Sat, 26 Jul 2008 07:24:46 BST CiteULike: matthewhflamm's model http://www.citeulike.org/user/matthewhflamm/tag/model CiteULike.org en-gb Copyright © 2004-2008 citeulike.org http://www.citeulike.org/user/matthewhflamm/article/2683091 <i>Biorheology, Vol. 39, No. 3-4. (2002), pp. 293-298.</i><br /><br />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, Mscr, characterises the importance of the bulk reaction and includes both convective and diffusive terms. For a high rate of blood flow (Mscr→0) the activation of platelets can effectively be terminated. In contrast, for (Mscr→∞) 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 Mscr) and in some cases an increased blood flow (low Mscr) can inhibit the activation of platelets completely. The model shows the critical balance that exists between convection, diffusion and reaction. Activation and extinction models for platelet adhesion T David PG Walker Biorheology, Vol. 39, No. 3-4. (2002), pp. 293-298. 2008-04-17T18:06:10-00:00 2002 Biorheology 39 3-4 293 298 activation model platelet shear_stress http://www.citeulike.org/user/matthewhflamm/article/2683026 <i>Journal of Mathematical Biology, Vol. 31, No. 7. (1993), pp. 675-701.</i><br /><br />Platelets cohere to one another to form platelet aggregates as part of the blood's clotting response. The ability of a platelet to participate in this process depends on its prior ‘activation’ by chemicals released into the blood plasma by other activated platelets. We study the piecewise-linear system of reaction-diffusion equations which, in one spatial dimension, describe the chemically-mediated spread of platelet activation. We establish the existence of classical solutions to this system of equations, and show that these solutions do not blow up in finite time. We also explicitly construct travelling front solutions and discuss their stability. Finally, we present numerical evidence which suggests that for a broad range of initial data with the correct limiting values at ± 8, the solution to the initial value problem rapidly evolves into the travelling front solution provided the front is linearly stable. Activation waves in a model of platelet aggregation: existence of solutions and stability of travelling fronts Victor Moll Aaron Fogelson doi:10.1007/BF00160419 Journal of Mathematical Biology, Vol. 31, No. 7. (1993), pp. 675-701. 2008-04-17T17:32:25-00:00 1993 Journal of Mathematical Biology 31 7 675 701 activation model platelet