A two dimensional model of curvilinear blood vessels with layered elastic walls

TL;DR

This paper develops a two-dimensional elastic model of curved blood vessels with layered walls, accounting for tissue interaction, vessel curvature, twist, and anisotropy, providing explicit differential equations for various vessel shapes.

Contribution

It introduces a novel dimension reduction approach for modeling complex layered vessel walls with curvature and anisotropy, including explicit equations for canonical vessel shapes.

Findings

Model captures elastic behavior of layered vessel walls

Explicit differential equations for canonical vessel geometries

Accounts for tissue interaction, curvature, and anisotropy

Abstract

We present a two dimensional model describing the elastic behaviour of the wall of a curved blood vessel. The wall has a laminate structure consisting of several anisotropic layers of varying thickness and is assumed to be much smaller in thickness than the radius of the vessel which itself is allowed to vary. Our two-dimensional model takes the interaction of the wall with the surrounding tissue and the blood flow into account and is obtained via a dimension reduction procedure. The curvature and twist of the vessel axis as well as the anisotropy of the laminate wall present the main challenges in applying the dimension reduction procedure so plenty of examples of canonical shapes of vessels and their walls are supplied with explicit systems of differential equations at the end.