Non-stationary effects in the mathematical model of platelet thrombus growth

The paper considers the effects that occur during numerical modeling of platelet thrombus growth during non-stationary flow. Since the detailed mathematical models of thrombus formation developed to date include a large number of equations, the authors propose to use a reduced mathematical model of thrombin production and a simple diffusion model of platelet transport and aggregation. FlowVision, based on the finite-volume approach to approximating the equations of fluid and gas motion, is used as a software package for numerical modeling. Two problems were considered in the test format. The first problem is associated with the formation of a platelet thrombus in the mouse cremaster arteriole at different heart rates. The second problem concerns a similar process in the human portal vein. For the first problem, it was found that platelet mobility increases in the flow near the growing thrombus, leading to the formation of structures ("columns") in the direction perpendicular to the flow velocity. The features of thrombus growth depending on heart rate are studied. As a result of solving the second problem, it was found that the nature of the flow in the portal vein is significantly more complex than in the cremaster. It is evident that the "pillars" are formed on the entire surface accessible to platelets. Changing the frequency of velocity oscillations leads to smoothing of the growing thrombus shape. Both problems are characterized by the existence of such a value of the frequency of flow velocity change at which a thrombus with a complex fractal-type surface is formed. The obtained results emphasize the importance of taking into account the dynamic charac-teristics of blood flow when studying thrombus formation processes. The use of simplified models made it possible to analyze key aspects without excessively complicating the computational procedures. The study of non-stationary effects during the growth of platelet thrombi can be useful in the numerical study of thrombotic complications during surgical operations. Further studies may include a more detailed study of the effect of hemodynamic parameters on the growth and structure of thrombi, as well as the development of new methods of numerical modeling to improve the accuracy of forecasts.