Growth of necrotic cores in atherosclerotic plaque

Plaques are fatty deposits that grow mainly in arteries and develop as a result of a chronic inflammatory response. Plaques are characterized as 'vulnerable' when they have large internal regions of necrosis and are heavily infiltrated by macrophages. The particular composition of a vulnerable plaque renders it susceptible to rupture, which releases thrombogenic agents into the bloodstream and can result in myocardial infarction. In this paper, we propose a mathematical model to predict the development of a plaque's necrotic core. By solving coupled reaction-diffusion equations for macrophages and dead cells, we focus on the joint effects of hypoxic cell death and chemoattraction to oxidized low-density lipoprotein (Ox-LDL), a molecule that is strongly linked to atherosclerosis. We do not model the mechanical properties of the plaque, its growth or rupture. Our model predicts cores that have approximately the right size and shape when compared to ultrasound images. Because our model is linear and autonomous, normal mode analysis and subsequent calculation of the smallest eigenvalue allow us to compute the times taken for the necrotic core to form. We find that the spatial distribution of Ox-LDL within the plaque determines not only the placement and size of cores, but their time of formation. Although plaques are biochemically complex, our study shows that certain aspects of their composition can be predicted and are, in fact, governed by simple physical models.