Finite Element Modeling of Three-Dimensional Pulsatile Flow in the Abdominal Aorta: Relevance to Atherosclerosis

The infrarenal abdominal aorta is particularly prone to atherosclerotic plaque formation while the thoracic aorta is relatively resistant. Localized differences in hemodynamic conditions, including differences in velocity profiles, wall shear stress, and recirculation zones have been implicated in the differential localization of disease in the infrarenal aorta. A comprehensive computational framework was developed, utilizing a stabilized, time accurate, finite element method, to solve the equations governing blood flow in a model of a normal human abdominal aorta under simulated rest, pulsatile, flow conditions. Flow patterns and wall shear stress were computed. A recirculation zone was observed to form along the posterior wall of the infrarenal aorta. Low time-averaged wall shear stress and high shear stress temporal oscillations, as measured by an oscillatory shear index, were present in this location, along the posterior wall opposite the superior mesenteric artery and along the anterior wall between the superior and inferior mesenteric arteries. These regions were noted to coincide with a high probability-of-occurrence of sudanophilic lesions as reported by Cornhill et al. (Monogr. Atheroscler. 15:13--19, 1990). This numerical investigation provides detailed quantitative data on hemodynamic conditions in the abdominal aorta heretofore lacking in the study of the localization of atherosclerotic disease. © 1998 Biomedical Engineering Society. PAC98: 8745Hw, 0270Dh, 8710+e     

Coupled fluid-wall modelling of steady flow in stenotic carotid arteries

Arterial stenoses may cause critical blood flow and wall conditions leading to clinical complications. In this paper computational models of stenotic carotid arteries are proposed and the vessel wall collapse phenomenon is studied. The models are based on fluid-structure interactions (FSI) between blood and the arterial walls. Coupled finite element and computational fluid dynamics methods are used to simultaneously solve for stress and displacement in the solid, and for pressure, velocity and shear stress in the fluid domain. Results show high wall shear stress at the stenosis throat and low (negative) values accompanied by disturbed flow patterns downstream of the stenosis. The wall circumferential stress varies abruptly from tensile to compressive along the stenosis with high stress concentration on the plaque shoulders showing regions of possible plaque rupture. Wall compression and collapse are observed for severe cases. Post-stenotic collapse of the arterial wall occurs for stenotic severity as low as 50%, with the assumption that a given amount of blood flow needs to pass the stenotic artery; whereas if constant pressure drop should be maintained across a constriction, then collapse happens at severity of 75% and above. The former assumption is based on the requirement of adequate blood supply to the downstream organs/tissue, while the latter stems from the fact that the pumping mechanism of the body has a limited capacity in regulating blood pressure, in case a stenosis appears in the vasculature.     

剪切流动下内皮细胞变形的模拟

血液流动和内皮的耦合是重要的生物医学问题 ,引起了学者们的广泛的兴趣。目前已知内皮细胞能感知流场的剪切应力而改变其形态和功能。由于剪切应力被认为是引起内皮细胞重建的始发信号 ,所以了解内皮细胞与流动应力之间的相互作用机制是十分重要的。我们建立了一个理论模型来模拟内皮细胞与流场应力之间的相互作用。根据二维计算流体动力学方法研究了内皮细胞应力、压力的分布以及内皮细胞在剪切应力作用下的变形情况。结果表明 :( 1)内皮细胞的变形随 α(对应于流体作用于细胞表面的切应力 )的变化而变化。当 α>0 .0 2 1时 ,细胞的变形随 α的增大而显著增大 ;( 2 )流动引起了细胞表面应力和压力分布的不均匀 ,从而导致了细胞的变形。但内皮细胞的最大应力总是位于细胞的顶点。同时 ,我们用流室系统提供剪切流动 ,测量了不同剪切应力作用下培养的人主动脉内皮细胞的变形。所得到的实验结果与上述数值模拟结果是吻合的。本文结果提示 ,由于剪切流动引起细胞表面应力和压力分布的不均一 ,可能在细胞激活和细胞功能的调节 (如细胞骨架的调节 ,粘附分子的表达与分布等 )机制上具有特殊的作用。本研究为综合应用动力学方程来建立内皮细胞模型提供了工作框架     

Flow studies in three-dimensional aorto-right coronary bypass graft system

This paper presents the fluid dynamics of blood flow in a coronary bypass model of the aorto-right coronary bypass system. Three-dimensional computational fluid dynamic simulations are developed of the blood flow in coronary artery-bypass systems, using the computational fluid dynamics software (FLUENT 6.0.1). These blood flow simulations are performed within small intervals of the cardiac cycle, using input data consisting of physiological measurements of flow rates in the aorta, obtained from earlier studies. We have calculated the flow-field distributions of the velocity and the wall shear stress at four typical instants of the cardiac cycle, two during systole and two during the diastole phase. Plots of velocity vector and the wall shear stress are displayed in the aorto-graft-coronary arterial flow-field domain, providing an insight into the link between fluid dynamics and arterial diseases. The prime regions of disturbed flow patterns are at the entrance into the graft from the aorta and at the exit from the graft into the right coronary artery. Our objective is to obtain an understanding of how the coronary artery is perfused by the graft, and thereby into the factors affecting graft patency.     

Flow studies in three-dimensional aorto-right coronary bypass graft system

This paper presents the fluid dynamics of blood flow in a coronary bypass model of the aorto-right coronary bypass system. Three-dimensional computational fluid dynamic simulations are developed of the blood flow in coronary artery-bypass systems, using the computational fluid dynamics software (FLUENT 6.0.1). These blood flow simulations are performed within small intervals of the cardiac cycle, using input data consisting of physiological measurements of flow rates in the aorta, obtained from earlier studies. We have calculated the flow-field distributions of the velocity and the wall shear stress at four typical instants of the cardiac cycle, two during systole and two during the diastole phase. Plots of velocity vector and the wall shear stress are displayed in the aorto-graft-coronary arterial flow-field domain, providing an insight into the link between fluid dynamics and arterial diseases. The prime regions of disturbed flow patterns are at the entrance into the graft from the aorta and at the exit from the graft into the right coronary artery. Our objective is to obtain an understanding of how the coronary artery is perfused by the graft, and thereby into the factors affecting graft patency.     

Influences of graft diameter on the blood flow in 2-way bypassing surgery

The graft diameter plays a critically important role in the long-term patency rates of bypass surgery. To clarify the influence of graft diameter on the blood flows in the femoral 2-way bypass surgery, the physiologically pulsatile flows in two femoral bypass models were simulated with numerical methods. For the sake of comparison, the models were constructed with identical geometry parameters except the different diameters of grafts. Two models with small and large grafts were studied. The boundary conditions for the simulation of blood flow were constant for both models. The maximum Reynolds number was 832.8, and the Womersley number was 6.14. The emphases of results were on the analysis of flow fields in the vicinity of the distal anastomosis. The temporal-spatial distributions of velocity vectors, pressure drop between the proximal and distal toe, wall shear stresses, wall shear stress gradients and oscillating shear index were compared. The present study indicated that femoral artery bypassed with a large graft demonstrated disturbed axial flow and secondary flow at the distal anastomosis while the axial flow at its downstream of toe was featured with larger and more uniform longitudinal velocities. Meanwhile, the large model exhibits less refluences, relatively uniform wall shear stresses, lower pressure and smaller wall shear stress gradients, whereas it does not have any advantages in the distributions of secondary flow and the oscillating shear index. In general, the large model exhibits better and more uniform hemodynamic phenomena near the vessel wall and may be effective in preventing the initiation and development of postoperative intimal hyperplasia and restenosis.     

Effects of turbulent stresses upon mechanical hemolysis: experimental and computational analysis

Experimental and computational studies were performed to elucidate the role of turbulent stresses in mechanical blood damage (hemolysis). A suspension of bovine red blood cells (RBC) was driven through a closed circulating loop by a centrifugal pump. A small capillary tube (inner diameter 1 mm and length 70 mm) was incorporated into the circulating loop via tapered connectors. The suspension of RBCs was diluted with saline to achieve an asymptotic apparent viscosity of 2.0 +/- 0.1 cP at 23 degrees C to produce turbulent flow at nominal flow rate and pressure. To study laminar flow at the identical wall shear stresses in the same capillary tube, the apparent viscosity of the RBC suspension was increased to 6.3 +/- 0.1 cP (at 23 degrees C) by addition of Dextran-40. Using various combinations of driving pressure and Dextran mediated adjustments in dynamic viscosity Reynolds numbers ranging from 300-5,000 were generated, and rates of hemolysis were measured. Pilot studies were performed to verify that the suspension media did not affect mechanical fragility of the RBCs. The results of these bench studies demonstrated that, at the same wall shear stress in a capillary tube, the level of hemolysis was significantly greater (p < 0.05) for turbulent flow as compared with laminar flow. This confirmed that turbulent stresses contribute strongly to blood mechanical trauma. Numerical predictions of hemolysis obtained by computational fluid dynamic modeling were in good agreement with these experimental data.     

Effect of LVAD outlet graft anastomosis angle on the aortic valve, wall, and flow

Left ventricular assist devices (LVADs), which pump blood from the left ventricle to the aorta are an important therapy option for patients with end-stage cardiovascular diseases. Recent publications show that even with optimized LVADs fatal complications can occur because of the blood deformations around the inflow cannula or through the LVAD outlet graft-aorta anastomosis. This study investigates the effects of the anastomosis geometry on the flow through the aorta, on the pressure and wall shear stress (WSS) distributions on the aortic wall and on the total entropy generation in the anastomosis region. Anastomosis geometry is defined with two angles, one on the coronal plane and the other on the transversal plane. Turbulent flow simulations are performed for each geometry. Results indicate that 3% to 5% of the work given by the LVAD is dissipated because of the viscous losses in the anastomosis region. The entropy generation, as well as the maximum WSS, increases as the inclination angle decreases. Some portion of the blood streaming out of the LVAD conduit flows toward the aortic valve; therefore the reverse-flow region extends up to the aortic valve in some cases, which may be one of the causes of aortic-valve dysfunction. Results of this study provide insight on the importance of the anastomosis geometry on the hemodynamics in the aorta and downstream the aortic valve, stresses on the aortic wall, and viscous losses.     

端对端缝合股动脉搭桥术的流动分析

在一般"端对侧"股动脉搭桥术中,由于缝合区几何结构的突变必然导致流场的不均匀.移植管中血流会对缝合区底面产生很大冲击,并影响手术效果.为改善此种现象,作者提出了"端对端"连接方式,并对"端对侧"和"端对端"两种连接模型中的血液流动进行了数值模拟.为便于比较,两种模型利用相同的几何参数进行建模,采用相同的边界条件,数值模拟利用计算流体动力学中的有限单元法进行计算.结果展示了流场、壁面剪切应力及其梯度等血流动力学的时空分布情况.经比较表明,"端对端"模型比"端对侧"模型具有较大的纵向速度、较小的二次流、较均匀的壁面剪切应力等.因此,"端对端"模型具有更好的血流动力学,可以改善搭桥效果.     

肝右静脉与下腔静脉位置对布-加综合征产生机制的影响

目的探讨不同肝右静脉与下腔静脉夹角变化对布-加综合征患者下腔静脉隔膜发生机制的影响。方法运用Mimics软件对临床磁共振成像血管造影下腔静脉和主要肝静脉图像进行三维实体模型重建,测得正常模型下腔静脉与肝右静脉夹角为56°。在保持模型基本结构不变基础上,分别构建肝右静脉与下腔静脉夹角为30°和120°的模型,并数值模拟计算3个模型的壁面剪切力、壁面压强、速度分布。结果 3个模型壁面压强、壁面剪切力差异显著。与正常人56°模型相比,30°模型有较高的壁面压强和较低的血液流速,120°模型有较低的壁面剪切力和血液流速,并伴随有涡流的出现,这些血流动力学因素的改变更易于血栓的形成。56°模型血管内血流流速最快。结论对下腔静脉与肝右静脉血液流场的数值模拟有助于了解布-加综合征的发病机制,提高下腔静脉阻塞隔膜形成风险的预测,为治疗提供理论依据。     

血管壁面剪切应力的测量及其临床研究进展

总结血管壁面剪切应力(WSS)的几种测量技术和计算方法,主要包括基于磁共振或磁共振结合计算流体动力学(CFD)、计算机断层扫描(CT)、血管内超声、传统超声、超声向量血流成像和超声粒子流的血流速度测量技术,以及根据速度计算WSS的几种不同运算方法。介绍WSS计算时的另一个重要参数--血液黏滞系数(又称“血黏度”),描述该参数在精确测量WSS时的选取和计算。此外,通过现有文献论述三维向量WSS的测量以及WSS相关临床参数的计算方法,对现有的WSS临床研究做综述性的讨论。针对颈动脉、主动脉、冠状动脉、肱动脉、股动脉等不同血管,列举WSS相关的临床研究结果,并从中归纳出绝大多数临床研究认可的3个主要结论。     

A computational model to predict aortic wall stresses in patients with systolic arterial hypertension

Computational cardiovascular mechanics has allowed scientists to create complex 3D models for the simulation of cardiovascular problems. Mechanical stress plays a crucial role in the function of the cardiovascular system; stress analysis is a useful tool for the understanding of vascular pathophysiology. By using the spiral CT imaging and computational structural analysis, we present a noninvasive method of wall stress analysis in the normal aorta. The aortic segment was extended from the origin of the inferior mesenteric artery to the aortic bifurcation. The length of this segment was 12 cm, while the maximum transverse diameter was 2.075+/-0.129 cm. A 3D aortic model was constructed based on the CT scan images. The aorta was assumed to have a uniform wall thickness of 1.5mm. The generated unstructured grid, which was used for the structural analysis, consisted of 14,440 hexahedral elements. The wall material was assumed to be hyperelastic, homogeneous, isotropic and nearly incompressible (Poisson ratio=0.45). According to experimental studies, the Young modulus of aortic wall was set equal to 4.66 MPa. The shear stress induced by the blood flow was neglected. A finite-element static structural analysis was performed. Three different cases were examined applying constant intraluminal systolic blood pressures of 120, 180 and 240 mmHg, respectively. The von Mises stress distribution and the displacements of the aortic wall were calculated. Peak wall stress for the normal load case of 120 mmHg was 22.5 N/cm2, while the max displacement was 0.44 mm. The case with the intraluminal pressure of 180 mmHg resulted into peak wall stress of 32 N/cm2 with max displacement 0.59 mm, while for 240 mmHg was 40.6N/cm2, max displacement 0.72 mm. The rise in blood pressure caused all stresses to increase. The pattern of stress distribution and the orientation of the stress were similar for all test cases. A quantitative evaluation of the aortic wall stresses under systolic hypertension is presented. The calculated values of peak wall stress are far lower to those of failure strength of healthy aortic wall specimens estimated by ex vivo mechanical testing (121.0 N/cm2). Our values are consistent with prior stress values predicted by experimental studies. The described methodology offers a significant advancement in incorporating biomechanical principles in the clinical assessment of hypertensive patients with normal or aneurysmatic aortas and can be applied in a patient-specific basis in both conditions in order to detect the vulnerable high stressed regions and the resultant risk of aortic dissection or rupture. We hypothesize that this could assist in deciding the timing of surgical intervention, especially in high-risk patients with abdominal aortic aneurysms.     

A numerical investigation on the steady and pulsatile flow characteristics in axi-symmetric abdominal aortic aneurysm models with some experimental evaluation

Steady and pulsatile flow characteristics in rigid abdominal aortic aneurysm (AAA) models were investigated computationally (using Fluent v. 4.3) over a range of Reynolds number (from 200 to 1600) and Womersley number (from 17 to 22). Some comparisons with measurements obtained by particle image velocimetry under the pulsatile flow conditions are also included. A sinusoidal inlet flow waveform 1 + sin omega t with thin inlet boundary layers was used to produce the required pulsatile flow conditions. The bulk features of the mean flow as well as some detailed features, such as wall shear stress distributions, are the foci of the present investigation. Recirculating vortices appeared at different phases of a flow cycle causing significant spatial and temporal variations in wall shear stresses and static pressure distributions. A high level of shear stresses usually appeared at the upstream and downstream ends of the bulge. Effects of pressure rise caused by the increase in cross-sectional area were transmitted into the downstream tube. Further simulation studies were conducted using simulated physiological waveforms under resting and exercise conditions so as to determine the possible implication of vortex dynamics inside the AAA model.     

A numerical investigation on the steady and pulsatile flow characteristics in axi-symmetric abdominal aortic aneurysm models with some experimental evaluation

Steady and pulsatile flow characteristics in rigid abdominal aortic aneurysm (AAA)models were investigated computationally (using Fluent v.4.3) over a range of Reynolds number (from 200 to 1600)and Womersley number (from 17 to 22). Some comparisons with measurements obtained by particle image velocimetry under the pulsatile flow conditions are also included. A sinusoidal inlet flow waveform 1+sin omega t with thin inlet boundary layers was used to produce the required pulsatile flow conditions. The bulk features of the mean flow as well as some detailed features, such as wall shear stress distributions, are the foci of the present investigation. Recirculating vortices appeared at different phases of a flow cycle causing significant spatial and temporal variations in wall shear stresses and static pressure distributions. A high level of shear stresses usually appeared at the upstream and downstream ends of the bulge. Effects of pressure rise caused by the increase in crosssectional area were transmitted into the downstream tube. Further simulation studies were conducted using simulated physiological waveforms under resting and exercise conditions so as to determine the possible implication of vortex dynamics inside the AAA model.     

附带局部突起的主动脉弓动脉瘤的血流动力学仿真

目的：为了弄清楚顶部附带局部突起的主动脉弓动脉瘤的血流动力学特征，因为针这种动脉瘤的血流动力学目前还较少有人研究。方法：建立了理想化的动脉瘤模型。利用计算流体力学的方法对模型中的生理性血液流动进行了仿真。结果：对流动情形、压力和壁面切应力分布进行了分析，以便评价血流动力学对动脉瘤的发展和破裂的影响。来自动脉的血流对下游瘤口和瘤顶局部突起的冲击较大。瘤顶局部突起区域的压力较高。在瘤口和突起口部位的局部壁面切应力比其他地方的要高。结论：下游瘤口和瘤顶局部突起部位是动脉瘤扩展和破裂的危险区域。     

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.     

具有不同移植管-宿主动脉直径比的冠状动脉搭桥术的血流动力学仿真比较

为了说明移植管-宿主动脉直径比对冠状动脉搭桥术的流场及壁面切应力的影响，构造了三个具有不同移植管-宿主动脉直径比的冠状动脉搭桥术模型，三个模型的移植管直径分别小于、等于和大于宿主动脉的直径；利用有限单元数值模拟方法对三个模型中的生理性脉动血流进行了仿真分析；对流场、壁面切应力及其相关系数的时空分布进行了显示和比较。结果表明，大直径比的模型具有相对较大的纵向速度、大而均匀的壁面切应力以及小的壁面切应力梯度，从而在一定程度上改善了血流动力学；在搭桥术应用中采用大于或等于1的直径比是可取的。然而，在三个模型中，与壁面切应力相关的时间参数并没有显著差别。为了提高冠状动脉搭桥术的畅通率，设计新的缝合结构是很有必要的。     

基于计算流体力学的Stanford B型主动脉夹层血流动力学分析

目的通过计算流体力学(computational fluid dynamics, CFD)分析Stanford B型夹层的血流动力学参数,从而有效全面评估疾病。方法基于1例复杂的Stanford B型主动脉夹层患者的增强CTA影像,构建三维模型和血流动力学的数值模拟研究,分析流场速度分布、夹层破口剖面速度分布以及壁面切应力。结果该病例在夹层入口、出口处的血液流速分别最高达到1.2、2 m/s,为进一步预测夹层破裂位置和评估夹层破裂风险提供依据。在夹层破口附近的假腔壁面形成明显的低壁面切应力区,与患者体内血栓位置相一致。结论 CFD能有效分析复杂主动脉夹层的血流动力学特征,获得主动脉弓部及其降主动脉的剪切力与主动脉夹层发生的相关性,有助于指导临床对主动脉进行功能学评估,进而预防疾病发生。     

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.     

Quantification of wall shear stress in large blood vessels using Lagrangian interpolation functions with cine phase-contrast magnetic resonance imaging

Arterial wall shear stress is hypothesized to be an important factor in the localization of atherosclerosis. Current methods to compute wall shear stress from magnetic resonance imaging (MRI) data do not account for flow profiles characteristic of pulsatile flow in noncircular vessel lumens. We describe a method to quantify wall shear stress in large blood vessels by differentiating velocity interpolation functions defined using cine phase-contrast MRI data on a band of elements in the neighborhood of the vessel wall. Validation was performed with software phantoms and an in vitro flow phantom. At an image resolution corresponding to in vivo imaging data of the human abdominal aorta, time-averaged, spatially averaged wall shear stress for steady and pulsatile flow were determined to be within 16% and 23% of the analytic solution, respectively. These errors were reduced to 5% and 8% with doubling in image resolution. For the pulsatile software phantom, the oscillation in shear stress was predicted to within 5%. The mean absolute error of circumferentially resolved shear stress for the nonaxisymmetric phantom decreased from 28% to 15% with a doubling in image resolution. The irregularly shaped phantom and in vitro investigation demonstrated convergence of the calculated values with increased image resolution. We quantified the shear stress at the supraceliac and infrarenal regions of a human abdominal aorta to be 3.4 and 2.3 dyn/cm², respectively. © 2002 Biomedical Engineering Society. PAC2002: 8761-c, 8719Uv