Traveling wave solutions in the mathematical model of blood coagulation

Abstract

Under normal conditions, blood coagulation provides an effective protective mechanism preventing bleeding in case of vessel damage. Details of its functioning are of particular importance since any blood coagulation disorders lead to severe physiological aggravations. Multiple experimental and computational studies demonstrate the thrombin concentration distribution to determine the spatio-temporal dynamics of clot formation. Propagating from the injury site with constant speed, thrombin concentration profile can be modeled with a traveling wave solution of the system of partial differential equations describing main reactions of the coagulation cascade. In the current study, we derive conditions on the existence and stability of such solutions and provide an analytic approach of their wave speed estimation.

Keywords:

• Blood coagulation
• reaction-diffusion waves
• speed of propagation

AMS Subject Classifications:

• 35C07
• 92C45
• 35K57

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The last author was supported by the grant of Russian Science Foundation [project number 15-11-00029]; the program PICS CNRS [6583 Matbio].