Key result
Mathematical model of early-stage atherosclerotic plaque formation links bifurcation branches to the LDL/HDL ratio.
Why the study?
While the LDL/HDL-cholesterol ratio strongly correlates with cardiovascular risk assessment, whether this correlation can be quantified mathematically remained an open question.
This study provides a mathematical framework to quantify the correlation between the LDL/HDL cholesterol ratio and early atherosclerotic plaque formation.
Answers are grounded in this paper and cite their sources.
Bifurcation analysis of LDL/HDL ratio in early plaque model is hypothesis-generating; clinical relevance requires validation in human cohorts.
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.
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Hao et al. (2020) studied Atherosclerosis. LDL/HDL-cholesterol ratio was evaluated on Bifurcation branches and stability of radially symmetric steady-state solutions. A mathematical model of early-stage atherosclerotic plaque formation established the existence of bifurcation branches related to the LDL/HDL cholesterol ratio.
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