Nonlinear evolution wave equation for an artery with an aneurysm: an exact solution obtained by the modified method of simplest equation

TL;DR

This paper derives an exact solution for nonlinear wave propagation in an artery with an aneurysm using a modified method, revealing how aneurysm geometry influences wave profiles in blood flow.

Contribution

It introduces an exact solution to a variable-coefficient Korteweg-de Vries-Burgers equation modeling blood flow in aneurysmal arteries using the modified method of simplest equation.

Findings

Affect of aneurysm geometry on wave shape analyzed

Exact traveling-wave solution obtained for the model

Insights into blood flow dynamics in aneurysmal arteries

Abstract

We study propagation of traveling waves in a blood filled elastic artery with an axially symmetric dilatation (an idealized aneurysm) in long-wave approximation.The processes in the injured artery are modelled by equations for the motion of the wall of the artery and by equation for the motion of the fluid (the blood). For the case when balance of nonlinearity, dispersion and dissipation in such a medium holds the model equations are reduced to a version of the Korteweg-deVries-Burgers 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 a simplest equation. Effects of the dilatation geometry on the travelling-wave profile are considered.