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Mathematical Biosciences and Engineering

2011, Volume 8, Issue 2: 425-443. doi: 10.3934/mbe.2011.8.425
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Blood coagulation dynamics: mathematical modeling and stability results

  • 1.
    Department of Mathematics and CEMAT/IST, Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais 1, 1049-001 Lisboa
  • 2.
    Department of Mathematics and CEMAT/IST, Faculty of Sciences and Technology, University of Algarve, Campus de Gambelas 8005-139 Faro
  • 3.
    Department of Technical Mathematics, Faculty of Mechanical Engineering, Czech Technical University, Náměstí 13, 121 35 Prague 2
  • Received: 01 March 2010 Accepted: 29 June 2018 Published: 01 April 2011

  • MSC : Primary: 76Z05, 92B05, 34D15, 34D20, 37B25, 93D99; Secondary: 76M12.

  • The hemostatic system is a highly complex multicomponent biosystem that under normal physiologic conditions maintains the fluidity of blood. Coagulation is initiated in response to endothelial surface vascular injury or certain biochemical stimuli, by the exposure of plasma to Tissue Factor (TF), that activates platelets and the coagulation cascade, inducing clot formation, growth and lysis. In recent years considerable advances have contributed to understand this highly complex process and some mathematical and numerical models have been developed. However, mathematical models that are both rigorous and comprehensive in terms of meaningful experimental data, are not available yet. In this paper a mathematical model of coagulation and fibrinolysis in flowing blood that integrates biochemical, physiologic and rheological factors, is revisited. Three-dimensional numerical simulations are performed in an idealized stenosed blood vessel where clot formation and growth are initialized through appropriate boundary conditions on a prescribed region of the vessel wall. Stability results are obtained for a simplified version of the clot model in quiescent plasma, involving some of the most relevant enzymatic reactions that follow Michaelis-Menten kinetics, and having a continuum of equilibria.

    Citation: Adélia Sequeira, Rafael F. Santos, Tomáš Bodnár. Blood coagulation dynamics: mathematicalmodeling and stability results[J]. Mathematical Biosciences and Engineering, 2011, 8(2): 425-443. doi: 10.3934/mbe.2011.8.425

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  • The hemostatic system is a highly complex multicomponent biosystem that under normal physiologic conditions maintains the fluidity of blood. Coagulation is initiated in response to endothelial surface vascular injury or certain biochemical stimuli, by the exposure of plasma to Tissue Factor (TF), that activates platelets and the coagulation cascade, inducing clot formation, growth and lysis. In recent years considerable advances have contributed to understand this highly complex process and some mathematical and numerical models have been developed. However, mathematical models that are both rigorous and comprehensive in terms of meaningful experimental data, are not available yet. In this paper a mathematical model of coagulation and fibrinolysis in flowing blood that integrates biochemical, physiologic and rheological factors, is revisited. Three-dimensional numerical simulations are performed in an idealized stenosed blood vessel where clot formation and growth are initialized through appropriate boundary conditions on a prescribed region of the vessel wall. Stability results are obtained for a simplified version of the clot model in quiescent plasma, involving some of the most relevant enzymatic reactions that follow Michaelis-Menten kinetics, and having a continuum of equilibria.


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