Different Types of Phenomenological Mathematical Models of Thrombus Growth
https://doi.org/10.18705/2311-4495-2015-0-6-53-63
Abstract
Phenomenological mathematical model of laser-induced thrombi growth is developed on the basis of Bogolubov’s hierarchy of time scales. The stochastic character of thrombi growth is revealed in the model by explicit introduction of the probability function. The main foundations of the model correspond to the basic experimental results concerning thrombus formation obtained in recent years. The modeling curves permit to achieve qualitative agreement between model and experimental data. The comparison of the model with other models of thrombus growth is performed.
About the Authors
A. S. Kondratyev
Herzen State Pedagogical University of Russia
Russian Federation
Russian Federation
A. V. Lyaptsev
Herzen State Pedagogical University of Russia
Russian Federation
Russian Federation
I. A. Mikhailova
Institute of Experimental Medicine, Federal Almazov Medical Research Centre; First Pavlov State Medical University
Russian Federation
Russian Federation
N. N. Petrishchev
Institute of Experimental Medicine, Federal Almazov Medical Research Centre; First Pavlov State Medical University
Russian Federation
Russian Federation
References
1. A. Kondratyev, I. Mikhailova, Mathematical Modeling of Laser-Induced Thrombus Formation in Microvasculature.In: Mathematical Modeling. (Ed. Christopher R. Brennan). N.Y.: Nova Science Publishers, Inc. 2011: Ch. 5.
2. J. D. Murray, Mathematical Biology. N.Y.: Springer-Verlag, 2004; 551 p.
3. A. Alenitsyn, A. Kondratyev, I. Mikhailova, I. Siddique, Mathematical modeling of thrombus growth in mesenteric vessels. Math. Biosc. 2010; 224: 29-34.
4. R. Ouared, B. Chopard, B. Stahl, D.A. Rufenacht, H. Yilmaz, G. Courbebaisse, Thrombosis modeling in intracranial aneurysms: a lattice Boltzmann numerical algorithm. Comput. Phys. Commun. 2008;179 : 128-131.
5. T. W. Secomb, Theoretical Models for Regulation of Blood Flow. Microcirculation. 2008;15: 765-775.
6. A.A. Tokarev, A.A. Butylin, F.I. Ataullakhanov, Platelet Adhesion from Shear Blood Flow is Controlled by Near-Wall Rebounding Collisions with Erythrocytes. Biophys. J. 2011;100: 799-808.
7. A.A. Tokarev, Yu.V. Krasotkina, M.V. Ovanesov, M.A. Panteleev, M.A. Azhigirova, V.A. Volpert, F.I. Ataullakhanov, A.A. Butylin, Spatial Dynamics of Contact-Activated Fibrin Clot Formation in vitro and in silico in Haemophilia B: Effects of Severity and Ahemphil B Treatment. Mathematical modeling of natural phenomena. 2006;1: 124-137.
8. A. Tokarev, I. Sirakov, G. Panasenko, V. Volpert,E. Shnjl, A. Butylin, F. Ataullakhanov, Continuous Mathematical Model of Platelet Thrombus Formation in Blood Flow. Russian Journal of Numerical Analysis and Mathematical Modeling. 2012;27: 191-212.
9. Z. Xu, N. Chen, S. Shadden, J.E. Marsden, M.M. Kamocka, E.D. Rosen, M.S. Alber, Study of blood flow impact on growth of thrombi using a multiscale model. Soft Matter. 2009;5 :769-779.
10. Z. Xu, N. Chen, S. Shadden, J.E. Marsden, M.M. Kamocka, E.D. Rosen, M.S. Alber, Study of blood flow impact on growth of thrombi using a multiscale model. Soft Matter. 2009; 5: 769-779.
11. N.Petrishchev, I.Mikhailova. Thrombi formation parameters in mesenteric arterioles and venules in rats. Thromb. Res. 1993; 72;347-352
12. B. Furie, B.C. Furie, Thrombus formation in vivo. J. Clin. Invest. 2005;5: 3355-3362.
13. S. Mordon, S. Begu, B. Buys, C. Tourne-Peteilh, J. Devoisselle, Study of platelet behavior in vivo after endothelial stimulation with laser irradiation using fluorescence intravital videomicroscopy and PEGylated liposome staining. Microvasc. Res. 2002;64: 316-325.
14. Z.M. Ruggeri, Old concepts and new developments in the study of platelet aggregation. J. Clin. Invest. 2000;105: 699-701.
15. Z.M. Ruggeri, G.L. Mendolicchio, Adhesion mechanisms in platelet function. Circ. Res. 2007;100: 1673-1685.
16. A. Tailor, D. Cooper, D.N. Granger, Platelet-Vessel Wall Interactions in the Microcirculation. Microcirculation. 2005; 12: 275-285.
17. D. Varga-Szabo, I. Pleines, B. Nieswandt, Cell adhesion mechanisms in platelets, Arterioscler. Thromb. Vasc. Biol. 2008; 28: 403-412.
18. T. David, P.G. Walker, Activation and extinction models for platelet adhesion. Biorheology. 2002; 39:293-298.
19. A. L. Kuharsky, A.L. Fogelson, Surface-mediated control of blood coagulation: the role of binding site densities and platelet deposition. Biophys. J. 2001;80: 1050-1074.
20. I.V. Pivkin, P.D. Richardson, G. Karniadakis, Blood flow velocity effects and role of activation delay time on growth and form of platelet thrombi. Proc. Natl. Acad. Sci. USA.2006; 103: 17164-17169.
21. D. Wootton, C. Marcou, S. Hanson, D. Ku, A mechanistic model of acute platelet accumulation in thrombogenic stenoses Ann. Biom. Eng. 2001;29: 321-329.
22. N. Begent, G.V.R. Born, Growth rate in vivo of platelet thrombi, produced by iontophoresis of ADP as a function of mean blood velocity. Nature. 1970; 227: 926-930.
23. A.S. Kondratyev, I.A. Mikhailova, N.N. Petrishchev, Effect of blood flow velocity on platelet thrombi formation in microvessels. Biophysics.1990;35: 469-472.
24. N.N. Petrishchev, A.S. Kondratyev, I.A. Mikhailova, Effect of blood flow on thrombus growth in mesenteric vessels. 6th World Congress for Microcirculation, Munich (Germany). 1996: 487-490.
25. M. Sato, N. Ohshima, Hemodynamics at stenosis formed by growing platelet thrombi in mesenteric microvasculature of rat. Microvasc. Res. 1986;31: 66-76.
26. P.D. Richardson, Effect of blood flow velocity on growth rate of platelet thrombi. Nature. 1970;245: 103-104.
27. A. Bonnefoy, Q. Lui, C. Legrand, M. Frojmovic, Efficiency of platelet adhesion to fibrinogen depends on both cell activation and flow. Biophys. J. 2000;78: 2834-2843.
28. M.F. Hockin, K.J. Jones, S.J. Everse, K.G. Mann. A model for the stoichiometric regulation of blood coagulation. J. Bio. Chem. 2002;277: 18322-18333.
29. S. Kulharni, S.M. Dopheide, C.L. Yap, C. Ravanat et al. A revised model of platelet aggregation, J. Clin. Invest. 2000; 105: 783-791.
30. L.D. Landau, E.M. Lifshitz. Fluid Mechanics.(Ed. Butterworth - Heinemann). 1987; Vol. 6.
Review
For citations:
Kondratyev A.S., Lyaptsev A.V., Mikhailova I.A., Petrishchev N.N. Different Types of Phenomenological Mathematical Models of Thrombus Growth. Translational Medicine. 2015;(6):53-63. (In Russ.) https://doi.org/10.18705/2311-4495-2015-0-6-53-63
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