and must be differentiated from other masses. Both US and magnetic resonance imaging can diagnose it but we suggest US as the first-line technique in its evaluation. (orig.)
Nissan, Noam; Furman-Haran, Edna; Shapiro-Feinberg, Myra; Grobgeld, Dov; Degani, Hadassa
2017-09-01
Lactation and the return to the pre-conception state during post-weaning are regulated by hormonal induced processes that modify the microstructure of the mammary gland, leading to changes in the features of the ductal / glandular tissue, the stroma and the fat tissue. These changes create a challenge in the radiological workup of breast disorder during lactation and early post-weaning. Here we present non-invasive MRI protocols designed to record in vivo high spatial resolution, T 2 -weighted images and diffusion tensor images of the entire mammary gland. Advanced imaging processing tools enabled tracking the changes in the anatomical and microstructural features of the mammary gland from the time of lactation to post-weaning. Specifically, by using diffusion tensor imaging (DTI) it was possible to quantitatively distinguish between the ductal / glandular tissue distention during lactation and the post-weaning involution. The application of the T 2 -weighted imaging and DTI is completely safe, non-invasive and uses intrinsic contrast based on differences in transverse relaxation rates and water diffusion rates in various directions, respectively. This study provides a basis for further in-vivo monitoring of changes during the mammary developmental stages, as well as identifying changes due to malignant transformation in patients with pregnancy associated breast cancer (PABC).
Diffusion tensor imaging in evaluation of posterior fossa tumors in children on a 3T MRI scanner
International Nuclear Information System (INIS)
Assis, Zarina Abdul; Saini, Jitender; Ranjan, Manish; Gupta, Arun Kumar; Sabharwal, Paramveer; Naidu, Purushotham R
2015-01-01
Primary intracranial tumors in children are commonly located in the posterior fossa. Conventional MRI offers limited information regarding the histopathological type of tumor which is essential for better patient management. The purpose of the study was to evaluate the usefulness of advanced MR imaging techniques like diffusion tensor imaging (DTI) in distinguishing the various histopathological types of posterior fossa tumors in children. DTI was performed on a 3T MRI scanner in 34 untreated children found to have posterior fossa lesions. Using third party software, various DTI parameters [apparent diffusion coefficient (ADC), fractional anisotropy (FA), radial diffusivity, planar index, spherical index, and linear index] were calculated for the lesion. Data were subjected to statistical analysis [analysis of variance (ANOVA)] using SPSS 15.0 software. We observed significant correlation (P < 0.01) between ADC mean and maximum, followed by radial diffusivity (RD) with the histopathological types of the lesions. Rest of the DTI parameters did not show any significant correlation in our study. The results of our study support the hypothesis that most cellular tumors and those with greater nuclear area like medulloblastoma would have the lowest ADC values, as compared to less cellular tumors like pilocytic astrocytoma
Muñoz-Ruiz, Miguel Ángel; Hartikainen, Päivi; Koikkalainen, Juha; Wolz, Robin; Julkunen, Valtteri; Niskanen, Eini; Herukka, Sanna-Kaisa; Kivipelto, Miia; Vanninen, Ritva; Rueckert, Daniel; Liu, Yawu; Lötjönen, Jyrki; Soininen, Hilkka
2012-01-01
MRI is an important clinical tool for diagnosing dementia-like diseases such as Frontemporal Dementia (FTD). However there is a need to develop more accurate and standardized MRI analysis methods. To compare FTD with Alzheimer's Disease (AD) and Mild Cognitive Impairment (MCI) with three automatic MRI analysis methods - Hippocampal Volumetry (HV), Tensor-based Morphometry (TBM) and Voxel-based Morphometry (VBM), in specific regions of interest in order to determine the highest classification accuracy. Thirty-seven patients with FTD, 46 patients with AD, 26 control subjects, 16 patients with progressive MCI (PMCI) and 48 patients with stable MCI (SMCI) were examined with HV, TBM for shape change, and VBM for gray matter density. We calculated the Correct Classification Rate (CCR), sensitivity (SS) and specificity (SP) between the study groups. We found unequivocal results differentiating controls from FTD with HV (hippocampus left side) (CCR = 0.83; SS = 0.84; SP = 0.80), with TBM (hippocampus and amygdala (CCR = 0.80/SS = 0.71/SP = 0.94), and with VBM (all the regions studied, especially in lateral ventricle frontal horn, central part and occipital horn) (CCR = 0.87/SS = 0.81/SP = 0.96). VBM achieved the highest accuracy in differentiating AD and FTD (CCR = 0.72/SS = 0.67/SP = 0.76), particularly in lateral ventricle (frontal horn, central part and occipital horn) (CCR = 0.73), whereas TBM in superior frontal gyrus also achieved a high accuracy (CCR = 0.71/SS = 0.68/SP = 0.73). TBM resulted in low accuracy (CCR = 0.62) in the differentiation of AD from FTD using all regions of interest, with similar results for HV (CCR = 0.55). Hippocampal atrophy is present not only in AD but also in FTD. Of the methods used, VBM achieved the highest accuracy in its ability to differentiate between FTD and AD.
Directory of Open Access Journals (Sweden)
Miguel Ángel Muñoz-Ruiz
Full Text Available BACKGROUND: MRI is an important clinical tool for diagnosing dementia-like diseases such as Frontemporal Dementia (FTD. However there is a need to develop more accurate and standardized MRI analysis methods. OBJECTIVE: To compare FTD with Alzheimer's Disease (AD and Mild Cognitive Impairment (MCI with three automatic MRI analysis methods - Hippocampal Volumetry (HV, Tensor-based Morphometry (TBM and Voxel-based Morphometry (VBM, in specific regions of interest in order to determine the highest classification accuracy. METHODS: Thirty-seven patients with FTD, 46 patients with AD, 26 control subjects, 16 patients with progressive MCI (PMCI and 48 patients with stable MCI (SMCI were examined with HV, TBM for shape change, and VBM for gray matter density. We calculated the Correct Classification Rate (CCR, sensitivity (SS and specificity (SP between the study groups. RESULTS: We found unequivocal results differentiating controls from FTD with HV (hippocampus left side (CCR = 0.83; SS = 0.84; SP = 0.80, with TBM (hippocampus and amygdala (CCR = 0.80/SS = 0.71/SP = 0.94, and with VBM (all the regions studied, especially in lateral ventricle frontal horn, central part and occipital horn (CCR = 0.87/SS = 0.81/SP = 0.96. VBM achieved the highest accuracy in differentiating AD and FTD (CCR = 0.72/SS = 0.67/SP = 0.76, particularly in lateral ventricle (frontal horn, central part and occipital horn (CCR = 0.73, whereas TBM in superior frontal gyrus also achieved a high accuracy (CCR = 0.71/SS = 0.68/SP = 0.73. TBM resulted in low accuracy (CCR = 0.62 in the differentiation of AD from FTD using all regions of interest, with similar results for HV (CCR = 0.55. CONCLUSION: Hippocampal atrophy is present not only in AD but also in FTD. Of the methods used, VBM achieved the highest accuracy in its ability to differentiate between FTD and AD.
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Yang, Young-Mi; Oh, Jae-Keun; Song, Ji-Sun [Hallym University Sacred Heart Hospital, College of Medicine, Hallym University, Spine Center, Anyang-si, Gyeonggi-do (Korea, Republic of); Yoo, Woo-Kyoung [Hallym University Sacred Heart Hospital, College of Medicine, Hallym University, Department of Physical Medicine and Rehabilitation, Anyang-si (Korea, Republic of); Hallym University Sacred Heart Hospital, College of Medicine, Hallym University, Hallym Institute for Translational Genomics and Bioinformatics, Anyang-si (Korea, Republic of); Yoo, Je Hyun; Kwak, Yoon Hae [Hallym University Sacred Heart Hospital, College of Medicine, Hallym University, Department of Orthopaedic surgery, Anyang-si (Korea, Republic of); Kim, Seok Woo [Hallym University Sacred Heart Hospital, College of Medicine, Hallym University, Spine Center, Anyang-si, Gyeonggi-do (Korea, Republic of); Hallym University Sacred Heart Hospital, College of Medicine, Hallym University, Department of Orthopaedic surgery, Anyang-si (Korea, Republic of)
2017-11-15
To determine the functional relevance of diffusion tensor imaging (DTI) metrics and conventional MRI (signal intensity change in T2, compression ratio) by measuring the correlation of these parameters with clinical outcome measured by the modified Japanese Orthopedic Association (mJOA) score. A total of 20 cervical myelopathy (CM) patients participated in this prospective cohort study. The severities of CM were assessed using the mJOA score. Conventional MRIs (T2-weighted images) measuring the signal changes of spinal cords and the degree of compression at the lesion level and DTI metrics [fractional anisotropy (FA), apparent diffusion coefficient (ADC)] at each lesion and below each lesion (C7/T1) level were acquired using a 3-T Achieva MRI. These parameters were correlated with the mJOA scores to determine the functional relevance. Ninety percent of CM patients showed signal changes and 30 % of patients noted a more than 40% canal compression ratio in conventional MRIs at the lesion level; however, these findings were not correlated with the mJOA score (p < 0.05). In contrast, FA values on DTI showed high sensitivity to CM (100%), which was well correlated with the mJOA score (p = 0.034, r = 0.475) below the lesion level (C7/T1). This study showed a meaningful symptomatic correlation between mJOA scores and FA values below the lesion levels in CM patients. It could give us more understanding of the pathological changes in spinal cords matched with various clinical findings in CM patients than the results from conventional MRI. (orig.)
Rose, Jessica; Butler, Erin E; Lamont, Lauren E; Barnes, Patrick D; Atlas, Scott W; Stevenson, David K
2009-07-01
The neurological basis of an increased incidence of cerebral palsy (CP) in preterm males is unknown. This study examined neonatal brain structure on magnetic resonance imaging (MRI) and diffusion tensor imaging (DTI) at term-equivalent age, sex, and neurodevelopment at 1 year 6 months on the basis of the Amiel-Tison neurological examination, Gross Motor Function Classification System, and Bayley Scales of Infant Development in 78 very-low-birthweight preterm children (41 males, 37 females; mean gestational age 27.6 wks, SD 2.5; mean birthweight 1021 g, SD 339). Brain abnormalities on MRI and DTI were not different between males and females except in the splenium of the corpus callosum, where males had lower DTI fractional anisotropy (p=0.025) and a higher apparent diffusion coefficient (p=0.013), indicating delayed splenium development. In the 26 infants who were at higher risk on the basis of DTI, males had more abnormalities on MRI (p=0.034) and had lower fractional anisotropy and a higher apparent diffusion coefficient in the splenium (p=0.049; p=0.025) and right posterior limb of the internal capsule (PLIC; p=0.003; p=0.033). Abnormal neurodevelopment was more common in males (n=9) than in females (n=2; p=0.036). Children with abnormal neurodevelopment had more abnormalities on MRI (p=0.014) and reduced splenium and right PLIC fractional anisotropy (p=0.001; p=0.035). In children with abnormal neurodevelopment, right PLIC fractional anisotropy was lower than left (p=0.035), whereas in those with normal neurodevelopment right PLIC fractional anisotropy was higher than left (p=0.001). Right PLIC fractional anisotropy correlated to neurodevelopment (rho=0.371, p=0.002). Logistic regression predicted neurodevelopment with 94% accuracy; only right PLIC fractional anisotropy was a significant logistic coefficient. Results indicate that the higher incidence of abnormal neurodevelopment in preterm males relates to greater incidence and severity of brain abnormalities
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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.
TensorLy: Tensor Learning in Python
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.
Ueda, Ryo; Yamada, Naoki; Kakuda, Wataru; Abo, Masahiro; Senoo, Atsushi
2016-03-15
Fractional anisotropy has been used in many studies that examined post-stroke changes in white matter. This study was performed to clarify cerebral white matter changes after stroke using generalized fractional anisotropy (GFA). White matter structure was visualized using diffusion tensor imaging in 72 patients with post-stroke arm paralysis. Exercise-related brain regions were examined in cerebral white matter using GFA. The relationship between GFA and clinical characteristics was examined. Overall, the mean GFA of the lesioned hemisphere was significantly lower than that of the non-lesioned hemisphere (PBrodmann area 5 of the non-lesioned hemisphere. Age correlated negatively with GFA in Brodmann areas 5 and 7 of the lesioned hemisphere. Though these results may be due to a decrease in the frequency of use of the paralyzed limb over time, GFA overall was significantly and negatively affected by the subject's age. The GFA values of patients with paralysis of the dominant hand were significantly different from those of patients with paralysis of the nondominant hand in Brodmann areas 4 and 6 of the non-lesioned hemisphere and Brodmann area 4 of the lesioned hemisphere (P<0.05). The stroke size and location were not associated with GFA differences. Differences between the GFA of the lesioned and non-lesioned hemispheres varied depending on the affected brain region, age at onset of paralysis, and paralysis of the dominant or non-dominant hand. Copyright © 2016 Elsevier B.V. All rights reserved.
Change-point analysis data of neonatal diffusion tensor MRI in preterm and term-born infants
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Dan Wu
2017-06-01
Full Text Available The data presented in this article are related to the research article entitled “Mapping the Critical Gestational Age at Birth that Alters Brain Development in Preterm-born Infants using Multi-Modal MRI” (Wu et al., 2017 [1]. Brain immaturity at birth poses critical neurological risks in the preterm-born infants. We used a novel change-point model to analyze the critical gestational age at birth (GAB that could affect postnatal development, based on diffusion tensor MRI (DTI acquired from 43 preterm and 43 term-born infants in 126 brain regions. In the corresponding research article, we presented change-point analysis of fractional anisotropy (FA and mean diffusivities (MD measurements in these infants. In this article, we offered the relative changes of axonal and radial diffusivities (AD and RD in relation to the change of FA and FA-based change-points, and we also provided the AD- and RD-based change-point results.
Friese, Uwe; Meindl, Thomas; Herpertz, Sabine C; Reiser, Maximilian F; Hampel, Harald; Teipel, Stefan J
2010-01-01
We report evidence that multivariate analyses of deformation-based morphometry and diffusion tensor imaging (DTI) data can be used to discriminate between healthy participants and patients with Alzheimer's disease (AD) with comparable diagnostic accuracy. In contrast to other studies on MRI-based biomarkers which usually only focus on a single modality, we derived deformation maps from high-dimensional normalization of T1-weighted images, as well as mean diffusivity maps and fractional anisotropy maps from DTI of the same group of 21 patients with AD and 20 healthy controls. Using an automated multivariate analysis of the entire brain volume, widespread decreased white matter integrity and atrophy effects were found in cortical and subcortical regions of AD patients. Mean diffusivity maps and deformation maps were equally effective in discriminating between AD patients and controls (AUC =0.88 vs. AUC=0.85) while fractional anisotropy maps performed slightly inferior. Combining the maps from different modalities in a logistic regression model resulted in a classification accuracy of AUC=0.86 after leave-one-out cross-validation. It remains to be shown if this automated multivariate analysis of DTI-measures can improve early diagnosis of AD in predementia stages.
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.
Test–retest reliability and repeatability of renal diffusion tensor MRI in healthy subjects
International Nuclear Information System (INIS)
Cutajar, Marica; Clayden, Jonathan D.; Clark, Christopher A.; Gordon, Isky
2011-01-01
Purpose: This study assessed test–retest reliability and repeatability of diffusion tensor imaging (DTI) in the kidneys. Materials and methods: Seven healthy volunteers (age range, 19–31 years), were imaged three consecutive times on the same day (short-term reliability) and the same imaging protocol was repeated after a month (long-term reliability). Diffusion-weighted magnetic resonance imaging scans in the coronal-oblique projection of the kidney were acquired on a 1.5 T scanner using a multi-section echo-planar sequence; six contiguous slices each 5 mm thick, diffusion sensitisation along 20 non-collinear directions, TR = 730 ms, TE = 73 ms and 2 b-values (0 and 400 s mm −2 ). Volunteers were asked to hold their breath throughout each data acquisition (approx. 20 s). The apparent diffusion coefficient (ADC) and fractional anisotropy (FA) values were obtained from maps generated using dedicated software MIStar (Apollo Medical Imaging, Melbourne, Australia). Results: Statistical analyses of both short- and long-term repeats were carried out from which the within-subject coefficient of variation (wsCV) was calculated. The wsCV obtained for both the ADC and FA values were less than 10% in all the analyses carried out. In addition, paired (repeated measures) t-test was used to measure the variation between the diffusion parameters collected from the two scanning sessions a month apart. It showed no significant difference and the wsCV obtained after comparing the first and second scans were found to be smaller than 15% for both ADC and FA. Conclusion: Renal DTI produces reliable and repeatable results which make longitudinal investigation of patients viable.
Muñoz-Ruiz, Miguel Ángel; Hartikainen, Päivi; Koikkalainen, Juha; Wolz, Robin; Julkunen, Valtteri; Niskanen, Eini; Herukka, Sanna-Kaisa; Kivipelto, Miia; Vanninen, Ritva; Rueckert, Daniel; Liu, Yawu; Lötjönen, Jyrki; Soininen, Hilkka
2012-01-01
Background MRI is an important clinical tool for diagnosing dementia-like diseases such as Frontemporal Dementia (FTD). However there is a need to develop more accurate and standardized MRI analysis methods. Objective To compare FTD with Alzheimer’s Disease (AD) and Mild Cognitive Impairment (MCI) with three automatic MRI analysis methods - Hippocampal Volumetry (HV), Tensor-based Morphometry (TBM) and Voxel-based Morphometry (VBM), in specific regions of interest in order to determine the highest classification accuracy. Methods Thirty-seven patients with FTD, 46 patients with AD, 26 control subjects, 16 patients with progressive MCI (PMCI) and 48 patients with stable MCI (SMCI) were examined with HV, TBM for shape change, and VBM for gray matter density. We calculated the Correct Classification Rate (CCR), sensitivity (SS) and specificity (SP) between the study groups. Results We found unequivocal results differentiating controls from FTD with HV (hippocampus left side) (CCR = 0.83; SS = 0.84; SP = 0.80), with TBM (hippocampus and amygdala (CCR = 0.80/SS = 0.71/SP = 0.94), and with VBM (all the regions studied, especially in lateral ventricle frontal horn, central part and occipital horn) (CCR = 0.87/SS = 0.81/SP = 0.96). VBM achieved the highest accuracy in differentiating AD and FTD (CCR = 0.72/SS = 0.67/SP = 0.76), particularly in lateral ventricle (frontal horn, central part and occipital horn) (CCR = 0.73), whereas TBM in superior frontal gyrus also achieved a high accuracy (CCR = 0.71/SS = 0.68/SP = 0.73). TBM resulted in low accuracy (CCR = 0.62) in the differentiation of AD from FTD using all regions of interest, with similar results for HV (CCR = 0.55). Conclusion Hippocampal atrophy is present not only in AD but also in FTD. Of the methods used, VBM achieved the highest accuracy in its ability to differentiate between FTD and AD. PMID:23285078
Jang, Sung Ho; You, Sung H; Kwon, Yong-Hyun; Hallett, Mark; Lee, Mi Young; Ahn, Sang Ho
2005-01-01
Recovery mechanisms supporting upper extremity motor recovery following stroke are well established, but cortical mechanism associated with lower extremity motor recovery is unknown. The aim of this study was to assess cortical reorganization associated with lower extremity motor recovery in a hemiparetic patient. Six control subjects and a 17 year-old woman with left intracerebral hemorrhage due to an arterio-venous malformation rupture were evaluated. The motor function of the paretic (left) hip and knee had recovered slowly to the extent of her being able to overcome gravity for 10 months after the onset of stroke. However, her paretic upper extremity showed no significant motor recovery. Blood oxygenation level dependent (BOLD) functional MRI at 1.5 Tesla was used to determine the acutual location of cortical activation in the predefined regions of interest. Concurrently, Diffusion Tensor Imaging (DTI) in combination with a novel 3D-fiber reconstruction algorithm was utilized to investigate the pattern of the corticospinal pathway connectivity between the areas of the motor stream. All subjects' body parts were secured in the scanner and performed a sequential knee flexion-extension with a predetermined angle of 0-60 degrees at 0.5 Hz. Controls showed anticipated activation in the contralateral sensorimotor cortex (SM1) and the descending corticospinal fibers stemming from motor cortex. In contrast to control normal subjects, the stroke patient showed fMRI activation only in the unaffected (right) primary SM1 during either paretic or nonparetic knee movements. DTT fiber tracing data showed that the corticospinal tract fibers were found only in the unaffected hemisphere but not in the affected hemisphere. Our results indicate that an ipsilateral motor pathway from the unaffected (right) motor cortex to the paretic (right) leg was present in this patient. This study raises the potential that the contralesional (ipsilateral) SM1 is involved in cortical
Diffusion tensor MRI of the kidney at 3.0 and 1.5 Tesla
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Kido, Aki; Kataoka, Masako; Yamamoto, Akira (Dept. of Diagnostic Imaging and Nuclear Medicine, Kyoto Univ., Kyoto (Japan)), e-mail: akikido@kuhp.kyoto-u.ac.jp (and others)
2010-11-15
Background: Diffusion tensor imaging (DTI) at 3 T provides information on the microstructure and pathophysiology of tissues that is not available from conventional imaging with an advantage of high signal to noise ratio (SNR). Purpose: To evaluate the feasibility of DTI of the normal kidney at 3.0 T compared to results obtained at 1.5 T. Material and Methods: DTI of the normal kidney of 15 healthy volunteers obtained with 3.0 and 1.5 T scanners using respiration-triggered acquisition was examined. Fractional anisotropy (FA) and apparent diffusion coefficient (ADC) values of both the renal cortex and the medulla and SNRs were measured (b-values 0 and 400 s/mm2, diffusion direction of 6). The image quality of FA and ADC maps was also compared subjectively. Results: The FA values of the renal cortex were 0.15 +- 0.03 at 3.0 T and 0.14+- 0.03 at 1.5 T on average. This difference was not significant. The FA values of the renal medulla were 0.49 +-0.04 at 3.0 T and 0.42 +- 0.05 at 1.5 T. ADC values of the renal cortex were 2.46 x 10-3+- 0.09 mm2/s at 3.0 T and 2.20 x10-3+-0.11 mm2/s at 1.5 T. The ADC values of the renal medulla were 2.08 x 10-3 +- 0.08 mm2/s at 3.0 T and 1.90 x 10-3+- 0.11 mm2/s at 1.5 T. These FA and ADC values were consistent with previous publications. The difference was significant for the FA value of the medulla (P< 0.01) and ADC values in both cortex and medulla (P < 0.01). The subjective image quality of the FA map with the 3.0 T scanner was significantly superior to that with the 1.5 T scanner (P< 0.01), but not significant for the ADC map (P = 0.18). There was a significant difference in SNR between 3.0 T (48.8 +- 6.6) and 1.5 T images (32.8 +- 5.0). Conclusion: The feasibility of renal DTI with a 3.0 T magnet resulting in improved SNR was demonstrated
Preliminary assessment of amyotrophic lateral sclerosis by using MRI and MR diffusion tensor imaging
International Nuclear Information System (INIS)
Ma Lin; Yin Hong; Cai Youquan; Li Dejun; Shen Dingguo
2003-01-01
Objective: To describe the characteristic MR findings in the brain in patients with amyotrophic lateral sclerosis (ALS), and to assess the diagnostic value of conventional MR imaging and fractional anisotropy (FA) of diffusion tensor imaging (DTI). Methods: Conventional MR imaging was performed in 14 clinically proved ALS patients and 12 age-matched normal controls. Contrast enhanced MR images were acquired in 2 patients. Axial and coronal DTI scans were performed in 10 patients and 12 normal controls with SE-EPI sequence. The b value was 1000 s/mm 2 , the number of diffusion sensitive gradient direction was 25. For quantitative assessment of the corticospinal tract (CST), FA value of bilateral CST was measured at the level of posterior limb (PL) of the internal capsule (IC) and the cerebral peduncle of the midbrain, respectively, and statistical analysis was performed. Results: Focal slight low signal intensity on T 1 WI and high signal intensity (hyperintense to gray matter) on T 2 WI was demonstrated in 6 ALS cases (42.9%) in bilateral PL of the IC, and the high signal was longitudinally continuous from the PL to the cerebral peduncle on T 2 WI coronal plane, corresponding to the course of CST. In another 8 ALS cases (57.1%), the focal slight low signal intensity on T 1 WI and slight high signal intensity (isointense to gray matter) on T 2 WI was revealed in bilateral PL of the IC. No abnormal contrast enhancement was detected in the 2 cases. In control group, the focal slight low signal intensity on T 1 WI and slight high signal intensity (isointense to gray matter) on T 2 WI was demonstrated in all 12 subjects in bilateral PL of the IC. FA values of the patient group were significantly lower than that of the control group at the level of the PL of the IC (F=7.38, P<0.01) and the cerebral peduncle (F=7.31, P=0.01), respectively. Conclusion: Clinical information must be considered when diagnosing ALS by using conventional MR imaging. The decreased FA value in
Diffusion tensor MRI of the kidney at 3.0 and 1.5 Tesla
International Nuclear Information System (INIS)
Kido, Aki; Kataoka, Masako; Yamamoto, Akira
2010-01-01
Background: Diffusion tensor imaging (DTI) at 3 T provides information on the microstructure and pathophysiology of tissues that is not available from conventional imaging with an advantage of high signal to noise ratio (SNR). Purpose: To evaluate the feasibility of DTI of the normal kidney at 3.0 T compared to results obtained at 1.5 T. Material and Methods: DTI of the normal kidney of 15 healthy volunteers obtained with 3.0 and 1.5 T scanners using respiration-triggered acquisition was examined. Fractional anisotropy (FA) and apparent diffusion coefficient (ADC) values of both the renal cortex and the medulla and SNRs were measured (b-values 0 and 400 s/mm 2 , diffusion direction of 6). The image quality of FA and ADC maps was also compared subjectively. Results: The FA values of the renal cortex were 0.15 ± 0.03 at 3.0 T and 0.14± 0.03 at 1.5 T on average. This difference was not significant. The FA values of the renal medulla were 0.49 ±0.04 at 3.0 T and 0.42 ± 0.05 at 1.5 T. ADC values of the renal cortex were 2.46 x 10 -3 ± 0.09 mm 2 /s at 3.0 T and 2.20 x10 -3 ±0.11 mm 2 /s at 1.5 T. The ADC values of the renal medulla were 2.08 x 10 -3 ± 0.08 mm 2 /s at 3.0 T and 1.90 x 10 -3 ± 0.11 mm 2 /s at 1.5 T. These FA and ADC values were consistent with previous publications. The difference was significant for the FA value of the medulla (P< 0.01) and ADC values in both cortex and medulla (P < 0.01). The subjective image quality of the FA map with the 3.0 T scanner was significantly superior to that with the 1.5 T scanner (P< 0.01), but not significant for the ADC map (P = 0.18). There was a significant difference in SNR between 3.0 T (48.8 ± 6.6) and 1.5 T images (32.8 ± 5.0). Conclusion: The feasibility of renal DTI with a 3.0 T magnet resulting in improved SNR was demonstrated
Zhang, Lei; Allen, John; Hu, Lingzhi; Caruthers, Shelton D; Wickline, Samuel A; Chen, Junjie
2013-01-15
Cardiomyocyte organization is a critical determinant of coordinated cardiac contractile function. Because of the acute opening of the pulmonary circulation, the relative workload of the left ventricle (LV) and right ventricle (RV) changes substantially immediately after birth. We hypothesized that three-dimensional cardiomyocyte architecture might be required to adapt rapidly to accommodate programmed perinatal changes of cardiac function. Isolated fixed hearts from pig fetuses or pigs at midgestation, preborn, postnatal day 1 (P1), postnatal day 5, postnatal day 14 (P14), and adulthood (n = 5 for each group) were acquired for diffusion-weighted magnetic resonance imaging. Cardiomyocyte architecture was visualized by three-dimensional fiber tracking and was quantitatively evaluated by the measured helix angle (α(h)). Upon the completion of MRI, hearts were sectioned and stained with hematoxylin/eosin (H&E) to evaluate cardiomyocyte alignment, with picrosirius red to evaluate collagen content, and with anti-Ki67 to evaluate postnatal cell proliferation. The helical architecture of cardiomyocyte was observed as early as the midgestational period. Postnatal changes of cardiomyocyte architecture were observed from P1 to P14, which primary occurred in the septum and RV free wall (RVFW). In the septum, the volume ratio of LV- vs. RV-associated cardiomyocytes rapidly changed from RV-LV balanced pattern at birth to LV dominant pattern by P14. In the RVFW, subendocardial α(h) decreased by ~30° from P1 to P14. These findings indicate that the helical architecture of cardiomyocyte is developed as early as the midgestation period. Substantial and rapid adaptive changes in cardiac microarchitecture suggested considerable developmental plasticity of cardiomyocyte form and function in the postnatal period in response to altered cardiac mechanical function.
Ho, April J; Hua, Xue; Lee, Suh; Leow, Alex D; Yanovsky, Igor; Gutman, Boris; Dinov, Ivo D; Leporé, Natasha; Stein, Jason L; Toga, Arthur W; Jack, Clifford R; Bernstein, Matt A; Reiman, Eric M; Harvey, Danielle J; Kornak, John; Schuff, Norbert; Alexander, Gene E; Weiner, Michael W; Thompson, Paul M
2010-04-01
A key question in designing MRI-based clinical trials is how the main magnetic field strength of the scanner affects the power to detect disease effects. In 110 subjects scanned longitudinally at both 3.0 and 1.5 T, including 24 patients with Alzheimer's Disease (AD) [74.8 +/- 9.2 years, MMSE: 22.6 +/- 2.0 at baseline], 51 individuals with mild cognitive impairment (MCI) [74.1 +/- 8.0 years, MMSE: 26.6 +/- 2.0], and 35 controls [75.9 +/- 4.6 years, MMSE: 29.3 +/- 0.8], we assessed whether higher-field MR imaging offers higher or lower power to detect longitudinal changes in the brain, using tensor-based morphometry (TBM) to reveal the location of progressive atrophy. As expected, at both field strengths, progressive atrophy was widespread in AD and more spatially restricted in MCI. Power analysis revealed that, to detect a 25% slowing of atrophy (with 80% power), 37 AD and 108 MCI subjects would be needed at 1.5 T versus 49 AD and 166 MCI subjects at 3 T; however, the increased power at 1.5 T was not statistically significant (alpha = 0.05) either for TBM, or for SIENA, a related method for computing volume loss rates. Analysis of cumulative distribution functions and false discovery rates showed that, at both field strengths, temporal lobe atrophy rates were correlated with interval decline in Alzheimer's Disease Assessment Scale-cognitive subscale (ADAS-cog), mini-mental status exam (MMSE), and Clinical Dementia Rating sum-of-boxes (CDR-SB) scores. Overall, 1.5 and 3 T scans did not significantly differ in their power to detect neurodegenerative changes over a year. Hum Brain Mapp, 2010. (c) 2009 Wiley-Liss, Inc.
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.
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Xiong, Ji [Huashan Hospital of Fudan University, Department of Radiology, Shanghai (China); Huashan Hospital of Fudan University, Department of Neuropathology, Shanghai (China); Tan, Wenli [Shuguang Hospital Affiliated to Shanghai University of Traditional Chinese Medicine, Department of Radiology, Shanghai (China); Wen, Jianbo; Pan, Jiawei; Zhang, Jun; Geng, Daoying [Huashan Hospital of Fudan University, Department of Radiology, Shanghai (China); Wang, Yin [Huashan Hospital of Fudan University, Department of Neuropathology, Shanghai (China)
2016-06-15
To explore the correlations of conventional MRI (cMRI) and diffusion tensor imaging (DTI) values with the 1p/19 codeletion and IDH mutations in oligodendroglial tumours (OTs). Eighty-four patients with OTs who underwent cMRI and DTI were retrospectively reviewed. The maximal fractional anisotropy and minimal apparent diffusion coefficient (ADC) were measured and compared using the Mann-Whitney U test. Receiver operating characteristic curves, logistic regression analysis and four-table statistics analysis were performed to predict genotypings. OTs with 1p/19q codeletion or IDH mutations were prone to locate in frontal (P = 0.106 and 0.005, respectively) and insular lobes and were associated with absent or blurry contrast enhancement (P = 0.040 and 0.013, respectively). DTI values showed significant differences between OTs with and without IDH mutations (P < 0.05) but not in OTs with and without 1p/19q loss. The Ki-67 index significantly correlated with IDH mutations (P = 0.002) but not with 1p/19q codeletion. A combination of DTI and cMRI for the identification of IDH mutations resulted in sensitivity, specificity, positive and negative predictive values of 92.2 %, 75.8 %, 93.8 % and 71.1 %, respectively. Combination of DTI and cMRI correlates with isocitrate dehydrogenase 1/2 mutations but not 1p/19q genotyping in OTs. (orig.)
Rotation, Reflection, and Frame Changes; Orthogonal tensors in computational engineering mechanics
Brannon, R. M.
2018-04-01
Whilst vast literature is available for the most common rotation-related tasks such as coordinate changes, most reference books tend to cover one or two methods, and resources for less-common tasks are scarce. Specialized research applications can be found in disparate journal articles, but a self-contained comprehensive review that covers both elementary and advanced concepts in a manner comprehensible to engineers is rare. Rotation, Reflection, and Frame Changes surveys a refreshingly broad range of rotation-related research that is routinely needed in engineering practice. By illustrating key concepts in computer source code, this book stands out as an unusually accessible guide for engineers and scientists in engineering mechanics.
TensorLy: Tensor Learning in Python
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...
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.
International Nuclear Information System (INIS)
Tanaka, Hideki; Matsuno, Akira; Okubo, Toshiyuki; Nakaguchi, Hiroshi; Murakami, Mineko; Ono, Seiichi; Takeuchi, Masato
2011-01-01
Motor impairment is one of the most frequent symptoms among stroke patients and often leads to post-stroke dependency, so evaluation of motor symptoms and underlining corticospinal tract (CST) damage is of prime importance. Motor impairment, ischemic lesion by diffusion weighted MRI, and clinical outcome were assessed in 15 acute to early subacute corona radiata infarct patients. Motor impairment was graded severe: limb movement synergy level, moderate: selective muscle activity possible and mild: isolated movements are well coordinated. Outcome at the time of discharge was assessed by modified Rankin Scale (mRS). Diffusion tensor MRI (GE Signa Excite system 1.5 T, Echo Planar Imaging, MPG 15) was conducted at 2.3±2.2 days from the onset of the clinical symptoms. CST was delineated 3-dimensionally with dTV.II.SR and Volume-one 1.72. CST-FA (fractional anisotropy) ratio and CST-Area % were calculated at the slice where CST-infarct overlap was maximal. CST-FA ratio and CST-Area % showed good correlation to motor impairment at presentation. Patients with severe motor impairment had lower CST-FA ratio and CSF-Area % than those with moderate or mild. CST-FA ratio was 0.73±0.22 in patients with poor clinical outcome (mRS 3-6) and 0.93±0.09 with good clinical outcome (mRS 0-2) (p=0.038). Diffusion tensor MRI is useful in evaluating ischemic CST damage and predicting functional outcome in patients with corona radiata infarcts in the acute to subacute stage. (author)
Bouzková, Kateřina; Babinský, Martin; Novosadová, Lucie; Marek, Radek
2013-06-11
An understanding of the role of intermolecular interactions in crystal formation is essential to control the generation of diverse crystalline forms which is an important concern for pharmaceutical industry. Very recently, we reported a new approach to interpret the relationships between intermolecular hydrogen bonding, redistribution of electron density in the system, and NMR chemical shifts (Babinský et al. J. Phys. Chem. A, 2013, 117, 497). Here, we employ this approach to characterize a full set of crystal interactions in a sample of anhydrous theobromine as reflected in (13)C NMR chemical shift tensors (CSTs). The important intermolecular contacts are identified by comparing the DFT-calculated NMR CSTs for an isolated theobromine molecule and for clusters composed of several molecules as selected from the available X-ray diffraction data. Furthermore, electron deformation density (EDD) and shielding deformation density (SDD) in the proximity of the nuclei involved in the proposed interactions are calculated and visualized. In addition to the recently reported observations for hydrogen bonding, we focus here particularly on the stacking interactions. Although the principal relations between the EDD and CST for hydrogen bonding (HB) and stacking interactions are similar, the real-space consequences are rather different. Whereas the C-H···X hydrogen bonding influences predominantly and significantly the in-plane principal component of the (13)C CST perpendicular to the HB path and the C═O···H hydrogen bonding modulates both in-plane components of the carbonyl (13)C CST, the stacking modulates the out-of-plane electron density resulting in weak deshielding (2-8 ppm) of both in-plane principal components of the CST and weak shielding (∼ 5 ppm) of the out-of-plane component. The hydrogen-bonding and stacking interactions may add to or subtract from one another to produce total values observed experimentally. On the example of theobromine, we demonstrate
Ponrartana, Skorn; Andrade, Kristine E; Wren, Tishya A L; Ramos-Platt, Leigh; Hu, Houchun H; Bluml, Stefan; Gilsanz, Vicente
2014-06-01
The purpose of this study was to assess the repeatability of water-fat MRI and diffusion-tensor imaging (DTI) as quantitative biomarkers of pediatric lower extremity skeletal muscle. MRI at 3 T of a randomly selected thigh and lower leg of seven healthy children was studied using water-fat separation and DTI techniques. Muscle-fat fraction, apparent diffusion coefficient (ADC), and fractional anisotropy (FA) values were calculated. Test-retest and interrater repeatability were assessed by calculating the Pearson correlation coefficient, intraclass correlation coefficient, and Bland-Altman analysis. Bland-Altman plots show that the mean difference between test-retest and interrater measurements of muscle-fat fraction, ADC, and FA was near 0. The correlation coefficients and intraclass correlation coefficients were all between 0.88 and 0.99 (p DTI measurements in lower extremity skeletal muscles are objective repeatable biomarkers in children. This knowledge should aid in the understanding of the number of participants needed in clinical trials when using these determinations as an outcome measure to noninvasively monitor neuromuscular disease.
Hua, Xue; Leow, Alex D; Parikshak, Neelroop; Lee, Suh; Chiang, Ming-Chang; Toga, Arthur W; Jack, Clifford R; Weiner, Michael W; Thompson, Paul M
2008-11-15
In one of the largest brain MRI studies to date, we used tensor-based morphometry (TBM) to create 3D maps of structural atrophy in 676 subjects with Alzheimer's disease (AD), mild cognitive impairment (MCI), and healthy elderly controls, scanned as part of the Alzheimer's Disease Neuroimaging Initiative (ADNI). Using inverse-consistent 3D non-linear elastic image registration, we warped 676 individual brain MRI volumes to a population mean geometric template. Jacobian determinant maps were created, revealing the 3D profile of local volumetric expansion and compression. We compared the anatomical distribution of atrophy in 165 AD patients (age: 75.6+/-7.6 years), 330 MCI subjects (74.8+/-7.5), and 181 controls (75.9+/-5.1). Brain atrophy in selected regions-of-interest was correlated with clinical measurements--the sum-of-boxes clinical dementia rating (CDR-SB), mini-mental state examination (MMSE), and the logical memory test scores - at voxel level followed by correction for multiple comparisons. Baseline temporal lobe atrophy correlated with current cognitive performance, future cognitive decline, and conversion from MCI to AD over the following year; it predicted future decline even in healthy subjects. Over half of the AD and MCI subjects carried the ApoE4 (apolipoprotein E4) gene, which increases risk for AD; they showed greater hippocampal and temporal lobe deficits than non-carriers. ApoE2 gene carriers--1/6 of the normal group--showed reduced ventricular expansion, suggesting a protective effect. As an automated image analysis technique, TBM reveals 3D correlations between neuroimaging markers, genes, and future clinical changes, and is highly efficient for large-scale MRI studies.
International Nuclear Information System (INIS)
Tanaka, Hideki
2010-01-01
Motor impairment is one of the most frequent symptoms among stroke patients and often leads to poststroke dependency. Recent advances of diffusion tensor MR imaging made it possible to identify corticospinal tract (CST) three-dimensionally and evaluate structural damage, so precise evaluation of the ischemic CST damage became feasible.Motor impairment, lesion size and location upon diffusion weighted MR image and clinical outcome were assessed in 23 acute to subacute capsular and corona radiata infarct patients. According to the lesion size, patients were grouped into A, maximal diameter below 15 mm and B, that above 15 mm. Motor impairment was graded severe: limb movement synergy level, moderate: selective muscle activity possible and mild: isolated movements well co-ordinated, each corresponding to Brunnstrom stage 1-3, 4-5, and 6, respectively. Outcome at the time of discharge was assessed by modified Rankin Scale (mRS), discharge destination and length of hospital stay were also registered. Diffusion tensor MR imaging was conducted in 15 corona radiata infarct patients at 2.3+-2.2 days from the onset of the clinical symptoms. CST was 3-dimensionally identified with dTV. II. SR and Volume-one 1.72 and CST-FA ratio (ipsi-/contralesional CST-FA) and CST-Area% (CST lesion free area/whole CST area) were obtained at the level where ischemic damage was most prominent and correlation of these parameters to motor impairment and clinical outcome was studied. CST-FA ratio and CST-Area% were in good correlation to motor impairment at presentation. Patients with severe motor impairment had lower CST-FA ratio and CSF-Area% than those with moderate or mild. CST-FA ratio was 0.73+-0.22 in patients with poor clinical outcome (mRS 3-6) and 0.93+-0.09 with good clinical outcome (mRS 0-2) (p=0.038). Diffusion tensor MR imaging is useful in evaluating motor impairment and predicting functional outcome of corona radiata infarct patient in the acute to subacute stage. (author)
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Yasmin, Hasina; Abe, Osamu; Nakata, Yasuhiro; Hayashi, Naoto; Masutani, Yoshitaka; Goto, Masami; Ohtomo, Kuni [University of Tokyo, Department of Radiology, Bunkyo-ku, Tokyo (Japan); Aoki, Shigeki [Juntendo University, Department of Radiology, Bunkyo-ku, Tokyo (Japan)
2009-12-15
To date, very scant data is available regarding normal diffusion properties of white matter (WM) fibers. The present study aimed to initiate the establishment of a database of normal diffusion tensor metrics of cerebral WM fibers, including the uncinate fasciculus (UF), posterior cingulum (PC), fornix, and corticospinal tract (CST) for healthy adults using tract-specific analysis by diffusion tensor tractography (DTT). We also attempted to clarify whether age and laterality exerted any effects on this study group. DTT of WM fibers were generated for 100 healthy subjects, then mean diffusivity (MD) and fractional anisotropy (FA) of the tracts were measured. Pearson correlation analysis was used to evaluate age relationships. Paired t testing was used to compare hemispheric asymmetry. Interobserver correlation tests were also performed. Our results showed FA values for UF (right, 0.42 {+-} 0.03; left, 0.40{+-}0.03), PC (0.51 {+-} 0.06, 0.52 {+-} 0.06), fornix (0.37 {+-} 0.06, 0.38 {+-} 0.06), CST (0.70 {+-} 0.06, 0.69 {+-} 0.07), and MD values for UF (0.81 {+-} 0.03, 0.82 {+-} 0.04), PC (0.72 {+-} 0.03, 0.72 {+-} 0.04), fornix (1.86 {+-} 0.32, 1.94 {+-} 0.37), and CST (0.72 {+-} 0.03, 0.74 {+-} 0.04). We identified a significant positive correlation between age and MD in the right UF and bilateral fornices, and a negative correlation between age and FA in bilateral fornices. Hemispheric asymmetry was observed in FA of UF (right > left) and MD of CST (left > right). The results constitute a normative dataset for diffusion parameters of four WM tracts that can be used to identify, characterize, and establish the significance of changes in diseases affecting specific tracts. (orig.)
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Jung, Eun Joo; Ryu, Chun Geun; Kim, Gangmi; Kim, Su Ran; Nam, Sang Eun; Park, Hee Sun; Kim, Young Jun; Hwang, Dae-Yong
2012-01-01
An objective method for determining the location of the cancer with respect to peritoneal reflection would be helpful to decide the treatment modality for rectal cancer. This study was designed to evaluate the accuracy and usefulness of rectal MRI to determine spatial relations between the peritoneal reflection and rectal cancer and to compare these with operative findings. Patients that underwent a rectal cancer operation after a rectal MRI check between November 2008 and June 2010 were considered for the study. The patients that received preoperative concurrent chemoradiation or trans-anal local excision were excluded. Fifty-four patients constituted the study cohort. By comparing surgical and radiologic findings, the accuracy for predicting tumour location in relation to the peritoneal reflection by rectal MRI in all patients was 90.7%. In terms of tumour location in relation to peritoneal reflection, the accuracy of rectal MRI was 93.5% in patients with a tumour located above the peritoneal reflection, 90.0% in patients with a tumour located on the peritoneal reflection, and 84.6% in patients with a tumour located below the peritoneal reflection (p=0.061). When the cohort was subdivided by gender, body mass index (BMI), operative findings, or tumour size, no significant difference was observed among subgroups. Rectal MRI could be a useful tool for evaluating the relation between rectal cancer and peritoneal reflection especially when tumour size is less than 8cm. Rectal MRI can provide information regarding the location of rectal cancer in relation to the peritoneal reflection for treatment planning purposes
Li, Chunmei; Chen, Min; Li, Saying; Zhao, Xuna; Zhang, Chen; Luo, Xiaojie; Zhou, Cheng
2014-03-01
Previous studies have shown that the diagnostic accuracy for prostate cancer improved with diffusion tensor imaging (DTI) or quantitative dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) only. However, the efficacy of combined DTI and quantitative DCE-MRI in detecting prostate cancer at 3.0 T is still indeterminate. To investigate the utility of diffusion tensor imaging (DTI), quantitative DCE-MRI, and the two techniques combined at 3.0 T in detecting prostate cancer of the peripheral zone (PZ). DTI and DCE-MRI of 33 patients was acquired prior to prostate biopsy. Regions of interest (ROIs) were drawn according to biopsy zones which were apex, mid-gland, and base on each side of the PZ. Apparent diffusion coefficient (ADC), fractional anisotropy (FA), volume transfer constant (K(trans)), and rate constant (kep) values of cancerous sextants and non-cancerous sextants in PZ were calculated. Logistic regression models were generated for DTI, DCE-MRI, and DTI + DCE-MRI. Receiver-operating characteristic (ROC) curves were used to compare the ability of these models to differentiate cancerous sextants from non-cancerous sextants of PZ. There were significant differences in the ADC, FA, K(trans), and kep values between cancerous sextants and non-cancerous sextants in PZ (P < 0.0001, P < 0.0001, P < 0.0001, and P < 0.0001, respectively). The area under curve (AUC) for DTI + DCE-MRI was significantly greater than that for either DTI (0.93 vs. 0.86, P = 0.0017) or DCE-MRI (0.93 vs. 0.84, P = 0.0034) alone. The combination of DTI and quantitative DCE-MRI has better diagnostic performance in detecting prostate cancer of the PZ than either technique alone.
U.S. Department of Health & Human Services — The NIH Study of Normal Brain Development is a longitudinal study using anatomical MRI, diffusion tensor imaging (DTI), and MR spectroscopy (MRS) to map pediatric...
Senda, Joe; Kato, Shigenori; Kaga, Tomotsugu; Ito, Mizuki; Atsuta, Naoki; Nakamura, Tomohiko; Watanabe, Hirohisa; Tanaka, Fumiaki; Naganawa, Shinji; Sobue, Gen
2011-01-01
We investigated 17 patients with sporadic amyotrophic lateral sclerosis (ALS) using voxel-based morphometry (VBM) and voxel-based analysis of diffusion tensor images (DTI) at baseline and after a six-month follow-up. Compared with 17 healthy controls, ALS patients at baseline showed only minimal white matter volume decreases in the inferior frontal gyrus but marked decreases in the gray matter of several regions, especially in the bilateral paracentral lobule of the premotor cortex. DTI revealed reduced fractional anisotropy in the bilateral corticospinal tracts, insula, ventrolateral premotor cortex, and parietal cortex. Increased mean diffusivity was noted bilaterally in the motor cortex, ventrolateral premotor cortex, insula, hippocampal formation, and temporal gyrus. At the six-month follow-up, ALS patients showed widespread volume decreases in gray matter, and DTI abnormalities extended mainly into the bilateral frontal lobes, while volume changes in the white matter remained minimal but more distinct. Our combined VBM and DTI techniques revealed extra-corticospinal tract neuronal degeneration mainly in the frontotemporal lobe of ALS patients. In particular, follow-up examinations in these patients showed that whole-brain DTI changes occurred predominantly in the regions of brain atrophy. These objective analyses can be used to assess the disease condition of the ALS brain.
Directory of Open Access Journals (Sweden)
Rishu Rathee
2016-01-01
Full Text Available The aim is to investigate the relationship between microstructural white matter (WM diffusivity indices and macrostructural WM volume (WMV among healthy individuals (20–85 years. Whole-brain diffusion measures were calculated from diffusion tensor imaging using FMRIB software library while WMV was estimated through voxel-based morphometry, and voxel-based analysis was carried out using tract-based spatial statistics. Our results revealed that mean diffusivity, axial diffusivity, and radial diffusivity had shown good correlation with WMV but not for fractional anisotropy (FA. Voxel-wise tract-based spatial statistics analysis for FA showed a significant decrease in four regions for middle-aged group compared to young-aged group, in 22 regions for old-aged group compared to middle-aged group, and in 26 regions for old-aged group compared to young-aged group ( P < 0.05. We found significantly lower WMV, FA, and mean diffusivity values in females than males and inverted-U trend for FA in males. We conclude differential age- and gender-related changes for structural WMV and WM diffusion indices.
Tensor surgery and tensor rank
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
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
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
Airspace Dimension Assessment with nanoparticles reflects lung density as quantified by MRI
Jakobsson, Jonas K; Löndahl, Jakob; Olsson, Lars E; Diaz, Sandra; Zackrisson, Sophia; Wollmer, Per
2018-01-01
Background Airspace Dimension Assessment with inhaled nanoparticles is a novel method to determine distal airway morphology. This is the first empirical study using Airspace Dimension Assessment with nanoparticles (AiDA) to estimate distal airspace radius. The technology is relatively simple and potentially accessible in clinical outpatient settings. Method Nineteen never-smoking volunteers performed nanoparticle inhalation tests at multiple breath-hold times, and the difference in nanoparticle concentration of inhaled and exhaled gas was measured. An exponential decay curve was fitted to the concentration of recovered nanoparticles, and airspace dimensions were assessed from the half-life of the decay. Pulmonary tissue density was measured using magnetic resonance imaging (MRI). Results The distal airspace radius measured by AiDA correlated with lung tissue density as measured by MRI (ρ = −0.584; p = 0.0086). The linear intercept of the logarithm of the exponential decay curve correlated with forced expiratory volume in one second (FEV1) (ρ = 0.549; p = 0.0149). Conclusion The AiDA method shows potential to be developed into a tool to assess conditions involving changes in distal airways, eg, emphysema. The intercept may reflect airway properties; this finding should be further investigated.
Abnormal diffusion-weighted MRI in medulloblastoma: does it reflect small cell histology?
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Kotsenas, A.L.; Roth, T.C.; Manness, W.K.; Faerber, E.N.
1999-01-01
A 12-year-old boy presented with the classic CT and MRI findings of medulloblastoma and the unusual finding of increased signal on diffusion MRI. The small-cell histology of medulloblastoma may account for the increased signal seen on diffusion MRI. Diffusion MRI with echoplanar technique may be useful in evaluation of these tumors and metastatic disease. (orig.)
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
Diffusion tensor image registration using hybrid connectivity and tensor features.
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.
Self-reflection and the psychosis-prone brain: an fMRI study.
Modinos, Gemma; Renken, Remco; Ormel, Johan; Aleman, André
2011-05-01
The Cortical Midline Structures (CMS) play a critical role in self-reflection, together with the insula. Abnormalities in self-referential processing and its neural underpinnings have been reported in schizophrenia and at-risk populations, suggesting they might be markers of psychotic vulnerability. Psychometric measures of schizotypal traits may be used to index psychosis proneness (PP) in nonclinical samples. It remains an unresolved question whether differences in self-reflective processing are associated with PP. Six hundred students completed the Community Assessment of Psychic Experiences Questionnaire, positive subscale. Two groups were formed from the extremes of the distribution (total N = 36). fMRI was used to examine CMS/insula function during a self-reflection task. Participants judged personality trait sentences about self and about an acquaintance. High PP subjects attributed less positive traits to others (i.e., acquaintances) than subjects with low PP. Across groups, the contrasts self > semantic and self > other induced activation in CMS and insula, whereas other > semantic did not produce insula activation. Other > self induced posterior cingulate cortex activation in low PP but not in high PP. In addition, high PP subjects showed stronger activation than low PP in left insula during self > semantic. Examining valence effects revealed that high PP individuals showed increased activation in left insula, right dMPFC, and left vMPFC for positive self-related traits, and in bilateral insula, ACC, and right dMPFC for negative self-related traits. The findings suggest that aspects of self-referential processing and underlying brain mechanisms are similar in clinical and subclinical (high PP) forms of psychosis, suggesting that these may be associated with vulnerability to psychosis.
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
Sigmund, E E; Baete, S H; Luo, T; Patel, K; Wang, D; Rossi, I; Duarte, A; Bruno, M; Mossa, D; Femia, A; Ramachandran, S; Stoffel, D; Babb, J S; Franks, A; Bencardino, J
2018-06-04
Dermatomyositis (DM) is an idiopathic inflammatory myopathy involving severe debilitation in need of diagnostics. We evaluated the proximal lower extremity musculature with diffusion tensor imaging (DTI), intravoxel incoherent motion (IVIM) and dynamic DTI in DM patients and controls and compared with standard clinical workup. METHODS: In this IRB-approved, HIPAA-compliant study with written informed consent, anatomical, Dixon fat/water and diffusion imaging were collected in bilateral thigh MRI of 22 controls and 27 DM patients in a 3T scanner. Compartments were scored on T1/T2 scales. Single voxel dynamic DTI metrics in quadriceps before and after 3-min leg exercise were measured. Spearman rank correlation and mixed model analysis of variance/covariance (ANOVA/ANCOVA) were used to correlate with T1 and T2 scores and to compare patients with controls. DM patients showed significantly lower pseudo-diffusion and volume in quadriceps than controls. All subjects showed significant correlation between T1 score and signal-weighted fat fraction; tissue diffusion and pseudo-diffusion varied significantly with T1 and T2 score in patients. Radial and mean diffusion exercise response in patients was significantly higher than controls. Static and dynamic diffusion imaging metrics show correlation with conventional imaging scores, reveal spatial heterogeneity, and provide means to differentiate dermatomyositis patients from controls. • Diffusion imaging shows regional differences between thigh muscles of dermatomyositis patients and controls. • Signal-weighted fat fraction and diffusion metrics correlate with T1/T2 scores of disease severity. • Dermatomyositis patients show significantly higher radial diffusion exercise response than controls.
3D reconstruction of tensors and vectors
International Nuclear Information System (INIS)
Defrise, Michel; Gullberg, Grant T.
2005-01-01
Here we have developed formulations for the reconstruction of 3D tensor fields from planar (Radon) and line-integral (X-ray) projections of 3D vector and tensor fields. Much of the motivation for this work is the potential application of MRI to perform diffusion tensor tomography. The goal is to develop a theory for the reconstruction of both Radon planar and X-ray or line-integral projections because of the flexibility of MRI to obtain both of these type of projections in 3D. The development presented here for the linear tensor tomography problem provides insight into the structure of the nonlinear MRI diffusion tensor inverse problem. A particular application of tensor imaging in MRI is the potential application of cardiac diffusion tensor tomography for determining in vivo cardiac fiber structure. One difficulty in the cardiac application is the motion of the heart. This presents a need for developing future theory for tensor tomography in a motion field. This means developing a better understanding of the MRI signal for diffusion processes in a deforming media. The techniques developed may allow the application of MRI tensor tomography for the study of structure of fiber tracts in the brain, atherosclerotic plaque, and spine in addition to fiber structure in the heart. However, the relations presented are also applicable to other fields in medical imaging such as diffraction tomography using ultrasound. The mathematics presented can also be extended to exponential Radon transform of tensor fields and to other geometric acquisitions such as cone beam tomography of tensor fields
Shape anisotropy: tensor distance to anisotropy measure
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.
DEFF Research Database (Denmark)
Schroeter, Aileen; Rudin, Markus; Gianolio, Eliana
2017-01-01
This chapter discusses principles of nuclear magnetic resonance (NMR) and MRI followed by a survey on the major classes of MRI contrast agents (CA), their modes of action, and some of the most significative applications. The two more established classes of MRI-CA are represented by paramagnetic...... been attained that markedly increase the number and typology of systems with CEST properties. Currently much attention is also devoted to hyperpolarized molecules that display a sensitivity enhancement sufficient for their direct exploitation for the formation of the MR image. A real breakthrough...
... the room. Pins, hairpins, metal zippers, and similar metallic items can distort the images. Removable dental work ... an MRI can cause heart pacemakers and other implants not to work as well. The magnets can ...
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
Nketiah, G.; Elschot, M.; Kim, E.; Teruel, J.R.; Scheenen, T.W.J.; Bathen, T.F.; Selnaes, K.M.
2017-01-01
PURPOSE: To evaluate the diagnostic relevance of T2-weighted (T2W) MRI-derived textural features relative to quantitative physiological parameters derived from diffusion-weighted (DW) and dynamic contrast-enhanced (DCE) MRI in Gleason score (GS) 3+4 and 4+3 prostate cancers. MATERIALS AND METHODS:
Nketiah, Gabriel; Elschot, Mattijs; Kim, Eugene; Teruel, Jose R; Scheenen, Tom W; Bathen, Tone F; Selnæs, Kirsten M
2017-07-01
To evaluate the diagnostic relevance of T2-weighted (T2W) MRI-derived textural features relative to quantitative physiological parameters derived from diffusion-weighted (DW) and dynamic contrast-enhanced (DCE) MRI in Gleason score (GS) 3+4 and 4+3 prostate cancers. 3T multiparametric-MRI was performed on 23 prostate cancer patients prior to prostatectomy. Textural features [angular second moment (ASM), contrast, correlation, entropy], apparent diffusion coefficient (ADC), and DCE pharmacokinetic parameters (K trans and V e ) were calculated from index tumours delineated on the T2W, DW, and DCE images, respectively. The association between the textural features and prostatectomy GS and the MRI-derived parameters, and the utility of the parameters in differentiating between GS 3+4 and 4+3 prostate cancers were assessed statistically. ASM and entropy correlated significantly (p textural features correlated insignificantly with K trans and V e . GS 4+3 cancers had significantly lower ASM and higher entropy than 3+4 cancers, but insignificant differences in median ADC, K trans , and V e . The combined texture-MRI parameters yielded higher classification accuracy (91%) than the individual parameter sets. T2W MRI-derived textural features could serve as potential diagnostic markers, sensitive to the pathological differences in prostate cancers. • T2W MRI-derived textural features correlate significantly with Gleason score and ADC. • T2W MRI-derived textural features differentiate Gleason score 3+4 from 4+3 cancers. • T2W image textural features could augment tumour characterization.
Energy Technology Data Exchange (ETDEWEB)
Nketiah, Gabriel; Elschot, Mattijs; Kim, Eugene; Teruel, Jose R. [NTNU, Norwegian University of Science and Technology, Department of Circulation and Medical Imaging, Faculty of Medicine, Trondheim (Norway); Scheenen, Tom W. [Radboud University Medical Center, Department of Radiology and Nuclear Medicine, Nijmegen (Netherlands); Bathen, Tone F.; Selnaes, Kirsten M. [NTNU, Norwegian University of Science and Technology, Department of Circulation and Medical Imaging, Faculty of Medicine, Trondheim (Norway); St. Olavs Hospital, Trondheim University Hospital, Trondheim (Norway)
2017-07-15
To evaluate the diagnostic relevance of T2-weighted (T2W) MRI-derived textural features relative to quantitative physiological parameters derived from diffusion-weighted (DW) and dynamic contrast-enhanced (DCE) MRI in Gleason score (GS) 3+4 and 4+3 prostate cancers. 3T multiparametric-MRI was performed on 23 prostate cancer patients prior to prostatectomy. Textural features [angular second moment (ASM), contrast, correlation, entropy], apparent diffusion coefficient (ADC), and DCE pharmacokinetic parameters (K{sup trans} and V{sub e}) were calculated from index tumours delineated on the T2W, DW, and DCE images, respectively. The association between the textural features and prostatectomy GS and the MRI-derived parameters, and the utility of the parameters in differentiating between GS 3+4 and 4+3 prostate cancers were assessed statistically. ASM and entropy correlated significantly (p < 0.05) with both GS and median ADC. Contrast correlated moderately with median ADC. The textural features correlated insignificantly with K{sup trans} and V{sub e}. GS 4+3 cancers had significantly lower ASM and higher entropy than 3+4 cancers, but insignificant differences in median ADC, K{sup trans}, and V{sub e}. The combined texture-MRI parameters yielded higher classification accuracy (91%) than the individual parameter sets. T2W MRI-derived textural features could serve as potential diagnostic markers, sensitive to the pathological differences in prostate cancers. (orig.)
Meyer, Hans-Jonas; Schob, Stefan; Höhn, Anne Kathrin; Surov, Alexey
2017-12-01
Thyroid cancer represents the most frequent malignancy of the endocrine system with an increasing incidence worldwide. Novel imaging techniques are able to further characterize tumors and even predict histopathology features. Texture analysis is an emergent imaging technique to extract extensive data from an radiology images. The present study was therefore conducted to identify possible associations between texture analysis and histopathology parameters in thyroid cancer. The radiological database was retrospectively reviewed for thyroid carcinoma. Overall, 13 patients (3 females, 23.1%) with a mean age of 61.6 years were identified. The MaZda program was used for texture analysis. The T1-precontrast and T2-weighted images were analyzed and overall 279 texture feature for each sequence was investigated. For every patient cell count, Ki67-index and p53 count were investigated. Several significant correlations between texture features and histopathology were identified. Regarding T1-weighted images, S(0;1)Sum Averg correlated the most with cell count (r=0.82). An inverse correlations with S(5;0)AngScMom, S(5;0)DifVarnc S(5;0), DiffEntrp and GrNonZeros (r=-0.69, -0.66, -0.69 and -0.63, respectively) was also identified. For T2-weighted images, Variance with r=0.63 was the highest coefficient, WavEnLL_S3 correlated inversely with cell count (r=-0.57). WavEnLL_S2 derived from T1-weighted images was the highest coefficient r=-0.80, S(0;5)SumVarnc was positively with r=0.74. Regarding T2-weighted images WavEnHL_s-1 was inverse correlated with Ki67 index (r=-0.77). S(1;0)Correlat was with r=0.75 the best correlation with Ki67 index. For T1-weighed images S(5;0)SumofSqs was the best with r=0.65 with p53 count. For T2-weighted images S(1;-1)SumEntrp was the inverse correlation with r=-0.72, whereas S(0;4)AngScMom correlated positively with r=0.63. MRI texture analysis derived from conventional sequences reflects histopathology features in thyroid cancer. This technique
Clerx, L.; Visser, P.J.; Verhey, F.; Aalten, P.
2012-01-01
The aim of the present study is to evaluate the diagnostic value of diffusion tensor imaging (DTI) for early Alzheimer's disease (AD) in comparison to widely accepted medial temporal lobe (MTL) atrophy measurements. A systematic literature research was performed into DTI and MTL atrophy in AD and
Directory of Open Access Journals (Sweden)
Fabio L Urresta
2003-09-01
Full Text Available Since its introduction more than two decades ago, Magnetic Resonance Imaging (MRI has not only allowed for visualization of the macrostructure of the CNS, but also has been able to study dynamic processes which constitute the substrate of currently available MRI variants. While conventional Diffusion Weighted Imaging (DWI permits a robust visualization of lesions just a few minutes after the onset of cerebral ischemia, Diffusion Tensor Imaging (DTI measures the magnitude and direction of diffusion, leading to the characterization of cerebral white matter (WM microstructural integrity. In this paper, the potential role of MRI techniques, particularly DTI, for the study of the relationship between changes in the microstructural integrity of WM and cognitive impairment in the context of cerebrovascular disease are discussed. Significant correlations between scores of behavioral measures of cognitive function and regional anisotropy values are an example of the potential efficacy of DTI for in vivo studies of brain connectivity in vascular neurodegenerative conditions.Desde a sua introdução há mais de duas décadas, as Imagens de Ressonância Magnética (MRI não somente permitiram a visualização da macroestrutura do sistema nervoso central, mas também foram capazes de estudar múltiplos processos dinâmicos, os quais são o substrato para as variantes atuais da técnica. Enquanto que as Imagens de Difusão Ponderada permitem uma robusta visualização de lesões, apenas há minutos de iniciar-se a isquemia cerebral, as Imagens de Tensores de Difusão medem a magnitude e direção da difusão, caracterizando a integridade estrutural da substância branca (WM cerebral. Neste artigo, discute-se a utilidade potencial das técnicas de MRI, particularmente DTI, para o estudo da relação entre mudanças da integridade microestrutural da WM e a deterioração cognitiva, no contexto da doença cerebrovascular. As correlações significativas entre as
Directory of Open Access Journals (Sweden)
Hans-Jonas Meyer
2017-12-01
Full Text Available OBJECT: Thyroid cancer represents the most frequent malignancy of the endocrine system with an increasing incidence worldwide. Novel imaging techniques are able to further characterize tumors and even predict histopathology features. Texture analysis is an emergent imaging technique to extract extensive data from an radiology images. The present study was therefore conducted to identify possible associations between texture analysis and histopathology parameters in thyroid cancer. METHODS: The radiological database was retrospectively reviewed for thyroid carcinoma. Overall, 13 patients (3 females, 23.1% with a mean age of 61.6 years were identified. The MaZda program was used for texture analysis. The T1-precontrast and T2-weighted images were analyzed and overall 279 texture feature for each sequence was investigated. For every patient cell count, Ki67-index and p53 count were investigated. RESULTS: Several significant correlations between texture features and histopathology were identified. Regarding T1-weighted images, S(0;1Sum Averg correlated the most with cell count (r = 0.82. An inverse correlations with S(5;0AngScMom, S(5;0DifVarnc S(5;0, DiffEntrp and GrNonZeros (r = −0.69, −0.66, −0.69 and −0.63, respectively was also identified. For T2-weighted images, Variance with r = 0.63 was the highest coefficient, WavEnLL_S3 correlated inversely with cell count (r = −0.57. WavEnLL_S2 derived from T1-weighted images was the highest coefficient r = −0.80, S(0;5SumVarnc was positively with r = 0.74. Regarding T2-weighted images WavEnHL_s-1 was inverse correlated with Ki67 index (r = −0.77. S(1;0Correlat was with r = 0.75 the best correlation with Ki67 index. For T1-weighed images S(5;0SumofSqs was the best with r = 0.65 with p53 count. For T2-weighted images S(1;−1SumEntrp was the inverse correlation with r = −0.72, whereas S(0;4AngScMom correlated positively with r = 0.63. CONCLUSIONS: MRI texture analysis
A Tensor Statistical Model for Quantifying Dynamic Functional Connectivity.
Zhu, Yingying; Zhu, Xiaofeng; Kim, Minjeong; Yan, Jin; Wu, Guorong
2017-06-01
Functional connectivity (FC) has been widely investigated in many imaging-based neuroscience and clinical studies. Since functional Magnetic Resonance Image (MRI) signal is just an indirect reflection of brain activity, it is difficult to accurately quantify the FC strength only based on signal correlation. To address this limitation, we propose a learning-based tensor model to derive high sensitivity and specificity connectome biomarkers at the individual level from resting-state fMRI images. First, we propose a learning-based approach to estimate the intrinsic functional connectivity. In addition to the low level region-to-region signal correlation, latent module-to-module connection is also estimated and used to provide high level heuristics for measuring connectivity strength. Furthermore, sparsity constraint is employed to automatically remove the spurious connections, thus alleviating the issue of searching for optimal threshold. Second, we integrate our learning-based approach with the sliding-window technique to further reveal the dynamics of functional connectivity. Specifically, we stack the functional connectivity matrix within each sliding window and form a 3D tensor where the third dimension denotes for time. Then we obtain dynamic functional connectivity (dFC) for each individual subject by simultaneously estimating the within-sliding-window functional connectivity and characterizing the across-sliding-window temporal dynamics. Third, in order to enhance the robustness of the connectome patterns extracted from dFC, we extend the individual-based 3D tensors to a population-based 4D tensor (with the fourth dimension stands for the training subjects) and learn the statistics of connectome patterns via 4D tensor analysis. Since our 4D tensor model jointly (1) optimizes dFC for each training subject and (2) captures the principle connectome patterns, our statistical model gains more statistical power of representing new subject than current state
Directory of Open Access Journals (Sweden)
Gopikrishna Deshpande
2017-06-01
Full Text Available A Brain-Computer Interface (BCI is a setup permitting the control of external devices by decoding brain activity. Electroencephalography (EEG has been extensively used for decoding brain activity since it is non-invasive, cheap, portable, and has high temporal resolution to allow real-time operation. Due to its poor spatial specificity, BCIs based on EEG can require extensive training and multiple trials to decode brain activity (consequently slowing down the operation of the BCI. On the other hand, BCIs based on functional magnetic resonance imaging (fMRI are more accurate owing to its superior spatial resolution and sensitivity to underlying neuronal processes which are functionally localized. However, due to its relatively low temporal resolution, high cost, and lack of portability, fMRI is unlikely to be used for routine BCI. We propose a new approach for transferring the capabilities of fMRI to EEG, which includes simultaneous EEG/fMRI sessions for finding a mapping from EEG to fMRI, followed by a BCI run from only EEG data, but driven by fMRI-like features obtained from the mapping identified previously. Our novel data-driven method is likely to discover latent linkages between electrical and hemodynamic signatures of neural activity hitherto unexplored using model-driven methods, and is likely to serve as a template for a novel multi-modal strategy wherein cross-modal EEG-fMRI interactions are exploited for the operation of a unimodal EEG system, leading to a new generation of EEG-based BCIs.
Deshpande, Gopikrishna; Rangaprakash, D; Oeding, Luke; Cichocki, Andrzej; Hu, Xiaoping P
2017-01-01
A Brain-Computer Interface (BCI) is a setup permitting the control of external devices by decoding brain activity. Electroencephalography (EEG) has been extensively used for decoding brain activity since it is non-invasive, cheap, portable, and has high temporal resolution to allow real-time operation. Due to its poor spatial specificity, BCIs based on EEG can require extensive training and multiple trials to decode brain activity (consequently slowing down the operation of the BCI). On the other hand, BCIs based on functional magnetic resonance imaging (fMRI) are more accurate owing to its superior spatial resolution and sensitivity to underlying neuronal processes which are functionally localized. However, due to its relatively low temporal resolution, high cost, and lack of portability, fMRI is unlikely to be used for routine BCI. We propose a new approach for transferring the capabilities of fMRI to EEG, which includes simultaneous EEG/fMRI sessions for finding a mapping from EEG to fMRI, followed by a BCI run from only EEG data, but driven by fMRI-like features obtained from the mapping identified previously. Our novel data-driven method is likely to discover latent linkages between electrical and hemodynamic signatures of neural activity hitherto unexplored using model-driven methods, and is likely to serve as a template for a novel multi-modal strategy wherein cross-modal EEG-fMRI interactions are exploited for the operation of a unimodal EEG system, leading to a new generation of EEG-based BCIs.
Tensor Transpose and Its Properties
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.
Directory of Open Access Journals (Sweden)
Melissa M. Littlefield
2014-03-01
Full Text Available Recent neuroscience initiatives (including the E.U.’s Human Brain Project and the U.S.’s BRAIN Initiative have reinvigorated discussions about the possibilities for transdisciplinary collaboration between the neurosciences, the social sciences, and the humanities. As STS scholars have argued for decades, however, such inter- and transdisciplinary collaborations are potentially fraught with tensions between researchers. This essay build on such claims by arguing that the tensions of transdisciplinary research also exist within researchers’ own experiences of working between disciplines – a phenomenon that we call ‘Disciplinary Double Consciousness’ (DDC. Building on previous work that has characterized similar spaces (and especially on the Critical Neuroscience literature, we argue that ‘neuro-collaborations’ inevitably engage researchers in DDC – a phenomenon that allows us to explore the useful dissonance that researchers can experience when working between a home discipline and a secondary discipline. Our case study is a five-year case study in fMRI lie detection involving a transdisciplinary research team made up of social scientists, a neuroscientist, and a humanist. In addition to theorizing neuro-collaborations from the inside-out, this essay presents practical suggestions for developing transdisciplinary infrastructures that could support future neuro-collaborations.
Arcaro, Michael J; Honey, Christopher J; Mruczek, Ryan EB; Kastner, Sabine; Hasson, Uri
2015-01-01
The human visual system can be divided into over two-dozen distinct areas, each of which contains a topographic map of the visual field. A fundamental question in vision neuroscience is how the visual system integrates information from the environment across different areas. Using neuroimaging, we investigated the spatial pattern of correlated BOLD signal across eight visual areas on data collected during rest conditions and during naturalistic movie viewing. The correlation pattern between areas reflected the underlying receptive field organization with higher correlations between cortical sites containing overlapping representations of visual space. In addition, the correlation pattern reflected the underlying widespread eccentricity organization of visual cortex, in which the highest correlations were observed for cortical sites with iso-eccentricity representations including regions with non-overlapping representations of visual space. This eccentricity-based correlation pattern appears to be part of an intrinsic functional architecture that supports the integration of information across functionally specialized visual areas. DOI: http://dx.doi.org/10.7554/eLife.03952.001 PMID:25695154
The effects of noise over the complete space of diffusion tensor shape.
Gahm, Jin Kyu; Kindlmann, Gordon; Ennis, Daniel B
2014-01-01
Diffusion tensor magnetic resonance imaging (DT-MRI) is a technique used to quantify the microstructural organization of biological tissues. Multiple images are necessary to reconstruct the tensor data and each acquisition is subject to complex thermal noise. As such, measures of tensor invariants, which characterize components of tensor shape, derived from the tensor data will be biased from their true values. Previous work has examined this bias, but over a narrow range of tensor shape. Herein, we define the mathematics for constructing a tensor from tensor invariants, which permits an intuitive and principled means for building tensors with a complete range of tensor shape and salient microstructural properties. Thereafter, we use this development to evaluate by simulation the effects of noise on characterizing tensor shape over the complete space of tensor shape for three encoding schemes with different SNR and gradient directions. We also define a new framework for determining the distribution of the true values of tensor invariants given their measures, which provides guidance about the confidence the observer should have in the measures. Finally, we present the statistics of tensor invariant estimates over the complete space of tensor shape to demonstrate how the noise sensitivity of tensor invariants varies across the space of tensor shape as well as how the imaging protocol impacts measures of tensor invariants. Copyright © 2013 Elsevier B.V. All rights reserved.
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-...
Gurau, Razvan
2017-01-01
Written by the creator of the modern theory of random tensors, this book is the first self-contained introductory text to this rapidly developing theory. Starting from notions familiar to the average researcher or PhD student in mathematical or theoretical physics, the book presents in detail the theory and its applications to physics. The recent detections of the Higgs boson at the LHC and gravitational waves at LIGO mark new milestones in Physics confirming long standing predictions of Quantum Field Theory and General Relativity. These two experimental results only reinforce today the need to find an underlying common framework of the two: the elusive theory of Quantum Gravity. Over the past thirty years, several alternatives have been proposed as theories of Quantum Gravity, chief among them String Theory. While these theories are yet to be tested experimentally, key lessons have already been learned. Whatever the theory of Quantum Gravity may be, it must incorporate random geometry in one form or another....
International Nuclear Information System (INIS)
Lu, Chin-Song; Weng, Yi-Hsin; Lin, Wey-Yil; Ng, Shu-Hang; Cheng, Jur-Shan; Wai, Yau-Yau; Chen, Yao-Liang; Wang, Jiun-Jie
2016-01-01
To investigate the diagnostic performance of diffusion tensor imaging in patients with Parkinson's disease (PD). We examined a total of 126 PD patients (68 males/58 females, mean age: 62.0 ±7.6 years) and 91 healthy controls (43 males/48 females, mean age: 59.8 ±7.2 years). Images were acquired on a 3 Tesla magnetic resonance scanner. The Camino software was used to normalize and parcellate diffusion-weighted images into 90 cerebral regions based on the automatic anatomical labelling template. The minimum, median, and maximum values of the mean/radial/axial diffusivity/fractional anisotropy were determined. The diagnostic performance was assessed by receiver operating characteristic analysis. The associations of imaging parameters with disease severity were tested using Pearson's correlation coefficients after adjustment for disease duration. Compared with healthy controls, PD patients showed increased diffusivity in multiple cortical regions that extended beyond the basal ganglia. An area under curve of 85 % was identified for the maximum values of mean diffusivity in the ipsilateral middle temporal gyrus. The most significant intergroup difference was 26.8 % for the ipsilateral inferior parietal gyrus. The measurement of water diffusion from the parcellated cortex may be clinically useful for the assessment of PD patients. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Lu, Chin-Song; Weng, Yi-Hsin; Lin, Wey-Yil [Chang Gung Memorial Hospital, Division of Movement Disorders,Department of Neurology, Taoyuan (China); Chang Gung Memorial Hospital, Neuroscience Research Center, Taoyuan (China); Chang Gung University, School of Traditional Chinese Medicine, Taoyuan (China); Ng, Shu-Hang [Chang Gung Memorial Hospital, Department of Medical Imaging and Intervention, Linkou (China); Chang Gung University, Department of Medical Imaging and Radiological Sciences, Taoyuan County (China); Cheng, Jur-Shan [Chang Gung University, Clinical Informatics and Medical Statistics Research Center,College of Medicine, Taoyuan (China); Wai, Yau-Yau [Chang Gung Memorial Hospital, Department of Medical Imaging and Intervention, Keelung (China); Chen, Yao-Liang [Chang Gung Memorial Hospital, Department of Medical Imaging and Intervention, Linkou (China); Chang Gung Memorial Hospital, Department of Medical Imaging and Intervention, Keelung (China); Wang, Jiun-Jie [Chang Gung Memorial Hospital, Neuroscience Research Center, Taoyuan (China); Chang Gung Memorial Hospital, Department of Medical Imaging and Intervention, Linkou (China); Chang Gung University, Department of Medical Imaging and Radiological Sciences, Taoyuan County (China); Chang Gung University / Chang Gung Memorial Hospital, Linkou, Medical Imaging Research Center, Institute for Radiological Research, Taoyuan (China)
2016-11-15
To investigate the diagnostic performance of diffusion tensor imaging in patients with Parkinson's disease (PD). We examined a total of 126 PD patients (68 males/58 females, mean age: 62.0 ±7.6 years) and 91 healthy controls (43 males/48 females, mean age: 59.8 ±7.2 years). Images were acquired on a 3 Tesla magnetic resonance scanner. The Camino software was used to normalize and parcellate diffusion-weighted images into 90 cerebral regions based on the automatic anatomical labelling template. The minimum, median, and maximum values of the mean/radial/axial diffusivity/fractional anisotropy were determined. The diagnostic performance was assessed by receiver operating characteristic analysis. The associations of imaging parameters with disease severity were tested using Pearson's correlation coefficients after adjustment for disease duration. Compared with healthy controls, PD patients showed increased diffusivity in multiple cortical regions that extended beyond the basal ganglia. An area under curve of 85 % was identified for the maximum values of mean diffusivity in the ipsilateral middle temporal gyrus. The most significant intergroup difference was 26.8 % for the ipsilateral inferior parietal gyrus. The measurement of water diffusion from the parcellated cortex may be clinically useful for the assessment of PD patients. (orig.)
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...
Tensor rank is not multiplicative under the tensor product
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
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
Schnyer, David M; Clasen, Peter C; Gonzalez, Christopher; Beevers, Christopher G
2017-06-30
Using MRI to diagnose mental disorders has been a long-term goal. Despite this, the vast majority of prior neuroimaging work has been descriptive rather than predictive. The current study applies support vector machine (SVM) learning to MRI measures of brain white matter to classify adults with Major Depressive Disorder (MDD) and healthy controls. In a precisely matched group of individuals with MDD (n =25) and healthy controls (n =25), SVM learning accurately (74%) classified patients and controls across a brain map of white matter fractional anisotropy values (FA). The study revealed three main findings: 1) SVM applied to DTI derived FA maps can accurately classify MDD vs. healthy controls; 2) prediction is strongest when only right hemisphere white matter is examined; and 3) removing FA values from a region identified by univariate contrast as significantly different between MDD and healthy controls does not change the SVM accuracy. These results indicate that SVM learning applied to neuroimaging data can classify the presence versus absence of MDD and that predictive information is distributed across brain networks rather than being highly localized. Finally, MDD group differences revealed through typical univariate contrasts do not necessarily reveal patterns that provide accurate predictive information. Copyright © 2017 Elsevier Ireland Ltd. All rights reserved.
Salo, Raimo A; Miettinen, Tuukka; Laitinen, Teemu; Gröhn, Olli; Sierra, Alejandra
2017-05-15
Imaging markers for monitoring disease progression, recovery, and treatment efficacy are a major unmet need for many neurological diseases, including epilepsy. Recent evidence suggests that diffusion tensor imaging (DTI) provides high microstructural contrast even outside major white matter tracts. We hypothesized that in vivo DTI could detect progressive microstructural changes in the dentate gyrus and the hippocampal CA3bc in the rat brain after status epilepticus (SE). To test this hypothesis, we induced SE with systemic kainic acid or pilocarpine in adult male Wistar rats and subsequently scanned them using in vivo DTI at five time-points: prior to SE, and 10, 20, 34, and 79 days post SE. In order to tie the DTI findings to changes in the tissue microstructure, myelin- and glial fibrillary acidic protein (GFAP)-stained sections from the same animals underwent Fourier analysis. We compared the Fourier analysis parameters, anisotropy index and angle of myelinated axons or astrocyte processes, to corresponding DTI parameters, fractional anisotropy (FA) and the orientation angle of the principal eigenvector. We found progressive detectable changes in DTI parameters in both the dentate gyrus (FA, axial diffusivity [D || ], linear anisotropy [CL] and spherical anisotropy [CS], pFourier analysis revealed that both myelinated axons and astrocyte processes played a role in the water diffusion anisotropy changes detected by DTI in individual portions of the dentate gyrus (suprapyramidal blade, mid-portion, and infrapyramidal blade). In the whole dentate gyrus, myelinated axons markedly contributed to the water diffusion changes. In CA3bc as well as in CA3b and CA3c, both myelinated axons and astrocyte processes contributed to water diffusion anisotropy and orientation. Our study revealed that DTI is a promising method for noninvasive detection of microstructural alterations in the hippocampus proper. These alterations may be potential imaging markers for epileptogenesis
Ulrich, Nils H; Ahmadli, Uzeyir; Woernle, Christoph M; Alzarhani, Yahea A; Bertalanffy, Helmut; Kollias, Spyros S
2014-11-01
With continuous refinement of neurosurgical techniques and higher resolution in neuroimaging, the management of pontine lesions is constantly improving. Among pontine structures with vital functions that are at risk of being damaged by surgical manipulation, cranial nerves (CN) and cranial nerve nuclei (CNN) such as CN V, VI, and VII are critical. Pre-operative localization of the intrapontine course of CN and CNN should be beneficial for surgical outcomes. Our objective was to accurately localize CN and CNN in patients with intra-axial lesions in the pons using diffusion tensor imaging (DTI) and estimate its input in surgical planning for avoiding unintended loss of their function during surgery. DTI of the pons obtained pre-operatively on a 3Tesla MR scanner was analyzed prospectively for the accurate localization of CN and CNN V, VI and VII in seven patients with intra-axial lesions in the pons. Anatomical sections in the pons were used to estimate abnormalities on color-coded fractional anisotropy maps. Imaging abnormalities were correlated with CN symptoms before and after surgery. The course of CN and the area of CNN were identified using DTI pre- and post-operatively. Clinical associations between post-operative improvements and the corresponding CN area of the pons were demonstrated. Our results suggest that pre- and post-operative DTI allows identification of key anatomical structures in the pons and enables estimation of their involvement by pathology. It may predict clinical outcome and help us to better understand the involvement of the intrinsic anatomy by pathological processes. Copyright © 2014 Elsevier Ltd. All rights reserved.
Tensor Based Representation and Analysis of Diffusion-Weighted Magnetic Resonance Images
Barmpoutis, Angelos
2009-01-01
Cartesian tensor bases have been widely used to model spherical functions. In medical imaging, tensors of various orders can approximate the diffusivity function at each voxel of a diffusion-weighted MRI data set. This approximation produces tensor-valued datasets that contain information about the underlying local structure of the scanned tissue.…
Directory of Open Access Journals (Sweden)
Joanne Embree
2001-01-01
Full Text Available Ideally, editorials are written one to two months before publication in the Journal. It was my turn to write this one. I had planned to write the first draft the evening after my clinic on Tuesday, September 11. It didn't get done that night or during the next week. Somehow, the topic that I had originally chosen just didn't seem that important anymore as I, along my friends and colleagues, reflected on the changes that the events of that day were likely to have on our lives.
Tensor rank is not multiplicative under the tensor product
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...
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.
Tensor gauge condition and tensor field decomposition
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 structure for Nori motives
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.
Tensor eigenvalues and their applications
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.
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.
DEFF Research Database (Denmark)
Østergaard, Mikkel; Hansen, M; Stoltenberg, M
1996-01-01
Determination of the synovial membrane volume in the rheumatoid arthritis (RA) wrist by gadolinium-DTPA-enhanced MRI is introduced. Moreover, dynamic imaging and an MRI score of synovial hypertrophy, based on gradings in six regions, are evaluated as substitutes of the time-consuming volume...
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.
Susceptibility tensor imaging (STI) of the brain.
Li, Wei; Liu, Chunlei; Duong, Timothy Q; van Zijl, Peter C M; Li, Xu
2017-04-01
Susceptibility tensor imaging (STI) is a recently developed MRI technique that allows quantitative determination of orientation-independent magnetic susceptibility parameters from the dependence of gradient echo signal phase on the orientation of biological tissues with respect to the main magnetic field. By modeling the magnetic susceptibility of each voxel as a symmetric rank-2 tensor, individual magnetic susceptibility tensor elements as well as the mean magnetic susceptibility and magnetic susceptibility anisotropy can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping to remove such dependence. Similar to diffusion tensor imaging, STI allows mapping of brain white matter fiber orientations and reconstruction of 3D white matter pathways using the principal eigenvectors of the susceptibility tensor. In contrast to diffusion anisotropy, the main determinant factor of the susceptibility anisotropy in brain white matter is myelin. Another unique feature of the susceptibility anisotropy of white matter is its sensitivity to gadolinium-based contrast agents. Mechanistically, MRI-observed susceptibility anisotropy is mainly attributed to the highly ordered lipid molecules in the myelin sheath. STI provides a consistent interpretation of the dependence of phase and susceptibility on orientation at multiple scales. This article reviews the key experimental findings and physical theories that led to the development of STI, its practical implementations, and its applications for brain research. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Susceptibility Tensor Imaging (STI) of the Brain
Li, Wei; Liu, Chunlei; Duong, Timothy Q.; van Zijl, Peter C.M.; Li, Xu
2016-01-01
Susceptibility tensor imaging (STI) is a recently developed MRI technique that allows quantitative determination of orientation-independent magnetic susceptibility parameters from the dependence of gradient echo signal phase on the orientation of biological tissues with respect to the main magnetic field. By modeling the magnetic susceptibility of each voxel as a symmetric rank-2 tensor, individual magnetic susceptibility tensor elements as well as the mean magnetic susceptibility (MMS) and magnetic susceptibility anisotropy (MSA) can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping (QSM) to remove such dependence. Similar to diffusion tensor imaging (DTI), STI allows mapping of brain white matter fiber orientations and reconstruction of 3D white matter pathways using the principal eigenvectors of the susceptibility tensor. In contrast to diffusion anisotropy, the main determinant factor of susceptibility anisotropy in brain white matter is myelin. Another unique feature of susceptibility anisotropy of white matter is its sensitivity to gadolinium-based contrast agents. Mechanistically, MRI-observed susceptibility anisotropy is mainly attributed to the highly ordered lipid molecules in myelin sheath. STI provides a consistent interpretation of the dependence of phase and susceptibility on orientation at multiple scales. This article reviews the key experimental findings and physical theories that led to the development of STI, its practical implementations, and its applications for brain research. PMID:27120169
Clinical functional MRI. Persurgical functional neuroimaging. 2. ed.
International Nuclear Information System (INIS)
Stippich, Christoph
2015-01-01
The second, revised edition of this successful textbook provides an up-to-date description of the use of preoperative fMRI in patients with brain tumors and epilepsies. State of the art fMRI procedures are presented, with detailed consideration of practical aspects, imaging and data processing, normal and pathological findings, and diagnostic possibilities and limitations. Relevant information on brain physiology, functional neuroanatomy, imaging technique, and methodology is provided by recognized experts in these fields. Compared with the first edition, chapters have been updated to reflect the latest developments and in particular the current use of diffusion tensor imaging (DTI) and resting-state fMRI. Entirely new chapters are included on resting-state presurgical fMRI and the role of DTI and tractography in brain tumor surgery. Further chapters address multimodality functional neuroimaging, brain plasticity, and pitfalls, tips, and tricks.
Clinical functional MRI. Persurgical functional neuroimaging. 2. ed.
Energy Technology Data Exchange (ETDEWEB)
Stippich, Christoph (ed.) [Univ. Hospitals Basel (Switzerland). Division of Diagnostic and Inventional Neuroradiology
2015-06-01
The second, revised edition of this successful textbook provides an up-to-date description of the use of preoperative fMRI in patients with brain tumors and epilepsies. State of the art fMRI procedures are presented, with detailed consideration of practical aspects, imaging and data processing, normal and pathological findings, and diagnostic possibilities and limitations. Relevant information on brain physiology, functional neuroanatomy, imaging technique, and methodology is provided by recognized experts in these fields. Compared with the first edition, chapters have been updated to reflect the latest developments and in particular the current use of diffusion tensor imaging (DTI) and resting-state fMRI. Entirely new chapters are included on resting-state presurgical fMRI and the role of DTI and tractography in brain tumor surgery. Further chapters address multimodality functional neuroimaging, brain plasticity, and pitfalls, tips, and tricks.
Diffusion tensor optical coherence tomography
Marks, Daniel L.; Blackmon, Richard L.; Oldenburg, Amy L.
2018-01-01
In situ measurements of diffusive particle transport provide insight into tissue architecture, drug delivery, and cellular function. Analogous to diffusion-tensor magnetic resonance imaging (DT-MRI), where the anisotropic diffusion of water molecules is mapped on the millimeter scale to elucidate the fibrous structure of tissue, here we propose diffusion-tensor optical coherence tomography (DT-OCT) for measuring directional diffusivity and flow of optically scattering particles within tissue. Because DT-OCT is sensitive to the sub-resolution motion of Brownian particles as they are constrained by tissue macromolecules, it has the potential to quantify nanoporous anisotropic tissue structure at micrometer resolution as relevant to extracellular matrices, neurons, and capillaries. Here we derive the principles of DT-OCT, relating the detected optical signal from a minimum of six probe beams with the six unique diffusion tensor and three flow vector components. The optimal geometry of the probe beams is determined given a finite numerical aperture, and a high-speed hardware implementation is proposed. Finally, Monte Carlo simulations are employed to assess the ability of the proposed DT-OCT system to quantify anisotropic diffusion of nanoparticles in a collagen matrix, an extracellular constituent that is known to become highly aligned during tumor development.
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
Tensor estimation for double-pulsed diffusional kurtosis imaging.
Shaw, Calvin B; Hui, Edward S; Helpern, Joseph A; Jensen, Jens H
2017-07-01
Double-pulsed diffusional kurtosis imaging (DP-DKI) represents the double diffusion encoding (DDE) MRI signal in terms of six-dimensional (6D) diffusion and kurtosis tensors. Here a method for estimating these tensors from experimental data is described. A standard numerical algorithm for tensor estimation from conventional (i.e. single diffusion encoding) diffusional kurtosis imaging (DKI) data is generalized to DP-DKI. This algorithm is based on a weighted least squares (WLS) fit of the signal model to the data combined with constraints designed to minimize unphysical parameter estimates. The numerical algorithm then takes the form of a quadratic programming problem. The principal change required to adapt the conventional DKI fitting algorithm to DP-DKI is replacing the three-dimensional diffusion and kurtosis tensors with the 6D tensors needed for DP-DKI. In this way, the 6D diffusion and kurtosis tensors for DP-DKI can be conveniently estimated from DDE data by using constrained WLS, providing a practical means for condensing DDE measurements into well-defined mathematical constructs that may be useful for interpreting and applying DDE MRI. Data from healthy volunteers for brain are used to demonstrate the DP-DKI tensor estimation algorithm. In particular, representative parametric maps of selected tensor-derived rotational invariants are presented. Copyright © 2017 John Wiley & Sons, Ltd.
Anisotropic conductivity tensor imaging in MREIT using directional diffusion rate of water molecules
International Nuclear Information System (INIS)
Kwon, Oh In; Jeong, Woo Chul; Sajib, Saurav Z K; Kim, Hyung Joong; Woo, Eung Je
2014-01-01
Magnetic resonance electrical impedance tomography (MREIT) is an emerging method to visualize electrical conductivity and/or current density images at low frequencies (below 1 KHz). Injecting currents into an imaging object, one component of the induced magnetic flux density is acquired using an MRI scanner for isotropic conductivity image reconstructions. Diffusion tensor MRI (DT-MRI) measures the intrinsic three-dimensional diffusion property of water molecules within a tissue. It characterizes the anisotropic water transport by the effective diffusion tensor. Combining the DT-MRI and MREIT techniques, we propose a novel direct method for absolute conductivity tensor image reconstructions based on a linear relationship between the water diffusion tensor and the electrical conductivity tensor. We first recover the projected current density, which is the best approximation of the internal current density one can obtain from the measured single component of the induced magnetic flux density. This enables us to estimate a scale factor between the diffusion tensor and the conductivity tensor. Combining these values at all pixels with the acquired diffusion tensor map, we can quantitatively recover the anisotropic conductivity tensor map. From numerical simulations and experimental verifications using a biological tissue phantom, we found that the new method overcomes the limitations of each method and successfully reconstructs both the direction and magnitude of the conductivity tensor for both the anisotropic and isotropic regions. (paper)
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.
Diffusion tensor smoothing through weighted Karcher means
Carmichael, Owen; Chen, Jun; Paul, Debashis; Peng, Jie
2014-01-01
Diffusion tensor magnetic resonance imaging (MRI) quantifies the spatial distribution of water Diffusion at each voxel on a regular grid of locations in a biological specimen by Diffusion tensors– 3 × 3 positive definite matrices. Removal of noise from DTI is an important problem due to the high scientific relevance of DTI and relatively low signal to noise ratio it provides. Leading approaches to this problem amount to estimation of weighted Karcher means of Diffusion tensors within spatial neighborhoods, under various metrics imposed on the space of tensors. However, it is unclear how the behavior of these estimators varies with the magnitude of DTI sensor noise (the noise resulting from the thermal e!ects of MRI scanning) as well as the geometric structure of the underlying Diffusion tensor neighborhoods. In this paper, we combine theoretical analysis, empirical analysis of simulated DTI data, and empirical analysis of real DTI scans to compare the noise removal performance of three kernel-based DTI smoothers that are based on Euclidean, log-Euclidean, and affine-invariant metrics. The results suggest, contrary to conventional wisdom, that imposing a simplistic Euclidean metric may in fact provide comparable or superior noise removal, especially in relatively unstructured regions and/or in the presence of moderate to high levels of sensor noise. On the contrary, log-Euclidean and affine-invariant metrics may lead to better noise removal in highly structured anatomical regions, especially when the sensor noise is of low magnitude. These findings emphasize the importance of considering the interplay of sensor noise magnitude and tensor field geometric structure when assessing Diffusion tensor smoothing options. They also point to the necessity for continued development of smoothing methods that perform well across a large range of scenarios. PMID:25419264
Cartesian tensors an introduction
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
Structural connectivity via the tensor-based morphometry
Kim, S.; Chung, M.; Hanson, J.; Avants, B.; Gee, J.; Davidson, R.; Pollak, S.
2011-01-01
The tensor-based morphometry (TBM) has been widely used in characterizing tissue volume difference between populations at voxel level. We present a novel computational framework for investigating the white matter connectivity using TBM. Unlike other diffusion tensor imaging (DTI) based white matter connectivity studies, we do not use DTI but only T1-weighted magnetic resonance imaging (MRI). To construct brain network graphs, we have developed a new data-driven approach called the ε-neighbor ...
Review of diffusion tensor imaging and its application in children
Energy Technology Data Exchange (ETDEWEB)
Vorona, Gregory A. [Children' s Hospital of Richmond at Virginia Commonwealth University, Department of Radiology, Richmond, VA (United States); Berman, Jeffrey I. [Children' s Hospital of Philadelphia, Department of Radiology, Philadelphia, PA (United States)
2015-09-15
Diffusion MRI is an imaging technique that uses the random motion of water to probe tissue microstructure. Diffusion tensor imaging (DTI) can quantitatively depict the organization and connectivity of white matter. Given the non-invasiveness of the technique, DTI has become a widely used tool for researchers and clinicians to examine the white matter of children. This review covers the basics of diffusion-weighted imaging and diffusion tensor imaging and discusses examples of their clinical application in children. (orig.)
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.)
Time integration of tensor trains
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...
DEFF Research Database (Denmark)
Tinggaard, Jeanette; Hagen, Casper P; Christensen, Anders Nymark
2017-01-01
Background Abdominal fat distribution is associated with the development of cardio-metabolic disease independently of body mass index (BMI). We assessed anthropometry, serum adipokines, and DXA as markers of abdominal subcutaneous adipose tissue (SAT) and visceral adipose tissue (VAT) using...... to total abdominal volume. Results Girls had a higher SAT% than did boys in early and late puberty (16 vs. 13%, Pfat% (standard deviation score (SDS)), suprailiac skinfold...... magnetic resonance imaging (MRI). Methods We performed a cross-sectional study that included 197 healthy adolescents (114 boys) aged 10–15 years nested within a longitudinal population-based cohort. Clinical examination, blood sampling, DXA, and abdominal MRI were performed. SAT% and VAT% were adjusted...
International Nuclear Information System (INIS)
Kobayashi, Tetsuo
2010-01-01
Described is the technological aspect of MRI, MR diffusion-weighted imaging (MR-DWI), principles of its measurement and application for imaging the cerebral function and for aiding the quantitative diagnosis of brain diseases. The author explains the principle of MR imaging process; diffusion properties of water molecules, MR-DWI based on them and DW-fMRI of the brain; MR-diffusion tensor imaging (MR-DTI), its analysis and color acquisition, and tracking of white matter nerve fibers; analysis of white matter lesions by the tracking; and the new tracking method at the chiasm of nerve fascicles. The usual fMRI reflects the blood oxygen level depending (BOLD) signals whereas recently attracted DW-fMRI, the volume changes of nerve cells concomitant to nerve activation accompanying apparent changes of water diffusion coefficients in and out of cells which occur faster than BOLD signs, resulting in higher resolution of time and space. However, DWI requires the higher intensity of static magnetic field like 3T. MR-DTI acquires the anisotropic diffusion of water molecules using MR-DWI technique with application of 6 or more motion probing gradients, thus makes it possible to track the running directions of nerve fibers and capillary vessels, and is proposed to be a useful mean of specific fiber tracking in the white matter when displayed by 3 different colors exhibiting the directions like the right/left (x axis, red), anterior/posterior (y, green) and upper/lower (z, blue) sides of head. Recently, MR-DWI and MR-DTI have been found usable for pathogenic studies of brain diseases such as dementia. Tensor anisotropy is apparently lowered at the chiasm of nerve fascicles, the cause of tracking error, for which authors have developed a new method using the similarity of directional vector, not of tensor, before and behind the chiasm. As exemplified, MRI technology is further advancing even at present. (T.T.)
Visualizing Tensor Normal Distributions at Multiple Levels of Detail.
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.
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
Analysis and visualization methods for interpretation of diffusion MRI data
Vos, S.B.
2013-01-01
Diffusion MRI is an imaging technique that is very sensitive to microstructural changes in tissue. Diffusion tensor MRI, the most commonly used method, can estimate the magnitude and anisotropy of diffusion. These tensor-based diffusion parameters have been shown to change in many neuropathological
Multivariate Tensor-based Brain Anatomical Surface Morphometry via Holomorphic One-Forms
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...
Tensors and their applications
Islam, Nazrul
2006-01-01
About the Book: The book is written is in easy-to-read style with corresponding examples. The main aim of this book is to precisely explain the fundamentals of Tensors and their applications to Mechanics, Elasticity, Theory of Relativity, Electromagnetic, Riemannian Geometry and many other disciplines of science and engineering, in a lucid manner. The text has been explained section wise, every concept has been narrated in the form of definition, examples and questions related to the concept taught. The overall package of the book is highly useful and interesting for the people associated with the field. Contents: Preliminaries Tensor Algebra Metric Tensor and Riemannian Metric Christoffel`s Symbols and Covariant Differentiation Riemann-Christoffel Tensor The e-Systems and the Generalized Krönecker Deltas Geometry Analytical Mechanics Curvature of a Curve, Geodesic Parallelism of Vectors Ricci`s Coefficients of Rotation and Congruence Hyper Surfaces
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....
International Nuclear Information System (INIS)
Scheunert, M.
1982-10-01
We develop a graded tensor calculus corresponding to arbitrary Abelian groups of degrees and arbitrary commutation factors. The standard basic constructions and definitions like tensor products, spaces of multilinear mappings, contractions, symmetrization, symmetric algebra, as well as the transpose, adjoint, and trace of a linear mapping, are generalized to the graded case and a multitude of canonical isomorphisms is presented. Moreover, the graded versions of the classical Lie algebras are introduced and some of their basic properties are described. (orig.)
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.
A Review of Tensors and Tensor Signal Processing
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.
Noble, David J; Scoffings, Daniel; Ajithkumar, Thankamma; Williams, Michael V; Jefferies, Sarah J
2016-11-01
There is no consensus approach to covering skull base meningeal reflections-and cerebrospinal fluid (CSF) therein-of the posterior fossa cranial nerves (CNs VII-XII) when planning radiotherapy (RT) for medulloblastoma and ependymoma. We sought to determine whether MRI and specifically fast imaging employing steady-state acquisition (FIESTA) sequences can answer this anatomical question and guide RT planning. 96 posterior fossa FIESTA sequences were reviewed. Following exclusions, measurements were made on the following scans for each foramen respectively (left, right); internal acoustic meatus (IAM) (86, 84), jugular foramen (JF) (83, 85) and hypoglossal canal (HC) (42, 45). A protocol describes measurement procedure. Two observers measured distances for five cases and agreement was assessed. One observer measured all the remaining cases. IAM and JF measurement interobserver variability was compared. Mean measurement difference between observers was -0.275 mm (standard deviation 0.557). IAM and JF measurements were normally distributed. Mean IAM distance was 12.2 mm [95% confidence interval (CI) 8.8-15.6]; JF was 7.3 mm (95% CI 4.0-10.6). The HC was difficult to visualize on many images and data followed a bimodal distribution. Dural reflections of posterior fossa CNs are well demonstrated by FIESTA MRI. Measuring CSF extension into these structures is feasible and robust; mean CSF extension into IAM and JF was measured. We plan further work to assess coverage of these structures with photon and proton RT plans. Advances in knowledge: We have described CSF extension beyond the internal table of the skull into the IAM, JF and HC. Oncologists planning RT for patients with medulloblastoma and ependymoma may use these data to guide contouring.
Tensor spaces and exterior algebra
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.
Tensor analysis for physicists
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...
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
Johnson, Marcia K; Raye, Carol L; Mitchell, Karen J; Greene, Erich J; Cunningham, William A; Sanislow, Charles A
2005-09-01
Using fMRI, we investigated the functional organization of prefrontal cortex (PFC) as participants briefly thought of a single just-experienced item (i.e., refreshed an active representation). The results of six studies, and a meta-analysis including previous studies, identified regions in left dorsolateral, anterior, and ventrolateral PFC associated in varying degrees with refreshing different types of information (visual and auditory words, drawings, patterns, people, places, or locations). In addition, activity increased in anterior cingulate with selection demands and in orbitofrontal cortex when a nonselected item was emotionally salient, consistent with a role for these areas in cognitive control (e.g., overcoming "mental rubbernecking"). We also found evidence that presenting emotional information disrupted an anterior component of the refresh circuit. We suggest that refreshing accounts for some neural activity observed in more complex tasks, such as working memory, long-term memory, and problem solving, and that its disruption (e.g., from aging or emotion) could have a broad impact.
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
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.
Tensors, relativity, and cosmology
Dalarsson, Mirjana
2015-01-01
Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in m...
Functional connectivity analysis of the brain network using resting-state fMRI
International Nuclear Information System (INIS)
Hayashi, Toshihiro
2011-01-01
Spatial patterns of spontaneous fluctuations in blood oxygenation level-dependent (BOLD) signals reflect the underlying neural architecture. The study of the brain network based on these self-organized patterns is termed resting-state functional MRI (fMRI). This review article aims at briefly reviewing a basic concept of this technology and discussing its implications for neuropsychological studies. First, the technical aspects of resting-state fMRI, including signal sources, physiological artifacts, image acquisition, and analytical methods such as seed-based correlation analysis and independent component analysis, are explained, followed by a discussion on the major resting-state networks, including the default mode network. In addition, the structure-function correlation studied using diffuse tensor imaging and resting-state fMRI is briefly discussed. Second, I have discussed the reservations and potential pitfalls of 2 major imaging methods: voxel-based lesion-symptom mapping and task fMRI. Problems encountered with voxel-based lesion-symptom mapping can be overcome by using resting-state fMRI and evaluating undamaged brain networks in patients. Regarding task fMRI in patients, I have also emphasized the importance of evaluating the baseline brain activity because the amplitude of activation in BOLD fMRI is hard to interpret as the same baseline cannot be assumed for both patient and normal groups. (author)
Magnetic resonance imaging - cardiac; Magnetic resonance imaging - heart; Nuclear magnetic resonance - cardiac; NMR - cardiac; MRI of the heart; Cardiomyopathy - MRI; Heart failure - MRI; Congenital heart disease - MRI
International Nuclear Information System (INIS)
Alsing, Paul M; McDonald, Jonathan R; Miller, Warner A
2011-01-01
The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The three-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The four-dimensional Ric is the Einstein tensor for such spacetimes. More recently, the Ric was used by Hamilton to define a nonlinear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincare conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area-an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimensions.
Alsing, Paul M.; McDonald, Jonathan R.; Miller, Warner A.
2011-08-01
The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The three-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The four-dimensional Ric is the Einstein tensor for such spacetimes. More recently, the Ric was used by Hamilton to define a nonlinear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincarè conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area—an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimensions.
DEFF Research Database (Denmark)
Ziegel, Johanna; Nyengaard, Jens Randel; Jensen, Eva B. Vedel
In the present paper, statistical procedures for estimating shape and orientation of arbitrary three-dimensional particles are developed. The focus of this work is on the case where the particles cannot be observed directly, but only via sections. Volume tensors are used for describing particle s...
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
Tensor Calculus: Unlearning Vector Calculus
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…
Diffusion tensor imaging, white matter lesions, the corpus callosum, and gait in the elderly
Gait impairment is common in the elderly, especially affected by stroke and white matter hyper intensities found in conventional brain magnetic resonance imaging (MRI). Diffusion tensor imaging (DTI) is more sensitive to white matter damage than conventional MRI. The relationship between DTI measure...
He, Lifang; Kong, Xiangnan; Yu, Philip S.; Ragin, Ann B.; Hao, Zhifeng; Yang, Xiaowei
2015-01-01
With advances in data collection technologies, tensor data is assuming increasing prominence in many applications and the problem of supervised tensor learning has emerged as a topic of critical significance in the data mining and machine learning community. Conventional methods for supervised tensor learning mainly focus on learning kernels by flattening the tensor into vectors or matrices, however structural information within the tensors will be lost. In this paper, we introduce a new scheme to design structure-preserving kernels for supervised tensor learning. Specifically, we demonstrate how to leverage the naturally available structure within the tensorial representation to encode prior knowledge in the kernel. We proposed a tensor kernel that can preserve tensor structures based upon dual-tensorial mapping. The dual-tensorial mapping function can map each tensor instance in the input space to another tensor in the feature space while preserving the tensorial structure. Theoretically, our approach is an extension of the conventional kernels in the vector space to tensor space. We applied our novel kernel in conjunction with SVM to real-world tensor classification problems including brain fMRI classification for three different diseases (i.e., Alzheimer's disease, ADHD and brain damage by HIV). Extensive empirical studies demonstrate that our proposed approach can effectively boost tensor classification performances, particularly with small sample sizes. PMID:25927014
He, Lifang; Kong, Xiangnan; Yu, Philip S; Ragin, Ann B; Hao, Zhifeng; Yang, Xiaowei
With advances in data collection technologies, tensor data is assuming increasing prominence in many applications and the problem of supervised tensor learning has emerged as a topic of critical significance in the data mining and machine learning community. Conventional methods for supervised tensor learning mainly focus on learning kernels by flattening the tensor into vectors or matrices, however structural information within the tensors will be lost. In this paper, we introduce a new scheme to design structure-preserving kernels for supervised tensor learning. Specifically, we demonstrate how to leverage the naturally available structure within the tensorial representation to encode prior knowledge in the kernel. We proposed a tensor kernel that can preserve tensor structures based upon dual-tensorial mapping. The dual-tensorial mapping function can map each tensor instance in the input space to another tensor in the feature space while preserving the tensorial structure. Theoretically, our approach is an extension of the conventional kernels in the vector space to tensor space. We applied our novel kernel in conjunction with SVM to real-world tensor classification problems including brain fMRI classification for three different diseases ( i.e ., Alzheimer's disease, ADHD and brain damage by HIV). Extensive empirical studies demonstrate that our proposed approach can effectively boost tensor classification performances, particularly with small sample sizes.
STRUCTURAL CONNECTIVITY VIA THE TENSOR-BASED MORPHOMETRY.
Kim, Seung-Goo; Chung, Moo K; Hanson, Jamie L; Avants, Brian B; Gee, James C; Davidson, Richard J; Pollak, Seth D
2011-01-01
The tensor-based morphometry (TBM) has been widely used in characterizing tissue volume difference between populations at voxel level. We present a novel computational framework for investigating the white matter connectivity using TBM. Unlike other diffusion tensor imaging (DTI) based white matter connectivity studies, we do not use DTI but only T1-weighted magnetic resonance imaging (MRI). To construct brain network graphs, we have developed a new data-driven approach called the ε -neighbor method that does not need any predetermined parcellation. The proposed pipeline is applied in detecting the topological alteration of the white matter connectivity in maltreated children.
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.)
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...
Longitudinal diffusion tensor imaging in amyotrophic lateral sclerosis
Directory of Open Access Journals (Sweden)
Keil Carsten
2012-11-01
Full Text Available Abstract Background Amyotrophic lateral sclerosis (ALS is a fatal neurodegenerative disorder, caused by progressive loss of motor neurons. Changes are widespread in the subcortical white matter in ALS. Diffusion tensor imaging (DTI detects pathological changes in white matter fibres in vivo, based on alterations in the degree (diffusivity, ADC and directedness (fractional anisotropy, FA of proton movement. Methods 24 patients with ALS and 24 age-matched controls received 1.5T DTI. FA and ADC were analyzed using statistical parametric mapping. In 15 of the 24 ALS patients, a second DTI was obtained after 6 months. Results Decreased FA in the corticospinal tract (CST and frontal areas confirm existing results. With a direct comparison of baseline and follow-up dataset, the progression of upper motor neuron degeneration, reflected in FA decrease, could be captured along the CST and in frontal areas. The involvement of cerebellum in the pathology of ALS, as suspected from functional MRI studies, could be confirmed by a reduced FA (culmen, declive. These structural changes correlated well with disease duration, ALSFRS-R, and physical and executive functions. Conclusion DTI detects changes that are regarded as prominent features of ALS and thus, shows promise in its function as a biomarker. Using the technique herein, we could demonstrate DTI changes at follow-up which correlated well with clinical progression.
Diffusion tensor imaging tensor shape analysis for assessment of regional white matter differences.
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.
Pieper, C C; Konrad, C; Sommer, J; Teismann, I; Schiffbauer, H
2013-05-01
Spinobulbar muscular atrophy [Kennedy's disease (KD)] is a rare X-linked neurodegenerative disorder of mainly spinal and bulbar motoneurons. Recent studies suggest a multisystem character of this disease. The aim of this study was to identify and characterize structural changes of gray (GM) and white matter (WM) in the central nervous system. Whole-brain-based voxel-based morphometry (VBM) and diffusion tensor imaging (DTI) analyses were applied to MRI data of eight genetically proven patients with KD and compared with 16 healthy age-matched controls. Diffusion tensor imaging analysis showed not only decreased fractional anisotropy (FA) values in the brainstem, but also widespread changes in central WM tracts, whereas VBM analysis of the WM showed alterations primarily in the brainstem and cerebellum. There were no changes in GM volume. The FA value decrease in the brainstem correlated with the disease duration. Diffusion tensor imaging analysis revealed subtle changes of central WM tract integrity, while GM and WM volume remained unaffected. In our patient sample, KD had more extended effects than previously reported. These changes could either be attributed primarily to neurodegeneration or reflect secondary plastic changes due to atrophy of lower motor neurons and reorganization of cortical structures. © 2012 John Wiley & Sons A/S.
X-ray strain tensor imaging: FEM simulation and experiments with a micro-CT.
Kim, Jae G; Park, So E; Lee, Soo Y
2014-01-01
In tissue elasticity imaging, measuring the strain tensor components is necessary to solve the inverse problem. However, it is impractical to measure all the tensor components in ultrasound or MRI elastography because of their anisotropic spatial resolution. The objective of this study is to compute 3D strain tensor maps from the 3D CT images of a tissue-mimicking phantom. We took 3D micro-CT images of the phantom twice with applying two different mechanical compressions to it. Applying the 3D image correlation technique to the CT images under different compression, we computed 3D displacement vectors and strain tensors at every pixel. To evaluate the accuracy of the strain tensor maps, we made a 3D FEM model of the phantom, and we computed strain tensor maps through FEM simulation. Experimentally obtained strain tensor maps showed similar patterns to the FEM-simulated ones in visual inspection. The correlation between the strain tensor maps obtained from the experiment and the FEM simulation ranges from 0.03 to 0.93. Even though the strain tensor maps suffer from high level noise, we expect the x-ray strain tensor imaging may find some biomedical applications such as malignant tissue characterization and stress analysis inside the tissues.
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.
International Nuclear Information System (INIS)
Littlejohn, R.G.
1982-01-01
The Hamiltonian structures discovered by Morrison and Greene for various fluid equations were obtained by guessing a Hamiltonian and a suitable Poisson bracket formula, expressed in terms of noncanonical (but physical) coordinates. In general, such a procedure for obtaining a Hamiltonian system does not produce a Hamiltonian phase space in the usual sense (a symplectic manifold), but rather a family of symplectic manifolds. To state the matter in terms of a system with a finite number of degrees of freedom, the family of symplectic manifolds is parametrized by a set of Casimir functions, which are characterized by having vanishing Poisson brackets with all other functions. The number of independent Casimir functions is the corank of the Poisson tensor J/sup ij/, the components of which are the Poisson brackets of the coordinates among themselves. Thus, these Casimir functions exist only when the Poisson tensor is singular
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...
The tensor distribution function.
Leow, A D; Zhu, S; Zhan, L; McMahon, K; de Zubicaray, G I; Meredith, M; Wright, M J; Toga, A W; Thompson, P M
2009-01-01
Diffusion weighted magnetic resonance imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of six directions, second-order tensors (represented by three-by-three positive definite matrices) can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g., crossing fiber tracts. Recently, a number of high-angular resolution schemes with more than six gradient directions have been employed to address this issue. In this article, we introduce the tensor distribution function (TDF), a probability function defined on the space of symmetric positive definite matrices. Using the calculus of variations, we solve the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function. Moreover, a tensor orientation distribution function (TOD) may also be derived from the TDF, allowing for the estimation of principal fiber directions and their corresponding eigenvalues.
Vilanova, Anna; Burgeth, Bernhard; Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data
2014-01-01
Arising from the fourth Dagstuhl conference entitled Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data (2011), this book offers a broad and vivid view of current work in this emerging field. Topics covered range from applications of the analysis of tensor fields to research on their mathematical and analytical properties. Part I, Tensor Data Visualization, surveys techniques for visualization of tensors and tensor fields in engineering, discusses the current state of the art and challenges, and examines tensor invariants and glyph design, including an overview of common glyphs. The second Part, Representation and Processing of Higher-order Descriptors, describes a matrix representation of local phase, outlines mathematical morphological operations techniques, extended for use in vector images, and generalizes erosion to the space of diffusion weighted MRI. Part III, Higher Order Tensors and Riemannian-Finsler Geometry, offers powerful mathematical language to model and...
Farrar, Danielle; Budson, Andrew E
2017-04-01
While the relationship between diffusion tensor imaging (DTI) measurements and training effects is explored by Voelker et al. (this issue), a cursory discussion of functional magnetic resonance imaging (fMRI) measurements categorizes increased activation with findings of greater white matter integrity. Evidence of the relationship between fMRI activation and white matter integrity is conflicting, as is the relationship between fMRI activation and training effects. An examination of the changes in fMRI activation in response to training is helpful, but the relationship between DTI and fMRI activation, particularly in the context of white matter changes, must be examined further before general conclusions can be drawn.
Tensor Permutation Matrices in Finite Dimensions
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...
Tensor Factorization for Low-Rank Tensor Completion.
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.
Diffusion tensor and diffusion weighted imaging. Pictorial mathematics
Energy Technology Data Exchange (ETDEWEB)
Nakada, Tsutomu [California Univ., Davis, CA (United States)
1995-06-01
A new imaging algorithm for the treatment of a second order apparent diffusion tensor, D{sub app}{sup {xi}} is described. The method calls for only mathematics of images (pictorial mathematics) without necessity of eigenvalues/eigenvectors estimation. Nevertheless, it is capable of extracting properties of D{sub app}{sup {xi}} invariant to observation axes. While trace image is an example of images weighted by invariance of the tensor matrix, three dimensional anisotropy (3DAC) contrast represents the imaging method making use to anisotropic direction of tensor ellipsoid producing color coded contrast of exceptionally high anatomic resolution. Contrary to intuition, the processes require only a simple algorithm directly applicable to clinical magnetic resonance imaging (MRI). As a contrast method which precisely represents physical characteristics of a target tissue, invariant D{sub app}{sup {xi}} images produced by pictorial mathematics possess significant potential for a number of biological and clinical applications. (author).
Multivariate analysis of eigenvalues and eigenvectors in tensor based morphometry
Rajagopalan, Vidya; Schwartzman, Armin; Hua, Xue; Leow, Alex; Thompson, Paul; Lepore, Natasha
2015-01-01
We develop a new algorithm to compute voxel-wise shape differences in tensor-based morphometry (TBM). As in standard TBM, we non-linearly register brain T1-weighed MRI data from a patient and control group to a template, and compute the Jacobian of the deformation fields. In standard TBM, the determinants of the Jacobian matrix at each voxel are statistically compared between the two groups. More recently, a multivariate extension of the statistical analysis involving the deformation tensors derived from the Jacobian matrices has been shown to improve statistical detection power.7 However, multivariate methods comprising large numbers of variables are computationally intensive and may be subject to noise. In addition, the anatomical interpretation of results is sometimes difficult. Here instead, we analyze the eigenvalues and the eigenvectors of the Jacobian matrices. Our method is validated on brain MRI data from Alzheimer's patients and healthy elderly controls from the Alzheimer's Disease Neuro Imaging Database.
Diffusion tensor imaging and tractography in clinical neuro sciences
International Nuclear Information System (INIS)
Zarei, M.; Johansen-Berg, H.; Matthews, P.M.
2003-01-01
Rapidly evolving MR technology has allowed better understanding of structure and function of the human brain. Diffusion weighted MRI was developed two decades ago and it is now well established in diagnosis of acute ischaemia in patients with stroke. Diffusion tensor MRI uses the same principles but takes a step further allowing US to measure magnitude of the diffusion along different directions. This lead to the development of diffusion tensor tractography, a technique by which major neural pathways in the living brain can be visualized. There is a growing interest in exploring possible use of these techniques in clinical neurology and psychiatry. This article aims to review the principles of this technique and recent discoveries which may help US to better understand neurological and psychiatric disorders
Tensor Train Neighborhood Preserving Embedding
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.
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.
Tensor norms and operator ideals
Defant, A; Floret, K
1992-01-01
The three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resumé and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series of exer
International Nuclear Information System (INIS)
Provata, A.; Katsaloulis, P.; Verganelakis, D.A.
2012-01-01
Highlights: ► Calculation of human brain multifractal spectra. ► Calculations are based on Diffusion Tensor MRI Images. ► Spectra are modelled by coupled Ikeda map dynamics. ► Coupled lattice Ikeda maps model well only positive multifractal spectra. ► Appropriately modified coupled lattice Ikeda maps give correct spectra. - Abstract: The multifractal spectra of 3d Diffusion Tensor Images (DTI) obtained by magnetic resonance imaging of the human brain are studied. They are shown to deviate substantially from artificial brain images with the same white matter intensity. All spectra, obtained from 12 healthy subjects, show common characteristics indicating non-trivial moments of the intensity. To model the spectra the dynamics of the chaotic Ikeda map are used. The DTI multifractal spectra for positive q are best approximated by 3d coupled Ikeda maps in the fully developed chaotic regime. The coupling constants are as small as α = 0.01. These results reflect not only the white tissue non-trivial architectural complexity in the human brain, but also demonstrate the presence and importance of coupling between neuron axons. The architectural complexity is also mirrored by the deviations in the negative q-spectra, where the rare events dominate. To obtain a good agreement in the DTI negative q-spectrum of the brain with the Ikeda dynamics, it is enough to slightly modify the most rare events of the coupled Ikeda distributions. The representation of Diffusion Tensor Images with coupled Ikeda maps is not unique: similar conclusions are drawn when other chaotic maps (Tent, Logistic or Henon maps) are employed in the modelling of the neuron axons network.
Diffusion tensor imaging of partial intractable epilepsy
International Nuclear Information System (INIS)
Dumas de la Roque, Anne; Oppenheim, Catherine; Rodrigo, Sebastian; Meder, Jean-Francois; Chassoux, Francine; Devaux, Bertrand; Beuvon, Frederic; Daumas-Duport, Catherine
2005-01-01
Our aim was to assess the value of diffusion tensor imaging (DTI) in patients with partial intractable epilepsy. We used DTI (25 non-collinear directions) in 15 patients with a cortical lesion on conventional MRI. Fractional anisotropy (FA) was measured in the internal capsule, and in the normal-appearing white matter (WM), adjacent tothe lesion, and away from the lesion, at a set distance of 2-3 cm. In each patient, increased or decreased FA measurements were those that varied from mirror values using an arbitrary 10% threshold. Over the whole population, ipsi- and contralateral FA measurements were also compared using a Wilcoxon test (p<0.05). Over the whole population, FA was significantly reduced in the WM adjacent to and away from the lesion, whilst being normal in the internal capsule. FA was reduced by more than 10% in the WM adjacent to and distant from the lesion in 13 and 12 patients respectively. For nine of the ten patients for whom the surgical resection encompassed the limits of the lesion on conventional MRI, histological data showed WM alterations (gliosis, axonal loss, abnormal cells). DTI often reveals WM abnormalities that are undetected on conventional MRI in patients with partial intractable epilepsy. (orig.)
Typesafe Abstractions for Tensor Operations
Chen, Tongfei
2017-01-01
We propose a typesafe abstraction to tensors (i.e. multidimensional arrays) exploiting the type-level programming capabilities of Scala through heterogeneous lists (HList), and showcase typesafe abstractions of common tensor operations and various neural layers such as convolution or recurrent neural networks. This abstraction could lay the foundation of future typesafe deep learning frameworks that runs on Scala/JVM.
Indicial tensor manipulation on MACSYMA
International Nuclear Information System (INIS)
Bogen, R.A.; Pavelle, R.
1977-01-01
A new computational tool for physical calculations is described. It is the first computer system capable of performing indicial tensor calculus (as opposed to component tensor calculus). It is now operational on the symbolic manipulation system MACSYMA. The authors outline the capabilities of the system and describe some of the physical problems considered as well as others being examined at this time. (Auth.)
Diffusion tensor imaging of spinal cord parenchyma lesion in rat with chronic spinal cord injury.
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
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
Energy-momentum tensor in quantum field theory
International Nuclear Information System (INIS)
Fujikawa, K.
1981-01-01
The definition of the energy-momentum tensor as a source current coupled to the background gravitational field receives an important modification in quantum theory. In the path-integral approach, the manifest covariance of the integral measure under general coordinate transformations dictates that field variables with weight 1/2 should be used as independent integration variables. An improved energy-momentum tensor is then generated by the variational derivative, and it gives rise to well-defined gravitational conformal (Weyl) anomalies. In the flat--space-time limit, all the Ward-Takahashi identities associated with space-time transformations including the global dilatation become free from anomalies in terms of this energy-momentum tensor, reflecting the general covariance of the integral measure; the trace of this tensor is thus finite at zero momentum transfer for renormalizable theories. The Jacobian for the local conformal transformation, however, becomes nontrivial, and it gives rise to an anomaly for the conformal identity. All the familiar anomalies are thus reduced to either chiral or conformal anomalies. The consistency of the dilatation and conformal identities at vanishing momentum transfer determines the trace anomaly of this energy-momentum tensor in terms of the renormalization-group b function and other parameters. In contrast, the trace of the conventional energy-momentum tensor generally diverges even at vanishing momentum transfer depending on the regularization scheme, and it is subtractively renormalized. We also explain how the apparently different renormalization properties of the chiral and trace anomalies arise
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.
Efficient tensor completion for color image and video recovery: Low-rank tensor train
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...
Random SU(2) invariant tensors
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.
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.
International Nuclear Information System (INIS)
Qiu Deqiang; Kwong, Dora; Chan, Godfrey; Leung, Lucullus; Khong, P.-L.
2007-01-01
Purpose: To test the hypothesis that fractional anisotropy (FA) is more severely reduced in white matter of the frontal lobe compared with the parietal lobe after receiving the same whole-brain irradiation dose in a cohort of childhood medulloblastoma survivors. Methods and Materials: Twenty-two medulloblastoma survivors (15 male, mean [± SD] age = 12.1 ± 4.6 years) and the same number of control subjects (15 male, aged 12.0 ± 4.2 years) were recruited for diffusion tensor magnetic resonance imaging scans. Using an automated tissue classification method and the Talairach Daemon atlas, FA values of frontal and parietal lobes receiving the same radiation dose, and the ratio between them were quantified and denoted as FFA, PFA, and FA f/p , respectively. The Mann-Whitney U test was used to test for significant differences of FFA, PFA, and FA f/p between medulloblastoma survivors and control subjects. Results: Frontal lobe and parietal lobe white matter FA were found to be significantly less in medulloblastoma survivors compared with control subjects (frontal p = 0.001, parietal p = 0.026). Moreover, these differences were found to be discrepant, with the frontal lobe having a significantly larger difference in FA compared with the parietal lobe. The FA f/p of control and medulloblastoma survivors was 1.110 and 1.082, respectively (p = 0.029). Conclusion: Discrepant FA changes after the same irradiation dose suggest radiosensitivity of the frontal lobe white matter compared with the parietal lobe. Special efforts to address the potentially vulnerable frontal lobe after treatment with whole-brain radiation may be needed so as to balance disease control and treatment-related morbidity
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.)
Tensor Product of Polygonal Cell Complexes
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.
The Einstein tensor characterizing some Riemann spaces
International Nuclear Information System (INIS)
Rahman, M.S.
1993-07-01
A formal definition of the Einstein tensor is given. Mention is made of how this tensor plays a role of expressing certain conditions in a precise form. The cases of reducing the Einstein tensor to a zero tensor are studied on its merit. A lucid account of results, formulated as theorems, on Einstein symmetric and Einstein recurrent spaces is then presented. (author). 5 refs
Diffusion tensor imaging in polymicrogyria: a report of three cases
International Nuclear Information System (INIS)
Trivedi, R.; Gupta, R.K.; Prasad, K.N.; Hasan, K.M.; Hou, P.; Narayana, P.A.
2006-01-01
Polymicrogyria (PMG), a neuronal migration disorder, commonly manifests as a seizure disorder. The aim of this study was to look for the abnormalities in the underlying white matter using diffusion tensor imaging (DTI) that appeared normal on conventional magnetic resonance imaging (MRI) in patients with PMG. DTI was performed in three patients with PMG and eight age- and sex-matched healthy controls. Fractional anisotropy (FA) and mean diffusivity (MD) values were calculated for the cortex and adjoining subcortical white matter in both controls and patients. We observed a significantly decreased mean FA value with no significant change in the MD value in subcortical white matter underlying polymicrogyric cortex (FA=0.23±0.04, MD=1.0±0.05 x 10 -3 mm 2 /s) as compared to both contralateral (FA=0.32±0.04, MD=1.0±0.05 x 10 -3 mm 2 /s) and normal control (FA=0.32±0.04, MD=1.0±0.06 x 10 -3 mm 2 /s) white matter. Significantly increased MD and decreased FA values were also observed in the polymicrogyric cortex (FA=0.08±0.01, MD=1.2±0.10 x 10 -3 mm 2 /s) as compared to normal contralateral (FA=0.12±0.04, MD=1.1±0.09 x 10 -3 mm 2 /s) and normal control (FA=0.12±0.01, MD=1.1±0.09 x 10 -3 mm 2 /s) cortex. Significantly decreased FA values with no change in MD values in the subcortical white matter subjacent to polymicrogyric cortex reflect microstructural changes in the white matter probably due to the presence of ectopic neurons. (orig.)
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.
The application of functional MRI in evaluating ischemic injuries of lower limb skeletal muscle
International Nuclear Information System (INIS)
Xia Caifeng; Gu Jianping
2011-01-01
The ischemic injury of lower limb skeletal muscle is caused by various reasons that lead to limb arterial blood flow insufficiency and subsequent muscle tissue hypoxia. Exact and correct evaluation of the ischemic degree of the skeletal muscle is very important for the physicians to guide the clinical treatment, to assess the therapeutic effect and to judge the prognosis. With the development and updating of scanning hardware and software, together with the use of diffusion-weighted imaging (DWI), diffusion tensor imaging (DTI), perfusion-weighted imaging (PWI), blood oxygen level dependent (BOLD) imaging and magnetic resonance spectroscopy (MRS), etc. the application of MRI has been dramatically expanded both in clinical practice and scientific researches. Nowadays, functional MRI can accurately reflect the physiological structures and pathologic changes in detail. This article aims mainly to make a comprehensive review about the application of these techniques in assessing the ischemic injuries of lower limb skeletal muscle. (authors)
Tensor Completion Algorithms in Big Data Analytics
Song, Qingquan; Ge, Hancheng; Caverlee, James; Hu, Xia
2017-01-01
Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications have received wide attention and achievement in areas like data mining, computer vision, signal processing, and neuroscience. In this survey, we provide a modern overview of recent advances in tensor completion algorithms from the perspective of big data an...
Development of the Tensoral Computer Language
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.
International Nuclear Information System (INIS)
Ponrartana, Skorn; Hu, Houchun Harry; Ramos-Platt, Leigh; Wren, Tishya Anne Leong; Gilsanz, Vicente; Perkins, Thomas Gardner; Chia, Jonathan Mawlin
2015-01-01
There is currently a lack of suitable objective endpoints to measure disease progression in Duchenne muscular dystrophy (DMD). Emerging research suggests that diffusion tensor imaging (DTI) has potential as an outcome measure for the evaluation of skeletal muscle injury. The objective of this study was to evaluate the potential of DTI as quantitative magnetic resonance imaging (MRI) markers of disease severity in DMD. Thirteen consecutive boys (8.9 years ± 3.0 years) with DMD were evaluated using DTI. Fractional anisotropy (FA) and apparent diffusion coefficient (ADC) were compared with clinical outcome measures of manual muscle testing and MRI determinations of muscle fat fraction (MFF) in the right lower extremity. Both MRI measures of FA and ADC strongly correlated with age and muscle strength. Values for FA positively correlated with age and negatively correlated with muscle strength (r = 0.78 and -0.96; both P ≤ 0.002) while measures of ADC negatively correlated age, but positively correlated with muscle strength (r = -0.87 and 0.83; both P ≤ 0.0004). Additionally, ADC and FA strongly correlated with MFF (r = -0.891 and 0.894, respectively; both P ≤ 0.0001). Mean MMF was negatively correlated with muscle strength (r = -0.89, P = 0.0001). DTI measures of muscle structure strongly correlated with muscle strength and adiposity in boys with DMD in this pilot study, although these markers may be more reflective of fat replacement rather than muscle damage in later stages of the disease. Further studies in presymptomatic younger children are needed to assess the ability of DTI to detect early changes in DMD. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Ponrartana, Skorn; Hu, Houchun Harry [Children' s Hospital Los Angeles, Department of Radiology, Los Angeles, CA (United States); Ramos-Platt, Leigh [Children' s Hospital Los Angeles, Department of Neurology, Los Angeles, CA (United States); Wren, Tishya Anne Leong; Gilsanz, Vicente [Children' s Hospital Los Angeles, Department of Radiology, Los Angeles, CA (United States); Children' s Hospital Los Angeles, Department of Orthopaedic Surgery, Los Angeles, CA (United States); Perkins, Thomas Gardner; Chia, Jonathan Mawlin [Philips Healthcare North America, Cleveland, OH (United States)
2015-04-01
There is currently a lack of suitable objective endpoints to measure disease progression in Duchenne muscular dystrophy (DMD). Emerging research suggests that diffusion tensor imaging (DTI) has potential as an outcome measure for the evaluation of skeletal muscle injury. The objective of this study was to evaluate the potential of DTI as quantitative magnetic resonance imaging (MRI) markers of disease severity in DMD. Thirteen consecutive boys (8.9 years ± 3.0 years) with DMD were evaluated using DTI. Fractional anisotropy (FA) and apparent diffusion coefficient (ADC) were compared with clinical outcome measures of manual muscle testing and MRI determinations of muscle fat fraction (MFF) in the right lower extremity. Both MRI measures of FA and ADC strongly correlated with age and muscle strength. Values for FA positively correlated with age and negatively correlated with muscle strength (r = 0.78 and -0.96; both P ≤ 0.002) while measures of ADC negatively correlated age, but positively correlated with muscle strength (r = -0.87 and 0.83; both P ≤ 0.0004). Additionally, ADC and FA strongly correlated with MFF (r = -0.891 and 0.894, respectively; both P ≤ 0.0001). Mean MMF was negatively correlated with muscle strength (r = -0.89, P = 0.0001). DTI measures of muscle structure strongly correlated with muscle strength and adiposity in boys with DMD in this pilot study, although these markers may be more reflective of fat replacement rather than muscle damage in later stages of the disease. Further studies in presymptomatic younger children are needed to assess the ability of DTI to detect early changes in DMD. (orig.)
Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature
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.
Energy-momentum tensor in quantum field theory
International Nuclear Information System (INIS)
Fujikawa, Kazuo.
1980-12-01
The definition of the energy-momentum tensor as a source current coupled to the background gravitational field receives an important modification in quantum theory. In the path integral approach, the manifest covariance of the integral measure under general coordinate transformations dictates that field variables with weight 1/2 should be used as independent integration variables. An improved energy-momentum tensor is then generated by the variational derivative, and it gives rise to well-defined gravitational conformal (Weyl) anomalies. In the flat space-time limit, all the Ward-Takahashi identities associate with space-time transformations including the global dilatation become free from anomalies, reflecting the general covariance of the integral measure; the trace of this energy-momentum tensor is thus finite at the zero momentum transfer. The Jacobian for the local conformal transformation however becomes non-trivial, and it gives rise to an anomaly for the conformal identity. All the familiar anomalies are thus reduced to either chiral or conformal anomalies. The consistency of the dilatation and conformal identities at the vanishing momentum transfer determines the trace anomaly of this energy-momentum tensor in terms of the renormalization group β-function and other parameters. In contrast, the trace of the conventional energy-momentum tensor generally diverges even at the vanishing momentum transfer depending on the regularization scheme, and it is subtractively renormalized. We also explain how the apparently different renormalization properties of the chiral and trace anomalies arise. (author)
Diekmann, Volker; Hoppner, Anselm Cornelius
2014-03-01
Patients suffering from musicogenic epilepsy have focal seizures triggered by auditory stimuli. In some of these patients, the emotions associated with the music appear to play a role in the process triggering the seizure, however, the significance of these emotions and the brain regions involved are unclear. In order to shed some light on this, we conducted fMRI and EEG in a case of musicogenic epilepsy. In a 32-year-old male patient with seizures induced by a specific piece of Russian music, we performed video-EEG monitoring as well as simultaneous fMRI and EEG registration. Video-EEG monitoring revealed a left temporo-frontal epileptogenic focus. During fMRI-EEG co-registration, BOLD signal alterations were not only found in the epileptogenic focus but also in areas known for their role in the processing of emotions. Prior to a seizure in some of these areas, BOLD contrasts exponentially increased or decreased. These results suggest that in our case, dysfunction of the regulation processes of the musically-induced emotions, and not the musical stimulus itself, led to the seizures.
Multivariate tensor-based brain anatomical surface morphometry via holomorphic one-forms.
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 ventricular surface morphometry in HIV/AIDS (19 subjects) and cortical surface morphometry in Williams Syndrome (WS; 80 subjects). Experimental results demonstrated that our method powerfully detected brain surface abnormalities. Multivariate statistics on the local tensors outperformed other TBM methods including analysis of the Jacobian determinant, the largest eigenvalue, or the pair of eigenvalues, of the surface Jacobian matrix.
The tensor rank of tensor product of two three-qubit W states is eight
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.
Anisotropic Conductivity Tensor Imaging of In Vivo Canine Brain Using DT-MREIT.
Jeong, Woo Chul; Sajib, Saurav Z K; Katoch, Nitish; Kim, Hyung Joong; Kwon, Oh In; Woo, Eung Je
2017-01-01
We present in vivo images of anisotropic electrical conductivity tensor distributions inside canine brains using diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT). The conductivity tensor is represented as a product of an ion mobility tensor and a scale factor of ion concentrations. Incorporating directional mobility information from water diffusion tensors, we developed a stable process to reconstruct anisotropic conductivity tensor images from measured magnetic flux density data using an MRI scanner. Devising a new image reconstruction algorithm, we reconstructed anisotropic conductivity tensor images of two canine brains with a pixel size of 1.25 mm. Though the reconstructed conductivity values matched well in general with those measured by using invasive probing methods, there were some discrepancies as well. The degree of white matter anisotropy was 2 to 4.5, which is smaller than previous findings of 5 to 10. The reconstructed conductivity value of the cerebrospinal fluid was about 1.3 S/m, which is smaller than previous measurements of about 1.8 S/m. Future studies of in vivo imaging experiments with disease models should follow this initial trial to validate clinical significance of DT-MREIT as a new diagnostic imaging modality. Applications in modeling and simulation studies of bioelectromagnetic phenomena including source imaging and electrical stimulation are also promising.
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....
Spectral Tensor-Train Decomposition
DEFF Research Database (Denmark)
Bigoni, Daniele; Engsig-Karup, Allan Peter; Marzouk, Youssef M.
2016-01-01
The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT) decomposition. We first define a functional version of the TT...... adaptive Smolyak approach. The method is also used to approximate the solution of an elliptic PDE with random input data. The open source software and examples presented in this work are available online (http://pypi.python.org/pypi/TensorToolbox/)....
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
Tensor product of quantum logics
Pulmannová, Sylvia
1985-01-01
A quantum logic is the couple (L,M) where L is an orthomodular σ-lattice and M is a strong set of states on L. The Jauch-Piron property in the σ-form is also supposed for any state of M. A ``tensor product'' of quantum logics is defined. This definition is compared with the definition of a free orthodistributive product of orthomodular σ-lattices. The existence and uniqueness of the tensor product in special cases of Hilbert space quantum logics and one quantum and one classical logic are studied.
Ultrasound elastic tensor imaging: comparison with MR diffusion tensor imaging in the myocardium
Lee, Wei-Ning; Larrat, Benoît; Pernot, Mathieu; Tanter, Mickaël
2012-08-01
We have previously proven the feasibility of ultrasound-based shear wave imaging (SWI) to non-invasively characterize myocardial fiber orientation in both in vitro porcine and in vivo ovine hearts. The SWI-estimated results were in good correlation with histology. In this study, we proposed a new and robust fiber angle estimation method through a tensor-based approach for SWI, coined together as elastic tensor imaging (ETI), and compared it with magnetic resonance diffusion tensor imaging (DTI), a current gold standard and extensively reported non-invasive imaging technique for mapping fiber architecture. Fresh porcine (n = 5) and ovine (n = 5) myocardial samples (20 × 20 × 30 mm3) were studied. ETI was firstly performed to generate shear waves and to acquire the wave events at ultrafast frame rate (8000 fps). A 2.8 MHz phased array probe (pitch = 0.28 mm), connected to a prototype ultrasound scanner, was mounted on a customized MRI-compatible rotation device, which allowed both the rotation of the probe from -90° to 90° at 5° increments and co-registration between two imaging modalities. Transmural shear wave speed at all propagation directions realized was firstly estimated. The fiber angles were determined from the shear wave speed map using the least-squares method and eigen decomposition. The test myocardial sample together with the rotation device was then placed inside a 7T MRI scanner. Diffusion was encoded in six directions. A total of 270 diffusion-weighted images (b = 1000 s mm-2, FOV = 30 mm, matrix size = 60 × 64, TR = 6 s, TE = 19 ms, 24 averages) and 45 B0 images were acquired in 14 h 30 min. The fiber structure was analyzed by the fiber-tracking module in software, MedINRIA. The fiber orientation in the overlapped myocardial region which both ETI and DTI accessed was therefore compared, thanks to the co-registered imaging system. Results from all ten samples showed good correlation (r2 = 0.81, p 0.05, unpaired, one-tailed t-test, N = 10). In
The 'gravitating' tensor in the dualistic theory
International Nuclear Information System (INIS)
Mahanta, M.N.
1989-01-01
The exact microscopic system of Einstein-type field equations of the dualistic gravitation theory is investigated as well as an analysis of the modified energy-momentum tensor or so called 'gravitating' tensor is presented
Tensor calculus for physics a concise guide
Neuenschwander, Dwight E
2015-01-01
Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarization in dielectrics; an unbalanced car wheel wobbling in the vertical plane while spinning about a horizontal axis; an electrostatic field on Earth observed to be a magnetic field by orbiting astronauts—these are some situations where physicists employ tensors. But the true beauty of tensors lies in this fact: When coordinates are transformed from one system to another, tensors change according to the same rules as the coordinates. Tensors, therefore, allow for the convenience of coordinates while also transcending them. This makes tensors the gold standard for expressing physical relationships in physics and geometry. Undergraduate physics majors are typically introduced to tensors in special-case applications. For example, in a classical mechanics course, they meet the "inertia tensor," and in electricity and magnetism...
Mean template for tensor-based morphometry using deformation tensors.
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.
Analyzing vortex breakdown flow structures by assignment of colors to tensor invariants.
Rütten, Markus; Chong, Min S
2006-01-01
Topological methods are often used to describe flow structures in fluid dynamics and topological flow field analysis usually relies on the invariants of the associated tensor fields. A visual impression of the local properties of tensor fields is often complex and the search of a suitable technique for achieving this is an ongoing topic in visualization. This paper introduces and assesses a method of representing the topological properties of tensor fields and their respective flow patterns with the use of colors. First, a tensor norm is introduced, which preserves the properties of the tensor and assigns the tensor invariants to values of the RGB color space. Secondly, the RGB colors of the tensor invariants are transferred to corresponding hue values as an alternative color representation. The vectorial tensor invariants field is reduced to a scalar hue field and visualization of iso-surfaces of this hue value field allows us to identify locations with equivalent flow topology. Additionally highlighting by the maximum of the eigenvalue difference field reflects the magnitude of the structural change of the flow. The method is applied on a vortex breakdown flow structure inside a cylinder with a rotating lid.
Reciprocal mass tensor : a general form
International Nuclear Information System (INIS)
Roy, C.L.
1978-01-01
Using the results of earlier treatment of wave packets, a general form of reciprocal mass tensor has been obtained. The elements of this tensor are seen to be dependent on momentum as well as space coordinates of the particle under consideration. The conditions under which the tensor would reduce to the usual space-independent form, are discussed and the impact of the space-dependence of this tensor on the motion of Bloch electrons, is examined. (author)
A new deteriorated energy-momentum tensor
International Nuclear Information System (INIS)
Duff, M.J.
1982-01-01
The stress-tensor of a scalar field theory is not unique because of the possibility of adding an 'improvement term'. In supersymmetric field theories the stress-tensor will appear in a super-current multiplet along with the sypersymmetry current. The general question of the supercurrent multiplet for arbitrary deteriorated stress tensors and their relationship to supercurrent multiplets for models with gauge antisymmetric tensors is answered for various models of N = 1, 2 and 4 supersymmetry. (U.K.)
Tensor-based spatiotemporal saliency detection
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.
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
Efficient Tensor Strategy for Recommendation
Directory of Open Access Journals (Sweden)
Aboagye Emelia Opoku
2017-07-01
Full Text Available The era of big data has witnessed the explosion of tensor datasets, and large scale Probabilistic Tensor Factorization (PTF analysis is important to accommodate such increasing trend of data. Sparsity, and Cold-Start are some of the inherent problems of recommender systems in the era of big data. This paper proposes a novel Sentiment-Based Probabilistic Tensor Analysis technique senti-PTF to address the problems. The propose framework first applies a Natural Language Processing technique to perform sentiment analysis taking advantage of the huge sums of textual data generated available from the social media which are predominantly left untouched. Although some current studies do employ review texts, many of them do not consider how sentiments in reviews influence recommendation algorithm for prediction. There is therefore this big data text analytics gap whose modeling is computationally expensive. From our experiments, our novel machine learning sentiment-based tensor analysis is computationally less expensive, and addresses the cold-start problem, for optimal recommendation prediction.
Weyl tensors for asymmetric complex curvatures
International Nuclear Information System (INIS)
Oliveira, C.G.
Considering a second rank Hermitian field tensor and a general Hermitian connection the associated complex curvature tensor is constructed. The Weyl tensor that corresponds to this complex curvature is determined. The formalism is applied to the Weyl unitary field theory and to the Moffat gravitational theory. (Author) [pt
Spherical Tensor Calculus for Local Adaptive Filtering
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.
Seuwen, Aline; Schroeter, Aileen; Grandjean, Joanes; Rudin, Markus
2015-10-15
Functional proton magnetic resonance spectroscopy (1H-MRS) enables the non-invasive assessment of neural activity by measuring signals arising from endogenous metabolites in a time resolved manner. Proof-of-principle of this approach has been demonstrated in humans and rats; yet functional 1H-MRS has not been applied in mice so far, although it would be of considerable interest given the many genetically engineered models of neurological disorders established in this species only. Mouse 1H-MRS is challenging as the high demands on spatial resolution typically result in long data acquisition times not commensurable with functional studies. Here, we propose an approach based on spectroscopic imaging in combination with the acquisition of the free induction decay to maximize signal intensity. Highly resolved metabolite maps have been recorded from mouse brain with 12 min temporal resolution. This enabled monitoring of metabolic changes following the administration of bicuculline, a GABA-A receptor antagonist. Changes in levels of metabolites involved in energy metabolism (lactate and phosphocreatine) and neurotransmitters (glutamate) were investigated in a region-dependent manner and shown to scale with the bicuculline dose. GABAergic inhibition induced spectral changes characteristic for increased neurotransmitter turnover and oxidative stress. In contrast to metabolic readouts, BOLD and CBV fMRI responses did not scale with the bicuculline dose indicative of the failure of neurovascular coupling. Nevertheless fMRI measurements supported the notion of increased oxidative stress revealed by functional MRS. Hence, the combined analysis of metabolic and hemodynamic changes in response to stimulation provides complementary insight into processes associated with neural activity. Copyright © 2015 Elsevier Inc. All rights reserved.
International Nuclear Information System (INIS)
Martola, Juha; Zhang, Yi; Aspelin, Peter; Kristoffersen Wiberg, Maria; Bergstroem, Jakob; Fredrikson, Sten; Stawiarz, Leszek; Hillert, Jan; Flodmark, Olof; Lilja, Anders; Ekbom, Anders
2010-01-01
Multiple sclerosis (MS) has a variable progression with an early onset of atrophy. Individual longitudinal radiological evaluations (over decades) are difficult to perform due to the limited availability of magnetic resonance imaging (MRI) in the past, patients lost in follow-up, and the continuous updating of scanners. We studied a cohort with widespread disease duration at baseline. The observed individual atrophy rates over time of 10 years represented four decades of disease span. Thirty-seven MS patients (age range 24-65 years with disease duration 1-33 years) were consecutively selected and evaluated with MRI at baseline 1995 and in 1996. They were followed up for a decade (mean of 9.25 years, range 7.3-10 years) up to 2003-2005. Brain parenchymal volume and volumes of the supratentorial ventricles were analyzed with semi-automated volumetric measurements at three time points (1995, 1996, and 2003-2005). Volumetric differences were found over shorter periods of time (1-7 months); however, differences vanished by the end of follow-up. A uniform longitudinal decrease in brain volume and increase in ventricle volumes were found. Frontal horn width (1D) correlated strongest to 3D measures. No statistical differences of atrophy rates between MS courses were found. Supratentorial ventricular volumes were associated with disability and this association persisted during follow-up. Despite variable clinical courses, the degenerative effects of MS progression expressed in brain atrophy seem to uniformly progress over longer periods of time. These volumetric changes can be detected using 1D and 2D measurements performed on a routine PACS workstation. (orig.)
A new Weyl-like tensor of geometric origin
Vishwakarma, Ram Gopal
2018-04-01
A set of new tensors of purely geometric origin have been investigated, which form a hierarchy. A tensor of a lower rank plays the role of the potential for the tensor of one rank higher. The tensors have interesting mathematical and physical properties. The highest rank tensor of the hierarchy possesses all the geometrical properties of the Weyl tensor.
Ramgolam, A.; Sablong, R.; Bou-Saïd, B.; Bouvard, S.; Saint-Jalmes, H.; Beuf, O.
2011-07-01
Conventional white light endoscopy (WLE) is the most widespread technique used today for colorectal cancer diagnosis and is considered as the gold standard when coupled to biopsy and histology. However for early stage colorectal cancer diagnosis, which is very often characterised by flat adenomas, the use of WLE is quite difficult due to subtle or quasiinvisible morphological changes of the colonic lining. Figures worldwide point out that diagnosing colorectal cancer in its early stages would significantly reduce the death toll all while increasing the 5-year survival rate. Several techniques are currently being investigated in the scope of providing new tools that would allow such a diagnostic or assist actual techniques in so doing. We hereby present a novel technique where High spatial Resolution MRI (HR-MRI) is coupled to optical spectroscopy (autofluorescence and reflectance) in a bimodal endoluminal probe to extract morphological data and biochemical information respectively. The design and conception of the endoluminal probe along with the preliminary results obtained with an organic phantom and in-vivo (rabbit) are presented and discussed.
MR diffusion tensor analysis of schizophrenic brain using statistical parametric mapping
International Nuclear Information System (INIS)
Yamada, Haruyasu; Abe, Osamu; Kasai, Kiyoto
2005-01-01
The purpose of this study is to investigate diffusion anisotropy in the schizophrenic brain by voxel-based analysis of diffusion tensor imaging (DTI), using statistical parametric mapping (SPM). We studied 33 patients with schizophrenia diagnosed by diagnostic and statistical manual of mental disorders (DSM)-IV criteria and 42 matched controls. The data was obtained with a 1.5 T MRI system. We used single-shot spin-echo planar sequences (repetition time/echo time (TR/TE)=5000/102 ms, 5 mm slice thickness and 1.5 mm gap, field of view (FOV)=21 x 21 cm 2 , number of excitation (NEX)=4, 128 x 128 pixel matrix) for diffusion tensor acquisition. Diffusion gradients (b-value of 500 or 1000 s/mm 2 ) were applied on two axes simultaneously. Diffusion properties were measured along 6 non-linear directions. The structural distortion induced by the large diffusion gradients was corrected, based on each T 2 -weighted echo-planar image (b=0 s/mm 2 ). The fractional anisotropy (FA) maps were generated on a voxel-by-voxel basis. T 2 -weighted echo-planar images were then segmented into gray matter, white matter, and cerebrospinal fluid, using SPM (Wellcome Department of Imaging, University College London, UK). All apparent diffusion coefficient (ADC) and FA maps in native space were transformed to the stereotactic space by registering each of the images to the same template image. The normalized data was smoothed and analyzed using SPM. The significant FA decrease in the patient group was found in the uncinate fasciculus, parahippocampal white matter, anterior cingulum and other areas (corrected p<0.05). No significant increased region was noted. Our results may reflect reduced diffusion anisotropy of the white matter pathway of the limbic system as shown by the decreased FA. Manual region-of-interest analysis is usually more sensitive than voxel-based analysis, but it is subjective and difficult to set with anatomical reproducibility. Voxel-based analysis of the diffusion tensor
Comparison of Magnetic Susceptibility Tensor and Diffusion Tensor of the Brain.
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.
Volume illustration of muscle from diffusion tensor images.
Chen, Wei; Yan, Zhicheng; Zhang, Song; Crow, John Allen; Ebert, David S; McLaughlin, Ronald M; Mullins, Katie B; Cooper, Robert; Ding, Zi'ang; Liao, Jun
2009-01-01
Medical illustration has demonstrated its effectiveness to depict salient anatomical features while hiding the irrelevant details. Current solutions are ineffective for visualizing fibrous structures such as muscle, because typical datasets (CT or MRI) do not contain directional details. In this paper, we introduce a new muscle illustration approach that leverages diffusion tensor imaging (DTI) data and example-based texture synthesis techniques. Beginning with a volumetric diffusion tensor image, we reformulate it into a scalar field and an auxiliary guidance vector field to represent the structure and orientation of a muscle bundle. A muscle mask derived from the input diffusion tensor image is used to classify the muscle structure. The guidance vector field is further refined to remove noise and clarify structure. To simulate the internal appearance of the muscle, we propose a new two-dimensional example based solid texture synthesis algorithm that builds a solid texture constrained by the guidance vector field. Illustrating the constructed scalar field and solid texture efficiently highlights the global appearance of the muscle as well as the local shape and structure of the muscle fibers in an illustrative fashion. We have applied the proposed approach to five example datasets (four pig hearts and a pig leg), demonstrating plausible illustration and expressiveness.
Tensor voting for robust color edge detection
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 ...
The Physical Interpretation of the Lanczos Tensor
Roberts, Mark D.
1999-01-01
The field equations of general relativity can be written as first order differential equations in the Weyl tensor, the Weyl tensor in turn can be written as a first order differential equation in a three index tensor called the Lanczos tensor. The Lanczos tensor plays a similar role in general relativity to that of the vector potential in electro-magnetic theory. The Aharonov-Bohm effect shows that when quantum mechanics is applied to electro-magnetic theory the vector potential is dynamicall...
Comparison of Biomarkers in Transgenic Alzheimer Rats Using Multi-shell Diffusion MRI
Fick , Rutger ,; Daianu , Madelaine; Pizzolato , Marco; Wassermann , Demian; Jacobs , Russel E.; Thompson , Paul M.; Town , Terrence; Deriche , Rachid
2016-01-01
International audience; In this study, we assessed the evolution of diffusion MRI (dMRI) derived markers from different white matter models as progressive neurodegeneration occurs in transgenic Alzheimer rats (TgF344-AD) at 10, 15 and 24 months. We compared biomarkers reconstructed from Diffusion Tensor Imaging (DTI), Neurite Orientation Dispersion and Density Imaging (NODDI) and Mean Apparent Propagator (MAP)-MRI in the hippocampus, cingulate cortex and corpus callosum using multi-shell dMRI...
... resonance imaging - chest; NMR - chest; MRI of the thorax; Thoracic MRI Patient Instructions ... Gotway MB, Panse PM, Gruden JF, Elicker BM. Thoracic radiology. In: Broaddus VC, Mason RJ, Ernst JD, et ...
Robust estimation of adaptive tensors of curvature by tensor voting.
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.
Antisymmetric tensor generalizations of affine vector fields.
Houri, Tsuyoshi; Morisawa, Yoshiyuki; Tomoda, Kentaro
2016-02-01
Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine tensor fields are closely related to one-lower-rank antisymmetric tensor fields which are parallelly transported along geodesics. It is also shown that the number of linear independent rank- p antisymmetric affine tensor fields in n -dimensions is bounded by ( n + 1)!/ p !( n - p )!. We also derive the integrability conditions for antisymmetric affine tensor fields. Using the integrability conditions, we discuss the existence of antisymmetric affine tensor fields on various spacetimes.
NODDI and Tensor-Based Microstructural Indices as Predictors of Functional Connectivity.
Directory of Open Access Journals (Sweden)
Fani Deligianni
Full Text Available In Diffusion Weighted MR Imaging (DWI, the signal is affected by the biophysical properties of neuronal cells and their relative placement, as well as extra-cellular tissue compartments. Typically, microstructural indices, such as fractional anisotropy (FA and mean diffusivity (MD, are based on a tensor model that cannot disentangle the influence of these parameters. Recently, Neurite Orientation Dispersion and Density Imaging (NODDI has exploited multi-shell acquisition protocols to model the diffusion signal as the contribution of three tissue compartments. NODDI microstructural indices, such as intra-cellular volume fraction (ICVF and orientation dispersion index (ODI are directly related to neuronal density and orientation dispersion, respectively. One way of examining the neurophysiological role of these microstructural indices across neuronal fibres is to look into how they relate to brain function. Here we exploit a statistical framework based on sparse Canonical Correlation Analysis (sCCA and randomised Lasso to identify structural connections that are highly correlated with resting-state functional connectivity measured with simultaneous EEG-fMRI. Our results reveal distinct structural fingerprints for each microstructural index that also reflect their inter-relationships.
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.)
Directory of Open Access Journals (Sweden)
Kei Omata
Full Text Available The emergence of the occipital alpha rhythm on brain electroencephalogram (EEG is associated with brain activity in the cerebral neocortex and deep brain structures. To further understand the mechanisms of alpha rhythm power fluctuation, we performed simultaneous EEGs and functional magnetic resonance imaging recordings in human subjects during a resting state and explored the dynamic relationship between alpha power fluctuation and blood oxygenation level-dependent (BOLD signals of the brain. Based on the frequency characteristics of the alpha power time series (APTS during 20-minute EEG recordings, we divided the APTS into two components: fast fluctuation (0.04-0.167 Hz and slow fluctuation (0-0.04 Hz. Analysis of the correlation between the MRI signal and each component revealed that the slow fluctuation component of alpha power was positively correlated with BOLD signal changes in the brain stem and the medial part of the thalamus and anterior cingulate cortex, while the fast fluctuation component was correlated with the lateral part of the thalamus and the anterior cingulate cortex, but not the brain stem. In summary, these data suggest that different subcortical structures contribute to slow and fast modulations of alpha spectra on brain EEG.
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Bosque-Freeman, L.; Leroy, C.; Galanaud, D.; Sureau, F.; Assouad, R.; Tourbah, A.; Papeix, C.; Comtat, C.; Trebossen, R.; Lubetzki, C.; Delforge, J.; Bottlaender, M.; Stankoff, B. [Serv. Hosp. Frederic Joliot, Orsay (France)
2009-07-01
Objective: To assess neuronal damage in deep gray matter structures by positron emission tomography (PET) using [{sup 11}C]-flumazenil (FMZ), a specific central benzodiazepine receptor antagonist, and [{sup 18}F]-fluorodeoxyglucose (FDG), which reflects neuronal metabolism. To compare results obtained by PET and those with multimodal magnetic resonance imaging (MRI). Background: It is now accepted that neuronal injury plays a crucial role in the occurrence and progression of neurological disability in multiple sclerosis (MS). To date, available MRI techniques do not specifically assess neuronal damage, but early abnormalities, such as iron deposition or atrophy, have been described in deep gray matter structures. Whether those MRI modifications correspond to neuronal damage remains to be further investigated. Materials and methods: Nine healthy volunteers were compared to 10 progressive and 9 relapsing remitting (RR) MS patients. Each subject performed two PET examinations with [{sup 11}C]-FMZ and [{sup 18}F]-FDG, on a high resolution research tomograph dedicated to brain imaging (Siemens Medical Solution, spatial resolution of 2.5 mm). Deep gray matter regions were manually segmented on T1-weighted MR images with the mutual information algorithm (www.brainvisa.info), and co-registered with PET images. A multimodal MRI including T1 pre and post gadolinium, T2-proton density sequences, magnetization transfer, diffusion tensor, and protonic spectroscopy was also performed for each subject. Results: On PET with [{sup 11}C]-FMZ, there was a pronounced decrease in receptor density for RR patients in all deep gray matter structures investigated, whereas the density was unchanged or even increased in the same regions for progressive patients. Whether the different patterns between RR and progressive patients reflect distinct pathogenic mechanisms is currently investigated by comparing PET and multimodal MRI results. Conclusion: Combination of PET and multimodal MR imaging
Sparse alignment for robust tensor learning.
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.
Transposes, L-Eigenvalues and Invariants of Third Order Tensors
Qi, Liqun
2017-01-01
Third order tensors have wide applications in mechanics, physics and engineering. The most famous and useful third order tensor is the piezoelectric tensor, which plays a key role in the piezoelectric effect, first discovered by Curie brothers. On the other hand, the Levi-Civita tensor is famous in tensor calculus. In this paper, we study third order tensors and (third order) hypermatrices systematically, by regarding a third order tensor as a linear operator which transforms a second order t...
Tensor SOM and tensor GTM: Nonlinear tensor analysis by topographic mappings.
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.
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)
Seamless warping of diffusion tensor fields
DEFF Research Database (Denmark)
Xu, Dongrong; Hao, Xuejun; Bansal, Ravi
2008-01-01
To warp diffusion tensor fields accurately, tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Existing algorithms for warping tensors typically use forward mapping...... of seams, including voxels in which the deformation is extensive. Backward mapping, however, cannot reorient tensors in the template space because information about the directional orientation of fiber tracts is contained in the original, unwarped imaging space only, and backward mapping alone cannot...... transfer that information to the template space. To combine the advantages of forward and backward mapping, we propose a novel method for the spatial normalization of diffusion tensor (DT) fields that uses a bijection (a bidirectional mapping with one-to-one correspondences between image spaces) to warp DT...
The Topology of Symmetric Tensor Fields
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 improving the efficiency of tensor voting
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...
Schrimpf, Martin
2016-01-01
Google's Machine Learning framework TensorFlow was open-sourced in November 2015 [1] and has since built a growing community around it. TensorFlow is supposed to be flexible for research purposes while also allowing its models to be deployed productively. This work is aimed towards people with experience in Machine Learning considering whether they should use TensorFlow in their environment. Several aspects of the framework important for such a decision are examined, such as the heterogenity,...
Efficient Low Rank Tensor Ring Completion
Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin
2017-01-01
Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors in the MPS representation. This development is motivated in part by the success of matrix completion algorithms that alternate over the (low-rank) factors. In this paper, we propose a spectral initialization for the tensor ring completion algorithm and ana...
The Riemann-Lovelock Curvature Tensor
Kastor, David
2012-01-01
In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth-order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k \\le D
The 1/ N Expansion of Tensor Models with Two Symmetric Tensors
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.
Dictionary-Based Tensor Canonical Polyadic Decomposition
Cohen, Jeremy Emile; Gillis, Nicolas
2018-04-01
To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images.
Bayesian regularization of diffusion tensor images
DEFF Research Database (Denmark)
Frandsen, Jesper; Hobolth, Asger; Østergaard, Leif
2007-01-01
Diffusion tensor imaging (DTI) is a powerful tool in the study of the course of nerve fibre bundles in the human brain. Using DTI, the local fibre orientation in each image voxel can be described by a diffusion tensor which is constructed from local measurements of diffusion coefficients along...... several directions. The measured diffusion coefficients and thereby the diffusion tensors are subject to noise, leading to possibly flawed representations of the three dimensional fibre bundles. In this paper we develop a Bayesian procedure for regularizing the diffusion tensor field, fully utilizing...
A RENORMALIZATION PROCEDURE FOR TENSOR MODELS AND SCALAR-TENSOR THEORIES OF GRAVITY
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...
The tensor network theory library
Al-Assam, S.; Clark, S. R.; Jaksch, D.
2017-09-01
In this technical paper we introduce the tensor network theory (TNT) library—an open-source software project aimed at providing a platform for rapidly developing robust, easy to use and highly optimised code for TNT calculations. The objectives of this paper are (i) to give an overview of the structure of TNT library, and (ii) to help scientists decide whether to use the TNT library in their research. We show how to employ the TNT routines by giving examples of ground-state and dynamical calculations of one-dimensional bosonic lattice system. We also discuss different options for gaining access to the software available at www.tensornetworktheory.org.
Dirac tensor with heavy photon
Energy Technology Data Exchange (ETDEWEB)
Bytev, V.V.; Kuraev, E.A. [Joint Institute of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics; Scherbakova, E.S. [Hamburg Univ. (Germany). 1. Inst. fuer Theoretische Physik
2012-01-15
For the large-angles hard photon emission by initial leptons in process of high energy annihilation of e{sup +}e{sup -} {yields} to hadrons the Dirac tensor is obtained, taking into account the lowest order radiative corrections. The case of large-angles emission of two hard photons by initial leptons is considered. This result is being completed by the kinematics case of collinear hard photons emission as well as soft virtual and real photons and can be used for construction of Monte-Carlo generators. (orig.)
Chen, Hua-Biao; Wan, Qi; Xu, Qi-Feng; Chen, Yi; Bai, Bo
2016-01-01
Background Correlating symptoms and physical examination findings with surgical levels based on common imaging results is not reliable. In patients who have no concordance between radiological and clinical symptoms, the surgical levels determined by conventional magnetic resonance imaging (MRI) and neurogenic examination (NE) may lead to a more extensive surgery and significant complications. We aimed to confirm that whether the use of diffusion tensor imaging (DTI) and paraspinal mapping (PM...
Reflecting reflection in supervision
DEFF Research Database (Denmark)
Lystbæk, Christian Tang
associated with reflection and an exploration of alternative conceptions that view reflection within the context of settings which have a more group- and team-based orientation. Drawing on an action research project on health care supervision, the paper questions whether we should reject earlier views...... of reflection, rehabilitate them in order to capture broader connotations or move to new ways of regarding reflection that are more in keeping with not only reflective but also emotive, normative and formative views on supervision. The paper presents a critical perspective on supervision that challenge...... the current reflective paradigm I supervision and relate this to emotive, normative and formative views supervision. The paper is relevant for Nordic educational research into the supervision and guidance...
International Nuclear Information System (INIS)
Seidl, G.; Ullrich, R.; Trattnig, S.; Dominkus, M.; Morscher, M.; Aringer, M.; Imhof, H.
1996-01-01
The appearance of gouty tophus in magnetic resonance imaging (MRI) is characteristic. On T1- and T2-weighted SE images, the signal intensity of tophaceous lesions is similar to that of muscles. According to the histology, T2-weighted SE images demonstrate extremely hyperintense signals, which reflect the high protein content in the amorpheous center of the tophus. The microscopic urate crystals deposited there have no MRI signal and are of no further diagnostic impact. Vascularized granulation tissue surrounding the tophus center enhance after intervenous application of contrast agents (Gadolinium). The inflammed tophus is associated with local edema, causing high signal intensity. MRI is superior to plain radiography for early detection of intraosseous tophi. Involvement of anatomical structures such as ligaments and tendons can be evaluated sufficiently. For peripheral joints, axial slice orientation is most helpful. (orig.) [de
Advanced MRI techniques of the fetal brain
International Nuclear Information System (INIS)
Schoepf, V.; Dittrich, E.; Berger-Kulemann, V.; Kasprian, G.; Kollndorfer, K.; Prayer, D.
2013-01-01
Evaluation of the normal and pathological fetal brain. Magnetic resonance imaging (MRI). Advanced MRI of the fetal brain. Diffusion tensor imaging (DTI) is used in clinical practice, all other methods are used at a research level. Serving as standard methods in the future. Combined structural and functional data for all gestational ages will allow more specific insight into the developmental processes of the fetal brain. This gain of information will help provide a common understanding of complex spatial and temporal procedures of early morphological features and their impact on cognitive and sensory abilities. (orig.) [de
Real-time MR diffusion tensor and Q-ball imaging using Kalman filtering
International Nuclear Information System (INIS)
Poupon, C.; Roche, A.; Dubois, J.; Mangin, J.F.; Poupon, F.
2008-01-01
Diffusion magnetic resonance imaging (dMRI) has become an established research tool for the investigation of tissue structure and orientation. In this paper, we present a method for real-time processing of diffusion tensor and Q-ball imaging. The basic idea is to use Kalman filtering framework to fit either the linear tensor or Q-ball model. Because the Kalman filter is designed to be an incremental algorithm, it naturally enables updating the model estimate after the acquisition of any new diffusion-weighted volume. Processing diffusion models and maps during ongoing scans provides a new useful tool for clinicians, especially when it is not possible to predict how long a subject may remain still in the magnet. First, we introduce the general linear models corresponding to the two diffusion tensor and analytical Q-ball models of interest. Then, we present the Kalman filtering framework and we focus on the optimization of the diffusion orientation sets in order to speed up the convergence of the online processing. Last, we give some results on a healthy volunteer for the online tensor and the Q-ball model, and we make some comparisons with the conventional offline techniques used in the literature. We could achieve full real-time for diffusion tensor imaging and deferred time for Q-ball imaging, using a single workstation. (authors)
Detecting brain dynamics during resting state: a tensor based evolutionary clustering approach
Al-sharoa, Esraa; Al-khassaweneh, Mahmood; Aviyente, Selin
2017-08-01
Human brain is a complex network with connections across different regions. Understanding the functional connectivity (FC) of the brain is important both during resting state and task; as disruptions in connectivity patterns are indicators of different psychopathological and neurological diseases. In this work, we study the resting state functional connectivity networks (FCNs) of the brain from fMRI BOLD signals. Recent studies have shown that FCNs are dynamic even during resting state and understanding the temporal dynamics of FCNs is important for differentiating between different conditions. Therefore, it is important to develop algorithms to track the dynamic formation and dissociation of FCNs of the brain during resting state. In this paper, we propose a two step tensor based community detection algorithm to identify and track the brain network community structure across time. First, we introduce an information-theoretic function to reduce the dynamic FCN and identify the time points that are similar topologically to combine them into a tensor. These time points will be used to identify the different FC states. Second, a tensor based spectral clustering approach is developed to identify the community structure of the constructed tensors. The proposed algorithm applies Tucker decomposition to the constructed tensors and extract the orthogonal factor matrices along the connectivity mode to determine the common subspace within each FC state. The detected community structure is summarized and described as FC states. The results illustrate the dynamic structure of resting state networks (RSNs), including the default mode network, somatomotor network, subcortical network and visual network.
Raman scattering tensors of tyrosine.
Tsuboi, M; Ezaki, Y; Aida, M; Suzuki, M; Yimit, A; Ushizawa, K; Ueda, T
1998-01-01
Polarized Raman scattering measurements have been made of a single crystal of L-tyrosine by the use of a Raman microscope with the 488.0-nm exciting beam from an argon ion laser. The L-tyrosine crystal belongs to the space group P2(1)2(1)2(1) (orthorhombic), and Raman scattering intensities corresponding to the aa, bb, cc, ab and ac components of the crystal Raman tensor have been determined for each prominent Raman band. A similar set of measurements has been made of L-tyrosine-d4, in which four hydrogen atoms on the benzene ring are replaced by deuterium atoms. The effects of NH3-->ND3 and OH-->OD on the Raman spectrum have also been examined. In addition, depolarization ratios of some bands of L-tyrosine in aqueous solutions of pH 13 and pH 1 were examined. For comparison with these experimental results, on the other hand, ab initio molecular orbital calculations have been made of the normal modes of vibration and their associated polarizability oscillations of the L-tyrosine molecule. On the basis of these experimental data and by referring to the results of the calculations, discussions have been presented on the Raman tensors associated to some Raman bands, including those at 829 cm-1 (benzene ring breathing), 642 cm-1 (benzene ring deformation), and 432 cm-1 (C alpha-C beta-C gamma bending).
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)
Gravitational Metric Tensor Exterior to Rotating Homogeneous ...
African Journals Online (AJOL)
The covariant and contravariant metric tensors exterior to a homogeneous spherical body rotating uniformly about a common φ axis with constant angular velocity ω is constructed. The constructed metric tensors in this gravitational field have seven non-zero distinct components.The Lagrangian for this gravitational field is ...
Tensor Network Quantum Virtual Machine (TNQVM)
Energy Technology Data Exchange (ETDEWEB)
2016-11-18
There is a lack of state-of-the-art quantum computing simulation software that scales on heterogeneous systems like Titan. Tensor Network Quantum Virtual Machine (TNQVM) provides a quantum simulator that leverages a distributed network of GPUs to simulate quantum circuits in a manner that leverages recent results from tensor network theory.
Tensor product varieties and crystals. GL case
Malkin, Anton
2001-01-01
The role of Spaltenstein varieties in the tensor product for GL is explained. In particular a direct (non-combinatorial) proof of the fact that the number of irreducible components of a Spaltenstein variety is equal to a Littlewood-Richardson coefficient (i.e. certain tensor product multiplicity) is obtained.
Differential invariants for higher-rank tensors. A progress report
International Nuclear Information System (INIS)
Tapial, V.
2004-07-01
We outline the construction of differential invariants for higher-rank tensors. In section 2 we outline the general method for the construction of differential invariants. A first result is that the simplest tensor differential invariant contains derivatives of the same order as the rank of the tensor. In section 3 we review the construction for the first-rank tensors (vectors) and second-rank tensors (metrics). In section 4 we outline the same construction for higher-rank tensors. (author)
Beyond Low Rank: A Data-Adaptive Tensor Completion Method
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...
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 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
Weyl curvature tensor in static spherical sources
International Nuclear Information System (INIS)
Ponce de Leon, J.
1988-01-01
The role of the Weyl curvature tensor in static sources of the Schwarzschild field is studied. It is shown that in general the contribution from the Weyl curvature tensor (the ''purely gravitational field energy'') to the mass-energy inside the body may be positive, negative, or zero. It is proved that a positive (negative) contribution from the Weyl tensor tends to increase (decrease) the effective gravitational mass, the red-shift (from a point in the sphere to infinity), as well as the gravitational force which acts on a constituent matter element of a body. It is also proved that the contribution from the Weyl tensor always is negative in sources with surface gravitational potential larger than (4/9. It is pointed out that large negative contributions from the Weyl tensor could give rise to the phenomenon of gravitational repulsion. A simple example which illustrates the results is discussed
A recursive reduction of tensor Feynman integrals
International Nuclear Information System (INIS)
Diakonidis, T.; Riemann, T.; Tausk, J.B.; Fleischer, J.
2009-07-01
We perform a recursive reduction of one-loop n-point rank R tensor Feynman integrals [in short: (n,R)-integrals] for n≤6 with R≤n by representing (n,R)-integrals in terms of (n,R-1)- and (n-1,R-1)-integrals. We use the known representation of tensor integrals in terms of scalar integrals in higher dimension, which are then reduced by recurrence relations to integrals in generic dimension. With a systematic application of metric tensor representations in terms of chords, and by decomposing and recombining these representations, we find the recursive reduction for the tensors. The procedure represents a compact, sequential algorithm for numerical evaluations of tensor Feynman integrals appearing in next-to-leading order contributions to massless and massive three- and four-particle production at LHC and ILC, as well as at meson factories. (orig.)
On Lovelock analogs of the Riemann tensor
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.
MRI assessment program. Consensus statement on clinical efficacy of MRI
International Nuclear Information System (INIS)
1998-05-01
This consensus statement is largely based on the experience gained at the MRI units at the four hospitals which have operated scanners in the MRI program. It reflects the considered opinion of the radiologists responsible for the MRI services at those hospitals. Account has also been taken of relevant overseas data. This collection of opinion relates particularly to comparison with other imaging modalities. The specific comments will require further consideration as technical developments with MRI become available, additional experience is gained with gadolinium contrast material and additional data are obtained on the influence of MRI on patient management. MRI, at present, is used either to improve diagnostic accuracy when other tests are negative or equivocal, when there is strong clinical suspicion of disease, or to improve surgical or other management planning when the diagnosis known. In some situations (eg syringomyelia, congenital spinal disease, posterior fossa/cerebello-pontine angle tumours) it may entirely replace other tests (eg myelography, air contrast, CT) which are substantially less accurate and/or more invasive. In other situations (eg hemispheric brain tumours, lumbar disc protrusions) when other tests, such as CT, can be as accurate, MRI is not usually or initially indicated because it is currently more expensive and of limited availability. However, balanced against this is the fact that it does not expose the patient to potentially harmful ionising radiation. It is also stressed that MRI images depend on complex, widely variable and, as yet, incompletely understood parameters. There is concern that this may result in false positive diagnoses, especially where MRI is used alone as a screening test, or used as the initial test. For several reasons (availability, cost, medical and diagnostic efficacy), the specific comments on indications for MRI presented are based upon the assumption that MRI is a tertiary and complementary imaging examination
International Nuclear Information System (INIS)
Oldendorf, W.; Oldendorf, W. Jr.
1991-01-01
Designed for studies, radiologists, and clinicians at all levels of training, this book provides a basic introduction to the principles, physics, and instrumentation of magnetic resonance imaging. The fundamental concepts that are essential for the optimal clinical use of MRI are thoroughly explained in easily accessible terms. To facilitate the reader's comprehension, the material is presented nonmathematically, using no equations and a minimum of symbols and abbreviations. MRI Primer presents a clear account of the phenomenon of nuclear magnetic resonance and the use of gradient magnetic fields to create clinically useful images of cross-sectional slices. Close attention is given to the magnetization vector as a means of expressing nuclear behavior, the role of T 1 and T 2 weighing in imaging, the use of contrast agents, and the pulse sequences most often used in clinical practice, as well as to the relative capabilities and limitations of MRI and CT. The basic hardware components of an MRI scanner are described in detail. Sample MRI scans illustrate how MRI characterizes tissue. An appendix provides a brief introduction to quantum processes in MRI
Energy Technology Data Exchange (ETDEWEB)
Cui, T [Duke University, Durham, NC (United States); Liang, X [Duke Unversity, Durham, NC (United States); Czito, B; Palta, M; Bashir, M; Yin, F; Cai, J [Duke University Medical Center, Durham, NC (United States)
2014-06-15
Purpose: Quantitative imaging of hepatic stiffness has significant potential in radiation therapy, ranging from treatment planning to response assessment. This study aims to develop a novel, noninvasive method to quantify liver stiffness with 3D strains liver maps using 4D-MRI and deformable image registration (DIR). Methods: Five patients with liver cancer were imaged with an institutionally developed 4D-MRI technique under an IRB-approved protocol. Displacement vector fields (DVFs) across the liver were generated via DIR of different phases of 4D-MRI. Strain tensor at each voxel of interest (VOI) was computed from the relative displacements between the VOI and each of the six adjacent voxels. Three principal strains (E{sub 1}, E{sub 2} and E{sub 3}) of the VOI were derived as the eigenvalue of the strain tensor, which represent the magnitudes of the maximum and minimum stretches. Strain tensors for two regions of interest (ROIs) were calculated and compared for each patient, one within the tumor (ROI{sub 1}) and the other in normal liver distant from the heart (ROI{sub 2}). Results: 3D strain maps were successfully generated fort each respiratory phase of 4D-MRI for all patients. Liver deformations induced by both respiration and cardiac motion were observed. Differences in strain values adjacent to the distant from the heart indicate significant deformation caused by cardiac expansion during diastole. The large E{sub 1}/E{sub 2} (∼2) and E{sub 1}/E{sub 2} (∼10) ratios reflect the predominance of liver deformation in the superior-inferior direction. The mean E{sub 1} in ROI{sub 1} (0.12±0.10) was smaller than in ROI{sub 2} (0.15±0.12), reflecting a higher degree of stiffness of the cirrhotic tumor. Conclusion: We have successfully developed a novel method for quantitatively evaluating regional hepatic stiffness based on DIR of 4D-MRI. Our initial findings indicate that liver strain is heterogeneous, and liver tumors may have lower principal strain values
International Nuclear Information System (INIS)
Cui, T; Liang, X; Czito, B; Palta, M; Bashir, M; Yin, F; Cai, J
2014-01-01
Purpose: Quantitative imaging of hepatic stiffness has significant potential in radiation therapy, ranging from treatment planning to response assessment. This study aims to develop a novel, noninvasive method to quantify liver stiffness with 3D strains liver maps using 4D-MRI and deformable image registration (DIR). Methods: Five patients with liver cancer were imaged with an institutionally developed 4D-MRI technique under an IRB-approved protocol. Displacement vector fields (DVFs) across the liver were generated via DIR of different phases of 4D-MRI. Strain tensor at each voxel of interest (VOI) was computed from the relative displacements between the VOI and each of the six adjacent voxels. Three principal strains (E 1 , E 2 and E 3 ) of the VOI were derived as the eigenvalue of the strain tensor, which represent the magnitudes of the maximum and minimum stretches. Strain tensors for two regions of interest (ROIs) were calculated and compared for each patient, one within the tumor (ROI 1 ) and the other in normal liver distant from the heart (ROI 2 ). Results: 3D strain maps were successfully generated fort each respiratory phase of 4D-MRI for all patients. Liver deformations induced by both respiration and cardiac motion were observed. Differences in strain values adjacent to the distant from the heart indicate significant deformation caused by cardiac expansion during diastole. The large E 1 /E 2 (∼2) and E 1 /E 2 (∼10) ratios reflect the predominance of liver deformation in the superior-inferior direction. The mean E 1 in ROI 1 (0.12±0.10) was smaller than in ROI 2 (0.15±0.12), reflecting a higher degree of stiffness of the cirrhotic tumor. Conclusion: We have successfully developed a novel method for quantitatively evaluating regional hepatic stiffness based on DIR of 4D-MRI. Our initial findings indicate that liver strain is heterogeneous, and liver tumors may have lower principal strain values than normal liver. Thorough validation of our method is
Efficient Tensor Completion for Color Image and Video Recovery: Low-Rank Tensor Train.
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.
Tensor network method for reversible classical computation
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.
On improving the efficiency of tensor voting.
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.
Conformal field theories and tensor categories. Proceedings
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Bai, Chengming [Nankai Univ., Tianjin (China). Chern Institute of Mathematics; Fuchs, Juergen [Karlstad Univ. (Sweden). Theoretical Physics; Huang, Yi-Zhi [Rutgers Univ., Piscataway, NJ (United States). Dept. of Mathematics; Kong, Liang [Tsinghua Univ., Beijing (China). Inst. for Advanced Study; Runkel, Ingo; Schweigert, Christoph (eds.) [Hamburg Univ. (Germany). Dept. of Mathematics
2014-08-01
First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications. Contributors include both mathematicians and physicists. Some long expository articles are especially suitable for beginners. The present volume is a collection of seven papers that are either based on the talks presented at the workshop ''Conformal field theories and tensor categories'' held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.
Conformal field theories and tensor categories. Proceedings
International Nuclear Information System (INIS)
Bai, Chengming; Fuchs, Juergen; Huang, Yi-Zhi; Kong, Liang; Runkel, Ingo; Schweigert, Christoph
2014-01-01
First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications. Contributors include both mathematicians and physicists. Some long expository articles are especially suitable for beginners. The present volume is a collection of seven papers that are either based on the talks presented at the workshop ''Conformal field theories and tensor categories'' held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.
... hearing aids Pins, hairpins, metal zippers, and similar metallic items Removable dental work How the Test will ... an MRI can make heart pacemakers and other implants not work as well. It can also cause ...
Tensor harmonic analysis on homogenous space
International Nuclear Information System (INIS)
Wrobel, G.
1997-01-01
The Hilbert space of tensor functions on a homogenous space with the compact stability group is considered. The functions are decomposed onto a sum of tensor plane waves (defined in the text), components of which are transformed by irreducible representations of the appropriate transformation group. The orthogonality relation and the completeness relation for tensor plane waves are found. The decomposition constitutes a unitary transformation, which allows to obtain the Parseval equality. The Fourier components can be calculated by means of the Fourier transformation, the form of which is given explicitly. (author)
Abelian gauge theories with tensor gauge fields
International Nuclear Information System (INIS)
Kapuscik, E.
1984-01-01
Gauge fields of arbitrary tensor type are introduced. In curved space-time the gravitational field serves as a bridge joining different gauge fields. The theory of second order tensor gauge field is developed on the basis of close analogy to Maxwell electrodynamics. The notion of tensor current is introduced and an experimental test of its detection is proposed. The main result consists in a coupled set of field equations representing a generalization of Maxwell theory in which the Einstein equivalence principle is not satisfied. (author)
Local Tensor Radiation Conditions For Elastic Waves
DEFF Research Database (Denmark)
Krenk, S.; Kirkegaard, Poul Henning
2001-01-01
A local boundary condition is formulated, representing radiation of elastic waves from an arbitrary point source. The boundary condition takes the form of a tensor relation between the stress at a point on an arbitrarily oriented section and the velocity and displacement vectors at the point....... The tensor relation generalizes the traditional normal incidence impedance condition by accounting for the angle between wave propagation and the surface normal and by including a generalized stiffness term due to spreading of the waves. The effectiveness of the local tensor radiation condition...
Scalable Tensor Factorizations with Missing Data
DEFF Research Database (Denmark)
Acar, Evrim; Dunlavy, Daniel M.; Kolda, Tamara G.
2010-01-01
of missing data, many important data sets will be discarded or improperly analyzed. Therefore, we need a robust and scalable approach for factorizing multi-way arrays (i.e., tensors) in the presence of missing data. We focus on one of the most well-known tensor factorizations, CANDECOMP/PARAFAC (CP...... is shown to successfully factor tensors with noise and up to 70% missing data. Moreover, our approach is significantly faster than the leading alternative and scales to larger problems. To show the real-world usefulness of CP-WOPT, we illustrate its applicability on a novel EEG (electroencephalogram...
Surface tensor estimation from linear sections
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel
From Crofton's formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In a design based setting we suggest three types of estimators....... These are based on isotropic uniform random lines, vertical sections, and non-isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting....
Surface tensor estimation from linear sections
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel
2015-01-01
From Crofton’s formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In a design based setting we suggest three types of estimators....... These are based on isotropic uniform random lines, vertical sections, and non-isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting....
Tensor products of higher almost split sequences
Pasquali, Andrea
2015-01-01
We investigate how the higher almost split sequences over a tensor product of algebras are related to those over each factor. Herschend and Iyama gave a precise criterion for when the tensor product of an $n$-representation finite algebra and an $m$-representation finite algebra is $(n+m)$-representation finite. In this case we give a complete description of the higher almost split sequences over the tensor product by expressing every higher almost split sequence as the mapping cone of a suit...
Scalable tensor factorizations for incomplete data
DEFF Research Database (Denmark)
Acar, Evrim; Dunlavy, Daniel M.; KOlda, Tamara G.
2011-01-01
to factorize data sets with missing values with the goal of capturing the underlying latent structure of the data and possibly reconstructing missing values (i.e., tensor completion). We focus on one of the most well-known tensor factorizations that captures multi-linear structure, CANDECOMP/PARAFAC (CP...... experiments, our algorithm is shown to successfully factorize tensors with noise and up to 99% missing data. A unique aspect of our approach is that it scales to sparse large-scale data, e.g., 1000 × 1000 × 1000 with five million known entries (0.5% dense). We further demonstrate the usefulness of CP...
Yoon, Bora; Shim, Yong-S; Hong, Yun-Jeong; Koo, Bang-Bon; Kim, Yong-Duk; Lee, Kee-Ook; Yang, Dong-Won
2011-03-15
Regional atrophy of gray matter (GM) in Alzheimer's disease (AD) is well known; however, the relationship between macroscopic and microscopic changes of cerebral white matter (WM) is uncertain. The aim of this study was to investigate the pattern of GM, WM atrophy, and microscopic WM changes in the same individuals with AD. All subjects (10AD and 15 healthy controls [HC]) underwent a MRI scanning at 1.5 T, including a 3-dimensional volumetric scan and diffusion tensor imaging (DTI). We performed statistical parametric mapping (SPM) with DTI to evaluate the patterns of the microscopic WM changes, as well as voxel-based morphometry (VBM) for GM and WM volume changes between patients with AD and HC. GM atrophy was detected, mainly in posterior regions, and WM atrophy was similarly distributed, but less involved on VBM analysis. Unlike WM atrophy on VBM analysis, microscopic WM changes were shown in the medial frontal, orbitofrontal, splenium of the corpus callosum, and cingulum on DTI analysis with SPM. We demonstrated that the pattern of macroscopic WM atrophy was similar to GM atrophy, while microscopic WM changes had a different pattern and distribution. Our findings suggest that WM atrophy may preferentially reflect the secondary changes of GM atrophy, while microscopic WM changes start earlier in frontal areas before GM and WM atrophy can be detected macroscopically. Copyright © 2010 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
Margaret R Lentz
Full Text Available There are currently no widely accepted neuro-HIV small animal models. We wanted to validate the HIV-1 Transgenic rat (Tg as an appropriate neuro-HIV model and then establish in vivo imaging biomarkers of neuropathology, within this model, using MR structural and diffusion tensor imaging (DTI.Young and middle-aged Tg and control rats were imaged using MRI. A subset of middle-aged animals underwent longitudinal repeat imaging six months later. Total brain volume (TBV, ventricular volume (VV and parenchymal volume (PV = TBV-VV were measured. Fractional anisotropy (FA and mean diffusivity (MD values of the corpus callosum (CC were calculated from DTI data.TBV and PV were smaller in Tg compared to control rats in young and middle-aged cohorts (p0.05.We detected brain volume loss in the Tg rat, probably due to astrocytic dysfunction/loss, loss of structural/axonal matrix and striatal neuronal loss as suggested by immunofluorescence. Increased MD and decreased FA in the CC probably reflect microstructural differences between the Tg and Control rats which could include increased extracellular space between white matter tracts, demyelination and axonal degeneration, among other pathologies. We believe that the Tg rat is an adequate model of neuropathology in HIV and that volumetric MR and DTI measures can be potentially used as biomarkers of disease progression.
Directory of Open Access Journals (Sweden)
Olena G. Filatova
2018-04-01
Full Text Available Better insight into white matter (WM alterations after stroke onset could help to understand the underlying recovery mechanisms and improve future interventions. MR diffusion imaging enables to assess such changes. Our goal was to investigate the relation of WM diffusion characteristics derived from diffusion models of increasing complexity with the motor function of the upper limb. Moreover, we aimed to evaluate the variation of such characteristics across different WM structures of chronic stroke patients in comparison to healthy subjects. Subjects were scanned with a two b-value diffusion-weighted MRI protocol to exploit multiple diffusion models: single tensor, single tensor with isotropic compartment, bi-tensor model, bi-tensor with isotropic compartment. From each model we derived the mean tract fractional anisotropy (FA, mean (MD, radial (RD and axial (AD diffusivities outside the lesion site based on a WM tracts atlas. Asymmetry of these measures was correlated with the Fugl-Meyer upper extremity assessment (FMA score and compared between patient and control groups. Eighteen chronic stroke patients and eight age-matched healthy individuals participated in the study. Significant correlation of the outcome measures with the clinical scores of stroke recovery was found. The lowest correlation of the corticospinal tract FAasymmetry and FMA was with the single tensor model (r = −0.3, p = 0.2 whereas the other models reported results in the range of r = −0.79 ÷ −0.81 and p = 4E-5 ÷ 8E-5. The corticospinal tract and superior longitudinal fasciculus showed most alterations in our patient group relative to controls. Multiple compartment models yielded superior correlation of the diffusion measures and FMA compared to the single tensor model.
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
General projective relativity and the vector-tensor gravitational field
International Nuclear Information System (INIS)
Arcidiacono, G.
1986-01-01
In the general projective relativity, the induced 4-dimensional metric is symmetric in three cases, and we obtain the vector-tensor, the scalar-tensor, and the scalar-vector-tensor theories of gravitation. In this work we examine the vector-tensor theory, similar to the Veblen's theory, but with a different physical interpretation
Tucker tensor analysis of Matern functions in spatial statistics
Litvinenko, Alexander
2018-04-20
Low-rank Tucker tensor methods in spatial statistics 1. Motivation: improve statistical models 2. Motivation: disadvantages of matrices 3. Tools: Tucker tensor format 4. Tensor approximation of Matern covariance function via FFT 5. Typical statistical operations in Tucker tensor format 6. Numerical experiments
TensorFlow Agents: Efficient Batched Reinforcement Learning in TensorFlow
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...
Lilja, Ylva; Gustafsson, Oscar; Ljungberg, Maria; Starck, Göran; Lindblom, Bertil; Skoglund, Thomas; Bergquist, Henrik; Jakobsson, Karl-Erik; Nilsson, Daniel
2017-09-01
OBJECTIVE Despite ample experience in surgical treatment of pituitary adenomas, little is known about objective indices that may reveal risk of visual impairment caused by tumor growth that leads to compression of the anterior visual pathways. This study aimed to explore diffusion tensor imaging (DTI) as a means for objective assessment of injury to the anterior visual pathways caused by pituitary adenomas. METHODS Twenty-three patients with pituitary adenomas, scheduled for transsphenoidal tumor resection, and 20 healthy control subjects were included in the study. A minimum suprasellar tumor extension of Grade 2-4, according to the SIPAP (suprasellar, infrasellar, parasellar, anterior, and posterior) scale, was required for inclusion. Neuroophthalmological examinations, conventional MRI, and DTI were completed in all subjects and were repeated 6 months after surgery. Quantitative assessment of chiasmal lift, visual field defect (VFD), and DTI parameters from the optic tracts was performed. Linear correlations, group comparisons, and prediction models were done in controls and patients. RESULTS Both the degree of VFD and chiasmal lift were significantly correlated with the radial diffusivity (r = 0.55, p visual pathways that were compressed by pituitary adenomas. The correlation between radial diffusivity and visual impairment may reflect a gradual demyelination in the visual pathways caused by an increased tumor effect. The low level of axial diffusivity found in the patient group may represent early atrophy in the visual pathways, detectable on DTI but not by conventional methods. DTI may provide objective data, detect early signs of injury, and be an additional diagnostic tool for determining indication for surgery in cases of pituitary adenomas.
Segmentation of the canine corpus callosum using diffusion-tensor imaging tractography.
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.
International Nuclear Information System (INIS)
Bao, L J; Zhu, Y M; Liu, W Y; Pu, Z B; Magnin, I E; Croisille, P; Robini, M
2009-01-01
Cardiac diffusion tensor magnetic resonance imaging (DT-MRI) is noise sensitive, and the noise can induce numerous systematic errors in subsequent parameter calculations. This paper proposes a sparse representation-based method for denoising cardiac DT-MRI images. The method first generates a dictionary of multiple bases according to the features of the observed image. A segmentation algorithm based on nonstationary degree detector is then introduced to make the selection of atoms in the dictionary adapted to the image's features. The denoising is achieved by gradually approximating the underlying image using the atoms selected from the generated dictionary. The results on both simulated image and real cardiac DT-MRI images from ex vivo human hearts show that the proposed denoising method performs better than conventional denoising techniques by preserving image contrast and fine structures.
Unilateral hypertrophy of tensor fascia lata: a soft tissue tumor simulator
Energy Technology Data Exchange (ETDEWEB)
Ilaslan, H. [Department of Radiology, Mayo Clinic, 200 First Street, 55905, SW Rochester, MN (United States); Department of Radiology A21, Cleveland Clinic, Cleveland, OH (United States); Wenger, D.E. [Department of Radiology, Mayo Clinic, 200 First Street, 55905, SW Rochester, MN (United States); Shives, T.C. [Department of Orthopedic Surgery, Mayo Clinic, Rochester, MN (United States); Unni, K.K. [Department of Laboratory Medicine and Pathology, Mayo Clinic, Rochester, MN (United States)
2003-11-01
To describe the imaging findings in eight cases of unilateral tensor fascia lata (TFL) hypertrophy presenting as soft tissue masses. Imaging studies and medical charts of eight patients were reviewed retrospectively. The imaging studies included five radiographs, five computed tomography (CT) and six magnetic resonance imaging (MRI) examinations. The majority of patients (seven of eight) presented with a palpable proximal anterior thigh mass. One patient was asymptomatic and incidentally diagnosed. There were six females and two males. Ages ranged from 27 to 86 years old (mean 61). MRI and CT showed unilateral enlargement of the TFL muscle in all cases. TFL muscle hypertrophy is an uncommon clinical entity, which can simulate a soft tissue tumor. The characteristic appearance on CT or MRI allows a confident diagnosis of muscle hypertrophy to be made, avoiding unnecessary biopsy or surgical intervention. (orig.)
Unilateral hypertrophy of tensor fascia lata: a soft tissue tumor simulator
International Nuclear Information System (INIS)
Ilaslan, H.; Wenger, D.E.; Shives, T.C.; Unni, K.K.
2003-01-01
To describe the imaging findings in eight cases of unilateral tensor fascia lata (TFL) hypertrophy presenting as soft tissue masses. Imaging studies and medical charts of eight patients were reviewed retrospectively. The imaging studies included five radiographs, five computed tomography (CT) and six magnetic resonance imaging (MRI) examinations. The majority of patients (seven of eight) presented with a palpable proximal anterior thigh mass. One patient was asymptomatic and incidentally diagnosed. There were six females and two males. Ages ranged from 27 to 86 years old (mean 61). MRI and CT showed unilateral enlargement of the TFL muscle in all cases. TFL muscle hypertrophy is an uncommon clinical entity, which can simulate a soft tissue tumor. The characteristic appearance on CT or MRI allows a confident diagnosis of muscle hypertrophy to be made, avoiding unnecessary biopsy or surgical intervention. (orig.)
Ke, Xiaoyan; Tang, Tianyu; Hong, Shanshan; Hang, Yueyue; Zou, Bing; Li, Huiguo; Zhou, Zhenyu; Ruan, Zongcai; Lu, Zuhong; Tao, Guotai; Liu, Yijun
2009-04-10
This study explored white matter abnormalities in a group of Chinese children with high functioning autism (HFA). Twelve male children with HFA and ten matched typically developing children underwent diffusion tensor imaging (DTI) as well three-dimensional T1-weighted MRI for voxel-based morphometry (VBM). We found a significant decrease of the white matter density in the right frontal lobe, left parietal lobe and right anterior cingulate and a significant increase in the right frontal lobe, left parietal lobe and left cingulate gyrus in the HFA group compared with the control group. The HFA group also had decreased FA in the frontal lobe and left temporal lobe. By combining DT-MRI FA and MRI volumetric analyses based on the VBM model, the results showed consistent white matter abnormalities in a group of Chinese children with HFA.
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....
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
Unsupervised Tensor Mining for Big Data Practitioners.
Papalexakis, Evangelos E; Faloutsos, Christos
2016-09-01
Multiaspect data are ubiquitous in modern Big Data applications. For instance, different aspects of a social network are the different types of communication between people, the time stamp of each interaction, and the location associated to each individual. How can we jointly model all those aspects and leverage the additional information that they introduce to our analysis? Tensors, which are multidimensional extensions of matrices, are a principled and mathematically sound way of modeling such multiaspect data. In this article, our goal is to popularize tensors and tensor decompositions to Big Data practitioners by demonstrating their effectiveness, outlining challenges that pertain to their application in Big Data scenarios, and presenting our recent work that tackles those challenges. We view this work as a step toward a fully automated, unsupervised tensor mining tool that can be easily and broadly adopted by practitioners in academia and industry.
Calculus of tensors and differential forms
Sinha, Rajnikant
2014-01-01
Calculus of tensors and differential forms is an introductory-level textbook. Through this book, students will familiarize themselves with tools they need in order to use for further study on general relativity and research, such as affine tensors, tensor calculus on manifolds, relative tensors, Lie derivatives, wedge products, differential forms, and Stokes' theorem. The treatment is concrete and in detail, so that abstract concepts do not deter even physics and engineering students. This self contained book requires undergraduate-level calculus of several variables and linear algebra as prerequisite. Fubini's theorem in real analysis, to be used in Stokes' theorem, has been proved earlier than Stokes' theorem so that students don't have to search elsewhere.
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)
Correlators in tensor models from character calculus
Directory of Open Access Journals (Sweden)
A. Mironov
2017-11-01
Full Text Available We explain how the calculations of [20], which provided the first evidence for non-trivial structures of Gaussian correlators in tensor models, are efficiently performed with the help of the (Hurwitz character calculus. This emphasizes a close similarity between technical methods in matrix and tensor models and supports a hope to understand the emerging structures in very similar terms. We claim that the 2m-fold Gaussian correlators of rank r tensors are given by r-linear combinations of dimensions with the Young diagrams of size m. The coefficients are made from the characters of the symmetric group Sm and their exact form depends on the choice of the correlator and on the symmetries of the model. As the simplest application of this new knowledge, we provide simple expressions for correlators in the Aristotelian tensor model as tri-linear combinations of dimensions.
Loop optimization for tensor network renormalization
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.
An introduction to linear algebra and tensors
Akivis, M A; Silverman, Richard A
1978-01-01
Eminently readable, completely elementary treatment begins with linear spaces and ends with analytic geometry, covering multilinear forms, tensors, linear transformation, and more. 250 problems, most with hints and answers. 1972 edition.
Algebraic classification of the conformal tensor
International Nuclear Information System (INIS)
Ares de Parga, Gonzalo; Chavoya, O.; Lopez B, J.L.; Ovando Z, Gerardo
1989-01-01
Starting from the Petrov matrix method, we deduce a new algorithm (adaptable to computers), within the Newman-Penrose formalism, to obtain the algebraic type of the Weyl tensor in general relativity. (author)
Effects of tensor forces in nuclei
International Nuclear Information System (INIS)
Tanihata, Isao
2013-01-01
Recent studies of nuclei far from the stability line have revealed drastic changes in nuclear orbitals and reported the appearance of new magic numbers and the disappearance of magic numbers observed at the stability line. One of the important reasons for such changes is considered to be because of the effect of tensor forces on nuclear structure. Although the role of tensor forces in binding very light nuclei such as deuterons and 4 He has been known, direct experimental evidence for the effect on nuclear structure is scarce. In this paper, I review known effects of tensor forces in nuclei and then discuss the recently raised question of s–p wave mixing in a halo nucleus of 11 Li. Following these reviews, the development of a new experiment to see the high-momentum components due to the tensor forces is discussed and some of the new data are presented. (paper)
Performance of unscented Kalman filter tractography in edema: Analysis of the two-tensor model.
Liao, Ruizhi; Ning, Lipeng; Chen, Zhenrui; Rigolo, Laura; Gong, Shun; Pasternak, Ofer; Golby, Alexandra J; Rathi, Yogesh; O'Donnell, Lauren J
2017-01-01
Diffusion MRI tractography is increasingly used in pre-operative neurosurgical planning to visualize critical fiber tracts. However, a major challenge for conventional tractography, especially in patients with brain tumors, is tracing fiber tracts that are affected by vasogenic edema, which increases water content in the tissue and lowers diffusion anisotropy. One strategy for improving fiber tracking is to use a tractography method that is more sensitive than the traditional single-tensor streamline tractography. We performed experiments to assess the performance of two-tensor unscented Kalman filter (UKF) tractography in edema. UKF tractography fits a diffusion model to the data during fiber tracking, taking advantage of prior information from the previous step along the fiber. We studied UKF performance in a synthetic diffusion MRI digital phantom with simulated edema and in retrospective data from two neurosurgical patients with edema affecting the arcuate fasciculus and corticospinal tracts. We compared the performance of several tractography methods including traditional streamline, UKF single-tensor, and UKF two-tensor. To provide practical guidance on how the UKF method could be employed, we evaluated the impact of using various seed regions both inside and outside the edematous regions, as well as the impact of parameter settings on the tractography sensitivity. We quantified the sensitivity of different methods by measuring the percentage of the patient-specific fMRI activation that was reached by the tractography. We expected that diffusion anisotropy threshold parameters, as well as the inclusion of a free water model, would significantly influence the reconstruction of edematous WM fiber tracts, because edema increases water content in the tissue and lowers anisotropy. Contrary to our initial expectations, varying the fractional anisotropy threshold and including a free water model did not affect the UKF two-tensor tractography output appreciably in
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.
Geometric decomposition of the conformation tensor in viscoelastic turbulence
Hameduddin, Ismail; Meneveau, Charles; Zaki, Tamer A.; Gayme, Dennice F.
2018-05-01
This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive-definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.
Estimation of Uncertainties of Full Moment Tensors
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
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)
Goldsborough, Peter
2016-01-01
Deep learning is a branch of artificial intelligence employing deep neural network architectures that has significantly advanced the state-of-the-art in computer vision, speech recognition, natural language processing and other domains. In November 2015, Google released $\\textit{TensorFlow}$, an open source deep learning software library for defining, training and deploying machine learning models. In this paper, we review TensorFlow and put it in context of modern deep learning concepts and ...
Geometrical foundations of tensor calculus and relativity
Schuller , Frédéric; Lorent , Vincent
2006-01-01
Manifolds, particularly space curves: basic notions 1 The first groundform, the covariant metric tensor 11 The second groundform, Meusnier's theorem 19 Transformation groups in the plane 28 Co- and contravariant components for a special affine transformation in the plane 29 Surface vectors 32 Elements of tensor calculus 36 Generalization of the first groundform to the space 46 The covariant (absolute) derivation 57 Examples from elasticity theory 61 Geodesic lines 63 Main curvatur...
Measuring Nematic Susceptibilities from the Elastoresistivity Tensor
Hristov, A. T.; Shapiro, M. C.; Hlobil, Patrick; Maharaj, Akash; Chu, Jiun-Haw; Fisher, Ian
The elastoresistivity tensor mijkl relates changes in resistivity to the strain on a material. As a fourth-rank tensor, it contains considerably more information about the material than the simpler (second-rank) resistivity tensor; in particular, certain elastoresistivity coefficients can be related to thermodynamic susceptibilities and serve as a direct probe of symmetry breaking at a phase transition. The aim of this talk is twofold. First, we enumerate how symmetry both constrains the structure of the elastoresistivity tensor into an easy-to-understand form and connects tensor elements to thermodynamic susceptibilities. In the process, we generalize previous studies of elastoresistivity to include the effects of magnetic field. Second, we describe an approach to measuring quantities in the elastoresistivity tensor with a novel transverse measurement, which is immune to relative strain offsets. These techniques are then applied to BaFe2As2 in a proof of principle measurement. This work is supported by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515.
Kim, Jinna
2010-01-01
Purpose Diffusion tensor imaging provides better understanding of pathophysiology of congenital anomalies, involving central nervous system. This study was aimed to specify the pathogenetic mechanism of heterotopia, proved by diffusion tensor imaging, and establish new findings of heterotopia on fractional anisotropy maps. Materials and Methods Diffusion-weighted imaging data from 11 patients (M : F = 7 : 4, aged from 1 to 22 years, mean = 12.3 years) who visited the epilepsy clinic and received a routine seizure protocol MRI exam were retrospectively analyzed. Fractional anisotropy (FA) maps were generated from diffusion tensor imaging of 11 patients with heterotopia. Regions of interests (ROI) were placed in cerebral cortex, heterotopic gray matter and deep gray matter, including putamen. ANOVA analysis was performed for comparison of different gray matter tissues. Results Heterotopic gray matter showed signal intensities similar to normal gray matter on T1 and T2 weighted MRI. The measured FA of heterotopic gray matter was higher than that of cortical gray matter (0.236 ± 0.011 vs. 0.169 ± 0.015, p < 0.01, one way ANOVA), and slightly lower than that of deep gray matter (0.236 ± 0.011 vs. 0.259 ± 0.016, p < 0.01). Conclusion Increased FA of heterotopic gray matter suggests arrested neuron during radial migration and provides better understanding of neurodevelopment. PMID:20499428
On the concircular curvature tensor of Riemannian manifolds
International Nuclear Information System (INIS)
Rahman, M.S.; Lal, S.
1990-06-01
Definition of the concircular curvature tensor, Z hijk , along with Z-tensor, Z ij , is given and some properties of Z hijk are described. Tensors identical with Z hijk are shown. A necessary and sufficient condition that a Riemannian V n has zero Z-tensor is found. A number of theorems on concircular symmetric space, concircular recurrent space (Z n -space) and Z n -space with zero Z-tensor are deduced. (author). 6 refs
(Ln-bar, g)-spaces. Special tensor fields
International Nuclear Information System (INIS)
Manoff, S.; Dimitrov, B.
1998-01-01
The Kronecker tensor field, the contraction tensor field, as well as the multi-Kronecker and multi-contraction tensor fields are determined and the action of the covariant differential operator, the Lie differential operator, the curvature operator, and the deviation operator on these tensor fields is established. The commutation relations between the operators Sym and Asym and the covariant and Lie differential operators are considered acting on symmetric and antisymmetric tensor fields over (L n bar, g)-spaces
Reliable Dual Tensor Model Estimation in Single and Crossing Fibers Based on Jeffreys Prior
Yang, Jianfei; Poot, Dirk H. J.; Caan, Matthan W. A.; Su, Tanja; Majoie, Charles B. L. M.; van Vliet, Lucas J.; Vos, Frans M.
2016-01-01
Purpose This paper presents and studies a framework for reliable modeling of diffusion MRI using a data-acquisition adaptive prior. Methods Automated relevance determination estimates the mean of the posterior distribution of a rank-2 dual tensor model exploiting Jeffreys prior (JARD). This data-acquisition prior is based on the Fisher information matrix and enables the assessment whether two tensors are mandatory to describe the data. The method is compared to Maximum Likelihood Estimation (MLE) of the dual tensor model and to FSL’s ball-and-stick approach. Results Monte Carlo experiments demonstrated that JARD’s volume fractions correlated well with the ground truth for single and crossing fiber configurations. In single fiber configurations JARD automatically reduced the volume fraction of one compartment to (almost) zero. The variance in fractional anisotropy (FA) of the main tensor component was thereby reduced compared to MLE. JARD and MLE gave a comparable outcome in data simulating crossing fibers. On brain data, JARD yielded a smaller spread in FA along the corpus callosum compared to MLE. Tract-based spatial statistics demonstrated a higher sensitivity in detecting age-related white matter atrophy using JARD compared to both MLE and the ball-and-stick approach. Conclusions The proposed framework offers accurate and precise estimation of diffusion properties in single and dual fiber regions. PMID:27760166
Gaussian mixtures on tensor fields for segmentation: applications to medical imaging.
de Luis-García, Rodrigo; Westin, Carl-Fredrik; Alberola-López, Carlos
2011-01-01
In this paper, we introduce a new approach for tensor field segmentation based on the definition of mixtures of Gaussians on tensors as a statistical model. Working over the well-known Geodesic Active Regions segmentation framework, this scheme presents several interesting advantages. First, it yields a more flexible model than the use of a single Gaussian distribution, which enables the method to better adapt to the complexity of the data. Second, it can work directly on tensor-valued images or, through a parallel scheme that processes independently the intensity and the local structure tensor, on scalar textured images. Two different applications have been considered to show the suitability of the proposed method for medical imaging segmentation. First, we address DT-MRI segmentation on a dataset of 32 volumes, showing a successful segmentation of the corpus callosum and favourable comparisons with related approaches in the literature. Second, the segmentation of bones from hand radiographs is studied, and a complete automatic-semiautomatic approach has been developed that makes use of anatomical prior knowledge to produce accurate segmentation results. Copyright © 2010 Elsevier Ltd. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Espy, Michelle A. [Los Alamos National Laboratory
2012-06-29
This project proposes to: (1) provide the power of MRI to situations where it presently isn't available; (2) perform the engineering required to move from lab to a functional prototype; and (3) leverage significant existing infrastructure and capability in ultra-low field MRI. The reasons for doing this: (1) MRI is the most powerful tool for imaging soft-tissue (e.g. brain); (2) Billions don't have access due to cost or safety issues; (3) metal will heat/move in high magnetic fields; (4) Millions of cases of traumatic brain injury in US alone; (5) even more of non-traumatic brain injury; (6) (e.g. stroke, infection, chemical exposure); (7) Need for early diagnostic; (8) 'Signature' wound of recent conflicts; (9) 22% of injuries; (10) Implications for post-traumatic stress disorder; and (11) chronic traumatic encephalopathy.
International Nuclear Information System (INIS)
Espy, Michelle A.
2012-01-01
This project proposes to: (1) provide the power of MRI to situations where it presently isn't available; (2) perform the engineering required to move from lab to a functional prototype; and (3) leverage significant existing infrastructure and capability in ultra-low field MRI. The reasons for doing this: (1) MRI is the most powerful tool for imaging soft-tissue (e.g. brain); (2) Billions don't have access due to cost or safety issues; (3) metal will heat/move in high magnetic fields; (4) Millions of cases of traumatic brain injury in US alone; (5) even more of non-traumatic brain injury; (6) (e.g. stroke, infection, chemical exposure); (7) Need for early diagnostic; (8) 'Signature' wound of recent conflicts; (9) 22% of injuries; (10) Implications for post-traumatic stress disorder; and (11) chronic traumatic encephalopathy.
International Nuclear Information System (INIS)
Papma, Janne M.; Koudstaal, Peter J.; Swieten, John C. van; Smits, Marion; Lugt, Aad van der; Groot, Marius de; Vrooman, Henri A.; Mattace Raso, Francesco U.; Niessen, Wiro J.; Veen, Frederik M. van der; Prins, Niels D.
2017-01-01
Diminished function of the posterior cingulate cortex (PCC) is a typical finding in early Alzheimer's disease (AD). It is hypothesized that in early stage AD, PCC functioning relates to or reflects hippocampal dysfunction or atrophy. The aim of this study was to examine the relationship between hippocampus function, volume and structural connectivity, and PCC activation during an episodic memory task-related fMRI study in mild cognitive impairment (MCI). MCI patients (n = 27) underwent episodic memory task-related fMRI, 3D-T1w MRI, 2D T2-FLAIR MRI and diffusion tensor imaging. Stepwise linear regression analysis was performed to examine the relationship between PCC activation and hippocampal activation, hippocampal volume and diffusion measures within the cingulum along the hippocampus. We found a significant relationship between PCC and hippocampus activation during successful episodic memory encoding and correct recognition in MCI patients. We found no relationship between the PCC and structural hippocampal predictors. Our results indicate a relationship between PCC and hippocampus activation during episodic memory engagement in MCI. This may suggest that during episodic memory, functional network deterioration is the most important predictor of PCC functioning in MCI. (orig.)
Papma, Janne M; Smits, Marion; de Groot, Marius; Mattace Raso, Francesco U; van der Lugt, Aad; Vrooman, Henri A; Niessen, Wiro J; Koudstaal, Peter J; van Swieten, John C; van der Veen, Frederik M; Prins, Niels D
2017-09-01
Diminished function of the posterior cingulate cortex (PCC) is a typical finding in early Alzheimer's disease (AD). It is hypothesized that in early stage AD, PCC functioning relates to or reflects hippocampal dysfunction or atrophy. The aim of this study was to examine the relationship between hippocampus function, volume and structural connectivity, and PCC activation during an episodic memory task-related fMRI study in mild cognitive impairment (MCI). MCI patients (n = 27) underwent episodic memory task-related fMRI, 3D-T1w MRI, 2D T2-FLAIR MRI and diffusion tensor imaging. Stepwise linear regression analysis was performed to examine the relationship between PCC activation and hippocampal activation, hippocampal volume and diffusion measures within the cingulum along the hippocampus. We found a significant relationship between PCC and hippocampus activation during successful episodic memory encoding and correct recognition in MCI patients. We found no relationship between the PCC and structural hippocampal predictors. Our results indicate a relationship between PCC and hippocampus activation during episodic memory engagement in MCI. This may suggest that during episodic memory, functional network deterioration is the most important predictor of PCC functioning in MCI. • PCC functioning during episodic memory relates to hippocampal functioning in MCI. • PCC functioning during episodic memory does not relate to hippocampal structure in MCI. • Functional network changes are an important predictor of PCC functioning in MCI.
Energy Technology Data Exchange (ETDEWEB)
Papma, Janne M.; Koudstaal, Peter J.; Swieten, John C. van [Erasmus MC - University Medical Center Rotterdam, Department of Neurology, Rotterdam (Netherlands); Smits, Marion; Lugt, Aad van der [Erasmus MC - University Medical Center Rotterdam, Department of Radiology, Rotterdam (Netherlands); Groot, Marius de; Vrooman, Henri A. [Erasmus MC - University Medical Center Rotterdam, Department of Radiology, Rotterdam (Netherlands); Erasmus MC - University Medical Center Rotterdam, Department of Medical Informatics, Rotterdam (Netherlands); Mattace Raso, Francesco U. [Erasmus MC - University Medical Center Rotterdam, Department of Geriatrics, Rotterdam (Netherlands); Niessen, Wiro J. [Erasmus MC - University Medical Center Rotterdam, Department of Radiology, Rotterdam (Netherlands); Erasmus MC - University Medical Center Rotterdam, Department of Medical Informatics, Rotterdam (Netherlands); Delft University of Technology, Faculty of Applied Sciences, Delft (Netherlands); Veen, Frederik M. van der [Erasmus University Rotterdam, Institute of Psychology, Rotterdam (Netherlands); Prins, Niels D. [VU University Medical Center, Alzheimer Center, Department of Neurology, Amsterdam (Netherlands)
2017-09-15
Diminished function of the posterior cingulate cortex (PCC) is a typical finding in early Alzheimer's disease (AD). It is hypothesized that in early stage AD, PCC functioning relates to or reflects hippocampal dysfunction or atrophy. The aim of this study was to examine the relationship between hippocampus function, volume and structural connectivity, and PCC activation during an episodic memory task-related fMRI study in mild cognitive impairment (MCI). MCI patients (n = 27) underwent episodic memory task-related fMRI, 3D-T1w MRI, 2D T2-FLAIR MRI and diffusion tensor imaging. Stepwise linear regression analysis was performed to examine the relationship between PCC activation and hippocampal activation, hippocampal volume and diffusion measures within the cingulum along the hippocampus. We found a significant relationship between PCC and hippocampus activation during successful episodic memory encoding and correct recognition in MCI patients. We found no relationship between the PCC and structural hippocampal predictors. Our results indicate a relationship between PCC and hippocampus activation during episodic memory engagement in MCI. This may suggest that during episodic memory, functional network deterioration is the most important predictor of PCC functioning in MCI. (orig.)
Complex Wavelet transform for MRI
International Nuclear Information System (INIS)
Junor, P.; Janney, P.
2004-01-01
-tree complex wavelet transform (DTCWT) is an example of an over-complete or expansive wavelet transform. Compared with the Discrete Wavelet Transform it has the advantage of spatial invariance and directional selectivity though with greater computational burden. This processing load can be redressed by hardware approaches if necessary. It has recently been used for diffusion tensor imaging, but it has yet to be determined if it is optimal for the particular noise characteristics encountered in MRI (typically Rician-distributed amplitude distribution at low SNR, and with a 1/f, rather than exclusively white, spectral density suggested for some modalities). The complex wavelet transform offers a new possibility for MRI processing: the improved spatial invariance and directional selectivity promising both shorter overall acquisition time and improved image quality. Copyright (2004) Australasian College of Physical Scientists and Engineers in Medicine
International Nuclear Information System (INIS)
Prayer, D.; Brugger, P.C.
2004-01-01
New, ultrafast sequences have made it possible to obtain MR images of the fetus without maternal sedation or immobilization of the fetus itself. While fetal MRI began as an adjunct to ultrasound, it has now been shown that MRI can provide additional information that may change prognosis, the management of pregnancy, or the treatment of the newborn child. It is of particular value in the assessment of malformations of the central nervous system. The steady development and adaptation of MR-sequences to the needs of fetal imaging has led to new indications that can support prognostic and therapeutic decisions. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Harada, Junta; Dohi, Michiko; Yoshihiro, Akiko; Mogami, Takuji; Kuwada, Tomoko; Nakata, Norio [Jikei Univ., Chiba (Japan). Kashiwa Hospital
2000-06-01
Open type MR system and fast sequence is now available and MRI becomes a new modality for interventional Radiology, including biopsy, drainage operation, and monitoring for minimally invasive therapy. Experimental studies of temperature monitoring were performed under hot and cold status. Signal changes of porcine disc and meat under microwave and laser ablation were observed as low signal area by signal intensity method. Using proton chemical shift method, signal change by laser ablation was displaced color imaging and correlated with thermometric temperature measurement. The very T2 relaxation time of ice affords excellent contrast between ice and surrounding gelatin tissue allowing acute depiction of the extent of the iceball under MRI. (author)
Energy Technology Data Exchange (ETDEWEB)
Prayer, D.; Brugger, P.C. [University Hospital of Vienna (Austria). Division of Neuroradiology
2004-07-01
New, ultrafast sequences have made it possible to obtain MR images of the fetus without maternal sedation or immobilization of the fetus itself. While fetal MRI began as an adjunct to ultrasound, it has now been shown that MRI can provide additional information that may change prognosis, the management of pregnancy, or the treatment of the newborn child. It is of particular value in the assessment of malformations of the central nervous system. The steady development and adaptation of MR-sequences to the needs of fetal imaging has led to new indications that can support prognostic and therapeutic decisions. (orig.)
Advances in MRI diagnosis of prostate cancer
International Nuclear Information System (INIS)
Zhang Longmin; Liu Ailian
2014-01-01
Prostate cancer is the second most common cancer in the world, and the incidence of prostate cancer in China shows an upward trend. MRI has high soft tissue resolution and multi-dimensional imaging advantages, and it can better show the anatomy of the prostate and adjacent tissue structures. With the development of MR technique, it plays a more and more important role in prostate cancer diagnosis. This review starts from the imaging performance of routine MRI sequence of prostate cancer, and a variety of functional MRI applications in the diagnosis and differential diagnosis of prostate cancer are described in detail, such as MR perfusion-weighted imaging, MR spectroscopy, MR diffusion-weighted imaging, MR diffusion tensor imaging, intravoxel incoherent motion diffusion-weighted imaging, MR susceptibility-weighted imaging. Meanwhile this review introduces that functional MRI has more advantages and can provide more image information than routine MRI sequence. According to a series of semi-quantitative and quantitative data, functional MRI can further provide the blood perfusion of prostate cancer, water molecule diffusion and microcirculation state, metabolism and biochemical composition change information. (authors)
Marin Quintero, Maider J.
2013-01-01
The structure tensor for vector valued images is most often defined as the average of the scalar structure tensors in each band. The problem with this definition is the assumption that all bands provide the same amount of edge information giving them the same weights. As a result non-edge pixels can be reinforced and edges can be weakened…
Tensor network state correspondence and holography
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.
Sundram, Frederick; Campbell, Linda E.; Azuma, Rayna; Daly, Eileen; Bloemen, Oswald J. N.; Barker, Gareth J.; Chitnis, Xavier; Jones, Derek K.; van Amelsvoort, Therese; Murphy, Kieran C.; Murphy, Declan G. M.
2010-01-01
Young people with 22q11 Deletion Syndrome (22q11DS) are at substantial risk for developing psychosis and have significant differences in white matter (WM) volume. However, there are few in vivo studies of both WM microstructural integrity (as measured using Diffusion Tensor (DT)-MRI) and WM volume
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…
Chen, Zhenrui; Tie, Yanmei; Olubiyi, Olutayo; Rigolo, Laura; Mehrtash, Alireza; Norton, Isaiah; Pasternak, Ofer; Rathi, Yogesh; Golby, Alexandra J; O'Donnell, Lauren J
2015-01-01
Diffusion imaging tractography is increasingly used to trace critical fiber tracts in brain tumor patients to reduce the risk of post-operative neurological deficit. However, the effects of peritumoral edema pose a challenge to conventional tractography using the standard diffusion tensor model. The aim of this study was to present a novel technique using a two-tensor unscented Kalman filter (UKF) algorithm to track the arcuate fasciculus (AF) in brain tumor patients with peritumoral edema. Ten right-handed patients with left-sided brain tumors in the vicinity of language-related cortex and evidence of significant peritumoral edema were retrospectively selected for the study. All patients underwent 3-Tesla magnetic resonance imaging (MRI) including a diffusion-weighted dataset with 31 directions. Fiber tractography was performed using both single-tensor streamline and two-tensor UKF tractography. A two-regions-of-interest approach was applied to perform the delineation of the AF. Results from the two different tractography algorithms were compared visually and quantitatively. Using single-tensor streamline tractography, the AF appeared disrupted in four patients and contained few fibers in the remaining six patients. Two-tensor UKF tractography delineated an AF that traversed edematous brain areas in all patients. The volume of the AF was significantly larger on two-tensor UKF than on single-tensor streamline tractography (p tensor UKF tractography provides the ability to trace a larger volume AF than single-tensor streamline tractography in the setting of peritumoral edema in brain tumor patients.
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)
Structural MRI correlates of amyotrophic lateral sclerosis progression.
Senda, Joe; Atsuta, Naoki; Watanabe, Hirohisa; Bagarinao, Epifanio; Imai, Kazunori; Yokoi, Daichi; Riku, Yuichi; Masuda, Michihito; Nakamura, Ryoichi; Watanabe, Hazuki; Ito, Mizuki; Katsuno, Masahisa; Naganawa, Shinji; Sobue, Gen
2017-11-01
Amyotrophic lateral sclerosis (ALS) presents with varying degrees of brain degeneration that can extend beyond the corticospinal tract (CST). Furthermore, the clinical course and progression of ALS varies widely. Brain degeneration detected using structural MRI could reflect disease progression. On study registration, 3-Tesla volumetric MRI and diffusion tensor imaging scans were obtained at baseline in 38 healthy controls and 67 patients with sporadic ALS. Patients had Amyotrophic Lateral Sclerosis Functional Rating Scale-Revised (ALSFRS-R) scores of ≥36 and did not have the chromosome 9, open reading frame 72 repeat expansion. Six months later, changes in ALSFRS-R (ΔALSFRS-R) scores were calculated and patients were grouped into three categories, namely, patients with slow progression with ΔALSFRS-R scores ≤3 (n=19), intermediate progression with ΔALSFRS-R scores =4, 5 and 6 (n=36) and rapid progression with ΔALSFRS-R scores ≥7 (n=12). We analysed voxel-based morphometry and tract-based spatial statistics among these subgroups and controls. In comparison with controls, patients with ALS showed grey matter atrophy and decreased fractional anisotropy beyond the motor cortex and CST, especially in the frontotemporal lobes and basal ganglia. Moreover, the degree of change was highly proportional to ΔALSFRS-R at the 6-month assessment. A more rapid disease progression and poorer functional decline were associated with greater involvement of the extra-motor cortex and basal ganglia, suggesting that the spatial extent of brain involvement can be an indicator of the progression in ALS. © Article author(s) (or their employer(s) unless otherwise stated in the text of the article) 2017. All rights reserved. No commercial use is permitted unless otherwise expressly granted.
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
Impact of time-of-day on diffusivity measures of brain tissue derived from diffusion tensor imaging.
Thomas, Cibu; Sadeghi, Neda; Nayak, Amrita; Trefler, Aaron; Sarlls, Joelle; Baker, Chris I; Pierpaoli, Carlo
2018-06-01
Diurnal fluctuations in MRI measures of structural and functional properties of the brain have been reported recently. These fluctuations may have a physiological origin, since they have been detected using different MRI modalities, and cannot be explained by factors that are typically known to confound MRI measures. While preliminary evidence suggests that measures of structural properties of the brain based on diffusion tensor imaging (DTI) fluctuate as a function of time-of-day (TOD), the underlying mechanism has not been investigated. Here, we used a longitudinal within-subjects design to investigate the impact of time-of-day on DTI measures. In addition to using the conventional monoexponential tensor model to assess TOD-related fluctuations, we used a dual compartment tensor model that allowed us to directly assess if any change in DTI measures is due to an increase in CSF/free-water volume fraction or due to an increase in water diffusivity within the parenchyma. Our results show that Trace or mean diffusivity, as measured using the conventional monoexponential tensor model tends to increase systematically from morning to afternoon scans at the interface of grey matter/CSF, most prominently in the major fissures and the sulci of the brain. Interestingly, in a recent study of the glymphatic system, these same regions were found to show late enhancement after intrathecal injection of a CSF contrast agent. The increase in Trace also impacts DTI measures of diffusivity such as radial and axial diffusivity, but does not affect fractional anisotropy. The dual compartment analysis revealed that the increase in diffusivity measures from PM to AM was driven by an increase in the volume fraction of CSF-like free-water. Taken together, our findings provide important insight into the likely physiological origins of diurnal fluctuations in MRI measurements of structural properties of the brain. Published by Elsevier Inc.
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)
Energy-momentum tensor in the fermion-pairing model
International Nuclear Information System (INIS)
Kawati, S.; Miyata, H.
1980-01-01
The symmetric energy-momentum tensor for the self-interacting fermion theory (psi-barpsi) 2 is expressed in terms of the collective mode within the Hartree approximation. The divergent part of the energy-momentum tensor for the fermion theory induces an effective energy-momentum tensor for the collective mode, and this effective energy-momentum tensor automatically has the Callan-Coleman-Jackiw improved form. The renormalized energy-momentum tensor is structurally equivalent to the Callan-Coleman-Jackiw improved tensor for the Yukawa theory
(Ln-bar, g)-spaces. Ordinary and tensor differentials
International Nuclear Information System (INIS)
Manoff, S.; Dimitrov, B.
1998-01-01
Different types of differentials as special cases of differential operators acting on tensor fields over (L n bar, g)-spaces are considered. The ordinary differential, the covariant differential as a special case of the covariant differential operator, and the Lie differential as a special case of the Lie differential operator are investigated. The tensor differential and its special types (Covariant tensor differential, and Lie tensor differential) are determined and their properties are discussed. Covariant symmetric and antisymmetric (external) tensor differentials, Lie symmetric, and Lie antisymmetric (external) tensor differentials are determined and considered over (L n bar, g)-spaces
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
Federated Tensor Factorization for Computational Phenotyping
Kim, Yejin; Sun, Jimeng; Yu, Hwanjo; Jiang, Xiaoqian
2017-01-01
Tensor factorization models offer an effective approach to convert massive electronic health records into meaningful clinical concepts (phenotypes) for data analysis. These models need a large amount of diverse samples to avoid population bias. An open challenge is how to derive phenotypes jointly across multiple hospitals, in which direct patient-level data sharing is not possible (e.g., due to institutional policies). In this paper, we developed a novel solution to enable federated tensor factorization for computational phenotyping without sharing patient-level data. We developed secure data harmonization and federated computation procedures based on alternating direction method of multipliers (ADMM). Using this method, the multiple hospitals iteratively update tensors and transfer secure summarized information to a central server, and the server aggregates the information to generate phenotypes. We demonstrated with real medical datasets that our method resembles the centralized training model (based on combined datasets) in terms of accuracy and phenotypes discovery while respecting privacy. PMID:29071165
Tensor calculus for engineers and physicists
de Souza Sánchez Filho, Emil
2016-01-01
This textbook provides a rigorous approach to tensor manifolds in several aspects relevant for Engineers and Physicists working in industry or academia. With a thorough, comprehensive, and unified presentation, this book offers insights into several topics of tensor analysis, which covers all aspects of N dimensional spaces. The main purpose of this book is to give a self-contained yet simple, correct and comprehensive mathematical explanation of tensor calculus for undergraduate and graduate students and for professionals. In addition to many worked problems, this book features a selection of examples, solved step by step. Although no emphasis is placed on special and particular problems of Engineering or Physics, the text covers the fundamentals of these fields of science. The book makes a brief introduction into the basic concept of the tensorial formalism so as to allow the reader to make a quick and easy review of the essential topics that enable having the grounds for the subsequent themes, without need...
Exploring extra dimensions through inflationary tensor modes
Im, Sang Hui; Nilles, Hans Peter; Trautner, Andreas
2018-03-01
Predictions of inflationary schemes can be influenced by the presence of extra dimensions. This could be of particular relevance for the spectrum of gravitational waves in models where the extra dimensions provide a brane-world solution to the hierarchy problem. Apart from models of large as well as exponentially warped extra dimensions, we analyze the size of tensor modes in the Linear Dilaton scheme recently revived in the discussion of the "clockwork mechanism". The results are model dependent, significantly enhanced tensor modes on one side and a suppression on the other. In some cases we are led to a scheme of "remote inflation", where the expansion is driven by energies at a hidden brane. In all cases where tensor modes are enhanced, the requirement of perturbativity of gravity leads to a stringent upper limit on the allowed Hubble rate during inflation.
On an uninterpretated tensor in Dirac's theory
International Nuclear Information System (INIS)
Costa de Beauregard, O.
1989-01-01
Franz, in 1935, deduced systematically from the Dirac equation 10 tensorial equations, 5 with a mechanical interpretation, 5 with an electromagnetic interpretation, which are also consequences of Kemmer's formalism for spins 1 and 0; Durand, in 1944, operating similarly with the second order Dirac equation, obtained, 10 equations, 5 of which expressing the divergences of the Gordon type tensors. Of these equations, together with the tensors they imply, some are easily interpreted by reference to the classical theories, some other remain uniterpreted. Recently (1988) we proposed a theory of the coupling between Einstein's gravity field and the 5 Franz mechanical equations, yielding as a bonus the complete interpretation of the 5 Franz mechanical equations. This is an incitation to reexamine the 5 electromagnetic equations. We show here that two of these, together with one of the Durand equations, implying the same tensor, remain uninterpreted. This is proposed as a challenge to the reader's sagacity [fr
The Riemann-Lovelock curvature tensor
International Nuclear Information System (INIS)
Kastor, David
2012-01-01
In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k ≤ D < 4k. In D = 2k + 1 this identity implies that all solutions of pure kth-order Lovelock gravity are 'Riemann-Lovelock' flat. It is verified that the static, spherically symmetric solutions of these theories, which are missing solid angle spacetimes, indeed satisfy this flatness property. This generalizes results from Einstein gravity in D = 3, which corresponds to the k = 1 case. We speculate about some possible further consequences of Riemann-Lovelock curvature. (paper)
Nonlocal elasticity tensors in dislocation and disclination cores
International Nuclear Information System (INIS)
Taupin, V.; Gbemou, K.; Fressengeas, C.; Capolungo, L.
2017-01-01
We introduced nonlocal elastic constitutive laws for crystals containing defects such as dislocations and disclinations. Additionally, the pointwise elastic moduli tensors adequately reflect the elastic response of defect-free regions by relating stresses to strains and couple-stresses to curvatures, elastic cross-moduli tensors relating strains to couple-stresses and curvatures to stresses within convolution integrals are derived from a nonlocal analysis of strains and curvatures in the defects cores. Sufficient conditions are derived for positive-definiteness of the resulting free energy, and stability of elastic solutions is ensured. The elastic stress/couple stress fields associated with prescribed dislocation/disclination density distributions and solving the momentum and moment of momentum balance equations in periodic media are determined by using a Fast Fourier Transform spectral method. Here, the convoluted cross-moduli bring the following results: (i) Nonlocal stresses and couple stresses oppose their local counterparts in the defects core regions, playing the role of restoring forces and possibly ensuring spatio-temporal stability of the simulated defects, (ii) The couple stress fields are strongly affected by nonlocality. Such effects favor the stability of the simulated grain boundaries and allow investigating their elastic interactions with extrinsic defects, (iii) Driving forces inducing grain growth or refinement derive from the self-stress and couple stress fields of grain boundaries in nanocrystalline configurations.
Aspects of the Antisymmetric Tensor Field
Lahiri, Amitabha
1991-02-01
With the possible exception of gravitation, fundamental interactions are generally described by theories of point particles interacting via massless gauge fields. Since the advent of string theories the picture of physical interaction has changed to accommodate one in which extended objects interact with each other. The generalization of the gauge theories to extended objects leads to theories of antisymmetric tensor fields. At scales corresponding to present-day laboratory experiments one expects to see only point particles, their interactions modified by the presence of antisymmetric tensor fields in the theory. Therefore, in order to establish the validity of any theory with antisymmetric tensor fields one needs to look for manifestations of these fields at low energies. The principal problem of gauge theories is the failure to provide a suitable explanation for the generation of masses for the fields in the theory. While there is a known mechanism (spontaneous symmetry breaking) for generating masses for both the matter fields and the gauge fields, the lack of experimental evidence in support of an elementary scalar field suggests that one look for alternative ways of generating masses for the fields. The interaction of gauge fields with an antisymmetric tensor field seems to be an attractive way of doing so, especially since all indications point to the possibility that there will be no remnant degrees of freedom. On the other hand the interaction of such a field with black holes suggest an independent way of verifying the existence of such fields. In this dissertation the origins of the antisymmetric tensor field are discussed in terms of string theory. The interaction of black holes with such a field is discussed next. The last chapter discusses the effects of an antisymmetric tensor field on quantum electrodynamics when the fields are minimally coupled.
Tensor hypercontraction. II. Least-squares renormalization
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.
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
Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery.
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.
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...
Improving Tensor Based Recommenders with Clustering
DEFF Research Database (Denmark)
Leginus, Martin; Dolog, Peter; Zemaitis, Valdas
2012-01-01
Social tagging systems (STS) model three types of entities (i.e. tag-user-item) and relationships between them are encoded into a 3-order tensor. Latent relationships and patterns can be discovered by applying tensor factorization techniques like Higher Order Singular Value Decomposition (HOSVD),...... of the recommendations and execution time are improved and memory requirements are decreased. The clustering is motivated by the fact that many tags in a tag space are semantically similar thus the tags can be grouped. Finally, promising experimental results are presented...
Tensor modes in pure natural inflation
Nomura, Yasunori; Yamazaki, Masahito
2018-05-01
We study tensor modes in pure natural inflation [1], a recently-proposed inflationary model in which an axionic inflaton couples to pure Yang-Mills gauge fields. We find that the tensor-to-scalar ratio r is naturally bounded from below. This bound originates from the finiteness of the number of metastable branches of vacua in pure Yang-Mills theories. Details of the model can be probed by future cosmic microwave background experiments and improved lattice gauge theory calculations of the θ-angle dependence of the vacuum energy.
International Nuclear Information System (INIS)
Poncelet, B.; Baleriiaux, D.; struyven, J.; Segebarth, C.
1989-01-01
In MRI angiography two basis images are measured which only differ by the signal intensity of the flowing blood in the vessels. Subtraction of these two images produces a high contrast-to-noise representation of the vessels. Contrast between stationary tissues and flowing blood is changed, for one image compared to the second one, using a selective modification of the phase of the signal from the flowing blood, and/or using a selective modification of its longitudinal magnetization: The macroscopic spin motions along the selection and the measurement gradient directions affect the phase of the nuclear signal; assuming constant velocity, the phase is proportional to the velocity and to the first moment of the gradient waveforms applied. This work concentrates on the generarion of MRI angiograms, following a phase-based approach, of the carotid bifurcation and of different intracranical regions including the carotid syphon and the circle of Willis. (author). 21 refs.; 3 figs
DEFF Research Database (Denmark)
Jensen, Morten B; Guldberg, Trine L; Harbøll, Anja
2017-01-01
the microscopic tumor cell spread. Gliomas favor spread along the white matter fiber tracts. Tumor growth models incorporating the MRI diffusion tensors (DTI) allow to account more consistently for the glioma growth. The aim of the study was to investigate the potential of a DTI driven growth model to improve...... target definition in glioblastoma (GBM). MATERIAL AND METHODS: Eleven GBM patients were scanned using T1w, T2w FLAIR, T1w + Gd and DTI. The brain was segmented into white matter, gray matter and cerebrospinal fluid. The Fisher-Kolmogorov growth model was used assuming uniform proliferation...
DEFF Research Database (Denmark)
Laustsen, Christoffer
The basic idea was to use MRI to produce a sequence of 3D gray scale image slices of various animals, subsequentlyimaged with a clinical CT system. For this purpose, these animals were used: toad, lungfish, python snake and a horseshoe crab. Each animal was sacrificed according to standard...... visually inspected, both in 2D and 3D, and compared with photographs and anatomy atlases found at library and on the internet....
Tucker Tensor analysis of Matern functions in spatial statistics
Litvinenko, Alexander; Keyes, David E.; Khoromskaia, Venera; Khoromskij, Boris N.; Matthies, Hermann G.
2018-01-01
in a low-rank tensor format. We apply the Tucker and canonical tensor decompositions to a family of Matern- and Slater-type functions with varying parameters and demonstrate numerically that their approximations exhibit exponentially fast convergence
Clinical application of functional MRI
International Nuclear Information System (INIS)
Taniwaki, Takayuki
2010-01-01
Described is the present state of clinical application of fMRI in the preoperative assessment of brain tumors, and plasticity in and pathophysiology of central diseases. For the tumor resection, fMRI is useful for risk assessment of postoperative nerve dysfunction, for selection of the patient rather suitable for brain mapping at the invasive surgery than at the pre-operation and for guidance of the operation itself. Preoperative fMRI alone can neither distinguish the regions of the primary and secondary functions nor exhibit the relation between the tumor and white matter fibers but there are compensatory means for these drawbacks. Benefit of preoperative fMRI has not yet been based on the evidence on double blind trials. Combination of fMRI imaging and electroencephalography (EEG) finding has shown that, in generalized epilepsy, extensive and stimulated activation occurs in both frontal/occipital regions and in thalamus area, respectively, and that the concomitant lowered activities are conceivably the reflection of burst discharge in normal brain functions. Plasticity in the human brain has been demonstrated by fMRI in cerebral vascular diseases, multiple sclerosis and amyotrophic lateral sclerosis. Pathogenesis of Parkinson disease and depression has been better understood by fMRI investigations revealing regions with elevated and reduced activities. Studies of attention deficit hyperactivity disorder have shown similar change of activities with functional reductions of the right dorsolateral frontal anterior area and of dorsal frontal cingulate gyrus, together with stimulated wider regions to given tasks. As above, fMRI has greatly contributed to our understanding of diseases of central nervous system and is to be expected to expand wider in this field. (T.T.)
Pediatric brain MRI. Pt. 2. Advanced techniques
Energy Technology Data Exchange (ETDEWEB)
Ho, Mai-Lan; Campeau, Norbert G.; Welker, Kirk M. [Mayo Clinic, Department of Radiology, Rochester, MN (United States); Ngo, Thang D. [Nemours Children' s Hospital, Department of Radiology, Orlando, FL (United States); Udayasankar, Unni K. [University of Arizona, Department of Radiology, Tucson, AZ (United States)
2017-05-15
Pediatric neuroimaging is a complex and specialized field that uses magnetic resonance (MR) imaging as the workhorse for diagnosis. MR protocols should be tailored to the specific indication and reviewed by the supervising radiologist in real time. Targeted advanced imaging sequences can be added to provide information regarding tissue microstructure, perfusion, metabolism and function. In part 2 of this review, we highlight the utility of advanced imaging techniques for superior evaluation of pediatric neurologic disease. We focus on the following techniques, with clinical examples: phase-contrast imaging, perfusion-weighted imaging, vessel wall imaging, diffusion tensor imaging, task-based functional MRI and MR spectroscopy. (orig.)
Tensor completion for PDEs with uncertain coefficients and Bayesian Update
Litvinenko, Alexander
2017-03-05
In this work, we tried to show connections between Bayesian update and tensor completion techniques. Usually, only a small/sparse vector/tensor of measurements is available. The typical measurement is a function of the solution. The solution of a stochastic PDE is a tensor, the measurement as well. The idea is to use completion techniques to compute all "missing" values of the measurement tensor and only then apply the Bayesian technique.
Tensor completion for PDEs with uncertain coefficients and Bayesian Update
Litvinenko, Alexander
2017-01-01
In this work, we tried to show connections between Bayesian update and tensor completion techniques. Usually, only a small/sparse vector/tensor of measurements is available. The typical measurement is a function of the solution. The solution of a stochastic PDE is a tensor, the measurement as well. The idea is to use completion techniques to compute all "missing" values of the measurement tensor and only then apply the Bayesian technique.
Concatenated image completion via tensor augmentation and completion
Bengua, Johann A.; Tuan, Hoang D.; Phien, Ho N.; Do, Minh N.
2016-01-01
This paper proposes a novel framework called concatenated image completion via tensor augmentation and completion (ICTAC), which recovers missing entries of color images with high accuracy. Typical images are second- or third-order tensors (2D/3D) depending if they are grayscale or color, hence tensor completion algorithms are ideal for their recovery. The proposed framework performs image completion by concatenating copies of a single image that has missing entries into a third-order tensor,...
Norm of the Riemannian Curvature Tensor
Indian Academy of Sciences (India)
We consider the Riemannian functional R p ( g ) = ∫ M | R ( g ) | p d v g defined on the space of Riemannian metrics with unit volume on a closed smooth manifold where R ( g ) and d v g denote the corresponding Riemannian curvature tensor and volume form and p ∈ ( 0 , ∞ ) . First we prove that the Riemannian metrics ...
Abelian tensor models on the lattice
Chaudhuri, Soumyadeep; Giraldo-Rivera, Victor I.; Joseph, Anosh; Loganayagam, R.; Yoon, Junggi
2018-04-01
We consider a chain of Abelian Klebanov-Tarnopolsky fermionic tensor models coupled through quartic nearest-neighbor interactions. We characterize the gauge-singlet spectrum for small chains (L =2 ,3 ,4 ,5 ) and observe that the spectral statistics exhibits strong evidence in favor of quasi-many-body localization.
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.
Fermionic topological quantum states as tensor networks
Wille, C.; Buerschaper, O.; Eisert, J.
2017-06-01
Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation methods, but also provide a framework for classifying phases of quantum matter and capture notions of topological order in a stringent and rigorous language. The rapid development in this field for spin models and bosonic systems has not yet been mirrored by an analogous development for fermionic models. In this work, we introduce a tensor network formalism capable of capturing notions of topological order for quantum systems with fermionic components. At the heart of the formalism are axioms of fermionic matrix-product operator injectivity, stable under concatenation. Building upon that, we formulate a Grassmann number tensor network ansatz for the ground state of fermionic twisted quantum double models. A specific focus is put on the paradigmatic example of the fermionic toric code. This work shows that the program of describing topologically ordered systems using tensor networks carries over to fermionic models.
Higher-order tensors in diffusion imaging
Schultz, T.; Fuster, A.; Ghosh, A.; Deriche, R.; Florack, L.M.J.; Lim, L.H.; Westin, C.-F.; Vilanova, A.; Burgeth, B.
2014-01-01
Diffusion imaging is a noninvasive tool for probing the microstructure of fibrous nerve and muscle tissue. Higher-order tensors provide a powerful mathematical language to model and analyze the large and complex data that is generated by its modern variants such as High Angular Resolution Diffusion
Visualization and processing of tensor fields
Weickert, Joachim
2007-01-01
Presents information on the visualization and processing of tensor fields. This book serves as an overview for the inquiring scientist, as a basic foundation for developers and practitioners, and as a textbook for specialized classes and seminars for graduate and doctoral students.
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.)
Introduction to vector and tensor analysis
Wrede, Robert C
1972-01-01
A broad introductory treatment, this volume examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, fundamental notions in n-space, Riemannian geometry, algebraic properties of the curvature tensor, and more. 1963 edition.
Curvature tensor copies in affine geometry
International Nuclear Information System (INIS)
Srivastava, P.P.
1981-01-01
The sets of space-time and spin-connections which give rise to the same curvature tensor are constructed. The corresponding geometries are compared. Results are illustrated by an explicit calculation and comment on the copies in Einstein-Cartan and Weyl-Cartan geometries. (Author) [pt
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.
An introduction to diffusion tensor image analysis.
O'Donnell, Lauren J; Westin, Carl-Fredrik
2011-04-01
Diffusion tensor magnetic resonance imaging (DTI) is a relatively new technology that is popular for imaging the white matter of the brain. This article provides a basic and broad overview of DTI to enable the reader to develop an intuitive understanding of these types of data, and an awareness of their strengths and weaknesses. Copyright © 2011 Elsevier Inc. All rights reserved.
Primordial tensor modes from quantum corrected inflation
DEFF Research Database (Denmark)
Joergensen, Jakob; Sannino, Francesco; Svendsen, Ole
2014-01-01
. Finally we confront these theories with the Planck and BICEP2 data. We demonstrate that the discovery of primordial tensor modes by BICEP2 require the presence of sizable quantum departures from the $\\phi^4$-Inflaton model for the non-minimally coupled scenario which we parametrize and quantify. We...
From stochastic completion fields to tensor voting
Almsick, van M.A.; Duits, R.; Franken, E.M.; Haar Romenij, ter B.M.; Olsen, O.F.; Florack, L.M.J.; Kuijper, A.
2005-01-01
Several image processing algorithms imitate the lateral interaction of neurons in the visual striate cortex V1 to account for the correlations along contours and lines. Here we focus on two methodologies: tensor voting by Guy and Medioni, and stochastic completion fields by Mumford, Williams and
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
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.)
Tensors in image processing and computer vision
De Luis García, Rodrigo; Tao, Dacheng; Li, Xuelong
2009-01-01
Tensor signal processing is an emerging field with important applications to computer vision and image processing. This book presents the developments in this branch of signal processing, offering research and discussions by experts in the area. It is suitable for advanced students working in the area of computer vision and image processing.
Tensor B mode and stochastic Faraday mixing
Giovannini, Massimo
2014-01-01
This paper investigates the Faraday effect as a different source of B mode polarization. The E mode polarization is Faraday rotated provided a stochastic large-scale magnetic field is present prior to photon decoupling. In the first part of the paper we discuss the case where the tensor modes of the geometry are absent and we argue that the B mode recently detected by the Bicep2 collaboration cannot be explained by a large-scale magnetic field rotating, through the Faraday effect, the well established E mode polarization. In this case, the observed temperature autocorrelations would be excessively distorted by the magnetic field. In the second part of the paper the formation of Faraday rotation is treated as a stationary, random and Markovian process with the aim of generalizing a set of scaling laws originally derived in the absence of the tensor modes of the geometry. We show that the scalar, vector and tensor modes of the brightness perturbations can all be Faraday rotated even if the vector and tensor par...
Tensor operators in R-matrix approach
International Nuclear Information System (INIS)
Bytsko, A.G.; Rossijskaya Akademiya Nauk, St. Petersburg
1995-12-01
The definitions and some properties (e.g. the Wigner-Eckart theorem, the fusion procedure) of covariant and contravariant q-tensor operators for quasitriangular quantum Lie algebras are formulated in the R-matrix language. The case of U q (sl(n)) (in particular, for n=2) is discussed in more detail. (orig.)
Tensors, differential forms, and variational principles
Lovelock, David
1989-01-01
Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques, with large number of problems, from routine manipulative exercises to technically difficult assignments.
Tensor algebra and tensor analysis for engineers with applications to continuum mechanics
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.
Baust, Maximilian; Weinmann, Andreas; Wieczorek, Matthias; Lasser, Tobias; Storath, Martin; Navab, Nassir
2016-08-01
In this paper, we consider combined TV denoising and diffusion tensor fitting in DTI using the affine-invariant Riemannian metric on the space of diffusion tensors. Instead of first fitting the diffusion tensors, and then denoising them, we define a suitable TV type energy functional which incorporates the measured DWIs (using an inverse problem setup) and which measures the nearness of neighboring tensors in the manifold. To approach this functional, we propose generalized forward- backward splitting algorithms which combine an explicit and several implicit steps performed on a decomposition of the functional. We validate the performance of the derived algorithms on synthetic and real DTI data. In particular, we work on real 3D data. To our knowledge, the present paper describes the first approach to TV regularization in a combined manifold and inverse problem setup.
The nonabelian tensor square of a bieberbach group with ...
African Journals Online (AJOL)
The main objective of this paper is to compute the nonabelian tensor square of one Bieberbach group with elementary abelian 2-group point group of dimension three by using the computational method of the nonabelian tensor square for polycyclic groups. The finding of the computation showed that the nonabelian tensor ...
[An Improved Spectral Quaternion Interpolation Method of Diffusion Tensor Imaging].
Xu, Yonghong; Gao, Shangce; Hao, Xiaofei
2016-04-01
Diffusion tensor imaging(DTI)is a rapid development technology in recent years of magnetic resonance imaging.The diffusion tensor interpolation is a very important procedure in DTI image processing.The traditional spectral quaternion interpolation method revises the direction of the interpolation tensor and can preserve tensors anisotropy,but the method does not revise the size of tensors.The present study puts forward an improved spectral quaternion interpolation method on the basis of traditional spectral quaternion interpolation.Firstly,we decomposed diffusion tensors with the direction of tensors being represented by quaternion.Then we revised the size and direction of the tensor respectively according to different situations.Finally,we acquired the tensor of interpolation point by calculating the weighted average.We compared the improved method with the spectral quaternion method and the Log-Euclidean method by the simulation data and the real data.The results showed that the improved method could not only keep the monotonicity of the fractional anisotropy(FA)and the determinant of tensors,but also preserve the tensor anisotropy at the same time.In conclusion,the improved method provides a kind of important interpolation method for diffusion tensor image processing.
Tensor based structure estimation in multi-channel images
DEFF Research Database (Denmark)
Schou, Jesper; Dierking, Wolfgang; Skriver, Henning
2000-01-01
. In the second part tensors are used for representing the structure information. This approach has the advantage, that tensors can be averaged either spatially or by applying several images, and the resulting tensor provides information of the average strength as well as orientation of the structure...
Relativistic particles with spin and antisymmetric tensor fields
International Nuclear Information System (INIS)
Sandoval Junior, L.
1990-09-01
A study is made on antisymmetric tensor fields particularly on second order tensor field as far as his equivalence to other fields and quantization through the path integral are concerned. Also, a particle model is studied which has been recently proposed and reveals to be equivalent to antisymmetric tensor fields of any order. (L.C.J.A.)
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.
Interpolation of vector fields from human cardiac DT-MRI
International Nuclear Information System (INIS)
Yang, F; Zhu, Y M; Rapacchi, S; Robini, M; Croisille, P; Luo, J H
2011-01-01
There has recently been increased interest in developing tensor data processing methods for the new medical imaging modality referred to as diffusion tensor magnetic resonance imaging (DT-MRI). This paper proposes a method for interpolating the primary vector fields from human cardiac DT-MRI, with the particularity of achieving interpolation and denoising simultaneously. The method consists of localizing the noise-corrupted vectors using the local statistical properties of vector fields, removing the noise-corrupted vectors and reconstructing them by using the thin plate spline (TPS) model, and finally applying global TPS interpolation to increase the resolution in the spatial domain. Experiments on 17 human hearts show that the proposed method allows us to obtain higher resolution while reducing noise, preserving details and improving direction coherence (DC) of vector fields as well as fiber tracking. Moreover, the proposed method perfectly reconstructs azimuth and elevation angle maps.
Lepore, Natasha; Brun, Caroline; Chou, Yi-Yu; Chiang, Ming-Chang; Dutton, Rebecca A.; Hayashi, Kiralee M.; Luders, Eileen; Lopez, Oscar L.; Aizenstein, Howard J.; Toga, Arthur W.; Becker, James T.; Thompson, Paul 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...
The Reflective Learning Continuum: Reflecting on Reflection
Peltier, James W.; Hay, Amanda; Drago, William
2005-01-01
The importance of reflection to marketing educators is increasingly recognized. However, there is a lack of empirical research that considers reflection within the context of both the marketing and general business education literature. This article describes the use of an instrument that can be used to measure four identified levels of a…
Diffusion tensor imaging of the normal prostate at 3 Tesla
International Nuclear Information System (INIS)
Guerses, Bengi; Kabakci, Neslihan; Kovanlikaya, Arzu; Firat, Zeynep; Bayram, Ali; Kovanlikaya, Ilhami; Ulud, Aziz M.
2008-01-01
The aim of this study was to assess the feasibility of diffusion tensor imaging (DTI) of the prostate and to determine normative fractional anisotropy (FA) and apparent diffusion coefficient (ADC) values of healthy prostate with a 3-Tesla magnetic resonance imaging (MRI) system. Thirty volunteers with a mean age of 28 (25-35) years were scanned with a 3-Tesla MRI (Intera Achieva; Philips, The Netherlands) system using a six-channel phased array coil. Initially, T2-weighted turbo spin-echo (TSE) axial images of the prostate were obtained. In two subjects, a millimetric hypointense signal change was detected in the peripheral zones on T2-weighted TSE images. These two subjects were excluded from the study. DTI with single-shot echo-planar imaging (ssEPI) was performed in the remaining 28 subjects. ADC and FA values were measured using the manufacturer supplied software by positioning 9-pixel ROIs on each zone. Differences between parameters of the central and peripheral zones were assessed. Mean ADC value of the central (1.220 ± 0.271 x 10 -3 mm 2 /s) was found to be significantly lower when compared with the peripheral gland (1.610 ± 0.347 x 10 -3 mm 2 /s) (P < 0.01). Mean FA of the central gland was significantly higher (0.26), compared with the peripheral gland (0.16) (P < 0.01). This study shows the feasibility of prostate DTI with a 3-Tesla MR system and the normative FA and ADC values of peripheral and central zones of the normal prostate. The results are compatible with the microstructural organization of the gland. (orig.)
Human brain functional MRI and DTI visualization with virtual reality.
Chen, Bin; Moreland, John; Zhang, Jingyu
2011-12-01
Magnetic resonance diffusion tensor imaging (DTI) and functional MRI (fMRI) are two active research areas in neuroimaging. DTI is sensitive to the anisotropic diffusion of water exerted by its macromolecular environment and has been shown useful in characterizing structures of ordered tissues such as the brain white matter, myocardium, and cartilage. The diffusion tensor provides two new types of information of water diffusion: the magnitude and the spatial orientation of water diffusivity inside the tissue. This information has been used for white matter fiber tracking to review physical neuronal pathways inside the brain. Functional MRI measures brain activations using the hemodynamic response. The statistically derived activation map corresponds to human brain functional activities caused by neuronal activities. The combination of these two methods provides a new way to understand human brain from the anatomical neuronal fiber connectivity to functional activities between different brain regions. In this study, virtual reality (VR) based MR DTI and fMRI visualization with high resolution anatomical image segmentation and registration, ROI definition and neuronal white matter fiber tractography visualization and fMRI activation map integration is proposed. Rationale and methods for producing and distributing stereoscopic videos are also discussed.
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Harmonization of multi-site diffusion tensor imaging data.
Fortin, Jean-Philippe; Parker, Drew; Tunç, Birkan; Watanabe, Takanori; Elliott, Mark A; Ruparel, Kosha; Roalf, David R; Satterthwaite, Theodore D; Gur, Ruben C; Gur, Raquel E; Schultz, Robert T; Verma, Ragini; Shinohara, Russell T
2017-11-01
Diffusion tensor imaging (DTI) is a well-established magnetic resonance imaging (MRI) technique used for studying microstructural changes in the white matter. As with many other imaging modalities, DTI images suffer from technical between-scanner variation that hinders comparisons of images across imaging sites, scanners and over time. Using fractional anisotropy (FA) and mean diffusivity (MD) maps of 205 healthy participants acquired on two different scanners, we show that the DTI measurements are highly site-specific, highlighting the need of correcting for site effects before performing downstream statistical analyses. We first show evidence that combining DTI data from multiple sites, without harmonization, may be counter-productive and negatively impacts the inference. Then, we propose and compare several harmonization approaches for DTI data, and show that ComBat, a popular batch-effect correction tool used in genomics, performs best at modeling and removing the unwanted inter-site variability in FA and MD maps. Using age as a biological phenotype of interest, we show that ComBat both preserves biological variability and removes the unwanted variation introduced by site. Finally, we assess the different harmonization methods in the presence of different levels of confounding between site and age, in addition to test robustness to small sample size studies. Copyright © 2017 Elsevier Inc. All rights reserved.
Diffusion tensor imaging in children and adolescents with tuberous sclerosis
Energy Technology Data Exchange (ETDEWEB)
Karadag, Demet [Institute of Diagnostic and Interventional Radiology, Friedrich Schiller University, Department of Paediatric Radiology, Jena (Germany); Kirikkale Yuksek Ihtisas Hospital, Department of Radiology, Kirirkale (Turkey); Mentzel, Hans-J.; Loebel, Ulrike; Reichenbach, Juergen R.; Kaiser, Werner A. [Institute of Diagnostic and Interventional Radiology, Friedrich Schiller University, Department of Paediatric Radiology, Jena (Germany); Guellmar, Daniel [Institute of Diagnostic and Interventional Radiology, Friedrich Schiller University, Department of Paediatric Radiology, Jena (Germany); Friedrich Schiller University, Biomagnetic Centre, Clinic of Neurology, Jena (Germany); Rating, Tina; Brandl, Ulrich [Friedrich Schiller University, Department of Paediatric Neurology, Jena (Germany)
2005-10-01
Tuberous sclerosis (TS) is characterised by benign hamartomatous lesions in many organs. Diffusion tensor imaging (DTI) can detect microstructural changes in pathological processes. To determine apparent diffusion coefficient (ADC) and fractional anisotropy (FA) maps in children with TS and to investigate the diffusion properties in cortical tubers, white-matter lesions, perilesional white matter, and contralateral normal-appearing white matter, and to compare the results with ADC and FA maps of normal age- and sex-matched volunteers. Seven children and adolescents (age range 2-20 years) suffering from TS were included. MRI was performed on a 1.5-T scanner using a transmit/receive coil with T1-W and T2-W spin-echo and FLAIR sequences. DT images were acquired by using a single-shot echo-planar pulse sequence. Diffusion gradients were applied in six different directions with a b value of 1,000 s/mm{sup 2}. ADC was higher in cortical tubers than in the corresponding cortical location of controls. ADC values were higher and FA values were lower in white-matter lesions and perilesional white matter than in both the contralateral normal-appearing white matter of patients and in controls. There were no significant differences for both ADC and FA values in the normal-appearing white matter of patients with TS compared to controls. DTI provides important information about cortical tubers, white-matter abnormalities, and perilesional white matter in patients with TS. (orig.)
Bayesian uncertainty quantification in linear models for diffusion MRI.
Sjölund, Jens; Eklund, Anders; Özarslan, Evren; Herberthson, Magnus; Bånkestad, Maria; Knutsson, Hans
2018-03-29
Diffusion MRI (dMRI) is a valuable tool in the assessment of tissue microstructure. By fitting a model to the dMRI signal it is possible to derive various quantitative features. Several of the most popular dMRI signal models are expansions in an appropriately chosen basis, where the coefficients are determined using some variation of least-squares. However, such approaches lack any notion of uncertainty, which could be valuable in e.g. group analyses. In this work, we use a probabilistic interpretation of linear least-squares methods to recast popular dMRI models as Bayesian ones. This makes it possible to quantify the uncertainty of any derived quantity. In particular, for quantities that are affine functions of the coefficients, the posterior distribution can be expressed in closed-form. We simulated measurements from single- and double-tensor models where the correct values of several quantities are known, to validate that the theoretically derived quantiles agree with those observed empirically. We included results from residual bootstrap for comparison and found good agreement. The validation employed several different models: Diffusion Tensor Imaging (DTI), Mean Apparent Propagator MRI (MAP-MRI) and Constrained Spherical Deconvolution (CSD). We also used in vivo data to visualize maps of quantitative features and corresponding uncertainties, and to show how our approach can be used in a group analysis to downweight subjects with high uncertainty. In summary, we convert successful linear models for dMRI signal estimation to probabilistic models, capable of accurate uncertainty quantification. Copyright © 2018 Elsevier Inc. All rights reserved.
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)
Usefulness of Diffusion Tensor Imaging of White Matter in Alzheimer Disease and Vascular Dementia
International Nuclear Information System (INIS)
Sugihara, S.; Kinoshita, T.; Matsusue, E.; Fujii, S.; Ogawa, T.
2004-01-01
Purpose: To evaluate the usefulness of diffusion tensor imaging in detecting the water diffusivity caused by neuro pathological change in Alzheimer disease and vascular dementia. Material and Methods: Twenty patients with Alzheimer disease, 20 with vascular dementia, and 10 control subjects were examined. Diffusion tensor imaging applied diffusion gradient encoding in six non-collinear directions. Fractional anisotropy values were compared in the genu and splenium of the corpus callosum, and anterior and posterior white matter among the three groups. Results: In the patients with Alzheimer disease, fractional anisotropy values of the posterior white matter were significantly lower than those of controls. In patients with vascular dementia, fractional anisotropy values of the anterior white matter tended to be lower than those of the posterior white matter (P=0.07). Conclusion: Diffusion tensor imaging reflects the neuro pathological changes in the white matter, and may be useful in the diagnosis of Alzheimer disease and vascular dementia. Keywords: Alzheimer disease, .; diffusion tensor imaging, .; vascular dementia
Federal Laboratory Consortium — The Animal Magnetic Resonance Imaging (MRI) Core develops and optimizes MRI methods for cardiovascular imaging of mice and rats. The Core provides imaging expertise,...
Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold.
Palacios, Jonathan; Yeh, Harry; Wang, Wenping; Zhang, Yue; Laramee, Robert S; Sharma, Ritesh; Schultz, Thomas; Zhang, Eugene
2016-03-01
Three-dimensional symmetric tensor fields have a wide range of applications in solid and fluid mechanics. Recent advances in the (topological) analysis of 3D symmetric tensor fields focus on degenerate tensors which form curves. In this paper, we introduce a number of feature surfaces, such as neutral surfaces and traceless surfaces, into tensor field analysis, based on the notion of eigenvalue manifold. Neutral surfaces are the boundary between linear tensors and planar tensors, and the traceless surfaces are the boundary between tensors of positive traces and those of negative traces. Degenerate curves, neutral surfaces, and traceless surfaces together form a partition of the eigenvalue manifold, which provides a more complete tensor field analysis than degenerate curves alone. We also extract and visualize the isosurfaces of tensor modes, tensor isotropy, and tensor magnitude, which we have found useful for domain applications in fluid and solid mechanics. Extracting neutral and traceless surfaces using the Marching Tetrahedra method can cause the loss of geometric and topological details, which can lead to false physical interpretation. To robustly extract neutral surfaces and traceless surfaces, we develop a polynomial description of them which enables us to borrow techniques from algebraic surface extraction, a topic well-researched by the computer-aided design (CAD) community as well as the algebraic geometry community. In addition, we adapt the surface extraction technique, called A-patches, to improve the speed of finding degenerate curves. Finally, we apply our analysis to data from solid and fluid mechanics as well as scalar field analysis.
Glyph-Based Comparative Visualization for Diffusion Tensor Fields.
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.
Tensoral for post-processing users and simulation authors
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.
Energy-momentum tensor of the electromagnetic field
International Nuclear Information System (INIS)
Horndeski, G.W.; Wainwright, J.
1977-01-01
In this paper we investigate the energy-momentum tensor of the most general second-order vector-tensor theory of gravitation and electromagnetism which has field equations which are (i) derivable from a variational principle, (ii) consistent with the notion of conservation of charge, and (iii) compatible with Maxwell's equations in a flat space. This energy-momentum tensor turns out to be quadratic in the first partial derivatives of the electromagnetic field tensor and depends upon the curvature tensor. The asymptotic behavior of this energy-momentum tensor is examined for solutions to Maxwell's equations in Minkowski space, and it is demonstrated that this energy-momentum tensor predicts regions of negative energy density in the vicinity of point sources
Quantum mechanics of Yano tensors: Dirac equation in curved spacetime
International Nuclear Information System (INIS)
Cariglia, Marco
2004-01-01
In spacetimes admitting Yano tensors, the classical theory of the spinning particle possesses enhanced worldline supersymmetry. Quantum mechanically generators of extra supersymmetries correspond to operators that in the classical limit commute with the Dirac operator and generate conserved quantities. We show that the result is preserved in the full quantum theory, that is, Yano symmetries are not anomalous. This was known for Yano tensors of rank 2, but our main result is to show that it extends to Yano tensors of arbitrary rank. We also describe the conformal Yano equation and show that is invariant under Hodge duality. There is a natural relationship between Yano tensors and supergravity theories. As the simplest possible example, we show that when the spacetime admits a Killing spinor then this generates Yano and conformal Yano tensors. As an application, we construct Yano tensors on maximally symmetric spaces: they are spanned by tensor products of Killing vectors
Algebraic and computational aspects of real tensor ranks
Sakata, Toshio; Miyazaki, Mitsuhiro
2016-01-01
This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications in statistics. The book provides several interesting ideas, including determinant polynomials, determinantal ideals, absolutely nonsingular tensors, absolutely full column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in details, global theories such as the Jacobian method are also reviewed in details. The book includes as well an accessible and comprehensive introduction of mathematical backgrounds, with basics of positive polynomials and calculations by using the Groebner basis. Furthermore, this book provides insights into numerical methods of finding tensor ranks through...
Kaufman, Jason A; Ahrens, Eric T; Laidlaw, David H; Zhang, Song; Allman, John M
2005-11-01
This report presents initial results of a multimodal analysis of tissue volume and microstructure in the brain of an aye-aye (Daubentonia madagascariensis). The left hemisphere of an aye-aye brain was scanned using T2-weighted structural magnetic resonance imaging (MRI) and diffusion-tensor imaging (DTI) prior to histological processing and staining for Nissl substance and myelinated fibers. The objectives of the experiment were to estimate the volume of gross brain regions for comparison with published data on other prosimians and to validate DTI data on fiber anisotropy with histological measurements of fiber spread. Measurements of brain structure volumes in the specimen are consistent with those reported in the literature: the aye-aye has a very large brain for its body size, a reduced volume of visual structures (V1 and LGN), and an increased volume of the olfactory lobe. This trade-off between visual and olfactory reliance is likely a reflection of the nocturnal extractive foraging behavior practiced by Daubentonia. Additionally, frontal cortex volume is large in the aye-aye, a feature that may also be related to its complex foraging behavior and sensorimotor demands. Analysis of DTI data in the anterior cingulum bundle demonstrates a strong correlation between fiber spread as measured from histological sections and fiber spread as measured from DTI. These results represent the first quantitative comparison of DTI data and fiber-stained histology in the brain. (c) 2005 Wiley-Liss, Inc.
Energy Technology Data Exchange (ETDEWEB)
Lentine, Anthony L.; Nielson, Gregory N.; Cruz-Campa, Jose Luis; Okandan, Murat; Goeke, Ronald S.
2018-03-06
A photovoltaic module includes colorized reflective photovoltaic cells that act as pixels. The colorized reflective photovoltaic cells are arranged so that reflections from the photovoltaic cells or pixels visually combine into an image on the photovoltaic module. The colorized photovoltaic cell or pixel is composed of a set of 100 to 256 base color sub-pixel reflective segments or sub-pixels. The color of each pixel is determined by the combination of base color sub-pixels forming the pixel. As a result, each pixel can have a wide variety of colors using a set of base colors, which are created, from sub-pixel reflective segments having standard film thicknesses.
Directory of Open Access Journals (Sweden)
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.
Detecting brain growth patterns in normal children using tensor-based morphometry.
Hua, Xue; Leow, Alex D; Levitt, Jennifer G; Caplan, Rochelle; Thompson, Paul M; Toga, Arthur W
2009-01-01
Previous magnetic resonance imaging (MRI)-based volumetric studies have shown age-related increases in the volume of total white matter and decreases in the volume of total gray matter of normal children. Recent adaptations of image analysis strategies enable the detection of human brain growth with improved spatial resolution. In this article, we further explore the spatio-temporal complexity of adolescent brain maturation with tensor-based morphometry. By utilizing a novel non-linear elastic intensity-based registration algorithm on the serial structural MRI scans of 13 healthy children, individual Jacobian growth maps are generated and then registered to a common anatomical space. Statistical analyses reveal significant tissue growth in cerebral white matter, contrasted with gray matter loss in parietal, temporal, and occipital lobe. In addition, a linear regression with age and gender suggests a slowing down of the growth rate in regions with the greatest white matter growth. We demonstrate that a tensor-based Jacobian map is a sensitive and reliable method to detect regional tissue changes during development. (c) 2007 Wiley-Liss, Inc.
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)
Chen, Hua-Biao; Wan, Qi; Xu, Qi-Feng; Chen, Yi; Bai, Bo
2016-04-25
Correlating symptoms and physical examination findings with surgical levels based on common imaging results is not reliable. In patients who have no concordance between radiological and clinical symptoms, the surgical levels determined by conventional magnetic resonance imaging (MRI) and neurogenic examination (NE) may lead to a more extensive surgery and significant complications. We aimed to confirm that whether the use of diffusion tensor imaging (DTI) and paraspinal mapping (PM) techniques can further prevent the occurrence of false positives with conventional MRI, distinguish which are clinically relevant from levels of cauda equina and/or nerve root lesions based on MRI, and determine and reduce the decompression levels of lumbar spinal stenosis than MRI + NE, while ensuring or improving surgical outcomes. We compared the data between patients who underwent MRI + (PM or DTI) and patients who underwent conventional MRI + NE to determine levels of decompression for the treatment of lumbar spinal stenosis. Outcome measures were assessed at 2 weeks, 3 months, 6 months, and 12 months postoperatively. One hundred fourteen patients (59 in the control group, 54 in the experimental group) underwent decompression. The levels of decompression determined by MRI + (PM or DTI) in the experimental group were significantly less than that determined by MRI + NE in the control group (p = 0.000). The surgical time, blood loss, and surgical transfusion were significantly less in the experimental group (p = 0.001, p = 0.011, p = 0.001, respectively). There were no differences in improvement of the visual analog scale back and leg pain (VAS-BP, VAS-LP) scores and Oswestry Disability Index (ODI) scores at 2 weeks, 3 months, 6 months, and 12 months after operation between the experimental and control groups. MRI + (PM or DTI) showed clear benefits in determining decompression levels of lumbar spinal stenosis than MRI + NE. In patients with lumbar spinal
Patel, Samir P.; Smith, Taylor D.; VanRooyen, Jenna L.; Powell, David; Cox, David H.; Sullivan, Patrick G.
2016-01-01
Abstract The current study demonstrates the feasibility of using serial magnetic resonance imaging (MRI) and diffusion tensor imaging (DTI) in vivo to quantify temporally spinal cord injury (SCI) pathology in adult female Sprague-Dawley rats that were scanned prior to a moderate or severe upper lumbar contusion SCI. Injured rats were behaviorally tested for hind limb locomotion (Basso, Beattie, Bresnahan [BBB] scores) weekly for 4 weeks and scanned immediately after each session, ending with terminal gait analyses prior to euthanasia. As a measure of tissue integrity, fractional anisotropy (FA) values were significantly lower throughout the spinal cord in both injury cohorts at all time-points examined versus pre-injury. Moreover, FA values were significantly lower following severe versus moderate SCI at all time-points, and FA values at the injury epicenters at all time-points were significantly correlated with both spared white and gray matter volumes, as well as lesion volumes. Critically, quantified FA values at subacute (24 h) and all subsequent time-points were highly predictive of terminal behavior, reflected in significant correlations with both weekly BBB scores and terminal gait parameters. Critically, the finding that clinically relevant subacute (24 h) FA values accurately predict long-term functional recovery may obviate long-term studies to assess the efficacy of therapeutics tested experimentally or clinically. In summary, this study demonstrates a reproducible serial MRI procedure to predict the long-term impact of contusion SCI on both behavior and histopathology using subacute DTI metrics obtained in vivo to accurately predict multiple terminal outcome measures, which can be particularly valuable when comparing experimental interventions. PMID:26650623
DEFF Research Database (Denmark)
Haakma, Wieke; Jongbloed, Bas A.; Froeling, Martijn
2017-01-01
Objectives To study disease mechanisms in multifocal motor neuropathy (MMN) with magnetic resonance imaging (MRI) and diffusion tensor imaging (DTI) of the median and ulnar nerves. Methods We enrolled ten MMN patients, ten patients with amyotrophic lateral sclerosis (ALS) and ten healthy controls...
Automatic MRI Quantifying Methods in Behavioral-Variant Frontotemporal Dementia Diagnosis
DEFF Research Database (Denmark)
Cajanus, Antti; Hall, Anette; Koikkalainen, Juha
2018-01-01
genetic status in the differentiation sensitivity. Methods: The MRI scans of 50 patients with bvFTD (17 C9ORF72 expansion carriers) were analyzed using 6 quantification methods as follows: voxel-based morphometry (VBM), tensor-based morphometry, volumetry (VOL), manifold learning, grading, and white...
Hua, Xue; Leow, Alex D.; Lee, Suh; Klunder, Andrea D.; Toga, Arthur W.; Lepore, Natasha; Chou, Yi-Yu; Brun, Caroline; Chiang, Ming-Chang; Barysheva, Marina; Jack, Clifford R.; Bernstein, Matt A.; Britson, Paula J.; Ward, Chadwick P.; Whitwell, Jennifer L.; Borowski, Bret; Fleisher, Adam S.; Fox, Nick C.; Boyes, Richard G.; Barnes, Josephine; Harvey, Danielle; Kornak, John; Schuff, Norbert; Boreta, Lauren; Alexander, Gene E.; Weiner, Michael W.; Thompson, Paul M.
2008-01-01
Tensor-based morphometry (TBM) creates three-dimensional maps of disease-related differences in brain structure, based on nonlinearly registering brain MRI scans to a common image template. Using two different TBM designs (averaging individual differences versus aligning group average templates), we compared the anatomical distribution of brain atrophy in 40 patients with Alzheimer's disease (AD), 40 healthy elderly controls, and 40 individuals with amnestic mild cognitive impairment (aMCI), a condition conferring increased risk for AD. We created an unbiased geometrical average image template for each of the three groups, which were matched for sex and age (mean age: 76.1 years+/−7.7 SD). We warped each individual brain image (N=120) to the control group average template to create Jacobian maps, which show the local expansion or compression factor at each point in the image, reflecting individual volumetric differences. Statistical maps of group differences revealed widespread medial temporal and limbic atrophy in AD, with a lesser, more restricted distribution in MCI. Atrophy and CSF space expansion both correlated strongly with Mini-Mental State Exam (MMSE) scores and Clinical Dementia Rating (CDR). Using cumulative p-value plots, we investigated how detection sensitivity was influenced by the sample size, the choice of search region (whole brain, temporal lobe, hippocampus), the initial linear registration method (9- versus 12-parameter), and the type of TBM design. In the future, TBM may help to (1) identify factors that resist or accelerate the disease process, and (2) measure disease burden in treatment trials. PMID:18378167
Li, Qian; Jiang, Qinying; Guo, Mingxia; Li, Qingji; Cai, Chunquan; Yin, Xiaohui
2013-04-01
To investigate the potential morphological alterations of grey and white matter in monocular amblyopic children using voxel-based morphometry (VBM) and diffusion tensor imaging (DTI). A total of 20 monocular amblyopic children and 20 age-matched controls were recruited. Whole-brain MRI scans were performed after a series of ophthalmologic exams. The imaging data were processed and two-sample t-tests were employed to identify group differences in grey matter volume (GMV), white matter volume (WMV) and fractional anisotropy (FA). After image screening, there were 12 amblyopic participants and 15 normal controls qualified for the VBM analyses. For DTI analysis, 14 amblyopes and 14 controls were included. Compared to the normal controls, reduced GMVs were observed in the left inferior occipital gyrus, the bilateral parahippocampal gyrus and the left supramarginal/postcentral gyrus in the monocular amblyopic group, with the lingual gyrus presenting augmented GMV. Meanwhile, WMVs reduced in the left calcarine, the bilateral inferior frontal and the right precuneus areas, and growth in the WMVs was seen in the right cuneus, right middle occipital and left orbital frontal areas. Diminished FA values in optic radiation and increased FA in the left middle occipital area and right precuneus were detected in amblyopic patients. In monocular amblyopia, cortices related to spatial vision underwent volume loss, which provided neuroanatomical evidence of stereoscopic defects. Additionally, white matter development was also hindered due to visual defects in amblyopes. Growth in the GMVs, WMVs and FA in the occipital lobe and precuneus may reflect a compensation effect by the unaffected eye in monocular amblyopia.
Mascalchi, Mario; Diciotti, Stefano; Giannelli, Marco; Ginestroni, Andrea; Soricelli, Andrea; Nicolai, Emanuele; Aiello, Marco; Tessa, Carlo; Galli, Lucia; Dotti, Maria Teresa; Piacentini, Silvia; Salvatore, Elena; Toschi, Nicola
2014-01-01
Spinocerebellar ataxia type 2 (SCA2) is the second most frequent autosomal dominant inherited ataxia worldwide. We investigated the capability of magnetic resonance imaging (MRI) to track in vivo progression of brain atrophy in SCA2 by examining twice 10 SCA2 patients (mean interval 3.6 years) and 16 age- and gender-matched healthy controls (mean interval 3.3 years) on the same 1.5 T MRI scanner. We used T1-weighted images and tensor-based morphometry (TBM) to investigate volume changes and the Inherited Ataxia Clinical Rating Scale to assess the clinical deficit. With respect to controls, SCA2 patients showed significant higher atrophy rates in the midbrain, including substantia nigra, basis pontis, middle cerebellar peduncles and posterior medulla corresponding to the gracilis and cuneatus tracts and nuclei, cerebellar white matter (WM) and cortical gray matter (GM) in the inferior portions of the cerebellar hemisphers. No differences in WM or GM volume loss were observed in the supratentorial compartment. TBM findings did not correlate with modifications of the neurological deficit. In conclusion, MRI volumetry using TBM is capable of demonstrating the progression of pontocerebellar atrophy in SCA2, supporting a possible role of MRI as biomarker in future trials.
Directory of Open Access Journals (Sweden)
Mario Mascalchi
Full Text Available Spinocerebellar ataxia type 2 (SCA2 is the second most frequent autosomal dominant inherited ataxia worldwide. We investigated the capability of magnetic resonance imaging (MRI to track in vivo progression of brain atrophy in SCA2 by examining twice 10 SCA2 patients (mean interval 3.6 years and 16 age- and gender-matched healthy controls (mean interval 3.3 years on the same 1.5 T MRI scanner. We used T1-weighted images and tensor-based morphometry (TBM to investigate volume changes and the Inherited Ataxia Clinical Rating Scale to assess the clinical deficit. With respect to controls, SCA2 patients showed significant higher atrophy rates in the midbrain, including substantia nigra, basis pontis, middle cerebellar peduncles and posterior medulla corresponding to the gracilis and cuneatus tracts and nuclei, cerebellar white matter (WM and cortical gray matter (GM in the inferior portions of the cerebellar hemisphers. No differences in WM or GM volume loss were observed in the supratentorial compartment. TBM findings did not correlate with modifications of the neurological deficit. In conclusion, MRI volumetry using TBM is capable of demonstrating the progression of pontocerebellar atrophy in SCA2, supporting a possible role of MRI as biomarker in future trials.
Energy Technology Data Exchange (ETDEWEB)
Jacob, S.; Ehrenreich, H. [Max-Planck-Institute for Experimental Medicine, Georg-August-University, Hermann-Rein-Strasse 3, 37075, Goettingen (Germany); Departments of Neurology and Psychiatry, Georg-August-University, Goettingen (Germany); Finsterbusch, J.; Frahm, J. [Biomedizinische NMR Forschungs GmbH, Max-Planck-Institute for Biophysical Chemistry, Georg-August-University, Goettingen (Germany); Weishaupt, J.H. [Departments of Neurology and Psychiatry, Georg-August-University, Goettingen (Germany); Khorram-Sefat, D. [Department of Neuroradiology, Georg-August-University, Goettingen (Germany)
2003-09-01
Amyotrophic lateral sclerosis (ALS) is a predominantly clinical and electromyographic diagnosis. Conventional MRI reveals atrophy of the motor system, particularly the pyramidal tract, in the advanced stages but does not provide a sensitive measure of disease progression. Three patients with different principal symptoms of ALS, i.e., with predominant involvement of the upper (UMN) or lower (UMN) motor neurons, or bulbar disease, respectively, underwent serial clinical examination including lung function tests, conventional MRI, and diffusion tensor imaging (DTI). MRI demonstrated changes in of the pyramidal tract without measurable variation on follow-up. The patient with UMN involvement showed remarkable progressive loss of diffusion anisotropy in the pyramidal tract. DTI might be useful, together with clinical follow-up, as an objective morphological marker in therapeutic trials. (orig.)
Entanglement entropy from the holographic stress tensor
International Nuclear Information System (INIS)
Bhattacharyya, Arpan; Sinha, Aninda
2013-01-01
We consider entanglement entropy in the context of gauge/gravity duality for conformal field theories in even dimensions. The holographic prescription due to Ryu and Takayanagi (RT) leads to an equation describing how the entangling surface extends into the bulk geometry. We show that setting to zero, the time–time component of the Brown–York stress tensor evaluated on the co-dimension 1 entangling surface, leads to the same equation. By considering a spherical entangling surface as an example, we observe that the Euclidean action methods in AdS/CFT will lead to the RT area functional arising as a counterterm needed to regularize the stress tensor. We present arguments leading to a justification for the minimal area prescription. (paper)
Tensor modes on the string theory landscape
International Nuclear Information System (INIS)
Westphal, Alexander
2012-06-01
We attempt an estimate for the distribution of the tensor mode fraction r over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum tunneling lead to a kind of democracy on the landscape, providing no bias towards large-field or small-field inflation regardless of the class of measure. The tensor mode fraction then follows the number frequency distributions of inflationary mechanisms of string theory over the landscape. We show that an estimate of the relative number frequencies for small-field vs large-field inflation, while unattainable on the whole landscape, may be within reach as a regional answer for warped Calabi-Yau flux compactifications of type IIB string theory.
Tensor modes on the string theory landscape
Energy Technology Data Exchange (ETDEWEB)
Westphal, Alexander
2012-06-15
We attempt an estimate for the distribution of the tensor mode fraction r over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum tunneling lead to a kind of democracy on the landscape, providing no bias towards large-field or small-field inflation regardless of the class of measure. The tensor mode fraction then follows the number frequency distributions of inflationary mechanisms of string theory over the landscape. We show that an estimate of the relative number frequencies for small-field vs large-field inflation, while unattainable on the whole landscape, may be within reach as a regional answer for warped Calabi-Yau flux compactifications of type IIB string theory.
International Nuclear Information System (INIS)
Kibler, M.; Grenet, G.
1979-07-01
The SU 2 unit tensor operators tsub(k,α) are studied. In the case where the spinor point group G* coincides with U 1 , then tsub(k α) reduces up to a constant to the Wigner-Racah-Schwinger tensor operator tsub(kqα), an operator which produces an angular momentum state. One first investigates those general properties of tsub(kα) which are independent of their realization. The tsub(kα) in terms of two pairs of boson creation and annihilation operators are realized. This leads to look at the Schwinger calculus relative to one angular momentum of two coupled angular momenta. As a by-product, a procedure is given for producing recursion relationships between SU 2 Wigner coefficients. Finally, some of the properties of the Wigner and Racah operators for an arbitrary compact group and the SU 2 coupling coefficients are studied
International Nuclear Information System (INIS)
Balzar, D.; Popa, N.C.; Vogel, S.
2010-01-01
We report the complete macroscopic average strain and stress tensors for a cold-rolled uranium plate, based on the neutron TOF measurements. Both tensors were determined by the least-squares refinement of the interplanar spacings of 19 Bragg reflections. Based on the pole figures, as determined by GSAS, a triclinic sample symmetry of the uranium plate was assumed. Strain and stress are tensile in both the transverse and rolling directions and very small in the normal direction (through the thickness of the plate). Shear strain and stress components are compressive and of significant magnitude.
Tensor Networks and Quantum Error Correction
Ferris, Andrew J.; Poulin, David
2014-07-01
We establish several relations between quantum error correction (QEC) and tensor network (TN) methods of quantum many-body physics. We exhibit correspondences between well-known families of QEC codes and TNs, and demonstrate a formal equivalence between decoding a QEC code and contracting a TN. We build on this equivalence to propose a new family of quantum codes and decoding algorithms that generalize and improve upon quantum polar codes and successive cancellation decoding in a natural way.
Old tensor mesons in QCD sum rules
International Nuclear Information System (INIS)
Aliev, T.M.; Shifman, M.A.
1981-01-01
Tensor mesons f, A 2 and A 3 are analyzed within the framework of QCD sum rules. The effects of gluon and quark condensate is accounted for phenomenologically. Accurate estimates of meson masses and coupling constants of the lowest-lying states are obtained. It is shown that the masses are reproduced within theoretical uncertainty of about 80 MeV. The coupling of f meson to the corresponding quark current is determined. The results are in good aqreement with experimental data [ru
Energy-momentum-tensor in quantumelectrodynamics
Energy Technology Data Exchange (ETDEWEB)
Schott, T
1974-01-01
This work deals with the operator properties of the energy-momentum-tensor (ET) in the framework of quantum electrodynamics. The principles of construction of the ET are discussed for quantized fields in the Schwinger variation principle. Dealing with the conserved quantities for quantized fields operator problems are coming up in the Coulomb gauge because Dirac- and Maxwellfield do not commute completely. Further on contemporary commutators of the ET components are investigated mutually. Finally non-canonical methods are developed.
Embryo Cell Membranes Reconstruction by Tensor Voting
Michelin , Gaël; Guignard , Léo; Fiuza , Ulla-Maj; Malandain , Grégoire
2014-01-01
International audience; Image-based studies of developing organs or embryos produce a huge quantity of data. To handle such high-throughput experimental protocols, automated computer-assisted methods are highly desirable. This article aims at designing an efficient cell segmentation method from microscopic images. The proposed approach is twofold: first, cell membranes are enhanced or extracted by the means of structure-based filters, and then perceptual grouping (i.e. tensor voting) allows t...
Sasakian manifolds with purely transversal Bach tensor
Ghosh, Amalendu; Sharma, Ramesh
2017-10-01
We show that a (2n + 1)-dimensional Sasakian manifold (M, g) with a purely transversal Bach tensor has constant scalar curvature ≥2 n (2 n +1 ) , equality holding if and only if (M, g) is Einstein. For dimension 3, M is locally isometric to the unit sphere S3. For dimension 5, if in addition (M, g) is complete, then it has positive Ricci curvature and is compact with finite fundamental group π1(M).
Vector-tensor interaction of gravitation
Energy Technology Data Exchange (ETDEWEB)
Zhang Yuan-zhong; Guo han-ying
1982-11-01
In the paper, by using the equation of motion a particle, we show that the antigravity exist in the vector-tensor model of gravitation. Thus the motion of a particle deviates from the geodesic equation. In Newtonian approximation and weak gravitational field, acceleration of a particle in a spherically symmetric and astatic gravitation field is zero. The result is obviously not in agreement with gravitational phenomena.
Anisotropic diffusion tensor applied to temporal mammograms
DEFF Research Database (Denmark)
Karemore, Gopal; Brandt, Sami; Sporring, Jon
2010-01-01
changes related to specific effects like Hormonal Replacement Therapy (HRT) and aging. Given effect-grouped patient data, we demonstrated how anisotropic diffusion tensor and its coherence features computed in an anatomically oriented breast coordinate system followed by statistical learning...
Numerical CP Decomposition of Some Difficult Tensors
Czech Academy of Sciences Publication Activity Database
Tichavský, Petr; Phan, A. H.; Cichocki, A.
2017-01-01
Roč. 317, č. 1 (2017), s. 362-370 ISSN 0377-0427 R&D Projects: GA ČR(CZ) GA14-13713S Institutional support: RVO:67985556 Keywords : Small matrix multiplication * Canonical polyadic tensor decomposition * Levenberg-Marquardt method Subject RIV: BB - Applied Statistics, Operational Research OBOR OECD: Applied mathematics Impact factor: 1.357, year: 2016 http://library.utia.cas.cz/separaty/2017/SI/tichavsky-0468385. pdf
Experimental status of scalar and tensor mesons
International Nuclear Information System (INIS)
Von Dombrowski, S.
1997-01-01
The recent discoveries of a 0 (1450) and f 0 (1370)/f 0 (1500) in antiproton-proton annihilation at rest shed new light on the interpretation of light scalar mesons. The properties of f 0 (1500) match the expectations of a scalar glueball mixed with nearby qq states. New decay modes of the ξ(2230) are reported in radiative J/Ψ decays, pointing also towards a (tensor) glueball nature of this state. Results from different experiments are discussed and compared. (orig.)
Bayesian approach to magnetotelluric tensor decomposition
Czech Academy of Sciences Publication Activity Database
Červ, Václav; Pek, Josef; Menvielle, M.
2010-01-01
Roč. 53, č. 2 (2010), s. 21-32 ISSN 1593-5213 R&D Projects: GA AV ČR IAA200120701; GA ČR GA205/04/0746; GA ČR GA205/07/0292 Institutional research plan: CEZ:AV0Z30120515 Keywords : galvanic distortion * telluric distortion * impedance tensor * basic procedure * inversion * noise Subject RIV: DE - Earth Magnetism, Geodesy, Geography Impact factor: 0.336, year: 2010
Monte Carlo Volcano Seismic Moment Tensors
Waite, G. P.; Brill, K. A.; Lanza, F.
2015-12-01
Inverse modeling of volcano seismic sources can provide insight into the geometry and dynamics of volcanic conduits. But given the logistical challenges of working on an active volcano, seismic networks are typically deficient in spatial and temporal coverage; this potentially leads to large errors in source models. In addition, uncertainties in the centroid location and moment-tensor components, including volumetric components, are difficult to constrain from the linear inversion results, which leads to a poor understanding of the model space. In this study, we employ a nonlinear inversion using a Monte Carlo scheme with the objective of defining robustly resolved elements of model space. The model space is randomized by centroid location and moment tensor eigenvectors. Point sources densely sample the summit area and moment tensors are constrained to a randomly chosen geometry within the inversion; Green's functions for the random moment tensors are all calculated from modeled single forces, making the nonlinear inversion computationally reasonable. We apply this method to very-long-period (VLP) seismic events that accompany minor eruptions at Fuego volcano, Guatemala. The library of single force Green's functions is computed with a 3D finite-difference modeling algorithm through a homogeneous velocity-density model that includes topography, for a 3D grid of nodes, spaced 40 m apart, within the summit region. The homogenous velocity and density model is justified by long wavelength of VLP data. The nonlinear inversion reveals well resolved model features and informs the interpretation through a better understanding of the possible models. This approach can also be used to evaluate possible station geometries in order to optimize networks prior to deployment.
Retrospective correction of bias in diffusion tensor imaging arising from coil combination mode.
Sakaie, Ken; Lowe, Mark
2017-04-01
To quantify and retrospectively correct for systematic differences in diffusion tensor imaging (DTI) measurements due to differences in coil combination mode. Multi-channel coils are now standard among MRI systems. There are several options for combining signal from multiple coils during image reconstruction, including sum-of-squares (SOS) and adaptive combine (AC). This contribution examines the bias between SOS- and AC-derived measures of tissue microstructure and a strategy for limiting that bias. Five healthy subjects were scanned under an institutional review board-approved protocol. Each set of raw image data was reconstructed twice-once with SOS and once with AC. The diffusion tensor was calculated from SOS- and AC-derived data by two algorithms-standard log-linear least squares and an approach that accounts for the impact of coil combination on signal statistics. Systematic differences between SOS and AC in terms of tissue microstructure (axial diffusivity, radial diffusivity, mean diffusivity and fractional anisotropy) were evaluated on a voxel-by-voxel basis. SOS-based tissue microstructure values are systematically lower than AC-based measures throughout the brain in each subject when using the standard tensor calculation method. The difference between SOS and AC can be virtually eliminated by taking into account the signal statistics associated with coil combination. The impact of coil combination mode on diffusion tensor-based measures of tissue microstructure is statistically significant but can be corrected retrospectively. The ability to do so is expected to facilitate pooling of data among imaging protocols. Copyright Â© 2016 Elsevier Inc. All rights reserved.
Abductor tendon tears are associated with hypertrophy of the tensor fasciae latae muscle.
Sutter, Reto; Kalberer, Fabian; Binkert, Christoph A; Graf, Nicole; Pfirrmann, Christian W A; Gutzeit, Andreas
2013-05-01
To evaluate the association between hypertrophy of the tensor fasciae latae muscle and abductor tendon tears. Thirty-five patients who underwent MRI of the abductor tendons of the hip were included in this retrospective study. A subgroup of 18 patients was examined bilaterally. The area of the tensor fasciae latae muscle and the area of the sartorius muscle (size reference) were quantified at the level of the femoral head, and a ratio was calculated. Two radiologists assessed the integrity of the gluteus medius and minimus tendon in consensus. Data were analyzed with a Mann-Whitney U test. Sixteen out of 35 patients (46 %) had a tear of the gluteus medius or minimus tendon. The ratio of the area of the tensor fasciae latae to the sartorius muscle was significantly higher (p = .028) in the group with an abductor tendon tear (median 2.25; Interquartile Range [IQR] = 1.97-3.21) compared to the group without any tears (median 1.91; IQR = 1.52-2.26). The bilateral subanalysis showed that in patients without a tear, the ratio of the two areas did not differ between each side (p = .966), with a median of 1.54 (primary side) and 1.76 (contralateral side). In patients with an abductor tendon tear the ratio was significantly higher (p = .031) on the side with a tear (median 2.81) compared to the contralateral healthy side (1.67). Patients with abductor tendon tears showed hypertrophy of the tensor fasciae latae muscle when compared to the contralateral healthy side and to patients without a tear.
The search for neuroimaging biomarkers of Alzheimer's disease with advanced MRI techniques
Energy Technology Data Exchange (ETDEWEB)
Li, Tie-Qiang (Karolinska Huddinge - Medical Physics, Stockholm (Sweden)), email: tieqiang.li@karolinska.se; Wahlund, Lars-Olof (Dept. of Neurobiology, Care Sciences and Society, Karolinska Institute, Stockholm (Sweden))
2011-02-15
The aim of this review is to examine the recent literature on using advanced magnetic resonance imaging (MRI) techniques for finding neuroimaging biomarkers that are sensitive to the detection of risks for Alzheimer's disease (AD). Since structural MRI techniques, such as brain structural volumetry and voxel based morphometry (VBM), have been widely used for AD studies and extensively reviewed, we will only briefly touch on the topics of volumetry and morphometry. The focus of the current review is about the more recent developments in the search for AD neuroimaging biomarkers with functional MRI (fMRI), resting-state functional connectivity MRI (fcMRI), diffusion tensor imaging (DTI), arterial spin-labeling (ASL), and magnetic resonance spectroscopy (MRS)
Advance MRI for pediatric brain tumors with emphasis on clinical benefits
Energy Technology Data Exchange (ETDEWEB)
Goo, Hyun Woo; Ra, Young Shin [Asan Medical Center, University of Ulsan College of Medicine, Seoul(Korea, Republic of)
2017-01-15
Conventional anatomic brain MRI is often limited in evaluating pediatric brain tumors, the most common solid tumors and a leading cause of death in children. Advanced brain MRI techniques have great potential to improve diagnostic performance in children with brain tumors and overcome diagnostic pitfalls resulting from diverse tumor pathologies as well as nonspecific or overlapped imaging findings. Advanced MRI techniques used for evaluating pediatric brain tumors include diffusion-weighted imaging, diffusion tensor imaging, functional MRI, perfusion imaging, spectroscopy, susceptibility-weighted imaging, and chemical exchange saturation transfer imaging. Because pediatric brain tumors differ from adult counterparts in various aspects, MRI protocols should be designed to achieve maximal clinical benefits in pediatric brain tumors. In this study, we review advanced MRI techniques and interpretation algorithms for pediatric brain tumors.
The search for neuroimaging biomarkers of Alzheimer's disease with advanced MRI techniques
International Nuclear Information System (INIS)
Li, Tie-Qiang; Wahlund, Lars-Olof
2011-01-01
The aim of this review is to examine the recent literature on using advanced magnetic resonance imaging (MRI) techniques for finding neuroimaging biomarkers that are sensitive to the detection of risks for Alzheimer's disease (AD). Since structural MRI techniques, such as brain structural volumetry and voxel based morphometry (VBM), have been widely used for AD studies and extensively reviewed, we will only briefly touch on the topics of volumetry and morphometry. The focus of the current review is about the more recent developments in the search for AD neuroimaging biomarkers with functional MRI (fMRI), resting-state functional connectivity MRI (fcMRI), diffusion tensor imaging (DTI), arterial spin-labeling (ASL), and magnetic resonance spectroscopy (MRS)
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 integrand reduction via Laurent expansion
Energy Technology Data Exchange (ETDEWEB)
Hirschi, Valentin [SLAC, National Accelerator Laboratory,2575 Sand Hill Road, Menlo Park, CA 94025-7090 (United States); Peraro, Tiziano [Higgs Centre for Theoretical Physics, School of Physics and Astronomy,The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom)
2016-06-09
We introduce a new method for the application of one-loop integrand reduction via the Laurent expansion algorithm, as implemented in the public C++ library Ninja. We show how the coefficients of the Laurent expansion can be computed by suitable contractions of the loop numerator tensor with cut-dependent projectors, making it possible to interface Ninja to any one-loop matrix element generator that can provide the components of this tensor. We implemented this technique in the Ninja library and interfaced it to MADLOOP, which is part of the public MADGRAPH5{sub A}MC@NLO framework. We performed a detailed performance study, comparing against other public reduction tools, namely CUTTOOLS, SAMURAI, IREGI, PJFRY++ and GOLEM95. We find that Ninja outperforms traditional integrand reduction in both speed and numerical stability, the latter being on par with that of the tensor integral reduction tool GOLEM95 which is however more limited and slower than Ninja. We considered many benchmark multi-scale processes of increasing complexity, involving QCD and electro-weak corrections as well as effective non-renormalizable couplings, showing that Ninja’s performance scales well with both the rank and multiplicity of the considered process.
Non-Newtonian stress tensor and thermal conductivity tensor in granular plane shear flow
Alam, Meheboob; Saha, Saikat
2014-11-01
The non-Newtonian stress tensor and the heat flux in the plane shear flow of smooth inelastic disks are analysed from the Grad-level moment equations using the anisotropic Gaussian as a reference. Closed-form expressions for shear viscosity, pressure, first normal stress difference (N1) and the dissipation rate are given as functions of (i) the density or the area fraction (ν), (ii) the restitution coefficient (e), (iii) the dimensionless shear rate (R), (iv) the temperature anisotropy [ η, the difference between the principal eigenvalues of the second moment tensor] and (v) the angle (ϕ) between the principal directions of the shear tensor and the second moment tensor. Particle simulation data for a sheared hard-disk system is compared with theoretical results, with good agreement for p, μ and N1 over a large range of density. In contrast, the predictions from a Navier-Stokes order constitutive model are found to deviate significantly from both the simulation and the moment theory even at moderate values of e. We show that the gradient of the deviatoric part of the kinetic stress drives a heat current and the thermal conductivity is characterized by an anisotropic 2nd rank tensor for which explicit expressions are derived.
Diffusion tensor analysis of corpus callosum in progressive supranuclear palsy
Energy Technology Data Exchange (ETDEWEB)
Ito, Shoichi; Makino, Takahiro; Shirai, Wakako; Hattori, Takamichi [Department of Neurology, Graduate School of Medicine, Chiba University (Japan)
2008-11-15
Progressive supranuclear palsy (PSP) is a neurodegenerative disease featuring parkinsonism, supranuclear ophthalmoplegia, dysphagia, and frontal lobe dysfunction. The corpus callosum which consists of many commissure fibers probably reflects cerebral cortical function. Several previous reports showed atrophy or diffusion abnormalities of anterior corpus callosum in PSP patients, but partitioning method used in these studies was based on data obtained in nonhuman primates. In this study, we performed a diffusion tensor analysis using a new partitioning method for the human corpus callosum. Seven consecutive patients with PSP were compared with 29 age-matched patients with Parkinson's Disease (PD) and 19 age-matched healthy control subjects. All subjects underwent diffusion tensor magnetic resonance imaging, and the corpus callosum was partitioned into five areas on the mid-sagittal plane according to a recently established topography of human corpus callosum (CC1-prefrontal area, CC2-premotor and supplementary motor area, CC3-motor area, CC4-sensory area, CC5-parietal, temporal, and occipital area). Fractional anisotropy (FA) and apparent diffusion coefficient (ADC) were measured in each area and differences between groups were analyzed. In the PSP group, FA values were significantly decreased in CC1 and CC2, and ADC values were significantly increased in CC1 and CC2. Receiver operating characteristic analysis showed excellent reliability of FA and ADC analyses of CC1 for differentiating PSP from PD. The anterior corpus callosum corresponding to the prefrontal, premotor, and supplementary motor cortices is affected in PSP patients. This analysis can be an additional test for further confirmation of the diagnosis of PSP.
Diffusion tensor analysis of corpus callosum in progressive supranuclear palsy
International Nuclear Information System (INIS)
Ito, Shoichi; Makino, Takahiro; Shirai, Wakako; Hattori, Takamichi
2008-01-01
Progressive supranuclear palsy (PSP) is a neurodegenerative disease featuring parkinsonism, supranuclear ophthalmoplegia, dysphagia, and frontal lobe dysfunction. The corpus callosum which consists of many commissure fibers probably reflects cerebral cortical function. Several previous reports showed atrophy or diffusion abnormalities of anterior corpus callosum in PSP patients, but partitioning method used in these studies was based on data obtained in nonhuman primates. In this study, we performed a diffusion tensor analysis using a new partitioning method for the human corpus callosum. Seven consecutive patients with PSP were compared with 29 age-matched patients with Parkinson's Disease (PD) and 19 age-matched healthy control subjects. All subjects underwent diffusion tensor magnetic resonance imaging, and the corpus callosum was partitioned into five areas on the mid-sagittal plane according to a recently established topography of human corpus callosum (CC1-prefrontal area, CC2-premotor and supplementary motor area, CC3-motor area, CC4-sensory area, CC5-parietal, temporal, and occipital area). Fractional anisotropy (FA) and apparent diffusion coefficient (ADC) were measured in each area and differences between groups were analyzed. In the PSP group, FA values were significantly decreased in CC1 and CC2, and ADC values were significantly increased in CC1 and CC2. Receiver operating characteristic analysis showed excellent reliability of FA and ADC analyses of CC1 for differentiating PSP from PD. The anterior corpus callosum corresponding to the prefrontal, premotor, and supplementary motor cortices is affected in PSP patients. This analysis can be an additional test for further confirmation of the diagnosis of PSP
Tensor interaction in heavy-ion scattering. Pt. 1
International Nuclear Information System (INIS)
Nishioka, H.; Johnson, R.C.
1985-01-01
The Heidelberg shape-effect model for heavy-ion tensor interactions is reformulated and generalized using the Hooton-Johnson formulation. The generalized semiclassical model (the turning-point model) predicts that the components of the tensor analysing power anti Tsub(2q) have certain relations with each other for each type of tensor interaction (Tsub(R), Tsub(P) and Tsub(L) types). The predicted relations between the anti Tsub(2q) are very simple and have a direct connection with the properties of the tensor interaction at the turning point. The model predictions are satisfied in quantum-mechanical calculations for 7 Li and 23 Na elastic scattering from 58 Ni in the Fresnel-diffraction energy region. As a consequence of this model, it becomes possible to single out effects from a Tsub(P)- or Tsub(L)-type tensor interaction in polarized heavy-ion scattering. The presence of a Tsub(P)-type tensor interaction is suggested by measured anti T 20 /anti T 22 ratios for 7 Li + 58 Ni scattering. In the turning-point model the three types of tensor operator are not independent, and this is found to be true also in a quantum-mechanical calculation. The model also predicts relations between the components of higher-rank tensor analysing power in the presence of a higher-rank tensor interaction. The rank-3 tensor case is discussed in detail. (orig.)
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.
International Nuclear Information System (INIS)
Forger, M.; Mannheim Univ.; Laartz, J.; Schaeper, U.
1994-01-01
The recently derived current algrbra of classical non-linear sigma models on arbitrary Riemannian manifolds is extended to include the energy-momentum tensor. It is found that in two dimensions the energy-momentum tensor θ μv , the Noether current j μ associated with the global symmetry of the theory and the composite field j appearing as the coefficient of the Schwinger term in the current algebra, together with the derivatives of j μ and j, generte a closed algebra. The subalgebra generated by the light-cone components of the energy-momentum tensor consists of two commuting copies of the Virasoro algebra, with central charge c=0, reflecting the classical conformal invariance of the theory, but the current algebra part and the semidirect product structure are quite different from the usual Kac-Moody/Sugawara type contruction. (orig.)
Rossi, Marcel M; Alderson, Jacqueline; El-Sallam, Amar; Dowling, James; Reinbolt, Jeffrey; Donnelly, Cyril J
2016-12-08
The aims of this study were to: (i) establish a new criterion method to validate inertia tensor estimates by setting the experimental angular velocity data of an airborne objects as ground truth against simulations run with the estimated tensors, and (ii) test the sensitivity of the simulations to changes in the inertia tensor components. A rigid steel cylinder was covered with reflective kinematic markers and projected through a calibrated motion capture volume. Simulations of the airborne motion were run with two models, using inertia tensor estimated with geometric formula or the compound pendulum technique. The deviation angles between experimental (ground truth) and simulated angular velocity vectors and the root mean squared deviation angle were computed for every simulation. Monte Carlo analyses were performed to assess the sensitivity of simulations to changes in magnitude of principal moments of inertia within ±10% and to changes in orientation of principal axes of inertia within ±10° (of the geometric-based inertia tensor). Root mean squared deviation angles ranged between 2.9° and 4.3° for the inertia tensor estimated geometrically, and between 11.7° and 15.2° for the compound pendulum values. Errors up to 10% in magnitude of principal moments of inertia yielded root mean squared deviation angles ranging between 3.2° and 6.6°, and between 5.5° and 7.9° when lumped with errors of 10° in principal axes of inertia orientation. The proposed technique can effectively validate inertia tensors from novel estimation methods of body segment inertial parameter. Principal axes of inertia orientation should not be neglected when modelling human/animal mechanics. Copyright © 2016 Elsevier Ltd. All rights reserved.
Multimodal structural MRI in the diagnosis of motor neuron diseases.
Ferraro, Pilar M; Agosta, Federica; Riva, Nilo; Copetti, Massimiliano; Spinelli, Edoardo Gioele; Falzone, Yuri; Sorarù, Gianni; Comi, Giancarlo; Chiò, Adriano; Filippi, Massimo
2017-01-01
This prospective study developed an MRI-based method for identification of individual motor neuron disease (MND) patients and test its accuracy at the individual patient level in an independent sample compared with mimic disorders. 123 patients with amyotrophic lateral sclerosis (ALS), 44 patients with predominantly upper motor neuron disease (PUMN), 20 patients with ALS-mimic disorders, and 78 healthy controls were studied. The diagnostic accuracy of precentral cortical thickness and diffusion tensor (DT) MRI metrics of corticospinal and motor callosal tracts were assessed in a training cohort and externally proved in a validation cohort using a random forest analysis. In the training set, precentral cortical thickness showed 0.86 and 0.89 accuracy in differentiating ALS and PUMN patients from controls, while DT MRI distinguished the two groups from controls with 0.78 and 0.92 accuracy. In ALS vs controls, the combination of cortical thickness and DT MRI metrics (combined model) improved the classification pattern (0.91 accuracy). In the validation cohort, the best accuracy was reached by DT MRI (0.87 and 0.95 accuracy in ALS and PUMN vs mimic disorders). The combined model distinguished ALS and PUMN patients from mimic syndromes with 0.87 and 0.94 accuracy. A multimodal MRI approach that incorporates motor cortical and white matter alterations yields statistically significant improvement in accuracy over using each modality separately in the individual MND patient classification. DT MRI represents the most powerful tool to distinguish MND from mimic disorders.
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.
An in vivo MRI Template Set for Morphometry, Tissue Segmentation, and fMRI Localization in Rats
Valdés-Hernández, Pedro Antonio; Sumiyoshi, Akira; Nonaka, Hiroi; Haga, Risa; Aubert-Vásquez, Eduardo; Ogawa, Takeshi; Iturria-Medina, Yasser; Riera, Jorge J.; Kawashima, Ryuta
2011-01-01
Over the last decade, several papers have focused on the construction of highly detailed mouse high field magnetic resonance image (MRI) templates via non-linear registration to unbiased reference spaces, allowing for a variety of neuroimaging applications such as robust morphometric analyses. However, work in rats has only provided medium field MRI averages based on linear registration to biased spaces with the sole purpose of approximate functional MRI (fMRI) localization. This precludes any morphometric analysis in spite of the need of exploring in detail the neuroanatomical substrates of diseases in a recent advent of rat models. In this paper we present a new in vivo rat T2 MRI template set, comprising average images of both intensity and shape, obtained via non-linear registration. Also, unlike previous rat template sets, we include white and gray matter probabilistic segmentations, expanding its use to those applications demanding prior-based tissue segmentation, e.g., statistical parametric mapping (SPM) voxel-based morphometry. We also provide a preliminary digitalization of latest Paxinos and Watson atlas for anatomical and functional interpretations within the cerebral cortex. We confirmed that, like with previous templates, forepaw and hindpaw fMRI activations can be correctly localized in the expected atlas structure. To exemplify the use of our new MRI template set, were reported the volumes of brain tissues and cortical structures and probed their relationships with ontogenetic development. Other in vivo applications in the near future can be tensor-, deformation-, or voxel-based morphometry, morphological connectivity, and diffusion tensor-based anatomical connectivity. Our template set, freely available through the SPM extension website, could be an important tool for future longitudinal and/or functional extensive preclinical studies. PMID:22275894
An in vivo MRI Template Set for Morphometry, Tissue Segmentation, and fMRI Localization in Rats.
Valdés-Hernández, Pedro Antonio; Sumiyoshi, Akira; Nonaka, Hiroi; Haga, Risa; Aubert-Vásquez, Eduardo; Ogawa, Takeshi; Iturria-Medina, Yasser; Riera, Jorge J; Kawashima, Ryuta
2011-01-01
Over the last decade, several papers have focused on the construction of highly detailed mouse high field magnetic resonance image (MRI) templates via non-linear registration to unbiased reference spaces, allowing for a variety of neuroimaging applications such as robust morphometric analyses. However, work in rats has only provided medium field MRI averages based on linear registration to biased spaces with the sole purpose of approximate functional MRI (fMRI) localization. This precludes any morphometric analysis in spite of the need of exploring in detail the neuroanatomical substrates of diseases in a recent advent of rat models. In this paper we present a new in vivo rat T2 MRI template set, comprising average images of both intensity and shape, obtained via non-linear registration. Also, unlike previous rat template sets, we include white and gray matter probabilistic segmentations, expanding its use to those applications demanding prior-based tissue segmentation, e.g., statistical parametric mapping (SPM) voxel-based morphometry. We also provide a preliminary digitalization of latest Paxinos and Watson atlas for anatomical and functional interpretations within the cerebral cortex. We confirmed that, like with previous templates, forepaw and hindpaw fMRI activations can be correctly localized in the expected atlas structure. To exemplify the use of our new MRI template set, were reported the volumes of brain tissues and cortical structures and probed their relationships with ontogenetic development. Other in vivo applications in the near future can be tensor-, deformation-, or voxel-based morphometry, morphological connectivity, and diffusion tensor-based anatomical connectivity. Our template set, freely available through the SPM extension website, could be an important tool for future longitudinal and/or functional extensive preclinical studies.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education. Personal Reflections. Articles in Resonance – Journal of Science Education. Volume 6 Issue 3 March 2001 pp 90-93 Personal Reflections. Why did I opt for Career in Science? Jayant V Narlikar · More Details Fulltext PDF. Volume 9 Issue 8 August 2004 pp 89-89 ...
International Nuclear Information System (INIS)
Eggermont, G.
2006-01-01
In 2005, PISA organised proactive meetings of reflection groups on involvement in decision making, expert culture and ethical aspects of radiation protection.All reflection group meetings address particular targeted audiences while the output publication in book form is put forward
DEFF Research Database (Denmark)
Boura, Christina; Canteaut, Anne; Knudsen, Lars Ramkilde
2017-01-01
study the necessary properties for this coupling permutation. Special care has to be taken of some related-key distinguishers since, in the context of reflection ciphers, they may provide attacks in the single-key setting.We then derive some criteria for constructing secure reflection ciphers...
Srinivasan, K; Thomas, B; Shah, D; Kannath, S K; Menon, G; Sandhyamani, S; Kesavadas, C; Kapilamoorthy, T R
2016-12-01
To quantitatively evaluate the diffusion tensor metrics p, q, L and fractional anisotropy in intracranial epidermoids in comparison with normal white matter in the splenium of the corpus callosum. This retrospective study included 20 consecutive patients referred to our institute. All patients had a magnetic resonance imaging (MRI) study on a 1.5-Tesla MR system. A spin-echo echo-planar DTI sequence with diffusion gradients along 30 non-collinear directions was performed. The eigen values (λ 1 , λ 2 , λ 3 ) were computed for each voxel and, using p: q tensor decomposition, the DTI metrics p, q and L-values and fractional anositropy (FA) were calculated. The region of interest (ROI) (6 pixels each) was placed within the lesion in all the cases and in the splenium of the corpus callosum. The mean FA in the lesion and splenium were 0.50 and 0.88 respectively, with a statistically significant difference between them (Ptensor decomposition, the mean p-value in the epidermoid was 1.55±0.24 and 1.35±0.20 in the splenium; the mean q-values in the epidermoid was 0.67±0.13 and 1.27±0.17 in the splenium; the differences were statistically significant (P=0.01 and <0.01 respectively). The significant difference between p- and q-values in epidermoids compared with the splenium of callosum was probably due to structural and orientation differences in the keratin flakes in epidermoids and white matter bundles in the callosum. However, no significant statistical difference in L-values was noted (P=0.44). DTI metrics p and q have the potential to quantify the diffusion and anisotropy in various tissues thereby gaining information about their internal architecture. The results also suggest that significant differences of DTI metrics p and q between epidermoid and the splenium of the corpus callosum are due to the difference in structural organization within them. Copyright © 2016. Published by Elsevier Masson SAS.
Seely, Jeffrey S; Kaufman, Matthew T; Ryu, Stephen I; Shenoy, Krishna V; Cunningham, John P; Churchland, Mark M
2016-11-01
Cortical firing rates frequently display elaborate and heterogeneous temporal structure. One often wishes to compute quantitative summaries of such structure-a basic example is the frequency spectrum-and compare with model-based predictions. The advent of large-scale population recordings affords the opportunity to do so in new ways, with the hope of distinguishing between potential explanations for why responses vary with time. We introduce a method that assesses a basic but previously unexplored form of population-level structure: when data contain responses across multiple neurons, conditions, and times, they are naturally expressed as a third-order tensor. We examined tensor structure for multiple datasets from primary visual cortex (V1) and primary motor cortex (M1). All V1 datasets were 'simplest' (there were relatively few degrees of freedom) along the neuron mode, while all M1 datasets were simplest along the condition mode. These differences could not be inferred from surface-level response features. Formal considerations suggest why tensor structure might differ across modes. For idealized linear models, structure is simplest across the neuron mode when responses reflect external variables, and simplest across the condition mode when responses reflect population dynamics. This same pattern was present for existing models that seek to explain motor cortex responses. Critically, only dynamical models displayed tensor structure that agreed with the empirical M1 data. These results illustrate that tensor structure is a basic feature of the data. For M1 the tensor structure was compatible with only a subset of existing models.
Directory of Open Access Journals (Sweden)
Jeffrey S Seely
2016-11-01
Full Text Available Cortical firing rates frequently display elaborate and heterogeneous temporal structure. One often wishes to compute quantitative summaries of such structure-a basic example is the frequency spectrum-and compare with model-based predictions. The advent of large-scale population recordings affords the opportunity to do so in new ways, with the hope of distinguishing between potential explanations for why responses vary with time. We introduce a method that assesses a basic but previously unexplored form of population-level structure: when data contain responses across multiple neurons, conditions, and times, they are naturally expressed as a third-order tensor. We examined tensor structure for multiple datasets from primary visual cortex (V1 and primary motor cortex (M1. All V1 datasets were 'simplest' (there were relatively few degrees of freedom along the neuron mode, while all M1 datasets were simplest along the condition mode. These differences could not be inferred from surface-level response features. Formal considerations suggest why tensor structure might differ across modes. For idealized linear models, structure is simplest across the neuron mode when responses reflect external variables, and simplest across the condition mode when responses reflect population dynamics. This same pattern was present for existing models that seek to explain motor cortex responses. Critically, only dynamical models displayed tensor structure that agreed with the empirical M1 data. These results illustrate that tensor structure is a basic feature of the data. For M1 the tensor structure was compatible with only a subset of existing models.
Asselmeyer-Maluga, Torsten
2016-01-01
In this book, leading theorists present new contributions and reviews addressing longstanding challenges and ongoing progress in spacetime physics. In the anniversary year of Einstein's General Theory of Relativity, developed 100 years ago, this collection reflects the subsequent and continuing fruitful development of spacetime theories. The volume is published in honour of Carl Brans on the occasion of his 80th birthday. Carl H. Brans, who also contributes personally, is a creative and independent researcher and one of the founders of the scalar-tensor theory, also known as Jordan-Brans-Dicke theory. In the present book, much space is devoted to scalar-tensor theories. Since the beginning of the 1990s, Brans has worked on new models of spacetime, collectively known as exotic smoothness, a field largely established by him. In this Festschrift, one finds an outstanding and unique collection of articles about exotic smoothness. Also featured are Bell's inequality and Mach's principle. Personal memories and hist...
A MAPLE Package for Energy-Momentum Tensor Assessment in Curved Space-Time
International Nuclear Information System (INIS)
Murariu, Gabriel; Praisler, Mirela
2010-01-01
One of the most interesting problem which remain unsolved, since the birth of the General Theory of Relativity (GR), is the energy-momentum localization. All our reflections are within the Lagrange formalism of the field theory. The concept of the energy-momentum tensor for gravitational interactions has a long history. To find a generally accepted expression, there have been different attempts. This paper is dedicated to the investigation of the energy-momentum problem in the theory of General Relativity. We use Einstein [1], Landau-Lifshitz [2], Bergmann-Thomson [3] and Moller's [4] prescriptions to evaluate energy-momentum distribution. In order to cover the huge volume of computation and, bearing in mind to make a general approaching for different space-time configurations, a MAPLE application to succeed in studying the energy momentum tensor was built. In the second part of the paper for two space-time configuration, the comparative results were presented.
DEFF Research Database (Denmark)
Alcock, Gordon Lindsay
2013-01-01
´ These are all based on Blooms taxonomy and levels of competence and form a major part of individual student and group learning portfolios. Key Words :Project-Based learning, Reflective Portfolios, Self assessment, Defining learning gains, Developing learning strategies , Reflections on and for learning....... It contrasts the students’ self-assessment in a range of ‘product’ skills such as Revit, Structural Design, Mathematics of construction, Technical Installations; as well as ‘process’ competencies such as ‘Working in a team’, Sharing knowledge, Maintaining a portfolio and Reflecting ON learning and FOR learning......This paper documents 1st semester student reflections on “learning to learn” in a team-based PBL environment with quantitative and qualitative student reflective feedback on the learning gains of 60 Architectural Technology and Construction Management students at VIA University College, Denmark...
An introduction to tensors and group theory for physicists
Jeevanjee, Nadir
2011-01-01
An Introduction to Tensors and Group Theory for Physicists provides both an intuitive and rigorous approach to tensors and groups and their role in theoretical physics and applied mathematics. A particular aim is to demystify tensors and provide a unified framework for understanding them in the context of classical and quantum physics. Connecting the component formalism prevalent in physics calculations with the abstract but more conceptual formulation found in many mathematical texts, the work will be a welcome addition to the literature on tensors and group theory. Part I of the text begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to classical and quantum physics through the use of tensor products. Part II introduces abstract groups along with matrix Lie groups and Lie algebras, then intertwines this material with that of Part I by introducing representation theory. Exercises and examples are provided throughout for go...
Theoretical study of lithium clusters by electronic stress tensor
International Nuclear Information System (INIS)
Ichikawa, Kazuhide; Nozaki, Hiroo; Komazawa, Naoya; Tachibana, Akitomo
2012-01-01
We study the electronic structure of small lithium clusters Li_n (n = 2 ∼ 8) using the electronic stress tensor. We find that the three eigenvalues of the electronic stress tensor of the Li clusters are negative and degenerate, just like the stress tensor of liquid. This leads us to propose that we may characterize a metallic bond in terms of the electronic stress tensor. Our proposal is that in addition to the negativity of the three eigenvalues of the electronic stress tensor, their degeneracy characterizes some aspects of the metallic nature of chemical bonding. To quantify the degree of degeneracy, we use the differential eigenvalues of the electronic stress tensor. By comparing the Li clusters and hydrocarbon molecules, we show that the sign of the largest eigenvalue and the differential eigenvalues could be useful indices to evaluate the metallicity or covalency of a chemical bond.
Radiative corrections in a vector-tensor model
International Nuclear Information System (INIS)
Chishtie, F.; Gagne-Portelance, M.; Hanif, T.; Homayouni, S.; McKeon, D.G.C.
2006-01-01
In a recently proposed model in which a vector non-Abelian gauge field interacts with an antisymmetric tensor field, it has been shown that the tensor field possesses no physical degrees of freedom. This formal demonstration is tested by computing the one-loop contributions of the tensor field to the self-energy of the vector field. It is shown that despite the large number of Feynman diagrams in which the tensor field contributes, the sum of these diagrams vanishes, confirming that it is not physical. Furthermore, if the tensor field were to couple with a spinor field, it is shown at one-loop order that the spinor self-energy is not renormalizable, and hence this coupling must be excluded. In principle though, this tensor field does couple to the gravitational field
MRI: update on technology diffusion and acquisition.
Hoppszallern, S; Hughes, C; Zimmerman, R A
1991-04-01
-site MRI providers have been constantly upgrading their MRI capability while planning on adding more units. The technology itself has continued to improve, primarily through the implementation of new software that permits new techniques such as MR angiography (MRA) to be performed. Units are available in a wide price range, price usually reflecting both the field strength (0.5 tesla units cost less) as well as the additional capabilities beyond routine imaging (MRA, spectroscopy).(ABSTRACT TRUNCATED AT 400 WORDS)
Supergravity tensor calculus in 5D from 6D
International Nuclear Information System (INIS)
Kugo, Taichiro; Ohashi, Keisuke
2000-01-01
Supergravity tensor calculus in five spacetime dimensions is derived by dimensional reduction from the d=6 superconformal tensor calculus. In particular, we obtain an off-shell hypermultiplet in 5D from the on-shell hypermultiplet in 6D. Our tensor calculus retains the dilatation gauge symmetry, so that it is a trivial gauge fixing to make the Einstein term canonical in a general matter-Yang-Mills-supergravity coupled system. (author)
Mesh Denoising based on Normal Voting Tensor and Binary Optimization
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...
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....