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.     

3D CFD Simulation of Pulsatile Blood Flow in the Human Aorta

INTRODUCTION　　The human aorta is the majorblood vessel of complex geometry including curva-tures in multiple planes,branches at the apex of the arch,significant tapering andwith distensible vessel wall ( as shown in Fig.1 ) . The blood flow structures in theaorta are very complex and attribute a lot to the development of atherosclerotic le-sions,which always occur in the vicinity of arterial branches,curvatures and bifur-cations〔1～ 5〕.In order to understand the complex nature of the …     

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.     

The effect of angulation in abdominal aortic aneurysms: fluid–structure interaction simulations of idealized geometries

Abdominal aortic aneurysm (AAA) represents a degenerative disease process of the abdominal aorta that results in dilation and permanent remodeling of the arterial wall. A fluid structure interaction (FSI) parametric study was conducted to evaluate the progression of aneurysmal disease and its possible implications on risk of rupture. Two parametric studies were conducted using (i) the iliac bifurcation angle and (ii) the AAA neck angulation. Idealized streamlined AAA geometries were employed. The simulations were carried out using both isotropic and anisotropic wall material models. The parameters were based on CT scans measurements obtained from a population of patients. The results indicate that the peak wall stresses increased with increasing iliac and neck inlet angles. Wall shear stress (WSS) and fluid pressure were analyzed and correlated with the wall stresses for both sets of studies. An adaptation response of a temporary reduction of the peak wall stresses seem to correlate to a certain extent with increasing iliac angles. For the neck angulation studies it appears that a breakdown from symmetric vortices at the AAA inlet into a single larger vortex significantly increases the wall stress. Our parametric FSI study demonstrates the adaptation response during aneurysmal disease progression and its possible effects on the AAA risk of rupture. This dependence on geometric parameters of the AAA can be used as an additional diagnostic tool to help clinicians reach informed decisions in establishing whether a risky surgical intervention is warranted.     

基于MRA的个体化腹主动脉瘤计算机仿真

目的探讨基于MRA图像进行个体化腹主动脉瘤(abdominal aortic aneurysm,AAA)计算机仿真研究的可行性,并从血流动力学层面探讨AAA的发生、发展和破裂机制。方法基于AAA患者的MRA数据采用逆向建模法建立AAA的三维几何模型;采用FLUENT软件进行数值模拟,假设血管壁为刚性壁,血液为不可压缩牛顿流体,建立瞬态模型。将收敛之后的数据导入到CFD-Post中进行结果分析,输出心动周期内不同时刻的血流流线图、流速分布图、血管壁面切应力分布图以及压力分布图。结果AAA瘤颈处血液流动的方式以层流为主,瘤腔内血流以涡流、湍流为主,且在瘤体膨大处较明显;瘤颈处血液流速快于瘤腔,瘤腔大部分区域在整个心动周期内都处于较低的流速水平,且波动不明显,瘤腔内的高流速区域多位于入口血流直接延续的部位;射血期的壁面切应力的量值及其变化幅度均大于充盈期,壁面切应力较高的区域总是分布于瘤颈附近,瘤腔的切应力在整个心动周期内始终处于较低水平;瘤体的壁面压力量值及其分布范围在射血峰值(t=0.08 s)时最大。加速射血期的壁面压力及其变化范围均较减速射血期及充盈期大。结论基于MRA图像可建立个体化的AAA计算机仿真模型,通过计算机仿真得到的AAA内血流分布规律对AAA的研究和临床个体化的诊治有一定的帮助。     

Numerical study of nonlinear pulsatile flow in S-shaped curved arteries

The nonlinear pulsatile blood flow in S-shaped curved arteries was studied with finite element method. Numerical simulations for flows in two models of S-shaped curved arteries with different diameters and under the same boundary conditions were performed. The temporal and spatial distributions of hemodynamic variables during the cardiac cycle such as velocity field, secondary flow, pressure, and wall shear stresses in the arteries were analyzed. Results of numerical simulations showed that the secondary flow in the larger S-shaped curved artery is more complex than that in the smaller one; stronger eddy flow occurred in the inner bends of curved arteries; pressure and wall shear stresses changed violently in the curved arteries, especially in the larger model. These hemodynamic variables in curved arteries will cause important effects on the function of arterial endothelium in the region. For instance, they may lead to the proliferation of smooth muscle cells and the thickening of the intima, and cardiovascular diseases such as atherosclerosis may develop in such regions. Due to having the special blood flow characteristics in the S-shaped arteries, it is worthwhile to study flow in this kind of curved artery. The comprehensive theoretical foundation showed in the present study can be extended to approach problems of nonlinear pulsatile flow in curved arteries with more complex geometrical shape.     

腹主动脉血管瘤的定常流动的模拟

目的 应用两维对称模型模拟腹主动肪血管瘤的定常流动。方法 运用计算力学软件（FLUENTv4.3.2)进行数值模拟。结果 该研究给出了各种情况下的流动状态、流线分布、壁面剪切力和壁面压降的分布。结论 结果表明，腹主动脉血管瘤的形状和大小对流动状态影响不大，而雷诺数的增大会增大腹主动脉血管瘤内涡的强度。     

腹主动脉瘤的数值计算模型比较研究

目的分别采用纯流体模型和流固耦合模型来计算腹主动脉瘤的血流动力学特征,比较两种数值模型的不同,并讨论在研究腹主动脉瘤中的应用。方法使用Gambit 2.2.30和COMSOL Multiphysics 4.2建立腹主动脉瘤的理想模型,分别基于有限体的方法分析纯流体模型,基于任意拉格朗日-欧拉算法(Arbitrary Lagrangian-Eulerian)计算流固耦合模型。结果同样的入口速度下,纯流体模型出现4个涡流和6个局部压力集中;流固耦合模型只有2个涡流和局部压力集中,且涡流中心更接近腹主动脉瘤的远端。在边界层分离点、血流回帖位置以及腹主动脉瘤的近端和远端,两种模型均出现壁剪切力极值。血管壁的最大形变和最大壁应力出现在腹主动脉瘤的近端和远端。结论两种模型的涡流个数和涡流中心的位置均不一样,与瘤体的生长有着密切的关联;流固耦合模型中的最大壁剪切力比纯流体模型要小36%;最大壁应力和最大血管壁的形变量与出口血压呈正相关。在研究血管瘤生长与血流动力学的关系时需要考虑使用流固耦合模型。     

蜿蜒型脑动脉瘤的血流动力学仿真

目的分析在一个心动周期中蜿蜒型脑动脉瘤的血液流动情形、压力和壁面切应力分布和变化情况。方法构建了二维理想化的蜿蜒型脑动脉瘤（有2个动脉瘤）几何模型。利用计算流体力学方法对生理性脉动流进行了数值仿真。选择6个相继的心动时刻来显示流腔内的流动。结果2个流腔内的流动情形和壁面切应力分布呈现相似的特征,而第2个动脉瘤的末端瘤口则呈现非常高的壁面切应力和很高的压力梯度,这将更易于导致动脉瘤的发展和破裂。结论血液流动特征可以帮助人们更好地理解在S形弯曲动脉上滋生的在体蜿蜒型动脉瘤的血流动力学特性。     

In vitro comparison of steady and pulsatile flow characteristics of jellyfish heart valve

In examining the hydrodynamic performance of artificial heart valves in vitro, experiments are carried out under either steady or pulsatile flow conditions. Steady flow experiments are simple to set up and analysis of the data is also simple; however, their validity and accuracy have been questioned. In this study, the flow characteristics of jellyfish valves are evaluated and analyzed for steady and pulsatile flow conditions. The analysis is given in terms of velocity and shear stress distributions for a cardiac flow rate of 4.5l/min, and the corresponding steady flow rate is measured at two locations, 0.5D and 1D downstream of the valve face (D being the diameter of the pipe). At the 0.5D location, the velocity profile results obtained for both flow conditions indicated that jetting flow occurred close to the wall, and flow reversal as well as stagnation zones occurred in the core of the valve chamber. These phenomena were also evident in the shear stress profiles for both pulsatile and steady flow conditions. At this location, the maximum difference between the steady and pulsatile values of peak velocity is about 18%. However, the maximum difference between the peak shear stresses was in the range of 5%–7%. At the 1D location, the flow characteristics observed under both the pulsatile and steady flow conditions were almost identical, with a maximum difference between the peak values of less than 4%. From the data presented here, it can be stated that, at least in the initial optimization of the valve hemodynamic performance, the steady hydrodynamic evaluation of the valve could be an effective tool for analyzing the flow characteristics.     

非定常流动情况下Womersley数和Reynolds数对腹主动脉瘤流动的影响

目的讨论非定常流动情况下，各参数对管壁压力和壁面切应力的影响，进而分析血液流动对内皮细胞和血管弹性的影响。方法应用两维对称模型模拟腹主动脉瘤中的非定常流动。结果Womersley数和Reynolds数越大，流动状态越复杂，涡的强度越大，对壁面切应力和压力都有很大的影响。结论壁面切应力和压力长期且快速的改变对内皮细胞和血管的强度产生影响，进而影响到动脉瘤的形成、成长和破裂。     

Blood flow and structure interactions in a stented abdominal aortic aneurysm model

Since the introduction of endovascular techniques in the early 1990s for the treatment of abdominal aortic aneurysms (AAAs), the insertion of an endovascular graft (EVG) into the affected artery segment has been greatly successful for a certain group of AAA patients and is continuously evolving. However, although minimally invasive endovascular aneurysm repair (EVAR) is very attractive, post-operative complications may occur. Typically, they are the result of excessive fluid-structure interaction dynamics, possibly leading to EVG migration. Considering a 3D stented AAA, a coupled fluid flow and solid mechanics solver was employed to simulate and analyze the interactive dynamics, i.e., pulsatile blood flow in the EVG lumen, pressure levels in the stagnant blood filling the AAA cavity, as well as stresses and displacements in the EVG and AAA walls. The validated numerical results show that a securely placed EVG shields the diseased AAA wall from the pulsatile blood pressure and hence keeps the maximum wall stress 20 times below the wall stress value in the non-stented AAA. The sac pressure is reduced significantly but remains non-zero and transient, caused by the complex fluid-structure interactions between luminal blood flow, EVG wall, stagnant sac blood, and aneurysm wall. The time-varying drag force on the EVG exerted by physiological blood flow is unavoidable, where for patients with severe hypertension the risk of EVG migration is very high.     

平行平板流动腔中Casson流体脉动流的摄动解

高度远小于横向和纵向几何尺寸的矩形平行平板流动腔是人们用以体外研究细胞在切应力作用下力学行为的主要工具之一，考虑到通常采用的矩形平行平板流动腔内的流动属于小雷诺数流动，本文用雷诺数作为摄动参数求出了矩形平行流动腔内Casson流体脉动流的摄动解，给出了腔内切应力随压力梯度和流量的变化规律。数值结果表明，相同压力梯度下Casson流体和牛顿流体对应的腔内切应力分布无明显不同，而在相同流量条件下，Casson流体和牛顿流体对应的腔内切应力分布有明显差异，本文为Casson流体脉动流条件下平行平板流动腔切应力的确定方法提供了理论依据。     

Studies of arterial branching in models using flow birefringence

Steady and pulsatile flows through model branches simulating those of the arterial system were studied using flow birefringence. As the upstream Reynolds number is increased from zero, flow disturbances in branches are generated and propagated by: (1) readjustment of the initial laminar velocity profile; (2) boundary-layer separation; and (3) onset of secondary flows. At Reynolds numbers between 20 and 50, local flow stasis and boundary-layer separation occur along the outer branch walls. When the Reynolds number exceeds 150, regions of locally increased shear, where stresses exceed upstream wall stress, occur along the inner walls of the branch. With pulsatile flow, these regions remain centered approximately one diameter downstream from the point of bifurcation. Similar effects on the arterial intima at sites of branching have been suggested as the most probable physical mechanism for initiating the wall trauma associated with atherosclerotic disease. The ratio of the cross-sectional areas of the branch arms appears more significant than the branching angle or the terminal impedances in determining the entrance lengths and distribution of the disturbed flow.     

Large-Eddy simulation of pulsatile blood flow

Large-Eddy simulation (LES) is performed to study pulsatile blood flow through a 3D model of arterial stenosis. The model is chosen as a simple channel with a biological type stenosis formed on the top wall. A sinusoidal non-additive type pulsation is assumed at the inlet of the model to generate time dependent oscillating flow in the channel and the Reynolds number of 1200, based on the channel height and the bulk velocity, is chosen in the simulations. We investigate in detail the transition-to-turbulent phenomena of the non-additive pulsatile blood flow downstream of the stenosis. Results show that the high level of flow recirculation associated with complex patterns of transient blood flow have a significant contribution to the generation of the turbulent fluctuations found in the post-stenosis region. The importance of using LES in modelling pulsatile blood flow is also assessed in the paper through the prediction of its sub-grid scale contributions. In addition, some important results of the flow physics are achieved from the simulations, these are presented in the paper in terms of blood flow velocity, pressure distribution, vortices, shear stress, turbulent fluctuations and energy spectra, along with their importance to the relevant medical pathophysiology.     

Wall shear stresses in small and large two-way bypass grafts

Wall shear stress, as one of the most important hemodynamic parameters of the cardiovascular system, has been studied extensively in the numerical and experimental approaches to blood flow in various arteries. In order to clarify the influence of graft diameter on the wall shear stress in a femoral two-way bypass graft, the pulsatile blood flows in two models were simulated with the finite element method. Both models were constructed with different diameters of grafts. The main geometric structure and the boundary conditions were identical for both models. The emphasis was on the comparison analysis of wall shear stresses in the vicinity of the distal anastomosis. The temporal-spatial distributions of wall shear stresses, wall shear stress gradients, and oscillating shear index were analyzed and compared. The present study indicated that femoral artery bypassed with a large graft demonstrated relatively uniform wall shear stresses and small wall shear stress gradients, whereas it does not have advantages in the oscillating shear index. The large model exhibits better and more regular hemodynamic phenomena and may be effective in decreasing the probability of the initiation and development of postoperative intimal hyperplasia and restenosis. Thus, appropriately large grafts are applicable in the clinical practice of femoral two-way bypass operation. More detailed studies are necessary on this problem for the purpose of increasing the success rates of the femoral bypass grafts.     

LES of non-Newtonian physiological blood flow in a model of arterial stenosis

Large Eddy Simulation (LES) is performed to study the physiological pulsatile transition-to-turbulent non-Newtonian blood flow through a 3D model of arterial stenosis by using five different blood viscosity models: (i) Power-law, (ii) Carreau, (iii) Quemada, (iv) Cross and (v) modified-Casson. The computational domain has been chosen is a simple channel with a biological type stenosis formed eccentrically on the top wall. The physiological pulsation is generated at the inlet of the model using the first four harmonic series of the physiological pressure pulse (Loudon and Tordesillas [1]). The effects of the various viscosity models are investigated in terms of the global maximum shear rate, post-stenotic re-circulation zone, mean shear stress, mean pressure, and turbulent kinetic energy. We find that the non-Newtonian viscosity models enlarge the length of the post-stenotic re-circulation region by moving the reattachment point of the shear layer separating from the upper wall further downstream. But the turbulent kinetic energy at the immediate post-lip of the stenosis drops due to the effects of the non-Newtonian viscosity. The importance of using LES in modelling the non-Newtonian physiological pulsatile blood flow is also assessed for the different viscosity models in terms of the results of the dynamic subgrid-scale (SGS) stress Smagorinsky model constant, C(s), and the corresponding SGS normalised viscosity.     

Turbulence downstream from the Ionescu-Shiley bioprosthesis in steady and pulsatile flow

The turbulence generated downstream from an aortic Ionescu-Shiley bioprosthesis has been investigated in vitro with both steady and pulsatile flow; Instantaneous point velocities were measured using laser-Doppler anemometry (LDA) at numerous preselected locations in the flow. The mean and RMS velocities from these data at each location were then used to estimate the laminar and turbulent shear in the bulk flow as a function of radial position on a cross-section of the flow system downstream from the mounted prosthesis. Estimated total shear stresses were found in the bulk flow that were of sufficient magnitude to possibly cause haemolysis and initiate platelet chemical-release reactions. For steady flow and at peak pulsatile flow, maximum total shear stresses were estimated to be 120 N m⁻² and 100 N m⁻², respectively, over more than 5 per cent of the flow cross-section. The spatial distribution of the elevated shear stresses correlates well with the valve superstructure. It is concluded that these elevated stresses are a direct consequence of the notable flow constriction generated by the valve’s fully opened leaflets. deceased     

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。     

Turbulence characteristics downstream of a new trileaflet mechanical heart valve

Design limitations of current mechanical heart valves cause blood flow to separate at the leaflet edges and annular valve base, forming downstream vortex mixing and high turbulent shear stresses. The closing behavior of a bileaflet valve is associated with reverse flow and may lead to cavitation phenomenon. The new trileaflet (TRI) design opens similar to a physiologic valve with central flow and closes primarily due to the vortices in the aortic sinus. In this study, we measured the St. Jude Medical 27 mm and the TRI 27 mm valves in the aortic position of a pulsatile circulatory mock loop under physiologic conditions with digital particle image velocimetry (DPIV). Our results showed the major principal Reynolds shear stresses were <100 N/m2 for both valves, and turbulent viscous shear stresses were smaller than 15 N/m2. The TRI valve closed more slowly than the St. Jude Medical valve. As the magnitudes of the shear stresses were similar, the closing velocity of the valves should be considered as an important factor and might reduce the risks of thrombosis and thromboembolism.