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Influence of Antithrombin on the Regimes of Blood Coagulation: Insights from the Mathematical Model

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Abstract

Blood coagulation is regulated through a complex network of biochemical reactions of blood factors. The main acting enzyme is thrombin whose propagation in blood plasma leads to fibrin clot formation. Spontaneous clot formation is normally controlled through the action of different plasma inhibitors, in particular, through the thrombin binding by antithrombin. In the current study we develop a mathematical model of clot formation both in quiescent plasma and in blood flow and determine the analytical conditions on the antithrombin concentration corresponding to different regimes of blood coagulation.

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Authors and Affiliations

  1. Camille Jordan Institute, University Lyon 1, Villeurbanne, 69622, France

    Anass Bouchnita, Tatiana Galochkina & Vitaly Volpert

  2. Laboratoire de Biométrie et Biologie Evolutive, UMR 5558 CNRS, University Lyon 1, 69376, Lyon, France

    Anass Bouchnita

  3. Laboratory of Study and Research in Applied Mathematics, Mohammadia School of Engineers, Mohamed V University, Rabat, Morocco

    Anass Bouchnita

  4. Department of Biophysics, Faculty of Biology, M.V. Lomonosov Moscow State University, Leninskie gory 1, Moscow, Russia, 119992

    Tatiana Galochkina

  5. Federal Research Clinical Center of Federal Medical and Biological Agency of Russia, Orekhovy boulevard 28, Moscow, Russia, 115682

    Tatiana Galochkina

Authors
  1. Anass Bouchnita
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  2. Tatiana Galochkina
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  3. Vitaly Volpert
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Corresponding author

Correspondence to Tatiana Galochkina.

Appendix

Appendix

1.1 Model of the Intrinsic Pathway Functioning

We model the reactions of coagulation cascade presented in the Fig. 8. Straight arrows indicate factors activation, curved arrows indicate the catalytic actions of factors on other factors activation reactions. Ia, IIa, Va, VIIIa, IXa, Xa, XIa denote the concentrations of activated factor forms and I, II, V, VIII, IX, X, XI denote the inactivated forms. Coagulation cascade is launched when sufficient initial amount of thrombin (IIa) is formed and starts the positive feedback loops. As the result we have the conversion of fibrinogen (I) to fibrin (Ia) and fibrin polymerization (Ip). Fibrin polymer finally forms the clot scaffold.

Fig. 8
figure 8

Schematic representation of the coagulation intrinsic pathway of coagulation cascade

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1.2 Parameter Values for Numerical Simulations

Parameter values are taken from Zarnitsina et al. (2001), and Butenas and Mann (2001) (Table 1).

Table 1 The values of the parameters used in numerical simulations
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Bouchnita, A., Galochkina, T. & Volpert, V. Influence of Antithrombin on the Regimes of Blood Coagulation: Insights from the Mathematical Model. Acta Biotheor 64, 327–342 (2016). https://doi.org/10.1007/s10441-016-9291-2

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  • DOI: https://doi.org/10.1007/s10441-016-9291-2

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