一种确定均匀动脉壁面切应力的非线性方法  

A NONLINEAR METHOD TO DETERMINE THE WALL SHEAR STRESS INTHE STRAIGHT ARTERY IN VIVO

作　　者：覃开蓉[1] 姜宗来[2] 

机构地区：[1]复旦大学力学与工程科学系,上海200433 [2]上海交通大学医学院,上海200030

出　　处：《力学学报》2005年第2期225-231,共7页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金资助项目(10132020)

摘　　要：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.With the aid of Ling and Atabek's 'local flow' assumption for the nonlinear convective acceleration terms of the Navier-Stokes equation governing the pulsatile blood flow in large arteries, a nonlinear method to determine the wall shear stress in straight arteries was proposed by use of the measured blood viscosity, center-line velocity, blood pressure and arterial radius. Comparing with the results from the linear method proposed by Liu Zhaorong et al., where the wall shear stress was calculated using the measured blood viscosity, center-line velocity and average arterial radius, the results from the nonlinear method demonstrated that, no obvious difference exists between the pressure gradients, the velocity profiles, and the wall shear stresses calculated from the two different methods when the wall motion (dR/R - 2.4%) is small, however, an obvious difference occurs when the wall motion is large (dR/R = 12%). It was concluded that the linear method has high accuracy when the wall motion is small but the nonlinear effects on the wall shear stress must be taken into consideration when the wall motion becomes large. Because the inputs such as the blood viscosity, the center-line velocity, the blood pressure and the arterial radius could be measured by use of non-invasive and/or micro-invasive methods, the nonlinear method provided the methodology base for the in vivo and/or ex-vivo study of the relationship between the wall shear stress and arterial remodeling.

关 键 词：管壁切应力 非线性脉动流 动脉重建 哺乳动物 血流速度 血液黏性 

分 类 号：O357[理学—流体力学] Q66[理学—力学]