Mathematical Sciences: Computational Modelling of Platelet Aggregation and the Flow of Fluid-Particle Suspensions

这项研究将改进研究血液凝结和流体-颗粒悬浮液流动过程中的血小板聚集的数学模型和数值方法。这些都是相当复杂的大规模问题。因此，这项研究将涉及高度的计算，其中大部分将需要使用超级计算机。提出了一种新的求解多维对流占优对流扩散方程的粒子算法。使用局部力来表示血小板和悬浮颗粒将扩展到表示血管壁。这项工作将阐明聚集中的一个中心问题：血液的局部流体动力学和血管的几何形状如何相互作用，影响聚集的位置、速度和程度。这将有助于非血栓形成的人工内脏的设计。

This research will improve mathematical models and numerical methods for studying platelet aggregation during blood clotting and the flow of fluid-particle suspensions. These are large- scale problems of considerable complexity. Consequently, the research will involve a high degree of computation, much of which will require use of a supercomputer. A new particle-based algorithm for solving a multidimensional convection-dominated convection-diffusion equation will be developed. The use of localized forces to represent platelets and suspended particles will be extended to the representation of blood vessel walls. This work should shed light on a central question in aggregation: how the blood's local fluid dynamics and the geometry of the blood vessel interact to influence the location, rate, and extent of aggregate formation. It will aid in the design of nonthrombogenic artificial internal organs.