Reproducibility Study of Magnetic Resonance Image-Based Computational Fluid Dynamics Prediction of Carotid Bifurcation Flow

The importance of shear stress in the initiation and progression of atherosclerosis has been recognized for some time. A novel way to quantify wall shear stress under physiologically realistic conditions is to combine magnetic resonance imaging (MRI) and computational fluid dynamics. The present study aims to investigate the reproducibility of the simulated flow by using this combined approach. The right carotid bifurcations of eight healthy subjects were scanned twice with MRI within a few weeks. Three-dimensional geometries of the vessels were reconstructed for each scan and each subject. Pulsatile flows through these models were calculated to assess errors associated with the predicted flow parameters. This was done by comparing various wall shear stress indices, including the time-averaged wall shear stress (WSS), oscillating shear index (OSI), WSS Gradients (WSSG) and WSS Angle Deviation (WSSAD). Qualitatively, all the wall shear parameters proved to be highly reproducible. Quantitatively, the reproducibility was over 90% for OSI and WSSAD, but less impressive (60%) for other parameters. Our results indicated that WSS and WSSG values were extremely sensitive to subtle variations in local geometry and mesh design, particularly in regions around the bifurcation apex where WSS values were high and least reproducible. © 2003 Biomedical Engineering Society. PAC2003: 8385Pt, 8719Xx, 8761Lh, 8719Uv     

Endothelial Cell Layer Subjected to Impinging Flow Mimicking the Apex of an Arterial Bifurcation

Little is known about endothelial responses to the impinging flow hemodynamics that occur at arterial bifurcation apices, where intracranial aneurysms usually form. Such hemodynamic environments are characterized by high wall shear stress (WSS >40 dynes/cm²) and high wall shear stress gradients (WSSG >300 dynes/cm³). In this study, confluent bovine aortic endothelial cells were exposed to impinging flow in a T-shaped chamber designed to mimic a bifurcation. After 24–72 h under flow, cells around the stagnation point maintained polygonal shapes but cell density was reduced, whereas cells in adjacent downstream regions exposed to very high WSS and WSSG were elongated, aligned parallel to flow, and at higher density. Such behavior was not blocked by inhibiting proliferation, indicating that cells migrated downstream from the stagnation point in response to impinging flow. Furthermore, although the area of highest cell density moved downstream and away from the impingement point over time, it never moved beyond the WSS maximum. The accumulation of cells upstream of maximal WSS and downstream of maximal WSSG suggests that positive WSSG is responsible for the observed migration. These results demonstrate a unique endothelial response to aneurysm-promoting flow environments at bifurcation apices.     

Quantifying turbulent wall shear stress in a subject specific human aorta using large eddy simulation

In this study, large-eddy simulation (LES) is employed to calculate the disturbed flow field and the wall shear stress (WSS) in a subject specific human aorta. Velocity and geometry measurements using magnetic resonance imaging (MRI) are taken as input to the model to provide accurate boundary conditions and to assure the physiological relevance. In total, 50 consecutive cardiac cycles were simulated from which a phase average was computed to get a statistically reliable result. A decomposition similar to Reynolds decomposition is introduced, where the WSS signal is divided into a pulsating part (due to the mass flow rate) and a fluctuating part (originating from the disturbed flow). Oscillatory shear index (OSI) is plotted against time-averaged WSS in a novel way, and locations on the aortic wall where elevated values existed could easily be found. In general, high and oscillating WSS values were found in the vicinity of the branches in the aortic arch, while low and oscillating WSS were present in the inner curvature of the descending aorta. The decomposition of WSS into a pulsating and a fluctuating part increases the understanding of how WSS affects the aortic wall, which enables both qualitative and quantitative comparisons.     

Effect of head posture on the healthy human carotid bifurcation hemodynamics

Head and neck postures may cause morphology changes to the geometry of the carotid bifurcation (CB) that alter the low and oscillating wall shear stress (WSS) regions previously reported as important in the development of atherosclerosis. Here the right and left CB were imaged by MRI in two healthy subjects in the neutral head posture with the subject in the supine position and in two other head postures with the subject in the prone position: (1) rightward rotation up to 80°, and (2) leftward rotation up to 80°. Image-based computational models were constructed to investigate the effect of posture on arterial geometry and local hemodynamics. The area exposure to unfavorable hemodynamics, based on thresholds set for oscillatory shear index (OSI), WSS and relative residence time, was used to quantify the hemodynamic impact on the wall. Torsion of the head was found to: (1) cause notable changes in the bifurcation and internal carotid artery angles and, in most cases, on cross-sectional area ratios for common, internal and external carotid artery, (2) change the spatial distribution of wall regions exposed to unfavorable hemodynamics, and (3) cause a marked change in the hemodynamic burden on the wall when the OSI was considered. These findings suggest that head posture may be associated with the genesis and development of atherosclerotic disease as well as complications in stenotic and stented vessels.     

左主干分叉病变严重程度的血流动力学功能性评价

目的无保护左主干分叉病变的治疗方式选择很大程度上依赖于病变的严重程度。SYNTAX评分是基于冠脉造影图像对冠脉病变严重程度进行评价的方法,是一种完全解剖学的评价,缺少功能性的分析。本文以总灌注量作为判断病变严重程度的参考量,从血流动力学的角度对不同类型分叉病变严重程度做出评价。方法采用患者三维模型(three-dimensional,3D)耦合个性化的集中参数模型(lumped parameter model,LPM,0D)对不同的分叉病变进行多尺度数值仿真计算,提取不同分支的流量、分叉区域的壁面切应力(wall shear stress,WSS)、壁面切应力振荡指数(oscillatory shear index,OSI)3个血流动力学参数,通过对比这些参数,从血流动力学的角度对不同类型分叉病变严重程度做出分析。结果分支(回旋支)是否病变对总灌注量是有影响的,当分支存在病变时,总灌注量会降低,与SYNTAX评分中对分叉病变严重程度的分类是一致的。从恶化风险(WSS,OSI)来看,当左主干存在狭窄时,分叉区域平均WSS相对比较大,OSI并没有呈现出一定的规律。结论分支存在狭窄的左主干分叉病变比分支不存在狭窄的病变总灌注量更小,心肌缺血程度更严重,狭窄进一步恶化并无明显差异。     

Investigation of Pulsatile Flowfield in Healthy Thoracic Aorta Models

Cardiovascular disease is the primary cause of morbidity and mortality in the western world. Complex hemodynamics plays a critical role in the development of aortic dissection and atherosclerosis, as well as many other diseases. Since fundamental fluid mechanics are important for the understanding of the blood flow in the cardiovascular circulatory system of the human body aspects, a joint experimental and numerical study was conducted in this study to determine the distributions of wall shear stress and pressure and oscillatory WSS index, and to examine their correlation with the aortic disorders, especially dissection. Experimentally, the Phase-Contrast Magnetic Resonance Imaging (PC-MRI) method was used to acquire the true geometry of a normal human thoracic aorta, which was readily converted into a transparent thoracic aorta model by the rapid prototyping (RP) technique. The thoracic aorta model was then used in the in vitro experiments and computations. Simulations were performed using the computational fluid dynamic (CFD) code ACE+^® to determine flow characteristics of the three-dimensional, pulsatile, incompressible, and Newtonian fluid in the thoracic aorta model. The unsteady boundary conditions at the inlet and the outlet of the aortic flow were specified from the measured flowrate and pressure results during in vitro experiments. For the code validation, the predicted axial velocity reasonably agrees with the PC-MRI experimental data in the oblique sagittal plane of the thoracic aorta model. The thorough analyses of the thoracic aorta flow, WSSs, WSS index (OSI), and wall pressures are presented. The predicted locations of the maxima of WSS and the wall pressure can be then correlated with that of the thoracic aorta dissection, and thereby may lead to a useful biological significance. The numerical results also suggest that the effects of low WSS and high OSI tend to cause wall thickening occurred along the inferior wall of the aortic arch and the anterior wall of the brachiocephalic artery, similar implication reported in a number of previous studies.     

腹主动脉叉血流动力学边界元分析

本文利用边界元方法计算了腹主动脉叉。在动脉粥样硬化前后的血液流场、血管壁切应力等血液流体动力学特性,通过对动脉粥样硬化产生前后,左、右髂总动脉壁切应力的计算结果分析,对粥样斑块病变产生和发展的血液流体动力学原因做出了判断。结果显示:腹主动脉叉几何形状的不对称性导致分叉处血液流速、血管壁切应力分布的不对称,内侧壁切应力大于外侧壁,右髂总动脉内侧壁切应力大于左髂总动脉。动脉粥样硬化处由于血管腔变窄血液流速明显变大、切应力变大,容易使斑块表面撕裂出现组织增生,粥样斑块下游处血流速度、切应力减小,形成血液分离区,使血细胞聚集,造成动脉粥样硬化发展、加剧。     

Hemodynamic effects on atherosclerosis-prone coronary artery: wall shear stress/rate distribution and impedance phase angle in coronary and aortic circulation

The objective of the present study was to evaluate the hemodynamic characteristics of an atherosclerosis-prone coronary artery compared to the aorta. We describe three- dimensional spatial patterns of wall shear stress (WSS) according to the impedance phase angle in pulsatile coronary and aorta models using in vivo hemodynamic parameters and computed numerical simulations both qualitatively and quantitatively. Angiography of coronary arteries and aortas were done to obtain a standard model of vascular geometry. Simultaneously to the physiologic studies, flow-velocity and pressure profiles from in vivo data of the intravascular Doppler and pressure wire studies allowed us to include in vitro numerical simulations. Hemodynamic variables, such as flow-velocity, pressure and WSS in the coronary and aorta models were calculated taking into account the effects of vessel compliance and phase angle between pressure and flow waveforms. We found that there were spatial fluctuations of WSS and in the recirculation areas at the curved outer wall surface of the coronary artery. The mean WSS of the calculated negative phase angle increased in the coronary artery model over that in the aorta model and the phase angle effect was most prominent on the calculated amplitude of WSS of the coronary artery. This study suggests that the rheologic property of coronary circulation, such as the fluctuation of WSS/WSR induces several hemodynamic characteristics. A separation of flow-velocity, a difference in phase between pressure conductance and blood flow and prominent temporal and/or spatial oscillatory fluctuations of the shear forces as a function of pulsatile flow might be important factors in atherogenesis and progression of atherosclerosis.     

Characterization of the Atherosclerotic Carotid Bifurcation Using MRI, Finite Element Modeling, and Histology

Atherogenesis is known to be associated with the stresses that act on or within the arterial wall. Still, the uneven distribution of atherosclerotic lesions and the impact of vessel remodeling on disease progression are poorly understood. A methodology is proposed to study the correlations between fluid dynamic parameters and histological markers of atherosclerosis. Trends suggested by preliminary data from four patients with advanced carotid bifurcation arterial disease are examined and compared to hypotheses in the literature. Four patients were scanned using MRI and ultrasound, and subsequently underwent carotid endarterectomy. For each patient. a geometric model and a numerical mesh were constructed from MR data, and velocity boundary conditions established. Computations yield values for average wall shear stress (WSS), maximum wall shear stress temporal gradient (WSSTG), and Oscillatory Shear Index (OSI). Following surgery, the excised plaques were sectioned, stained for smooth muscle cells (SMC), macrophages (M phi), lipid (LIP), and collagen (COL), and analyzed quantitatively. Correlations attempted between the various fluid dynamic variables and the biological markers were interesting but inconclusive. Tendencies of WSSTG and WSS to correlate negatively with M phi and LIP, and positively with COL and SMC, as well as tendencies of OSI to correlate positively with Mphi and LIP and negatively with COL and SMC, were observed. These trends agree with hypotheses in the literature, which are based on ex vivo and in vitro experimental studies.     

颅内动脉瘤径颈比对瘤体与分支血管血流动力学影响的数值模拟研究

动脉瘤的血流动力学是影响其生长与破裂的重要因素,尤其是形态学参数径颈比(aspect ratio,AR,瘤体长径/瘤颈宽度)对其血流动力学影响较大。本研究使用基于计算流体力学(computational fluid dynamics,CFD)技术的ANSYS 16.0软件包,数值仿真分析了不同径颈比对颅内动脉瘤瘤体与分支血管血流动力学的影响,为临床上制定合理的形态学与血流动力学指标来筛选高危的动脉瘤患者,并进行积极的干预治疗提供一定的理论依据。通过使用空间直角坐标系建立径颈比为3.33、2.5、2、1.67、1.43、1.25的理想颅内动脉瘤几何模型,分析和比较了包括血液流场与涡量分布、流速与流量、壁面压力、壁面切应力(wall shear stress,WSS)、瘤颈近远侧端与分支血管剪切应变率(shear strain rate,SSR)在内的血流动力学参数。数值模拟结果给出了动脉瘤与分支血管内的流线图、涡核图、压力分布云图、WSS分布云图以及随X轴变化的流速与压力峰值分布曲线。分析得出,径颈比决定瘤内血流模式,径颈比减小,瘤顶的流速与SSR增大,瘤壁上的压力与WSS增大,分支血管壁上的压力增大,且WSS/SSR瘤颈远侧端>WSS/SSR瘤颈近侧端>WSS/SSR分支血管中心,涡核区域由瘤体远侧壁增大至覆盖整个动脉瘤,但对分支血管内血流的阻碍作用减小。     

基于病例研究冠状动脉扭曲对血流动力学的影响

目的探讨扭曲冠状动脉血流动力学的改变,从而阐明扭曲对冠状动脉血流灌注和壁面切应力(wall shear stress,WSS)的影响。方法选取冠状动脉左前降支(left anterior descending,LAD)扭曲和无扭曲两例个体病例,在Mimics软件中重建出LAD扭曲和无扭曲血管模型,并将模型导入ANSYS Fluent软件中进行血流动力学模拟计算,比较两种不同LAD模型的血流动力学情况。结果扭曲的冠状动脉在最大曲率大于1 mm~(-1)的弯曲处WSS下降较为明显,这种情况可能导致下游供血不足;弯曲外侧具有较低WSS(0~26 Pa),而弯曲内侧WSS相对较高(100 Pa);无扭曲和扭曲血管WSS均值分别为10.79、36.12 Pa,相比于无扭曲血管,扭曲血管整体WSS增高。结论扭曲冠状动脉整体WSS增高,从而可能延缓冠状动脉粥样硬化的进展。     

A Follow-up MRI-based Geometry and Computational Fluid Dynamics Study of Carotid Bifurcation

Cardiovascular disease is the leading causes of death in the developed world. Wall shear stress(WSS) is associated with the initiation and progression of atherogenesis. This study combined the recent advances in MR imaging and computational fluid dynanucs(CFD) and evaluated the patient-specific carotid bifurcation. The patient was followed up for 3 years. The geometry changes(tortuosity,curvature, ICA/CCA area ratios, central to the cross-sectional curvature, maximum stenosis) and the CFD factors(velocity distribute, wall shear stress(WSS) and oscillatory shear index(OSI) were compared at different time points.The carotid stenosis was a slight increase in the central to the cross-sectional curvature, and it was minor and variable curvature changes for carotid centerline. The OSI distribution presents a high-values in the same region where carotid stenosis and normal border,indicating complex flow and recirculation.The significant geometric changes observed during the follow-up may also cause significant changes in bifurcation hemodynamics.     

Effects of Arterial Bifurcation Geometry on Nucleotide Concentration at the Endothelium

A mathematical and computational analysis of nucleotide concentration for a two-dimensional artery bifurcation has been developed. This region of the vasculature is known to be exposed to spatially varying wall shear stress (WSS), hence the variation of adenosine nucleotides is of interest. A previously derived similarity solution for mass transport in blood boundary layers for arbitrary wall shear stress function has been used. For the analytical model, the geometric condition has been incorporated into the system using the theory for flow past a wedge. As the bifurcation angle varies different characteristics are exhibited, such as maxima in ADP concentration and the existence of a low wall shear stress region around the stagnation point, for large angles. In the limiting case of two-dimensional stagnation point flow the concentration was constant throughout the domain length. The computational simulations provided a more detailed understanding into how nucleotides vary. Similarities existed between the two solution methods in the vicinity of the stagnation point, but deviated as the fully developed condition prevailed. Additionally, the effect of pulsatile flow has been included, leading to considerable gradients in wall shear stress, both temporal and spatial. However, the resulting nucleotide concentration is determined by the time-averaged wall shear stress. The effects of flow-induced ATP release have also been included, leading to significant changes in ATP concentration. Under rapid release, the concentration at the surface increased relative to the bulk concentration.     

A Computational Study of Flow in a Compliant Carotid Bifurcation–Stress Phase Angle Correlation with Shear Stress

The present study presents a three-dimensional, unsteady supercomputer simulation of the coupled fluid–solid interaction problem associated with flow through a compliant model of the bifurcation of the common carotid artery into the internal and external carotid arteries. The fluid wall shear stress (WSS) and solid circumferential stress/strain (CS) are computed and analyzed for the first time using the complex ratio of CS to WSS (CS/WSS). This analysis reveals a large negative phase angle between CS and WSS (stress phase angle—SPA) on the outer wall of the carotid sinus where atherosclerotic plaques are localized. This finding is consistent with other measurements and computations of the SPA in coronary arteries and the aortic bifurcation that show large negative SPA correlating with sites of plaque location and in vitro studies of endothelial cells showing that large negative SPA induces pro-atherogenic gene expression and metabolite release profiles.     

Hemodynamic Computation Using Multiphase Flow Dynamics in a Right Coronary Artery

Hemodynamic data on the roles of physiologically critical blood particulates are needed to better understand cardiovascular diseases. The blood flow patterns and particulate buildup were numerically simulated using the multiphase non-Newtonian theory of dense suspension hemodynamics in a realistic right coronary artery (RCA) having various cross sections. The local hemodynamic factors, such as wall shear stress (WSS), red blood cell (RBC) buildup, viscosity, and velocity, varied with the spatially nonuniform vessel structures and temporal cardiac cycles. The model generally predicted higher RBC buildup on the inside radius of curvature. A low WSS region was found in the high RBC buildup region, in particular, on the area of maximum curvature of a realistic human RCA. The complex recirculation patterns, the oscillatory flow with flow reversal, and vessel geometry resulted in RBC buildup due to the prolonged particulate residence time, specifically, at the end of the diastole cycle. The increase of the initial plasma viscosity caused the lower WSS. These predictions have significant implications for understanding the local hemodynamic phenomena that may contribute to the earliest stage of atherosclerosis, as clinically observed on the inside curvatures and torsion of coronary arteries.     

Influence of Vasoactive Drugs on Wall Shear Stress Distribution in the Abdominal Aortic Bifurcation: An In Vitro Study

The present study compares the wall shear stress (rate) distribution in a compliant aortic bifurcation model under three different hemodynamic states: normal state, angiotensin II infusion state (vasoconstrictor), and isoproterenol infusion state (vasodilator). Using a Newtonian blood analog fluid, flow wave forms corresponding to each flow state were generated in an in vitro flow loop and a photographic flow visualization technique was employed to measure wall shear rate. The results indicate a zone of low mean wall shear stress and highly oscillatory shear stress on the outer (lateral) wall of the bifurcation. In this zone, the mean wall shear stress became negative for all three hemodynamic states indicating flow separation. However, the spatial extent of the flow separation zone was not affected significantly by the flow state. The study also revealed a large spatial variation of the phase angle between the hoop strain (circumferential strain due to radial artery expansion) and the wall shear stress, the two main mechanical stimuli acting on endothelial cells which affect their biology. In the zone of low mean wall shear stress on the outer wall, the two stimuli were more out of phase relative to the mother branch, whereas they were less out of phase (by about 50°) on the inner wall (flow divider side). This phase angle was affected significantly by the flow state. For angiotensin II, the phase angle reached a maximum of 125° in the low mean shear zone while the maximum was 94° and 66° for the normal and isoproterenol states, respectively. Our observation that large phase angles between the hoop strain and wall shear stress wave forms are localized in the low shear stress region where atherosclerotic disease occurs suggests the possible physiological relevance of this phase angle to the development of atherosclerosis. © 1998 Biomedical Engineering Society. PAC98: 8745Hw     

Reproducibility of Image-Based Computational Fluid Dynamics Models of the Human Carotid Bifurcation

Recent studies have demonstrated the ability of magnetic resonance imaging (MRI) to provide anatomically realistic boundary conditions for computational fluid dynamics (CFD) simulations of arterial hemodynamics. To date, however, little is known about the overall reproducibility of such image-based CFD techniques. Towards this end we used serial black blood and cine phase contrast MRI to reconstruct CFD models of the carotid bifurcations of three subjects with early atherosclerosis, each imaged three times at weekly intervals. The lumen geometry was found to be precise on average to within 0.15 mm or 5%, while measured flow and heart rates varied by less than 10%. Spatial patterns of a variety of wall shear stress (WSS) indices were largely preserved among the three repeat models. Time-averaged WSS was reproduced best, on average to within 5 dyn/cm² or 37%, followed by WSS spatial gradients, angle gradients, and oscillatory shear index. The intrasubject flow rate variations were found to contribute little to the overall WSS variability. Instead, reproducibility was determined largely by the precision of the lumen boundary extraction from the individual MR images, itself shown to be a function of the image quality and proximity to the geometrically complex bifurcation region. © 2003 Biomedical Engineering Society. PAC2003: 8761Lh, 8757Nk, 8719Hh, 8719Rr, 8719Uv     

左冠状动脉曲率与左前降支狭窄对局部血流动力学的影响

目的 探究不同的左前降支(left anterior descending, LAD)狭窄程度和分叉血管曲率对血流动力学的影响。方法 建立不同分叉血管曲率半径和 LAD 分支狭窄率的理想模型,使用流固耦合( fluid-structure interaction, FSI)方法评估不同曲率半径和不同狭窄率情况下对血流和壁面剪切力相关指标的影响。 结果 LAD 发生狭窄后,高震荡剪切指数(oscillatory shear index, OSI)和高相对滞留时间(relative residence time, RRT)区域主要分布于 LAD 分叉脊对侧、弯曲外侧狭窄位置下游近端和弯曲内侧下游远端,并且随着狭窄程度的增加会扩大其区域与程度;由于曲率半径减小,弯曲内侧中的高 OSI 和 RRT 会向 LAD 下游远端分布,高 RRT 区域面积相对整个血管面积平均降幅能够达到 35. 68% 。 结论 LAD 狭窄的存在会增加狭窄位置下游和 LAD 分叉脊对侧发生继发性狭窄的风险。 曲率降低会促进弯曲内侧斑块的形成与发展,但从整个血管来看,又会细微地降低斑块形成概率。 研究结果可为治疗 LAD 病变与预防继发性狭窄提供方案设计与优化的理论参考。     

动脉粥样硬化病变在颈总动脉分叉处分布特征

为探讨动脉粥样硬化的始动机理,对58例尸体颈动脉分叉标本通过大体及辅以苏丹Ⅲ、Ⅳ染色后观察,采用Mitchell点计数法,以动脉粥样硬化病损频率、面积及粥样化指数为参数得到结论是颈动脉叉处动脉粥样硬化病损以分叉处内、后侧壁高切应力区为好发部位,文内并对切应力作用进行了讨论.     

A Simulation of Vessel–Clamp Interaction: Transient Closure Dynamics

Cross-clamping of aorta is routinely performed in cardiac surgery. The objective of this study was to simulate cross-clamping of the aorta to elucidate the perturbation of stresses in the wall (solid mechanics) and lumen of the vessel (fluid mechanics). Models of the aorta and clamp were created in Computer Assisted Design and Finite Element Analysis packages. The vessel wall was considered as a non-linear anisotropic material while the fluid was simulated as Newtonian with pulsatile flow. The clamp was applied to produce total occlusion in approximately 1 s. A cylindrical and rectangular geometry for the clamp were considered. High jet speed and flow reversal were demonstrated during clamping. It was found that the clamp design and vessel wall anisotropy affected both the fluid wall shear stress (WSS) and solid stresses in vessel wall. The maximum wall stresses increased by about 170 and 220% during closure in the cases of plate and cylindrical clamps, respectively. The plate clamp design was superior for reduction of both solid stresses as well as fluid shear stresses. The cylindrical clamp causes much larger stresses than the plate clamp in each of the stress components; e.g., radial compression of −180 vs. −50 kPa. Vibrations, flow and WSS oscillations were detected immediately before total vessel occlusion. The present findings provide valuable insights into the mode of tissue injury during clamping and may also be useful for improving surgical clamp designs.