Nonlinear Model of Blood Flow Through Stenosed Coronary Arteries

Abstract

Blood flow and pulse wave propagation in the blood vessels are usually studied on the incompressible linearized axsymmetric Navier-Stokes equations (Womersley model) coupled with linear and nonlinear viscoelastic equations for the vessel walls. A brief review of the nonlinear models is given. Blood flow and wave propagation through the stenosed artery terminated by a viscoelastic chamber with different resistivity and compliance has been considered. The material parameters of the wall corresponded to healthy elastic and degenerated compliant human arteries. Both 2d linearized and 1d nonlinear models have been applied for numerical solution of the problem. The computational results for the pressure P(t), flow U(t) and diameter d(t) oscillations have been compared to the measurement data. It is shown that the dynamics of the fluid-filled vessels with healthy elastic walls is satisfactory described by the linearized equations while for the age-related degenerative walls, stenosed or diluted vessels the nonlinear models are preferable.