Dynamics of atherosclerotic plaque formation, growth and regression

该项目旨在提供一个数学框架来解释斑块生长。许多生物学过程导致动脉内动脉粥样硬化斑块的生长。脂蛋白进入动脉壁，刺激组织向细胞发出信号，这些细胞及时做出反应，从而形成脂肪条纹，并生长成危险的斑块，导致心脏病发作或中风。这些过程通常是非线性的，并且在广泛变化的时间尺度上操作。该项目计划使用常微分方程系统，具有非标准边界条件的偏微分方程和分叉理论来发现非线性过程如何塑造斑块生长。预期的结果可能会证明分叉，动力学和非线性系统在斑块生长的重要性，并提供新的模型来解释生物数据。

This project aims to provide a mathematical framework to interpret plaque growth. Many biological processes contribute to the growth of atherosclerotic plaques inside arteries. Lipoproteins enter the artery walls and stimulate tissues to signal to cells which duly respond so that fatty streaks form and grow into dangerous plaques that cause heart attacks or stroke. These processes are often nonlinear and operate on widely varying time scales. The project plans to use systems of ordinary differential equations, partial differential equations with non-standard boundary conditions, and bifurcation theory to find how nonlinear processes shape plaque growth. The expected results may demonstrate the importance of bifurcations, dynamics and nonlinear systems in plaque growth and provide new models to interpret biological data.