Oxygen transfer in human carotid artery bifurcation
Institute of Scientific and Technical Information of China (English)
Z.G.Zhang; Y.B.Fan; X.Y.Deng
2007-01-01
Arterial bifurcations are places where blood flow may be disturbed and slow recirculation flow may occur.To reveal the correlation between local oxygen transfer and atherogenesis, a finite element method was employed to simulate the blood flow and the oxygen transfer in the human carotid artery bifurcation. Under steady-state flow conditions, the numerical simulation demonstrated a variation in local oxygen transfer at the bifurcation, showing that the convective condition in the disturbed flow region may produce uneven local oxygen transfer at the blood/wall interface.The disturbed blood flow with formation of slow eddies in the carotid sinus resulted in a depression in oxygen supply to the arterial wall at the entry of the sinus, which in turn may lead to an atherogenic response of the arterial wall, and contribute to the development of atherosclerotic stenosis there.
Sex differences in intracranial arterial bifurcations
DEFF Research Database (Denmark)
Lindekleiv, Haakon M; Valen-Sendstad, Kristian; Morgan, Michael K; Mardal, Kent-Andre; Faulder, Kenneth; Magnus, Jeanette H; Waterloo, Knut; Romner, Bertil; Ingebrigtsen, Tor
2010-01-01
Subarachnoid hemorrhage (SAH) is a serious condition, occurring more frequently in females than in males. SAH is mainly caused by rupture of an intracranial aneurysm, which is formed by localized dilation of the intracranial arterial vessel wall, usually at the apex of the arterial bifurcation. T...... female preponderance is usually explained by systemic factors (hormonal influences and intrinsic wall weakness); however, the uneven sex distribution of intracranial aneurysms suggests a possible physiologic factor-a local sex difference in the intracranial arteries....
Shape optimization of the carotid artery bifurcation
Bressloff, N. W.; Forrester, A.I.J.; Banks, J.; Bhaskar, K.V.
2004-01-01
A parametric CAD model of the human carotid artery bifurcation is employed in an initial exploration of the response of shear stress to the variation of the angle of the internal carotid artery and the width of the sinus bulb. Design of experiment and response surface technologies are harnessed for the first time in such an application with the aim of developing a better understanding of the relationship between geometry (anatomy) and sites of arterial disease.
Internal carotid artery bifurcation aneurysms. Surgical experience
International Nuclear Information System (INIS)
Internal carotid artery (ICA) bifurcation aneurysms are relatively uncommon and frequently rupture at a younger age compared to other intracranial aneurysms. We have treated a total of 999 patients for intracranial aneurysms, of whom 89 (8.9%) had ICA bifurcation aneurysms, and 42 of the 89 patients were 30 years of age or younger. The present study analyzed the clinical records of 70 patients with ICA bifurcation aneurysms treated from mid 1997 to mid 2003. Multiple aneurysms were present in 15 patients. Digital subtraction angiography films were studied in 55 patients to identify vasospasm and aneurysm projection. The aneurysm projected superiorly in most of these patients (37/55, 67.3%). We preferred to minimize frontal lobe retraction, so widely opened the sylvian fissure to approach the ICA bifurcation and aneurysm neck. Elective temporary clipping was employed before the final dissection and permanent clip application. Vasospasm was present in 24 (43.6%) of 55 patients. Forty-eight (68.6%) of the 70 patients had good outcome, 14 (20%) had poor outcome, and eight (11.4%) died. Patients with ICA bifurcation aneurysms tend to bleed at a much younger age compared to those with other intracranial aneurysms. Wide opening of the sylvian fissure and elective temporary clipping of the ICA reduces the risk of intraoperative rupture and perforator injury. Mortality was mainly due to poor clinical grade and intraoperative premature aneurysm rupture. (author)
International Nuclear Information System (INIS)
The aim of this study was to investigate the plaques at the left coronary artery (LCA) and their effect on the haemodynamic and wall shear stress (WSS) in realistic patient models. Three sample patients with left coronary disease were selected based on CT data. The plaques were present at the left anterior descending and left circumflex branches with more than 50 % lumen narrowing. Computational fluid dynamics analysis was used to perform simulation of patient-specific models with realistic physiological conditions that demonstrate in vivo cardiac flow. WSS and blood flow in the LCA were measured during cardiac cycles. Our results showed that WSS was found to increase at the stenotic locations and decrease at pre- and post-plaque locations, whilst the recirculation location was found at post-plaque regions. There is a strong correlation between coronary bifurcation plaques and hemodynamic and WSS changes, based on the realistic coronary disease models.
HIGH BIFURCATION OF THE BRACHIAL ARTERY - A COMMON VARIANT
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Sesi
2015-10-01
Full Text Available 28 cadavers were dissected for variations in the bifurcation of brachial artery bilaterally {n=56} at the department of anatomy, Rangaraya Medical College, Kakinada, A.P. from 2010 to 2015 . Found variations during routine dissections for first year MBBS students. The findings have thrown light on the common as well as rare variants in the anatomy of brachial artery bifurcation and the course of radial and ulnar arteries in current study
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Lee, Cheng-Hung [Division of Cardiology, Department of Internal Medicine, Chang Gung Memorial Hospital, Linkou, Chang Gung University College of Medicine, Tao-Yuan, Taiwan (China); Department of Mechanical Engineering, Chang Gung University, Tao-Yuan, Taiwan (China); Jhong, Guan-Heng [Graduate Institute of Medical Mechatronics, Chang Gung University, Tao-Yuan, Taiwan (China); Hsu, Ming-Yi; Wang, Chao-Jan [Department of Medical Imaging and Intervention, Chang Gung Memorial Hospital, Linkou, Tao-Yuan, Taiwan (China); Liu, Shih-Jung, E-mail: shihjung@mail.cgu.edu.tw [Department of Mechanical Engineering, Chang Gung University, Tao-Yuan, Taiwan (China); Hung, Kuo-Chun [Division of Cardiology, Department of Internal Medicine, Chang Gung Memorial Hospital, Linkou, Chang Gung University College of Medicine, Tao-Yuan, Taiwan (China)
2014-05-28
The deployment of metallic stents during percutaneous coronary intervention has become common in the treatment of coronary bifurcation lesions. However, restenosis occurs mostly at the bifurcation area even in present era of drug-eluting stents. To achieve adequate deployment, physicians may unintentionally apply force to the strut of the stents through balloon, guiding catheters, or other devices. This force may deform the struts and impose excessive mechanical stresses on the arterial vessels, resulting in detrimental outcomes. This study investigated the relationship between the distribution of stress in a stent and bifurcation angle using finite element analysis. The unintentionally applied force following stent implantation was measured using a force sensor that was made in the laboratory. Geometrical information on the coronary arteries of 11 subjects was extracted from contrast-enhanced computed tomography scan data. The numerical results reveal that the application of force by physicians generated significantly higher mechanical stresses in the arterial bifurcation than in the proximal and distal parts of the stent (post hoc P < 0.01). The maximal stress on the vessels was significantly higher at bifurcation angle <70° than at angle ≧70° (P < 0.05). The maximal stress on the vessels was negatively correlated with bifurcation angle (P < 0.01). Stresses at the bifurcation ostium may cause arterial wall injury and restenosis, especially at small bifurcation angles. These finding highlight the effect of force-induced mechanical stress at coronary artery bifurcation stenting, and potential mechanisms of in-stent restenosis, along with their relationship with bifurcation angle.
Wall Shear Stress Distribution in Patient Specific Coronary Artery Bifurcation
Directory of Open Access Journals (Sweden)
Vahab Dehlaghi
2010-01-01
Full Text Available Problem statement: Atherogenesis is affected by hemodynamic parameters, such as wall shear stress and wall shear stress spatial gradient. These parameters are largely dependent on the geometry of arterial tree. Arterial bifurcations contain significant flow disturbances. Approach: The effects of branch angle and vessel diameter ratio at the bifurcations on the wall shear stress distribution in the coronary arterial tree based on CT images were studied. CT images were digitally processed to extract geometrical contours representing the coronary vessel walls. The lumen of the coronary arteries of the patients was segmented using the open source software package (VMTK. The resulting lumens of coronary arteries were fed into a commercial mesh generator (GAMBIT, Fluent Inc. to generate a volume that was filled with tetrahedral elements. The FIDAP software (Fluent Corp. was used to carry out the simulation by solving Navier-Stokes equations. The FIELDVIEW software (Version 10.0, Intelligent Light, Lyndhurst, NJ was used for the visualization of flow patterns and the quantification of wall shear stress. Post processing was done with VMTK and MATLAB. A parabolic velocity profile was prescribed at the inlets and outlets, except for 1. Stress free outlet was assigned to the remaining outlet. Results: The results show that for angle lower than 90°, low shear stress regions are observed at the non-flow divider and the apex. For angle larger than 90°, low shear stress regions only at the non-flow divider. By increasing of diameter of side branch ratio, low shear stress regions in the side branch appear at the non-flow divider. Conclusion: It is concluded that not only angle and diameter are important, but also the overall 3D shape of the artery. More research is required to further quantify the effects angle and diameter on shear stress patterns in coronaries.
Sultanov, Renat A
2008-01-01
We report computational results of blood flow through a model of the human aortic arch and a vessel of actual diameter and length. On the top of the aortic arch the branching of the %%three arteries are included: the subclavian and jugular. A realistic pulsatile flow is used in all simulations. Calculations for bifurcation type vessels are also carried out and presented. Different mathematical methods for numerical solution of the fluid dynamics equations have been considered. The non-Newtonian behaviour of the human blood is investigated together with turbulence effects. A detailed time-dependent mathematical convergence test has been carried out. The results of computer simulations of the blood flow in vessels of three different geometries are presented: for pressure, strain rate and velocity component distributions we found significant disagreements between our results obtained with realistic non-Newtonian treatment of human blood and the widely used method in the literature: a simple Newtonian approximati...
Huang, Xu; Yin, Xiaoping; Xu, Yingjin; Jia, Xinwei; Li, Jianhui; Niu, Pei; Shen, Wenzeng; Kassab, Ghassan S; Tan, Wenchang; Huo, Yunlong
2016-03-01
Although atherosclerosis has been widely investigated at carotid artery bifurcation, there is a lack of morphometric and hemodynamic data at different stages of the disease. The purpose of this study was to determine the lesion difference in patients with carotid artery disease compared with healthy control subjects. The three-dimensional (3D) geometry of carotid artery bifurcation was reconstructed from computed tomography angiography (CTA) images of Chinese control subjects (n = 30) and patients with carotid artery disease (n = 30). We defined two novel vector angles (i.e., angles 1 and 2) that were tangential to the reconstructed contour of the 3D vessel. The best-fit diameter was computed along the internal carotid artery (ICA) center line. Hemodynamic analysis was performed at various bifurcations. Patients with stenotic vessels have larger angles 1 and 2 (151 ± 11° and 42 ± 20°) and smaller diameters of the external carotid artery (ECA) (4.6 ± 0.85 mm) compared with control subjects (144 ± 13° and 36 ± 16°, 5.2 ± 0.57 mm) although there is no significant difference in the common carotid artery (CCA) (7.1 ± 1.2 vs. 7.5 ± 1.0 mm, P = 0.18). In particular, all patients with carotid artery disease have a stenosis at the proximal ICA (including both sinus and carina regions), while 20% of patients have stenosis at the middle ICA and 20% have stenosis expansion to the entire cervical ICA. Morphometric and hemodynamic analyses suggest that atherosclerotic plaques initiate at both sinus and carina regions of ICA and progress downstream. PMID:26747497
Narayan, Hari K; Glatz, Andrew C; Rome, Jonathan J
2015-10-01
Balloon angioplasty and stent placement in close proximity to the bifurcation of the branch pulmonary arteries can be challenging. Multiple approaches have been previously described, though none of these approaches both treats bilateral proximal branch pulmonary artery stenosis and provides an anchor for a transcatheter pulmonary valve replacement. We report a novel approach that involves serial stent placement and balloon dilation through the struts of the stent in each pulmonary artery, along with balloon expansion of the proximal portion of the stents to the diameter of the main pulmonary artery. In the two cases we describe, this strategy resulted in significant relief of branch pulmonary artery obstruction without compromising the anatomy of the main pulmonary artery segment. This technique can be an effective way to alleviate stenoses of the bilateral proximal branch pulmonary arteries and provides a landing zone for a future transcatheter pulmonary valve. PMID:26256829
Rotational digital subtraction angiography of carotid artery bifurcation stenoses
International Nuclear Information System (INIS)
Purpose: A prospektive study was designed to evaluate, whether multiplanar imaging with rotational digital subtraction angiography (R-DSA) could improve assessment of carotid artery bifurcation stenosis. Patients and methods: 45 patients with suspected stenosis of the ICA were examined with DSA in standard projections (0 -(45 )-90 ) and additional R-DSA of each ICA from 0-90 in 10 steps. We compared imaging quality and degree of stenosis as well as exposure of the patients to radiation and contrast media. Results: 79/82 R-DSA (96%) were suitable for evaluation of stenosis, 58/82 (70%) matched the quality standard of single projection DSA. Specificity and sensitivity of the R-DSA to diagnose high grade ACI stenosis were 100% and 94%, respectively. 7/79 R-DSA revealed a higher and 3/79 a lower degree of stenosis than the corresponding DSA. Regarding the degree of stenosis there was no significant difference between the two modalities (p>0,05), but R-DSA detected 4 stenoses greater than 60% that were estimated to be lower than 60% by DSA. Radiation dose for R-DSA was equivalent to one DSA run (170 cGycm2). The average amount of contrast media (25 ml) was slightly higher than for 2-3 single-projection DSA (19,8 ml). Conclusions: R-DSA provides high quality imaging of the carotid bifurcation with multiplanar projections facilitating exact grading of vessel stenosis. The number of cases (n=2) is to small to judge the value of R-DSA as to (tandem-) stenosis of the distal ICA. Still, diagnostic value and low radiation exposure justify the use of R-DSA as additional series to standard protocols. (orig.)
Endovascular coil embolization in internal carotid artery bifurcation aneurysms
International Nuclear Information System (INIS)
Aim: To present the clinical and radiological results of coil embolization in internal carotid artery (ICA) bifurcation aneurysms (BA). Materials and methods: The records of 65 patients with 66 ICA BA were retrieved from data prospectively accrued between September 1999 and July 2013. Clinical and morphological outcomes of the aneurysms were assessed, including technical aspects of treatment. Results: The aneurysms under study were directed either superiorly (41/66, 62.1%), anteriorly (24/66, 36.4%), or posteriorly (1/66, 1.5%), and all were devoid of perforators. Aneurysmal necks were situated symmetrically at the terminal ICA (37/66, 56.1%) or slightly deviated to the proximal A1 segment (29/66, 43.9%). The steam-shaped S microcatheter (73.8%) was most commonly used to select the aneurysms, and the single microcatheter technique was most commonly applied (56.1%) to perform coil embolization, followed by balloon remodelling (21.2%), multiple microcatheter (15.1%), and stent-protection (7.6%). Successful aneurysmal occlusion was achieved in 100% of cases, with no procedure-related morbidity or mortality. Imaging performed in the course of follow-up (mean duration 27.3 months) confirmed stable occlusion of most lesions (47/53, 88.7%). Conclusion: Through tailored technical strategies, ICA BA are amenable to safe and effective endovascular coil embolization, with a tendency for stable occlusion long-term
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Objective: to evaluate the efficacy and safety of percutaneous endovascular management with single stent in treating symptomatic series stenosis located at subclavian-vertebral artery bifurcation. Methods: Between February 2009 and April 2010, percutaneous single-stent endovascular treatment was carried out in 7 consecutive patients with symptomatic series stenosis located at subclavian-vertebral artery bifurcation. After implantation of cerebral protection device, percutaneous single-stent endovascular procedure was performed to treat two stenoses at subclavian-vertebral artery bifurcation. All patients were followed up for 3∼15 months. The therapeutic efficacy was evaluated with the observation of clinical symptoms and Doppler ultrasonic examination, the possible occurrence of re-stenosis was checked. Results: Technical success was achieved in all seven patients. After the implantation the residual stenosis of both subclavian and vertebral arteries was less than 10%. No procedure-related complications occurred. During the follow-up period no re-stenosis was observed on Doppler ultrasonography, the clinical symptoms were markedly improved, and no cerebrovascular accident or new cerebral infarction occurred. Conclusion: For the treatment of series stenosis located at subclavian-vertebral artery bifurcation percutaneous single-stent endovascular implantation is a feasible technique. Compared with other methods, this technique carries the advantages of easier manipulation and higher safety for patient although long-term efficacy needs to be further observed. (authors)
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Aim: To investigate the angle changes of the parent arteries after stent-assisted coil embolization of wide-necked intracranial bifurcation aneurysms. Materials and methods: The adjacent parent arterial angles before and after stent-assisted coil embolization were measured in 38 patients with aneurysms of the anterior communicating artery (ACoAA) and 41 patients with bifurcation aneurysms of the middle cerebral artery (MCABA). Variables were analysed in relation to the angle changes. Results: Vascular angles of the parent arteries significantly increased by 27.8° (±18.5°) immediately after stent-assisted coil embolization in 79 cases (p < 0.001), with 25.7° (±14.8°) in ACoAA and 29.7° (±21.4°) in MCABA, respectively. In 51 (64.6%) cases with follow-up angiography (mean interval 13.5 ± 4.1 months), vascular angles increased by 27.2° (±17.1°) immediately after treatment and further increased by 20.7° (±14.3°) at the last follow-up (all p < 0.001). More acute pre-stent angles of the parent arteries correlated with greater post-stent angle changes (p = 0.006). Younger age tended to be inversely related to post-stent angle changes (p = 0.091). Conclusion: Stent placement during coil embolization induced significant changes in the aneurysm–parent artery relationship. Further study is needed to elicit the association between angle change of the parent arteries and aneurysmal stability after coil embolization
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Background: Carpal tunnel syndrome is a sporadically occurring abnormality due to compression of median nerve. It is exceedingly rare for it to be caused by thrombosis of persistent median artery. Case Report: A forty two year old female was referred for ultrasound examination due to ongoing wrist pain, not relived by pain killers and mild paraesthesia on the radial side of the hand. High resolution ultrasound and Doppler revealed a thrombosed persistent median artery and associated bifurcated median nerve. The thrombus resolved on treatment with anticoagulants. Conclusions: Ultrasound examination of the wrist when done for patients with carpal tunnel syndrome should preferably include looking for persistent median artery and its patency. (authors)
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Chen, Yong, E-mail: cheny102@163.com; Ye, Peng, E-mail: thomas19871223@163.com [Southern Medical University, Department of Interventional Radiology, Nanfang Hospital (China); Jiang, Wen-jin, E-mail: 18653501187@163.com [Yantai Yuhuangding Hospital (China); Ma, Shuo-yi, E-mail: mazelong123456789@126.com; Zhao, Jian-bo, E-mail: zhaojianbohgl@163.com; Zeng, Qing-le, E-mail: doctorzengqingle@126.com [Southern Medical University, Department of Interventional Radiology, Nanfang Hospital (China)
2015-10-15
Bifurcation stenoses after end-to-side anastomosis of transplant renal artery (TRA) and external iliac artery (EIA), including stenoses at the anastomosis and the iliac artery proximal to the TRA, are rare. In the present article, we report two successfully managed cases of bifurcation stenoses after end-to-side anastomosis of the TRA and EIA using the technique of T-stenting and small protrusion (TAP stenting)
International Nuclear Information System (INIS)
Bifurcation stenoses after end-to-side anastomosis of transplant renal artery (TRA) and external iliac artery (EIA), including stenoses at the anastomosis and the iliac artery proximal to the TRA, are rare. In the present article, we report two successfully managed cases of bifurcation stenoses after end-to-side anastomosis of the TRA and EIA using the technique of T-stenting and small protrusion (TAP stenting)
Perwaiz Khan, Samia; Gul, Pashmina; Khemani, Saleem; Yaqub, Zia
2013-01-01
Objective: To determine site specific carotid intima-media thickness: common–carotid artery and carotid bifurcation in hypercholesterolemia patients as a marker for atherosclerosis. Methods: Fifty patients with hypercholesterolemia and twenty controls were selected after getting informed consent regarding the investigation of carotid- intima media thickness by B-mode ultrasound. All the patients of hypercholesterolemia with LDL-C > 160mg/dL had family history of coronary artery diseases. This...
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Objective: To preliminarily evaluate the feasibility, safety and efficacy of stent placement for the treatment of wide-necked aneurysms located at internal carotid artery bifurcation. Methods: Eleven patients with wide-necked aneurysms located at internal carotid artery bifurcation, who were encountered during the period from Jan. 2004 to Dec. 2010 in hospital, were collected. A total of 16 intracranial aneurysms were detected, of which 11 were wide-necked and were located at internal carotid artery bifurcation. The diameters of the aneurysms ranged from 2.5 mm to 18 mm. Individual stent type and stenting technique was employed for each patient. Follow-up at 1, 3, 6 and 12 months after the procedure was conducted. Results: A total of 11 different stents were successfully deployed in the eleven patients. The stents included balloon expandable stent (n=1) and self-expanding stent (n=10). According to Raymond grading for the immediate occlusion of the aneurysm, grade Ⅰ (complete obliteration) was obtained in 4, grade Ⅱ (residual neck) in 2 and grade Ⅲ (residual aneurysm) in 5 cases. No procedure-related complications occurred. At the time of discharge, the modified Rankin score was 0-1 in the eleven patients. During the follow-up period lasting for 1-108 months, all the patients were in stable condition and no newly-developed neurological dysfunction or bleeding observed. Follow-up examination with angiography (1-48 months) showed that the aneurysms were cured (no visualization) in 4 cases, improved in 2 cases and in stable condition in one case. Conclusion: For the treatment of wide-necked aneurysms located at internal carotid artery bifurcation, stent implantation is clinically feasible, safe and effective. Further studies are required to evaluate its long-term efficacy. (authors)
Atherosclerosis at arterial bifurcations: evidence for the role of haemodynamics and geometry.
Morbiducci, Umberto; Kok, Annette M; Kwak, Brenda R; Stone, Peter H; Steinman, David A; Wentzel, Jolanda J
2016-03-01
Atherosclerotic plaques are found at distinct locations in the arterial system, despite the exposure to systemic risk factors of the entire vascular tree. From the study of arterial bifurcation regions, emerges ample evidence that haemodynamics are involved in the local onset and progression of the atherosclerotic disease. This observed co-localisation of disturbed flow regions and lesion prevalence at geometrically predisposed districts such as arterial bifurcations has led to the formulation of a 'haemodynamic hypothesis', that in this review is grounded to the most current research concerning localising factors of vascular disease. In particular, this review focuses on carotid and coronary bifurcations because of their primary relevance to stroke and heart attack. We highlight reported relationships between atherosclerotic plaque location, progression and composition, and fluid forces at vessel's wall, in particular shear stress and its 'easier-to-measure' surrogates, i.e. vascular geometric attributes (because geometry shapes the flow) and intravascular flow features (because they mediate disturbed shear stress), in order to give more insight in plaque initiation and destabilisation. Analogous to Virchow's triad for thrombosis, atherosclerosis must be thought of as subject to a triad of, and especially interactions among, haemodynamic forces, systemic risk factors, and the biological response of the wall. PMID:26740210
Directory of Open Access Journals (Sweden)
Cüneyt Eriş
2013-09-01
Full Text Available Arteriosclerosis, is mostly affect coronary and carotid arteriesespecially the ostium and bifurcation due to the natureof the flow. Arterial bifurcation lesions cause dilemmafor the treating physician during both surgical and invasiveprocedures because they require a higher clinical experienceand longer processing time. In carotid artery surgery,it is accepted that patchplasty prevents perioperativeand postoperative restenosis, and as a result of this, itreduces the incidence of ipsilateral stroke. In the presenttime synthetic patch materials (PTFE, Dacron and autologouspatch materials (saphenous and jugular veins areused. We report a case of carotid endarterectomy and ‘Y’shaped saphenous patchplasty to the carotid bifurcation.According to our research in the literature, we didn’t findany case with ‘Y’ shaped saphenous vein patch. Therewas only one Y shaped carotid patchplasty case by usingPTFE material. Our original technic is advantageous interms of easy preparation and application as well as itssuccessful outcome.Key words: Carotid artery diseases, saphenous vein,patchplasty
International Nuclear Information System (INIS)
Purpose: Simple rating scale for calcification in the cervical arteries and the aortic arch on multi-detector computed tomography angiography (MDCTA) was evaluated its reliability and validity. Additionally, we investigated where is the most representative location for evaluating the calcification risk of carotid bifurcation stenosis and atherosclerotic infarction in the overall cervical arteries covering from the aortic arch to the carotid bifurcation. Method: The aortic arch and cervical arteries among 518 patients (292 men, 226 women) were evaluated the extent of calcification using a 4-point grading scale for MDCTA. Reliability, validity and the concomitant risk with vascular stenosis and atherosclerotic infarction were assessed. Results: Calcification was most frequently observed in the aortic arch itself, the orifices from the aortic arch, and the carotid bifurcation. Compared with the bilateral carotid bifurcations, the aortic arch itself had a stronger inter-observer agreement for the calcification score (Fleiss’ kappa coefficients; 0.77), but weaker associations with stenosis and atherosclerotic infarction. Calcification at the orifices of the aortic arch branches had a stronger inter-observer agreement (0.74) and enough associations with carotid bifurcation stenosis and intracranial stenosis. In addition, the extensive calcification at the orifices from the aortic arch was significantly associated with atherosclerotic infarction, similar to the calcification at the bilateral carotid bifurcations. Conclusions: The orifices of the aortic arch branches were the novel representative location of the aortic arch and overall cervical arteries for evaluating the calcification extent. Thus, calcification at the aortic arch should be evaluated with focus on the orifices of 3 main branches
Model generation of coronary artery bifurcations from CTA and single plane angiography
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Cardenes, Ruben; Diez, Jose L.; Duchateau, Nicolas; Pashaei, Ali; Frangi, Alejandro F. [Center for Computational Imaging and Simulation Technologies in Biomedicine (CISTIB)-Universitat Pompeu Fabra and Networking Biomedical Research Center on Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), Barcelona 08018 (Spain); Cardiology Department, University Hospital Dr. Peset, Valencia 46017 (Spain); Hospital Clinic Provincial de Barcelona, Institut d' investigacions Biomediques August Pi i Sunyer-Universitat de Barcelona, Barcelona 08036 (Spain); Center for Computational Imaging and Simulation Technologies in Biomedicine (CISTIB)-Universitat Pompeu Fabra and Networking Biomedical Research Center on Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), Barcelona 08018 (Spain); Center for Computational Imaging and Simulation Technologies in Biomedicine (CISTIB)-Universitat Pompeu Fabra and Networking Biomedical Research Center on Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), Barcelona 08018, Spain and Department of Mechanical Engineering, University of Sheffield, Sheffield S1 3JD (United Kingdom)
2013-01-15
Purpose: To generate accurate and realistic models of coronary artery bifurcations before and after percutaneous coronary intervention (PCI), using information from two image modalities. Because bifurcations are regions where atherosclerotic plaque appears frequently and intervention is more challenging, generation of such realistic models could be of high value to predict the risk of restenosis or thrombosis after stent implantation, and to study geometrical and hemodynamical changes. Methods: Two image modalities have been employed to generate the bifurcation models: computer tomography angiography (CTA) to obtain the 3D trajectory of vessels, and 2D conventional coronary angiography (CCA) to obtain radius information of the vessel lumen, due to its better contrast and image resolution. In addition, CCA can be acquired right before and after the intervention in the operation room; therefore, the combination of CTA and CCA allows the generation of realistic preprocedure and postprocedure models of coronary bifurcations. The method proposed is semiautomatic, based on landmarks manually placed on both image modalities. Results: A comparative study of the models obtained with the proposed method with models manually obtained using only CTA, shows more reliable results when both modalities are used together. The authors show that using preprocedure CTA and postprocedure CCA, realistic postprocedure models can be obtained. Analysis carried out of the Murray's law in all patient bifurcations shows the geometric improvement of PCI in our models, better than using manual models from CTA alone. An experiment using a cardiac phantom also shows the feasibility of the proposed method. Conclusions: The authors have shown that fusion of CTA and CCA is feasible for realistic generation of coronary bifurcation models before and after PCI. The method proposed is efficient, and relies on minimal user interaction, and therefore is of high value to study geometric and
Javadzadegan, Ashkan; Lotfi, Azadeh; Simmons, Anne; Barber, Tracie
2016-08-01
Thrombus in a femoral artery may form under stagnant flow conditions which vary depending on the local arterial waveform. Four different physiological flow waveforms - poor (blunt) monophasic, sharp monophasic, biphasic and triphasic - can exist in the femoral artery as a result of different levels of peripheral arterial disease progression. This study aims to examine the effect of different physiological waveforms on femoral artery haemodynamics. In this regard, a fluid-structure interaction analysis was carried out in idealised models of bifurcated common femoral artery. The results showed that recirculation zones occur in almost all flow waveforms; however, the sites at where these vortices are initiated, the size and structure of vortices are highly dependent on the type of flow waveform being used. It was shown that the reverse diastolic flow in biphasic and triphasic waveforms leads to the occurrence of a retrograde flow which aids in 'washout' of the disturbed flow regions. This may limit the likelihood of thrombus formation, indicating the antithrombotic role of retrograde flow in femoral arteries. Furthermore, our data revealed that the flow particles experience considerably higher residence time under blunt and sharp monophasic waveforms than under biphasic and triphasic waveforms. This confirms that the risk of atherothrombotic plaque initiation and development in femoral arteries is higher under blunt and sharp monophasic waveforms than under biphasic and triphasic flow waveforms. PMID:26582544
Effect of blood flow parameters on flow patterns at arterial bifurcations--studies in models.
Liepsch, D W
1990-01-01
Atherosclerotic lesions are found primarily at arterial bends and bifurcations. Flow disturbances at these anatomic sites play a major role in atherogenesis. How hemodynamic factors such as vessel geometry, the pulsatile nature of blood flow, vessel wall elasticity and the non-Newtonian flow behavior of blood influence the flow field at these sites must be clarified. We have performed fundamental studies using a birefringent solution in a simplified rigid 90 degree T-bifurcation and pulsatile flow. The velocity distribution was measured with a laser Doppler anemometer. Flow in an elastic abdominal aorta model has been visualized using magnetic resonance imaging. In both flow studies, zones with negative velocity were found. These model measurements demonstrate that no flow parameter can be neglected. Further detailed studies are necessary to examine the interaction between fluid dynamic and cellular surface properties. PMID:2404201
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McKinney, Alexander M.; Casey, Sean O.; Teksam, Mehmet; Truwit, Charles L.; Kieffer, Stephen [University of Minnesota Medical School, Departments of Radiology, Minneapolis, MN (United States); Lucato, Leandro T. [Clinics Hospital, University of Sao Paulo, Sao Paulo (Brazil); Smith, Maurice [Johns Hopkins University, Department of Biomedical Engineering, Baltimore, MD (United States)
2005-01-01
The aim of this paper was to determine the correlation between calcium burden (expressed as a volume) and extent of stenosis of the origin of the internal carotid artery (ICA) by CT angiography (CTA). Previous studies have shown that calcification in the coronary arteries correlates with significant vessel stenosis, and severe calcification (measured by CT) in the carotid siphon correlates with significant (greater than 50% stenosis) as determined angiographically. Sixty-one patients (age range 50-85 years) underwent CT of the neck with intravenous administration of iodinated contrast for a variety of conditions. Images were obtained with a helical multidetector array CT scanner and reviewed on a three-dimensional workstation. A single observer manipulated window and level to segment calcified plaque from vascular enhancement in order to quantify vascular calcium volume (cc) in the region of the bifurcation of the common carotid artery/ICA origin, and to measure the extent of ICA stenosis near the origin. A total of 117 common carotid artery bifurcations were reviewed. A ''significant'' stenosis was defined arbitrarily as >40% (to detect lesions before they become hemodynamically significant) of luminal diameter on CTA using NASCET-like criteria. All ''significant'' stenoses (21 out of 117 carotid bifurcations) had measurable calcium. We found a relatively strong correlation between percent stenosis and the calcium volume (Pearson's r= 0.65, P<0.0001). We also found that there was an even stronger correlation between the square root of the calcium volume and the percent stenosis as measured by CTA (r= 0.77, P<0.0001). Calcium volumes of 0.01, 0.03, 0.06, 0.09 and 0.12 cc were used as thresholds to evaluate for a ''significant'' stenosis. A receiver operating characteristic (ROC) curve demonstrated that thresholds of 0.06 cc (sensitivity 88%, specificity 87%) and 0.03 cc (sensitivity 94%, specificity
International Nuclear Information System (INIS)
The aim of this paper was to determine the correlation between calcium burden (expressed as a volume) and extent of stenosis of the origin of the internal carotid artery (ICA) by CT angiography (CTA). Previous studies have shown that calcification in the coronary arteries correlates with significant vessel stenosis, and severe calcification (measured by CT) in the carotid siphon correlates with significant (greater than 50% stenosis) as determined angiographically. Sixty-one patients (age range 50-85 years) underwent CT of the neck with intravenous administration of iodinated contrast for a variety of conditions. Images were obtained with a helical multidetector array CT scanner and reviewed on a three-dimensional workstation. A single observer manipulated window and level to segment calcified plaque from vascular enhancement in order to quantify vascular calcium volume (cc) in the region of the bifurcation of the common carotid artery/ICA origin, and to measure the extent of ICA stenosis near the origin. A total of 117 common carotid artery bifurcations were reviewed. A ''significant'' stenosis was defined arbitrarily as >40% (to detect lesions before they become hemodynamically significant) of luminal diameter on CTA using NASCET-like criteria. All ''significant'' stenoses (21 out of 117 carotid bifurcations) had measurable calcium. We found a relatively strong correlation between percent stenosis and the calcium volume (Pearson's r= 0.65, P<0.0001). We also found that there was an even stronger correlation between the square root of the calcium volume and the percent stenosis as measured by CTA (r= 0.77, P<0.0001). Calcium volumes of 0.01, 0.03, 0.06, 0.09 and 0.12 cc were used as thresholds to evaluate for a ''significant'' stenosis. A receiver operating characteristic (ROC) curve demonstrated that thresholds of 0.06 cc (sensitivity 88%, specificity 87%) and 0.03 cc (sensitivity 94%, specificity 76%) generated the best combinations of sensitivity and
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Kweon-Ho Nam
Full Text Available Despite considerable research efforts on the relationship between arterial geometry and cardiovascular pathology, information is lacking on the pulsatile geometrical variation caused by arterial distensibility and cardiomotility because of the lack of suitable in vivo experimental models and the methodological difficulties in examining the arterial dynamics. We aimed to investigate the feasibility of using a chick embryo system as an experimental model for basic research on the pulsatile variation of arterial geometry. Optical microscope video images of various arterial shapes in chick chorioallantoic circulation were recorded from different locations and different embryo samples. The high optical transparency of the chorioallantoic membrane (CAM allowed clear observation of tiny vessels and their movements. Systolic and diastolic changes in arterial geometry were visualized by detecting the wall boundaries from binary images. Several to hundreds of microns of wall displacement variations were recognized during a pulsatile cycle. The spatial maps of the wall motion harmonics and magnitude ratio of harmonic components were obtained by analyzing the temporal brightness variation at each pixel in sequential grayscale images using spectral analysis techniques. The local variations in the spectral characteristics of the arterial wall motion were reflected well in the analysis results. In addition, mapping the phase angle of the fundamental frequency identified the regional variations in the wall motion directivity and phase shift. Regional variations in wall motion phase angle and fundamental-to-second harmonic ratio were remarkable near the bifurcation area. In summary, wall motion in various arterial geometry including straight, curved and bifurcated shapes was well observed in the CAM artery model, and their local and cyclic variations could be characterized by Fourier and wavelet transforms of the acquired video images. The CAM artery model with
BOUKTIR, Yasser; Chalal, Hocine; HADDAD, Moussa; ABED-MERAIM, Farid
2015-01-01
The ductility limits of an St14 steel are investigated using an elastic‒plastic‒damage model and bifurcation theory. An associative J2-flow theory of plasticity is coupled with damage within the framework of continuum damage mechanics. For strain localization prediction, the bifurcation analysis is adopted. Both the constitutive equations and the localization bifurcation criterion are implemented into the finite element code ABAQUS, within the framework of large strains and a fully three-dime...
NUMERICAL ANALYSIS OF THE NON-NEWTONIAN BLOOD FLOW IN THE NON-PLANAR ARTERY WITH BIFURCATION
Institute of Scientific and Technical Information of China (English)
CHEN Jie; LU Xi-yun; ZHUANG Li-xian; WANG Wen
2004-01-01
A numerical analysis of non-Newtonian fluid flow in non-planar artery with bifurcation was performed by using a finite element method to solve the three-dimensional Navier-Stokes equations coupled with the non-Newtonian constitutive models, including Carreau,Cross and Bingham models. The objective of this study is to investigate the effects of the non-Newtonian properties of blood as well as curvature and out-of-plane geometry in the non-planar daughter vessels on the velocity distribution and wall shear stress. The results of this study support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are of important in hemodynamics and play a significant role in vascular biology and pathophysiology.
Denisenko, N. S.; Chupakhin, A. P.; Khe, A. K.; Cherevko, A. A.; Yanchenko, A. A.; Tulupov, A. A.; Boiko, A. V.; Krivoshapkin, A. L.; Orlov, K. Yu; Moshkin, M. P.; Akulov, A. E.
2016-06-01
In our experiments, we investigate a flow of a viscous fluid in the model of the common carotid artery bifurcation. The studies are carried out using three hardware equipments: two magnetic resonance scanners by Philips and Bruker, and intravascular guidewire ComboWire. The flux is generated by a special pump CompuFlow that is designed to reproduce a flow similar to the one in the blood vessels. A verification of the obtained data is carried out. Conducted research shows the capabilities of the measurement instruments and reflects the character of fluid flow inside the model.
Classification of coronary artery bifurcation lesions and treatments: Time for a consensus!
DEFF Research Database (Denmark)
Louvard, Yves; Thomas, Martyn; Dzavik, Vladimir;
2007-01-01
, heterogeneity, and inadequate description of techniques implemented. Methods: The aim is to propose a consensus established by the European Bifurcation Club (EBC), on the definition and classification of bifurcation lesions and treatments implemented with the purpose of allowing comparisons between techniques...... proposes a new classification of bifurcation lesions and their treatments to permit accurate comparisons of well described techniques in homogeneous lesion groups. (c) 2008 Wiley-Liss, Inc. Udgivelsesdato: 2007-Nov-5...
Clinical outcome after crush versus culotte stenting of coronary artery bifurcation lesions
DEFF Research Database (Denmark)
Kervinen, Kari; Niemelä, Matti; Romppanen, Hannu;
2013-01-01
The aim of the study was to compare long-term follow-up results of crush versus culotte stent techniques in coronary bifurcation lesions.......The aim of the study was to compare long-term follow-up results of crush versus culotte stent techniques in coronary bifurcation lesions....
Long-term results after simple versus complex stenting of coronary artery bifurcation lesions
DEFF Research Database (Denmark)
Maeng, Michael; Holm, Niels Ramsing; Erglis, Andrejs;
2013-01-01
Objectives This study sought to report the 5-year follow-up results of the Nordic Bifurcation Study. Background Randomized clinical trials with short-term follow-up have indicated that coronary bifurcation lesions may be optimally treated using the optional side branch stenting strategy. Methods ...
Saho, Tatsunori; Onishi, Hideo
2016-07-01
In this study, we evaluated the hemodynamics of carotid artery bifurcation with various geometries using simulated and volunteer models based on magnetic resonance imaging (MRI). Computational fluid dynamics (CFD) was analyzed by use of OpenFOAM. The velocity distribution, streamline, and wall shear stress (WSS) were evaluated in a simulated model with known bifurcation angles (30°, 40°, 50°, 60°, derived from patients' data) and in three-dimensional (3D) healthy volunteer models. Separated flow was observed at the outer side of the bifurcation, and large bifurcation models represented upstream transfer of the point. Local WSS values at the outer bifurcation [both simulated (100 Pa). The bifurcation angle had a significant negative correlation with the WSS value (p<0.05). The results of this study show that the carotid artery bifurcation angle is related to the WSS value. This suggests that hemodynamic stress can be estimated based on the carotid artery geometry. The construction of a clinical database for estimation of developing atherosclerosis is warranted. PMID:27255300
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Yamada, Shigeki, E-mail: shigekiyamada3@gmail.com [Department of Neurosurgery and Stroke Center, Rakuwakai Otowa Hospital, Otowachinji-cho 2, Yamashina-ku, Kyoto 607-8602 (Japan); Department of Neurosurgery, Hamamatsu Rosai Hospital, 25 Shogen-cho, Higashi-ku, Hamamatsu city, Shizuoka 430-8525 (Japan); Interfaculty Initiative in Information Studies/Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505 (Japan); Oshima, Marie, E-mail: marie@iis.u-tokyo.ac.jp [Interfaculty Initiative in Information Studies/Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505 (Japan); Watanabe, Yoshihiko, E-mail: ynabe@magic.odn.ne.jp [Department of Neurosurgery, Hamamatsu Rosai Hospital, 25 Shogen-cho, Higashi-ku, Hamamatsu city, Shizuoka 430-8525 (Japan); Ogata, Hideki, E-mail: hidogata@gmail.com [Department of Neurosurgery, Hamamatsu Rosai Hospital, 25 Shogen-cho, Higashi-ku, Hamamatsu city, Shizuoka 430-8525 (Japan); Hashimoto, Kenji, E-mail: hashiken8022@yahoo.co.jp [Department of Neurosurgery, Kishiwada Municipal Hospital, 1001 Gakuhara-cho, Kishiwada city, Osaka 596-8501 (Japan); Miyake, Hidenori, E-mail: hi-miyake@hamamatsuh.rofuku.go.jp [Department of Neurosurgery, Hamamatsu Rosai Hospital, 25 Shogen-cho, Higashi-ku, Hamamatsu city, Shizuoka 430-8525 (Japan)
2014-06-15
Purpose: The purpose of this study was to investigate the association between internal carotid artery (ICA) stenosis and intramural location and size of calcification at the ICA origins and the origins of the cervical arteries proximal to the ICA. Method: A total of 1139 ICAs were evaluated stenosis and calcification on the multi-detector row CT angiography. The intramural location was categorized into none, outside and inside location. The calcification size was evaluated on the 4-point grading scale. The multivariate analyses were adjusted for age, serum creatinine level, hypertension, hyperlipidemia, diabetes mellitus, smoking and alcohol habits. Results: Outside calcification at the ICA origins showed the highest multivariate odds ratio (OR) for the presence of ICA stenosis (30.0) and severe calcification (a semicircle or more of calcification at the arterial cross-sectional surfaces) did the second (14.3). In the subgroups of >70% ICA stenosis, the multivariate OR of outside location increased to 44.8 and that of severe calcification also increased to 32.7. Four of 5 calcified carotid plaque specimens extracted by carotid endarterectomy were histologically confirmed to be calcified burdens located outside the internal elastic lamia which were defined as arterial medial calcification. Conclusions: ICA stenosis was strongly associated with severe calcification located mainly outside the carotid plaque. Outside calcification at the ICA origins should be evaluated separately from inside calcification, as a marker for the ICA stenosis. Additionally, we found that calcification at the origins of the cervical arteries proximal to the ICA was significantly associated with the ICA stenosis.
International Nuclear Information System (INIS)
Purpose: The purpose of this study was to investigate the association between internal carotid artery (ICA) stenosis and intramural location and size of calcification at the ICA origins and the origins of the cervical arteries proximal to the ICA. Method: A total of 1139 ICAs were evaluated stenosis and calcification on the multi-detector row CT angiography. The intramural location was categorized into none, outside and inside location. The calcification size was evaluated on the 4-point grading scale. The multivariate analyses were adjusted for age, serum creatinine level, hypertension, hyperlipidemia, diabetes mellitus, smoking and alcohol habits. Results: Outside calcification at the ICA origins showed the highest multivariate odds ratio (OR) for the presence of ICA stenosis (30.0) and severe calcification (a semicircle or more of calcification at the arterial cross-sectional surfaces) did the second (14.3). In the subgroups of >70% ICA stenosis, the multivariate OR of outside location increased to 44.8 and that of severe calcification also increased to 32.7. Four of 5 calcified carotid plaque specimens extracted by carotid endarterectomy were histologically confirmed to be calcified burdens located outside the internal elastic lamia which were defined as arterial medial calcification. Conclusions: ICA stenosis was strongly associated with severe calcification located mainly outside the carotid plaque. Outside calcification at the ICA origins should be evaluated separately from inside calcification, as a marker for the ICA stenosis. Additionally, we found that calcification at the origins of the cervical arteries proximal to the ICA was significantly associated with the ICA stenosis
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Goltz, Jan Peter, E-mail: janpeter.goltz@uksh.de; Loesaus, Julia; Frydrychowicz, Alex; Barkhausen, Jörg [University Hospital of Schleswig-Holstein, Department for Radiology and Nuclear Medicine (Germany); Wiedner, Marcus [University Hospital of Schleswig-Holstein, Clinic for Surgery (Germany)
2016-02-15
We report an endovascular technique for the treatment of type Ia endoleak after a plain tubular stentgraft had been implanted for a large common iliac artery aneurysm with an insufficient proximal landing zone and without occlusion of the hypogastric in another hospital. CT follow-up showed an endoleak with continuous sac expansion over 12 months. This was classified as type Ia by means of dynamic contrast-enhanced MRI. Before a bifurcated stentgraft was implanted to relocate the landing zone more proximally, the still perfused ipsilateral hypogastric artery was embolized to prevent a type II endoleak. A guidewire was manipulated alongside the indwelling stentgraft. The internal iliac artery could then be selectively intubated followed by successful plug embolization of the vessel’s orifice despite the stentgraft being in place.
Investigation of homoclinic bifurcation of plasma fireball in a double plasma device
International Nuclear Information System (INIS)
Plasma fire balls are generated due to localized discharge and it is a sharp boundary of the glow region, which suggests a localized electric field such as an electrical sheath or double layer structure. In this paper, homoclinic bifurcation phenomena in the plasma fireball dynamics which is produced in the target chamber of double plasma device have been explored. Homoclinic bifurcation is noticed in the plasma fireball as the system evolving from large time period oscillation to small time period oscillation. The control parameters of this observations are density ratio of target to source chamber (nT/nS), applied electrode voltage to produce fireball, grid bias voltage etc. The dynamical transition of plasma fire balls have been investigated by recurrence quantification analysis (RQA) and by different statistical measures. The gradual increment of kurtosis and decrement of skewness with the change of nT has been observed which are strongly indicative of homoclinic bifurcation in the system. The visual changes of recurrence plot and the gradual changes in recurrence quantifiers reflect the bifurcation with the variation in the control parameter of the double plasma device. The combination of RQA and statistical measures like 1/f power spectrum, clearly conjectured the homoclinic bifurcation due to plasma fire ball in the experimental conditions. (author)
Institute of Scientific and Technical Information of China (English)
Jiang Junhao; Chen Bin; Dong Zhihui; Shi Yun; Li Weimiao; Yue Jianing
2014-01-01
Background Crossover stenting across the origin of the profunda femoral artery (PFA) and occasionally into the common femoral artery (CFA) is commonly used after suboptimal balloon angioplasty of ostial occlusive lesions of the superficial femoral artery (SFA) involving the bifurcation.Late stent occlusion at the bifurcation is not rare and results in severe lower extremity ischemia.Therefore,we tried to assess its possible causes,prevention and reintervention.Methods Using a prospectively maintained single-center database,12-month femoral bifurcation patency was retrospectively compared and lesion and procedural predictors of stent occlusion were determined among 63 patients (64 lesions) who between July 2011 and February 2013 underwent crossover (36 non-jailed and 15 jailed SFA,and 12 distal and 1 complete CFA) stenting of de novo ostial SFA lesions.Results Twelve-month overall patency rate at the femoral bifurcation was 88％,with no significant difference between jailed-ostial SFA (80％) and distal CFA (67％) stenting (P=0.731),and significant differences between either and non-jailed ostial stenting (100％,P=0.035 and 0.002).When PFA ostium was jailed by the stent,patients with preexisting CFA or PFA lesions had a 12-month bifurcation patency rate of 20％,significantly lower than those with simple ostial SFA lesions (83％,P=0.015).Stent induced intimal hyperplasia caused bifurcation occlusion in 6 surgical reintervention cases.Conclusions In crossover stenting of ostial lesions in SFA,bifurcation patency loss was significantly higher in distal CFA and jailed ostial SFA stenting than non-jailed ostial SFA stenting.Preexisting CFA or PFA lesion is a significant risk factor for bifurcation patency loss when PFA ostium is jailed by crossover stenting.
DK crush technique: modified treatment of bifurcation lesions in coronary artery
Institute of Scientific and Technical Information of China (English)
CHEN Shao-liang; GE Jun-bo; YE Fei; ZHANG Jun-jie; ZHU Zhong-sheng; LIN Song; SHAN Shou-jie; LIU Zhi-zhong; LIU Yan; DUAN Bao-xiang
2005-01-01
@@ Bifurcation lesions are still technically challenging even in the era of modern stents.1 High incidence of restenosis both in main vessel and side branch limits the long-term prognosis although several kinds of techniques have been identified to be successful for coronary bifurcations.2-5 Reports have demonstrated the main reason for higher incidence of ostial side branch even though drug-eluting stent used in side vessel lies in that there were gaps in metal coverage and drug application.6-9 Therefore, new technique ensuring complete vessel scaffolding without gaps in drug delivery at the bifurcation is crush technique which is similar to other techniques including T- and Y- stenting still needing postdilatation of kissing balloon angioplasty to expand the stent fully in the ostial side branch and to prevent stent distortion in main vessel.10 As a result, kissing balloon angioplasty is a key step to improve the final result and to reduce the restenosis after stenting bifurcation lesions. However, kissing angioplasty is difficult to be underwent or impossible because operators usually fail to rewire two layers of metal strut, which would result in suboptimal stent deployment, a main reason of high incidence of restenosis, and acute- or-late-thrombosus. The present study reports modified DK crush technique improving success rate of kissing balloon angioplasty under the guidance of intravascular ultrasound (IVUS).
Kabinejadian, Foad; Nezhadian, Mercedeh Kaabi; Cui, Fangsen; Ho, Pei; Leo, Hwa Liang
2016-02-01
In this study, a polymeric membrane has been designed and developed for carotid stents to prevent detachment of emboli from the arterial wall and subsequent stroke, while maintaining side-branch flow. Prototypes of different geometrical design parameters have been fabricated and their performance has been evaluated in vitro under physiological pulsatile flow condition in a life-size silicone anastomotic model of carotid artery bifurcation. These evaluations include both quantitative and qualitative experimental (in vitro) assessments of emboli prevention capability, side-branch flow preservation, and flow visualization. The covered stents with the novel membrane demonstrated significantly higher emboli prevention capability than the corresponding bare nitinol stent as well as some earlier related designs, while preserving more than 93% of the original flow of the external carotid artery (ECA). Flow in the ECA through these covered stents was uniform without evidence of undesirable flow recirculation or retrograde flow that might predispose the vessel wall to intimal thickening and atherosclerotic plaque formation. This study demonstrated the potential of these novel covered stent designs for the treatment of carotid atherosclerotic stenosis and prevention of late embolic stroke. However, further in vivo investigations of biological effects and mechanical performance of this covered stent design (e.g., its thrombogenicity potential and biocompatibility) are warranted. PMID:26147531
International Nuclear Information System (INIS)
We present a case of a 73-year-old man in whom a celiac trunk aneurysm close to the hepato-splenic bifurcation was discovered and treated by using celiac-hepatic stent-grafts implantation and splenic artery embolization
Directory of Open Access Journals (Sweden)
Patrick Bastos Metzger
2014-03-01
Full Text Available Embolization due to a firearm projectile entering the bloodstream is a rare event that is unlikely to be suspected during initial treatment of trauma patients. We describe and discuss a case of bullet embolism of the abdominal aortic bifurcation, complicated by a pseudoaneurysm of the thoracoabdominal aorta and occlusion of the right common iliac artery, but successfully treated using a combination of endovascular methods and conventional surgery.
International Nuclear Information System (INIS)
Objective: To investigate flow patterns at carotid bifurcation in vivo by combining computational fluid dynamics (CFD)and MR angiography imaging. Methods: Seven subjects underwent contrast-enhanced MR angiography of carotid artery in Siemens 3.0 T MR. Flow patterns of the carotid artery bifurcation were calculated and visualized by combining MR vascular imaging post-processing and CFD. Results: The flow patterns of the carotid bifurcations in 7 subjects were varied with different phases of a cardiac cycle. The turbulent flow and back flow occurred at bifurcation and proximal of internal carotid artery (ICA) and external carotid artery (ECA), their occurrence and conformation were varied with different phase of a cardiac cycle. The turbulent flow and back flow faded out quickly when the blood flow to the distal of ICA and ECA. Conclusion: CFD combined with MR angiography can be utilized to visualize the cyclical change of flow patterns of carotid bifurcation with different phases of a cardiac cycle. (authors)
The clinical application of 64-slice spiral CT angiography in carotid artery bifurcation disease
International Nuclear Information System (INIS)
Objective: To explore the clinical value of 64-slice spiral CT angiography (CTA) in carotid stenosis and atherosclerotic plaque. Methods: 40 patients (80 carotid arteries) underwent CTA and DSA. These two examinations within one week. The results of CTA were compared with that of DSA, the sensitivity and specificity of CTA and DSA were figured out. Results: CTA performed well in the detection of mild (0% to 29%) carotid stenosis, as well as carotid occlusion, with values for sensitivity and specificity both near 100%. In determining that a stenosis was >50% by DSA measurement, CTA with a sensitivity, specificity of 89% and 91% respectively. While CTA was quite specific in identifying degrees of stenoses in either the 50% to 69% or the 70% to 99% ranges, in this task it was much less sensitive: 65% and 73% respectively. CTA can detect all kinds of ulcers while DSA can not. Conclusions: 64-slice CTA and DSA were correctly identified in detecting carotid stenosis. CTA could demonstrate ulcers associated with the carotid stenosis, hut DSA only show stenosis. (authors)
Evaluation of the cervical carotid bifurcation using MR angiography and cine MRI
Energy Technology Data Exchange (ETDEWEB)
Yamane, Kanji; Shima, Takeshi; Okada, Yoshikazu; Nishida, Masahiro; Okita, Shinji; Hatayama, Takashi; Kagawa, Reiko [Chugoku Rousai Hospital, Kure, Hiroshima (Japan); Yokoyama, Noboru
1995-08-01
MR angiography (MRA) can less invasively evaluate the carotid bifurcation without contrast material. Previous reports on MRA of carotid bifurcation revealed problems of overestimation and false-positive interpretation of stenosis. To clarify reasons causing overestimation and false-positive interpretation we investigated flow dynamics in the carotid bifurcation by cine MRI. Twenty-eight patients who were suspected to have stenosis of the internal carotid artery by MRA were studied. Images of the carotid bifurcation were obtained with 3-D phase contrast method by 0.5-T MR scanner. All patients were examined by IV-DSA or direct carotid angiography. Cine MRI of the carotid bifurcation was obtained with gradinet-echo sequence by 1.5-T MR scanner. Comparison of MRA and conventional angiography in evaluating degree of stenosis in the carotid bifurcation demonstrated that there were 57.1% agreement, 32.1% false-positive estimation and 10.7% overestimation. Cine MRI demonstration turbulent flow in the normal carotid bifurcation and also in the sclerotic bifurcation. Turbulence in the carotid bifurcation with severe sclerosis was greater than that in the normal carotid bifurcation. Turbulent flow could be seen extending distally to the stenotic site of the internal carotid artery. Turbulent flow in the carotid bifurcation, causing a decrease or loss in signal intensity of MRA according to the severity of the turbulence, must be a major contributing factor in false-positive estimation and overestimation of stenosis. (author).
Energy Technology Data Exchange (ETDEWEB)
Saha, Debajyoti, E-mail: debajyoti.saha@saha.ac.in; Kumar Shaw, Pankaj; Janaki, M. S.; Sekar Iyengar, A. N.; Ghosh, Sabuj; Mitra, Vramori, E-mail: vramorimitra@yahoo.com; Michael Wharton, Alpha [Plasma Physics Division, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata 700064 (India)
2014-03-15
Order-chaos-order was observed in the relaxation oscillations of a glow discharge plasma with variation in the discharge voltage. The first transition exhibits an inverse homoclinic bifurcation followed by a homoclinic bifurcation in the second transition. For the two regimes of observations, a detailed analysis of correlation dimension, Lyapunov exponent, and Renyi entropy was carried out to explore the complex dynamics of the system.
Directory of Open Access Journals (Sweden)
Kirill Lykov
2015-08-01
Full Text Available When blood flows through a bifurcation, red blood cells (RBCs travel into side branches at different hematocrit levels, and it is even possible that all RBCs enter into one branch only, leading to a complete separation of plasma and RBCs. To quantify this phenomenon via particle-based mesoscopic simulations, we developed a general framework for open boundary conditions in multiphase flows that is effective even for high hematocrit levels. The inflow at the inlet is duplicated from a fully developed flow generated in a pilot simulation with periodic boundary conditions. The outflow is controlled by adaptive forces to maintain the flow rate and velocity gradient at fixed values, while the particles leaving the arteriole at the outlet are removed from the system. Upon validation of this approach, we performed systematic 3D simulations to study plasma skimming in arterioles of diameters 20 to 32 microns. For a flow rate ratio 6:1 at the branches, we observed the "all-or-nothing" phenomenon with plasma only entering the low flow rate branch. We then simulated blood-plasma separation in arteriolar bifurcations with different bifurcation angles and same diameter of the daughter branches. Our simulations predict a significant increase in RBC flux through the main daughter branch as the bifurcation angle is increased. Finally, we demonstrated the effectiveness of the new methodology in simulations of blood flow in vessels with multiple inlets and outlets, constructed using an angiogenesis model.
Energy Technology Data Exchange (ETDEWEB)
Peters, John W.; Miller, Anne-Frances; Jones, Anne K.; King, Paul W.; Adams, Michael W. W.
2016-04-01
Electron bifurcation is the recently recognized third mechanism of biological energy conservation. It simultaneously couples exergonic and endergonic oxidation-reduction reactions to circumvent thermodynamic barriers and minimize free energy loss. Little is known about the details of how electron bifurcating enzymes function, but specifics are beginning to emerge for several bifurcating enzymes. To date, those characterized contain a collection of redox cofactors including flavins and iron-sulfur clusters. Here we discuss the current understanding of bifurcating enzymes and the mechanistic features required to reversibly partition multiple electrons from a single redox site into exergonic and endergonic electron transfer paths.
An Experimental and Numerical Investigation of Bifurcations in a Kolmogorov-Like Flow
Tithof, Jeffrey; Pallantla, Ravi; Grigoriev, Roman O; Schatz, Michael F
2016-01-01
We present a combined experimental and numerical study of the primary and secondary bifurcations for a Kolmogorov-like flow. The experimental system is a quasi-two-dimensional incompressible fluid flow consisting of two immiscible layers of fluid for which electromagnetic forces drive a shear flow that approximates Kolmogorov flow. The two-dimensional (2D) direct numerical simulations (DNS) integrate a depth-averaged version of the full three-dimensional Navier-Stokes equations Suri ${\\it et}$ ${\\it al.}$ (2014), which contains a (non-unity) prefactor on the advection term, previously unaccounted for in all studies. Specifically, we present three separate 2D DNS: one that is doubly-periodic, one that is singly-periodic, and one that is non-periodic (i.e. no-slip is imposed at the lateral boundaries). All parameters are directly calculated or measured from experimental quantities. We show that inclusion of the advection term prefactor substantially improves agreement between experiment and numerics. However, g...
1991-01-01
Dynamical Bifurcation Theory is concerned with the phenomena that occur in one parameter families of dynamical systems (usually ordinary differential equations), when the parameter is a slowly varying function of time. During the last decade these phenomena were observed and studied by many mathematicians, both pure and applied, from eastern and western countries, using classical and nonstandard analysis. It is the purpose of this book to give an account of these developments. The first paper, by C. Lobry, is an introduction: the reader will find here an explanation of the problems and some easy examples; this paper also explains the role of each of the other paper within the volume and their relationship to one another. CONTENTS: C. Lobry: Dynamic Bifurcations.- T. Erneux, E.L. Reiss, L.J. Holden, M. Georgiou: Slow Passage through Bifurcation and Limit Points. Asymptotic Theory and Applications.- M. Canalis-Durand: Formal Expansion of van der Pol Equation Canard Solutions are Gevrey.- V. Gautheron, E. Isambe...
Feng, J; Rajeswaran, T; He, S; Wilkinson, F L; Serracino-Inglott, F; Azzawi, M; Parikh, V; Miraftab, M; Alexander, M Y
2015-08-01
Stroke is mainly caused by a narrowing of the carotid artery from a build-up of plaque. The risk of plaque rupture and subsequent stroke is dependent on plaque composition. Advances in imaging modalities offer a non-invasive means to assess the health of blood vessels and detect damage. However, the current diagnosis fails to identify patients with soft lipid plaque that are more susceptible to fissure, resulting in stroke. The aim of this study was to use waveform analysis to identify plaque composition and the risk of rupture. We have investigated pressure and flow by combining an artificial blood flow circuit with tubing containing different materials, to simulate plaques in a blood vessel. We used fat and bone to model lipid and calcification respectively to determine if the composition of plaques can be identified by arterial waveforms. We demonstrate that the arterial plaque models with different percentages of calcification and fat, results in significantly different arterial waveforms. These findings imply that arterial waveform analysis has the potential for further development to identify the vulnerable plaques prone to rupture. These findings could have implications for improved patient prognosis by speed of detection and a more appropriate treatment strategy. PMID:26736431
Liu, Yu; Jiang, Lanlan; Zhu, Ningjun; Zhao, Yuechao; Zhang, Yi; Wang, Dayong; Yang, Mingjun; Zhao, Jiafei; Song, Yongchen
2015-09-01
The study of immiscible fluid displacement between aqueous-phase liquids and non-aqueous-phase liquids in porous media is of great importance to oil recovery, groundwater contamination, and underground pollutant migration. Moreover, the attendant viscous, capillary, and gravitational forces are essential to describing the two-phase flows. In this study, magnetic resonance imaging was used to experimentally examine the detailed effects of the viscous, capillary, and gravitational forces on water-oil flows through a vertical straight capillary, bifurcate channel, and monolayered glass-bead pack. Water flooding experiments were performed at atmospheric pressure and 37.8°C, and the evolution of the distribution and saturation of the oil as well as the characteristics of the two-phase flow were investigated and analyzed. The results showed that the flow paths, i.e., the fingers of the displacing phase, during the immiscible displacement in the porous medium were determined by the viscous, capillary, and gravitational forces as well as the sizes of the pores and throats. The experimental results afford a fundamental understanding of immiscible fluid displacement in a porous medium. PMID:25940392
Ben Bettaieb, Mohamed; ABED-MERAIM, Farid
2015-01-01
Localized necking is often considered as precursor to failure in metal components. In modern technologies, functional components (e.g., in flexible electronic devices) may be affected by this necking phenomenon, and to avoid the occurrence of strain localization, elastomer substrates are bonded to the metal layers. This paper proposes an investigation of the development of localized necking in both freestanding metal layers and elastomer/metal bilayers. Finite strain versions of both rigid–pl...
Multiple Bifurcations in the Periodic Orbit around Eros
Ni, Yanshuo; Baoyin, Hexi
2016-01-01
We investigate the multiple bifurcations in periodic orbit families in the potential field of a highly irregular-shaped celestial body. Topological cases of periodic orbits and four kinds of basic bifurcations in periodic orbit families are studied. Multiple bifurcations in periodic orbit families consist of four kinds of basic bifurcations. We found both binary period-doubling bifurcations and binary tangent bifurcations in periodic orbit families around asteroid 433 Eros. The periodic orbit family with binary period-doubling bifurcations is nearly circular, with almost zero inclination, and is reversed relative to the body of the asteroid 433 Eros. This implies that there are two stable regions separated by one unstable region for the motion around this asteroid. In addition, we found triple bifurcations which consist of two real saddle bifurcations and one period-doubling bifurcation. A periodic orbit family generated from an equilibrium point of asteroid 433 Eros has five bifurcations, which are one real ...
Lee, Sang Hoon; Choi, Hyoung Gwon; Yoo, Jung Yul
2012-11-01
The effect of artery wall hypertrophy and stiffness on the flow field is investigated using three-dimensional finite element method for simulating the blood flow. To avoid the complexity due to the necessity of additional mechanical constraints, we use the combined formulation which includes both the fluid and structural equations of motion into single coupled variational equation. A P2P1 Galerkin finite element method is used to solve the Navier-Stokes equations for fluid flow and arbitrary Lagrangian-Eulerian formulation is used to achieve mesh movement. The Newmark method is employed for solving the dynamic equilibrium equations for linear elastic solid mechanics. The pulsatile, incompressible flows of Newtonian fluids constrained in the flexible wall are analyzed with Womersley velocity profile at the inlet and constant pressure at the outlet. The study shows that the stiffness of carotid artery wall affects significantly the flow phenomena during the pulse cycle. Similarly, it is found that the flow field is also strongly influenced by wall hypertrophy. This work was supported by Mid-career Researcher Program and Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0079936 & 2011-0029613).
Cakur, Binali; Yıldırım, Eren; Demirtaş, Ömer
2015-01-01
Aim: Carotid artery calcification can results in important vascular obstruction. It is reported that the combination of risk factors such as periodontitis, pulp stones contribute to carotid artery calcification. However in the literature, no study has yet investigated carotid artery calcification with respect to tonsillolith. The objective of this study was to investigate whether carotid artery calcification correlate with tonsillolith using dental panoramic radiography.Material and method: P...
Global Bifurcations With Symmetry
Porter, J B
2001-01-01
Symmetry is a ubiquitous feature of physical systems with profound implications for their dynamics. This thesis investigates the role of symmetry in global bifurcations. In particular, the structure imposed by symmetry can encourage the formation of complex solutions such as heteroclinic cycles and chaotic invariant sets. The first study focuses on the dynamics of 1:n steady-state mode interactions in the presence of O(2) symmetry. The normal form equations considered are relevant to a variety of physical problems including Rayleigh-Bénard convection with periodic boundary conditions. In open regions of parameter space these equations contain structurally stable heteroclinic cycles composed of connections between standing wave, pure mode, and trivial solutions. These structurally stable cycles exist between two global bifurcations, the second of which involves an additional mixed mode state and creates as many as four distinct kinds of structurally unstable heteroclinic cycles. The various cycles c...
Directory of Open Access Journals (Sweden)
Emin Gurleyik
2014-01-01
Full Text Available Background: Anatomical variations of the recurrent laryngeal nerve (RLN such as extralaryngeal terminal bifurcation is an important risk for its motor function. Aims: The objective is to study surgical anatomy of bilateral bifurcation of the RLNs in order to decrease risk of vocal cord palsy in patients with bifurcated nerves. Materials and Methods: Surgical anatomy including terminal bifurcation was established in 292 RLNs of 146 patients. We included patients with bilateral bifurcation of RLN in this study. Based on two anatomical landmarks (nerve-artery crossing and laryngeal entry, the cervical course of RLN was classified in four segments: Pre-arterial, arterial, post-arterial and pre-laryngeal. According to these segments, bifurcation point locations along the cervical course of RLNs were compared between both sides in bilateral cases. Results: RLNs were exposed throughout their entire courses. Seventy (48% patients had bifurcated RLNs. We identified terminal bifurcation in 90 (31% of 292 RLNs along the cervical course. Bilateral bifurcation was observed in 20 (28.6% patients with bifurcated RLNs. Bifurcation points were located on arterial and post-arterial segments in 37.5% and 32.5% of cases, respectively. Pre-arterial and pre-laryngeal segments contained bifurcations in 15% of cases. Comparison of both sides indicated that bifurcation points were similar in 5 (25% and different in 15 (75% patients with bilateral bifurcation. Permanent nerve injury did not occur in this series. Conclusion: Bilateral bifurcation of both RLNs was observed in approximately 30% of patients with extralaryngeal bifurcation which is a common anatomical variation. Bifurcation occurred in different segments along cervical course of RLN. Bifurcation point locations differed between both sides in the majority of bilateral cases. Increasing surgeons′ awareness of this variation may lead to safely exposing bifurcated nerves and prevent the injury to extralaryngeal
International Nuclear Information System (INIS)
This work aims to study effects of toroidal flow on the L-H transition phenomenon in tokamak plasmas using bifurcation concept. Two-field (thermal and particle) transport equations with both neoclassical and turbulent effects included are solved simultaneously. The transport suppression mechanism used in this work is flow shear, which is assumed to affect only the turbulent transport. The flow shear can be calculated from the force balance equation with toroidal flow as a main contributor. The toroidal velocity profile is calculated using three different models. The first model is an empirical model in which the velocity is dependent on local ion temperature. The second model is based on neoclassical toroidal viscosity theory in which the velocity is driven by ion temperature gradient. In the third model, the velocity is dependent on current density flow in plasma. The two transport equations are solved both analytically and numerically using MATLAB to study the criteria for H-mode formation, pedestal width and its dynamics. The results from three toroidal velocity models are compared and analyzed with respect to bifurcation behavior and plasma performance.
BIFURCATIONS OF AIRFOIL IN INCOMPRESSIBLE FLOW
Institute of Scientific and Technical Information of China (English)
LiuFei; YangYiren
2005-01-01
Bifurcations of an airfoil with nonlinear pitching stiffness in incompressible flow are investigated. The pitching spring is regarded as a spring with cubic stiffness. The motion equations of the airfoil are written as the four dimensional one order differential equations. Taking air speed and the linear part of pitching stiffness as the parameters, the analytic solutions of the critical boundaries of pitchfork bifurcations and Hopf bifurcations are obtained in 2 dimensional parameter plane. The stabilities of the equilibrium points and the limit cycles in different regions of 2 dimensional parameter plane are analyzed. By means of harmonic balance method, the approximate critical boundaries of 2-multiple semi-stable limit cycle bifurcations are obtained, and the bifurcation points of supercritical or subcritical Hopf bifurcation are found. Some numerical simulation results are given.
International Nuclear Information System (INIS)
A 42-year-old female with a giant intracranial aneurysm of the right IC bifurcation is reported. She had experienced severe headache with nausea and vomiting on July 6, 1984, and was admitted to a certain hospital. She was then transferred to our hospital on July 23; she was asymptomatic then. There was no neurological deficit, and a craniogram showed no abnormal findings. A plain CT scan, however, showed a round, homogenous, slightly high-density area on the right basal ganglia, and it was intensely enhanced by the infusion of a contrast medium. The right anterior horn was compressed to the anteromedial side. By the angiographical study, we found a large aneurysmal shadow with a bleb on its top, arising from the right IC bifurcation. While she waited for an operation, meanwhile undergoing reported Matas tests, the aneurysm began to bleed again. Suddenly generalized convulsions and the rapidly progressing left hemiparesis occurred, and she lost consciousness. The CT scan at that time showed a ring-shaped high-density area surrounding the aneurysms, accompanied by perifocal edema and a midline shift. An urgent operation was performed, but she died three days after the second attack. The autopsy showed a ruptured saccular aneurysm (3.5 x 4.0 x 4.0 cm in size) on the right IC bifurcation, with its neck extending to the M1 portion. There was neither calcification on the wall nor any organized thrombosis. Giant aneurysms usually affect the surrounding brain tissue as mass lesions. In this case, though, there was no sign or symptoms of any compression of the brain tissue or cranial nerves, though a CT scan soon after the rupture showed progressive perifocal edema. This suggests that there had been a previous disturbance of the autoregulation of the surrounding brain tissue, caused by the mass effect of the giant aneurysm. (author)
Investigation of Brain Arterial Circle Malformations Using Electrical Modelling and Simulation
Directory of Open Access Journals (Sweden)
Klara Capova
2006-01-01
Full Text Available The paper deals with the cerebral arterial system investigation by means of electrical modelling and simulations. The main attention is paid to the brain arterial circle malformations (stenoses and aneurysms and their determination and evaluation by computer-aided methods as tools of a non-invasive diagnostics. The compensation possibilities of brain arterial circle in case of presence of concrete arterial malformations are modelled and simulated. The simulation results of brain arteries blood pressures and volume flow velocities time dependences are presented and discussed under various health conditions.
Multiple bifurcations in the periodic orbit around Eros
Ni, Yanshuo; Jiang, Yu; Baoyin, Hexi
2016-05-01
We investigate the multiple bifurcations in periodic orbit families in the potential field of a highly irregular-shaped celestial body. Topological cases of periodic orbits and four kinds of basic bifurcations in periodic orbit families are studied. Multiple bifurcations in periodic orbit families consist of four kinds of basic bifurcations. We found both binary period-doubling bifurcations and binary tangent bifurcations in periodic orbit families around asteroid 433 Eros. The periodic orbit family with binary period-doubling bifurcations is nearly circular, with almost zero inclination, and is reversed relative to the body of the asteroid 433 Eros. This implies that there are two stable regions separated by one unstable region for the motion around this asteroid. In addition, we found triple bifurcations which consist of two real saddle bifurcations and one period-doubling bifurcation. A periodic orbit family generated from an equilibrium point of asteroid 433 Eros has five bifurcations, which are one real saddle bifurcation, two tangent bifurcations, and two period-doubling bifurcations.
International Nuclear Information System (INIS)
Background: A longstanding hypothesis that correlates fluid dynamic forces and atherosclerotic disease has led to numerous analytical, numerical, and experimental studies over the years because it is very difficult to measure the hemodynamic variables of blood in vivo. Purpose: To investigate the technique of visualization and quantitation of hemodynamic variables at carotid artery bifurcation in vivo by combining computational fluid dynamics (CFD) and vascular imaging. Material and Methods: Twenty-six healthy volunteers underwent magnetic resonance (MR) angiography of the bilateral carotid artery by a 3.0T whole-body scanner. Hemodynamic variables at these carotid bifurcations were calculated and visualized by combining vascular imaging post-processing and CFD. Results: The average velocity of the carotid bifurcation in the systolic phase and the diastolic phase was 0.46±0.24 m/s and 0.23±0.05 m/s, respectively. Eddy current and back flows were observed at bifurcation and the lateral part of the proximal internal carotid arteries (ICA) and external carotid arteries (ECA), and the shapes of them changed with phases of the cardiac cycle, which were significant at the middle of the systolic phase and faded out quickly downstream of the ICA and ECA. The average range of wall shear stress (WSS) at the bifurcation was 4.36±1.32 Pa, and the maximum WSS was 18.02±4.11 Pa. The WSS map revealed a large region of low WSS at the carotid bulb and extended to the outer wall in the proximal end of the ICA (the lowest value was below 0.5 Pa), and there was also a small region of low WSS at the outer wall in the proximal end of the ECA. Conclusion: CFD combined with vascular imaging can calculate and visualize hemodynamic variables at carotid bifurcation in vivo individually
About Bifurcational Parametric Simplification
Gol'dshtein, V; Yablonsky, G
2015-01-01
A concept of "critical" simplification was proposed by Yablonsky and Lazman in 1996 for the oxidation of carbon monoxide over a platinum catalyst using a Langmuir-Hinshelwood mechanism. The main observation was a simplification of the mechanism at ignition and extinction points. The critical simplification is an example of a much more general phenomenon that we call \\emph{a bifurcational parametric simplification}. Ignition and extinction points are points of equilibrium multiplicity bifurcations, i.e., they are points of a corresponding bifurcation set for parameters. Any bifurcation produces a dependence between system parameters. This is a mathematical explanation and/or justification of the "parametric simplification". It leads us to a conjecture that "maximal bifurcational parametric simplification" corresponds to the "maximal bifurcation complexity." This conjecture can have practical applications for experimental study, because at points of "maximal bifurcation complexity" the number of independent sys...
Tang, Abraham Yik-Sau; Chung, Wai-Choi; Liu, Eric Tian-Yang; Qu, Jie-Qiong; Tsang, Anderson Chun-On; Leung, Gilberto Ka-Kit; Leung, Kar-Ming; Yu, Alfred Cheuk-Hang; Chow, Kwok-Wing
2015-01-01
An intracranial aneurysm, abnormal swelling of the cerebral artery, may lead to undesirable rates of mortality and morbidity upon rupture. Endovascular treatment involves the deployment of a flow-diverting stent that covers the aneurysm orifice, thereby reducing the blood flow into the aneurysm and mitigating the risk of rupture. In this study, computational fluid dynamics analysis is performed on a bifurcation model to investigate the change in hemodynamics with various side branch diameters...
Singular limit cycle bifurcations to closed orbits and invariant tori
International Nuclear Information System (INIS)
This paper investigates singular limit cycle bifurcations for a singularly perturbed system. Based on a series of transformations (the modified curvilinear coordinate, blow-up, and near-identity transformation) and bifurcation theory of periodic orbits and invariant tori, the bifurcations of closed orbits and invariant tori near singular limit cycles are discussed
Singular limit cycle bifurcations to closed orbits and invariant tori
Energy Technology Data Exchange (ETDEWEB)
Ye Zhiyong [Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240 (China); Department of Mathematics, Chongqing Institute of Technology, Chongqing 400050 (China); E-mail: yezhiyong@sjtu.edu.cn; Han Maoan [Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240 (China); E-mail: mahan@sjtu.edu.cn
2006-02-01
This paper investigates singular limit cycle bifurcations for a singularly perturbed system. Based on a series of transformations (the modified curvilinear coordinate, blow-up, and near-identity transformation) and bifurcation theory of periodic orbits and invariant tori, the bifurcations of closed orbits and invariant tori near singular limit cycles are discussed.
Bifurcation of steady tearing states
International Nuclear Information System (INIS)
We apply the bifurcation theory for compact operators to the problem of the nonlinear solutions of the 3-dimensional incompressible visco-resistive MHD equations. For the plane plasma slab model we compute branches of nonlinear tearing modes, which are stationary for the range of parameters investigated up to now
Directory of Open Access Journals (Sweden)
JA Mitchell
2009-06-01
Full Text Available Blood flow to the hindbrain, via the paired vertebral arteries, must be uncompromised for adequate neurological functioning of its vital centres. Therefore, it would seem unlikely that the intracranial vertebral artery would need to vasoconstrict, thus reducing its blood flow. In order to investigate the existence and location of a noradrenaline-mediated constrictor mechanism in the wall of the intracranial vertebral artery, transverse sections of ten baboon and ten monkey vessels were stained with sucrose-potassium phosphate-glyoxylic acid (counterstained with malachite-green. This method allows the visualisation of catecholaminergic nerves when the sections are exposed to ultraviolet light. In this study of primate vascular tissue, however, none of the monkey or baboon vertebral artery sections showed the presence of noradrenergic nerves in the tunica media – tunica adventitia junction or penetrating the tunica media of the arteries. These findings indicate that the intracranial vertebral artery does not have a neurogenic vasomotor function in primates.
Preliminary study on hemodynamics in human carotid bifurcation by computational fluid dynamics
International Nuclear Information System (INIS)
Objective: To investigate the visualization and quantitation of hemodynamic variables at carotid artery bifurcation in vivo by combining computational fluid dynamics (CFD) and vascular imaging. Methods: A healthy volunteer underwent CT angiography of left carotid artery by SIEMENS multi-slice CT. Parameters of hemodynamics at this carotid bifurcation were calculated and visualized by combining vascular imaging post-processing and CFD. Results: (1) The average range of flow velocity was 0.04-0.36 m/s. A region of high velocity was seen at medial wall of internal carotid artery (ICA) and medial wall of external carotid artery (ECA), respectively. The largest contiguous region of low velocity occurred at the carotid bulb. (2)The average range of absolute pressure, static pressure and dynamic pressure was 100 266.70-101 615.90 Pa, -1058.34-290.88 Pa, and 6.12-553.25 Pa, respectively. (3) The average range of wall shear stress (WSS) at the bifurcation was 0.59-5.35 Pa. There was a large region of low WSS at carotid bulb and posterior wall of ICA, with the lowest value of 0.25 Pa. Also there was a small region of low WSS at anterior and lateral wall of ECA. Conclusion: CFD combined with vascular imaging can calculate and visualize the parameters of hemodynamics at carotid bifurcation in vivo individually. It is an interdisciplinary science of computer, radiology and hemodynamics and provides a new method to investigate the relationship of vascular geometry and flow condition with atherosclerotic pathological changes. (authors)
Unfolding the Riddling Bifurcation
DEFF Research Database (Denmark)
Maistrenko, Yu.; Popovych, O.; Mosekilde, Erik
1999-01-01
We present analytical conditions for the riddling bifurcation in a system of two symmetrically coupled, identical, smooth one-dimensional maps to be soft or hard and describe a generic scenario for the transformations of the basin of attraction following a soft riddling bifurcation.......We present analytical conditions for the riddling bifurcation in a system of two symmetrically coupled, identical, smooth one-dimensional maps to be soft or hard and describe a generic scenario for the transformations of the basin of attraction following a soft riddling bifurcation....
Comparative anatomical studies on the thyroid and thymic arteries. II. Polyprotodont marsupials.
Yamasaki, M
1993-01-01
The thyroid and thymic arteries were investigated in 27 specimens from 9 species belonging to the Australian Polyprotodont marsupials, which are subdivided into 2 superfamilies, Dasyuroidea and Perameloidea. The results were compared with those in rats and humans. The site of origin of the superior thyroid artery ranged from the external carotid artery to the common carotid in Dasyuroids, and converged on the external carotid and the bifurcation of the common carotid in Perameloids. The cours...
Anomalous origin of the occipital artery diagnosed by magnetic resonance angiography
Energy Technology Data Exchange (ETDEWEB)
Uchino, Akira; Saito, Naoko; Mizukoshi, Waka; Okada, Yoshitaka [Saitama Medical University International Medical Center, Department of Diagnostic Radiology, Hidaka, Saitama (Japan)
2011-11-15
It is well known that the occipital artery (OA) can arise from the internal carotid artery (ICA) or vertebral artery (VA). However, the incidence of an anomalously originating OA has not been reported. We investigate its incidence and characteristic features on magnetic resonance angiography (MRA). We retrospectively reviewed MRA images of 2,866 patients that included the carotid bifurcation; images were obtained using a standard noncontrast MRA protocol and two 1.5-T MR units. We diagnosed six cases (seven arteries) of anomalously originating OA, which represented an incidence of 0.21%. The OA arose from the ICA in four patients (five arteries), from the carotid bifurcation in one, and from the VA in one. Five of the seven arteries occurred on the right. Anomalously originating OA is rare and occurs with right-side predominance. Correct diagnosis is necessary before or during cerebral angiography, especially when selective catheterization to the OA is required. (orig.)
Codimension-Two Bifurcation Analysis in Hindmarsh-Rose Model with Two Parameters
Institute of Scientific and Technical Information of China (English)
DUAN Li-Xia; LU Qi-Shao
2005-01-01
@@ Bifurcation phenomena in a Hindmarsh-Rose neuron model are investigated. Special attention is paid to the bifurcation structures off two parameters, where codimension-two generalized-Hopf bifurcation and fold-Hopf bifurcation occur. The classification offiring patterns as well as the transition mechanism in different regions on the parameter plane are obtained.
Supercritical as well as subcritical Hopf bifurcation in nonlinear flutter systems
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The Hopf bifurcations of an airfoil flutter system with a cubic nonlinearity are investigated,with the flow speed as the bifurcation parameter.The center manifold theory and complex normal form method are used to obtain the bifurcation equation.Interestingly,for a certain linear pitching stiffness the Hopf bifurcation is both supercritical and subcritical.It is found,mathematically,this is caused by the fact that one coefficient in the bifurcation equation does not contain the first power of the bifurcation parameter.The solutions of the bifurcation equation are validated by the equivalent linearization method and incremental harmonic balance method.
Semiclassical interference of bifurcations
Schomerus, H
1997-01-01
In semiclassical studies of systems with mixed phase space, the neighbourhood of bifurcations of co-dimension two is felt strongly even though such bifurcations are ungeneric in classical mechanics. We discuss a scenario which reveals this fact and derive the correct semiclassical contribution of the bifurcating orbits to the trace of the unitary time evolution operator. That contribution has a certain collective character rather than being additive in the individual periodic orbits involved. The relevance of our observation is demonstrated by a numerical study of the kicked top; the collective contribution derived is found to considerably improve the semiclassical approximation of the trace.
Relative Lyapunov Center Bifurcations
DEFF Research Database (Denmark)
Wulff, Claudia; Schilder, Frank
2014-01-01
Relative equilibria (REs) and relative periodic orbits (RPOs) are ubiquitous in symmetric Hamiltonian systems and occur, for example, in celestial mechanics, molecular dynamics, and rigid body motion. REs are equilibria, and RPOs are periodic orbits of the symmetry reduced system. Relative Lyapunov...... center bifurcations are bifurcations of RPOs from REs corresponding to Lyapunov center bifurcations of the symmetry reduced dynamics. In this paper we first prove a relative Lyapunov center theorem by combining recent results on the persistence of RPOs in Hamiltonian systems with a symmetric Lyapunov...... center theorem of Montaldi, Roberts, and Stewart. We then develop numerical methods for the detection of relative Lyapunov center bifurcations along branches of RPOs and for their computation. We apply our methods to Lagrangian REs of the N-body problem....
Hemodynamics of Stent Implantation Procedures in Coronary Bifurcations: an in vitro study
Brindise, Melissa C; Burzotta, Francesco; Migliavacca, Francesco; Vlachos, Pavlos P
2016-01-01
Stent implantation in coronary bifurcations presents unique challenges and currently there is no universally accepted stent deployment approach. Despite clinical and computational studies, to date, the effect of each stent implantation method on the coronary artery hemodynamics is not well understood. In this study the hemodynamics of stented coronary bifurcations under pulsatile flow conditions were investigated experimentally. Three implantation methods, provisional side branch (PSB), culotte (CUL), and crush (CRU), were investigated using time-resolved particle image velocimetry (PIV) to measure the velocity fields. Subsequently, hemodynamic parameters including wall shear stress (WSS), oscillatory shear index (OSI), and relative residence time (RRT) were calculated and the pressure field through the vessel was non-invasively quantified. The effects of each stented case were evaluated and compared against an un-stented case. CRU provided the lowest compliance mismatch, but demonstrated detrimental stent in...
Wall shear stress in intracranial aneurysms and adjacent arteries
Institute of Scientific and Technical Information of China (English)
Fuyu Wang; Bainan Xu; Zhenghui Sun; Chen Wu; Xiaojun Zhang
2013-01-01
Hemodynamic parameters play an important role in aneurysm formation and growth. However, it is difficult to directly observe a rapidly growing de novo aneurysm in a patient. To investigate possible associations between hemodynamic parameters and the formation and growth of intracranial aneurysms, the present study constructed a computational model of a case with an internal carotid artery aneurysm and an anterior communicating artery aneurysm, based on the CT angiography findings of a patient. To simulate the formation of the anterior communicating artery aneurysm and the growth of the internal carotid artery aneurysm, we then constructed a model that virtually removed the anterior communicating artery aneurysm, and a further two models that also progressively decreased the size of the internal carotid artery aneurysm. Computational simulations of the fluid dynamics of the four models were performed under pulsatile flow conditions, and wall shear stress was compared among the different models. In the three aneurysm growth models, increasing size of the aneurysm was associated with an increased area of low wall shear stress, a significant decrease in wall shear stress at the dome of the aneurysm, and a significant change in the wall shear stress of the parent artery. The wall shear stress of the anterior communicating artery remained low, and was significantly lower than the wall shear stress at the bifurcation of the internal carotid artery or the bifurcation of the middle cerebral artery. After formation of the anterior communicating artery aneurysm, the wall shear stress at the dome of the internal carotid artery aneurysm increased significantly, and the wall shear stress in the upstream arteries also changed significantly. These findings indicate that low wall shear stress may be associated with the initiation and growth of aneurysms, and that aneurysm formation and growth may influence hemodynamic parameters in the local and adjacent arteries.
Bifurcation Analysis in a Delayed Diffusive Leslie-Gower Model
Directory of Open Access Journals (Sweden)
Shuling Yan
2013-01-01
Full Text Available We investigate a modified delayed Leslie-Gower model under homogeneous Neumann boundary conditions. We give the stability analysis of the equilibria of the model and show the existence of Hopf bifurcation at the positive equilibrium under some conditions. Furthermore, we investigate the stability and direction of bifurcating periodic orbits by using normal form theorem and the center manifold theorem.
Codimension 2 reversible heteroclinic bifurcations with inclination flips
Institute of Scientific and Technical Information of China (English)
2009-01-01
In this paper, the heteroclinic bifurcation problem with real eigenvalues and two incli- nation-flips is investigated in a four-dimensional reversible system. We perform a detailed study of this case by using the method originally established in the papers "Problems in Homoclinic Bifurcation with Higher Dimensions" and "Bifurcation of Heteroclinic Loops," and obtain fruitful results, such as the existence and coexistence of R-symmetric homoclinic orbit and R-symmetric heteroclinic loops, R-symmetric homoclinic orbit and R-symmetric periodic orbit. The double R-symmetric homoclinic bifurcation (i.e., two-fold R-symmetric homoclinic bifurcation) for reversible heteroclinic loops is found, and the existence of infinitely many R-symmetric periodic orbits accumulating onto a homoclinic orbit is demonstrated. The relevant bifurcation surfaces and the existence regions are also located.
Bifurcation Analysis for Neural Networks in Neutral Form
Chen, Hong-Bing; Sun, Xiao-Ke
2016-06-01
In this paper, a system of neural networks in neutral form with time delay is investigated. Further, by introducing delay τ as a bifurcation parameter, it is found that Hopf bifurcation occurs when τ is across some critical values. The direction of the Hopf bifurcations and the stability are determined by using normal form method and center manifold theory. Next, the global existence of periodic solution is established by using a global Hopf bifurcation result. Finally, an example is given to support the theoretical predictions.
Bifurcation phenomena in control flows
Colonius, Fritz; Fabbri, Roberta; Johnson, Russell; Spadini, Marco
2007-01-01
We study bifurcation phenomena in control flows and the bifurcation of control sets. A Mel'nikov method and the Conley index together with exponential dichotomy theory and integral manifold theory are used.
Digital subtraction angiography of carotid bifurcation
International Nuclear Information System (INIS)
This study demonstrates the reliability of digital subtraction angiography (DSA) by means of intra- and interobserver investigations as well as indicating the possibility of substituting catheterangiography by DSA in the diagnosis of carotid bifurcation. Whenever insufficient information is obtained from the combination of non-invasive investigation and DSA, a catheterangiogram will be necessary. (Auth.)
Energetics and monsoon bifurcations
Seshadri, Ashwin K.
2016-04-01
Monsoons involve increases in dry static energy (DSE), with primary contributions from increased shortwave radiation and condensation of water vapor, compensated by DSE export via horizontal fluxes in monsoonal circulations. We introduce a simple box-model characterizing evolution of the DSE budget to study nonlinear dynamics of steady-state monsoons. Horizontal fluxes of DSE are stabilizing during monsoons, exporting DSE and hence weakening the monsoonal circulation. By contrast latent heat addition (LHA) due to condensation of water vapor destabilizes, by increasing the DSE budget. These two factors, horizontal DSE fluxes and LHA, are most strongly dependent on the contrast in tropospheric mean temperature between land and ocean. For the steady-state DSE in the box-model to be stable, the DSE flux should depend more strongly on the temperature contrast than LHA; stronger circulation then reduces DSE and thereby restores equilibrium. We present conditions for this to occur. The main focus of the paper is describing conditions for bifurcation behavior of simple models. Previous authors presented a minimal model of abrupt monsoon transitions and argued that such behavior can be related to a positive feedback called the `moisture advection feedback'. However, by accounting for the effect of vertical lapse rate of temperature on the DSE flux, we show that bifurcations are not a generic property of such models despite these fluxes being nonlinear in the temperature contrast. We explain the origin of this behavior and describe conditions for a bifurcation to occur. This is illustrated for the case of the July-mean monsoon over India. The default model with mean parameter estimates does not contain a bifurcation, but the model admits bifurcation as parameters are varied.
Hopf Bifurcation in a Nonlinear Wave System
Institute of Scientific and Technical Information of China (English)
HE Kai-Fen
2004-01-01
@@ Bifurcation behaviour of a nonlinear wave system is studied by utilizing the data in solving the nonlinear wave equation. By shifting to the steady wave frame and taking into account the Doppler effect, the nonlinear wave can be transformed into a set of coupled oscillators with its (stable or unstable) steady wave as the fixed point.It is found that in the chosen parameter regime, both mode amplitudes and phases of the wave can bifurcate to limit cycles attributed to the Hopf instability. It is emphasized that the investigation is carried out in a pure nonlinear wave framework, and the method can be used for the further exploring routes to turbulence.
Stability and bifurcations in a nonlocal delayed reaction-diffusion population model
Chen, Shanshan; Yu, Jianshe
2016-01-01
A nonlocal delayed reaction-diffusion equation with Dirichlet boundary condition is considered in this paper. It is shown that a positive spatially nonhomogeneous equilibrium bifurcates from the trivial equilibrium. The stability/instability of the bifurcated positive equilibrium and associated Hopf bifurcation are investigated, providing us with a complete picture of the dynamics.
Stability and Hopf Bifurcation Analysis of a Vector-Borne Disease with Time Delay
Yuanyuan Chen; Ya-Qing Bi
2014-01-01
A delay-differential modelling of vector-borne is investigated. Its dynamics are studied in terms of local analysis and Hopf bifurcation theory, and its linear stability and Hopf bifurcation are demonstrated by studying the characteristic equation. The stability and direction of Hopf bifurcation are determined by applying the normal form theory and the center manifold argument.
Local and global bifurcation and its applications in a predator-prey system with several parameters
International Nuclear Information System (INIS)
A predator-prey system, depending on several parameters, is investigated for bifurcation of equilibria, Hopf bifurcation, global bifurcation occurring saddle connection, and global existence and non-existence of limit cycles, and changes of the topological structure of trajectory as parameters are varied. (author). 8 refs, 4 figs
Equilibrium Point Bifurcation and Singularity Analysis of HH Model with Constraint
2014-01-01
We present the equilibrium point bifurcation and singularity analysis of HH model with constraints. We investigate the effect of constraints and parameters on the type of equilibrium point bifurcation. HH model with constraints has more transition sets. The Matcont toolbox software environment was used for analysis of the bifurcation points in conjunction with Matlab. We also illustrate the stability of the equilibrium points.
Stability and Hopf bifurcation in a symmetric Lotka-Volterra predator-prey system with delays
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Jing Xia
2013-01-01
Full Text Available This article concerns a symmetrical Lotka-Volterra predator-prey system with delays. By analyzing the associated characteristic equation of the original system at the positive equilibrium and choosing the delay as the bifurcation parameter, the local stability and Hopf bifurcation of the system are investigated. Using the normal form theory, we also establish the direction and stability of the Hopf bifurcation. Numerical simulations suggest an existence of Hopf bifurcation near a critical value of time delay.
Stability and Bifurcation Analysis in a Diffusive Brusselator-Type System
Liao, Maoxin; Wang, Qi-Ru
2016-06-01
In this paper, the dynamic properties for a Brusselator-type system with diffusion are investigated. By employing the theory of Hopf bifurcation for ordinary and partial differential equations, we mainly obtain some conditions of the stability and Hopf bifurcation for the ODE system, diffusion-driven instability of the equilibrium solution, and the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions for the PDE system. Finally, some numerical simulations are presented to verify our results.
Noise induced Hopf bifurcation
Shuda, I. A.; Borysov, S S; A.I. Olemskoi
2008-01-01
We consider effect of stochastic sources upon self-organization process being initiated with creation of the limit cycle induced by the Hopf bifurcation. General relations obtained are applied to the stochastic Lorenz system to show that departure from equilibrium steady state can destroy the limit cycle in dependence of relation between characteristic scales of temporal variation of principle variables. Noise induced resonance related to the limit cycle is found to appear if the fastest vari...
Post-Treatment Hemodynamics of a Basilar Aneurysm and Bifurcation
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Ortega, J; Hartman, J; Rodriguez, J; Maitland, D
2008-01-16
Aneurysm re-growth and rupture can sometimes unexpectedly occur following treatment procedures that were initially considered to be successful at the time of treatment and post-operative angiography. In some cases, this can be attributed to surgical clip slippage or endovascular coil compaction. However, there are other cases in which the treatment devices function properly. In these instances, the subsequent complications are due to other factors, perhaps one of which is the post-treatment hemodynamic stress. To investigate whether or not a treatment procedure can subject the parent artery to harmful hemodynamic stresses, computational fluid dynamics simulations are performed on a patient-specific basilar aneurysm and bifurcation before and after a virtual endovascular treatment. The simulations demonstrate that the treatment procedure produces a substantial increase in the wall shear stress. Analysis of the post-treatment flow field indicates that the increase in wall shear stress is due to the impingement of the basilar artery flow upon the aneurysm filling material and to the close proximity of a vortex tube to the artery wall. Calculation of the time-averaged wall shear stress shows that there is a region of the artery exposed to a level of wall shear stress that can cause severe damage to endothelial cells. The results of this study demonstrate that it is possible for a treatment procedure, which successfully excludes the aneurysm from the vascular system and leaves no aneurysm neck remnant, to elevate the hemodynamic stresses to levels that are injurious to the immediately adjacent vessel wall.
Spiral blood flow in aorta-renal bifurcation models.
Javadzadegan, Ashkan; Simmons, Anne; Barber, Tracie
2016-07-01
The presence of a spiral arterial blood flow pattern in humans has been widely accepted. It is believed that this spiral component of the blood flow alters arterial haemodynamics in both positive and negative ways. The purpose of this study was to determine the effect of spiral flow on haemodynamic changes in aorta-renal bifurcations. In this regard, a computational fluid dynamics analysis of pulsatile blood flow was performed in two idealised models of aorta-renal bifurcations with and without flow diverter. The results show that the spirality effect causes a substantial variation in blood velocity distribution, while causing only slight changes in fluid shear stress patterns. The dominant observed effect of spiral flow is on turbulent kinetic energy and flow recirculation zones. As spiral flow intensity increases, the rate of turbulent kinetic energy production decreases, reducing the region of potential damage to red blood cells and endothelial cells. Furthermore, the recirculation zones which form on the cranial sides of the aorta and renal artery shrink in size in the presence of spirality effect; this may lower the rate of atherosclerosis development and progression in the aorta-renal bifurcation. These results indicate that the spiral nature of blood flow has atheroprotective effects in renal arteries and should be taken into consideration in analyses of the aorta and renal arteries. PMID:26414530
Dynamical Systems with a Codimension-One Invariant Manifold: The Unfoldings and Its Bifurcations
Saputra, Kie Van Ivanky
2015-06-01
We investigate a dynamical system having a special structure namely a codimension-one invariant manifold that is preserved under the variation of parameters. We derive conditions such that bifurcations of codimension-one and of codimension-two occur in the system. The normal forms of these bifurcations are derived explicitly. Both local and global bifurcations are analyzed and yield the transcritical bifurcation as the codimension-one bifurcation while the saddle-node-transcritical interaction and the Hopf-transcritical interactions as the codimension-two bifurcations. The unfolding of this degeneracy is also analyzed and reveal global bifurcations such as homoclinic and heteroclinic bifurcations. We apply our results to a modified Lotka-Volterra model and to an infection model in HIV diseases.
Symmetric/asymmetric bifurcation behaviours of a bogie system
Xue-jun, Gao; Ying-hui, Li; Yuan, Yue; True, Hans
2013-02-01
Based on the bifurcation and stability theory of dynamical systems, the symmetric/asymmetric bifurcation behaviours and chaotic motions of a railway bogie system under a complex nonlinear wheel-rail contact relation are investigated in detail by the 'resultant bifurcation diagram' method with slowly increasing and decreasing speed. It is found that the stationary equilibrium solution and the periodic motions coexist due to the sub-critical Hopf bifurcation in the railway bogie system. It is also found that multiple solutions coexist in many speed ranges. The coexistence of multiple solutions may result in a jump and hysteresis of the oscillating amplitude for different kinds of disturbances. It should be avoided in the normal operation. Furthermore, it is found that symmetry-breaking of the system through a pitchfork bifurcation leads to asymmetric chaotic motions in the railway bogie system. The speed ranges of asymmetric chaotic motions are, however, small.
The Analysis of PPG Morphology: Investigating the Effects of Aging on Arterial Compliance
Yousef, Q.; Reaz, M. B. I.; Ali, M. A. M.
2012-12-01
This study presents the variations of photoplethysmogram (PPG) morphology with age. PPG measurement is done noninvasively at the index finger on both right and left hands for a sample of erectile dysfunction (ED) subjects. Some parameters are derived from the analysis of PPG contour showed in association with age. The age is found to be an important factor that affects the contour of PPG signals which accelerates the disappearance of PPG’s dicrotic notch and PPG’s inflection point as well. Arterial compliance is found to be degraded with age due to the fall of arterial elasticity. This study approaches the establishment of usefulness of PPG’s contour analysis as an investigator to the changes in the elastic properties of the vascular system, and as a detector of early sub-clinical atherosclerosis.
International Nuclear Information System (INIS)
Two angiographic instances of anomalous external carotid artery (ECA) and internal carotid artery (ICA) anastomosis are described, each occurring at the C2-3 level and bearing remnants of proximal ICA. The ICA remnant of one patient (identifiable immediately upon bifurcation of the common carotid artery) was hypoplastic, and that of the other patient was an occluded arterial stump. These features are not typical of non-bifurcating ICA. The occipital artery originated from an anomalous connection in one instance and from the main trunk of the ECA (just past the ECA-ICA connection) in the other
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Kim, Chang Hun [Dept. of Neurology, Stroke Center, Myongji Hospital, Goyang (Korea, Republic of); Cho, Young Dae; Kang, Hyun Seung; Kim, Jeong Eun; Han, Moon Hee [Seoul National University Hospital, Seoul National University College of Medicine, Seoul (Korea, Republic of); Jung, Seung Chai [Dept. of Radiology, Asan Medical Center, University of Ulsan College of Medicine, Seoul (Korea, Republic of); Ahn, Jun Hyong [Dept. of Neurosurgery, Hallym University Sacred Heart Hospital, Hallym University College of Medicine, Anyang (Korea, Republic of)
2015-08-15
Two angiographic instances of anomalous external carotid artery (ECA) and internal carotid artery (ICA) anastomosis are described, each occurring at the C2-3 level and bearing remnants of proximal ICA. The ICA remnant of one patient (identifiable immediately upon bifurcation of the common carotid artery) was hypoplastic, and that of the other patient was an occluded arterial stump. These features are not typical of non-bifurcating ICA. The occipital artery originated from an anomalous connection in one instance and from the main trunk of the ECA (just past the ECA-ICA connection) in the other.
International Nuclear Information System (INIS)
Objective: To investigate the function of transferrin-DNA complex, transported by transferrin(Tf) and trans-arterial injection via interventional approach be the duel-target-orientated delivery and the transferring into malignant cells to get more effective therapy. Methods: p53-LipofectAMINE ligand with different concentrations of Tf (0, 10, 25, 50, 100 μg)transfected the 4 strains including LM6,Hep3B,YY and L02 in vitro to evaluate the gene transfection efficiency through western blot. Then, after setting up the VX2 hepatocarcinoma models, we delivered the Tf-p53-LipofectAMlNE complex into the hepatic arteries via interventional techniques to analyse the transfection efficiency in vivo. Results: Tf, within the range of l0 100 μg, could increase gene transfection efficiency mediated by liposome, and the efficiency increases with the raise of Tf concentration. Combination with interventional technique to inject Tf-DNA complex into tumor arteries, gene transfection efficiency was enhanced in rabbit models. Conclusion: Tf can enhance gene-liposome transfection efficiency, furthermore with combination of interventional catheter technique, there would be a potential duel-target-orientated gene therapy method. (authors)
International Nuclear Information System (INIS)
Highlights: • A ratio-dependent predator–prey system involving two discrete maturation time delays is studied. • Hopf bifurcations are analyzed by choosing delay parameters as bifurcation parameters. • When a delay parameter passes through a critical value, Hopf bifurcations occur. • The direction of bifurcation, the period and the stability of periodic solution are also obtained. - Abstract: In this paper we give a detailed Hopf bifurcation analysis of a ratio-dependent predator–prey system involving two different discrete delays. By analyzing the characteristic equation associated with the model, its linear stability is investigated. Choosing delay terms as bifurcation parameters the existence of Hopf bifurcations is demonstrated. Stability of the bifurcating periodic solutions is determined by using the center manifold theorem and the normal form theory introduced by Hassard et al. Furthermore, some of the bifurcation properties including direction, stability and period are given. Finally, theoretical results are supported by some numerical simulations
Directory of Open Access Journals (Sweden)
Zizhen Zhang
2013-01-01
Full Text Available Hopf bifurcation of a delayed predator-prey system with prey infection and the modified Leslie-Gower scheme is investigated. The conditions for the stability and existence of Hopf bifurcation of the system are obtained. The state feedback and parameter perturbation are used for controlling Hopf bifurcation in the system. In addition, direction of Hopf bifurcation and stability of the bifurcated periodic solutions of the controlled system are obtained by using normal form and center manifold theory. Finally, numerical simulation results are presented to show that the hybrid controller is efficient in controlling Hopf bifurcation.
Directory of Open Access Journals (Sweden)
Yanhui Zhai
2014-01-01
Full Text Available The paper investigated an avian influenza virus propagation model with nonlinear incidence rate and delay based on SIR epidemic model. We regard delay as bifurcating parameter to study the dynamical behaviors. At first, local asymptotical stability and existence of Hopf bifurcation are studied; Hopf bifurcation occurs when time delay passes through a sequence of critical values. An explicit algorithm for determining the direction of the Hopf bifurcations and stability of the bifurcation periodic solutions is derived by applying the normal form theory and center manifold theorem. What is more, the global existence of periodic solutions is established by using a global Hopf bifurcation result.
Introduction to bifurcation theory
International Nuclear Information System (INIS)
Bifurcation theory is a subject with classical mathematical origins. The modern development of the subject starts with Poincare and the qualitative theory of differential equations. In recent years, the theory has undergone a tremendous development with the infusion of new ideas and methods from dynamical systems theory, singularity theory, group theory, and computer-assisted studies of dynamics. As a result, it is difficult to draw the boundaries of the theory with any confidence. In this review, the objects in question will be parameterized families of dynamical systems (vector fields or maps). In the sciences these families commonly arise when one formulates equations of motion to model a physical system. We specifically analyze how the time evolution near an equilibrium can change as parameters are varied; for simplicity we consider the case of a single parameter only
Hopf bifurcations in a predator-prey system with multiple delays
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Hu Guangping [School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000 (China); School of Mathematics and Physics, Nanjing University of Information and Technology, Nanjing 210044 (China); Li Wantong [School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000 (China)], E-mail: wtli@lzu.edu.cn; Yan Xiangping [Department of Applied Mathematics, Lanzhou Jiaotong University, Lanzhou 730070 (China)
2009-10-30
This paper is concerned with a two species Lotka-Volterra predator-prey system with three discrete delays. By regarding the gestation period of two species as the bifurcation parameter, the stability of positive equilibrium and Hopf bifurcations of nonconstant periodic solutions are investigated. Furthermore, the direction of Hopf bifurcations and the stability of bifurcated periodic solutions are determined by applying the normal form theory and the center manifold reduction for functional differential equations (FDEs). In addition, the global existence of bifurcated periodic solutions are also established by employing the topological global Hopf bifurcation theorem, which shows that the local Hopf bifurcations imply the global ones after the second critical value of parameter. Finally, to verify our theoretical predictions, some numerical simulations are also included.
Hopf bifurcations in a predator-prey system with multiple delays
International Nuclear Information System (INIS)
This paper is concerned with a two species Lotka-Volterra predator-prey system with three discrete delays. By regarding the gestation period of two species as the bifurcation parameter, the stability of positive equilibrium and Hopf bifurcations of nonconstant periodic solutions are investigated. Furthermore, the direction of Hopf bifurcations and the stability of bifurcated periodic solutions are determined by applying the normal form theory and the center manifold reduction for functional differential equations (FDEs). In addition, the global existence of bifurcated periodic solutions are also established by employing the topological global Hopf bifurcation theorem, which shows that the local Hopf bifurcations imply the global ones after the second critical value of parameter. Finally, to verify our theoretical predictions, some numerical simulations are also included.
Bifurcations sights, sounds, and mathematics
Matsumoto, Takashi; Kokubu, Hiroshi; Tokunaga, Ryuji
1993-01-01
Bifurcation originally meant "splitting into two parts. " Namely, a system under goes a bifurcation when there is a qualitative change in the behavior of the sys tem. Bifurcation in the context of dynamical systems, where the time evolution of systems are involved, has been the subject of research for many scientists and engineers for the past hundred years simply because bifurcations are interesting. A very good way of understanding bifurcations would be to see them first and study theories second. Another way would be to first comprehend the basic concepts and theories and then see what they look like. In any event, it is best to both observe experiments and understand the theories of bifurcations. This book attempts to provide a general audience with both avenues toward understanding bifurcations. Specifically, (1) A variety of concrete experimental results obtained from electronic circuits are given in Chapter 1. All the circuits are very simple, which is crucial in any experiment. The circuits, howev...
Santer, R M; Owen, R. G.
1986-01-01
A combination of morphological and semiquantitative techniques has been employed to characterise the arterial supply to the rat superior cervical ganglion. Microfil and ink-injected preparations indicate that the major supply is from the carotid body artery which sends several branches to the rostral part of the ganglion and a recurrent branch to its caudal part. Occlusion of the proximal part of the external carotid artery, and hence the carotid body artery (whether it be derived from the ex...
International Nuclear Information System (INIS)
Objective: To investigate and analyze the cause of the tumble which occurs after transcatheter arterial chemoembolization (TACE), and to discuss its related factors. Methods: During the period from January 2003 to February 2010 in the Department of Interventional Radiology of Union Hospital (Wuhan city), post-TACE tumble occurred in 28 patients. The causes of the tumble were investigated and analyzed. Results: (1) The total number of the tumble occurrence after TACE was declining with the year. (2) Certain relationship existed between the occurrence of post-TACE tumble and the patient's age, drugs used in surgery, unit environment, nurse's shift, etc. Conclusion: Based on the patient's individual condition, intentionally enhancing the perioperative nursing care and adjusting the nurse's shift are very important measures to prevent the occurrence of post-TACE tumble. (authors)
Application of Bifurcation Theory to Subsynchronous Resonance in Power Systems
Harb, Ahmad M.
1996-01-01
A bifurcation analysis is used to investigate the complex dynamics of two heavily loaded single-machine-infinite-busbar power systems modeling the characteristics of the BOARDMAN generator with respect to the rest of the North-Western American Power System and the CHOLLA$#$ generator with respect to the SOWARO station. In the BOARDMAN system, we show that there are three Hopf bifurcations at practical co...
Bursting oscillations, bifurcation and synchronization in neuronal systems
International Nuclear Information System (INIS)
Highlights: → We investigate bursting oscillations and related bifurcation in the modified Morris-Lecar neuron. → Two types of fast-slow bursters are analyzed in detail. → We show the properties of some crucial bifurcation points. → Synchronization transition and the neural excitability are explored in the coupled bursters. - Abstract: This paper investigates bursting oscillations and related bifurcation in the modified Morris-Lecar neuron. It is shown that for some appropriate parameters, the modified Morris-Lecar neuron can exhibit two types of fast-slow bursters, that is 'circle/fold cycle' bursting and 'subHopf/homoclinic' bursting with class 1 and class 2 neural excitability, which have different neuro-computational properties. By means of the analysis of fast-slow dynamics and phase plane, we explore bifurcation mechanisms associated with the two types of bursters. Furthermore, the properties of some crucial bifurcation points, which can determine the type of the burster, are studied by the stability and bifurcation theory. In addition, we investigate the influence of the coupling strength on synchronization transition and the neural excitability in two electrically coupled bursters with the same bursting type. More interestingly, the multi-time-scale synchronization transition phenomenon is found as the coupling strength varies.
DYNAMIC BIFURCATION OF NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
MA TIAN; WANG SHOUHONG
2005-01-01
The authors introduce a notion of dynamic bifurcation for nonlinear evolution equations, which can be called attractor bifurcation. It is proved that as the control parameter crosses certain critical value, the system bifurcates from a trivial steady state solution to an attractor with dimension between m and m + 1, where m + 1 is the number of eigenvalues crossing the imaginary axis. The attractor bifurcation theory presented in this article generalizes the existing steady state bifurcations and the Hopf bifurcations. It provides a unified point of view on dynamic bifurcation and can be applied to many problems in physics and mechanics.
Bifurcation dynamics of the tempered fractional Langevin equation
Zeng, Caibin; Yang, Qigui; Chen, YangQuan
2016-08-01
Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings.
Bifurcation theory for hexagonal agglomeration in economic geography
Ikeda, Kiyohiro
2014-01-01
This book contributes to an understanding of how bifurcation theory adapts to the analysis of economic geography. It is easily accessible not only to mathematicians and economists, but also to upper-level undergraduate and graduate students who are interested in nonlinear mathematics. The self-organization of hexagonal agglomeration patterns of industrial regions was first predicted by the central place theory in economic geography based on investigations of southern Germany. The emergence of hexagonal agglomeration in economic geography models was envisaged by Krugman. In this book, after a brief introduction of central place theory and new economic geography, the missing link between them is discovered by elucidating the mechanism of the evolution of bifurcating hexagonal patterns. Pattern formation by such bifurcation is a well-studied topic in nonlinear mathematics, and group-theoretic bifurcation analysis is a well-developed theoretical tool. A finite hexagonal lattice is used to express uniformly distri...
Grazing bifurcation and chaos in response of rubbing rotor
International Nuclear Information System (INIS)
This paper investigates the grazing bifurcation in the nonlinear response of a complex rotor system. For a rotor with overhung disc, step diameter shaft and elastic supports, the motion equations are derived based on the Transition Matrix Method. When the rotor speed increases, the disc will touch the case and lead to rubbing of rotor. When the disc rubs with the case, the elastic force and friction force of the case will make the rotor exhibit nonlinear characteristics. For the piecewise ODEs, the numerical method is applied to obtain its nonlinear response. From the results, the grazing bifurcation, which happens at the moment of touching between disc and case, can be observed frequently. The grazing bifurcation can lead to the jump between periodic orbits. The response can go to chaos from periodic motion under grazing bifurcation. When grazing occurs, response can become quasi-period from period
Bifurcation dynamics of the tempered fractional Langevin equation.
Zeng, Caibin; Yang, Qigui; Chen, YangQuan
2016-08-01
Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings. PMID:27586627
Bifurcations, instabilities, degradation in geomechanics
Exadaktylos, George
2007-01-01
Leading international researchers and practitioners of bifurcations and instabilities in geomechanics debate the developments and applications which have occurred over the last few decades. The topics covered include modeling of bifurcation, structural failure of geomaterials and geostructures, advanced analytical, numerical and experimental techniques, and application and development of generalised continuum models etc. In addition analytical solutions, numerical methods, experimental techniques, and case histories are presented. Beside fundamental research findings, applications in geotechni
Does the principle of minimum work apply at the carotid bifurcation: a retrospective cohort study
International Nuclear Information System (INIS)
There is recent interest in the role of carotid bifurcation anatomy, geometry and hemodynamic factors in the pathogenesis of carotid artery atherosclerosis. Certain anatomical and geometric configurations at the carotid bifurcation have been linked to disturbed flow. It has been proposed that vascular dimensions are selected to minimize energy required to maintain blood flow, and that this occurs when an exponent of 3 relates the radii of parent and daughter arteries. We evaluate whether the dimensions of bifurcation of the extracranial carotid artery follow this principle of minimum work. This study involved subjects who had computed tomographic angiography (CTA) at our institution between 2006 and 2007. Radii of the common, internal and external carotid arteries were determined. The exponent was determined for individual bifurcations using numerical methods and for the sample using nonlinear regression. Mean age for 45 participants was 56.9 ± 16.5 years with 26 males. Prevalence of vascular risk factors was: hypertension-48%, smoking-23%, diabetes-16.7%, hyperlipidemia-51%, ischemic heart disease-18.7%. The value of the exponent ranged from 1.3 to 1.6, depending on estimation methodology. The principle of minimum work (defined by an exponent of 3) may not apply at the carotid bifurcation. Additional factors may play a role in the relationship between the radii of the parent and daughter vessels
Fast automatic algorithm for bifurcation detection in vascular CTA scans
Brozio, Matthias; Gorbunova, Vladlena; Godenschwager, Christian; Beck, Thomas; Bernhardt, Dominik
2012-02-01
Endovascular imaging aims at identifying vessels and their branches. Automatic vessel segmentation and bifurcation detection eases both clinical research and routine work. In this article a state of the art bifurcation detection algorithm is developed and applied on vascular computed tomography angiography (CTA) scans to mark the common iliac artery and its branches, the internal and external iliacs. In contrast to other methods our algorithm does not rely on a complete segmentation of a vessel in the 3D volume, but evaluates the cross-sections of the vessel slice by slice. Candidates for vessels are obtained by thresholding, following by 2D connected component labeling and prefiltering by size and position. The remaining candidates are connected in a squared distanced weighted graph. With Dijkstra algorithm the graph is traversed to get candidates for the arteries. We use another set of features considering length and shape of the paths to determine the best candidate and detect the bifurcation. The method was tested on 119 datasets acquired with different CT scanners and varying protocols. Both easy to evaluate datasets with high resolution and no apparent clinical diseases and difficult ones with low resolution, major calcifications, stents or poor contrast between the vessel and surrounding tissue were included. The presented results are promising, in 75.7% of the cases the bifurcation was labeled correctly, and in 82.7% the common artery and one of its branches were assigned correctly. The computation time was on average 0.49 s +/- 0.28 s, close to human interaction time, which makes the algorithm applicable for time-critical applications.
DEFF Research Database (Denmark)
Willerslev, Anne; Li, Xiao Q; Munch, Inger C;
2014-01-01
from the population-based, observational Copenhagen Child Cohort 2000 study. RESULTS: The blood stream in retinal arteries maintains a figure-of-8 SD-OCT profile consistent with a laminar flow in concentric sheets and a parabolic velocity distribution up to the point of divergence at arterial...... bifurcations. In contrast, the blood stream at the site of confluence of two retinal veins remains divided into two parallel sets of sheets with separate velocity distribution for a downstream distance of at least four trunk vessel diameters. Consequently, retinal trunk vessels near bifurcations...
Bifurcated Helical Core Equilibrium States in Tokamaks
International Nuclear Information System (INIS)
Full text: Tokamaks with weak to moderate reversed central magnetic shear in which the minimum of the inverse rotational transform qmin is in the neighbourhood of unity can trigger bifurcated MagnetoHydroDynamic (MHD) equilibrium states. In addition to the standard axisymmetric branch that can be obtained with standard Grad-Shafranov solvers, a novel branch with a three-dimensional (3D) helical core has been computed with the ANIMEC code, an anisotropic pressure extension of the VMEC code. The solutions have imposed nested magnetic flux surfaces and are similar to saturated ideal internal kink modes. The difference in energy between both possible branches is very small. Plasma elongation, current and β enhance the susceptibility for bifurcations to occur. An initial value nonlinear ideal MHD evolution of the axisymmetric branch compares favourably with the helical core equilibrium structures calculated. Peaked prescribed pressure profiles reproduce the 'snake' structures observed in many tokamaks which has led to a new explanation of the snake as a bifurcated helical equilibrium state that results from a saturated ideal internal kink in which pellets or impurities induce a hollow current profile. Snake equilibrium structures are computed in free boundary TCV tokamak simulations. Magnetic field ripple and resonant magnetic perturbations in MAST free boundary calculations do not alter the helical core deformation in a significant manner when qmin is near unity. These bifurcated solutions constitute a paradigm shift that motivates the application of tools developed for stellarator research in tokamak physics investigations. The examination of fast ion confinement in this class of equilibria is performed with the VENUS code in which a coordinate independent noncanonical phase-space Lagrangian formulation of guiding centre drift orbit theory has been implemented. (author)
International Nuclear Information System (INIS)
Atherosclerosis is a progressive disease that causes lesions in large and medium-sized arteries. There is increasing evidence that the function of vascular endothelial cells is impaired by oxidation reactions, and that metal ions may participate in these processes. The nuclear microscopy facility in NUS, which has the ability to focus a 2 MeV proton beam down to sub micron spot sizes, was used to investigate the trace elemental changes (e.g. Zn and Fe) in atherosclerotic lesions in the common carotid artery of apolipoprotein E deficient mice fed a high fat diet. In this preliminary study, which is part of a larger study to investigate the effects of probucol on carotid artery atherosclerosis, two sets of mice were used; a test set fed a high fat diet +1% probucol, and a control set which was fed a high fat diet only. The results show that the Zn/Fe ratio was significantly higher in the media of arteries of probucol treated animals without overlying lesion (4.3) compared to the media with overlying lesion (1.3) (p = 0.004) for test mice. For the control mice, the arterial Zn/Fe ratio was 1.8 for media without overlying lesion, compared with 1.0 for media with overlying lesion (p = 0.1). Thus, for media without overlying lesion, the Zn/Fe ratio was significantly higher (p = 0.009) in probucol-treated (4.3) than control mice (1.8), whereas there was little difference in the ratios between the two groups in media with overlying lesion (1.3 compared with 1.0). These preliminary results are consistent with the idea that the levels of iron and zinc concentrations within the artery wall may influence the formation of atherosclerotic plaque in the carotid artery
Effects of Bifurcations on Aft-Fan Engine Nacelle Noise
Nark, Douglas M.; Farassat, Fereidoun; Pope, D. Stuart; Vatsa, Veer N.
2004-01-01
Aft-fan engine nacelle noise is a significant factor in the increasingly important issue of aircraft community noise. The ability to predict such noise within complex duct geometries is a valuable tool in studying possible noise attenuation methods. A recent example of code development for such predictions is the ducted fan noise propagation and radiation code CDUCT-LaRC. This work focuses on predicting the effects of geometry changes (i.e. bifurcations, pylons) on aft fan noise propagation. Beginning with simplified geometries, calculations show that bifurcations lead to scattering of acoustic energy into higher order modes. In addition, when circumferential mode number and the number of bifurcations are properly commensurate, bifurcations increase the relative importance of the plane wave mode near the exhaust plane of the bypass duct. This is particularly evident when the bypass duct surfaces include acoustic treatment. Calculations involving more complex geometries further illustrate that bifurcations and pylons clearly affect modal content, in both propagation and radiation calculations. Additionally, results show that consideration of acoustic radiation results may provide further insight into acoustic treatment effectiveness for situations in which modal decomposition may not be straightforward. The ability of CDUCT-LaRC to handle complex (non-axisymmetric) multi-block geometries, as well as axially and circumferentially segmented liners, allows investigation into the effects of geometric elements (bifurcations, pylons).
Stability and Bifurcation of Two Kinds of Three-Dimensional Fractional Lotka-Volterra Systems
Directory of Open Access Journals (Sweden)
Jinglei Tian
2014-01-01
Full Text Available Two kinds of three-dimensional fractional Lotka-Volterra systems are discussed. For one system, the asymptotic stability of the equilibria is analyzed by providing some sufficient conditions. And bifurcation property is investigated by choosing the fractional order as the bifurcation parameter for the other system. In particular, the critical value of the fractional order is identified at which the Hopf bifurcation may occur. Furthermore, the numerical results are presented to verify the theoretical analysis.
Complex dynamics in biological systems arising from multiple limit cycle bifurcation.
Yu, P; Lin, W
2016-12-01
In this paper, we study complex dynamical behaviour in biological systems due to multiple limit cycles bifurcation. We use simple epidemic and predator-prey models to show exact routes to new types of bistability, that is, bistability between equilibrium and periodic oscillation, and bistability between two oscillations, which may more realistically describe the real situations. Bifurcation theory and normal form theory are applied to investigate the multiple limit cycles bifurcating from Hopf critical point. PMID:27042877
Stability and Hopf Bifurcation for a Delayed SLBRS Computer Virus Model
Zizhen Zhang; Huizhong Yang
2014-01-01
By incorporating the time delay due to the period that computers use antivirus software to clean the virus into the SLBRS model a delayed SLBRS computer virus model is proposed in this paper. The dynamical behaviors which include local stability and Hopf bifurcation are investigated by regarding the delay as bifurcating parameter. Specially, direction and stability of the Hopf bifurcation are derived by applying the normal form method and center manifold theory. Finally, an illustrative examp...
Schomerus, H
1997-01-01
We investigate classical and semiclassical aspects of codimension--two bifurcations of periodic orbits in Hamiltonian systems. A classification of these bifurcations in autonomous systems with two degrees of freedom or time-periodic systems with one degree of freedom is presented. We derive uniform approximations to be used in semiclassical trace formulas and determine also certain global bifurcations in conjunction with Stokes transitions that become important in the ensuing diffraction catastrophe integrals.
Pathological observation of brain arteries and spontaneous aneurysms in hypertensive rats
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
Objective To investigate the role of hypertension in the pathogenesis of cerebral aneurysms in rats.Methods Twenty spontaneous hypertensive rats (SHR) and 10 Wistar-Kyoto rats (WKY) were included in this observational study. Animals were fed with normal diet and drinking water. No experimental modifications were undertaken in either group. They were sacrificed at one year of age, the bifurcations of the circle of Willis were dissected and longitudinal serial sections were prepared for light microscopic and transmission electron microscopic study.Results In the SHR group, 2 of the 20 rats formed an aneurysm respectively at the bifurcations of the basilar artery. As revealed by electron microscopy, injury at the bifurcation of the artery first occurred on the steeper side of the intimal pad. Furthermore, loss of endothelial cells, small depressions on the intima, disruptive internal elastic lamina and lymphocytes or red blood cells infiltration were noted at the steeper side of the intimal pad. No significant changes were observed in WKY group.Conclusions Cerebral aneurysms can form spontaneously in SHR without ligation of the common carotid artery and without a diet containing β-aminoproprionitrile. Long-standing systemic arterial hypertension is one of the etiological factors that contributes to aneurysm formation in SHR rats.
Prediction of fibre architecture and adaptation in diseased carotid bifurcations.
LENUS (Irish Health Repository)
Creane, Arthur
2011-12-01
Many studies have used patient-specific finite element models to estimate the stress environment in atherosclerotic plaques, attempting to correlate the magnitude of stress to plaque vulnerability. In complex geometries, few studies have incorporated the anisotropic material response of arterial tissue. This paper presents a fibre remodelling algorithm to predict the fibre architecture, and thus anisotropic material response in four patient-specific models of the carotid bifurcation. The change in fibre architecture during disease progression and its affect on the stress environment in the plaque were predicted. The mean fibre directions were assumed to lie at an angle between the two positive principal strain directions. The angle and the degree of dispersion were assumed to depend on the ratio of principal strain values. Results were compared with experimental observations and other numerical studies. In non-branching regions of each model, the typical double helix arterial fibre pattern was predicted while at the bifurcation and in regions of plaque burden, more complex fibre architectures were found. The predicted change in fibre architecture in the arterial tissue during plaque progression was found to alter the stress environment in the plaque. This suggests that the specimen-specific anisotropic response of the tissue should be taken into account to accurately predict stresses in the plaque. Since determination of the fibre architecture in vivo is a difficult task, the system presented here provides a useful method of estimating the fibre architecture in complex arterial geometries.
Rarefaction and blood pressure in systemic and pulmonary arteries.
Olufsen, Mette S; Hill, N A; Vaughan, Gareth D A; Sainsbury, Christopher; Johnson, Martin
2012-08-01
The effects of vascular rarefaction (the loss of small arteries) on the circulation of blood are studied using a multiscale mathematical model that can predict blood flow and pressure in the systemic and pulmonary arteries. We augmented a model originally developed for the systemic arteries (Olufsen et al. 1998, 1999, 2000, 2004) to (a) predict flow and pressure in the pulmonary arteries, and (b) predict pressure propagation along the small arteries in the vascular beds. The systemic and pulmonary arteries are modelled as separate, bifurcating trees of compliant and tapering vessels. Each tree is divided into two parts representing the `large' and `small' arteries. Blood flow and pressure in the large arteries are predicted using a nonlinear cross-sectional area-averaged model for a Newtonian fluid in an elastic tube with inflow obtained from magnetic resonance measurements. Each terminal vessel within the network of the large arteries is coupled to a vascular bed of small `resistance' arteries, which are modelled as asymmetric structured trees with specified area and asymmetry ratios between the parent and daughter arteries. For the systemic circulation, each structured tree represents a specific vascular bed corresponding to major organs and limbs. For the pulmonary circulation, there are four vascular beds supplied by the interlobar arteries. This manuscript presents the first theoretical calculations of the propagation of the pressure and flow waves along systemic and pulmonary large and small arteries. Results for all networks were in agreement with published observations. Two studies were done with this model. First, we showed how rarefaction can be modelled by pruning the tree of arteries in the microvascular system. This was done by modulating parameters used for designing the structured trees. Results showed that rarefaction leads to increased mean and decreased pulse pressure in the large arteries. Second, we investigated the impact of decreasing vessel
Bifurcation analysis of a predator–prey model with anti-predator behaviour
International Nuclear Information System (INIS)
We investigated a predator–prey model with a nonmonotonic functional response and anti-predator behaviour such that the adult prey can attack vulnerable predators. By analyzing the existence and stability of all possible equilibria and conducting a bifurcation analysis, we obtained the global dynamics of the proposed system. The system could undergo a saddle-node bifurcation, (supercritical and subcritical) Hopf bifurcation, homoclinic bifurcation and a Bogdanov–Takens bifurcation of codimension 2. Further, we obtained a generic family unfolding for the system by choosing the environmental carrying capacity of the prey and the death rate of the predator as bifurcation parameters. Numerical studies showed that anti-predator behaviour not only makes the coexistence of the prey and predator populations less likely, but also damps the predator–prey oscillations. Therefore, anti-predator behaviour helps the prey population to resist predator aggression
Bifurcation Analysis of a Lotka-Volterra Mutualistic System with Multiple Delays
Directory of Open Access Journals (Sweden)
Xin-You Meng
2014-01-01
Full Text Available A class of Lotka-Volterra mutualistic system with time delays of benefit and feedback delays is introduced. By analyzing the associated characteristic equation, the local stability of the positive equilibrium and existence of Hopf bifurcation are obtained under all possible combinations of two or three delays selecting from multiple delays. Not only explicit formulas to determine the properties of the Hopf bifurcation are shown by using the normal form method and center manifold theorem, but also the global continuation of Hopf bifurcation is investigated by applying a global Hopf bifurcation result due to Wu (1998. Numerical simulations are given to support the theoretical results.
Control of Fold Bifurcation Application on Chemostat around Critical Dilution Rate
DEFF Research Database (Denmark)
Pedersen, Kurt; Jørgensen, Sten Bay
1999-01-01
Based on a bifurcation analysis of a process it is possible to point out where there might be operational problems due to change of stability of the process. One such change is investigated, Fold bifurcations. This type of bifurcation is associated with hysteresis/multiple steady states, which co...... complicates operation close to these bifurcations. Typically only one of the steady states is interesting from a production point of view. A novel control law is proposed herein which is able to cope with the operational problems of the process....
Stability and bifurcation analysis in a magnetic bearing system with time delays
International Nuclear Information System (INIS)
A kind of magnetic bearing system with time delay is considered. Firstly, linear stability of the model is investigated by analyzing the distribution of the roots of the associated characteristic equation. According to the analysis results, the bifurcation diagram is drawn in the appropriate parameter plane. It is found that the Ho pf bifurcation occurs when the delay passes through a sequence of critical values. Then the explicit algorithm for determining the direction of the Ho pf bifurcations and the stability of the bifurcating periodic solutions are derived, using the theory of normal form and center manifold. Finally, some numerical simulations are carried out to illustrate the results found
Stochastic bifurcation for a tumor-immune system with symmetric Lévy noise
Xu, Yong; Feng, Jing; Li, JuanJuan; Zhang, Huiqing
2013-10-01
In this paper, we investigate stochastic bifurcation for a tumor-immune system in the presence of a symmetric non-Gaussian Lévy noise. Stationary probability density functions will be numerically obtained to define stochastic bifurcation via the criteria of its qualitative change, and bifurcation diagram at parameter plane is presented to illustrate the bifurcation analysis versus noise intensity and stability index. The effects of both noise intensity and stability index on the average tumor population are also analyzed by simulation calculation. We find that stochastic dynamics induced by Gaussian and non-Gaussian Lévy noises are quite different.
Invariant manifolds and global bifurcations.
Guckenheimer, John; Krauskopf, Bernd; Osinga, Hinke M; Sandstede, Björn
2015-09-01
Invariant manifolds are key objects in describing how trajectories partition the phase spaces of a dynamical system. Examples include stable, unstable, and center manifolds of equilibria and periodic orbits, quasiperiodic invariant tori, and slow manifolds of systems with multiple timescales. Changes in these objects and their intersections with variation of system parameters give rise to global bifurcations. Bifurcation manifolds in the parameter spaces of multi-parameter families of dynamical systems also play a prominent role in dynamical systems theory. Much progress has been made in developing theory and computational methods for invariant manifolds during the past 25 years. This article highlights some of these achievements and remaining open problems. PMID:26428557
Bifurcations and intermittent magnetic activity
International Nuclear Information System (INIS)
The sequence of equilibria of two-dimensional reduced magnetohydrodynamics has been studied as a function of the tearing mode stability parameter Δ'. After a symmetry-breaking bifurcation occurring at Δ' ∼ 0, which originates a state with a small magnetic island, the system undergoes a second bifurcation, of tangent type, at Δ' ∼ 1. Above this value, no stationary solutions with small islands exist. The system rapidly develops an island of macroscopic size. This general property is proposed as a basic ingredient of the intermittent events observed in magnetically confined plasmas. (author)
Bifurcations and intermittent magnetic activity
Energy Technology Data Exchange (ETDEWEB)
Tebaldi, C.; Ottaviani, M.; Porcelli, F. [Commission of the European Communities, Abingdon (United Kingdom). JET Joint Undertaking
1996-04-01
The sequence of equilibria of two-dimensional reduced magnetohydrodynamics has been studied as a function of the tearing mode stability parameter {Delta}`. After a symmetry-breaking bifurcation occurring at {Delta}` {approx} 0, which originates a state with a small magnetic island, the system undergoes a second bifurcation, of tangent type, at {Delta}` {approx} 1. Above this value, no stationary solutions with small islands exist. The system rapidly develops an island of macroscopic size. This general property is proposed as a basic ingredient of the intermittent events observed in magnetically confined plasmas. (author).
Global Hopf Bifurcation on Two-Delays Leslie-Gower Predator-Prey System with a Prey Refuge
Directory of Open Access Journals (Sweden)
Qingsong Liu
2014-01-01
Full Text Available A modified Leslie-Gower predator-prey system with two delays is investigated. By choosing τ1 and τ2 as bifurcation parameters, we show that the Hopf bifurcations occur when time delay crosses some critical values. Moreover, we derive the equation describing the flow on the center manifold; then we give the formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the theoretical results and chaotic behaviors are observed. Finally, using a global Hopf bifurcation theorem for functional differential equations, we show the global existence of the periodic solutions.
Institute of Scientific and Technical Information of China (English)
DUAN XianZhong; WEN JinYu; CHENG ShiJie
2009-01-01
In this paper, an introduction to the bifurcation theory and its applicability to the study of sub-syn-chronous resonance (SSR) phenomenon in power system are presented. The continuation and bifur-cation analysis software AUTO97 is adopted to investigate SSR for a single-machine-infinite-bus power system with series capacitor compensation. The investigation results show that SSR is the result of unstable limit cycle after bifurcation. When the system exhibits SSR, some complex periodical orbit bifurcations, such as torus bifurcation and periodical fold bifurcation, may happen with the variation of limit cycle. Furthermore, the initial operation condition may greatly influence the ultimate state of the system. The time-domain simulation is carried out to verify the effectiveness of the results obtained from the bifurcation analysis.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper,an introduction to the bifurcation theory and its applicability to the study of sub-synchronous resonance (SSR) phenomenon in power system are presented. The continuation and bifurcation analysis software AUTO97 is adopted to investigate SSR for a single-machine-infinite-bus power system with series capacitor compensation. The investigation results show that SSR is the result of unstable limit cycle after bifurcation. When the system exhibits SSR, some complex periodical orbit bifurcations, such as torus bifurcation and periodical fold bifurcation, may happen with the variation of limit cycle. Furthermore, the initial operation condition may greatly influence the ultimate state of the system. The time-domain simulation is carried out to verify the effectiveness of the results obtained from the bifurcation analysis.
Multiple Bifurcations of a Cylindrical Dynamical System
Han Ning; Cao Qingjie
2016-01-01
This paper focuses on multiple bifurcations of a cylindrical dynamical system, which is evolved from a rotating pendulum with SD oscillator. The rotating pendulum system exhibits the coupling dynamics property of the bistable state and conventional pendulum with the ho- moclinic orbits of the first and second type. A double Andronov-Hopf bifurcation, two saddle-node bifurcations of periodic orbits and a pair of homoclinic bifurcations are detected by using analytical analysis and nu- merical ...
Bifurcations associated with sub-synchronous resonance
Mitani, Yasunori; K. Tsuji; M.Varghese; Wu, F. F.; VARAIYA, P
1998-01-01
This paper describes a set of results of detecting nonlinear phenomena appearing in a turbine generator power system with series-capacitor compensation. The analysis was based on the Floquet theory as well as the Hopf bifurcation theorem. After the first Hopf bifurcation, the stable limit cycle bifurcates to a stable torus and an unstable limit cycle which connects to a stable limit cycle by a supercritical torus bifurcation. The stable limit cycle joins with an unstable limit cycle at a cycl...
Institute of Scientific and Technical Information of China (English)
ZHANG Zi-Zhen; YANG Hui-Zhong
2013-01-01
In this paper,we consider a predator-prey system with modified Leslie-Gower and Holling type III schemes.By regarding the time delay as the bifurcation parameter,the local asymptotic stability of the positive equilibrium is investigated.And we find that Hopf bifurcations can occur as the time delay crosses some critical values.In particular,special attention is paid to the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions.In addition,the global existence of periodic solutions bifurcating from the Hopf bifurcation are considered by applying a global Hopf bifurcation result.Finally,numerical simulations are carried out to illustrate the main theoretical results.
Stability and Hopf bifurcations in a competitive Lotka-Volterra system with two delays
Energy Technology Data Exchange (ETDEWEB)
Song Yongli E-mail: songyl@sjtu.edu.cn; Han Maoan; Peng Yahong
2004-12-01
We consider a Lotka-Volterra competition system with two delays. We first investigate the stability of the positive equilibrium and the existence of Hopf bifurcations, and then using the normal form theory and center manifold argument, derive the explicit formulas which determine the stability, direction and other properties of bifurcating periodic solutions.
Bifurcation Analysis of Gene Propagation Model Governed by Reaction-Diffusion Equations
Directory of Open Access Journals (Sweden)
Guichen Lu
2016-01-01
Full Text Available We present a theoretical analysis of the attractor bifurcation for gene propagation model governed by reaction-diffusion equations. We investigate the dynamical transition problems of the model under the homogeneous boundary conditions. By using the dynamical transition theory, we give a complete characterization of the bifurcated objects in terms of the biological parameters of the problem.
Anti-control of Hopf Bifurcation in a Delayed Predator-prey Gomp ertz Mo del
Institute of Scientific and Technical Information of China (English)
XU Chang-jin; CHEN Da-xue
2013-01-01
A delayed predator-prey Gompertz model is investigated. The stability is ana-lyzed. Anti-control of Hopf bifurcation for the model is presented. Numerical simulations are performed to confirm that the new feedback controller using time delay is efficient in creating Hopf bifurcation. Finally, main conclusions are included.
Full system bifurcation analysis of endocrine bursting models.
Tsaneva-Atanasova, Krasimira; Osinga, Hinke M; Riess, Thorsten; Sherman, Arthur
2010-06-21
Plateau bursting is typical of many electrically excitable cells, such as endocrine cells that secrete hormones and some types of neurons that secrete neurotransmitters. Although in many of these cell types the bursting patterns are regulated by the interplay between voltage-gated calcium channels and calcium-sensitive potassium channels, they can be very different. We investigate so-called square-wave and pseudo-plateau bursting patterns found in endocrine cell models that are characterized by a super- or subcritical Hopf bifurcation in the fast subsystem, respectively. By using the polynomial model of Hindmarsh and Rose (Proceedings of the Royal Society of London B 221 (1222) 87-102), which preserves the main properties of the biophysical class of models that we consider, we perform a detailed bifurcation analysis of the full fast-slow system for both bursting patterns. We find that both cases lead to the same possibility of two routes to bursting, that is, the criticality of the Hopf bifurcation is not relevant for characterizing the route to bursting. The actual route depends on the relative location of the full-system's fixed point with respect to a homoclinic bifurcation of the fast subsystem. Our full-system bifurcation analysis reveals properties of endocrine bursting that are not captured by the standard fast-slow analysis. PMID:20307553
Research on bifurcation characters of rotor-SMA bearing system
International Nuclear Information System (INIS)
Based on Landau-Devonshire model, the bifurcation characteristic of rotor-shape memory alloy bearings(SMAB) system was investigated in this paper. Heteronomous system was transformed into autonomous system in averaging method and Van der Pol transformation, and the existence of Hopf bifurcation was proved in theory. The concept of broadened set of equilibrium point was introduced to improve centre manifold method to be adapted to heteronomous system. The equation of the flow on the centre manifold of rotor-SMAB system was obtained, and the existence of transcritical bifurcation and supercritical pitchfork bifurcation was proved in theory. Finally the results in centre manifold method and averaging method were compared with each other. The comparison shows that the results of the two methods were both the parts of global dynamic characteristic of rotor-SMAB system, while centre manifold method can be applied to research bifurcation behavior in the case of more dimensions. It means that the two methods both have limitation, and global dynamic characteristic must be obtained in kinds of method
Bifurcations analysis of turbulent energy cascade
Energy Technology Data Exchange (ETDEWEB)
Divitiis, Nicola de, E-mail: n.dedivitiis@gmail.com
2015-03-15
This note studies the mechanism of turbulent energy cascade through an opportune bifurcations analysis of the Navier–Stokes equations, and furnishes explanations on the more significant characteristics of the turbulence. A statistical bifurcations property of the Navier–Stokes equations in fully developed turbulence is proposed, and a spatial representation of the bifurcations is presented, which is based on a proper definition of the fixed points of the velocity field. The analysis first shows that the local deformation can be much more rapid than the fluid state variables, then explains the mechanism of energy cascade through the aforementioned property of the bifurcations, and gives reasonable argumentation of the fact that the bifurcations cascade can be expressed in terms of length scales. Furthermore, the study analyzes the characteristic length scales at the transition through global properties of the bifurcations, and estimates the order of magnitude of the critical Taylor-scale Reynolds number and the number of bifurcations at the onset of turbulence.
International Nuclear Information System (INIS)
Congenital absence of the unilateral internal carotid artery (ICA) was found in a patient during MR imaging examination for right trigeminal neuralgia. Magnetic resonance angiography showed complete absence of the right ICA and a large tortuous basilar artery (BA). The source images revealed a deformed right trigeminal nerve resulting from compression by the BA. Computed tomography of the skull base showed absence of the right carotid canal, suggesting agenesis of the right ICA. Longstanding hemodynamic stress may have caused the BA to become extremely tortuous, resulting in the trigeminal neuralgia. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Uchino, A.; Sawada, A.; Kudo, S. [Department of Radiology, Saga Medical School, 5-1-1, Nabeshima, Saga (Japan); Hirakawa, N.; Totoki, T. [Department of Anesthesiology, Saga Medical School, 5-1-1, Nabeshima, Saga (Japan)
2002-09-01
Congenital absence of the unilateral internal carotid artery (ICA) was found in a patient during MR imaging examination for right trigeminal neuralgia. Magnetic resonance angiography showed complete absence of the right ICA and a large tortuous basilar artery (BA). The source images revealed a deformed right trigeminal nerve resulting from compression by the BA. Computed tomography of the skull base showed absence of the right carotid canal, suggesting agenesis of the right ICA. Longstanding hemodynamic stress may have caused the BA to become extremely tortuous, resulting in the trigeminal neuralgia. (orig.)
Bifurcation and Secondary Bifurcation of Heavy Periodic Hydroelastic Travelling Waves
Baldi, Pietro; Toland, John F.
2008-01-01
The paper deals with a problem of interaction between hydrodynamics and mechanics of nonlinear elastic bodies. The existence question for two-dimensional symmetric steady waves travelling on the surface of a deep ocean beneath a heavy elastic membrane is analyzed as a problem in bifurcation theory. The behaviour of the two-dimensional cross-section of the membrane is modelled as a thin (unshearable), heavy, hyperelastic Cosserat rod, following Antman's elasticity theory, and the fluid beneath...
E. V. Nikolaeva; I. A. Kurmukov; N N Yudkina; A. V. Volkov
2015-01-01
Pulmonary arterial hypertension (PAH) associated with systemic connective tissue diseases (SCTD) is a poor prognostic manifestation of the latter that result in death if untreated. The invasive determination of hemodynamic parameters is prominent in diagnosing the disease and determining its treatment policy and prognosis.Objective: to analyze the results of catheterization in PAH-SCTD patients admitted to the V.A. Nasonova Research Institute of Rheumatology.Subjects and methods. The investig...
Bifurcations in the optimal elastic foundation for a buckling column
International Nuclear Information System (INIS)
We investigate the buckling under compression of a slender beam with a distributed lateral elastic support, for which there is an associated cost. For a given cost, we study the optimal choice of support to protect against Euler buckling. We show that with only weak lateral support, the optimum distribution is a delta-function at the centre of the beam. When more support is allowed, we find numerically that the optimal distribution undergoes a series of bifurcations. We obtain analytical expressions for the buckling load around the first bifurcation point and corresponding expansions for the optimal position of support. Our theoretical predictions, including the critical exponent of the bifurcation, are confirmed by computer simulations.
Bifurcations in the optimal elastic foundation for a buckling column
Rayneau-Kirkhope, Daniel; Farr, Robert; Ding, K.; Mao, Yong
2010-12-01
We investigate the buckling under compression of a slender beam with a distributed lateral elastic support, for which there is an associated cost. For a given cost, we study the optimal choice of support to protect against Euler buckling. We show that with only weak lateral support, the optimum distribution is a delta-function at the centre of the beam. When more support is allowed, we find numerically that the optimal distribution undergoes a series of bifurcations. We obtain analytical expressions for the buckling load around the first bifurcation point and corresponding expansions for the optimal position of support. Our theoretical predictions, including the critical exponent of the bifurcation, are confirmed by computer simulations.
Bifurcations in the optimal elastic foundation for a buckling column
Rayneau-Kirkhope, Daniel; Ding, K; Mao, Yong
2010-01-01
We investigate the buckling under compression of a slender beam with a distributed lateral elastic support, for which there is an associated cost. For a given cost, we study the optimal choice of support to protect against Euler buckling. We show that with only weak lateral support, the optimum distribution is a delta-function at the centre of the beam. When more support is allowed, we find numerically that the optimal distribution undergoes a series of bifurcations. We obtain analytical expressions for the buckling load around the first bifurcation point and corresponding expansions for the optimal position of support. Our theoretical predictions, including the critical exponent of the bifurcation, are confirmed by computer simulations.
Hopf bifurcation and chaos in macroeconomic models with policy lag
International Nuclear Information System (INIS)
In this paper, we consider the macroeconomic models with policy lag, and study how lags in policy response affect the macroeconomic stability. The local stability of the nonzero equilibrium of this equation is investigated by analyzing the corresponding transcendental characteristic equation of its linearized equation. Some general stability criteria involving the policy lag and the system parameter are derived. By choosing the policy lag as a bifurcation parameter, the model is found to undergo a sequence of Hopf bifurcation. The direction and stability of the bifurcating periodic solutions are determined by using the normal form theory and the center manifold theorem. Moreover, we show that the government can stabilize the intrinsically unstable economy if the policy lag is sufficiently short, but the system become locally unstable when the policy lag is too long. We also find the chaotic behavior in some range of the policy lag
Bifurcation Analysis for Surface Waves Generated by Wind
Schweizer, Ben
2001-01-01
We study the generation of surface waves on water as a bifurcation phenomenon. For a critical wind-speed there appear traveling wave solutions. While linear waves do not transport mass (in the mean), nonlinear effects create a shear-flow and result in a net mass transport in the direction of the wind. We derive an asymptotic formula for the average tangential velocity along the free surface. Numerical investigations confirm the appearance of the shear-flow and yield results on the bifurcation...
Song, Yongli; Zhang, Tonghua; Tadé, Moses O
2008-12-01
We investigate the dynamics of a damped harmonic oscillator with delayed feedback near zero eigenvalue singularity. We perform a linearized stability analysis and multiple bifurcations of the zero solution of the system near zero eigenvalue singularity. Taking the time delay as the bifurcation parameter, the presence of steady-state bifurcation, Bogdanov-Takens bifurcation, triple zero, and Hopf-zero singularities is demonstrated. In the case when the system has a simple zero eigenvalue, center manifold reduction and normal form theory are used to investigate the stability and the types of steady-state bifurcation. The stability of the zero solution of the system near the simple zero eigenvalue singularity is completely solved. PMID:19123623
Aberrant right hepatic artery; A case report
International Nuclear Information System (INIS)
We present a rare case of aberrant hepatic artery in a 40-year-old male with a history of chronic cholecystitis. During laparoscopic surgery, the artery found to pass anterior to the body the gallbladder and bifurcating anterior to the gallbladder body. The surgery was un eventful. We present this anomaly of the rare condition of aberrant right hepatic artery which should be in mind during laparoscopic cholecystectomy, because inadverant injury could lead to massive bleeding and increase co morbidities. (author)
International Nuclear Information System (INIS)
For the last two decades, pulse oximetry has been used as a standard procedure for monitoring arterial oxygen saturation (SpO2). However, SpO2 measurements made from extremities such as the finger, ear lobe and toes become susceptible to inaccuracies when peripheral perfusion is compromised. To overcome these limitations, the external auditory canal has been proposed as an alternative monitoring site for estimating SpO2, on the hypothesis that this central site will be better perfused. Therefore, a dual wavelength optoelectronic probe along with a processing system was developed to investigate the suitability of measuring photoplethysmographic (PPG) signals and SpO2 in the human auditory canal. A pilot study was carried out in 15 healthy volunteers to validate the feasibility of measuring PPGs and SpO2 from the ear canal (EC), and comparative studies were performed by acquiring the same signals from the left index finger (LIF) and the right index finger (RIF) in conditions of induced peripheral vasoconstriction (right hand immersion in ice water). Good quality baseline PPG signals with high signal-to-noise ratio were obtained from the EC, the LIF and the RIF sensors. During the ice water immersion, significant differences in the amplitude of the red and infrared PPG signals were observed from the RIF and the LIF sensors. The average drop in amplitude of red and infrared PPG signals from the RIF was 52.7% and 58.3%. Similarly, the LIF PPG signal amplitudes have reduced by 47.52% and 46.8% respectively. In contrast, no significant changes were seen in the red and infrared EC PPG amplitude measurements, which changed by +2.5% and −1.2% respectively. The RIF and LIF pulse oximeters have failed to estimate accurate SpO2 in seven and four volunteers respectively, while the EC pulse oximeter has only failed in one volunteer. These results suggest that the EC may be a suitable site for reliable monitoring of PPGs and SpO2s even in the presence of peripheral
Tibial hemimelia and femoral bifurcation.
Ugras, Ali Akin; Sungur, Ibrahim; Akyildiz, Mustafa Fehmi; Ercin, Ersin
2010-02-01
Femoral bifurcation and tibial agenesis are rare anomalies and have been described in both the Gollop-Wolfgang complex and tibial agenesis-ectrodactyly syndrome. This article presents a case of Gollop-Wolfgang complex without hand ectrodactyly. Tibial agenesis-ectrodactyly syndrome and Gollop-Wolfgang complex are variants of tibial field defect, which includes distal femoral duplication, tibial aplasia, oligo-ectrodactylous toe defects, and preaxial polydactyly, occasionally associated with hand ectrodactyly.This article describes the case of a patient with bilateral tibial hemimelia and left femoral bifurcation. The proximal tibial anlage had not been identified in the patient's left leg. After failed fibular transfer procedure, the knee was disarticulated. The other leg was treated with tibiofibular synostosis and centralization of fibula to os calcis. At 7-year follow-up, the patient ambulates with an above-knee prosthesis and uses an orthopedic boot for ankle stability.In patients with a congenital absence of the tibia, accurate diagnosis is of the utmost importance in planning future treatment. In the absence of proximal tibial anlage, especially in patients with femoral bifurcation, the knee should be disarticulated. Tibiofibular synostosis is a good choice in the presence of a proximal tibial anlage and good quadriceps function. PMID:20192156
Oscillatory flow in bifurcating tubes
International Nuclear Information System (INIS)
Respiratory fluid mechanics is characterized by flow through bifurcating, Y-shaped, tubes. Steady flow through such geometries has been studied in detail by several authors. However, the recent widespread use of high frequency mechanical assistance of ventilation has generated interest in unsteady flows. A symmetric, singly branching pipe has been constructed, with its bifurcation shaped to model pulmonary conditions. The form of the bifurcation is based on CAT scans of human tracheal carinas. Its features include an area change of the parent tube from circular to roughly elliptical near the junction, a pinch-off effect on the parent tube, smoothly curved outer walls at the junction, and a sharp flow divider. Parent and daughter tubes have an l/d ratio of > 50, so that entrance effects are avoided. In order to better understand the effects of unsteadiness, piston driven, laminar, purely oscillatory flow has been established in the pipe for a variety of Womersley numbers. By appropriate choices of flow frequency and amplitude, fluid viscosity, and pipe diameter, tracheal Reynolds and Womersley numbers have been matched for resting breathing (tidal volume of 600 ml to 0.25 Hz), high frequency breathing (50 ml at 5 Hz), and intermediate breathing levels
Experimental bifurcation analysis of an impact oscillator – Determining stability
DEFF Research Database (Denmark)
Bureau, Emil; Schilder, Frank; Elmegård, Michael; Santos, Ilmar; Thomsen, Jon Juel; Starke, Jens
2014-01-01
We propose and investigate three different methods for assessing stability of dynamical equilibrium states during experimental bifurcation analysis, using a control-based continuation method. The idea is to modify or turn off the control at an equilibrium state and study the resulting behavior. As...
Limit theorems for bifurcating integer-valued autoregressive processes
Blandin, Vassili
2012-01-01
We study the asymptotic behavior of the weighted least squares estimators of the unknown parameters of bifurcating integer-valued autoregressive processes. Under suitable assumptions on the immigration, we establish the almost sure convergence of our estimators, together with the quadratic strong law and central limit theorems. All our investigation relies on asymptotic results for vector-valued martingales.
Hahn, C; Mahajan, A; Chu, T; Schoen, M
2007-08-01
This paper presents a lumped-parameter model for the big-toe region that investigates the effect of plantar pressure on the diameter of the blood vessels, specifically the arteries, in the presence of arterial and/or tissue changes. The model developed in this paper uses a multi-domain energy system approach to develop the lumped-parameter differential equations. Blood flow is modelled as fluidic flow through compliant pipes that have inertia, stiffness, and damping. The tissue material is treated as a soft compliant material that transmits the external force to the blood vessels. Conclusions have been drawn to show the effect of plantar pressure, tissue damage, and their combination on the diameter of the blood vessels. The principles used here can be used to model the entire foot and the model used to investigate the effect of plantar pressure, tissue damage, and arterial changes on different parts of the foot. The work presented here may also have applications in other vascular diseases. PMID:17937206
Description of the celiac artery in domestic pigeons (Columba livia
Directory of Open Access Journals (Sweden)
Cibele Geeverghese
2012-06-01
Full Text Available This paper aimed to define the origin and distribution of the celiac artery and its collateral branches in 15 fowls from the Columba livia species, which were obtained from the Zoonosis Control Center of Brasilia, Brazil. In order to mark the arterial system of the specimens, the left brachiocephalic trunk was canullated and a colored water-latex solution was injected there. Afterwards, fowls were fixed in a 10% v/v formaldehyde solution and dissected with appropriate equipment, presenting the results described in this paper. The celiac artery originated from the ventral face of the descendent aorta. The first collateral branch arose from the celiac artery itself, forming the esophageal artery. Then, the celiac artery has bifurcated into two branches, named left and right branches of the celiac artery. The left branch emitted the proventricular ventral artery, followed by the splenic arteries, proventricular dorsal artery, and the left hepatic artery. The left branch has bifurcated into two branches, known as ventral and left gastric arteries. The right branch emitted the right hepatic artery, followed by the ileal artery and the right gastric artery. Finally, the right branch turned into the pancreaticoduodenal artery. Our findings showed a great similarity with the avian lineages of the Gallus gallus species, except for the lack of ileocecal artery, cystic branches, and dorsal gastric artery.
International Nuclear Information System (INIS)
This paper is concerned with a delayed cooperation diffusion system with Dirichlet boundary conditions. By applying the implicit function theorem, the normal form theory and the center manifold reduction, the asymptotic stability of positive equilibrium and Hopf bifurcation are investigated. It is shown that an increase in delay will destabilize the positive equilibrium and lead to the occurrence of a supercritical Hopf bifurcation when the delay crosses through a sequence of critical values. Based on the normal form theory and the center manifold reduction for partial functional differential equations (PFDEs), we find that the bifurcating periodic solution occurring from the first Hopf bifurcation point is stable on the center manifold and those occurring from the other bifurcation points are unstable. Finally, some numerical simulations are given to illustrate our results
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Li Wantong [School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000 (China)], E-mail: wtli@lzu.edu.cn; Yan Xiangping; Zhang Cunhua [School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000 (China); Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070 (China)
2008-10-15
This paper is concerned with a delayed cooperation diffusion system with Dirichlet boundary conditions. By applying the implicit function theorem, the normal form theory and the center manifold reduction, the asymptotic stability of positive equilibrium and Hopf bifurcation are investigated. It is shown that an increase in delay will destabilize the positive equilibrium and lead to the occurrence of a supercritical Hopf bifurcation when the delay crosses through a sequence of critical values. Based on the normal form theory and the center manifold reduction for partial functional differential equations (PFDEs), we find that the bifurcating periodic solution occurring from the first Hopf bifurcation point is stable on the center manifold and those occurring from the other bifurcation points are unstable. Finally, some numerical simulations are given to illustrate our results.
Bifurcation mechanisms of regular and chaotic network signaling in brain astrocytes
Matrosov, V. V.; Kazantsev, V. B.
2011-06-01
Bifurcation mechanisms underlying calcium oscillations in the network of astrocytes are investigated. Network model includes the dynamics of intracellular calcium concentration and intercellular diffusion of inositol 1,4,5-trisphosphate through gap junctions. Bifurcation analysis of underlying nonlinear dynamical system is presented. Parameter regions and principle bifurcation boundaries have been delineated and described. We show how variations of the diffusion rate can lead to generation of network calcium oscillations in originally nonoscillating cells. Different scenarios of regular activity and its transitions to chaotic dynamics have been obtained. Then, the bifurcations have been associated with statistical characteristics of calcium signals showing that different bifurcation scenarios yield qualitative changes in experimentally measurable quantities of the astrocyte activity, e.g., statistics of calcium spikes.
High resolution wavenumber analysis for investigation of arterial pulse wave propagation
Hasegawa, Hideyuki; Sato, Masakazu; Irie, Takasuke
2016-07-01
The propagation of the pulse wave along the artery is relatively fast (several m/s), and a high-temporal resolution is required to measure pulse wave velocity (PWV) in a regional segment of the artery. High-frame-rate ultrasound enables the measurement of the regional PWV. In analyses of wave propagation phenomena, the direction and propagation speed are generally identified in the frequency-wavenumber space using the two-dimensional Fourier transform. However, the wavelength of the pulse wave is very long (1 m at a propagation velocity of 10 m/s and a temporal frequency of 10 Hz) compared with a typical lateral field of view of 40 mm in ultrasound imaging. Therefore, PWV cannot be identified in the frequency-wavenumber space owing to the low resolution of the two-dimensional Fourier transform. In the present study, PWV was visualized in the wavenumber domain using phases of arterial wall acceleration waveforms measured by high-frame-rate ultrasound.
Scale dependence of branching in arterial and bronchial trees
Restrepo, J G; Hunt, B R; Restrepo, Juan G.; Ott, Edward; Hunt, Brian R.
2005-01-01
Although models of branching in arterial and bronchial trees often predict a dependence of bifurcation parameters on the scale of the bifurcating vessels, direct verifications of this dependence with data are uncommon. We compare measurements of bifurcation parameters in airways and arterial trees of different mammals as a function of scale to general features predicted by theoretical models. We find that the size dependence is more complex than existing theories based solely on energy minimization explain, and suggest additional factors that may govern the branching at different scales.
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Rebrov A.P.
2012-03-01
Full Text Available Aim: to evaluate arterial wall rigidity, clinical condition and prognosis in active and standard therapy of patients with chronic heart failure (CHF. Materials and methods. A total of 211 patients with CHF experienced Q-wave myocardial infarction was enrolled in the study. At admission to the hospital all patients were randomized into two groups. Patients of the first group (n=106 were managed actively after discharge from the hospital, patients of the second group (n=105 were managed conventionally after discharge from the hospital. Patients were observed for three years. Re-sults. Over three year-investigation actively managed patients demonstrated significant (p<0,05 decrease in systolic and diastolic blood pressure, heart rate, blood serum levels of total cholesterol, N-terminal cerebral natriuretic peptide, increase of 6-minute walk-test, left ventricle ejection fraction reduction and decrease in number hospitalization of patients with CHF as compared to those who were conventionally managed. At patients of II group pulse wave speed in aorta (PWVA since the first year, an index of augmentation of brachial artery and systolic pressure in aorta in three years of supervision above (p<0,05 in comparison with patients of group I. Conclusion. One of deterioration factors of systolic functions of the left ventricle and the prognosis in patients with CHF of group of standard therapy was progressing of arterial wall rigidity pathology
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In this investigation, surgical operations of blocked intestinal artery have been conducted on pigs to simulate the condition of acute mesenteric arterial occlusion. The empirical mode decomposition method and the algorithm of linguistic analysis were applied to verify the blood pressure signals in simulated situation. We assumed that there was some information hidden in the high-frequency part of the blood pressure signal when an intestinal artery is blocked. The empirical mode decomposition method (EMD) has been applied to decompose the intrinsic mode functions (IMF) from a complex time series. But, the end effects and phenomenon of intermittence damage the consistence of each IMF. Thus, we proposed the complementary ensemble empirical mode decomposition method (CEEMD) to solve the problems of end effects and the phenomenon of intermittence. The main wave of blood pressure signals can be reconstructed by the main components, identified by Monte Carlo verification, and removed from the original signal to derive a riding wave. Furthermore, the concept of linguistic analysis was applied to design the blocking index to verify the pattern of riding wave of blood pressure using the measurements of dissimilarity. Blocking index works well to identify the situation in which the sampled time series of blood pressure signal was recorded. Here, these two totally different algorithms are successfully integrated and the existence of the existence of information hidden in high-frequency part of blood pressure signal has been proven
Einstein's Field Equations as a Fold Bifurcation
Kohli, Ikjyot Singh
2016-01-01
It is shown that Einstein's field equations for \\emph{all} perfect-fluid $k=0$ FLRW cosmologies have the same form as the topological normal form of a fold bifurcation. In particular, we assume that the cosmological constant is a bifurcation parameter, and as such, fold bifurcation behaviour is shown to occur in a neighbourhood of Minkowski spacetime in the phase space. We show that as this cosmological constant parameter is varied, an expanding and contracting de Sitter universe \\emph{emerge} via this bifurcation.
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A delay-differential modelling with stage-structure for prey is investigated. Its dynamics are studied in terms of local analysis and Hopf bifurcation theory, and its linear stability and Hopf bifurcation are demonstrated by studying the characteristic equation. The stability and direction of Hopf bifurcation are determined by applying the normal form theory and the center manifold argument, and numerical simulations are given to illustrate the analytical result
Stability and Bifurcation in a Delayed Reaction-Diffusion Equation with Dirichlet Boundary Condition
Guo, Shangjiang; Ma, Li
2016-04-01
In this paper, we study the dynamics of a diffusive equation with time delay subject to Dirichlet boundary condition in a bounded domain. The existence of spatially nonhomogeneous steady-state solution is investigated by applying Lyapunov-Schmidt reduction. The existence of Hopf bifurcation at the spatially nonhomogeneous steady-state solution is derived by analyzing the distribution of the eigenvalues. The direction of Hopf bifurcation and stability of the bifurcating periodic solution are also investigated by means of normal form theory and center manifold reduction. Moreover, we illustrate our general results by applications to the Nicholson's blowflies models with one- dimensional spatial domain.
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Paun Marla
2007-03-01
Full Text Available Abstract Background In order to establish a consistent method for brachial artery reactivity assessment, we analyzed commonly used approaches to the test and their effects on the magnitude and time-course of flow mediated dilation (FMD, and on test variability and repeatability. As a popular and noninvasive assessment of endothelial function, several different approaches have been employed to measure brachial artery reactivity with B-mode ultrasound. Despite some efforts, there remains a lack of defined normal values and large variability in measurement technique. Methods Twenty-six healthy volunteers underwent repeated brachial artery diameter measurements by B-mode ultrasound. Following baseline diameter recordings we assessed endothelium-dependent flow mediated dilation by inflating a blood pressure cuff either on the upper arm (proximal or on the forearm (distal. Results Thirty-seven measures were performed using proximal occlusion and 25 with distal occlusion. Following proximal occlusion relative to distal occlusion, FMD was larger (16.2 ± 1.2% vs. 7.3 ± 0.9%, p p = 0.0001. Measurement of the test repeatability showed that differences between the repeated measures were greater on average when the measurements were done using the proximal method as compared to the distal method (2.4%; 95% CI 0.5–4.3; p = 0.013. Conclusion These findings suggest that forearm compression holds statistical advantages over upper arm compression. Added to documented physiological and practical reasons, we propose that future studies should use forearm compression in the assessment of endothelial function.
Bifurcation analysis of a semiconductor laser subject to phase conjugate feedback
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In this thesis we present a detailed bifurcation analysis of a semiconductor laser subject to phase-conjugate feedback (PCF). Mathematically, lasers with feedback are modelled by delay differential equations (DDEs) with an infinite-dimensional phase space. This is why, in the past, systems described by DDEs were only studied by numerical simulation. We employ new numerical bifurcation tools for DDEs that go much beyond mere simulation. More precisely, we continue steady states and periodic orbits, irrespective of their stability with the package DDE-BIFTOOL, and present here the first algorithm for computing unstable manifolds of saddle-periodic orbits with one unstable Floquet multiplier in systems of DDEs. Together, these tools make it possible, for the first time, to numerically study global bifurcations in DDEs. Specifically, we first show how periodic solutions of the PCF laser are all connected to one another via a locked steady state solution. A one-parameter study of these steady states reveals heteroclinic bifurcations, which turn out to be responsible for bistability and excitability at the locking boundaries. We then perform a full two-parameter investigation of the locking range, where we continue bifurcations of steady states and heteroclinic bifurcations. This leads to the identification of a number of codimension- two bifurcation points. Here, we also make a first attempt at providing a two-parameter study of bifurcations of periodic orbits in a system of DDEs. Finally, our new method for the computation of unstable manifolds of saddle periodic orbits is used to show how a torus breaks up with a sudden transition to chaos in a crisis bifurcation. In more general terms, we believe that the results presented in this thesis showcase the usefulness of continuation and manifold computations and will contribute to the theory of global bifurcations in DDEs. (author)
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The complex interplay of neural, metabolic, myogenic and mechanical mechanisms that regulate blood flow in skeletal muscle (MBF) is still incompletely understood. For the first time, a method is presented for high time-resolution recording of MBF from a purely muscular artery in physiological conditions. Ultrasound perivascular flow probes were implanted (n = 15) mono- or bilaterally around the masseteric branch of the facial artery in nine rabbits and tested up to 16 days after implant. Reliable and stable recordings were achieved in 50% of implants. Blood flow was observed to increase from a resting level of 0.2–0.3 ml min−1 up to 4.0–6.0 ml min−1 during spontaneous masticatory activity. In addition, within single masticatory cycles marked back flow transients could be observed (peak flow = −10 ml min−1) during powerful masticatory strokes but not during mild mastication. The possibility of (1) surgically removing the sympathetic supply to the relevant vascular bed and of (2) bilaterally monitoring the perfusion of masseter muscles thus allowing to use one side as control side for different types of interventions makes this model a useful tool for disentangling the different mechanisms involved in the control of MBF. (note)
Coronary bifurcation lesions treated with simple or complex stenting
DEFF Research Database (Denmark)
Behan, Miles W; Holm, Niels R; de Belder, Adam J;
2016-01-01
from two large bifurcation coronary stenting trials with similar methodology: the Nordic Bifurcation Study (NORDIC I) and the British Bifurcation Coronary Study: old, new, and evolving strategies (BBC ONE). METHODS AND RESULTS: Both multicentre randomized trials compared simple (provisional T...
Bifurcation Tools for Flight Dynamics Analysis and Control System Design Project
National Aeronautics and Space Administration — Modern bifurcation analysis methods have been proposed for investigating flight dynamics and control system design in highly nonlinear regimes and also for the...
Stability switches and Hopf bifurcations in a pair of identical tri-neuron network loops
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The dynamical behavior of a delayed neural network coupled by a pair of identical tri-neuron loops is considered. Conditional/absolute stability, stability switches and Hopf bifurcations induced by time delay are investigated.
Energy Technology Data Exchange (ETDEWEB)
Nagata, Shun-ichi; Kazekawa, Kiyoshi; Matsubara, Shuko [Fukuoka University Chikushi Hospital, Department of Neurosurgery, Chikushino, Fukuoka (Japan); Sugata, Sei [Bironoki Neurosurgical Hospital, Shibushi, Kagoshima (Japan)
2006-08-15
Obstructions of the supraaortic vessels are an important cause of morbidity associated with a variety of symptoms. Percutaneous transluminal angioplasty has evolved as an effective and safe treatment modality for occlusive lesions of the supraaortic vessels. However, the endovascular management of an innominate bifurcation has not previously been reported. A 53-year-old female with a history of systematic hypertension, diabetes mellitus and hypercholesterolemia presented with left hemiparesis and dysarthria. Angiography of the innominate artery showed a stenosis of the innominate bifurcation. The lesion was successfully treated using the retrograde kissing stent technique via a brachial approach and an exposed direct carotid approach. The retrograde kissing stent technique for the treatment of a stenosis of the innominate bifurcation was found to be a safe and effective alternative to conventional surgery. (orig.)
International Nuclear Information System (INIS)
Obstructions of the supraaortic vessels are an important cause of morbidity associated with a variety of symptoms. Percutaneous transluminal angioplasty has evolved as an effective and safe treatment modality for occlusive lesions of the supraaortic vessels. However, the endovascular management of an innominate bifurcation has not previously been reported. A 53-year-old female with a history of systematic hypertension, diabetes mellitus and hypercholesterolemia presented with left hemiparesis and dysarthria. Angiography of the innominate artery showed a stenosis of the innominate bifurcation. The lesion was successfully treated using the retrograde kissing stent technique via a brachial approach and an exposed direct carotid approach. The retrograde kissing stent technique for the treatment of a stenosis of the innominate bifurcation was found to be a safe and effective alternative to conventional surgery. (orig.)
Bifurcation Analysis and Chaos Control in a Discrete Epidemic System
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Wei Tan
2015-01-01
Full Text Available The dynamics of discrete SI epidemic model, which has been obtained by the forward Euler scheme, is investigated in detail. By using the center manifold theorem and bifurcation theorem in the interior R+2, the specific conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation have been derived. Numerical simulation not only presents our theoretical analysis but also exhibits rich and complex dynamical behavior existing in the case of the windows of period-1, period-3, period-5, period-6, period-7, period-9, period-11, period-15, period-19, period-23, period-34, period-42, and period-53 orbits. Meanwhile, there appears the cascade of period-doubling 2, 4, 8 bifurcation and chaos sets from the fixed point. These results show the discrete model has more richer dynamics compared with the continuous model. The computations of the largest Lyapunov exponents more than 0 confirm the chaotic behaviors of the system x→x+δ[rN(1-N/K-βxy/N-(μ+mx], y→y+δ[βxy/N-(μ+dy]. Specifically, the chaotic orbits at an unstable fixed point are stabilized by using the feedback control method.
Bifurcation of the spin-wave equations
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We study the bifurcations of the spin-wave equations that describe the parametric pumping of collective modes in magnetic media. Mechanisms describing the following dynamical phenomena are proposed: (i) sequential excitation of modes via zero eigenvalue bifurcations; (ii) Hopf bifurcations followed (or not) by Feingenbaum cascades of period doubling; (iii) local and global homoclinic phenomena. Two new organizing center for routes to chaos are identified; in the classification given by Guckenheimer and Holmes [GH], one is a codimension-two local bifurcation, with one pair of imaginary eigenvalues and a zero eigenvalue, to which many dynamical consequences are known; secondly, global homoclinic bifurcations associated to splitting of separatrices, in the limit where the system can be considered a Hamiltonian subjected to weak dissipation and forcing. We outline what further numerical and algebraic work is necessary for the detailed study following this program. (author)
Voltage stability, bifurcation parameters and continuation methods
Energy Technology Data Exchange (ETDEWEB)
Alvarado, F.L. [Wisconsin Univ., Madison, WI (United States)
1994-12-31
This paper considers the importance of the choice of bifurcation parameter in the determination of the voltage stability limit and the maximum power load ability of a system. When the bifurcation parameter is power demand, the two limits are equivalent. However, when other types of load models and bifurcation parameters are considered, the two concepts differ. The continuation method is considered as a method for determination of voltage stability margins. Three variants of the continuation method are described: the continuation parameter is the bifurcation parameter the continuation parameter is initially the bifurcation parameter, but is free to change, and the continuation parameter is a new `arc length` parameter. Implementations of voltage stability software using continuation methods are described. (author) 23 refs., 9 figs.
CENTER CONDITIONS AND BIFURCATION OF LIMIT CYCLES FOR A CLASS OF FIFTH DEGREE SYSTEMS
Institute of Scientific and Technical Information of China (English)
HuangWentao; LiuYirong
2004-01-01
The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated. Two recursive formulas to compute singular quantities at infinity and at the origin are given. The first nine singular point quantities at infinity and first seven singular point quantities at the origin for the system are given in order to get center conditions and study bifurcation of limit cycles. Two fifth degree systems are constructed. One allows the appearance of eight limit cycles in the neighborhood of infinity,which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity. The other perturbs six limit cycles at the origin.
Dynamics near manifolds of equilibria of codimension one and bifurcation without parameters
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Stefan Liebscher
2011-05-01
Full Text Available We investigate the breakdown of normal hyperbolicity of a manifold of equilibria of a flow. In contrast to classical bifurcation theory we assume the absence of any flow-invariant foliation at the singularity transverse to the manifold of equilibria. We call this setting bifurcation without parameters. We provide a description of general systems with a manifold of equilibria of codimension one as a first step towards a classification of bifurcations without parameters. This is done by relating the problem to singularity theory of maps.
Bifurcations, chaos, and sensitivity to parameter variations in the Sato cardiac cell model
Otte, Stefan; Berg, Sebastian; Luther, Stefan; Parlitz, Ulrich
2016-08-01
The dynamics of a detailed ionic cardiac cell model proposed by Sato et al. (2009) is investigated in terms of periodic and chaotic action potentials, bifurcation scenarios, and coexistence of attractors. Starting from the model's standard parameter values bifurcation diagrams are computed to evaluate the model's robustness with respect to (small) parameter changes. While for some parameters the dynamics turns out to be practically independent from their values, even minor changes of other parameters have a very strong impact and cause qualitative changes due to bifurcations or transitions to coexisting attractors. Implications of this lack of robustness are discussed.
Bifurcation in a thin liquid film flowing over a locally heated surface
Katkar, Harshwardhan H
2014-01-01
We investigate the non-linear dynamics of a two-dimensional film flowing down a finite heater, for a non-volatile and a volatile liquid. An oscillatory instability is predicted beyond a critical value of Marangoni number using linear stability theory. Continuation along the Marangoni number using non-linear evolution equation is used to trace bifurcation diagram associated with the oscillatory instability. Hysteresis, a characteristic attribute of a sub-critical Hopf bifurcation, is observed in a critical parametric region. The bifurcation is universally observed for both, a non-volatile film and a volatile film.
Bifurcation and solitary waves of the nonlinear wave equation with quartic polynomial potential
Institute of Scientific and Technical Information of China (English)
化存才; 刘延柱
2002-01-01
For the nonlinear wave equation with quartic polynomial potential, bifurcation and solitary waves are investigated. Based on the bifurcation and the energy integral of the two-dimensional dynamical system satisfied by the travelling waves, it is very interesting to find different sufficient and necessary conditions in terms of the bifurcation parameter for the existence and coexistence of bright, dark solitary waves and shock waves. The method of direct integration is developed to give all types of solitary wave solutions. Our method is simpler than other newly developed ones. Some results are similar to those obtained recently for the combined KdV-mKdV equation.
Stability and bifurcation analysis for a delayed Lotka-Volterra predator-prey system
Yan, Xiang-Ping; Chu, Yan-Dong
2006-11-01
The present paper deals with a delayed Lotka-Volterra predator-prey system. By linearizing the equations and by analyzing the locations on the complex plane of the roots of the characteristic equation, we find the necessary conditions that the parameters should verify in order to have the oscillations in the system. In addition, the normal form of the Hopf bifurcation arising in the system is determined to investigate the direction and the stability of periodic solutions bifurcating from these Hopf bifurcations. To verify the obtained conditions, a special numerical example is also included.
Stability and bifurcation analysis on a three-species food chain system with two delays
Cui, Guo-Hu; Yan, Xiang-Ping
2011-09-01
The present paper deals with a three-species Lotka-Volterra food chain system with two discrete delays. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium and existence of local Hopf bifurcations are investigated. Furthermore, by using the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions. Finally, to verify our theoretical predictions, some numerical simulations are also included at the end of this paper.
Bifurcation analysis of the logistic map via two periodic impulsive forces
International Nuclear Information System (INIS)
The complex dynamics of the logistic map via two periodic impulsive forces is investigated in this paper. The influences of the system parameter and the impulsive forces on the dynamics of the system are studied respectively. With the parameter varying, the system produces the phenomenon such as periodic solutions, chaotic solutions, and chaotic crisis. Furthermore, the system can evolve to chaos by a cascading of period-doubling bifurcations. The Poincaré map of the logistic map via two periodic impulsive forces is constructed and its bifurcation is analyzed. Finally, the Floquet theory is extended to explore the bifurcation mechanism for the periodic solutions of this non-smooth map. (general)
Bifurcation analysis of periodic orbits of a non-smooth Jeffcott rotor model
Páez Chávez, Joseph; Wiercigroch, Marian
2013-09-01
We investigate complex dynamics occurring in a non-smooth model of a Jeffcott rotor with a bearing clearance. A bifurcation analysis of the rotor system is carried out by means of the software TC-HAT [25], a toolbox of AUTO 97 [6] allowing path-following and detection of bifurcations of periodic trajectories of non-smooth dynamical systems. The study reveals a rich variety of dynamics, which includes grazing-induced fold and period-doubling bifurcations, as well as hysteresis loops produced by a cusp singularity. Furthermore, an analytical expression predicting grazing incidences is derived.
Bifurcation Analysis and Chaos Control in a Modified Finance System with Delayed Feedback
Yang, Jihua; Zhang, Erli; Liu, Mei
2016-06-01
We investigate the effect of delayed feedback on the finance system, which describes the time variation of the interest rate, for establishing the fiscal policy. By local stability analysis, we theoretically prove the existences of Hopf bifurcation and Hopf-zero bifurcation. By using the normal form method and center manifold theory, we determine the stability and direction of a bifurcating periodic solution. Finally, we give some numerical solutions, which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable equilibrium or periodic orbit.
STABILITY AND LOCAL BIFURCATION IN A SIMPLY-SUPPORTED BEAM CARRYING A MOVING MASS
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The stability and local bifurcation of a simply-supported flexible beam (Bernoulli-Euler type) carrying a moving mass and subjected to harmonic axial excitation are investigated.In the theoretical analysis, the partial differential equation of motion with the fifth-order nonlinear term is solved using the method of multiple scales (a perturbation technique). The stability and local bifurcation of the beam are analyzed for 1/2 sub harmonic resonance. The results show that some of the parameters, especially the velocity of moving mass and external excitation, affect the local bifurcation significantly. Therefore, these parameters play important roles in the system stability.
Analysis of the flow at a T-bifurcation for a ternary unit
Campero, P.; Beck, J.; Jung, A.
2014-03-01
The motivation of this research is to understand the flow behavior through a 90° T- type bifurcation, which connects a Francis turbine and the storage pump of a ternary unit, under different operating conditions (namely turbine, pump and hydraulic short-circuit operation). As a first step a CFD optimization process to define the hydraulic geometry of the bifurcation was performed. The CFD results show the complexity of the flow through the bifurcation, especially under hydraulic short-circuit operation. Therefore, it was decided to perform experimental investigations in addition to the CFD analysis, in order to get a better understanding of the flow. The aim of these studies was to investigate the flow development upstream and downstream the bifurcation, the estimation of the bifurcation loss coefficients and also to provide comprehensive data of the flow behavior for the whole operating range of the machine. In order to evaluate the development of the velocity field Stereo Particle Image Velocimetry (S-PIV) measurements at different sections upstream and downstream of the bifurcation on the main penstock and Laser Doppler Anemometrie (LDA) measurements at bifurcation inlet were performed. This paper presents the CFD results obtained for the final design for different operating conditions, the model test procedures and the model test results with special attention to: 1) The bifurcation head loss coefficients, and their extrapolation to prototype conditions, 2) S-PIV and LDA measurements. Additionally, criteria to define the minimal uniformity conditions for the velocity profiles entering the turbine are evaluated. Finally, based on the gathered flow information a better understanding to define the preferred location of a bifurcation is gained and can be applied to future projects.
Numerical bifurcation analysis of conformal formulations of the Einstein constraints
International Nuclear Information System (INIS)
The Einstein constraint equations have been the subject of study for more than 50 years. The introduction of the conformal method in the 1970s as a parametrization of initial data for the Einstein equations led to increased interest in the development of a complete solution theory for the constraints, with the theory for constant mean curvature (CMC) spatial slices and closed manifolds completely developed by 1995. The first general non-CMC existence result was establish by Holst et al. in 2008, with extensions to rough data by Holst et al. in 2009, and to vacuum spacetimes by Maxwell in 2009. The non-CMC theory remains mostly open; moreover, recent work of Maxwell on specific symmetry models sheds light on fundamental nonuniqueness problems with the conformal method as a parametrization in non-CMC settings. In parallel with these mathematical developments, computational physicists have uncovered surprising behavior in numerical solutions to the extended conformal thin sandwich formulation of the Einstein constraints. In particular, numerical evidence suggests the existence of multiple solutions with a quadratic fold, and a recent analysis of a simplified model supports this conclusion. In this article, we examine this apparent bifurcation phenomena in a methodical way, using modern techniques in bifurcation theory and in numerical homotopy methods. We first review the evidence for the presence of bifurcation in the Hamiltonian constraint in the time-symmetric case. We give a brief introduction to the mathematical framework for analyzing bifurcation phenomena, and then develop the main ideas behind the construction of numerical homotopy, or path-following, methods in the analysis of bifurcation phenomena. We then apply the continuation software package AUTO to this problem, and verify the presence of the fold with homotopy-based numerical methods. We discuss these results and their physical significance, which lead to some interesting remaining questions to
Assessment of carotid arteri calcification using 3D-CT angiography
International Nuclear Information System (INIS)
The aim of this study was to evaluate carotid arteri calcifications using 3D-CT angiography. We performed a retrospective review of 181 patients referred for 64-slice multi-detector row computed tomography. Using curved multiplanar reformation (curved MPR) images of ZIOSOFT M900 QUADRA, we evaluated the distribution of calcifications around the carotid bifurcation. Among the 181 patients, 66 patients (36%) had arterial calcifications. The present study found that almost arterial calcifications localized at the carotid bifurcation. Furthermore, in the group with carotid arterial stenosis, we found arterial calcifications localized not only at the carotid bifurcation, but also at the distal side of internal carotid artery. Curved MPR imaging using 3D-CT angiography is a helpful tool for evaluating calcification of carotid arteries. (author)
On the effect of AVR gain on bifurcations of subsynchronous resonance in power systems
Energy Technology Data Exchange (ETDEWEB)
Widyan, Mohammad S. [Electrical Engineering Department, The Hashemite University, 13115 Zarqa (Jordan)
2010-07-15
This paper presents the effect of the automatic voltage regulator (AVR) gain on the bifurcations of subsynchronous resonance (SSR) in power systems. The first system of the IEEE second benchmark model of SSR is chosen for numerical investigations. The dynamics of both axes damper windings of the generator and that of the power system stabilizer (PSS) are included. The bifurcation parameter is the compensation factor. Hopf bifurcation, where a pair of complex conjugate eigenvalues of the linearized model around the operating point transversally crosses from left- to right-half of the complex plane, is detected in all AVR gains. It is shown that the Hopf bifurcation is of subcritical type. The results also show that the location of the Hopf bifurcation point i.e. the stable operating point regions are affected by the value of the AVR gain. The variation of the location of the Hopf bifurcation point as function of the AVR gain for two operating conditions is obtained. Time domain simulation results based on the nonlinear dynamical mathematical model carried out at different compensation factors and AVR gains agree with that of the bifurcation analysis. (author)
Bifurcation Structures in a Family of 1D Discontinuous Linear-Hyperbolic Invertible Maps
Makrooni, Roya; Gardini, Laura; Sushko, Iryna
2015-12-01
We consider a family of one-dimensional discontinuous invertible maps from an application in engineering. It is defined by a linear function and by a hyperbolic function with real exponent. The presence of vertical and horizontal asymptotes of the hyperbolic branch leads to particular codimension-two border collision bifurcation (BCB) such that if the parameter point approaches the bifurcation value from one side then the related cycle undergoes a regular BCB, while if the same bifurcation value is approached from the other side then a nonregular BCB occurs, involving periodic points at infinity, related to the asymptotes of the map. We investigate the bifurcation structure in the parameter space. Depending on the exponent of the hyperbolic branch, different period incrementing structures can be observed, where the boundaries of a periodicity region are related either to subcritical, or supercritical, or degenerate flip bifurcations of the related cycle, as well as to a regular or nonregular BCB. In particular, if the exponent is positive and smaller than one, then the period incrementing structure with bistability regions is observed and the corresponding flip bifurcations are subcritical, while if the exponent is larger than one, then the related flip bifurcations are supercritical and, thus, also the regions associated with cycles of double period are involved into the incrementing structure.
Stability and Hopf bifurcation on a model for HIV infection of CD4+ T cells with delay
International Nuclear Information System (INIS)
In this paper, a delayed differential equation model that describes HIV infection of CD4+ T cells is considered. The stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. In succession, using the normal form theory and center manifold argument, we derive the explicit formulas which determine the stability, direction and other properties of bifurcating periodic solutions.
Judd, S L; Judd, Stephen L.; Silber, Mary
1998-01-01
This paper investigates the competition between both simple (e.g. stripes, hexagons) and ``superlattice'' (super squares, super hexagons) Turing patterns in two-component reaction-diffusion systems. ``Superlattice'' patterns are formed from eight or twelve Fourier modes, and feature structure at two different length scales. Using perturbation theory, we derive simple analytical expressions for the bifurcation equation coefficients on both rhombic and hexagonal lattices. These expressions show that, no matter how complicated the reaction kinectics, the nonlinear reaction terms reduce to just four effective terms within the bifurcation equation coefficients. Moreover, at the hexagonal degeneracy -- when the quadratic term in the hexagonal bifurcation equation disappears -- the number of effective system parameters drops to two, allowing a complete characterization of the possible bifurcation results at this degeneracy. The general results are then applied to specific model equations, to investigate the stabilit...
Nonlinear stability control and λ-bifurcation
International Nuclear Information System (INIS)
Passive techniques for nonlinear stability control are presented for a model of fluidelastic instability. They employ the phenomena of λ-bifurcation and a generalization of it. λ-bifurcation occurs when a branch of flutter solutions bifurcates supercritically from a basic solution and terminates with an infinite period orbit at a branch of divergence solutions which bifurcates subcritically from the basic solution. The shape of the bifurcation diagram then resembles the greek letter λ. When the system parameters are in the range where flutter occurs by λ-bifurcation, then as the flow velocity increase the flutter amplitude also increases, but the frequencies of the oscillations decrease to zero. This diminishes the damaging effects of structural fatigue by flutter, and permits the flow speed to exceed the critical flutter speed. If generalized λ-bifurcation occurs, then there is a jump transition from the flutter states to a divergence state with a substantially smaller amplitude, when the flow speed is sufficiently larger than the critical flutter speed
Santos, AMF; dos santos, rm; castro, pmac; Azevedo, E.; Sousa, L. de; tavares, jmrs
2013-01-01
A novel algorithm is proposed for the segmentation of the lumen and bifurcation boundaries of the carotid artery in B-mode ultrasound images. It uses the image contrast characteristics of the lumen and bifurcation of the carotid artery in relation to other tissues and structures for their identification. The relevant ultrasound data regarding the artery presented in the input image is identified using morphologic operators and processed by an anisotropic diffusion filter for speckle noise rem...
Stability and Hopf bifurcation in a delayed competitive web sites model
Energy Technology Data Exchange (ETDEWEB)
Xiao Min [Department of Mathematics, Southeast University, Nanjing 210096 (China): Department of Mathematics, Nanjing Xiaozhuang College, Nanjing 210017 (China); Cao Jinde [Department of Mathematics, Southeast University, Nanjing 210096 (China)]. E-mail: jdcao@seu.edu.cn
2006-04-24
The delayed differential equations modeling competitive web sites, based on the Lotka-Volterra competition equations, are considered. Firstly, the linear stability is investigated. It is found that there is a stability switch for time delay, and Hopf bifurcation occurs when time delay crosses through a critical value. Then the direction and stability of the bifurcated periodic solutions are determined, using the normal form theory and the center manifold reduction. Finally, some numerical simulations are carried out to illustrate the results found.
Stability and Hopf bifurcation in a delayed competitive web sites model
Xiao, Min; Cao, Jinde
2006-04-01
The delayed differential equations modeling competitive web sites, based on the Lotka Volterra competition equations, are considered. Firstly, the linear stability is investigated. It is found that there is a stability switch for time delay, and Hopf bifurcation occurs when time delay crosses through a critical value. Then the direction and stability of the bifurcated periodic solutions are determined, using the normal form theory and the center manifold reduction. Finally, some numerical simulations are carried out to illustrate the results found.
Bifurcation analysis and the travelling wave solutions of the Klein–Gordon–Zakharov equations
Indian Academy of Sciences (India)
Zaiyun Zhang; Fnag-Li Xia; Xin-Ping Li
2013-01-01
In this paper, we investigate the bifurcations and dynamic behaviour of travelling wave solutions of the Klein–Gordon–Zakharov equations given in Shang et al, Comput. Math. Appl. 56, 1441 (2008). Under different parameter conditions, we obtain some exact explicit parametric representations of travelling wave solutions by using the bifurcation method (Feng et al, Appl. Math. Comput. 189, 271 (2007); Li et al, Appl. Math. Comput. 175, 61 (2006)).
Hopf Bifurcation of an SIQR Computer Virus Model with Time Delay
2015-01-01
A delayed SIQR computer virus model is considered. It has been observed that there exists a critical value of delay for the stability of virus prevalence by choosing the delay as a bifurcation parameter. Furthermore, the properties of the Hopf bifurcation such as direction and stability are investigated by using the normal form method and center manifold theory. Finally, some numerical simulations for supporting our theoretical results are also performed.
Jianguo Ren; Yonghong Xu
2014-01-01
A new computer virus propagation model with delay and incomplete antivirus ability is formulated and its global dynamics is analyzed. The existence and stability of the equilibria are investigated by resorting to the threshold value R0. By analysis, it is found that the model may undergo a Hopf bifurcation induced by the delay. Correspondingly, the critical value of the Hopf bifurcation is obtained. Using Lyapunov functional approach, it is proved that, under suitable conditions, the unique v...
Bifurcations and sudden current change in ensembles of classically chaotic ratchets
Kenfack, A.; Sweetnam, S.; Pattanayak, A.K.
2007-01-01
In \\prl 84, 258 (2000), Mateos conjectured that current reversal in a classical deterministic ratchet is associated with bifurcations from chaotic to periodic regimes. This is based on the comparison of the current and the bifurcation diagram as a function of a given parameter for a periodic asymmetric potential. Barbi and Salerno, in \\pre 62, 1988 (2000), have further investigated this claim and argue that, contrary to Mateos' claim, current reversals can occur also in the absence of bifurca...
Abed-Meraim, F Farid; Peerlings, RHJ Ron; Geers, MGD Marc
2014-01-01
The present contribution deals with the prediction of diffuse necking in the context of forming and stretching of metal sheets. For this purpose, two approaches are investigated, namely bifurcation and the maximum force principle, with a systematic comparison of their respective ability to predict necking. While the bifurcation approach is of quite general applicability, some restrictions are shown for the application of maximum force conditions. Although the predictions of the two approaches...
Bifurcations of non-smooth systems
Angulo, Fabiola; Olivar, Gerard; Osorio, Gustavo A.; Escobar, Carlos M.; Ferreira, Jocirei D.; Redondo, Johan M.
2012-12-01
Non-smooth systems (namely piecewise-smooth systems) have received much attention in the last decade. Many contributions in this area show that theory and applications (to electronic circuits, mechanical systems, …) are relevant to problems in science and engineering. Specially, new bifurcations have been reported in the literature, and this was the topic of this minisymposium. Thus both bifurcation theory and its applications were included. Several contributions from different fields show that non-smooth bifurcations are a hot topic in research. Thus in this paper the reader can find contributions from electronics, energy markets and population dynamics. Also, a carefully-written specific algebraic software tool is presented.
Backward Bifurcation in Simple SIS Model
Institute of Scientific and Technical Information of China (English)
Zhan-wei Wang
2009-01-01
We describe and analyze a simple SIS model with treatment.In particular,we give a completely qualitative analysis by means of the theory of asymptotically autonomous system.It is found that a backward bifurcation occurs if the adequate contact rate or the capacity is small.It is also found that there exists bistable endemic equilibria.In the case of disease-induced death,it is shown that the backward bifurcation also occurs.Moreover,there is no limit cycle under some conditions,and the subcritical Hopf bifurcation occurs under another conditions.
Bifurcations of Periodic Orbits and Uniform Approximations
Schomerus, H; Schomerus, Henning; Sieber, Martin
1997-01-01
We derive uniform approximations for contributions to Gutzwiller's periodic-orbit sum for the spectral density which are valid close to bifurcations of periodic orbits in systems with mixed phase space. There, orbits lie close together and give collective contributions, while the individual contributions of Gutzwiller's type would diverge at the bifurcation. New results for the tangent, the period doubling and the period tripling bifurcation are given. They are obtained by going beyond the local approximation and including higher order terms in the normal form of the action. The uniform approximations obtained are tested on the kicked top and are found to be in excellent agreement with exact quantum results.
Cellular Cell Bifurcation of Cylindrical Detonations
Institute of Scientific and Technical Information of China (English)
HAN Gui-Lai; JIANG Zong-Lin; WANG Chun; ZHANG Fan
2008-01-01
Cellular cell pattern evolution of cylindrically-diverging detonations is numerically simulated successfully by solving two-dimensional Euler equations implemented with an improved two-step chemical kinetic model. From the simulation, three cell bifurcation modes are observed during the evolution and referred to as concave front focusing, kinked and wrinkled wave front instability, and self-merging of cellular cells. Numerical research demonstrates that the wave front expansion resulted from detonation front diverging plays a major role in the cellular cell bifurcation, which can disturb the nonlinearly self-sustained mechanism of detonations and finally lead to cell bifurcations.
Bifurcations and Transitions to Chaos in An Inverted Pendulum
Kim, Sang-Yoon; Hu, Bambi
1998-01-01
We consider a parametrically forced pendulum with a vertically oscillating suspension point. It is well known that, as the amplitude of the vertical oscillation is increased, its inverted state (corresponding to the vertically-up configuration) undergoes a cascade of ``resurrections,'' i.e., it becomes stabilized after its instability, destabilize again, and so forth ad infinitum. We make a detailed numerical investigation of the bifurcations associated with such resurrections of the inverted...
Computer simulation of the carotid artery
Santos, A.; Sousa, L. de; Tavares, J.; Santos, R.; Castro, P.; Azevedo, E.
2012-01-01
Background: Disturbed flow conditions at the bifurcation of common carotid artery and proximal internal carotid artery plays an important role in the development of local atherosclerotic plaques, which are important causes of stroke. Being able to build 3D models based on ultrasound imaging can improve diagnostic assessment and support interventions like endarterectomy or carotid stenting. Our aim was to describe a carotid segmentation algorithm to build these 3D models.Methods: We developed ...
Angiographic features of unilateral nonbifurcating cervical carotid artery: A case report
International Nuclear Information System (INIS)
Nonbifurcating cervical carotid artery is a rare anomaly of the common carotid artery (CCA), in which the branches of the external carotid artery (ECA) arise directly from the CCA or proximal internal carotid artery without bifurcation, and therefore there is no proximal main trunk of the ECA. We report a unilateral nonbifurcating cervical carotid artery of a 67-year-old woman, incidentally found during cerebral aneurismal treatment
Angiographic features of unilateral nonbifurcating cervical carotid artery: A case report
Energy Technology Data Exchange (ETDEWEB)
En, Na Lae [Dept. of Radiology, Gangnam Severance Hospital, Yonsei University College of Medicine, Seoul (Korea, Republic of); Lee, Seung Koo [Dept. of Radiology, Severance Hospital, Yonsei University College of Medicine, Seoul (Korea, Republic of)
2015-08-15
Nonbifurcating cervical carotid artery is a rare anomaly of the common carotid artery (CCA), in which the branches of the external carotid artery (ECA) arise directly from the CCA or proximal internal carotid artery without bifurcation, and therefore there is no proximal main trunk of the ECA. We report a unilateral nonbifurcating cervical carotid artery of a 67-year-old woman, incidentally found during cerebral aneurismal treatment.
Aortoiliac aneurysm with arteriocaval fistula treated by a bifurcated endovascular stent-graft
International Nuclear Information System (INIS)
A 71-year-old patient with high-output cardiac failure was found to have an aneurysmal distal aorta with evidence of an arteriocaval fistula on ultrasound scanning. CT demonstrated an aneurysm of the distal aorta and right common iliac artery and an intraarterial digital subtraction angiogram confirmed an arteriocaval fistula. In view of the patient's cardiac failure and general condition an endovascular stent was considered. The right internal iliac artery was occluded with Tungsten coils prior to the insertion of a bifurcated stent-graft. This resulted in total occlusion of the aneurysm and obliteration of the arteriocaval fistula. To our knolwedge such a case has not been previously reported.
Aortoiliac Aneurysm with Arteriocaval Fistula Treated by a Bifurcated Endovascular Stent-Graft
International Nuclear Information System (INIS)
A 71-year-old patient with high-output cardiac failure was found to have an aneurysmal distal aorta with evidence of an arteriocaval fistula on ultrasound scanning. CT demonstrated an aneurysm of the distal aorta and right common iliac artery and an intraarterial digital subtraction angiogram confirmed an arteriocaval fistula. In view of the patient's cardiac failure and general condition an endovascular stent was considered. The right internal iliac artery was occluded with Tungsten coils prior to the insertion of a bifurcated stent-graft. This resulted in total occlusion of the aneurysm and obliteration of the arteriocaval fistula. To our knowledge such a case has not been previously reported
Mining data from CFD simulation for aneurysm and carotid bifurcation models.
Miloš, Radović; Dejan, Petrović; Nenad, Filipović
2011-01-01
Arterial geometry variability is present both within and across individuals. To analyze the influence of geometric parameters, blood density, dynamic viscosity and blood velocity on wall shear stress (WSS) distribution in the human carotid artery bifurcation and aneurysm, the computer simulations were run to generate the data pertaining to this phenomenon. In our work we evaluate two prediction models for modeling these relationships: neural network model and k-nearest neighbor model. The results revealed that both models have high prediction ability for this prediction task. The achieved results represent progress in assessment of stroke risk for a given patient data in real time. PMID:22256273
Calcium deposits in the common carotid artery
International Nuclear Information System (INIS)
Complete text of publication follows. Arterial calcification consists mainly of calcium apatite and takes place at two sites in the vessel wall: the intima and the media. Intimal calcification occurs exclusively within atherosclerotic plaques, while medial calcification may develop independently [1]. Ultrasound examination of the carotid arteries is performed routinely to assess pathological alterations. Large calcified plaques in the carotid arteries can be detected by B-mode ultrasonography easily as high frequency ultrasound does not penetrate calcium and have been investigated extensively. In this study our aim was to determine the calcium distribution in the vessel wall itself, excluding large plaques, and to make the first step towards investigating the relationship between the calcium distributional maps and the respective ultrasonic images. The carotid arteries of five elderly (age 71±9 years) and one young (age 27 years) deceased patients were excised at autopsy and were investigated with a medical ultrasound equipment in a tank containing saline solution. Scan sequences were videotaped and images of previously marked cross-sections were transferred to a computer. Small pieces of the arteries were cut and quench frozen. Sections of 60μm from the middle of the scanned segments (30mm proximal to the bifurcation) were cut in a cryostat. The cryosections were transferred to microprobe target holders. The elemental distribution of the samples were determined by particle induced X-ray emission (PIXE) at the Debrecen microprobe [2]. True elemental maps and absolute concentration values were evaluated with a new software (True Pixe Imaging) [3]. The average calcium content of the scanned areas varied between 1000 and 9000μg/g in the slices of the common carotid arteries of the elderly patients. In contrast, scanned areas in the slices from the young subject contained only 600-800μg/g calcium. The concentration of calcium could reach even 3.75% along the wide
The influences of curvature and torsions on flows in a helical bifurcated stent-graft
Shim, Jeong Hyun; Eun Lee, Kyung; Yoo, Jung Yul
2008-11-01
A bifurcated stent-graft signifies an improvement in surgical technique for treatment of a lesion in the branched blood vessel. However, there still remains a high failure rate regarding bifurcated stent-graft due to the occurrence of thrombosis or re-stenosis. The objectives of this study are to understand the effect of torsion in helical bifurcated geometries, to explain how the mixing of flows there may be advantageous to the prevention of the occurrence of thrombosis, and to keep the patency of stent-graft in the aspect of hemodynamics. For clinical applications, flows in a helical bifurcated stent-graft are simulated three-dimensionally using an incompressible Navier-Stokes solver. In this study, the hemodynamics is investigated in terms of mechanical factors, i.e., velocity profiles, vortex patterns and wall shear stress distributions.
Hopf bifurcation in a environmental defensive expenditures model with time delay
International Nuclear Information System (INIS)
In this paper a three-dimensional environmental defensive expenditures model with delay is considered. The model is based on the interactions among visitors V, quality of ecosystem goods E, and capital K, intended as accommodation and entertainment facilities, in Protected Areas (PAs). The tourism user fees (TUFs) are used partly as a defensive expenditure and partly to increase the capital stock. The stability and existence of Hopf bifurcation are investigated. It is that stability switches and Hopf bifurcation occurs when the delay t passes through a sequence of critical values, τ0. It has been that the introduction of a delay is a destabilizing process, in the sense that increasing the delay could cause the bio-economics to fluctuate. Formulas about the stability of bifurcating periodic solution and the direction of Hopf bifurcation are exhibited by applying the normal form theory and the center manifold theorem. Numerical simulations are given to illustrate the results.
Bifurcation Analysis in an n-Dimensional Diffusive Competitive Lotka-Volterra System with Time Delay
Chang, Xiaoyuan; Wei, Junjie
2015-06-01
In this paper, we investigate the stability and Hopf bifurcation of an n-dimensional competitive Lotka-Volterra diffusion system with time delay and homogeneous Dirichlet boundary condition. We first show that there exists a positive nonconstant steady state solution satisfying the given asymptotic expressions and establish the stability of the positive nonconstant steady state solution. Regarding the time delay as a bifurcation parameter, we explore the system that undergoes a Hopf bifurcation near the positive nonconstant steady state solution and derive a calculation method for determining the direction of the Hopf bifurcation. Finally, we cite the stability of a three-dimensional competitive Lotka-Volterra diffusion system with time delay to illustrate our conclusions.
Bifurcation and chaos analysis of a nonlinear electromechanical coupling relative rotation system
International Nuclear Information System (INIS)
Hopf bifurcation and chaos of a nonlinear electromechanical coupling relative rotation system are studied in this paper. Considering the energy in air-gap field of AC motor, the dynamical equation of nonlinear electromechanical coupling relative rotation system is deduced by using the dissipation Lagrange equation. Choosing the electromagnetic stiffness as a bifurcation parameter, the necessary and sufficient conditions of Hopf bifurcation are given, and the bifurcation characteristics are studied. The mechanism and conditions of system parameters for chaotic motions are investigated rigorously based on the Silnikov method, and the homoclinic orbit is found by using the undetermined coefficient method. Therefore, Smale horseshoe chaos occurs when electromagnetic stiffness changes. Numerical simulations are also given, which confirm the analytical results. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
DNS of bifurcations in an air-filled rotating baroclinic annulus
Randriamampianina, A; Read, P L; Maubert, P; Randriamampianina, Anthony; Fruh, Wolf-Gerrit; Read, Peter L.; Maubert, Pierre
2006-01-01
Three-dimensional Direct Numerical Simulation (DNS) on the nonlinear dynamics and a route to chaos in a rotating fluid subjected to lateral heating is presented here and discussed in the context of laboratory experiments in the baroclinic annulus. Following two previous preliminary studies by Maubert and Randriamampianina, the fluid used is air rather than a liquid as used in all other previous work. This study investigated a bifurcation sequence from the axisymmetric flow to a number of complex flows. The transition sequence, on increase of the rotation rate, from the axisymmetric solution via a steady, fully-developed baroclinic wave to chaotic flow followed a variant of the classical quasi-periodic bifurcation route, starting with a subcritical Hopf and associated saddle-node bifurcation. This was followed by a sequence of two supercritical Hopf-type bifurcations, first to an amplitude vacillation, then to a three-frequency quasi-periodic modulated amplitude vacillation (MAV), and finally to a chaotic MAV\\...
Bifurcation and complex dynamics of a discrete-time predator-prey system involving group defense
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S. M. Sohel Rana
2015-09-01
Full Text Available In this paper, we investigate the dynamics of a discrete-time predator-prey system involving group defense. The existence and local stability of positive fixed point of the discrete dynamical system is analyzed algebraically. It is shown that the system undergoes a flip bifurcation and a Neimark-Sacker bifurcation in the interior of R+2 by using bifurcation theory. Numerical simulation results not only show the consistence with the theoretical analysis but also display the new and interesting dynamical behaviors, including phase portraits, period-7, 20-orbits, attracting invariant circle, cascade of period-doubling bifurcation from period-20 leading to chaos, quasi-periodic orbits, and sudden disappearance of the chaotic dynamics and attracting chaotic set. The Lyapunov exponents are numerically computed to characterize the complexity of the dynamical behaviors.
Hopf bifurcation and chaos from torus breakdown in voltage-mode controlled DC drive systems
International Nuclear Information System (INIS)
Period-doubling bifurcation and its route to chaos have been thoroughly investigated in voltage-mode and current-mode controlled DC motor drives under simple proportional control. In this paper, the phenomena of Hopf bifurcation and chaos from torus breakdown in a voltage-mode controlled DC drive system is reported. It has been shown that Hopf bifurcation may occur when the DC drive system adopts a more practical proportional-integral control. The phenomena of period-adding and phase-locking are also observed after the Hopf bifurcation. Furthermore, it is shown that the stable torus can breakdown and chaos emerges afterwards. The work presented in this paper provides more complete information about the dynamical behaviors of DC drive systems.
Stability and Bifurcation Analysis of a Modified Epidemic Model for Computer Viruses
Directory of Open Access Journals (Sweden)
Chuandong Li
2014-01-01
Full Text Available We extend the three-dimensional SIR model to four-dimensional case and then analyze its dynamical behavior including stability and bifurcation. It is shown that the new model makes a significant improvement to the epidemic model for computer viruses, which is more reasonable than the most existing SIR models. Furthermore, we investigate the stability of the possible equilibrium point and the existence of the Hopf bifurcation with respect to the delay. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when the delay passes through a sequence of critical values. An analytical condition for determining the direction, stability, and other properties of bifurcating periodic solutions is obtained by using the normal form theory and center manifold argument. The obtained results may provide a theoretical foundation to understand the spread of computer viruses and then to minimize virus risks.
Delay-induced stochastic bifurcations in a bistable system under white noise
Energy Technology Data Exchange (ETDEWEB)
Sun, Zhongkui, E-mail: sunzk@nwpu.edu.cn; Fu, Jin; Xu, Wei [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China); Xiao, Yuzhu [Department of Mathematics and Information Science, Chang' an University, Xi' an 710086 (China)
2015-08-15
In this paper, the effects of noise and time delay on stochastic bifurcations are investigated theoretically and numerically in a time-delayed Duffing-Van der Pol oscillator subjected to white noise. Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and the stationary probability density function for amplitude of the response. Based on the knowledge that stochastic bifurcation is characterized by the qualitative properties of the steady-state probability distribution, it is found that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic P-bifurcation. Besides, results demonstrated that the effects of the strength of the delayed displacement feedback on stochastic bifurcation are accompanied by the sensitive dependence on time delay. Furthermore, the results from numerical simulations best confirm the effectiveness of the theoretical analyses.
Delay-induced stochastic bifurcations in a bistable system under white noise.
Sun, Zhongkui; Fu, Jin; Xiao, Yuzhu; Xu, Wei
2015-08-01
In this paper, the effects of noise and time delay on stochastic bifurcations are investigated theoretically and numerically in a time-delayed Duffing-Van der Pol oscillator subjected to white noise. Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and the stationary probability density function for amplitude of the response. Based on the knowledge that stochastic bifurcation is characterized by the qualitative properties of the steady-state probability distribution, it is found that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic P-bifurcation. Besides, results demonstrated that the effects of the strength of the delayed displacement feedback on stochastic bifurcation are accompanied by the sensitive dependence on time delay. Furthermore, the results from numerical simulations best confirm the effectiveness of the theoretical analyses. PMID:26328553
BIFURCATIONS OF A CANTILEVERED PIPE CONVEYING STEADY FLUID WITH A TERMINAL NOZZLE
Institute of Scientific and Technical Information of China (English)
Xu Jian; Huang Yuying
2000-01-01
This paper studies interactions of pipe and fluid and deals with bifurcations of a cantilevered pipe conveying a steady fluid, clamped at one end and having a nozzle subjected to nonlinear constraints at the free end. Either the nozzle parameter or the flow velocity is taken as a variable parameter. The discrete equations of the system are obtained by the Ritz-Galerkin method. The static stability is studied by the Routh criteria. The method of averaging is employed to investigate the stability of the periodic motions. A Runge-Kutta scheme is used to examine the analytical results and the chaotic motions. Three critical values are given. The first one makes the system lose the static stability by pitchfork bifurcation. The second one makes the system lose the dynamical stability by Hopf bifurcation. The third one makes the periodic motions of the system lose the stability by doubling-period bifurcation.
Delay-induced stochastic bifurcations in a bistable system under white noise
International Nuclear Information System (INIS)
In this paper, the effects of noise and time delay on stochastic bifurcations are investigated theoretically and numerically in a time-delayed Duffing-Van der Pol oscillator subjected to white noise. Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and the stationary probability density function for amplitude of the response. Based on the knowledge that stochastic bifurcation is characterized by the qualitative properties of the steady-state probability distribution, it is found that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic P-bifurcation. Besides, results demonstrated that the effects of the strength of the delayed displacement feedback on stochastic bifurcation are accompanied by the sensitive dependence on time delay. Furthermore, the results from numerical simulations best confirm the effectiveness of the theoretical analyses
Coexistence of periods in a bifurcation
International Nuclear Information System (INIS)
Highlights: ► The bifurcation of the Varley–Gradwell–Hassell population model is revisited. ► The structure of the attractor mediating the bifurcation to chaos is studied. ► Geometric arguments are given for the coexistence of periods in the attractor. ► An algebraic method for the localization of these bifurcations is provided. - Abstract: A particular type of order-to-chaos transition mediated by an infinite set of coexisting neutrally stable limit cycles of different periods is studied in the Varley–Gradwell–Hassell population model. We prove by an algebraic method that this kind of transition can only happen for a particular bifurcation parameter value. Previous results on the structure of the attractor at the transition point are here simplified and extended.
Directory of Open Access Journals (Sweden)
M.D. Cabral
2009-05-01
Full Text Available Subclinical hypothyroidism (SHT is a disease for which exact therapeutic approaches have not yet been established. Previous studies have suggested an association between SHT and coronary heart disease. Whether this association is related to SHT-induced changes in serum lipid levels or to endothelial dysfunction is unclear. The aim of this study was to determine endothelial function measured by the flow-mediated vasodilatation of the brachial artery and the carotid artery intima-media thickness (IMT in a group of women with SHT compared with euthyroid subjects. Triglycerides, total cholesterol, HDL-C, LDL-C, apoprotein A (apo A, apo B, and lipoprotein(a were also determined. Twenty-one patients with SHT (mean age: 42.4 ± 10.8 years and mean thyroid-stimulating hormone (TSH levels: 8.2 ± 2.7 µIU/mL and 21 euthyroid controls matched for body mass index, age and atherosclerotic risk factors (mean age: 44.2 ± 8.5 years and mean TSH levels: 1.4 ± 0.6 µIU/mL participated in the study. Lipid parameters (except HDL-C and apo A, which were lower and IMT values were higher in the common carotid and carotid bifurcation of SHT patients with positive serum thyroid peroxidase antibodies (TPO-Ab (0.62 ± 0.2 and 0.62 ± 0.16 mm for the common carotid and carotid bifurcation, respectively when compared with the negative TPO-Ab group (0.55 ± 0.24 and 0.58 ± 0.13 mm, for common carotid and carotid bifurcation, respectively. The difference was not statistically significant. We conclude that minimal thyroid dysfunction had no adverse effects on endothelial function in the population studied. Further investigation is warranted to assess whether subclinical hypothyroidism, with and without TPO-Ab-positive serology, has any effect on endothelial function.
BIFURCATIONS AND CHAOS CONTROL IN TCP-RED SYSTEM
Institute of Scientific and Technical Information of China (English)
Liu Fang
2006-01-01
Objective Analyzing the nonlinear dynamics of the TCP-RED congestion control system is of great importance. This study will help investigate the loss of stability in Internet and design a proper method for controlling bifurcation and chaos in such system. Methods Based on bifurcation diagram, the effect of parameter on system performance is discussed. By using the state feedback and parameter variation strategy, a simple real time control method is proposed to modify the existing RED scheme. Results With our control method, the parametric sensitivity of RED mechanism is attenuated. Moreover, a sufficient condition on the robust stability of the system is also derived to adjust the parameters in TCP-RED system. Conclusion The proposed method has the advantages of simple implementation and unnecessary knowledge of the exact system.
Stability and bifurcation analysis of rotor-bearing-seal system
Ying, G. Y.; Liu, S. L.; Ma, R.; Zheng, S. Y.
2016-05-01
Labyrinth seals were extensively used in turbine units, and the seal fluid forces may induce self-excited vibrations of rotor under certain conditions. It has become the main factor to instability of rotor system. In this paper Muszynska seal fluid force model is used to investigate the stability of the rotor system. Nonlinear equations are numerically solved by Newmark integration method. The effect of different seal clearances and differential pressures on system stability is studied. The calculation results show that the dominant vibration component leading to instability changes with different seal clearance. With the differential pressure increased, the unstable speed is reduced. Then the bifurcation behavior of the system with and without seal force is calculated. Results show that the rotor vibration becomes severe and complicated, and the bifurcation behavior of the system has been changed when seal force is considered.
Morphological Transitions of Sliding Drops -- Dynamics and Bifurcations
Engelnkemper, Sebastian; Gurevich, Svetlana V; Thiele, Uwe
2016-01-01
We study fully three-dimensional droplets that slide down an incline employing a thin-film equation that accounts for capillarity, wettability and a lateral driving force in small-gradient (or long-wave) approximation. In particular, we focus on qualitative changes in the morphology and behavior of stationary sliding drops. We employ the inclination angle of the substrate as control parameter and use continuation techniques to analyze for several fixed droplet sizes the bifurcation diagram of stationary droplets, their linear stability and relevant eigenmodes. The obtained predictions on existence ranges and instabilities are tested via direct numerical simulations that are also used to investigate a branch of time-periodic behavior (corresponding to pearling-coalescence cycles) which emerges at a global instability, the related hysteresis in behavior and a period-doubling cascade. The non-trivial oscillatory behavior close to a Hopf bifurcation of drops with a finite-length tail is also studied. Finally, it ...