Skip to main content
Log in

Fibrin polymerization as a phase transition wave: A mathematical model

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

A mathematical model of fibrin polymerization is described. The problem of the propagation of phase transition wave is reduced to a nonlinear Stefan problem. A one-dimensional discontinuity fitting difference scheme is described, and the results of one-dimensional computations are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. O. M. Belotserkovskii, “Solution of complex problems on supercomputers: Experience and trends,” in Phystech Breakthrough—Angle of Attack: to the 80th Anniversary of O. M. Belotserkovskii (Nauka, Moscow, 2005), pp. 265–286 [in Russian].

    Google Scholar 

  2. O. M. Belotserkovskii, Numerical Simulation in Mechanics of Continuous Media (Nauka, Moscow, 1984) [in Russian].

    Google Scholar 

  3. M. Khanin and V. Semenov, “A mathematical model of the kinetics of blood coagulation,” J. Theor. Biol. 136, 127–134 (1989).

    Article  MathSciNet  Google Scholar 

  4. F. I. Ataullakhanov and G. T. Guriya, “Spatial aspects of blood coagulation dynamics: I. Hypothesis,” Biofiz. 39 (1), 89–96 (1994).

    Google Scholar 

  5. F. I. Ataullakhanov, G. T. Guriya, and A. Yu. Safroshkina, “Spatial aspects of blood coagulation dynamics. II. Phenomenological model,” Biofiz. 39 (1), 97–104 (1994).

    Google Scholar 

  6. Computer Models and Advances in Medicine, Ed. by O. M. Belotserkovskii and A. S. Kholodov (Nauka, Moscow, 2001) [in Russian].

  7. Computer and Brain: New Technologies, Ed. by O. M. Belotserkovskii (Nauka, Moscow, 2005) [in Russian].

  8. Medicine in the Mirror of Information Science Ed. by O. M. Belotserkovskii and A. S. Kholodov (Nauka, Moscow, 2008) [in Russian].

  9. V. I. Zarnitsina, F. I. Ataullakhanov, A. I. Lobanov, and O. L. Morozova, “Dynamics of spatially nonuniform patterning in the model of blood coagulation,” Chaos 11 (1), 57–70 (2001).

    Article  MATH  Google Scholar 

  10. A. I. Lobanov, T. K. Starozhilova, V. I. Zarnitsina, and F. I. Ataullakhanov, “Comparison of two mathematical models for the description of the spatial dynamics of blood coagulation,” Mat. Model. 15 (1), 14 (2003).

    MathSciNet  MATH  Google Scholar 

  11. F. I. Ataullakhanov, V. I. Zarnitsina, A. Yu. Kondratovich, et al., “A special class of autowaves—autowaves with a stop—determines the spatial dynamics of blood coagulation,” Usp. Fiz. Nauk 172, 671–690 (2002).

    Article  Google Scholar 

  12. F. I. Ataullakhanov, E. S. Lobanova, O. L. Morozova, et al., “Complex regimes of propagation of excitation and self-organization in a model of blood coagulation, Usp. Fiz. Nauk 177, 87–104 (2007).

    Article  Google Scholar 

  13. M. A. Panteleev, A. N. Balandina, E. N. Lipets, et al., “Task-oriented modular decomposition of biological networks: Trigger mechanism in blood coagulation,” Biophys. J. 98 (9), 1751–1761 (2010).

    Article  Google Scholar 

  14. M. Anand, “A model incorporating some of the mechanical and biochemical factors underlying clot formation and dissolution in flowing blood,” J. Theor. Med. 5, 183–218 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  15. A. S. Rukhlenko, K. E. Zlobina, and G. T. Guriya, “Hydrodynamic activation of blood coagulation in stenotic vessels: A theoretical analysis,” Comput. Issled. Model. 4 (1), 155–183 (2012).

    Google Scholar 

  16. A. I. Lobanov, A. V. Nikolaev, and T. K. Starozhilova, “Mathematical model of fibrin polymerization,” Math. Model. Nat. Phenom. 6 (7), 55–69 (2001).

    Article  MathSciNet  Google Scholar 

  17. O. M. Belotserkovskii, “Mathematical modeling for supercomputers: Background and tendencies,” Comput. Math. Math. Phys. 40, 1173–1187 (2000).

    MATH  Google Scholar 

  18. M. A. Panteleev, M. V. Ovanesov, et al., “Spatial propagation and localization of blood coagulation are regulated by intrinsic and protein C pathways, respectively,” Biophys J. 90 (5), 1489–1500 (2006).

    Article  Google Scholar 

  19. E. A. Ermakova, M. A. Panteleev, and E. E. Shnol, “Blood coagulation and propagation of autowaves in flow,” Pathophysiol. Haemost. Thromb. 34 (2–3), 135–142 (2005).

    Google Scholar 

  20. J. P. Collet, D. Park, C. Lesty, J. Soria, C. Soria, G. Montalescot, and J. W. Weisel, “Influence of fibrin network conformation and fibrin fiber diameter on fibrinolysis speed: Dynamic and structural approaches by confocal microscopy,” Arterioscler. Thromb. Vasc. Biol. 20 (5), 1354–1361 (2000).

    Article  Google Scholar 

  21. A. I. Lobanov, T. K. Starozhilova, and G. T. Guriya, “Numerical investigation of structure formation in blood coagulation,” Mat. Model. 9 (8), 83–95 (1997).

    MATH  Google Scholar 

  22. G. T. Guriya, T. K. Starozhilova, and A. I. Lobanov, “Formation of axially symmetric structures in excitable media with active restoration,” Biofiz. 43, 526–534 (1998).

    Google Scholar 

  23. A. A. Samarskii, Theory of Finite Difference Schemes (Nauka, Moscow, 1989; Marcel Dekker, New York, 2001).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. I. Lobanov.

Additional information

Original Russian Text © A.I. Lobanov, 2016, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2016, Vol. 56, No. 6, pp. 1138–1148.

To the memory of O.M. Belotserkovskii

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lobanov, A.I. Fibrin polymerization as a phase transition wave: A mathematical model. Comput. Math. and Math. Phys. 56, 1118–1127 (2016). https://doi.org/10.1134/S096554251606018X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S096554251606018X

Keywords

Navigation