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.     

Large-Eddy simulation of pulsatile blood flow

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

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.     

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.     

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 &lt; 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.     

Simulation of a pulsatile non-Newtonian flow past a stenosed 2D artery with atherosclerosis

Atherosclerotic plaque can cause severe stenosis in the artery lumen. Blood flow through a substantially narrowed artery may have different flow characteristics and produce different forces acting on the plaque surface and artery wall. The disturbed flow and force fields in the lumen may have serious implications on vascular endothelial cells, smooth muscle cells, and circulating blood cells. In this work a simplified model is used to simulate a pulsatile non-Newtonian blood flow past a stenosed artery caused by atherosclerotic plaques of different severity. The focus is on a systematic parameter study of the effects of plaque size/geometry, flow Reynolds number, shear-rate dependent viscosity and flow pulsatility on the fluid wall shear stress and its gradient, fluid wall normal stress, and flow shear rate. The computational results obtained from this idealized model may shed light on the flow and force characteristics of more realistic blood flow through an atherosclerotic vessel.     

Non-Newtonian models for molecular viscosity and wall shear stress in a 3D reconstructed human left coronary artery

The capabilities and limitations of various molecular viscosity models, in the left coronary arterial tree, were analyzed via: molecular viscosity, local and global non-Newtonian importance factors, wall shear stress (WSS) and wall shear stress gradient (WSSG). The vessel geometry was acquired using geometrically correct 3D intravascular ultrasound (3D IVUS). Seven non-Newtonian molecular viscosity models, plus the Newtonian one, were compared. The WSS distribution yielded a consistent LCA pattern for nearly all non-Newtonian models. High molecular viscosity, low WSS and low WSSG values occurred at the outer walls of the major bifurcation in proximal LCA regions. The Newtonian blood flow was found to be a good approximation at mid- and high-strain rates. The non-Newtonian Power Law, Generalized Power Law, Carreau and Casson and Modified Cross blood viscosity models gave comparable molecular viscosity, WSS and WSSG values. The Power Law and Walburn-Schneck models over-estimated the non-Newtonian global importance factor I(G) and under-estimated the area averaged WSS and WSSG values. The non-Newtonian Power Law and the Generalized Power Law blood viscosity models were found to approximate the molecular viscosity and WSS calculations in a more satisfactory way.     

Three-phase CFD analytical modeling of blood flow

The behavior of blood cells in disturbed flow regions of arteries has significant relevance for understanding atherogenesis. However, their distribution with red blood cells (RBCs) and leukocytes is not so well studied and understood. Our three-phase computational fluid dynamics approach including plasma, RBCs, and leukocytes was used to numerically simulate the local hemodynamics in such a flow regime. This model has tracked the wall shear stress (WSS), phase distributions, and flow patterns for each phase in a concentrated suspension shear flow of blood. Unlike other computational approaches, this approach does not require dispersion coefficients as an input. The non-Newtonian viscosity model was applied to a wide physiological range of hematocrits, including low shear rates. The migration and segregation of blood cells in disturbed flow regions were computed, and the results compared favorably with available experimental data. The predicted higher leukocyte concentration was correlated with relatively low WSS near the stenosis having a high WSS. This behavior was attributed to flow-dependent interactions of the leukocytes with RBCs in pulsatile flow. This three-phase hemodynamic analysis may have application to vulnerable plaque formation in arteries with in vivo complex flow conditions.     

On the Characterization of a Non-Newtonian Blood Analog and Its Response to Pulsatile Flow Downstream of a Simplified Stenosis

Particle image velocimetry (PIV) was used to investigate the influence of a non-Newtonian blood analog of aqueous xanthan gum on flow separation in laminar and transitional environments and in both steady and pulsatile flow. Initial steady pressure drop measurements in laminar and transitional flow for a Newtonian analog showed an extension of laminar behavior to Reynolds number (Re) ~ 2900 for the non-Newtonian case. On a macroscale level, this showed good agreement with porcine blood. Subsequently, PIV was used to measure flow patterns and turbulent statistics downstream of an axisymmetric stenosis in the aqueous xanthan gum solution and for a Newtonian analog at Re ~ 520 and Re ~ 1250. The recirculation length for the non-Newtonian case was reduced at Re ~ 520 resultant from increased viscosity at low shear strain rates. At Re ~ 1250, peak turbulent intensities and turbulent shear stresses were dampened by the non-Newtonian fluid in close proximity to the blockage outlet. Although the non-Newtonian case’s recirculation length was increased at peak pulsatile flow, turbulent shear stress was found to be elevated for the Newtonian case downstream from the blockage, suggesting shear layer fragmentation and radial transport. Our findings conclude that the xanthan gum elastic polymer prolongs flow stabilization, which in turn emphasizes the importance of non-Newtonian blood characteristics on the resulting flow patterns in such cardiovascular environments.     

Hemodynamic analysis of coronary circulation in angulated coronary stenosis following stenting

The present study in angulated coronary stenosis used human in vivo hemodynamic parameters and computed simulation, both qualitatively and qualitatively, to evaluate the influence of flow velocity and wall shear stress (WSS) on coronary atherosclerosis, the changes of hemodynamic indices following coronary stenting, and their effect on evolving in-stent restenosis. Initial and follow-up coronary angiographies in patients with angulated coronary stenosis were performed (n=60). The optimal degree of coronary stenting for angulated coronary stenosis had two models, the less than 50% angle changed group (model 1, n=33) and the more than 50% angle changed group (model 2, n=27). This angle change was based on the percentage change of vascular angle between pre- and post-intracoronary stenting. The flow-velocity wave obtained from in vivo intracoronary Doppler study data was used for in vitro numerical simulation. Spatial and temporal patterns of the flow-velocity vector and recirculation area were drawn throughout the selected segment of coronary models. WSS of pre- and post-intracoronary stenting was calculated from three-dimensional computer simulation. As results, follow-up coronary angiogram demonstrated significant difference in the percentage of diameter stenosis between the two groups (group 1: 40.3 +/- 30.2 vs. group 2: 25.5 +/- 22.5%, p < 0.05). Negative shear area on 3D simulation, which is consistent with the re-circulation area of flow vector, was noted on the inner wall of the post-stenotic area before stenting. The negative WSS disappeared after stenting. High spatial and temporal WSS before stenting fell within the range of physiologic WSS after stenting. This finding was more prominent in model 2 (p < 0.01). The present study suggests that hemodynamic forces exerted by pulsatile coronary circulation, termed WSS, might affect the evolution of atherosclerosis within the angulated vascular curvature. Moreover, geometric characteristics, such as the angular difference between pre- and post- intracoronary stenting might define optimal rheologic properties for vascular repair after stenting.     

Experimental flow studies in an elastic Y-model.

To determine the causes and history of atherosclerosis it is necessary to understand the hemodynamic parameters of blood circulation. Hemodynamic parameters play an important role in the formation of atherosclerotic plaques, especially near bends and bifurcations where the flow separates from the wall. Here the flow is laminar and non-axial with eddies, secondary flow, flow separation and stagnation points. Stenoses are found predominantly in flow separation areas. Therefore, it is important to separately study the following flow parameters: steady and pulsatile flow, wall elasticity and non-Newtonian flow behavior of blood. A simplified silicon elastic y-model simulating the human carotid artery was used for the analysis of these parameters. This model can be used for numerical studies as well. Flow was visualized at steady flow using dyes and at pulsatile flow with a photoelastic apparatus and a birefringent solution. The local axial velocity at steady and pulsatile flow was determined with a one-component Laser-Doppler-Anemometer (LDA). Pulsatile flow was generated by a piston membrane pump. A glycerin-water solution was used to simulate the Newtonian flow behavior of blood. A DMSO-Separan water solution was used to simulate the non-Newtonian flow behavior. Pulsatile flow creates higher and lower shear rates so called oscillating shear rate compare to steady flow depending on the velocity amplitude. The non-Newtonian fluid showed a markedly different flow behavior than the Newtonian fluid especially in areas of flow separation. Shear gradients were calculated from these velocity measurements using a bicubic spline interpolation. Shear stresses were calculated from these velocity shear gradients and the viscosity of the non-Newtonian fluid at these shear gradients. At special areas, high shear stresses > 10 Pa were found. The elasticity of the model wall also influences the flow behavior. The measurements showed that the characteristics of pulsatile flow and the elasticity of the model wall should be observed concomitantly. This paper presents the steady and pulsatile flow with a Newtonian and non-Newtonian fluid in an elastic model.     

Unsteady simulation of distal blood flow in an end-to-side anastomosed coronary bypass graft with stenosis

In this paper, we report on the unsteady state modeling of blood flow in an end-to-side anastomosed bypass graft, which has a stenosis upstream from the junction. In coronary artery bypass grafting/surgery (CABG), new arteries are created in order to provide blood to the heart using other blood vessels as conduits to bypass the blocked section in the patient's coronary arteries. The failure of coronary artery bypass procedures has been attributed to both intimal hyperplasia (IH) and atherosclerosis. It is believed that these two phenomena are, in turn, related to the local hemodynamic factors. In this work, a three-dimensional computational fluid dynamics analysis is used to simulate the physiological blood flow through a model of a stenosed coronary bypass graft with the realistic assumption of non-Newtonian flow for human blood. For different flow repartitions and at different times of the cycle, both the recirculating areas and wall shear stress (WSS) are studied. Based on the different distribution of flow rates in the bypass graft and the host artery, the flow features are investigated and the influence of non-Newtonian behavior is discussed in terms of separation points, reattachment points, and the wall shear stresses. Various differences are observed based on the assumption of non-Newtonian behavior of blood, which have not been reported before when a simplified Newtonian approach is utilized.     

Flow and stress characteristics in rigid walled and compliant carotid artery bifurcation models

Computer simulation of pulsatile non-Newtonian blood flow has been carried out in different human carotid artery bifurcation models. In the first part of the investigation, two rigid walled models are analysed, differing in the bifurcation angle (wide angle and acute angle bifurcation) and in the shape of both the sinus (narrow and larger sinus width) and the bifurcation region (small and larger rounding of the flow divider), in order to contribute to the study of the geometric factor in atherosclerosis. The results show a significant difference in the wall shear stress and in the flow separation. Flow recirculation in the sinus is much more pronounced in the acute angle carotid. An important factor in flow separation is the sinus width. In the second part of the study, flow velocity and wall shear stress distribution have been analysed in a compliant carotid artery bifurcation model. In the mathematical model, the non-Newtonian flow field and the idealised elastic wall displacement are coupled and calculated iteratively at each time step. Maximum displacement of approximately 6% of the diastolic vessel diameter occurs at the side wall of the bifurcation region. The investigation demonstrates that the wall distensibility alters the flow feld and the wall shear stress during the systolic phase. Comparison with corresponding rigid wall results shows that flow separation and wall shear stress are reduced in the distensible wall model.     

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.     

Fontan术血流动力学非牛顿特性研究

目的 分析计算模拟中血液非牛顿特性对Fontan术后血流动力学的影响。方法 基于Fontan术后患者个体化三维血管模型,临床超声实测数据作为边界条件,分别选取常用的牛顿流体模型、非牛顿流体模型中的Casson模型与Carreau模型进行血流动力学模拟,计算血流分配比、能量损失、壁面切应力、非牛顿重要性系数等血流动力学参数,比较不同流体模型之间血流动力学参数差异。结果 流体模型对血流分配比影响小,非牛顿流体模型的能量损失较牛顿流体模型高,其中Casson模型最高。在下腔静脉中有明显回流、血流扰乱区域,并伴有低壁面切应力分布。在低流速时,牛顿流体模型下腔静脉血流扰乱更明显。非牛顿重要性系数显示在下腔静脉的非牛顿特性显著。结论 非牛顿特性在下腔静脉的低速回流区域影响显著,模拟患者个体化的Fontan血流动力学时应考虑血液的非牛顿特性。     

基于三维医学影像的脑动脉瘤内血液流动的数值模拟

目的 利用数值模拟研究具有病人特异性的脑动脉瘤内的血液流动,为脑动脉瘤的破裂风险的评价和动脉瘤介入栓塞后复发风险的评价提供帮助。方法 从两例脑动脉瘤病人的3D-RA数据中重建动脉瘤几何模型,血液流变学模型选择假塑性非牛顿流体模型,利用商用CFD软件Fluent对两例动脉瘤内的血液流动进行数值模拟。结果 数值模拟给出了动脉瘤内的流线图、重要截面上的速度分布图、壁面上的切应力分布和压力分布图。并且绘制了在收缩期时刻动脉瘤颈部和瘤顶部各20个点上的壁面切应力和压力的变化情况。结论 血流动力学因素如流速、压力、壁面切应力、流动对壁面的冲击状况等因素与动脉瘤的生长和破裂密切相关,而由于脑动脉瘤形态各异、载瘤动脉与动脉瘤体的几何关系复杂,所以具有病人特异性的数值模拟对于研究动脉瘤破裂和复发风险具有重要价值。动脉瘤颈部的壁面切应力和壁面切应力的波动的变化规律并不相同,需要进一步研究壁面切应力的波动与脑动脉瘤生长与破裂之间的定量关系。     

A numerical investigation on the steady and pulsatile flow characteristics in axi-symmetric abdominal aortic aneurysm models with some experimental evaluation

Steady and pulsatile flow characteristics in rigid abdominal aortic aneurysm (AAA) models were investigated computationally (using Fluent v. 4.3) over a range of Reynolds number (from 200 to 1600) and Womersley number (from 17 to 22). Some comparisons with measurements obtained by particle image velocimetry under the pulsatile flow conditions are also included. A sinusoidal inlet flow waveform 1 + sin omega t with thin inlet boundary layers was used to produce the required pulsatile flow conditions. The bulk features of the mean flow as well as some detailed features, such as wall shear stress distributions, are the foci of the present investigation. Recirculating vortices appeared at different phases of a flow cycle causing significant spatial and temporal variations in wall shear stresses and static pressure distributions. A high level of shear stresses usually appeared at the upstream and downstream ends of the bulge. Effects of pressure rise caused by the increase in cross-sectional area were transmitted into the downstream tube. Further simulation studies were conducted using simulated physiological waveforms under resting and exercise conditions so as to determine the possible implication of vortex dynamics inside the AAA model.     

A numerical investigation on the steady and pulsatile flow characteristics in axi-symmetric abdominal aortic aneurysm models with some experimental evaluation

Steady and pulsatile flow characteristics in rigid abdominal aortic aneurysm (AAA)models were investigated computationally (using Fluent v.4.3) over a range of Reynolds number (from 200 to 1600)and Womersley number (from 17 to 22). Some comparisons with measurements obtained by particle image velocimetry under the pulsatile flow conditions are also included. A sinusoidal inlet flow waveform 1+sin omega t with thin inlet boundary layers was used to produce the required pulsatile flow conditions. The bulk features of the mean flow as well as some detailed features, such as wall shear stress distributions, are the foci of the present investigation. Recirculating vortices appeared at different phases of a flow cycle causing significant spatial and temporal variations in wall shear stresses and static pressure distributions. A high level of shear stresses usually appeared at the upstream and downstream ends of the bulge. Effects of pressure rise caused by the increase in crosssectional area were transmitted into the downstream tube. Further simulation studies were conducted using simulated physiological waveforms under resting and exercise conditions so as to determine the possible implication of vortex dynamics inside the AAA model.     

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.     

Effect of magnetic field on haemodynamic perturbations in atherosclerotic coronary arteries

Haemodynamic perturbations including elevated blood viscosity, low and oscillatory shear stress are understood to be important pathogenic mediators in atherosclerosis. These haemodynamic abnormalities are influenced by the presence of a magnetic field. This study conducted computational fluid dynamics (CFD) analysis in 4 coronary artery models, derived from authentic human coronaries, with mild and moderate and severe stenosis severity. The aim was to investigate the effect of a static magnetic field of varying intensities on blood viscosity, areas of low wall shear stress (ALWSS), maximum wall shear stress (MWSS) and length and volume of flow recirculation zones. The results showed that the magnetic field results in both beneficial and detrimental changes in haemodynamics. The beneficial effects are lowered viscosity, decreased size of ALWSS and flow recirculation zones whereas the detrimental effect is increased MWSS. With increasing stenosis severity the effect of magnetic field becomes more prominent. An externally applied magnetic field can improve haemodynamics perturbations in human coronary arteries, especially in the setting of moderate-to-severe stenosis severity.