脉动流条件下血管壁的应力分布  

STRESS DISTRIBUTION ON ARTERIAL WALL UNDER PULSATILE FLOW

作　　者：柳兆荣[1] 滕忠照[1] 覃开蓉[1] 

机构地区：[1]复旦大学生物力学实验室,上海200433

出　　处：《力学学报》2002年第5期696-704,共9页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金重点项目(19732003)资助

摘　　要：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.Fung~[1]has demonstrated that the growth of living tissue will be determined by stress and strain, the physiological stress must be considered as a factor that influence growth of vessel wall. Furthermore, Fung et al.~[2,3] has shown that the residual stress in the unloaded state of arterial wall, although small in magnitude, is significant in reducing the high circumferential stress concentration at the inner wall and makes its distribution through the vessel wall more uniform when the mean pressure lies in the physiological rang. They pointed out that the deformation or strain of vessel wall must be measured from the zero-stress state. Although the stress distribution of vessel wall under unsteady condition has be studied~[4,5], they are not taking blood-vessel wall coupling motion into account.In order to study the influence of pulsatile pressure load induced by blood-vessel coupling motion on stress distribution of the arterial wall, in this paper, the expressions of Green strain were obtained by using the Womersley Solution of linerized blood-vessel coupling motion equations. And then the stress distribution of the arterial wall was determined by using Fung's strain energy density function. The numerical results show that, under unsteady pulsatile conditions, taking blood-vessel coupling motion into account, circumferential stress is of the highest value, axial stress is in between and radial stress is of least value. Residual stress significantly reduce the stress concentration of the inner wall which is best agreement with the result presented by Fung under steady state~[1～3]. Furthermore, the stress on the arterial all will also be pulsatile and the magnitude of the pulsation increases when Womersley number a and parameter K* increase. It follows that the influence of blood-vessel coupling motion on the stress distribution of the arterial wall is very important when one studies vascular remodeling, which should give us much information on how blood vessel tissues adept themselves to their mechanical env

关 键 词：脉动流 血管壁 应力分布 Womersley理论 零应力状态 应变能密度函数 残余应力 

分 类 号：R322.1[医药卫生—人体解剖和组织胚胎学] R318.01[医药卫生—基础医学]