Continuous mathematical model of platelet thrombus formation in blood flow

An injury of a blood vessel requires quick repairing of the wound in order to prevent a loss of blood. This is done by the hemostatic system. The key point of its work is the formation of an aggregate from special blood elements, namely, platelets. The construction of a mathematical model of the formation of a thrombocyte aggregate with an adequate representation of its physical, chemical, and biological processes is an extremely complicated problem. A large size of platelets compared to that of molecules, strong inhomogeneity of their distribution across the blood flow, high shear velocities, the moving boundary of the aggregate, the interdependence of its growth and the blood flux hamper the construction of closed mathematical models convenient for biologists. We propose a new PDE-based model of a thrombocyte aggregate formation. In this model, the movement of its boundary due to the adhesion and detachment of platelets is determined by the level set method. The model takes into account the distribution inhomogeneity of erythrocytes and platelets across the blood flow, the invertible adhesion of platelets, their activation, secretion, and aggregation. The calculation results are in accordance with the experimental data concerning the kinetics of the ADP-evoked growth of a thrombus in vivo for different flow velocities. The model constructed here can be easily extended to the case of other hemostatic mechanisms and can be integrated into different continuous blood flow models.