Several results from numerical investigation of nonlinear waves connected to blood flow in an elastic tube of variable radius

TL;DR

This paper models nonlinear wave propagation in elastic tubes with variable radius, simulating blood flow in arteries, using a variable-coefficient Korteweg-de Vries equation and analyzing periodic solutions related to heart pulsations.

Contribution

It introduces a reduced model for blood flow in elastic arteries with variable radius, connecting nonlinear wave theory to physiological pulsations.

Findings

Low probability of solitary wave formation.

Periodic wave solutions can model irregular heart pulsations.

The model links nonlinear wave dynamics to blood flow behavior.

Abstract

We investigate flow of incompressible fluid in a cylindrical tube with elastic walls. The radius of the tube may change along its length. The discussed problem is connected to the blood flow in large human arteries and especially to nonlinear wave propagation due to the pulsations of the heart. The long-wave approximation for modeling of waves in blood is applied. The obtained model Korteweg-deVries equation possessing a variable coefficient is reduced to a nonlinear dynamical system of 3 first order differential equations. The low probability of arising of a solitary wave is shown. Periodic wave solutions of the model system of equations are studied and it is shown that the waves that are consequence of the irregular heart pulsations may be modeled by a sequence of parts of such periodic wave solutions.