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Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 4196-4212. doi: 10.3934/mbe.2019209
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Existence of pulses for a reaction-diffusion system of blood coagulation in flow

  • 1.
    Institut Camille Jordan, UMR 5585 CNRS, Ecole Centrale de Lyon, 69134 Ecully, France
  • 2.
    Institut Camille Jordan, UMR 5585 CNRS, University Lyon 1, 69622 Villeurbanne, France
  • 3.
    INRIA, Université de Lyon, Université Lyon 1, Institut Camille Jordan, 43 Bd. du 11 Novembre 1918, 69200 Villeurbanne Cedex, France
  • 4.
    Peoples’ Friendship University of Russia (RUDN University) 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
  • 5.
    Marchuk Institute of Numerical Mathematics of the RAS, ul. Gubkina 8, 119333 Moscow, Russian Federation
  • Received: 31 January 2019 Accepted: 14 March 2019 Published: 13 May 2019

  • A reaction-diffusion system describing blood coagulation in flow is studied. We prove the existence of stationary solutions provided that the speed of the travelling wave problem for the limiting value of the velocity is positive. The implications to the problem of clot growth are discussed.

    Citation: Nicolas Ratto, Martine Marion, Vitaly Volpert. Existence of pulses for a reaction-diffusion system of blood coagulation in flow[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 4196-4212. doi: 10.3934/mbe.2019209

    Related Papers:

  • A reaction-diffusion system describing blood coagulation in flow is studied. We prove the existence of stationary solutions provided that the speed of the travelling wave problem for the limiting value of the velocity is positive. The implications to the problem of clot growth are discussed.


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    [1] T. Galochkina, H. Ouzzane, A. Bouchnita, et al., Traveling wave solutions in the mathematical model of blood coagulation. Appl. Anal., 96 (2017), 2891–2905.
    [2] V. I. Zarnitsina, A. V. Pokhilko and F. I. Ataullakhanov, A mathematical model for the spatio-temporal dynamics of intrinsic pathway of blood coagulation. I. The model description, Thromb. Res., 84 (1996), 225–236.
    [3] Y. V. Krasotkina, E. I. Sinauridze and F. I. Ataullakhanov, Spatiotemporal dynamics of fibrin formation and spreading of active thrombin entering non-recalcified plasma by diffusion, BBA- Bioenergetics-General Subjects, 1474 (2000), 337–345.
    [4] E. A. Pogorelova and A. I. Lobanov, Influence of enzymatic reactions on blood coagulation autowave, Biophysics, 59 (2014), 10–118.
    [5] A. A. Tokarev, Y. V. Krasotkina, M. V. Ovanesov, et al., Spatial dynamics of contact-activated fibrin clot formation in vitro and in silico in haemophilia b: Effects of severity and ahemphil b treatment, Math. Modell. Nat. Phenom., 1 (2006), 124–137.
    [6] V. I. Zarnitsina, F. I. Ataullakhanov, A. I. Lobanov, et al., Dynamics of spatially nonuniform patterning in the model of blood coagulation, Chaos, 11 (2001), 57–70.
    [7] A. I. Volpert, V. A. Volpert and V. A. Volpert, Traveling Wave Solutions of Parabolic Systems, AMS, Translations of Mathematical Monographs, 1994
    [8] M. Marion and V. Volpert, Existence of pulses for a monotone reaction-diffusion system. J Pure Appl. Funct. Anal., 1 (2016), 97–122.
    [9] N. Ratto, M. Marion and V. Volpert, Existence of pulses for a reaction-diffusion system of blood coagulation, Topol. Methods Nonlinear Anal. (2019), in press.
    [10] V. Volpert and A. Volpert, Properness and topological degree for general elliptic operators, Abstr. Appl. Anal., 3 (2003), 129–182.
    [11] V. Volpert, Elliptic partial differential equations. Volume 1. Fredholm theory of elliptic problems in unbounded domains, Math. Gazette, 98 (2014), 172–174.
    [12] A. V. Belyaev, J. L. Dunster, J. M. Gibbins, et al., Modeling thrombosis in silico: Frontiers, challenges, unresolved problems and milestones. Phys. Life Rev., 26 (2018), 57–95.
    [13] A. Fasano and A. Sequeira, Hemomath, The Mathematics of Blood, Springer, 2017.
    [14] K. G. Mann, T. Orfeo, S. Butenas, et al., Blood coagulation dynamics in haemostasis, Hemostaseologie, 29 (2009), 7–16.
    [15] A. Bouchnita, T. Galochkina, P. Kurbatova, et al., Conditions of microvessel occlusion for blood coagulation in flow, Int. J. Numer. Meth. Bio., (2017), e2850.
    [16] B. Osterud, E. S. Breimo and J. O. Olsen, Blood borne tissue factor revisited, Thromb. Res., 122 (2008), 432–344.
    [17] J. I. Weitz and J. C. Fredenburgh, Platelet polyphosphate: the long and the short of it, Blood, 129 (2017), 1574.
    [18] J. C. Chapin and K. A. Hajjar, Fibrinolysis and the control of blood coagulation, Blood Rev., 29 (2015), 17–24.
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  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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