Asymptotic Models of Anisotropic Heterogeneous Elastic Walls of Blood Vessels

Abstract

Using the dimension reduction procedure for a three-dimensional elasticity system, we derive a two-dimensional model for elastic laminate walls of a blood vessel. In the case of a sufficiently small wall thickness, we derive a system of limit equations coupled with the Navier–Stokes equations through the stress and velocity, i.e., dynamic and kinematic conditions on the interior surface of the wall. We deduce explicit formulas for the effective rigidity tensor of the wall in two natural cases. We show that if the blood flow remains laminar, then the cross-section of the orthotropic homogeneous blood vessel becomes circular.