局部扩张动脉管血液振荡流的切应力分布

本文求解局部缓慢扩张动脉管中血液振荡流的基本方程，得到血管内血液的流速与压力梯度的关系。通过导出压力梯度沿局部扩张管轴向的变化特性。建立利用扩张段上游血管均匀段中心流速波形确定局部扩张管中血液流的速度和切应力分布的方法，文章以人体颈动脉余弦扩张为例进行分析。详细讨论了局部扩张对血管壁切应力及其梯度分布的影响。数值结果表明，在与刚性均匀管中管壁切应力沿轴向保持不变不同，在局部扩张段，管壁切应力将随着血管半径的增大而减小，因而管壁切应力梯度一般不为零，甚至在某些位置达到相当大的数值。另外，随着血管扩张程度的增加，管壁切应力还将进一步减小，而且管壁切应力梯度也将进一步增大，血管扩张导致管壁切应力的这些变化将直接影响血管壁的结构和功能，使其产生适应性的变化。     

刚性圆管中血液周期振荡流的切应力分布

本文通过求解圆管内血液振荡流的基本方程，求得圆管内血液流的压力梯度与切应力之间的关系式。在此基础上，详细讲座了圆管中轴向流速和切变率谐波的变化规律，指出流速谐波和切变率谐波的幅值都将随着谐波次数的增大而逐渐减小。为了使所得结果便于应用。文章通过管轴向中心线流速与压力梯度之间的关系式，进一步给出一种利用管轴向中心线流速计算管内切应力分布的简便方法。该方法用于检测活体血管内血液振荡流的切应力分布，具有操作简单，精度较高的优点。最后，以人体颈动脉为例，讨论血液周期振荡流的切应力的分布特性。发现在任意时刻，除了邻近管壁处切应力急剧增大到一定数值之外，沿管截面切应力分布相当均匀且接近于零，呈现出与定常流不同的切应力分布特征。     

一种确定均匀动脉壁面切应力的非线性方法

从Ling和Atabek提出的``局部流'理论出发，提出一种利用测量血液黏度、管轴上 的血流速度、压力和管径波形计算均匀动脉管壁切应力的非线性方法. 将这种方法与柳兆荣 等提出的利用测量血液黏度、管轴上的血流速度和平均管径计算切应力的线性方法比较，结 果表明，当管壁脉动幅度较小时，两种方法计算的压力梯度、流速剖面和管壁切应力差别较 小；而当管壁脉动幅度增大时，两种方法计算的压力梯度、流速剖面和管壁切应力差别增大. 对于小幅脉动均匀动脉，用线性方法计算管壁切应力有较高的精度；而对于大变形 均匀动脉，则需要考虑非线性因素对管壁切应力的影响. 由于作为输入量的血液黏度、轴心 血流速度、压力波形和管径波形可在活体上通过无损伤或微损伤的检测方法得到， 所提出的计算切应力的方法为在体或离体研究切应力与动脉重建的关系提供了方法学基础.     

用管轴流速确定动脉中血液振荡流的速度剖面

本文通过求解圆管内血液振荡流的基本方程，求得圆管内血液流的速度与压力梯度之间的关系式，文章提出一种利用管轴外流速计算管内压力梯度，进而确定血液振荡流动速度分布的方法，该方法用于检测活体血管内血液振荡流的速度剖面，具有操作简单，精度较高的优点，最后，以人体颈动脉为例，讨论血液周期振荡流的速度分布特征，发现在任意时刻，除了邻近管壁速度迅速降为零之外，沿管截面速度分布相当均匀，呈现出与定常流不同的速度分布特征。     

弯曲狭窄管内血液流的分析

与血管狭窄有关的异常血液动力学特征在血管疾病的发生和发展过程中起着重要的作用,由于血管狭窄和弯曲的综合影响,将会出现一系列有趣的流体力学现象,本文研究具有对称狭窄的弯曲小动脉内定常血液流动,在一定的假设条件下,直接从支配血液流动的Navier-Stokes方程求出问题的摄动解,由此求得弯曲狭窄管內血液流动的轴向速度、二次流速度及压力梯度等分析表达式,并进一步求得轴向和周向血管壁切应力。本文的结果是先前有关狭窄直管和弯曲均匀管流动研究的拓广。     

动脉压对静脉血管壁周向应力分布的影响

自体静脉是病变动脉管段常用的替代物。移植后因承受压力急剧升高引起的静脉管壁应力改变是影响移植手术的主要因素之一。为了比较移植前(静脉压作用下)和移植后(动脉压作用下)静脉管壁的周向应力分布，本文通过检测一定轴向伸长比条件下静脉管的p(压力)——V(容积)试验数据，利用3参数的应变能密度函数对实验数据进行拟合，进而求得静脉管壁的残余应力和沿血管壁的周向应力分布。对狗的股静脉和颈静脉的分析结果表明，在动脉压作用下静脉管壁周向应力将急剧增大。与处于静脉压环境相比，处于动脉压环境中的颈静脉管周向应力将增大差不多2个数量级。计算结果还显示，静脉管壁残余应力的数值虽然比动脉管壁的相应值小很多，但是与动脉管相同，血管壁残余应力依然对静脉管壁上的周向应力分布影响显著，残余应力的存在将大大削弱在静脉管内壁处的周向应力集中，使周向应力沿静脉管壁厚的变化梯度明显减小。     

动脉狭窄对血液流速的影响

为了定量计算动脉局部狭窄对动脉管中血液流动速度的影响，本文分别对狭窄区域内定常流和非定常流动进行了求解，得出了狭窄区域内定常流和脉动流的速度表达式。本文将均匀段的流速形经Ｆｏｕｒｉｅｒ分解成定常和脉动两部分，然后分别计算出狭窄区域内对应的定常和脉动流速，经Ｆｏｕｒｉｅｒ合成还原成流速时域波形，同时针对各种情况将不同狭窄对不同的流速波形的作了分析比较。     

脉劝流条件下血管壁的应力分布

为了分析血液-血管耦合运动所产生血液脉动压力载荷对血管壁应力分布的影响,利用线性化的血液-血管耦合运动方程的Womersley解,导得血液脉动压力载荷下的血管壁Green应变,同时利用Fung的血管壁应变能密度函数,导得相应血管壁应力分布的一般表达式.数值结果表明,在脉动流条件下,当考虑血液-血管耦合运动时,血管壁中周向应力最大,轴向应力居中,径向应力最小;血管壁的残余应力将明显减小血管内壁的应力集中;脉动压力载荷将导致血管壁周向应力在一个心动周期中随时间的脉动,而且随着Womersley数α和血管轴向约束参数K～＊的增大,血管壁周向应力的脉动将明显加剧,提示在分析动脉重建时必须计及血液-血管耦合运动对血管壁应力分布的影响.     

弯曲动脉的血流动力学数值分析

利用计算流体力学的理论和方法对弯曲动脉中的血流动力学进行数值分析，是研究心血管疾病流体动力学机理的一种行之有效的方法。本文将升主动脉、主动脉弓和降主动脉联系起来作为弯曲动脉几何模型，给出了血液流动的边界条件以及计算条件。根据生理脉动流条件，对狗的弯曲动脉几何模型内发展中的血液流动进行了有限元数值模拟，并利用可视化方法对血液流动的轴向速度、二次流、壁面切应力等计算结果进行了分析。研究结果表明，在弯管内侧壁处，同时存在主流方向和二次流方向的回流，此处容易形成涡流。弯管内侧壁比外侧壁的壁面切应力具有更强的脉动性。     

脉动流条件下血管壁的应力分布

为了分析血液-血管耦合运动所产生血液脉动压力载荷对血管壁应力分布的影响,利用线性化的血液-血管耦合运动方程的Womersley解,导得血液脉动压力载荷下的血管壁Green应变,同时利用Fung的血管壁应变能密度函数,导得相应血管壁应力分布的一般表达式.数值结果表明,在脉动流条件下,当考虑血液-血管耦合运动时,血管壁中周向应力最大,轴向应力居中,径向应力最小;血管壁的残余应力将明显减小血管内壁的应力集中;脉动压力载荷将导致血管壁周向应力在一个心动周期中随时间的脉动,而且随着Womersley数α和血管轴向约束参数K*的增大,血管壁周向应力的脉动将明显加剧,提示在分析动脉重建时必须计及血液-血管耦合运动对血管壁应力分布的影响.     

Two-phase non-linear model for blood flow in asymmetric and axisymmetric stenosed arteries

The pulsatile flow of a two-phase model for blood flow through axisymmetric and asymmetric stenosed narrow arteries is analyzed, treating blood as a two-phase model with the suspension of all the erythrocytes in the core region as the Herschel-Bulkley material and plasma in the peripheral layer as the Newtonian fluid. The perturbation method is applied to solve the resulting non-linear implicit system of partial differential equations. The expressions for various flow quantities are obtained. It is found that the pressure drop, plug core radius, wall shear stress increase as the yield stress or stenosis height increases. It is noted that the velocity increases, longitudinal impedance decreases as the amplitude increases. For asymmetric stenosis, the wall shear stress increases non-linearly with the increase of the axial distance. The estimates of the increase in longitudinal impedance to flow of the two-phase Herschel-Bulkley material are significantly lower than those of the single-phase Herschel-Bulkley material. The results show the advantages of two-phase flow over single-phase flow in small diameter arteries with stenosis.     

动脉局部狭窄时脉动流的有限元分析

本文利用有限元方法研究动脉局部狭窄下的脉动流流场,重点考查在50％与80％面积狭窄下的速度分布、压力分布、壁面剪应力分布及流动分离情况。几何形状及边界条件均模拟相应的脉动流实验模型。采用测得的随时间变化的速度分布作为入口端条件,并利用罚函数和逆风格式等计算技巧得出了光滑的与实验基本相符的速度、压力波形。本文讨论了不同狭窄下速度、压力、壁面剪应力的分布形态,给出了脉动流中狭窄处局部流动分离的间歇性变化规律,并结合实验与临床应用进行了讨论。     

Magnetic field effect on heat transfer and fluid flow characteristics of blood flow in multi-stenosis arteries

Heat and fluid flow characteristics of blood flow in multi-stenosis arteries in the presence of magnetic field is considered. A mathematical model of the multi-stenosis inside the arteries is introduced. A finite difference scheme is used to solve the governing equations in terms of vorticity-stream function along with their boundary conditions. The effect of magnetic field and the degree of stenosis on wall shear stress and Nusselt number is investigated. It was found that magnetic field modifies the flow patterns and increases the heat transfer rate. The severity of the stenosis affects the wall shear stress characteristics significantly. The magnetic field torque will increase the thermal boundary layer thickness and the temperature gradient in the streaming blood, and hence increasing the local Nusselt number     

Blood flow in stenosed arteries with radially variable viscosity, peripheral plasma layer thickness and magnetic field

A novel approach of combined mathematical and computational models has been developed to investigate the oscillatory two-layered flow of blood through arterial stenosis in the presence of a transverse uniform magnetic field applied. Blood in the core region and plasma fluid in the peripheral layer region are assumed to obey the law of Newtonian fluid. An analytical solution is obtained for velocity profile and volumetric flow rate in the peripheral plasma region and also wall shear stress. Finite difference method is employed to solve the momentum equation for the core region. The numerical solutions for velocity, flow rate and flow resistance are computed. The effects of various parameters associated with the present flow problem such as radially variable viscosity, hematocrit, plasma layer thickness, magnetic field and pulsatile Reynolds number on the physiologically important flow characteristics namely velocity distribution, flow rate, wall shear stress and resistance to flow have been investigated. It is observed that the velocity increases with the increase of plasma layer thickness. An increase or a decrease in the velocity and wall shear stress against the increase in the value of magnetic parameter (Hartmann number) and hematocrit is dependent on the value of t. An increase in magnetic field leads to an increase in the flow resistance and it decreases with the increase in the plasma layer thickness and pulsatile Reynolds number. The information concerning the phase lag between the flow characteristics and how it is affected by the hematocrit, plasma layer thickness and Hartmann number has, for the first time, been added to the literature.     

A Two-Layer Mathematical Model of Blood Flow in Porous Constricted Blood Vessels

In this paper, we discussed a mathematical model for two-layered non-Newtonian blood flow through porous constricted blood vessels. The core region of blood flow contains the suspension of erythrocytes as non-Newtonian Casson fluid and the peripheral region contains the plasma flow as Newtonian fluid. The wall of porous constricted blood vessel configured as thin transition Brinkman layer over layered by Darcy region. The boundary of fluid layer is defined as stress jump condition of Ocha-Tapiya and Beavers–Joseph. In this paper, we obtained an analytic expression for velocity, flow rate, wall shear stress. The effect of permeability, plasma layer thickness, yield stress and shape of the constriction on velocity in core & peripheral region, wall shear stress and flow rate is discussed graphically. This is found throughout the discussion that permeability and plasma layer thickness have accountable effect on various flow parameters which gives an important observation for diseased blood vessels.     

A STUDY ON THE UNSTEADY FLOW IN A HELICAL PIPE

IntroductionRecently ,theresearchofunsteadyflowincurvedpipesmaintainsclosetiewiththatofbloodflowinbio_mechanics.Sothecharacteristicsofbloodflowinvesselscanbestudiedthroughtheresearchofflowincurvedpipesandthelocationthattheatherosclerosistakeplacecanbeprejudged[1].Theessentialcauseofatherosclerosiscanbeprobedinto ,too .In 1 971 ,Lyne[2 ]successfullysolvedtheproblemofflowinacircularcross_sectioncurvedpipeundertheconditionthattheaxialpressuregradientvariedinaccordwiththecosinelawusingthemethodof…     

Study of laminar–turbulent flow transition under pulsatile conditions in a constricted channel

In this paper, direct numerical simulation is performed to investigate a pulsatile flow in a constricted channel to gain physical insights into laminar–turbulent–laminar flow transitions. An in-house computer code is used to conduct numerical simulations based on available high-performance shared memory parallel computing facilities. The Womersley number tested is fixed to 10.5 and the Reynolds number varies from 500 to 2000. The influences of the degree of stenosis and pulsatile conditions on flow transitions and structures are investigated. In the region upstream of the stenosis, the flow pattern is primarily laminar. Immediately after the stenosis, the flow recirculates under an adverse streamwise pressure gradient, and the flow pattern transitions from laminar to turbulent. In the region far downstream of the stenosis, the flow becomes re-laminarised. The physical characteristics of the flow field have been thoroughly analysed in terms of the mean streamwise velocity, turbulence kinetic energy, viscous wall shear stresses, wall pressure and turbulence kinetic energy spectra.