Modelling Preferential Phagocytosis in Atherosclerosis: Delineating Timescales in Plaque Development

Atherosclerotic plaques develop over a long time and can cause heart attacks and strokes. There are no simple mathematical models that capture the different timescales of rapid macrophage and lipid dynamics and slow plaque growth. We propose a simple ODE model for lipid dynamics that includes macrophage preference for ingesting apoptotic material and modified low-density lipoproteins (modLDL) over ingesting necrotic material. We use multiple timescale analysis to show that if the necrosis rate is small then the necrotic core in the model plaque may continue to develop slowly even when the lipid levels in plaque macrophages, apoptotic material and modLDL appear to have reached equilibrium. We use the model to explore the effect of macrophage emigration, apoptotic cell necrosis, total rate of macrophage phagocytosis and modLDL influx into the plaque on plaque lipid accumulation.