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

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Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics

Abstract

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.

The author “A. Tokarev” was working in the institute “Dmitry Rogachev” at the time of presentation of this work in a session of the BIOMAT 2018 in Morocco.

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Acknowledgements

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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Authors and Affiliations

  1. Peoples’ Friendship University of Russia (RUDN University), Moscow, Russian Federation

    Alexey Tokarev, Nicolas Ratto & Vitaly Volpert

  2. Dmitry Rogachev National Research Center of Pediatric Hematology, Oncology and Immunology, Moscow, Russian Federation

    Alexey Tokarev

  3. Institute Camille Jordan, UMR 5208 CNRS, University Lyon 1, Villeurbanne, France

    Nicolas Ratto & Vitaly Volpert

  4. INRIA, Universit de Lyon, Universit Lyon 1, Institute Camille Jordan, Villeurbanne, France

    Nicolas Ratto & Vitaly Volpert

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  1. Alexey Tokarev
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  2. Nicolas Ratto
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Correspondence to Vitaly Volpert .

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  1. Federal University of Rio de Janeiro, President, BIOMAT Consortium – International Institute for Interdisciplinary Sciences, Rio de Janeiro, Rio de Janeiro, Brazil

    Rubem P. Mondaini

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Tokarev, A., Ratto, N., Volpert, V. (2019). Mathematical Modeling of Thrombin Generation and Wave Propagation: From Simple to Complex Models and Backwards. In: Mondaini, R. (eds) Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-030-23433-1_1

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