Mathematical modeling of atherosclerosis. (c2019)

Abstract

Atherosclerosis is a chronic in ammatory cardiovascular disease in which arteries harden through the build-up of plaques. This work is devoted to the mathematical modeling and analysis of the in ammatory process of atherosclerosis. We propose a mathematical model formed by three coupled partial di erential equations of reaction-di usion type. We take into account three key-role players: the immune cells (M), the in ammatory cytokines (A) and the oxidized LDL (L). 8>>>>>>>>>>< >>>>>>>>>>: @M @t = d1 @2M @x2 + L + 1A 1 + A= 1 + ML ð€€€ ML ð€€€ 1M @A @t = d2 @2A @x2 + 2A 1 + A= 2 M ð€€€ 2A @L @t = d3 @2L @x2 + M 1 +M= 3 ð€€€ 3L A stability analysis of the kinetic system is performed followed by a detailed discussion about the biological interpretation. Several cases may occur ; every case corresponds to a biological situation. Then a holistic conclusion is established. We investigate as well the existence of solutions of traveling waves type along with numerical simulations that show the wave propagation in the di erent cases. These results con rm and generalize previous results published in [1, 2].