Platelet-wall interactions in continuum models of platelet thrombosis: formulation and numerical solution

A model is developed to describe the formation of platelet thrombi in coronary-artery-sized blood vessels. It involves interactions among a viscous, incompressible fluid; populations of non-activated and activated platelets; activating chemicals; and the vessel walls. Adhesion of platelets to the injured wall and cohesion between activated platelets is modelled using distributions of elastic links which generate stresses that can influence the fluid motion. The first version of the model presented involves two spatial scales: the microscale of the platelets and the macroscale of the vessel. A closure approximation is introduced that allows essential microscale behaviour to be computed while eliminating the necessity to explicitly track events on this scale. Computational methods are presented that meet the diverse challenges posed by the coupled nonlinear partial differential equations of the model and by the complex geometry of the constricted vessels in which the thrombosis simulations are carried out. Simulation results demonstrate that the model can produce thrombi that grow to occlude the vessel, that shear-stress exerted by the fluid on the thrombi can modify their subsequent growth and cause remodelling of their shape through small-scale local changes or large-scale structural breakup.