Evolution equation for propagation of blood pressure waves in an artery with an aneurysm

Abstract

In this study we derive an evolution equation for propagation of perturbed pressure waves in a blood-filled artery with a local dilatation (an aneurysm) in a longwave approximation. The equation is a version of the perturbed Korteweg-deVries (KdV) equation with variable coefficients. Exact travelling-wave solution of this equation is obtained by the modified method of simplest equation where the differential equation of Riccati is used as simplest equation. Numerical simulations of the obtained solution are performed and discussed from the point of view of arterial disease geometry.