Bifurcation for a free boundary problem modeling a small arterial plaque

TL;DR

This paper analyzes a complex PDE model of arterial plaque growth, revealing bifurcations that explain how plaques develop asymmetric shapes, which are common in real-world atherosclerosis.

Contribution

It establishes finite branches of symmetry-breaking solutions in a nonlinear PDE model, advancing understanding of plaque morphology.

Findings

Bifurcation points from symmetric solutions identified

Existence of asymmetric plaque shapes demonstrated

Model links biological factors to plaque asymmetry

Abstract

Atherosclerosis, hardening of the arteries, originates from small plaque in the arteries; it is a major cause of disability and premature death in the United States and worldwide. In this paper, we study the bifurcation of a highly nonlinear and highly coupled PDE model describing the growth of arterial plaque in the early stage of atherosclerosis. The model involves LDL and HDL cholesterols, macrophage cells as well as foam cells, with the interface separating the plaque and blood flow regions being a free boundary. We establish finite branches of symmetry-breaking stationary solutions which bifurcate from the radially symmetric solution. Since plaque in reality is unlikely to be strictly radially symmetric, our result would be useful to explain the asymmetric shapes of plaque.