ABSTRACT

In Chapter 5, the moving boundary partial differential equation (MBPDE) system of Eqs. (5.1) through (5.3) is applied to plaque formation in atherosclerosis. The six PDE dependent variables are

ℓ(x, t) concentration of modified LDL

h(x, t) concentration of HDL

p(x, t) concentration of chemoattractants

q(x, t) concentration of ES cytokines

m(x, t) density of monocytes/macrophages

N(x, t) density of foam cells

x is the distance through the arterial endothelial inner layer (EIL), and t is time.

Of particular interest is the evolution of the foam cell density, N(x,t), which is a precursor to EIL plaque formation. The inner plaque boundary rl (t) moves with plaque formation as illustrated in the rl (t) and d r l ( t ) d t https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429275128/bc1acef7-dd43-4bcb-9532-bbbe7bb88ee1/content/equ_3.tif"/> against t plots. The change in rl (t) is a response to the bloodstream LDL and HDL.

Plaque formation can restrict blood ow with serious consequences such as stroke and myocardial infarction (heart attack).