Dynamic response of pulsatile flow of blood in a stenosed tapered artery

The aim of this paper is to throw some light on the rheological study of pulsatile blood flow in a stenosed tapered arterial segment. Arterial wall is considered to be rigid and flexible separately for improving the similarity to the in vivo situation. The streaming blood is considered to be Newtonian. The governing nonlinear equations of motion are sought using the well‐known stream function‐vorticity method and are solved numerically by finite difference technique. Important rheological parameters, such as axial velocity component, wall shear stress, and flow separation region are estimated in the neighborhood of the stenosis. Effects of stenosis height, vessel tapering, and wall flexibility on the blood flow are investigated properly and are explained in detail through their graphical representations.     

Power law fluid model for blood flow through a tapered artery with a stenosis

In the present paper, blood flow through a tapered artery with a stenosis is analyzed, assuming the flow is steady and blood is treated as non-Newtonian power law fluid model. Exact solution has been evaluated for velocity, resistance impedance, wall shear stress and shearing stress at the stenosis throat. The graphical results of different types of tapered arteries (i.e. converging tapering, diverging tapering, non-tapered artery) have been examined for different parameters of interest. Some special cases of the problem are also presented.     

Investigation of physiological pulsatile flow in a model arterial stenosis using large-eddy and direct numerical simulations

Physiological pulsatile flow in a 3D model of arterial stenosis is investigated by using large eddy simulation (LES) technique. The computational domain chosen is a simple channel with a biological type stenosis formed eccentrically on the top wall. The physiological pulsation is generated at the inlet using the first harmonic of the Fourier series of pressure pulse. In LES, the large scale flows are resolved fully while the unresolved subgrid scale (SGS) motions are modelled using a localized dynamic model. Due to the narrowing of artery the pulsatile flow becomes transition-to-turbulent in the downstream region of the stenosis, where a high level of turbulent fluctuations is achieved, and some detailed information about the nature of these fluctuations are revealed through the investigation of the turbulent energy spectra. Transition-to-turbulent of the pulsatile flow in the post stenosis is examined through the various numerical results such as velocity, streamlines, velocity vectors, vortices, wall pressure and shear stresses, turbulent kinetic energy, and pressure gradient. A comparison of the LES results with the coarse DNS are given for the Reynolds number of 2000 in terms of the mean pressure, wall shear stress as well as the turbulent characteristics. The results show that the shear stress at the upper wall is low just prior to the centre of the stenosis, while it is maximum in the throat of the stenosis. But, at the immediate post stenotic region, the wall shear stress takes the oscillating form which is quite harmful to the blood cells and vessels. In addition, the pressure drops at the throat of the stenosis where the re-circulated flow region is created due to the adverse pressure gradient. The maximum turbulent kinetic energy is located at the post stenosis with the presence of the inertial sub-range region of slope −5/3.     

Mathematical modelling of blood flow through an overlapping arterial stenosis

Of concern in the paper is a theoretical study of blood flow in an arterial segment in the presence of a time-dependent overlapping stenosis using an appropriate mathematical model. A remarkably new shape of the stenosis in the realm of the formation of the arterial narrowing caused by atheroma is constructed mathematically. The artery is simulated as an elastic (moving wall) cylindrical tube containing a viscoelastic fluid representing blood. The unsteady flow mechanism of the present investigation is subjected to a pulsatile pressure gradient arising from the normal functioning of the heart. The equations governing the motion of the system are sought in the Laplace transform space and their relevant solutions supplemented by the suitable boundary conditions are obtained numerically in the transformed domain through the use of an appropriate finite difference technique. Laplace inversion is also carried out by employing numerical techniques. A thorough quantitative analysis is performed at the end of the paper for the flow velocity, the flux, the resistive impedances, and the wall shear stresses together with their variations with the time, the pressure gradient, and the severity of the stenosis in order to illustrate the applicability of the present mathematical model under consideration.     

Factors Influencing the Disturbed Flow Patterns Downstream of Curved Atherosclerotic Arteries

Pulsatile blood flows in curved atherosclerotic arteries are studied by com- puter simulations.Computations are carried out with various values of physiological parameters to examine the effects of flow parameters on the disturbed flow patterns downstream of a curved artery with a stenosis at the inner wall.The numerical re- suits indicate a strong dependence of flow pattern on the blood viscosity and inlet flow rate,while the influence of the inlet flow profile to the flow pattem in downstream is negligible.     

动脉中血液脉动流的一种分析方法

动脉中的血液流动被分解为平衡状态(相当于平均压定常流状态)和叠加在平衡状态上的周期脉动流,利用Fung的血管应变能密度函数分析血管壁在平衡状态下的应力-应变关系,确定相对于平衡状态血管作微小变形所对应的周向弹性模量和轴向弹性模量,并建立在脉动压力作用下相应的管壁运动方程,与线性化Navier-Stokes方程联立,求得血液流动速度和血管壁位移的分析表达式,详细讨论血管壁周向和轴向弹性性质差异对脉博波、血液脉动流特性以及血管壁运动的影响.     

Numerical computation of pulsatile flow through a locally constricted channel

This paper deals with the numerical solution of a pulsatile laminar flow through a locally constricted channel. A finite difference technique has been employed to solve the governing equations. The effects of the flow parameters such as Reynolds number, flow pulsation in terms of Strouhal number, constriction height and length on the flow behaviour have been studied. It is found that the peak value of the wall shear stress has significantly changed with the variation of Reynolds numbers and constriction heights. It is also noted that the Strouhal number and constriction length have little effect on the peak value of the wall shear stress. The flow computation reveals that the peak value of the wall shear stress at maximum flow rate time in pulsatile flow situation is much larger than that due to steady flow. The constriction and the flow pulsation produce flow disturbances at the vicinity of the constriction of the channel in the downstream direction.     

Mass transfer to blood flowing through arterial stenosis

The present investigation deals with a mathematical model representing the mass transfer to blood streaming through the arteries under stenotic condition. The mass transport refers to the movement of atherogenic molecules, that is, blood-borne components, such as oxygen and low-density lipoproteins from flowing blood into the arterial walls or vice versa. The blood flowing through the artery is treated to be Newtonian and the arterial wall is considered to be rigid having differently shaped stenoses in its lumen arising from various types of abnormal growth or plaque formation. The nonlinear unsteady pulsatile flow phenomenon unaffected by concentration-field of the macromolecules is governed by the Navier–Stokes equations together with the equation of continuity while that of mass transfer is controlled by the convection-diffusion equation. The governing equations of motion accompanied by appropriate choice of the boundary conditions are solved numerically by MAC(Marker and Cell) method and checked numerical stability with desired degree of accuracy. The quantitative analysis carried out finally includes the respective profiles of the flow-field and concentration along with their distributions over the entire arterial segment as well. The key factors like the wall shear stress and Sherwood number are also examined for further qualitative insight into the flow and mass transport phenomena through arterial stenosis. The present results show quite consistency with several existing results in the literature which substantiate sufficiently to validate the applicability of the model under consideration.      

Mass transfer to blood flowing through arterial stenosis

The present investigation deals with a mathematical model representing the mass transfer to blood streaming through the arteries under stenotic condition. The mass transport refers to the movement of atherogenic molecules, that is, blood-borne components, such as oxygen and low-density lipoproteins from flowing blood into the arterial walls or vice versa. The blood flowing through the artery is treated to be Newtonian and the arterial wall is considered to be rigid having differently shaped stenoses in its lumen arising from various types of abnormal growth or plaque formation. The nonlinear unsteady pulsatile flow phenomenon unaffected by concentration-field of the macromolecules is governed by the Navier–Stokes equations together with the equation of continuity while that of mass transfer is controlled by the convection-diffusion equation. The governing equations of motion accompanied by appropriate choice of the boundary conditions are solved numerically by MAC(Marker and Cell) method and checked numerical stability with desired degree of accuracy. The quantitative analysis carried out finally includes the respective profiles of the flow-field and concentration along with their distributions over the entire arterial segment as well. The key factors like the wall shear stress and Sherwood number are also examined for further qualitative insight into the flow and mass transport phenomena through arterial stenosis. The present results show quite consistency with several existing results in the literature which substantiate sufficiently to validate the applicability of the model under consideration.     

Nonlinear mathematical analysis for blood flow in a constricted artery under periodic body acceleration

This study analyses the pulsatile flow of blood through mild stenosed narrow arteries, treating the blood in the core region as a Casson fluid and the plasma in the peripheral layer as a Newtonian fluid. Perturbation method is employed to solve the resulting coupled implicit system of non-linear partial differential equations. The expressions for shear stress, velocity, wall shear stress, plug core radius, flow rate and longitudinal impedance to flow are obtained. The effects of pulsatility, stenosis depth, peripheral layer thickness, body acceleration and non-Newtonian behavior of blood on these flow quantities are discussed. It is noted that the plug core radius, wall shear stress and longitudinal impedance to flow increase as the yield stress and stenosis depth increase and they decrease with the increase of the body acceleration, pressure gradient, width of the peripheral layer thickness. It is observed that the plug flow velocity and flow rate increase with the increase of the pulsatile Reynolds number, body acceleration, pressure gradient and the width of the peripheral layer thickness and the reverse behavior is found when the yield stress, stenosis depth and lead angle increase. It is also recorded that the wall shear stress and longitudinal impedance to flow are considerably lower for the two-fluid Casson model than that of the single-fluid Casson model. It is found that the presence of body acceleration and peripheral layer influences the mean flow rate and mean velocity by increasing their magnitude significantly in the arteries.     

Mathematical modeling of pulsatile flow of non-Newtonian fluid in stenosed arteries

The pulsatile flow of blood through mild stenosed artery is studied. The effects of pulsatility, stenosis and non-Newtonian behavior of blood, treating the blood as Herschel–Bulkley fluid, are simultaneously considered. A perturbation method is used to analyze the flow. The expressions for the shear stress, velocity, flow rate, wall shear stress, longitudinal impedance and the plug core radius have been obtained. The variations of these flow quantities with different parameters of the fluid have been analyzed. It is found that, the plug core radius, pressure drop and wall shear stress increase with the increase of yield stress or the stenosis height. The velocity and the wall shear stress increase considerably with the increase in the amplitude of the pressure drop. It is clear that for a given value of stenosis height and for the increasing values of the stenosis shape parameter from 3 to 6, there is a sharp increase in the impedance of the flow and also the plots are skewed to the right-hand side. It is observed that the estimates of the increase in the longitudinal impedance increase with the increase of the axial distance or with the increase of the stenosis height. The present study also brings out the effects of asymmetric of the stenosis on the flow quantities.     

A micropolar fluid model of blood flow through a tapered artery with a stenosis

A nonlinear two‐dimensional micropolar fluid model for blood flow in a tapered artery with a single stenosis is considered. This model takes into account blood rheology in which blood consists of microelements suspended in plasma. The classical Navier–Stokes theory is inadequate to describe the microrotations or particles' spin of such suspension in a viscous medium. The governing equations involving unsteady nonlinear partial differential equations are solved using a finite difference scheme. A quantitative analysis performed through numerical computation shows that the axial velocity profile and the flow rate decrease and the wall shear stress increases once the artery is narrower in the presence of the polar effect. Furthermore, the taper angle certainly bears the potential to influence the velocity and the flow characteristics to considerable extent. Copyright © 2010 John Wiley & Sons, Ltd.     

Study of magnetohydrodynamic pulsatile flow in a constricted channel

The present work reports the study of steady and pulsatile flows of an electrically conducting fluid in a differently shaped locally constricted channel in presence of an external transverse uniform magnetic field. The governing nonlinear magnetohydrodynamic equations simplified for low conducting fluids are solved numerically by finite difference method using stream function-vorticity formulation. The analysis reveals that the flow separation region is diminished with increasing values of magnetic parameter. It is noticed that the increase in the magnetic field strength results in the progressive flattening of axial velocity. The variations of wall shear stress with increasing values of the magnetic parameter are shown for both steady and pulsatile flow conditions. The streamline and vorticity distributions in magnetohydrodynamic flow are also shown graphically and discussed.     

Pulsatile flow of Herschel–Bulkley fluid through catheterized arteries – A mathematical model

The pulsatile flow of blood through catheterized artery has been studied in this paper by modeling blood as Herschel–Bulkley fluid and the catheter and artery as rigid coaxial circular cylinders. The Herschel–Bulkley fluid has two parameters, the yield stress θ and the power index n. Perturbation method is used to solve the resulting quasi-steady nonlinear coupled implicit system of differential equations. The effects of catheterization and non-Newtonian nature of blood on yield plane locations, velocity, flow rate, wall shear stress and longitudinal impedance of the artery are discussed. The existence of two yield plane locations is investigated and their dependence on yield stress θ, amplitude A, and time t are analyzed. The width of the plug core region increases with increasing value of yield stress at any time. The velocity and flow rate decrease, whereas wall shear stress and longitudinal impedance increase for increasing value of yield stress with other parameters held fixed. On the other hand, the velocity, flow rate and wall shear stress decrease but resistance to flow increases as the catheter radius ratio (ratio of catheter radius to vessel radius) increases with other parameters fixed. The results for power law fluid, Newtonian fluid and Bingham fluid are obtained as special cases from this model.     

存在周围粘弹组织约束时动脉管内的脉动流

由于在动脉管外侧牢牢地粘附着结缔组织,而且这些结缔组织是一种粘弹体。为了分析周围粘弹组织对动脉中脉动流的影响,本文将周围结缔组织考虑为Voigt粘弹体,由动脉管内血液流动方程(Navier-Stokes方程)与管壁运动方程(Lamb方程)导出动脉管中脉搏波波速的一般表达式与管内脉动流的速度表达式。Womersley关于不存在周围组织约束的结果[4]与仅考虑周围组织是纯弹性体的结果[6]都做为本文结果的特例而包含在本文的结果之中。     

Application of Adomian's approximation to blood flow through arteries in the presence of a magnetic field

The present investigation deals with the application of Adomian's decomposition method to blood flow through a constricted artery in the presence of an external transverse magnetic field which is applied uniformly. The blood flowing through the tube is assumed to be Newtonian in character. The expressions for the two-term approximation to the solution of stream function, axial velocity component and wall shear stress are obtained in this analysis. The numerical solutions of the wall shear stress for different values of Reynold number and Hartmann number are shown graphically. The solution of this theoretical result for a particular Hartmann number is compared with the integral method solution of Morgan and Young [17].     

恒磁场对刚性圆直管中脉动流的影响*

本文研究了恒磁场对于刚性圆直管中脉动流的影响,并根据现有的实验资料考虑了磁场对于血液粘度的影响,给出了恒磁场作用下刚性圆直管脉动流的分析解以及恒磁场对刚性圆直管中的流速分布、流量以及阻抗的影响的计算结果.这些结果对于深入研究磁场对于血液动力学的影响具有一定参考价值.     

流固耦合作用下狭窄颈动脉内非Newton血流分析

采用计算流体力学方法分别对6种狭窄率的颈动脉内非Newton瞬态血流进行流固耦合数值分析.研究了狭窄率对颈动脉内血流动力学分布的影响,以探索狭窄率与颈动脉内粥样斑块形成的关系.结果表明,狭窄率不同的颈动脉内血流动力学分布特性明显不同,与0.05,0.1,0.2,0.3和04这5种狭窄率的颈动脉内血流动力学分布特性相比,狭窄率为0.5的颈动脉内血流动力学分布独特,狭窄部位附近区域存在面积较大的低速涡流区;复杂血流作用下,该区域分布低壁面压力,异常壁面切应力,较大管壁形变量和von Mises应力;血流速度低使血液中脂质、纤维蛋白等大分子易沉积,低壁面压力引起的明显“负压”效应引发脑部供血障碍,异常壁面切应力作用下粥样斑块易破裂与脱落,并堵塞脑血管,较大的von Mises应力易引起应力集中,导致血管破裂,为脑卒中发生提供有利条件.因此,狭窄率越大对颈动脉内血流动力学分布的影响越显著,促进颈动脉粥样斑块形成与发展,并引发缺血性脑卒中.     

A lattice Boltzmann model for blood flows

A lattice Boltzmann model for blood flows is proposed. The lattice Boltzmann Bi-viscosity constitutive relations and control dynamics equations of blood flow are presented. A non-equilibrium phase is added to the equilibrium distribution function in order to adjust the viscosity coefficient. By comparison with the rheology models, we find that the lattice Boltzmann Bi-viscosity model is more suitable to study blood flow problems. To demonstrate the potential of this approach and its suitability for the application, based on this validate model, as examples, the blood flow inside the stenotic artery is investigated.     

Numerical simulation of Casson fluid flow through differently shaped arterial stenoses

The present investigation deals with a mathematical model of blood flow through an asymmetric (about its narrowest point) arterial constriction obtained from casting of a mildly stenosed artery. The flowing blood is represented as the suspension of all red cells (erythrocytes) in plasma assumed to be Casson fluid, while the arterial wall is considered to be rigid having differently shaped stenoses in its lumen arising from various types of abnormal growth or plaque formation. The governing equations of motion accompanied by the appropriate choice of the boundary conditions are solved numerically by Marker and Cell method in order to compute the physiologically significant quantities with desired degree of accuracy. The necessary checking for numerical stability has been incorporated in the algorithm for better precision of the results computed. The quantitative analyses have been carried out finally with the inclusion of the respective profiles of the flow field over the entire arterial segment as well. The key factors such as the wall shear stress, the pressure drop and the velocity profiles are exhibited graphically and examined thoroughly for qualitative insight into blood flow phenomena through arterial stenosis.