A reduced model for solute transport in compliant blood vessels with arbitrary axial velocity profile

TL;DR

This paper develops a simplified one-dimensional model for solute transport in compliant blood vessels with arbitrary velocity profiles, using center manifold theory to couple flow and transport dynamics.

Contribution

It introduces a novel reduced model for solute transport that accounts for arbitrary axial velocity profiles and vessel compliance, extending previous models.

Findings

The model accurately captures the influence of velocity profile shape on diffusion.

Numerical solutions show dependence of diffusion coefficients on velocity profile shape.

The approach provides a framework for analyzing solute transport in realistic blood vessel geometries.

Abstract

We derive a reduced model of solute transport in blood based on the center manifold theory. The derivation is carried out on a convection diffusion equation with general axial and radial velocity profiles in a blood vessel of varying cross section. We couple the resulting one dimensional equation to a reduced model for blood flow in a compliant vessel. In the special case of a no--slip axial velocity profile, we study the dependence of the diffusion coefficient and corresponding numerical solutions on the shape of the profile.