The effect of aneurismal-wall mechanical properties on patient-specific hemodynamic simulations： two clinical case reports

Hemodynamic factors such as the wall shear stress play an important role in the pathogenesis and treatment of cerebral aneurysms. In present study, we apply computational fluid-structure interaction analyses on cerebral aneurysms with two different constitutive relations for aneurismal wall in order to investigate the effect of the aneurismal wall mechanical properties on the simulation results. We carry out these analyses by using two patient-specific models of cerebral aneurysms of different sizes located in different branches of the circle of Willis. The models are constructed from 3D rotational angiography image data and blood flow dynamics is studied under physiologically representative waveform of inflow. From the patient models analyzed in this investigation, we find that the deformations of cerebral aneurysms are very small. But due to the nonlinear character of the Navier-Stokes equations, these small deformations could have significant influences on the flow characteristics. In addition, we find that the aneurismal-wall mechanical properties have great effects on the deformation distribution of the aneurysm, which also affects the wall shear stress distribution and flow patterns. Therefore, how to define a proper constitutive relation for aneurismal wall should be considered carefully in the hemodynamic simulation.     

BLOOD FLOW AND MACROMOLECULAR TRANSPORT IN CURVED BLOOD VESSELS

A numerical analysis of the steady/pulsatile flow and macromolecular (such as LDL and Albumin) transport in curved blood vessels was carried out. The computational results predict that the vortex of the secondary flow is time-dependent in the aortic arch. The concentration of macromolecule concentrates at the region of sharp curve, and the wall concentration at the outer part is higher than that at the inner part. Atherosclerosis and thrombosis are prone to develop in such regions with sharp flow.     

Mathematical modelling of couple stresses on fluid flow in constricted tapered artery in presence of slip velocity-effects of catheter

This paper explores the mathematical model for couple stress fluid flow through an annular region. The above model is used for studying the blood flow be-tween the clogged （stenotic） artery and the catheter. The asymmetric nature of the stenosis is considered. The closed form expressions for the physiological parameters such as impedance and shear stress at the wall are obtained. The effects of various geomet-ric parameters and the parameters arising out of the fluid considered are discussed by considering the slip velocity and tapering angle. The study of the above model is very significant as it has direct applications in the treatment of cardiovascular diseases.     

Numerical simulation of pulsatile non-Newtonian flow in the carotid artery bifurcation

Both clinical and post mortem studies indicate that, in humans, the carotid sinus of the carotid artery bifurcation is one of the favored sites for the genesis and development of atherosclerotic lesions. Hemodynamic factors have been suggested to be important in atherogenesis. To understand the correlation between atherogenesis and fluid dynamics in the carotid sinus, the blood flow in artery was simulated numerically. In those studies, the property of blood was treated as an incompressible, Newtonian fluid. In fact, however, the blood is a complicated non-Newtonian fluid with shear thinning and viscoelastic properties, especially when the shear rate is low. A variety of non-Newtonian models have been applied in the numerical studies. Among them, the Casson equation was widely used. However, the Casson equation agrees well only when the shear rate is less than 10 s-1. The flow field of the carotid bifurcation usually covers a wide range of shear rate. We therefore believe that it may not be sufficient to describe the property of blood only using the Casson equation in the whole flow field of the carotid bifurcation. In the present study, three different blood constitutive models, namely, the Newtonian, the Casson and the hybrid fluid constitutive models were used in the flow simulation of the human carotid bifurcation. The results were compared among the three models. The results showed that the Newtonian model and the hybrid model had verysimilar distributions of the axial velocity, secondary flow and wall shear stress, but the Casson model resulted in significant differences in these distributions from the other two models. This study suggests that it is not appropriate to only use the Casson equation to simulate the whole flow field of the carotid bifurcation, and on the other hand, Newtonian fluid is a good approximation to blood for flow simulations in the carotid artery bifurcation.     

Peristaltic flow of Walter’s B fluid in endoscope

The peristaltic flow of a Walter’s B fluid in an endoscope is studied.The problem is modeled in a cylindrical coordinate system.The main theme of the present analysis is to study the endoscopic effects on the peristaltic flow of the Walter’s B fluid.To the best of the authors’ knowledge,no investigation has been made so far in the literatures to study the Walter’s B fluid in an endoscope.Analytical solutions are obtained using the regular perturbation method by taking δ as a perturbation parameter.The appro...     

Effects of renal artery stenosis on realistic model of abdominal aorta and renal arteries incorporating fluid-structure interaction and pulsatile non-Newtonian blood flow

The effects of the renal artery stenosis(RAS) on the blood flow and vesselwalls are investigated.The pulsatile blood flow through an anatomically realistic model ofthe abdominal aorta and renal arteries reconstructed from CT-scan images is simulated,which incorporates the fluid-structure interaction(FSI).In addition to the investigationof the RAS effects on the wall shear stress and the displacement of the vessel wall,it isdetermined that the RAS leads to decrease in the renal mass flow.This may cause theactivation of the renin-angiotension system and results in severe hypertension.     

Transient analysis of diffusive chemical reactive species for couple stress fluid flow over vertical cylinder

The unsteady natural convective couple stress fluid flow over a semi-infinite vertical cylinder is analyzed for the homogeneous first-order chemical reaction effect. The couple stress fluid flow model introduces the length dependent effect based on the material constant and dynamic viscosity. Also, it introduces the biharmonic operator in the Navier-Stokes equations, which is absent in the case of Newtonian fluids. The solution to the time-dependent non-linear and coupled governing equations is carried out with an unconditionally stable Crank-Nicolson type of numerical schemes. Numerical results for the transient flow variables, the average wall shear stress, the Nusselt number, and the Sherwood number are shown graphically for both generative and destructive reactions. The time to reach the temporal maximum increases as the reaction constant K increases. The average values of the wall shear stress and the heat transfer rate decrease as K increases, while increase with the increase in the Sherwood number.     

MHD flow and heat transfer of micropolar fluid between two porous disks

A numerical study is carried out for the axisymmetric steady laminar incompressible flow of an electrically conducting micropolar fluid between two infinite parallel porous disks with the constant uniform injection through the surface of the disks. The fluid is subjected to an external transverse magnetic field. The governing nonlinear equations of motion are transformed into a dimensionless form through von Karman’s similarity transformation. An algorithm based on a finite difference scheme is used to solve the reduced coupled ordinary differential equations under associated boundary conditions. The effects of the Reynolds number, the magnetic parameter, the micropolar parameter, and the Prandtl number on the flow velocity and temperature distributions are discussed. The results agree well with those of the previously published work for special cases. The investigation predicts that the heat transfer rate at the surfaces of the disks increases with the increases in the Reynolds number, the magnetic parameter, and the Prandtl number. The shear stresses decrease with the increase in the injection while increase with the increase in the applied magnetic field. The shear stress factor is lower for micropolar fluids than for Newtonian fluids, which may be beneficial in the flow and thermal control in the polymeric processing.     

Minimax principle on energy dissipation of incompressible shear flow

The energy dissipation rate is an important concept in the theory of turbulence. Doering-Constantin＇s variational principle characterizes the upper bounds （maxi- mum） of the time-averaged rate of viscous energy dissipation. In the present study, an optimization theoretical point of view was adopted to recast Doering-Constantin＇s formu- lation into a minimax principle for the energy dissipation of an incompressible shear flow. Then, the Kakutani minimax theorem in the game theory is applied to obtain a set of conditions, under which the maximization and the minimization in the minimax principle are commutative. The results explain the spectral constraint of Doering-Constantin, and confirm the equivalence between Doering-Constantin＇s variational principle and Howard- Busse＇s statistical turbulence theory.     

Robust design of natural laminar flow supercritical airfoil by multi-objective evolution method

A transonic, high Reynolds number natural laminar flow airfoil is designed and studied. The γ-θ transition model is combined with the shear stress transport(SST)k-w turbulence model to predict the transition region for a laminar-turbulent boundary layer. The non-uniform free-form deformation(NFFD) method based on the non-uniform rational B-spline(NURBS) basis function is introduced to the airfoil parameterization.The non-dominated sorting genetic algorithm-II(NSGA-II) is used as the search algorithm, and the surrogate model based on the Kriging models is introduced to improve the efficiency of the optimization system. The optimization system is set up based on the above technologies, and the robust design about the uncertainty of the Mach number is carried out for NASA0412 airfoil. The optimized airfoil is analyzed and compared with the original airfoil. The results show that natural laminar flow can be achieved on a supercritical airfoil to improve the aerodynamic characteristic of airfoils.     

Study on the effect of steady,simple pulsatile and physiological pulsatile flows through a stenosed artery

In the present paper, the comparison of steady, simple pulsatile flow and physiological pulsatile flow on flow reversal zone and hemodynamic wall parameters [wall shear stress (WSS) and oscillatory shear index (OSI)] for the progression of the disease, atherosclerosis has been investigated numerically. The governing equations have been solved by finite volume method. For the numerical analysis, Womersley number, Reynolds number and percentage of restriction are taken as 10, 100 and 50 % respectively. From this study it is revealed that the separated flow from the stenosis strongly depends on inlet flow situations, the maximum chance of deposition of plaque material due to streamline contour is higher at time step t* = 0.75 for simple pulsatile flow and at time step t* = 0 for physiological pulsatile flow and this chance is lower in case of steady flow. The effect of WSS on the disease is higher in physiological pulsatile flow compared to steady as well as simple pulsatile flow. The maximum possibility of initiation as well as progression for atherosclerosis in arterial wall due to high WSS takes place at t* = 0.25 for physiological pulsatile flow. OSI indicates same length of separation for two cases of transient flow, but the rate of cyclic departure of WSS is higher in case of physiological pulsatile flow.     

HEMODYNAMIC CHANGES OF THE LEFT CORONARY ARTERY DURING PERCUTANEOUS CORONARY WEI Chijun*, QIU Yue*, FAN Yubo†, PENG Liqing**, ZHENG Tinghui*,2)*

经皮冠状动脉介入治疗(percutaneous coronary intervention, PCI)是检查和治疗冠心病的常用手段,冠状动脉支架植入过程中可能引发急性血栓的发生。本文通过血流动力学计算探究PCI支架植入手术过程对急性血栓形成的影响。根据真实的冠状动脉计算机断层扫描影像进行建模,在脉动生理血流条件下模拟该手术过程中导丝介入的5个阶段,获得各项血流动力学参数。计算结果表明,导丝介入过程会导致冠状动脉内各项血流动力学参数发生改变,即冠状动脉内血流出现偏心现象,时均壁面剪切力升高,振荡剪切指数下降,粒子相对停留时间降低,横向壁面剪切应力小幅上升,使得血管的内皮细胞暴露在高壁面剪切力的环境下。虽然较短的相对粒子 停留时间、 较小的振荡剪切指数对急性血栓的形成具有阻碍作用,但高时均壁面剪切力与血流偏心对急性血栓形成的诱导作用可能更加明显。     

动脉中非平稳流动壁面剪切力及其Hilbert-Huang变换

本文通过数值方法求解均匀动脉中的非平稳脉动流,给出了通过测量非平稳脉动血流量确定壁面切应力的方法.作为算例,采用实测的大鼠颈总动脉流量信号,求出了均匀动脉壁面切应力波形.进一步对求得的切应力波形进行经验模态分解(EMD),得到了切应力波形的各内在模态(IMF),以及Hilbert幅值谱.从切应力波形经Hilbert-Huang变换得到的IMF和Hilbert谱图可以明显地看出切应力各频率成分的物理意义.所得结果为进一步深入研究非平稳脉动切应力与血管重建的关系提供了一种方法学基础.     

Numerical simulation of the haemodynamics in end‐to‐side anastomoses

In this paper, the commercial CFD package Ansys workbench 11 was used to analyse the three‐dimensional haemodynamics of a typical stenotic Coronary Artery Bypass Grafting (CABG). Two end‐to‐side CABG configurations with anastomosis angle of 20^° and 40^° and graft–artery diameter ratios of 1/0.6, 1/1 and 1/1.6 were examined. The flow measurements from in vitro Doppler guide wire technique acquired in left interior mammary artery (LIMA) and grafted to the left anterior descending artery (LAD) were used to impose the physiologically flow conditions at proximal and distal CABG inlet and outlet, respectively. The blood flow was considered to be incompressible, pulsatile, Newtonian, and laminar rheology. The main objective was to determine the effect of anastomosis angle and graft–artery diameter ratio on the flow patterns and the long‐term functionality of the graft. In analysing the results, the distributions of temporal and spatial wall shear stress (WSS) gradient and oscillating shear index (OSI) in the critical regions of CABG such as heel, toe and the centre of the junction were presented and the vortex motions and the occurrence of recirculation zones were examined. The findings showed asymmetrically disturbed flows in the localized regions of the proximal and distal host artery for all models considered and the movement of the recirculation zones from heel to toe was found to depend on the time at the cardiac cycle. These regions are known as susceptible sites to thrombosis and re‐stenosis due to their association with low values of WSS. Copyright © 2010 John Wiley & Sons, Ltd.     

Non‐Newtonian blood flow study in a model cavopulmonary vascular system

A transient haemodynamic study in a model cavopulmonary vascular system has been carried out for a typical range of parameters using a finite element‐based Navier–Stokes solver. The focus of this study is to investigate the influence of non‐Newtonian behaviour of the blood on the haemodynamic quantities, such as wall shear stress (WSS) and flow pattern. The computational fluid dynamics (CFD) model is based on an artificial compressibility characteristic‐based split (AC‐CBS) scheme, which has been adopted to solve the Navier–Stokes equations in space–time domain. A power law model has been implemented to characterize the shear thinning nature of the blood depending on the local strain rate. Using the computational model, numerical investigations have been performed for Newtonian and non‐Newtonian flows for different frequencies and input pulse forms. The haemodynamic quantities observed in total cavopulmonary connection (TCPC) for the above conditions suggest that there are considerable differences in average (about 25–40%) and peak (about 50%) WSS distributions, when the non‐Newtonian behaviour of the blood is taken into account. The lower WSS levels observed for non‐Newtonian cases point to the higher risk of lesion formation, especially at higher pulsation frequencies. A realistic pulse form is relatively safer than a sinusoidal pulse as it has more energy distributed in the higher harmonics, which results in higher average WSS values. The present study highlights the importance of including non‐Newtonian shear thinning behaviour for modelling blood flow in the vicinity of repaired arterial connections. Copyright © 2010 John Wiley & Sons, Ltd.     

Multiphase non‐Newtonian effects on pulsatile hemodynamics in a coronary artery

Hemodynamic stresses are involved in the development and progression of vascular diseases. This study investigates the influence of mechanical factors on the hemodynamics of the curved coronary artery in an attempt to identify critical factors of non‐Newtonian models. Multiphase non‐Newtonian fluid simulations of pulsatile flow were performed and compared with the standard Newtonian fluid models. Different inlet hematocrit levels were used with the simulations to analyze the relationship that hematocrit levels have with red blood cell (RBC) viscosity, shear stress, velocity, and secondary flow. Our results demonstrated that high hematocrit levels induce secondary flow on the inside curvature of the vessel. In addition, RBC viscosity and wall shear stress (WSS) vary as a function of hematocrit level. Low WSS was found to be associated with areas of high hematocrit. These results describe how RBCs interact with the curvature of artery walls. It is concluded that although all models have a good approximation in blood behavior, the multiphase non‐Newtonian viscosity model is optimal to demonstrate effects of changes in hematocrit. They provide a better stimulation of realistic blood flow analysis. Copyright © 2008 John Wiley & Sons, Ltd.     

Computer Simulation of Non-Newtonian Flow and Mass Transport Through Coronary Arterial Stenosis

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｍｏｓｔｏｂｖｉｏｕｓｃｈａｒａｃｔｅｒｏｆａｔｈｅｒｏｓｃｌｅｒｏｓｉｓｉｓｔｈｅｌｏｃａｌｉｎｔｉｍａｌａｃｃｕｍｕｌａｔｉｏｎｏｆｌｏｗ＿ｄｅｎｓｉｔｙｌｉｐｏｐｒｏｔｅｉｎ(ＬＤＬ) ,ｔｈｅｉｎｃｒｅａｓｅｏｆｔｈｅｆｉｂｅｒａｌｔｉｓｓｕｅａｎｄｔｈｅｓｔｅｎｏｓｉｓ.Ｏｎｏｎｅｈａｎｄ ,ｉｔｉｓｆｏｕｎｄｔｈａｔｔｈｅｄｉｓｅａｓｅｏｆｔｅｎｏｃｃｕｒｓａｔｔｈｅｃｏｍｐｌｅｘｇｅｏｍｅｔｒｙｒｅｇｉｏｎ ,ｓｕｃｈａｓｂｉｆｕｒｃａｔｉｏｎｚｏｎｅ,ｃｕｒｅ…     

Blood flow dynamics and fluid–structure interaction in patient‐specific bifurcating cerebral aneurysms

Hemodynamics plays an important role in the progression and rupture of cerebral aneurysms. The current work describes the blood flow dynamics and fluid–structure interaction in seven patient‐specific models of bifurcating cerebral aneurysms located in the anterior and posterior circulation regions of the circle of Willis. The models were obtained from 3D rotational angiography image data, and blood flow dynamics and fluid–structure interaction were studied under physiologically representative waveform of inflow. The arterial wall was assumed to be elastic, isotropic and homogeneous. The flow was assumed to be laminar, non‐Newtonian and incompressible. In one case, the effects of different model suppositions and boundary conditions were reported in detail. The fully coupled fluid and structure models were solved with the finite elements package ADINA. The vortex structure, pressure, wall shear stress (WSS), effective stress and displacement of the aneurysm wall showed large variations, depending on the morphology of the artery, aneurysm size and position. The time‐averaged WSS, effective stress and displacement at the aneurysm fundus vary between 0.17 and 4.86 Pa, 4.35 and 170.2 kPa and 0.16 and 0.74 mm, respectively, for the seven patient‐specific models of bifurcating cerebral aneurysms. Copyright © 2008 John Wiley & Sons, Ltd.     

脉动流条件下动脉狭窄血管内脂质浓度极化现象的计算机数值模拟

在脉动流条件下,用计算机数值模拟的方法对低密度脂蛋白(LDL)在动脉狭窄血管段内的质量传输进行了研究。计算结果表明．无论是在定常流还是在脉动流条件下．LDL都将聚积于血管狭窄处峰口附近的流动分离点,LDL壁面浓度在此处最高。在脉动流条件下,LDL在血流受扰动区的聚积高于定常流的值;而且．流动分离点处LDL壁面浓度峰值覆盖的区域也宽于定常流。本文所揭示出的LDL在血管狭窄处的质量传输现象可能在动脉粥样硬化的局部性和动脉狭窄的形成中起着很重要的作用。