Reaction-diffusion-advection models for collagenous cap formation in atherosclerotic plaques

Abstract

Atherosclerosis is a disease characterised by the formation of lesions and plaques within the intimas of chronically inflamed arteries. The formation of plaques is comprised of a number of stages which we generalise chronologically as lesion initiation, smooth muscle cell migration, collagen synthesis, and necrotic core formation. Existing mathematical models describe these stages with varying degrees of complexity. In this thesis we build a reaction-diffusion PDE framework that is extendable to model the stages of atherosclerotic plaque formation and avoids unnecessary complexity. We begin by creating a base reaction-diffusion model that describes smooth muscle cell (SMC) migration by analysing the dynamics of platelet-derived growth factors (PDGF) and SMCs in the intima. We compare this framework to more complex multiphase models from our research group to produce a model that is simpler and produces qualitatively similar results. The framework is extended to produce models that include more factors involved in plaque growth. The first extended model describes collagen synthesis and the role of extracellular matrix (ECM) and transforming growth factors on the size of the collagenous cap. Subsequent extended models analyse the role of macrophage and modified low density lipoproteins (modLDL) dynamics in lesion initiation, and simulate foam cell and debris growth in the late necrotic core formation stage. We integrate the extended models to produce a multi-stage model of atherosclerotic cap formation that continuously depicts the main stages of atherosclerotic plaque formation. Using the multi-stage model, we compare the roles of SMCs, macrophages and foam cells on cap formation and stability. We investigate a number of phenomena, including the production of PDGF by macrophages, the motility of SMCs and macrophages, ECM synthesis by SMCs, and the conversion of macrophages into foam cells.