锥形血管入口区域内管壁与血液的耦合运动

本文研究了锥形血管入口区域内血管壁与血液间的耦合问题。对具有锥度角的弹性血管入口区域内的管壁运动和血液流动建立的相互耦合作用的数学模型，在满足相应的边界条件下求得了一组血液流动的速度分布公式、压力分布公式以及管壁运动公式，得出了一些重要的结论。     

主动脉弓及分支血管内非稳态血流分析

运用流体力学中的三维非定常Navier-Stokes方程作为血液流动的控制方程,并采用计算流体力学方法对人体主动脉弓及分支血管内非Newton(牛顿)血液黏度模型下血流进行瞬态数值模拟.分析了一个心动周期内不同时刻血流动力学特征参数的分布对动脉粥样硬化斑块形成的影响,并与Newton血液黏度模型下的血管壁面压力和壁面切应力特征参数进行对比,结果表明:与Newton血液模型相比,非Newton血液模型下血流分布更符合真实血流特性;在心动收缩期,分支血管外侧壁附近存在面积较大的低速涡流区,该区域内血管壁面压力与壁面切应力具有较大的变化量,血液中的血小板、脂质和纤维蛋白等易沉积,血管内壁易疲劳损伤并发生血管重构,促使动脉粥样硬化斑块形成;而在心动舒张期,分支血管内血流速度分布均匀,血管壁面压力与壁面切应力变化量较小,血管壁受到较小的应力作用,对动脉粥样硬化斑块形成的作用较小.     

双向流固耦合作用下狭窄左冠状动脉内两相血流分析

基于血流与血管壁间双向流固耦合作用,将血液设为两相流体,运用计算流体力学方法对左冠状动脉内血流进行瞬态数值模拟.研究了一个心动周期内典型时刻下左冠状动脉内血流分布特性,并与Newton(牛顿)血液和两相血液模型对比,分析了两相血液和流固耦合作用对血流特性的影响.结果表明,左冠状动脉左回旋支远段和钝缘支近心端外侧分布了低速涡流区,该区域内壁面切应力和红细胞体积分数均较小,为动脉粥样硬化的形成与发展提供了合适的生理环境.左冠状动脉分叉处管壁形变量较大,引起管壁内膜功能发生紊乱,促进了粥样硬化斑块的形成.3种血液模型对比可知,红细胞的流动特性对血流速度及壁面切应力等血流动力学特性影响较大,双向流固耦合模型更符合真实的血液流动情况.     

内压作用下异径弯管的应力分析

为了对异径管的设计、生产提供理论依据和计算方法,对内压力作用下的异径弯管进行了有限元分析研究。建立了异径弯管的力学模型,计算了异径弯管在内压力作用下的应力,讨论了异径弯管的环向、径向和轴向应力的变化特征,确定了异径弯管的危险部位及其应力变化规律;并对异径比对异径弯管危险点的应力集中的影响情况进行了研究,指出异径弯管危险点的应力随异径比的增大而增加;同时探讨了改善异径弯管应力集中的途径,指出增加异径弯管壁厚是减小应力集中的有效手段。     

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相，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搏波，血液脉动特性以及血管壁运动的影响。     

考虑到渗透效应的一种血液流动的计算方法

得到了定常情况下,狗二分叉动脉横截面的三维Navier＿Stokes方程的有限元处理方法,并考虑到管壁的渗透影响,数值方法还包括直角坐标和曲线坐标的变换·　详细讨论了渗透性影响下的定常流、分叉流以及切应力情况·　以分支和主干血管的速度比为参量,计算雷诺数为1000情况下管壁切应力,数值结果和先前的实验结果符合得很好·　该文的工作是Sharma等(2001)工作的改进,使计算量更小,能够处理的雷诺数范围更大·     

血液流动与血管壁运动

本文讨论了哺乳动物循环系统的血液流动与血管壁运动之间的相互作用问题.在假定流动处于稳定的振荡流动情况下,导得了一组血液流动速度分布公式,压力分布公式以及约束应力公式,管壁位移公式.把Kuchar的公式从定常流动情况推广到非定常的振荡流动情况.文中还讨论了动脉血管壁的弹性效应问题.     

梁受正弦分布压力作用的解析解

对梁受正弦分布压力作用的情况，本文以矩形截面简支梁为例，通过构造满足所有边界条件和双调和方程的应力函数给出了相应的解析解，这为求解梁受任意分布压力作用的解的问题打下了基础。     

充液弹性毛细管低温相变的力学分析

充液弹性毛细管广泛存在于生物体（如毛细血管、植物导管等）和工程领域（如微流控冰阀门、制冷系统热管、MEMS微通道谐振器等）.低温工作环境中,充液弹性毛细管内部的液柱会发生相变并引发冻胀效应,从而导致管壁的变形、损伤乃至断裂.该文建立并求解了考虑温度梯度、界面张力及液体冻胀作用的弹性毛细管平衡方程,分析了液柱低温相变过程中毛细管壁的径向和环向应力,发现管壁应力分布受热毛细弹性数和冻毛细弹性数的影响,且影响大小跟壁厚相关.该研究不仅有助于理解生物体内充液弹性毛细管冻胀失效机制,还可为MEMS微流控芯片的抗冻胀失效设计提供理论指导.     

两平行圆盘间或两圆球间存在二阶流体时的挤压流动

为了进行湿颗粒群的离散元模拟，研究两圆球颗粒间二阶流体在挤压流动时的法向粘性力．首先用小参数法对两平行圆盘间二阶流体挤压流动的速度场和正应力分布进行了近似分析，然后用类似的方法，分析任意两圆球间二阶流体的挤压流动，得到了压力分布和法向粘性力的解析解．     

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.     

Non-Newtonian characteristics of peristaltic flow of blood in micro-vessels

Of concern in the paper is a generalized theoretical study of the non-Newtonian characteristics of peristaltic flow of blood through micro-vessels, e.g. arterioles. The vessel is considered to be of variable cross-section and blood to be a Herschel–Bulkley type of fluid. The progressive wave front of the peristaltic flow is supposed sinusoidal/straight section dominated (SSD) (expansion/contraction type); Reynolds number is considered to be small with reference to blood flow in the micro-circulatory system. The equations that govern the non-Newtonian peristaltic flow of blood are considered to be non-linear. The objective of the study has been to examine the effect of amplitude ratio, mean pressure gradient, yield stress and the power law index on the velocity distribution, wall shear stress, streamline pattern and trapping. It is observed that the numerical estimates for the aforesaid quantities in the case of peristaltic transport of blood in a channel are much different from those for flow in an axisymmetric vessel of circular cross-section. The study further shows that peristaltic pumping, flow velocity and wall shear stress are significantly altered due to the non-uniformity of the cross-sectional radius of blood vessels of the micro-circulatory system. Moreover, the magnitude of the amplitude ratio and the value of the fluid index are important parameters that affect the flow behaviour. Novel features of SSD wave propagation that affect the flow behaviour of blood have also been discussed.     

肾动脉变窄和流-固结构相互作用对非Newton脉动流的影响——一个真实的腹部主动脉和肾动脉模型

研究肾动脉狭窄(RAS)对血液流动和血管壁的影响.根据CT扫描图像,重建腹部主动脉和肾动脉的解剖模型,通过模型的脉动流进行了仿真计算,计算中考虑了流体-固体结构的相互作用(FSI).研究RAS对血管壁剪切应力和位移的影响,RAS使得肾动脉中流量减少,肾素-血管紧缩素系统可能被激活,从而导致严重的高血压.     

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.     

Gas Near a Wall: Shortened Mean Free Path,Reduced Viscosity,and the Manifestation of the Knudsen Layer in the Navier–Stokes Solution of a Shear Flow

For the gas near a solid planar wall, we propose a scaling formula for the mean free path of a molecule as a function of the distance from the wall, under the assumption of a uniform distribution of the incident directions of the molecular free flight. We subsequently impose the same scaling onto the viscosity of the gas near the wall and compute the Navier–Stokes solution of the velocity of a shear flow parallel to the wall. Under the simplifying assumption of constant temperature of the gas, the velocity profile becomes an explicit nonlinear function of the distance from the wall and exhibits a Knudsen boundary layer near the wall. To verify the validity of the obtained formula, we perform the Direct Simulation Monte Carlo computations for the shear flow of argon and nitrogen at normal density and temperature. We find excellent agreement between our velocity approximation and the computed DSMC velocity profiles both within the Knudsen boundary layer and away from it.     

Determination of arterial wall shear stress

The arteries can remodel their structure and function to adapt themselves to the mechanical environment. In various factors that lead to vascular remodeling, the shear stress on the arterial wall induced by the blood flow is of great importance. However, there are many technique difficulties in measuring the wall shear stress directly at present. In this paper, through analyzing the pulsatile blood flow in arteries, a method has been proposed that can determine the wall shear stress quantitatively by measuring the velocity on the arterial axis, and that provides a necessary means to discuss the influence of arterial wall shear stress on vascular remodeling.     

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.     

A non-Newtonian fluid flow model for blood flow through a catheterized artery—Steady flow

In this paper the effects catheterization and non-Newtonian nature of blood in small arteries of diameter less than 100 μm, on velocity, flow resistance and wall shear stress are analyzed mathematically by modeling blood as a Herschel–Bulkley fluid with parameters n and θ and the artery and catheter by coaxial rigid circular cylinders. The influence of the catheter radius and the yield stress of the fluid on the yield plane locations, velocity distributions, flow rate, wall shear stress and frictional resistance are investigated assuming the flow to be steady. It is shown that the velocity decreases as the yield stress increases for given values of other parameters. The frictional resistance as well as the wall shear stress increases with increasing yield stress, whereas the frictional resistance increases and the wall shear stress decreases with increasing catheter radius ratio k (catheter radius to vessel radius). For the range of catheter radius ratio 0.3–0.6, in smaller arteries where blood is modeled by Herschel–Bulkley fluid with yield stress θ = 0.1, the resistance increases by a factor 3.98–21.12 for n = 0.95 and by a factor 4.35–25.09 for n = 1.05. When θ = 0.3, these factors are 7.47–124.6 when n = 0.95 and 8.97–247.76 when n = 1.05.