Ox R H
Biophys J. 1968 Jun;8(6):691-709. doi: 10.1016/s0006-3495(68)86515-4.
The propagation of harmonic pressure waves through a Newtonian fluid contained within a thick-walled, viscoelastic tube is considered as a model of arterial blood flow. The fluid is assumed to be homogeneous and Newtonian, and its motion to be laminar and axisymmetric. The wall is assumed to be isotropic, incompressible, linear, and viscoelastic. It is also assumed that the motion is such that the convective acceleration is negligible. The motion of the fluid is described by the linearized form of the Navier-Stokes equations and the motion of the wall by classical elasticity theory. The frequency dependence of the wall mechanical properties are represented by a three parameter, relaxation-type model. Using boundary conditions describing the continuity of stress and velocity components in the fluid and the wall, explicit solutions for the system of equations of the model have been obtained. The longitudinal fluid impedance has been expressed in terms of frequency and the system parameters. The frequency equation has been solved and the propagation constant also expressed in terms of frequency and system parameters. The results indicate that the fluid impedance is smaller than predicted by the rigid tube model or by Womersley's constrained elastic tube model. Also, the velocity of propagation is generally slower and the transmission per wavelength less than predicted by Womersley's elastic tube model. The propagation constant is very sensitive to changes in the degree of wall viscoelasticity.
谐波压力波在厚壁粘弹性管内所含牛顿流体中的传播被视为动脉血流的一种模型。假定流体是均匀的牛顿流体，其运动为层流且轴对称。假定管壁是各向同性、不可压缩、线性且粘弹性的。还假定运动使得对流加速度可忽略不计。流体的运动由线性化的纳维 - 斯托克斯方程描述，管壁的运动由经典弹性理论描述。管壁力学性能的频率依赖性由一个三参数松弛型模型表示。利用描述流体和管壁中应力与速度分量连续性的边界条件，已得到该模型方程组的显式解。纵向流体阻抗已用频率和系统参数表示。频率方程已求解，传播常数也用频率和系统参数表示。结果表明，流体阻抗比刚性管模型或沃默斯利的约束弹性管模型所预测的要小。而且，传播速度通常较慢，每波长的传输比沃默斯利的弹性管模型所预测的要小。传播常数对管壁粘弹性程度的变化非常敏感。
