On the first bifurcation point for a free boundary problem modeling small arterial plaque

TL;DR

This paper analyzes a complex PDE model of early atherosclerosis, identifying the first bifurcation point that explains asymmetric plaque accumulation in arteries.

Contribution

It establishes the first bifurcation point for a nonlinear coupled PDE system modeling plaque formation, revealing symmetry-breaking solutions.

Findings

Identified the first bifurcation point for the PDE system.

Discovered symmetry-breaking stationary solutions.

Provides insights into asymmetric plaque buildup.

Abstract

Atherosclerosis occurs when plaque clogs the arteries. It is a leading cause of death in the United States and worldwide. In this paper, we study the bifurcation for a highly nonlinear and highly coupled PDE model of plaque formation 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 region being a free boundary. We establish the first bifurcation point for the system corresponding to $n=1$ mode. The symmetry-breaking stationary solution studied in this paper might be helpful in understanding why there exists arterial plaque that is often accumulated more on one side of the artery than the other.