A synthetic model for blood coagulation including blood slip at the vessel wall

Modeling blood coagulation has taken various directions in recent years, depending on the aspects that authors wish to emphasize. In this paper we want to address an issue that has been systematically ignored in the relevant literature, namely the effect of blood slip at the vessels wall. The presence of a slip results in an increased supply of activated platelets to the clotting site. We calculate such a contribution showing that, in extreme cases, it can be even dominant. Indeed, raising the concentration of activated platelets induces an acceleration of thrombin production and eventually of the whole clot progression. The model explains the difference between arterial and venous thrombi. We confine to the coagulation stage known as "propagation phase" in the context of the so called cell based model. The paper is preparatory for a deeper analysis in which the clotting process is coupled to blood rheology and that will be carried out in the future by the same authors. At the present stage, the extremely complex biochemistry has been simplified adopting a leaner, though virtual, system of diffusion-convection-reaction equations, in the optics of providing "modular" models, that can be reduced or enlarged so to meet specific modeling requirements.