On nonlinear waves of the blood flow through arteries

TL;DR

This paper models nonlinear wave propagation in arteries with aneurysms using a perturbed Korteweg-de Vries equation and finds exact traveling wave solutions, providing insights into blood flow dynamics in injured arteries.

Contribution

It introduces a novel application of the modified method of simplest equation to solve for exact traveling wave solutions in arterial blood flow models.

Findings

Exact solutions for nonlinear blood flow waves in aneurysmal arteries.

Reduction of complex artery-blood interaction to a perturbed KdV equation.

Insights into wave behavior in injured arterial segments.

Abstract

We discuss propagation of traveling waves in a blood filled elastic artery with an axially symmetric dilatation (an idealized aneurysm). 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 long-wave approximation holds the model equations are reduced to a version of the perturbed Korteweg-deVries equation. Exact travelling-wave solutions of this equation are obtained by the modified method of simplest equation where the differential equation of Abel is used as a simplest equation. A particular case of the obtained exact solution is discussed from the point of view of arterial mechanics.