Department of Mathematics, Morgan State University, Baltimore, MD, USA.
J Biol Dyn. 2023 Dec;17(1):2257734. doi: 10.1080/17513758.2023.2257734.
Atherosclerosis is a leading cause of death worldwide. Making matters worse, nearly 463 million people have diabetes, which increases atherosclerosis-related inflammation. Diabetic patients are twice as likely to have a heart attack or stroke. In this paper, we consider a simplified mathematical model for diabetic atherosclerosis involving LDL, HDL, glucose, insulin, free radicals (ROS), cells, macrophages and foam cells, which satisfy a system of partial differential equations with a free boundary, the interface between the blood flow and the plaque. We establish the existence of small radially symmetric stationary solutions to the model and study their stability. Our analysis shows that the plague will persist due to hyperglycemia even when LDL and HDL are in normal range, hence confirms that diabetes increase the risk of atherosclerosis.
动脉粥样硬化是全球范围内主要的致死原因。更糟糕的是，全球近 4.63 亿人患有糖尿病，这会增加与动脉粥样硬化相关的炎症。糖尿病患者心脏病发作或中风的可能性是正常人的两倍。在本文中，我们考虑了一个简化的糖尿病动脉粥样硬化数学模型，其中涉及 LDL、HDL、葡萄糖、胰岛素、自由基（ROS）、细胞、巨噬细胞和泡沫细胞，这些物质满足带有自由边界的偏微分方程组，该自由边界位于血流和斑块之间。我们建立了模型的小径向对称定态解的存在性，并研究了它们的稳定性。我们的分析表明，即使 LDL 和 HDL 处于正常范围内，由于高血糖，斑块也会持续存在，这证实了糖尿病会增加动脉粥样硬化的风险。
