Mathematical Modeling of Atherosclerosis

Abstract

In this thesis, we suggest a one and two dimensional mathematical models of reaction-diffusion type that study the inflammatory process of atherosclerosis in the intima. They consider the concentration of five main agents: LDL, free radicals, oxidized LDL, macrophages and cytokines. The existence and stability analysis of fixed points for the kinetic system is performed. All obtained results are analyzed and compared to those in [1] in order to provide an appropriate biological interpretation. We prove the existence of solution of traveling wave type which decribes the set up of the in ammatory reaction as a reaction-diffusion wave inside the intima. This result is shown theoretically and numerically. We prove as well the convergence of the 2D model to the 1D case in the thin domain.