Pattern Formation in Atherosclerotic Plaques
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Atherosclerosis is a disease of the cardiovascular system of humans that can lead to myocardial infarction and stroke. It begins in the arterial walls (intima) as an inﬂammatory response to dysfunction of the endothelium and access of the intima by oxidized low-density lipoproteins (oxLDLs). In response to this, white blood cells, speciﬁcally monocytes, are recruited from the bloodstream. Trapped in the intima, the monocytes diﬀerentiate into macrophages which, after engulﬁng oxLDLs, become foam cells, leading to the production of inﬂammatory cytokines and further recruitment of white blood cells. This self-accelerating process results in an increase of the thickness of arteries, in the formation of atherosclerotic plaques and, possibly, in their rupture. We suggest a one-dimensional mathematical model of the initial events of atherosclerosis. This model consists of a reaction–diﬀusion system with Neumann boundary conditions, and describes the recruitment of monocytes as a function of the concentration of inﬂammatory cytokines.