Mathematical Sciences: Modelling, Analysis, and Computational Simulation of Platelet Aggregation in Large and Small Vessels

血小板聚集在血管壁上是对血管损伤的反应；它们也是与血管疾病和心血管假体使用相关的危及生命的血块的主要成分。微观尺度的聚集模型涉及血液流体动力学和血小板力学化学之间的相互作用，适合研究微循环小血管中的聚集。该项目将探索模型的变化，以获得更现实的总增长率，并改进相关的数值方法，将模拟扩展到三维和更长的时间。这些变化将补充实验技术的最新进展，使模拟与实验的首次详细比较成为可能。为了便于这些比较，研究者与领先的实验科学家建立了合作关系。研究者还将继续计算和分析一类新的连续体模型的探索，他已经制定了研究聚集在较大的血管，如冠状动脉。特别令人感兴趣的是这些模型所显示的化学诱导的液相到固相转变。该项目将描述其对流量和化学参数的依赖。在本项目中进行的数学分析和模拟是对传统实验室实验的补充。它们提供了关于聚合反应各组成部分之间动态相互作用的详细信息，这种信息通常无法在实验室中获得。这些额外的信息将增加对聚合过程的物理和化学控制的了解。这些研究也将为进一步发展聚集模型奠定基础，并将其应用于临床有趣的问题，如血流和血管几何形状如何相互作用以影响天然血管（如冠状动脉）或假体装置（如血管移植或人工心脏）内的聚集。

Platelet aggregates form on blood vessel walls in response to vascular injury; they are also major constituents of the life-threatening blood clots associated with vascular disease and with the use of cardiovascular prostheses. Microscopic-scale models of aggregation, which involve interactions among the blood's fluid dynamics and the mechanics and chemistry of the platelets, are appropriate for studying aggregation in the small vessels of the microcirculation. The project will explore changes in the models to attain more realistic aggregate growth rates, and improvements in the associated numerical methods to extend simulations to three dimensions and to substantially longer time periods. These changes will complement recent advances in experimental technique to allow the first detailed comparison of simulations with experiments. To facilitate these comparisons, the investigator has established collaborations with leading experimental scientists. The investigator will also continue computational and analytical exploration of a new class of continuum models he has formulated for studying aggregation in larger vessels such as the coronary arteries. Of particular interest is the chemically-induced liquid-to-solid phase transition exhibited by these models. The project will characterize its dependence on flow and chemical parameters. The mathematical analysis and simulations to be carried out in this project complement traditional laboratory experimentation. They provide detailed information, of a type which is generally not attainable in the laboratory, about the dynamic interactions among the components of the aggregation response. This additional information will increase insight into the physical and chemical controls on the aggregation process. These studies will also lay the foundations for further development of models of aggregation and for their application to clinically interesting questions such as how flow and vessel geometry interact to influence aggregation within natural vessels, such as the coronary arteries, or prosthetic devices, such as vascular grafts or artificial hearts.