Influence of microflow on hepatic sinusoid blood flow and red blood cell deformation

Hepatic sinusoids present complex anatomical structures such as the endothelial sieve pores and the Disse space, which govern the microscopic blood flow in the sinusoids and are associated with structural variations in liver fibrosis and cirrhosis. However, the contributions of the permeability of endothelial and collagen layers and the roughness of hepatocyte microvilli to the features of this microflow remain largely unknown. Here, an immersed boundary method coupled with a lattice Boltzmann method was adopted in an in vitro hepatic sinusoidal model, and flow field and erythrocyte deformation analyses were conducted by introducing three new source terms including permeability of the endothelial layer, resistance of hepatocyte microvilli and collagen layers, and deformation of red blood cells (RBCs). Numerical calculations indicated that alterations in endothelial permeability could significantly affect the flow velocity and flow rate distributions in hepatic sinusoids. Interestingly, a biphasic regulating pattern of shear stress occurred simultaneously on the surface of hepatocytes and the lower side of endothelium, i.e., the shear stress increased with increased thickness of hepatocyte microvilli and collagen layer when the endothelial permeability was high but decreased with the increase of the thickness at low endothelial permeability. Additionally, this specified microflow manipulates typical RBC deformation inside the sinusoid, yielding one-third of the variation of deformable index with varied endothelial permeability. These simulations not only are consistent with experimental measurements using in vitro liver sinusoidal chip but also elaborate the contributions of endothelial and collagen layer permeability and wall roughness. Thus, our results provide a basis for further characterizing this microflow and understanding its effects on cellular migration and deformation in the hepatic sinusoids.     

Computer simulations of atherosclerotic plaque growth in coronary arteries

A three dimensional mathematical model with a linear plaque growth function was developed to investigate the geometrical adaptation of atherosclerotic plaques in coronary arteries and study the influences of flow wall shear stress (WSS), blood viscosity and the inlet flow rate on the growth of atherosclerotic plaques using computational plaque growth simulations. The simulation results indicated that the plaque wall thickness at the neck of the stenosis increased at a decreasing rate in the atherosclerosis progression. The simulation results also showed a strong dependence of the plaque wall thickness increase on the blood viscosity and the inlet flow rate. The progression rate in a coronary artery was lower with a higher inlet velocity flow rate and higher with a smaller value of the blood viscosity.     

Fluid-structure interaction in abdominal aortic aneurysms: effects of asymmetry and wall thickness

Background  

Abdominal aortic aneurysm (AAA) is a prevalent disease which is of significant concern because of the morbidity associated with the continuing expansion of the abdominal aorta and its ultimate rupture. The transient interaction between blood flow and the wall contributes to wall stress which, if it exceeds the failure strength of the dilated arterial wall, will lead to aneurysm rupture. Utilizing a computational approach, the biomechanical environment of virtual AAAs can be evaluated to study the affects of asymmetry and wall thickness on this stress, two parameters that contribute to increased risk of aneurysm rupture.     

Numerical simulation of sinusoidal flow in a straight elastic tube: effects of phase angles

Numerical simulations of flow in straight elastic (moving wall) tubes subjected to a sinusoidal pressure gradient were performed for conditions prevailing in large and medium sized arteries. The effects of varying the phase angle between the pressure gradient and the tube radius, the amplitude of wall motion, and the unsteadiness parameter (alpha) on flow rate and wall shear stress were investigated. Mean and peak flow rates and shear stresses were found to be strongly affected by the phase angle between the pressure gradient and the tube radius with greater sensitivity at higher diameter variation and higher alpha. In large artery simulations (alpha = 12), means flow rate was found to be 60% higher and peak flow rate to be 73% higher than corresponding rigid tube values for certain phase angles, while a threefold increase in mean wall shear stress and sevenfold increase in peak wall shear stress were observed in a sensitive phase angle range. Significant reversal in the wall shear stress direction occurred in the sensitive phase angle range even when there was negligible flow rate reversal. All effects were greatly diminished in simulations of medium sized vessels (alpha = 4). Some experimental evidence to support the predictions of a strong effect of phase angle on wall shear stress in large vessels is presented. Finally, physiological implications of the present work are discussed from a basis of aortic input impedance data, and a physical explanation for the extreme sensitivity of the flow field to small amplitude wall motion at high alpha is given.     

Biomechanical signals in the coronary artery triggering the metabolic processes during cardiac overload

Peculiarities in structure and deformability of epicardial conduit coronary arteries are described. The thin wall of animal coronary artery contrasts the human coronary artery in which the remarkable wall thickness is due namely by the intima thickness. Deformation in length and diameter of conduit coronary arteries, due to the left and right ventricle volume increase, has been defined in non-beating canine heart. Ramus interventricularis anterior being firmly tethered to the myocardium undergoes about 3 times larger deformation than ramus circumflexus In anaesthetized dogs a 30% increase in blood pressure, elicited by aortic constriction, induces an increase in diameter of coronary artery, in segment lenght, in blood flow and consequently in shear stress which represents a load for circumferentially running smooth muscle bundles, longitudinally running smooth muscle bundles, as well as for the endothelium. The above load lasting 4 h is already reflected by an increase in total RNA content and [¹⁴C] leucin incorporation in the left ventricle myocardium in the wall of ramus interventricularis anterior, not in ramus circumflexus. The finding fit completely with the different range of deformation of both the above coronary branches and indicates an increase in proteosynthesis not only in myocardium, but in ramus interventricularis anterior as well. An increase in ornithindecarboxylase activity in coronary wall leading to an increase in biogenic polyamines, is present in the case only, when blood pressure increase is induced by infusion of noradrenaline.     

Pulsatile extracorporeal circulation during on-pump cardiac surgery enhances aortic wall shear stress

Controversy on superiority of pulsatile versus non-pulsatile extracorporeal circulation in cardiac surgery still continues. Stroke as one of the major adverse events during cardiopulmonary bypass is, in the majority of cases, caused by mobilization of aortic arteriosclerotic plaques that is inducible by pathologically elevated wall shear stress values. The present study employs computational fluid dynamics to evaluate the aortic blood flow and wall shear stress profiles under the influence of antegrade or retrograde perfusion with pulsatile versus non-pulsatile extracorporeal circulation. While, compared to physiological flow, a non-pulsatile perfusion resulted in generally decreased blood velocities and only moderately increased shear forces (48 Pa versus 20 Pa antegradely and 127 Pa versus 30 Pa retrogradely), a pulsatile perfusion extensively enhanced the occurrence of turbulences, maximum blood flow speed and maximum wall shear stress (1020 Pa versus 20 Pa antegradely and 1178 Pa versus 30 Pa retrogradely). Under these circumstances arteriosclerotic embolism has to be considered. Further simulations and experimental work are necessary to elucidate the impact of our findings on the scientific discourse of pulsatile versus non-pulsatile extracorporeal circulation.     

Fluid flow and plaque formation in an aortic bifurcation

Considering steady laminar flow in a two-dimensional symmetric branching channel with local occlusions, a finite element model has been developed to study velocity fields including reverse flow regions, pressure profiles and wall shear stress distributions for different Reynolds numbers, bifurcation angles and lumen reductions. The flow analysis has been extended to include a new submodel for the pseudo-transient formation of plaque at sites and deposition rates defined by the physical characteristics of the flow. Specifically, simulating the onset of atherosclerotic lesions, sinusoidal plaque layers have been placed in areas of critically low wall shear stresses, and simulating the growth of particle depositions, plaque layers have been added in a stepwise fashion in regions of critically high and low shear. Thus two somewhat conflicting hypothetical correlations between critical wall shear stress levels and atheroma have been tested and a solution has been postulated. The validated computer simulation model is a predictive tool for analyzing the effects of local changes in wall curvature due to surgical reconstruction and/or atherosclerotic lesions, and for investigating the design of aortic bifurcations which mitigate plaque formation.     

Stanford B型主动脉夹层撕破口局部计算流体力学研究

目的:探索Stanford B型主动脉夹层局部血流动力学改变对主动脉夹层发生、发展以及临床预后评估的作用,为临床治疗方案选择提供理论依据。方法:通过CT扫描获取临床常见典型形态的Stanford B型主动脉夹层断层序列,重建出三维主动脉夹层计算流体力学分析模型,对主动脉夹层真假腔内血液流场进行数值模拟计算。结果:血液流经Stanford B型主动脉夹层撕破口时会对血管局部壁面产生冲击,造成动脉管壁局部压强升高,此种"冲击效应"不但会出现在近端夹层撕破口附近管腔壁面,也会出现在中间段及远端夹层撕破口附近,当入口血流压强升高时,夹层撕破口附近局部壁面压强差值也会增加。在心动周期内,Stanford B型主动脉夹层壁面剪切应力异常升高区也主要集中在撕破口区附近的动脉壁面上。结论:对于Stanford B型主动脉夹层而言,撕破口的位置相对于撕破口直径而言似乎更有临床意义。对B型夹层患者采用降低血压治疗,可减低局部动脉管壁上的壁面压强差值,但无法消除此壁面压强差,即主动脉夹层管壁上的局部危险区始终存在。此现象揭示主动脉夹层中远端撕破口也可能是造成夹层局部危险因素的原因,采用手术治疗方法封闭撕破口,以消除局部壁面压强增高区,降低破裂风险,可能是更理想的治疗方法。     

The effect of asymmetry in abdominal aortic aneurysms under physiologically realistic pulsatile flow conditions

In the abdominal segment of the human aorta under a patient's average resting conditions, pulsatile blood flow exhibits complex laminar patterns with secondary flows induced by adjacent branches and irregular vessel geometries. The flow dynamics becomes more complex when there is a pathological condition that causes changes in the normal structural composition of the vessel wall, for example, in the presence of an aneurysm. This work examines the hemodynamics of pulsatile blood flow in hypothetical three-dimensional models of abdominal aortic aneurysms (AAAs). Numerical predictions of blood flow patterns and hemodynamic stresses in AAAs are performed in single-aneurysm, asymmetric, rigid wall models using the finite element method. We characterize pulsatile flow dynamics in AAAs for average resting conditions by means of identifying regions of disturbed flow and quantifying the disturbance by evaluating flow-induced stresses at the aneurysm wall, specifically wall pressure and wall shear stress. Physiologically realistic abdominal aortic blood flow is simulated under pulsatile conditions for the range of time-average Reynolds numbers 50 < or = Rem < or = 300, corresponding to a range of peak Reynolds numbers 262.5 < or = Repeak < or = 1575. The vortex dynamics induced by pulsatile flow in AAAs is depicted by a sequence of four different flow phases in one period of the cardiac pulse. Peak wall shear stress and peak wall pressure are reported as a function of the time-average Reynolds number and aneurysm asymmetry. The effect of asymmetry in hypothetically shaped AAAs is to increase the maximum wall shear stress at peak flow and to induce the appearance of secondary flows in late diastole.     

Wall stress and flow dynamics in abdominal aortic aneurysms: finite element analysis vs. fluid–structure interaction

Abdominal aortic aneurysm (AAA) rupture is the clinical manifestation of an induced force exceeding the resistance provided by the strength of the arterial wall. This force is most frequently assumed to be the product of a uniform luminal pressure acting along the diseased wall. However fluid dynamics is a known contributor to the pathogenesis of AAAs, and the dynamic interaction of blood flow and the arterial wall represents the in vivo environment at the macro-scale. The primary objective of this investigation is to assess the significance of assuming an arbitrary estimated peak fluid pressure inside the aneurysm sac for the evaluation of AAA wall mechanics, as compared with the non-uniform pressure resulting from a coupled fluid–structure interaction (FSI) analysis. In addition, a finite element approach is utilised to estimate the effects of asymmetry and wall thickness on the wall stress and fluid dynamics of ten idealised AAA models and one non-aneurysmal control. Five degrees of asymmetry with uniform and variable wall thickness are used. Each was modelled under a static pressure-deformation analysis, as well as a transient FSI. The results show that the inclusion of fluid flow yields a maximum AAA wall stress up to 20% higher compared to that obtained with a static wall stress analysis with an assumed peak luminal pressure of 117 mmHg. The variable wall models have a maximum wall stress nearly four times that of a uniform wall thickness, and also increasing with asymmetry in both instances. The inclusion of an axial stretch and external pressure to the computational domain decreases the wall stress by 17%.     

Wall stress and flow dynamics in abdominal aortic aneurysms: finite element analysis vs. fluid-structure interaction

Abdominal aortic aneurysm (AAA) rupture is the clinical manifestation of an induced force exceeding the resistance provided by the strength of the arterial wall. This force is most frequently assumed to be the product of a uniform luminal pressure acting along the diseased wall. However fluid dynamics is a known contributor to the pathogenesis of AAAs, and the dynamic interaction of blood flow and the arterial wall represents the in vivo environment at the macro-scale. The primary objective of this investigation is to assess the significance of assuming an arbitrary estimated peak fluid pressure inside the aneurysm sac for the evaluation of AAA wall mechanics, as compared with the non-uniform pressure resulting from a coupled fluid-structure interaction (FSI) analysis. In addition, a finite element approach is utilised to estimate the effects of asymmetry and wall thickness on the wall stress and fluid dynamics of ten idealised AAA models and one non-aneurysmal control. Five degrees of asymmetry with uniform and variable wall thickness are used. Each was modelled under a static pressure-deformation analysis, as well as a transient FSI. The results show that the inclusion of fluid flow yields a maximum AAA wall stress up to 20% higher compared to that obtained with a static wall stress analysis with an assumed peak luminal pressure of 117 mmHg. The variable wall models have a maximum wall stress nearly four times that of a uniform wall thickness, and also increasing with asymmetry in both instances. The inclusion of an axial stretch and external pressure to the computational domain decreases the wall stress by 17%.     

Investigation of hemodynamics in the development of dissecting aneurysm within patient-specific dissecting aneurismal aortas using computational fluid dynamics (CFD) simulations

Aortic dissecting aneurysm is one of the most catastrophic cardiovascular emergencies that carries high mortality. It was pointed out from clinical observations that the aneurysm development is likely to be related to the hemodynamics condition of the dissected aorta. In order to gain more insight on the formation and progression of dissecting aneurysm, hemodynamic parameters including flow pattern, velocity distribution, aortic wall pressure and shear stress, which are difficult to measure in vivo, are evaluated using numerical simulations. Pulsatile blood flow in patient-specific dissecting aneurismal aortas before and after the formation of lumenal aneurysm (pre-aneurysm and post-aneurysm) is investigated by computational fluid dynamics (CFD) simulations. Realistic time-dependent boundary conditions are prescribed at various arteries of the complete aorta models. This study suggests the helical development of false lumen around true lumen may be related to the helical nature of hemodynamic flow in aorta. Narrowing of the aorta is responsible for the massive recirculation in the poststenosis region in the lumenal aneurysm development. High pressure difference of 0.21 kPa between true and false lumens in the pre-aneurismal aorta infers the possible lumenal aneurysm site in the descending aorta. It is also found that relatively high time-averaged wall shear stress (in the range of 4-8 kPa) may be associated with tear initiation and propagation. CFD modeling assists in medical planning by providing blood flow patterns, wall pressure and wall shear stress. This helps to understand various phenomena in the development of dissecting aneurysm.     

Unsteady and three-dimensional simulation of blood flow in the human aortic arch

A three-dimensional and pulsatile blood flow in a human aortic arch and its three major branches has been studied numerically for a peak Reynolds number of 2500 and a frequency (or Womersley) parameter of 10. The simulation geometry was derived from the three-dimensional reconstruction of a series of two-dimensional slices obtained in vivo using CAT scan imaging on a human aorta. The numerical simulations were obtained using a projection method, and a finite-volume formulation of the Navier-Stokes equations was used on a system of overset grids. Our results demonstrate that the primary flow velocity is skewed towards the inner aortic wall in the ascending aorta, but this skewness shifts to the outer wall in the descending thoracic aorta. Within the arch branches, the flow velocities were skewed to the distal walls with flow reversal along the proximal walls. Extensive secondary flow motion was observed in the aorta, and the structure of these secondary flows was influenced considerably by the presence of the branches. Within the aorta, wall shear stresses were highly dynamic, but were generally high along the outer wall in the vicinity of the branches and low along the inner wall, particularly in the descending thoracic aorta. Within the branches, the shear stresses were considerably higher along the distal walls than along the proximal walls. Wall pressure was low along the inner aortic wall and high around the branches and along the outer wall in the ascending thoracic aorta. Comparison of our numerical results with the localization of early atherosclerotic lesions broadly suggests preferential development of these lesions in regions of extrema (either maxima or minima) in wall shear stress and pressure.     

Numerical simulation of blood flow in the left ventricle and aortic sinus using magnetic resonance imaging and computational fluid dynamics

Understanding cardiac blood flow patterns has many applications in analysing haemodynamics and for the clinical assessment of heart function. In this study, numerical simulations of blood flow in a patient-specific anatomical model of the left ventricle (LV) and the aortic sinus are presented. The realistic 3D geometry of both LV and aortic sinus is extracted from the processing of magnetic resonance imaging (MRI). Furthermore, motion of inner walls of LV and aortic sinus is obtained from cine-MR image analysis and is used as a constraint to a numerical computational fluid dynamics (CFD) model based on the moving boundary approach. Arbitrary Lagrangian–Eulerian finite element method formulation is used for the numerical solution of the transient dynamic equations of the fluid domain. Simulation results include detailed flow characteristics such as velocity, pressure and wall shear stress for the whole domain. The aortic outflow is compared with data obtained by phase-contrast MRI. Good agreement was found between simulation results and these measurements.     

Sex hormones and aortic wall remodeling in an arteriovenous fistula

Background: An arteriovenous fistula (AVF) creates high blood flow through the artery and fistula. With this high flow, there is flow-induced remodeling and an increase in diameter, but no intimal hyperplasia. Estrogen has been shown to modify vascular remodeling, decreasing intimal hyperplasia after endothelial injury.Objective: These experiments tested the hypothesis that estrogen administration would decrease wall thickness in an AVE model. Because estrogen may decrease wall thickness, we also tested the hypothesis that testosterone would increase wall thickness.Methods: A fistula was created between the abdominal aorta and the inferior vena cava in Sprague-Dawley rats to generate high blood flow conditions in the aorta. Four groups of female animals were examined: sham, control with AVE ovariectomized (OVX) with AVE and OVX plus testosterone with AVE Four groups of male animals were also examined: sham, control with AVE castrated with AVE and castrated plus estrogen with AVE Five weeks after creation of the AVF, the aortas were collected and fixed; wall thickness was measured both proximal and distal to the AVEResults: Ovariectomy resulted in a significant decrease in estrogen levels (P < 0.01). Testosterone administration tended to increase testosterone levels in the OVX females, but values did not approach levels observed in the control males. No difference was noted in the proximal wall thickness between the control and the OVX animals. The OVX females receiving testosterone exhibited a significant increase in both proximal and distal wall thickness compared with control females (P < 0.001). In the male animals, there was no significant change in aortic wall thickness in the castrated rats compared with the controls. Estrogen administration in the castrated males resulted in a significant decrease in wall thickness in the proximal and distal aorta (P < 0.05).Conclusion: These studies suggest that, in a model of vascular remodeling, estrogen administration decreases wall thickness, and testosterone administration increases wall thickness.     

Hemodynamics in the carotid artery bifurcation: a comparison between numerical simulations and in vitro MRI measurements

The presence of atherosclerotic plaques has been shown to be closely related to the vessel geometry. Studies on postmortem human arteries and on the experimental animal show positive correlation between the presence of plaque thickness and low shear stress, departure of unidirectional flow and regions of flow separation and recirculation. Numerical simulations of arterial blood flow and direct blood flow velocity measurements by magnetic resonance imaging (MRI) are two approaches for the assessment of arterial blood flow patterns. In order to verify that both approaches give equivalent results magnetic resonance velocity data measured in a compliant anatomical carotid bifurcation model were compared to the results of numerical simulations performed for a corresponding computational vessel model. Cross sectional axial velocity profiles were calculated and measured for the midsinus and endsinus internal carotid artery. At both locations a skewed velocity profile with slow velocities at the outer vessel wall, medium velocities at the side walls and high velocities at the flow divider (inner) wall were observed. Qualitative comparison of the axial velocity patterns revealed no significant differences between simulations and in vitro measurements. Even quantitative differences such as for axial peak flow velocities were less than 10%. Secondary flow patterns revealed some minor differences concerning the form of the vortices but maximum circumferential velocities were in the same range for both methods.     

Fluid–structure interaction analysis of turbulent pulsatile flow within a layered aortic wall as related to aortic dissection

Turbulent pulsatile flow and wall mechanics were studied numerically in an axisymmetric three-layered wall model of a descending aorta. The transport equations were solved using the finite element formulation based on the Galerkin method of weighted residuals. A fully-coupled fluid–structure interaction (FSI) analysis was utilized in this investigation. We calculated Von Mises wall stress, streamlines and fluid pressure contours. The findings of this study show that peak wall stress and maximum shear stress are highest in the media layer. The difference in the elastic properties of contiguous layers of the wall of the aorta probably determines the occurrence of dissection in the media layer. Moreover, the presence of aortic intramural hematoma is found to have a significant effect on the peak wall stress acting on the inner layer.     

Approaches for treatment of aortic arch aneurysm,a numerical study

Aortic arch aneurysm is a complex pathology which requires coverage of one or more aortic arch vessels. In this study we explore the hemodynamic behavior of the aortic arch in aneurysmatic and treated cases with three currently available treatment approaches: Surgery Graft, hybrid Stent-Graft and chimney Stent Graft. The analysis included four models of the time-dependent fluid domains of aneurysmatic arch and of the surgery, hybrid and chimney endovascular techniques. Dimensions of the models are based on typical anatomy, and boundary conditions are based on typical physiological flow.The simulations used computational fluid dynamics (CFD) methods to delineate the time-dependent flow dynamics in the four geometric models.Results of velocity vectors, flow patterns, blood pressure and wall shear stress distributions are presented.The results delineate disturbed and recirculating flow in the aortic arch aneurysm accompanied with low wall shear stress and velocities, compared to a uniformly directed flow and nominal wall shear stress (WSS) in the model of Surgery graft. Out of the two endograft procedures, the hybrid procedure clearly exhibits better hemodynamic performances over the chimney model, with lower WSS, lower pressure drop and less disturbed and vortical flow regions. Although the chimney procedure requires less manufacturing time and cost, it is associated with higher risk rates, and therefore, it is recommended only for emergency cases. This study may shed light on the hemodynamic factors for these complications and provide insight into ways to improve the procedure.     

Morphological structure of the aortic wall in three Delphinid species with shallow or intermediate diving habits: Evidence for diving adaptation

Some modifications in the vascular system of marine mammals provide adaptive advantages for diving. This study analyses the organisation of the aortic wall in dolphins, observing artery changes in volume and blood pressure for diving behaviour. Samples of three aortic segments (ascending, thoracic and abdominal) of three dolphin species were processed for histological and morphometric studies. The three dolphin species used, striped dolphin (Stenella coeruleoalba), Atlantic spotted dolphin (Stenella frontalis) and common dolphin (Delphinus delphis), have shallow or intermediate diving habits. Our results indicated that the components of the aortic wall of the dolphins had different dispositions in the three selected segments. The aortic wall decreased in thickness along its length due to a loss of the lamellar units in the tunica media and a thinning of the main elements of the lamellar units along the artery. The life stage had little influence on the thickness of the aortic wall except for the ascending aorta. The weight, body length, species or sex of the specimen did not significantly influence the thickness of the wall or the lamellar units. In summary, the histological and morphometric aortic structure in dolphins, in relation to the studied parameters, seems to be similar to that previously described of terrestrial mammals such as pigs, except for a larger difference in the proportion of lamellar units between the ascending and thoracic segments.     

Fluid-structure interaction effects on sac-blood pressure and wall stress in a stented aneurysm

An aneurysm is a local artery ballooning greater than 50% of its nominal diameter with a risk of sudden rupture. Minimally invasive repair can be achieved by inserting surgically a stent-graft, called an endovascular graft (EVG), which is either straight tubular curved tubular or bifurcating. However post-procedural complications may arise because of elevated stagnant blood pressure in the cavity, i.e., the sac formed by the EVG and the weakened aneurysm wall In order to investigate the underlying mechanisms leading to elevated sac-pressures and hence to potentially dangerous wall stress levels and aneurysm rupture, a transient 3-D stented abdominal aortic aneurysm model and a coupled fluid-structure interaction solver were employed. Simulation results indicate that, even without the presence of endoleaks (blood flowing into the cavity), elevated sac pressure can occur due to complex fluid-structure interactions between the luminal blood flow, EVG wall, intra-sac stagnant blood, including an intra-luminal thrombus, and the aneurysm wall. Nevertheless, the impact of sac-blood volume changes due to leakage on the sac pressure and aneurysm wall stress was analyzed as well. While blood flow conditions, EVG and aneurysm geometries as well as wall mechanical properties play important roles in both sac pressure and wall stress generation, it is always the maximum wall stress that is one of the most critical parameters in aneurysm rupture prediction. All simulation results are in agreement with experimental data and clinical observations.