Cardiovascular disease remains the leading cause of death in developed countries. Recently significant progress has been achieved in understanding the role of chronic inflammation of the endothelial or inner most layer of the arterial wall in the onset and progression of the disease and the many biochemical pathways leading to the genesis of atherosclerotic lesions. In this talk, I present recent modeling attempts of the main processes behind atherogenesis. A surprisingly simple system of six reaction/diffusion equations of the Keller-Segal chemotaxic type for three cellular species and three chemical species seems to capture many of the important features observed in atherogenesis. On a fixed domain, this system can exhibit rapid blow-up in finite time after a threshold has been surpassed which can be interpreted as a runaway diseased state. This blow-up is of the Dirac point mass type. The free boundary value problem for this system corresponding to the growth and encroachment of the lesion into the arterial lumen (interior flow region) is also discussed.

A second problem area to be discussed concerns modeling growth and remodeling of the medial (central muscular) layer of an arterial wall due to chronic hypertension. The model differentiates between three type of growth processes, hypertrophy in which smooth muscles grow is mass through either the production of intracellular proteins or extracellular matrix proteins and hyperplasia or smooth muscle proliferation. A key step in the modeling involves a pair of partial differential equations, one non-linear parabolic and the other non-linear hyperbolic, keeping track of both the number density of smooth muscle cells and their average mass. The issue of traveling wave solutions for this system is discussed.