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

Currently the best indicator for surgical treatment of arterio-sclerosis 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 two-dimensional 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 low oscillatory 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。     

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.     

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.     

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.     

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.     

Computational haemodynamics analysis and comparison study of arterio-venous grafts

Haemodialysis arterio-venous graft failure is related to the development of stenotic lesions most commonly located near the venous anastomosis, especially in the toe region. 'Disturbed flow' interaction with the vessel wall surface, characterized by haemodynamic parameters based on the local wall shear stress or the radial pressure gradient, have been widely recognized as the trigger mechanism of a cascade of abnormal biological events leading to occlusive developments. Assuming incompressible laminar flow and rigid, in-plane vessel walls, validated haemodynamics are numerically simulated for a constant-diameter end-to-side base case, the Venaflo^TM graft, and an improved graft-end configuration. The geometric design of the new graft-end was based on the reduction of three time- and area-averaged haemodynamic parameters, i.e. the wall shear stress gradient, wall shear stress angle gradient, and radial pressuregradient. Considering the critical toeregion, the Venaflo^TM graft has demonstrated measurable improvements over the base case configuration in predictive computer simulations as well as in clinical trials. The performance improvement should be further enhanced with the modifications illustrated by the new design.     

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.     

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.     

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。     

Development of a novel endothelial cell-seeded endovascular stent for intracranial aneurysm therapy

The metallic stent has been widely used in endovascular treatment of intracranial aneurysms and arterial stenosis. Endothelialization at the neck of the aneurysm or stenotic lesion after stent deployment plays a pivotal role in preventing aneurysm recurrence, as well as local thrombus formation and restenosis. To deliver autologous endothelial cells and to promote the endothelialization on the luminal wall of the parent artery, we established an endothelial cell-seeded intracranial stent device. Endothelial cells were isolated from canine jugular vein and identified by FACS assay and immunohistochemistry. We demonstrated that the seeded endothelial cells formed a confluent endothelial layer on the stent's surface. After being brushed with 100 dyne/cm(2) of shear stress, we found that this endothelial layer remained intact for at least 48 h on the heparinized polymer coated stent, rather than the poly-lactic-acid coated stent (p < 0.05). The results suggest that an autologous endothelial cell-seeded stent may be a feasible and optimal tool for endothelial delivery during stenting and may overcome some limitations of the traditional bare stent in the treatment of intracranial aneurysms and arterial stenosis.     

The Influence of Valve Leaflet Stiffness Variability on Aortic Wall Shear Stress

Aortic stenosis is a common cardiac condition that impacts the aorta’s hemodynamics downstream of the affected valve. We sought to better understand how non-uniform stiffening of a stenotic aortic valve would affect the wall shear stress (WSS) experienced by the walls of the aorta and the residence time near the valve. Several experimental configurations were created by individually stiffening leaflets of a polymer aortic valve. These configurations were mounted inside an in vitro experimental setup. Digital particle image velocimetry (DPIV) was used to measure velocity profiles inside a model aorta. The DPIV results were used to estimate the WSS and residence time. Our analysis suggests that leaflet asymmetry greatly affects the amount of WSS by vectoring the systolic jet and stiffened leaflets have an increased residence time. This study indicates that valve leaflets with different stiffness conditions can have a more significant impact on wall shear stress than stenosis caused by the uniform increase in all three leaflets (and the subsequent increased systolic velocity) alone. This finding is promising for creating customizable (patient-specific) prosthetic heart valves tailored to individual patients.

     

Anticonstrictor effect of endothelium sensitivity to shear stress

The lumen of arterial vessels is controlled by shear stress at the endothelium; increased shear stress relaxes the smooth muscle thus evoking arterial dilatation. Since shear stress relates directly to flow rate and inversely to the third power of the internal diameter, a decrease in diameter at a constant arterial blood flow augments the shear stress which should result in smooth muscle relaxation counteracting the constriction. This anticonstrictor effect must be stronger the higher the arterial blood flow. To demonstrate the effect of endothelium sensitivity to shear stress on arterial constriction we compared constrictions of endothelium-intact femoral arteries of anaesthetized cats at different blood flow rates. An abrupt decrease in transmural pressure from 120 to 90 or 70 mm Hg at almost zero blood flow rate (where the shear stress mechanism is practically inactive) evoked a fast passive decrease in diameter with further progressive constriction. On the other hand, at flow rates of 8–15 ml/min, after passive constriction the artery began to dilate and the resultant constrictor effect appeared to be considerably smaller than in the virtual absence of flow. Analogously, responses to norepinephrine (3 · 10⁻⁷ or 10⁻⁶M) were smaller the higher the blood flow. The difference in the magnitudes of the responses at different flow rates was precisely equal to the value calculated using the experimental data characterizing the diameter/flow rate relation. Endothelium removal abolished the dependence of the magnitude of the constrictor responses on blood flow. These data suggest that the endothelium sensitivity to shear stress provides considerable inhibition of arterial constrictor responses, whatever the nature of constrictor stimulus.     

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