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arXiv · 2008.07075

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

Wenrui Hao·Chunyue Zheng
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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.

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Wenrui Hao, Chunyue Zheng. 2020-08-17. Bifurcation analysis of a free boundary model of plaque formation associated with the cholesterol ratio. https://arxiv.org/abs/2008.07075

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