The coagulation cascade of blood may be initiated by flow induced platelet activation, which prompts clot formation in prosthetic cardiovascular devices and arterial disease processes. While platelet activation may be induced by biochemical agonists, shear stresses arising from pathological flow patterns enhance the propensity of platelets to activate and initiate the intrinsic pathway of coagulation, leading to thrombosis. Upon activation platelets undergo complex biochemical and morphological changes: organelles are centralized, membrane glycoproteins undergo conformational changes, and adhesive pseudopods are extended. Activated platelets polymerize fibrinogen into a fibrin network that enmeshes red blood cells. Activated platelets also cross-talk and aggregate to form thrombi. Current numerical simulations to model this complex process mostly treat blood as a continuum and solve the Navier-Stokes equations governing blood flow, coupled with diffusion-convection-reaction equations. It requires various complex constitutive relations or simplifying assumptions, and is limited to μm level scales. However, molecular mechanisms governing platelet shape change upon activation and their effect on rheological properties can be in the nm level scales. To address this challenge, a multiscale approach which departs from continuum approaches, may offer an effective means to bridge the gap between macroscopic flow and cellular scales. Molecular dynamics (MD) and dissipative particle dynamics (DPD) methods have been employed in recent years to simulate complex processes at the molecular scales, and various viscous fluids at low-to-high Reynolds numbers at mesoscopic scales. Such particle methods possess important properties at the mesoscopic scale: complex fluids with heterogeneous particles can be modeled, allowing the simulation of processes which are otherwise very difficult to solve by continuum approaches. It is becoming a powerful tool for simulating complex blood flow, red blood cells interactions, and platelet-mediated thrombosis involving platelet activation, aggregation, and adhesion.
Mathematical Models for Some Aspects of Blood Microcirculation
