动脉中血液脉动流的一种分析方法  

An Analysis Model of Pulsatile Blood Flow in Arteries

作　　者：柳兆荣[1] 徐刚[1] 陈泳[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：《应用数学和力学》2003年第2期205-214,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(19732003);国家自然科学青年基金资助项目(19702002)

摘　　要：　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。Blood flow in artery was treated as the flow under equilibrium state (the steady flow under mean pressure)combined with the periodically small pulsatile flow.Using vascular strain energy function advanced by Fung,the vascular stress_strain relationship under equilibrium state was analyzed and the circumferential and axial elastic moduli were deduced that are expressed while the arterial strains around the equilibrium state are relatively small, so that the equations of vessel wall motion under the pulsatile pressure could be established here.Through solving both the vessel equations and the linear Navier_Stokes equations,the analytic expressions of the blood flow velocities and the vascular displacements were obtained.The influence of the difference between vascular circumferential and axial elasticities on pulsatile blood flow and vascular motion was discussed in details.

关 键 词：动脉 血液脉动流 脉博波 应变能密度函数 零应力状态 

分 类 号：Q66[生物学—生物物理学]