Nonlinear Pressure Wave Propagation in Arteries

Abstract

The nonlinear pressure wave propagation in a straight thin elastic tube having a slowly varying radius and containing an incompressible fluid is considered. The motion of walls is represented by that of the middle surface by the shell theories which are extended to the second order of the displacements. Nonlinearities being taken into account are due to the convective motion of fluid, nonlinear strains and stress-strain relations. By assuming some asymptotic state, the systems of basic equations are reduced to the perturbed Korteweg-de Vries equation in which perturbation terms represent the effects of the variation in the tube radius and dissipation. It is shown that the taper effect influences remarkably the pressure wave propagation.