Modeling of the early stage of atherosclerosis with emphasis on the regulation of the endothelial permeability.

In this paper, we develop a mathematical model for the early stage of atherosclerosis, as a chronic inflammatory disease. It includes also processes that are relevant for the "thickening" of the vessel walls, and prepares a more complete model including also the later stages of atherosclerosis. The model consists of partial differential equations: Navier-Stokes equations modeling blood flow, Biot equations modeling the fluid flow inside the poroelastic vessel wall, and convection/chemotaxis-reaction-diffusion equations modeling transport, signaling and interaction processes initiating inflammation and atherosclerosis. The main innovations of this model are: a) quantifying the endothelial permeability to low-density-lipoproteins (LDL) and to the monocytes as a function of WSS, cytokines and LDL on the endothelial surface; b) transport of monocytes on the endothelial surface, mimicking the monocytes adhesion and rolling; c) the monocytes influx in the lumen, as a function of factor increasing monocytopoiesis; d) coupling between Navier-Stokes system, Biot system and convection/chemotaxis-reaction-diffusion equations. Numerical simulations of a simplified model were performed in an idealized two-dimensional geometry in order to investigate the dynamics of endothelial permeability, and the growth and spread of immune cells populations and their dependence in particular on low-density-lipoprotein and wall-shear stress.