A continuum model of platelet aggregation: Closure, computational methods and simulation

An existing continuum model of platelet aggregation in large arteries is presented. The blood and aggregating platelets are treated as a single fluid with varying material properties to account for links between platelets. There are two distinct spatial scales, the scale of the fluid and the much smaller scale of platelet-platelet interactions. Activated platelets interact to form elastic links on the smaller scale. These links influence the fluid flow by the addition of an extra stress.; The presence of two spatial scales makes the problem extremely difficult to analyze or to simulate. However, under the assumptions that the links act as linear springs with zero resting length and the breaking rate of the links is independent of the strain, the equations on the platelet scale can be eliminated in favor of an evolution equation for the stress tensor. In this dissertation, a closure model is presented that allows the breaking rate of a link to depend on its length while only working with variables on the fluid length scale. The closure model is compared with the full model using asymptotic analysis and computational tests.; The closure is used to explore the behavior of the model by simulating a growing aggregate on an injured vessel wall. These tests show that the model platelet aggregate is capable of covering an injury and redirecting the fluid. The results of the tests also reveal aspects of the model that need to be improved in future versions, such as the boundary condition at solid walls and the treatment of the aggregate as a single phase material. In creating these simulations, some computational challenges were encountered. The stability of an approximate projection method for solving the incompressible Navier-Stokes equations on a cell-centered grid is analyzed. The boundary conditions at the upstream and downstream boundaries are discussed, and a numerical method is proposed and analyzed.