Mathematical Modeling and Analysis of Atherosclerosis Based on Fluid-Multilayered Poroelastic Structure Interaction Model

Abstract

In this paper, we establish a model of atherosclerosis in the early stage based on fluid-structure interaction (FSI) model of blood vessel and prove the existence of weak solutions. The model consists of Navier–Stokes equation, Biot equations, and reaction–diffusion equations, which involves the effect of blood flow velocity on the concentration of low-density lipoprotein (LDL) and other biological components. We first divide the model into an FSI submodel and a coupled reaction–diffusion submodel, respectively. Then, by using Rothe's method and operator splitting numerical scheme, we obtain the existence of weak solution of FSI submodel. In order to solve the nonlinear term representing the consumption of oxidized low-density lipoprotein (oxLDL), we construct a regular system. The results in FSI submodel together with Schauder's fixed-point theorem allow us to obtain the existence of nonnegative weak solutions for the reaction–diffusion submodel by showing the existence and nonnegativity of weak solutions for the regular system. Numerical simulations were performed in an idealized two-dimensional geometry in order to verify that vascular narrowing caused by plaque further exacerbates plaque growth.