Coupling blood clot coagulation cascade and blood flow dynamics

Introduction: Thrombosis is a global health concern that is linked to a number of cardiovascular events and their related death rates. At present, there is a need for the mathematical description of the process of thrombus formation in order to introduce new devices and decrease a number of complications.

Methods: We proposed a mathematical model of thrombus formation in a vessel, taking into account the coagulation and blood flow effects on fibrin clot growth. The mathematical formulation includes non-steady Navier–Stokes equations and incompressibility equations to describe the blood motion and five coupled convection–diffusion reaction equations to describe the temporal and spatial evolution of thrombus. The sub-model of blood coagulation including the kinetics of metabolites (VIIIa and Xa factors, thrombin, protein C, and fibrin concentrations) was adopted. A special equation connecting thrombus growth rate and fibrin concentration based on the proposed hypothesis was also introduced.

Results and Discussion: The concentrations of the components of the blood coagulation cascade were computed. The dependence of thrombus size on velocity magnitudes was also obtained. Additionally, pressure distribution and wall shear stress were evaluated. The maximum flow rate increased by 14% with a thrombus size of 16 mm³. The proposed model describes changes in the key metabolites of the blood coagulation cascade. The results were compared with clinical and in vitro data from the literature and showed a good corelation.

Conclusions: A simulation of thrombus growth is planned to be incorporated into problems related to the mid- and long-term predictions of cardiovascular devices' behavior, such as grafts, stents, and artificial aortic valves.

This research was funded by the Ministry of science and higher education of the Russian Federation (Project № FSNM-2024-0009).

Authors and Affiliations:

Nikita Pil (nikitapil32@gmail.com) * / Biofluids laboratory, Perm National Research Polytechnic University, Perm, Komsomolskiy Prospect 29

Alex G. Kuchumov (kychymov@inbox.ru) / Biofluids laboratory, Perm National Research Polytechnic University, Perm, Komsomolskiy Prospect 29