Activation and extinction models for platelet adhesion

Adherent platelets are an important part of both thrombus formation and in certain stages of atherogenesis. Platelets can be activated by potent chemicals released from adherent platelets and adhere far more readily than unactivated ones. An analytical and numerical model is presented utilising high Peclet number for the activation and adhesion of platelets in shear flows. The model uses a similarity transformation, which characterises the relationship between convective, diffusive transport and the bulk platelet activating reaction mechanism. A first order surface reaction mechanism is used to model platelet adhesion at the wall (cell) surface. The reduced Damköhler number, M, characterises the importance of the bulk reaction and includes both convective and diffusive terms. For a high rate of blood flow (M-->0) the activation of platelets can effectively be terminated. In contrast, for (M-->infinity) an inner layer of activated platelets exists with an infinitesimally thin reaction sheet separating activated and non-activated platelets. This characterisation by the Damköhler number highlights results found clinically, in that thrombus forms in areas of low shear (high M) and in some cases an increased blood flow (low M) can inhibit the activation of platelets completely. The model shows the critical balance that exists between convection, diffusion and reaction.