Asymptotic nonlinear and dispersive pulsatile flow in elastic vessels with cylindrical symmetry

TL;DR

This paper derives and analyzes new one-dimensional nonlinear and dispersive models for blood flow in elastic vessels, incorporating viscosity and validating against existing models, with applications to both constant and tapered arteries.

Contribution

It introduces a novel family of asymptotic models for pulsatile flow in elastic vessels, improving upon existing blood flow equations by including dispersion and viscosity effects.

Findings

Models accurately capture linear dispersion characteristics.

Analytical properties such as symmetries and conservation laws are established.

Flow differences are significant in tapered vessels.

Abstract

The asymptotic derivation of a new family of one-dimensional, weakly nonlinear and weakly dispersive equations that model the flow of an ideal fluid in an elastic vessel is presented. Dissipative effects due to the viscous nature of the fluid are also taken into account. The new models validate by asymptotic reasoning other non-dispersive systems of equations that are commonly used, and improve other nonlinear and dispersive mathematical models derived to describe the blood flow in elastic vessels. The new systems are studied analytically in terms of their basic characteristic properties such as the linear dispersion characteristics, symmetries, conservation laws and solitary waves. Unidirectional model equations are also derived and analysed in the case of vessels of constant radius. The capacity of the models to be used in practical problems is being demonstrated by employing a particular system with favourable properties to study the blood flow in a large artery. Two different cases are considered: A vessel with constant radius and a tapered vessel. Significant changes in the flow can be observed in the case of the tapered vessel.