Mathematical Modeling of Thrombin Generation and Wave Propagation: From Simple to Complex Models and Backwards

  • Alexey Tokarev
  • Nicolas Ratto
  • Vitaly VolpertEmail author


Blood coagulation is an extremely complex biochemical system consisting of more than twenty proteins involved in more than a hundred chemical reactions. Correct functioning of this system is indispensable for normal hemostasis, thus its malfunctions lead to life threatening bleedings and thromboses. Huge efforts are directed to understand how this system is organized and controlled, how its response can be predicted, and what experimental methods should be used in patient diagnostics and treatment. Here, we briefly review mathematical modeling approaches existing in this field. We pay special attention to the transitions from simple to complex models and to the reduction of complex models back to simple ones, as such reduction actually provides possibility to understand the fundamental mechanisms of functioning of complex biological systems besides coagulation.


Blood coagulation Blood diseases Active media Autowaves Mathematical modeling Detailed models Phenomenological models Reduced models 



This work was partially supported by the “RUDN University Program 5-100” to A.T. and V.V. and by the Dynasty Foundation Fellowship to A.T.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Alexey Tokarev
    • 1
    • 2
  • Nicolas Ratto
    • 1
    • 3
    • 4
  • Vitaly Volpert
    • 1
    • 3
    • 4
    Email author
  1. 1.Peoples’ Friendship University of Russia (RUDN University)MoscowRussian Federation
  2. 2.Dmitry Rogachev National Research Center of Pediatric HematologyOncology and ImmunologyMoscowRussian Federation
  3. 3.Institute Camille Jordan, UMR 5208 CNRSUniversity Lyon 1VilleurbanneFrance
  4. 4.INRIAUniversit de Lyon, Universit Lyon 1, Institute Camille JordanVilleurbanneFrance

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