论文标题
与胆固醇比相关的斑块形成的自由边界模型的分叉分析
Bifurcation analysis of a free boundary model of plaque formation associated with the cholesterol ratio
论文作者
论文摘要
低密度脂蛋白（LDL）/高密度脂蛋白（HDL） - 胆固醇比已显示与心血管风险评估具有很高的相关性。是否可以数学上量化相关性？在本文中，我们为在动脉粥样硬化的早期阶段的牙菌斑形成的数学模型进行了分叉分析。该分叉分析与LDL/HDL的比率基于径向对称稳态溶液的明确配方。通过对这些解决方案进行扰动分析，我们确定了分叉分支的存在，并得出了一种理论条件，该条件是针对不同模式发生分叉的。然后，我们还分析了径向对称稳态溶液的稳定性，并进行数值模拟以验证所有理论结果。
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.
