A lipid-structured model for macrophage populations in atherosclerotic plaques.

Atherosclerosis is a chronic inflammatory disease driven by the accumulation of pro-inflammatory, lipid-loaded macrophages at sites inside artery walls. These accumulations lead to the development of atherosclerotic plaques. The rupture of plaques that contain lipid-rich necrotic cores can trigger heart attacks and strokes via occlusion of blood vessels. We construct and analyse a system of partial integro-differential equations that model lipid accumulation by macrophages, the generation of apoptotic cells and the formation of the necrotic core. The model accounts for the following cell behaviours: monocyte recruitment into the plaque and differentiation into macrophages; macrophage ingestion of low density lipoproteins (LDL) and of apoptotic cells and necrotic material; lipid offloading to high density lipoproteins (HDL); macrophage emigration; and apoptosis of macrophages and necrosis of apoptotic cells. With this model, we study how changes in parameters predict the characteristic features of plaque pathology. In particular, we find the qualitative form of lipid distribution across the macrophage population and show that high lipid loads can occur in the absence of LDL ingestion. We also demonstrate the importance of macrophage emigration in mitigating and resolving inflammation and plaque lipid accumulation.