Initiation of reaction–diffusion waves of blood coagulation

Tatiana Galochkina (1) , Martine Marion (2, 3) , Vitaly Volpert (4, 2)

1 ICJ - Institut Camille Jordan
2 MMCS - Modélisation mathématique, calcul scientifique
3 ECL - École Centrale de Lyon
4 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis

Formation of blood clot in response to the vessel damage is triggered by the complex network of biochemical reactions of the coagulation cascade. The process of clot growth can be modeled as a traveling wave solution of the bistable reaction–diffusion system. The critical value of the initial condition which leads to convergence of the solution to the traveling wave corresponds to the pulse solution of the corresponding stationary problem. In the current study we prove the existence of the pulse solution for the stationary problem in the model of the main reactions of the blood coagulation cascade using the Leray–Schauder method.

Domains: Analysis of PDEs [math.AP]

Tatiana Galochkina, Martine Marion, Vitaly Volpert. Initiation of reaction–diffusion waves of blood coagulation. Physica D: Nonlinear Phenomena, 2018, 376-377, pp.160-170. ⟨10.1016/j.physd.2017.11.006⟩. ⟨hal-01941465⟩