Multiphase models of early atherosclerotic plaque development

Atherosclerosis is a complex disease caused by a cascade of interactions between the artery wall, immune cells, cholesterol-carrying lipoproteins, and a host of other cellular and chemical species. In this thesis, we build and investigate a series of partial differential equation models for the early atherosclerotic plaque based on a multiphase framework. We first develop a general approach for building multiphase PDE models that can account for cell crowding effects, while also supporting a variable domain size by using a free boundary. Using this framework, we build a series of increasingly complex models to address different aspects of early plaque development. The first is a simple two-phase model comprising macrophage foam cells and atherogenic low density lipoproteins (LDL). Subsequent models extend this basic model to incorporate spatial heterogeneity in macrophage lipid content, apoptotic cell death, the recycling of dead material via efferocytosis, and the atheroprotective role of high density lipoproteins (HDL). Where appropriate, we also make use of simplified ODE submodels for local plaque composition. We use these PDE models to address a number of phenomena, including the competing effects of LDL and HDL, the balance between cell death and recycling, the cytotoxic effects of intracellular cholesterol, the ability for inflammation to either relieve or exacerbate plaque growth, and the ability of HDL and foam cell emigration to slow plaque growth and potentially stabilise plaque size. The full model is also applied to several experimental setups. We first simulate therapies that affect blood lipid profiles, examining how their efficacy depends on when and how long they are administered. We also simulate mouse model studies involving bead-tagged macrophages, and we assess hypotheses regarding macrophage motility in the deep plaque by comparing simulated and experimental bead distributions