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

Wenrui Hao, Chunyue Zheng

Research output: Contribution to journalArticlepeer-review

Abstract

The low-density lipoprotein (LDL)/high-density lipoprotein (HDL)-cholesterol ratio has been shown to have 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 explicit formulations 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. We also analyze the stability of radially symmetric steady-state solutions and conduct numerical simulations to verify all theoretical results.

Original languageEnglish (US)
Article number093113
JournalChaos
Volume30
Issue number9
DOIs
StatePublished - Sep 1 2020

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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