Young Researchers Workshop: Kinetic descriptions in theory and applications

Mathematical modeling and computational simulations of a chronic inflammatory disease

Telma Silva

University of Cape Verde

In this talk we will present a mathematical model which describe the early stage of atherosclerosis as a chronic inflammatory disease. This model consists of partial differential equations: Navier-Stokes equations modeling blood flow, Biot equations modeling the fluid flow inside the poroelastic ves- sel 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 LDL and to 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 results from simulations in an idealized two dimensional geometry aiming to demon- strate some important features of the early atherosclerosis process, also will be presented.