Numerical study of unsteady stenosis flow: parametric evaluation of power-law model

Currently the best indicator for surgical treatment of arteriosclerosis is the degree of stenosis. Although X-ray angiography is currently the standard, cost and morbidity are distinct disadvantages. By modelling stenosis and studying its biofluid mechanics, one can apply its results in the field of arterial disease research. This formed the motivation for this work. A non-Newtonian (power law) incompressible Navier-Stokes (N- S) solver was developed using the method of operator splitting and artificial compressibility. The vehicle used is the computational fluid dynamics (CFD) numerical library FASTFLO. The power-law model developed is then used to do a parametric study of the effect of 'n' on blood flow mechanics where 'n' is the power index that determines the haematocrit of blood. A pulsatile pressure wave over a cardiac cycle of a second was used to simulate transient flow over a hypothetical twodimensional stenotic geometry. By comparing the different velocity pressure, wall shear stress and viscosity profiles, it has been found when 'n' increases, the vortex formation and peak wall shear stress decreases (magnitudes of < 1.5 Pa). Since the formation of vortices and lowoscillatory wall shear stress on the stenotic wall is detrimental to the well-being of the arterial tract, it can therefore be inferred that there might be a relationship between the diseased state of blood (power law) and early genesis of atherosclerosis. However, the conclusion of this paper marks the advent of new research directions in this field of study.     

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.     

Coupling of shear–circumferential stress pulses investigation through stress phase angle in FSI models of stenotic artery using experimental data

Many cardiovascular diseases are closely associated with hemodynamic parameters. The main purpose of this study is mimicking a physiological blood flow in stenotic arteries to provide an understanding of hemodynamic parameters. An experimental setup was designed to produce original pulsatile flow and measure pressure pulse waves through a compliant tube. Moreover, a numerical model considering fluid–solid interaction was developed to investigate wall shear stress and circumferential stress waves, based on the results of the experiments. Results described elevated mean pressure by increasing stenosis severity especially at the critical obstacle of 50 %, which the pressure rose significantly and raised up by 10 mm Hg that may cause damage in endothelial cells. Increasing in stenosis severity led to: more negative wall shear stress and more oscillation of shear stress at the post-stenotic region and also more absolute value of angular phase difference between wall shear stress and circumferential stress waves at the stenotic throat. All of the aforementioned parameters determinant the endothelial cell pathology in predication of potential sites of progression of atherosclerotic plaques. Therefore, results can be applied in study of plaque growth and mechanisms of arterial remodeling in atherosclerosis.     

Unsteady stenosis flow prediction: a comparative study of non-Newtonian models with operator splitting scheme

This paper presents a comparative study of non-Newtonian and Newtonian models of blood. A non-Newtonian incompressible 2-D Navier-Stokes (N-S) solver has been developed using Fasttalk language within the Fastflo environment. It is based on the method of operator splitting with artificial compressibility technique. The Power law and Casson models have been used as the constitutive equations for blood with a hematocrit of approximately 45%. These two non-Newtonian models and the Newtonian model are used to simulate unsteady flow through a hypothetical stenotic geometry over an aperiodic time interval of 1 s. Through comparison of the results of the three models, it was found that the wall shear stress (WSS) distribution over the time interval was comparable for both non-Newtonian models. The peak WSS for the Newtonian model had the lowest value. The peak wall shear stress gradient (WSSG) for the Power law was the highest, followed by the Casson and Newtonian models. Flow characteristics such as higher pressure drop across the stenosis, location and movement of vortex were similar in all three models. Non-Newtonian effects were most significant in the vicinity of the stenosis.     

A new multiphysics model for the physiological responses of vascular endothelial cells to fluid shear stress

Vascular endothelial cell (VEC) responds to wall shear stress that has not only spatial variation, but also temporal gradient. To simplify the problem, we first studied how the calcium dynamics of VEC responded to the steady wall shear stress of varying magnitude in a stenosed artery. We then studied how the VEC responded to the periodic shear stress that had temporal variation, as in the pulsatile blood flow. To investigate the multiphysics model of VEC in vitro, we used a mathematical model for intracellular calcium dynamics and a computational fluid dynamics (CFD) method for arterial wall shear stress, either steady or periodic. The CFD results showed that for the steady stenotic flow, the wall shear stress in the recirculating flow was lower than the threshold value, 4 dyne/cm(2), at two particular points: flow separation and flow reattachment. For these subthreshold shear stresses, the peak value of the transient calcium response did not hit the normal saturated level, but reached a reduced magnitude. We investigated the effect of severity of stenosis (SOS) of the stenosed artery. For the pulsatile flow, the so-called shear stress slew rate or the temporal gradient of the first upsurge of the periodic flow was an important factor for the VEC calcium dynamics. The calcium response had a finite range of parameter for SOS and shear stress slew rate in which the calcium response was more sensitive than elsewhere, showing a sigmoid pattern.     

Computational modelling of blood flow through curved stenosed arteries

A computational model of three-dimensional blood flow in curved arteries with elliptic stenosis was developed. Two groups of models, (a) different angles of curvature and (b) degrees of stenosis, have been studied under typical conditions for stenosed coronary artery. Useful information on the haemodynamics has been obtained. Results of pressure drop show that the presence of the curvature augments the increased flow resistance due to stenotic lesions. The study also demonstrates the significant presence of secondary flow in a curved artery. In addition, the results have shown that the secondary flow in a curved artery brings about elevated shear stress on the vessel wall. These results indicated that both curvature and stenosis should be considered together by cardiologists to assess or quantify the severity of the stenosis. This study employed a powerful computer-aided design (CAD) package to construct the model and a commercial computational fluid dynamics (CFD) code for the analysis of blood flow in stenosed arteries. The long-term application of this form of research promises to be an effective tool for gaining insights into the pathology of arterial diseases.     

Computational modelling of blood flow through curved stenosed arteries

A computational model of three-dimensional blood flow in curved arteries with elliptic stenosis was developed. Two groups of models, (a) different angles of curvature and (b) degrees of stenosis, have been studied under typical conditions for stenosed coronary artery. Useful information on the haemodynamics has been obtained. Results of pressure drop show that the presence of the curvature augments the increased flow resistance due to stenotic lesions. The study also demonstrates the significant presence of secondary flow in a curved artery. In addition, the results have shown that the secondary flow in a curved artery brings about elevated shear stress on the vessel wall. These results indicated that both curvature and stenosis should be considered together by cardiologists to assess or quantify the severity of the stenosis. This study employed a powerful computer-aided design (CAD) package to construct the model and a commercial computational fluid dynamics (CFD) code for the analysis of blood flow in stenosed arteries. The long-term application of this form of research promises to be an effective tool for gaining insights into the pathology of arterial diseases.     

兔腹主动脉狭窄后剪切力的变化对局部内皮细胞形态和通透性的影响

兔腹主动脉狭窄至正常的55.2％，伊文思蓝对动脉染色，在扫描电镜下观察内皮细胞形态，计算细胞形态指数。动脉狭窄血管内流动壁面剪切率的分布由计算机数值模拟确定。结果表明，在紧接狭窄处的近远两侧，血流受到严重干扰，内皮细胞的形态和对伊文思蓝白蛋白复合物通透性发生明显改变。研究表明，这些改变不但与剪切应力的大小有关，还与血液流动的状态有关。这与动脉粥样硬化一般好发于血液流动受到干扰，流动发生分离区域的解剖观察一致。     

血流动力学的医学应用与发展

血流动力学是指血液在血管系统中流动的力学,主要研究血流量、血流阻力、血压、切应力、扰动流等,以及它们之间的相互关系,对人类生命健康具有重要的影响。血流动力学在血管的弯曲、狭窄、堵塞、分叉以及肿瘤的治疗等方面具有重要的临床研究意义。目前,血流动力学在动脉血管搭桥、冠状动脉狭窄、腹主动脉瘤、动脉粥样硬化、脑动脉肿瘤以及旋动流等方面引起广泛研究。伴随着血流动力学的深入研究,心脑血管的手术规划、介入治疗等得到快速发展,基于血流动力学的临床检测和治疗仪器也越来越多。血流动力学因素,如血管压力、血管阻力、血流量、壁面切应力、血液黏度、流动分离、湍流、涡流等对常见血管疾病以及术后并发症的影响机理正在逐步深入探索之中,并已经取得了一定成果。     

Lipid Deposition in Rat Aortas with Intraluminal Hemispherical Plug Stenosis : A Morphological and Biophysical Study

A new method was devised to create a stenosis in the rat abdominal aorta. To restrict blood flow, a hemispherical plug was inserted into the aorta through a renal artery. This type of intrinsic (intraluminal) stenosis minimizes possible intramural effects associated with external compression or ligation which severely deform the arterial wall. In the aorta of hypercholesterolemic rats, lipid deposits were distributed in crescent-shaped patches proximal and distal to the plug, whereas lipid deposition in the opposite aortic wall was inhibited. Based on enlarged physical scale models used to study the flow field, the regions of lipid deposition were found to coincide with regions of low shear stress, stagnation, and recirculation. Shear stress was elevated at the wall opposite the plug. These results show that when confounding mural effects are minimized, lipid deposition is promoted in regions of low shear stress with recirculation and inhibited in regions of elevated shear stress.     

The influences of stenosis on the downstream flow pattern in curved arteries

The influence of stenosis on the pulsatile blood flow pattern in curved arteries with stenosis at inner wall was investigated by computer simulations. Numerical calculations were performed with various values of physiological parameters to examine the effect of a stenosis on the hemodynamic characteristics such as secondary flow, flow separation, wall shear stress (WSS) and pressure drop. The results demonstrated that when the severity of a stenosis at the inner wall of a curved artery reaches a certain level, the flow pattern in the downstream of the artery shows a dramatic change compared to that of a curved artery with no stenosis. According to previous studies, a flow separation occurs at the inner wall of the bend in a curved artery. The present work reports an analysis of such a flow separation area at the inner wall of the post stenosis region in curved arteries with a stenosis. In addition, another area of flow separation with low and oscillating WSS and blood pressure at the outer wall in a downstream tube was also found and investigated. The observed characteristic change of the flow downstream may suggest a formation of a new plaque at the outer wall downstream.     

血管粘弹性对法推拿作用下血管切应力的影响

目的研究血管粘弹性对脉动血流在(扌衮)法推拿作用下切应力的影响.方法建立具有局部轴向运动狭窄的粘弹性血管中脉动血流模型.设血液为牛顿流体,血管壁为线性粘弹体.在(扌衮)法推拿作用下血管受水平外力作用形成轴向运动缓变狭窄,血流遵循线化Navier-stokes方程.结果粘弹性血管在(扌衮)法作用下,距离血管入口z=31 cm处的平均切应力、最大切应力和瞬时切应力以及最大狭窄下游血管段最大切应力随着血管粘性系数和手法频率的改变而有较大变化.结论(扌衮)法推拿作用下粘弹性血管的血管切应力有显著变化,这与中医推拿的活血化淤相吻合.     

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.     

Evaluation of the hemodynamics in straight 6-mm and tapered 6- to 8-mm grafts as upper arm hemodialysis vascular access

The present study is intended to investigate and compare the hemodynamics in two different sizes of hemodialysis arteriovenous grafts for upper arm hemodialysis vascular access: 8-mm tapered to 6-mm at the arterial side and straight 6 mm. A computational simulation approach is presented for this study, which is validated against the available experimental and numerical pressure measurements in the literature. The imposed boundary conditions at the arterial inlet and venous outlet boundaries of the models are physiological velocity and pressure waveforms, respectively. Blood flow fields and distribution patterns of the hemodynamic indices including wall shear stress (WSS) as one of the major hemodynamic parameters of the cardiovascular system and spatial wall shear stress gradient (SWSSG) as an indicator of disturbed flow patterns and hence susceptible sites of lesion developments are analyzed and compared between the two grafts. The tapered 6- to 8-mm graft seemingly is associated with less disturbed flow patterns within the venous anastomosis (VA) and the vein downstream while benefiting from higher blood flow rates within. Also, it shows a definitive advantage in terms of WSS and SWSSG distribution patterns around the VA and throughout the vein downstream with significantly lower values, which reduce the risk of thrombosis formation and stenotic lesion developments. The only disadvantage encountered in using 6- to 8-mm tapered graft is higher values of hemodynamic parameters at the arterial junction attributable to its significantly higher mean blood flow rate within. The results clearly indicate that the tapered 6- to 8-mm graft entirely outperforms straight 6-mm graft hemodynamically as an upper arm hemodialysis vascular access graft and confirms clinical data in the literature, which suggests advantageous use of tapered 6- to 8-mm grafts in the creation of upper arm brachioaxillary hemodialysis vascular access grafts in selected groups of patients with expectably higher patency rates and lower complications.     

弹性动脉狭窄血管内血液流动的ALE方法分析

针对弹性动脉狭窄血管中血液的流动状况,采用任意拉格朗日-欧拉方法(ALE),在给定相同的边界条件下模拟出了弹性血管和刚性血管中血流速度和压力的变化情况,分析了不同狭窄程度模型的血流状态.结果表明:随着动脉的狭窄程度增加,其中心流速越来越大,窄前压力逐渐升高,窄后压力逐渐降低,狭窄前后的压差单调增加;刚性血管无法对人体正常生理状态进行比较好的模拟,其计算所得结论与实际情况差距较大.说明ALE方法对血液流动的数值研究是可行的.     

Haemodynamic of blood flow through stenotic aortic valve

Aortic valve (AV) stenosis is described as the deposition of calcium within the valve leaflets. With the growth of stenosis, haemodynamic, mechanical performances of the AV and blood flow through the valve are changed. In this study, we proposed two fluid–structure interaction (FSI) finite element (FE) models. The hyperelastic material model was considered for leaflets tissue. The leaflet tissue was considered stiffer in stenotic valve than the healthy leaflets because of its calcium content. Therefore, the valve could not open completely and this led to a decrease in the orifice area of the valve. The orifice area decreased from 2.4?cm² for the healthy AV to 1.4?cm² for the stenosis case. Mean pressure gradient increased in mid systole and the axial velocity experienced a three times increment in magnitude. Higher blood shear stress magnitudes were observed in stenotic valve due to the structure of the leaflet. In addition, strain concentration and higher stress values were observed on the leaflets in stenotic valve and the effective stress was greater than healthy case. In addition, pressure and velocity results were consistent with the echocardiography data literature. We have compared the performance of healthy and stenotic AV models during a complete cardiac cycle. Although improvements are still needed, there was good agreement between our computed data and other published studies.     

Adaptation and remodeling of vascular wall; biomechanical response to hypertension

Living organs, tissues, and cells functionally adapt themselves to mechanical demands, and remodel by changing geometry, structure, and properties. The key factor for this phenomenon is “Mechanical Stress”. Major stresses applied to blood vessels inside the body are: (1) hoop stress induced by blood pressure, that is normal stress in the wall circumferential direction, (2) wall shear stress developed by blood flow, and (3) axial stress by elongation in the axial direction. This review article deals with biomechanical studies on the responses of arterial and venous wall to the elevation of blood pressure. One of the specific biomechanical manifestations to arterial wall adaptation in response to hypertension is wall hypertrophy. This restores circumferential wall stress, i.e. hoop stress, at in vivo operating pressure to a normal value, and changes arterial stiffness to an optimal level. Vascular smooth muscle cells are activated by hypertension. Essentially similar phenomena are also observed in venous wall.     

椎动脉狭窄临床病例介入治疗前后椎基底动脉血流状况分析

目的:基于血液和弹性血管壁相互作用的流固耦合方法,探究1例椎动脉颅内段狭窄的临床病例支架植入前后椎基底动脉的血流动力学特性。方法:应用医学建模软件对二维CT数据进行三维重建,得到支架植入前后的椎基底动脉血管模型,采用流固耦合方法对支架植入前后的椎基底动脉血流特性进行数值模拟,分析椎基底动脉的血流动力学特性。结果:支架植入前后椎基底动脉的血液流场、血液压力、血管壁面切应力以及管壁形变量有显著的变化。在支架植入后,基底动脉中间部位两侧受力变得均匀,椎基底动脉内血流速度明显增大,支架植入处压力增大,支架上游压力和支架处切应力减小。结论:在介入治疗后,椎基底动脉内的血流环境及受力情况得到明显改善,当椎动脉发生狭窄后应及时干预治疗,避免累及基底动脉和后循环系统。     

Effect of Stenosis Asymmetry on Blood Flow and Artery Compression: A Three-Dimensional Fluid-Structure Interaction Model

A nonlinear three-dimensional thick-wall model with fluid-structure interactions is introduced to simulate blood flow in carotid arteries with an asymmetric stenosis to quantify the effects of stenosis severity, eccentricity, and pressure conditions on blood flow and artery compression (compressive stress in the wall). Mechanical properties of the tube wall are measured using a thick-wall stenosis model made of polyvinyl alcohal hydrogel whose mechanical properties are close to that of carotid arteries. A hyperelastic Mooney–Rivlin model is used to implement the experimentally measured nonlinear elastic properties of the tube wall. A 36.5% pre-axial stretch is applied to make the simulation physiological. The Navier–Stokes equations in curvilinear form are used for the fluid model. Our results indicate that severe stenosis causes critical flow conditions, high tensile stress, and considerable compressive stress in the stenosis plaque which may be related to artery compression and plaque cap rupture. Stenosis asymmetry leads to higher artery compression, higher shear stress and a larger flow separation region. Computational results are verified by available experimental data. © 2003 Biomedical Engineering Society. PAC2003: 8719Uv, 8710+e     

Hemodynamically Driven Stent Strut Design

Stents are deployed to physically reopen stenotic regions of arteries and to restore blood flow. However, inflammation and localized stent thrombosis remain a risk for all current commercial stent designs. Computational fluid dynamics results predict that nonstreamlined stent struts deployed at the arterial surface in contact with flowing blood, regardless of the strut height, promote the creation of proximal and distal flow conditions that are characterized by flow recirculation, low flow (shear) rates, and prolonged particle residence time. Furthermore, low shear rates yield an environment less conducive for endothelialization, while local flow recirculation zones can serve as micro-reaction chambers where procoagulant and pro-inflammatory elements from the blood and vessel wall accumulate. By merging aerodynamic theory with local hemodynamic conditions we propose a streamlined stent strut design that promotes the development of a local flow field free of recirculation zones, which is predicted to inhibit thrombosis and is more conducive for endothelialization.