Mathematical Modeling of Inflammatory Processes of Atherosclerosis

Abstract

In this paper we study the early stages of atherosclerosis via a mathematical model of partial differential equations of reaction-diffusion type. The model includes several key species and identifies endothelial hyperpermeability, believed to be a precursor on the onset of atherosclerosis. We reduce the system to a monotone system and provide a biological interpretation for the stability analysis according to endothelial functionality. We investigate as well the existence of solutions of traveling waves type along with numerical simulations. The obtained results are in good agreement with current biological knowledge. Likewise, they confirm and generalize results of mathematical models previously performed in literature. Then, we study the non monotone reduced model and prove the existence of perturbed solutions and perturbed waves, particularly in the bistable case. Finally, we consider the complete model proposed initially, perform numerical simulations and provide more specific results. We study the consistency between the reduced and complete models for a certain range of parameters. We elaborate bifurcation diagrams showing the evolution of inflammation upon endothelial permeability and LDL accumulation. We show that the regulation of atherosclerosis progression is mediated by anti-inflammatory responses that, up to certain extent, lead to plaque regression.