Numerical simulation of a porous medium-type atherosclerosis initiation model

Atherosclerosis is an inflammatory disease due to the accumulation of low-density lipoproteins (LDLs) in the arteries wall, with the consequence that plaque is built up inside the arteries. Different mathematical models have been proposed to represent the first stages of atherosclerosis development. In this work we propose a mathematical model based on [1,2] but including a nonlinear diffusion porous medium-type in the 1D system of PDEs. The numerical solution is obtained by means of an ADER-WENO approach in the finite volume framework. First results theoretically obtained and numerically proved has been reported in [1], for the linear diffusion model. In this work we extend those results to the nonlinear diffusion model.