Modelling atherosclerotic plaque formation: Boundaries, balances and bifurcations

Abstract: 

Why do some people develop cardiovascular disease while others with similar risk profiles do not? What causes plaques to regress? Why does raising HDL (“good cholesterol”) reduce cardiovascular disease in some but not all cases? Why does atherosclerosis sometimes progress in fits and starts? Can atherosclerotic plaques ever disappear once they have formed?

At first sight, none of these appears to be a question that can be answered mathematically. But the formation and progress of atherosclerotic plaques are outcomes of many interlinked biochemical, physiological and cellular processes. Most of these processes are nonlinear and many are influenced by slow changes in physiological conditions both in the arteries where the plaques form, and in the body as a whole. I will present models for the formation of plaques in the artery wall based on ordinary and partial differential equations. The solutions show a variety of bifurcation behaviour and nonlinear dynamical effects that explain published experimental outcomes and are relevant to drug therapies that are currently under clinical trial.