Abstract
In this work we study the in∞ammatory process resulting in the development of atherosclerosis. We develop a one- and two-dimensional models based on reaction-difiusion systems to describe the set up of a chronic in∞ammatory response in the intima of an artery vessel wall. The concentration of the oxidized low density lipoproteins (ox-LDL) in the intima is the critical parameter of the model. Low ox-LDL concentrations do not lead to a chronic in∞ammatory reaction. Intermediate ox-LDL concentrations correspond to a bistable system and can lead to a travelling wave propagation corresponding to a chronic in∞ammatory reaction. In this case the disease development depends on the initial condition. If the concentration of monocytes in the intima is su-ciently high, which can be caused by an in∞ammation related to other factors, then the development of atherosclerosis can start. Otherwise, the system returns to the stable disease free equilibrium. High ox-LDL concentrations correspond to a monostable system and even a small perturbation of the non in∞ammatory case leads to a travelling wave propagation which corresponds to a chronic in∞ammatory response.
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