Nonlinear dynamics of early atherosclerotic plaque formation may determine the efficacy of high density lipoproteins (HDL) in plaque regression.

We use a computational model to explore the effect of foam cell accumulation on plaque regression following an increase in high density lipoprotein (HDL) influx into the plaque. Atherosclerotic plaque formation is the outcome of cellular and cytokine responses to low density lipoproteins (LDL) that penetrate the artery wall following an injury to the endothelium and become modified. We modelled the cells and cytokines that are most important in plaque formation using partial differential equations. The model includes monocytes and macrophages, foam cells, macrophage chemoattractants, endothelium-stimulating cytokines, modified low density lipoproteins (mod LDL) and HDL. We included interactions both at the endothelium surface and inside the artery wall. The model predicts that when HDL influx into a well-established plaque with large numbers of foam cells is increased, the plaque may not regress but may continue to grow at a slower rate. If HDL influx is increased when a model plaque is recently established and has fewer foam cells, then the plaque does regress. If modLDL influx into the plaque is lowered at the same time that HDL influx increased or the capacity of the HDL to remove cholesterol from foam cells is increased, then the plaque is more likely to regress. The predictions of the model are in qualitative agreement with experimental studies in mice and rabbits. The results suggest that the intrinsic dynamics of reverse cholesterol transport by HDL are important in determining the success of HDL raising in promoting plaque regression.

Bifurcation and dynamics in a mathematical model of early atherosclerosis: How acute inflammation drives lesion development.

We present here a mathematical model describing the primary mechanisms that drive the early stages of atherosclerosis. This involves the interactions between modified low density lipoprotein (LDL), monocytes/macrophages, cytokines and foam cells. This model suggests that there is an initial inflammatory phase associated with atherosclerotic lesion development and a longer, quasi-static process of plaque development inside the arterial wall that follows the initial transient. We will show results that show how different LDL concentrations in the blood stream and different immune responses can affect the development of a plaque. Through numerical bifurcation analysis, we show the existence of a fold bifurcation when the flux of LDL from the blood is sufficiently high. By analysing the model presented in this paper, we gain a greater insight into this inflammatory response qualitatively and quantitatively.