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

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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.