Bifurcation analysis of a free boundary model of plaque formation associated with the cholesterol ratio

TL;DR

This paper develops a bifurcation analysis for a mathematical model of early-stage plaque formation in atherosclerosis, linking LDL/HDL cholesterol ratio to bifurcation behavior and stability, supported by numerical simulations.

Contribution

It introduces a bifurcation analysis framework for a free boundary model of plaque formation, explicitly relating it to cholesterol ratios and analyzing stability.

Findings

Bifurcation branches exist for different modes.

Theoretical conditions for bifurcation are derived.

Numerical simulations confirm analytical results.

Abstract

The low-density lipoprotein (LDL)/high-density lipoprotein (HDL)-cholesterol ratio has been shown a high correlation with the cardiovascular risk assessment. Is it possible to quantify the correlation mathematically? In this paper, we develop a bifurcation analysis for a mathematical model of the plaque formation with a free boundary in the early stage of atherosclerosis. This bifurcation analysis, to the ratio of LDL/HDL, is based on the explicit formulation of radially symmetric steady-state solutions. By performing the perturbation analysis to these solutions, we establish the existence of bifurcation branches and derive a theoretical condition that a bifurcation occurs for different modes. Then we also analyze the stability of radially symmetric steady-state solutions and conduct numerical simulations to verify all the theoretical results.