From Discrete to Continuous Structured Modelling of Macrophage Populations in Early Atherosclerotic Plaque

EleonoraAgostinelli

University of Oxford

"From Discrete to Continuous Structured Modelling of Macrophage Populations in Early Atherosclerotic Plaque"

Atherosclerosis is a chronic inflammatory disease characterised by lipid accumulation within arterial walls and driven by macrophage interactions with extracellular material, particularly lipid. In this work, we use mathematical modelling to investigate the dynamics of the macrophages in early atherosclerosis. We develop a discrete, lipid-structured mathematical model that accounts for cell proliferation and crowding, and also extracellular material uptake and offloading. With this model we are able to describe the dynamics of key biophysical quantities in the plaque, in particular the total number of macrophages and the total amount of intracellular material contained within the macrophages. Moreover, we rigorously derive a continuum approximation of the discrete model using the method of discrete multiple scales and asymptotic analysis techniques. In this way, we systematically derive a partial differential equation that accurately describes the distribution of macrophage content at leading order. We take advantage of the continuum form to analyse the mathematical system and understand its biological implications, such as the effects of proliferation and crowding on plaque composition. We also investigate the important spatio-temporal regions that appear degenerate but can be understood via boundary layer analysis.
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