Two-dimensional stationary sructures in the mathematical model of the blood coagulation with the hypothesis of thrombin activity switching
Matematičeskoe modelirovanie, Tome 16 (2004) no. 12, pp. 85-95.

Voir la notice de l'article provenant de la source Math-Net.Ru

Mathematical model of the clot formation taking into account the hypothesis of thrombin activity switching was investigated. Numerical calculations of the pattern formation in two dimensional systems are carried out. The stationary structures in the model can be exist due to division of the back front of propagating pulses. Moving and stationary structures in the model are not sensitive to the convective flux.
@article{MM_2004_16_12_a7,
     author = {M. P. Krutikova and I. A. Kurilenko and A. I. Lobanov and T. K. Starogilova},
     title = {Two-dimensional stationary sructures in the mathematical model of the blood coagulation with the hypothesis of thrombin activity switching},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {85--95},
     publisher = {mathdoc},
     volume = {16},
     number = {12},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2004_16_12_a7/}
}
TY  - JOUR
AU  - M. P. Krutikova
AU  - I. A. Kurilenko
AU  - A. I. Lobanov
AU  - T. K. Starogilova
TI  - Two-dimensional stationary sructures in the mathematical model of the blood coagulation with the hypothesis of thrombin activity switching
JO  - Matematičeskoe modelirovanie
PY  - 2004
SP  - 85
EP  - 95
VL  - 16
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2004_16_12_a7/
LA  - ru
ID  - MM_2004_16_12_a7
ER  - 
%0 Journal Article
%A M. P. Krutikova
%A I. A. Kurilenko
%A A. I. Lobanov
%A T. K. Starogilova
%T Two-dimensional stationary sructures in the mathematical model of the blood coagulation with the hypothesis of thrombin activity switching
%J Matematičeskoe modelirovanie
%D 2004
%P 85-95
%V 16
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2004_16_12_a7/
%G ru
%F MM_2004_16_12_a7
M. P. Krutikova; I. A. Kurilenko; A. I. Lobanov; T. K. Starogilova. Two-dimensional stationary sructures in the mathematical model of the blood coagulation with the hypothesis of thrombin activity switching. Matematičeskoe modelirovanie, Tome 16 (2004) no. 12, pp. 85-95. http://geodesic.mathdoc.fr/item/MM_2004_16_12_a7/

[1] A. Kuharsky, A. L. Fogelson, “Surfase-Mediated control of Blood Coagulation: the Role of Binding Site Densities and Platelet Deposition”, Biophysical Journal, 80:3 (2001), 1050–1074 | DOI

[2] R. G. Macfarlane, “An enzyme cascade in the blood clotting mechanism, and its function as a biochemical amplifier”, Nature, 202(4931) (1964), 498–499 | DOI

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

[4] Yu. A. Barynin, I. A. Starkov, M. A. Khanin, “Matematicheskie modeli fiziologii gemostaza”, Izv. AN. Seriya biologicheskaya, 1999, no. 1, 59–66

[5] G. M. Willems, T. Lindhout, H. Coenraad, W. T. Hermens, H. C. Hemker, “Simulation model for thrombin generation in plasma”, Haemostasis, 21 (1991), 197–207 | MR

[6] H. Kessels, G. M. Willems, H. C. Hemker, “Analysis of trombin generation in plasma”, Comput. Biol. Med., 24 (1994), 277–288 | DOI

[7] C. J. Jones, K. G. Mann, “A model for the tissue factor pathway to thrombin. II. A mathematical simulation”, J. Biol. Chem., 269:37 (1994), 23367–23373

[8] F. I. Ataullakhanov, G. T. Guriya, “Prostranstvennye aspekty dinamiki svertyvaniya krovi. I. Gipoteza”, Biofizika, 39:1 (1994), 87–96

[9] F. I. Ataullakhanov, R. I. Volkova, G. T. Guriya, V. I. Sarbash, “Prostranstvennye aspekty dinamiki svertyvaniya krovi. III Rost tromba in vitro”, Biofizika, 40:6 (1994), 1320–1328

[10] F. I. Ataullakhanov, G. T. Guria, V. I. Sarbash, R. I. Volkova, “Spatio-temporal dynamics of clotting and pattern formation in human blood”, Biochimica et Biophysica Acta, 1425 (1998), 453–468

[11] E. I. Sinauridze, R. I. Volkova, Yu. V. Krasotkina, V. I. Sarbash, F. I. Ataullakhanov, “Dynamics of clot growth induced by thrombin diffusion into nonstirred citrate human plasma”, Biochimica et Biophysica Acta, 1425 (1998), 607–616

[12] F. I. Ataullakhanov, G. T. Guriya, A. Yu. Safroshkina, “Prostranstvennye aspekty dinamiki svertyvaniya krovi. II. Fenomenologicheskaya model”, Biofizika, 39:1 (1994), 97–104

[13] T. K. Starozhilova, A. I. Lobanov, G. T. Guriya, “Chislennoe issledovanie obrazovaniya dvumernykh struktur v modeli vozbudimoi sredy s aktivnym vosstanovleniem”, Matematicheskoe modelirovanie, 9:2 (1997), 21–24 | MR | Zbl

[14] A. I. Lobanov, T. K. Starozhilova, G. T. Guriya, “Chislennoe issledovanie strukturoobrazovaniya pri svertyvanii krovi”, Matematicheskoe modelirovanie, 9:8 (1997), 83–95 | MR | Zbl

[15] G. T. Guriya, A. I. Lobanov, T. K. Starozhilova, “Formirovanie aksialno-simmetrichnykh struktur v vozbudimykh sredakh s aktivnym vosstanovleniem”, Biofizika, 43:Z (1998), 526–534

[16] G. T. Guriya, A. I. Lobanov, T. K. Starozhilova, “Modelirovanie rosta otorvavshegosya tromba v pristenochnom potoke”, Kompyuternye modeli i progress meditsiny, Nauka, M., 2001, 250–263

[17] V. I. Zarnitsina, A. V. Pokhilko, F. I. Ataullakhanov, “A mathematical model for the spatio-temporal dynamics of intrinsic pathway of blood coagulation. I. The model description”, Thrombosis Research, 84:4 (1996), 225–236 | DOI

[18] V. I. Zarnitsina, A. V. Pokhilko, F. I. Ataullakhanov, “A mathematical model for the spatio-temporal dynamics of intrinsic pathway of blood coagulation. II. Results”, Thrombosis Research, 84:5 (1996), 333–344 | DOI

[19] V. I. Zarnitsina, F. I. Ataullakhanov, A. I. Lobanov, O. L. Morozova, “Dynamics of stationary spatial-nonuniform patterning in the model of blood coagulation”, Chaos: Interdisciplinary Journal of Nonlinear Sciences, 11:1 (2001), 57–70 | DOI | Zbl

[20] F. I. Ataullakhanov, V. I. Zarnitsina, A. V. Pokhilko, A. I. Lobanov, O. L. Morozova, “Spatio-temporal dynamics of blood coagulation and pattern formation. A theoretical approach”, International Journal of Bifurcations and Chaos, 2001 | MR | Zbl

[21] A. I. Lobanov, T. K. Starozhilova, V. I. Zarnitsyna, F. I. Ataullakhanov, “Sravnenie dvukh matematicheskikh modelei dlya opisaniya prostranstvennoi dinamiki protsessa svertyvaniya krovi”, Matematicheskoe modelirovanie, 15:1 (2002), 14–28 | MR

[22] V. I. Zarnitsina, A. I. Lobanov, O. L. Morozova, F. L. Ataullakhanov, “Dynamics of stationary spatial-nonuniform structures formation in blood coagulating reaction-diffusion model”, JSST International Conference of Modeling, Control and Computation in Simulation, Oct. 22–24, 2000, Tokyo, 84–89

[23] B. N. Belintsev, B. F. Dibrov, M. A. Lifshits, M. V. Volkenshtein, “Nelineinaya ustoichivost v raspredelennoi triggernoi sisteme. Biologicheskii barer”, Biofizika, 23:5 (1978), 864–869

[24] A. I. Lobanov, T. K. Starozhilova, “Kachestvennoe issledovanie nachalnogo etapa formirovaniya neravnovesnykh struktur v modeli tipa “reaktsiya-diffuziya””, Matematicheskoe modelirovanie, 9:12 (1997), 3–15 | MR | Zbl

[25] V. A. Vasilev, Yu. M. Romanovskii, V. G. Yakhno, Avtovolnovye protsessy, Nauka, M., 1987, 240 pp.

[26] A. N. Kolmogorov, I. G. Petrovskii, I. S. Piskunov, “Issledovanie uravneniya diffuzii, soedinennoi s vozrastaniem veschestva, i ego primenenie k odnoi biologicheskoi probleme”, Byull. MGU, seriya A, 1:6 (1937), 1–25 | MR | Zbl

[27] A. I. Lobanov, T. K. Starozhilova, “Effect of convective flow on formation of two-dimensional structures in the model of blood coagulation”, Phystech Journal, 3:2 (1997), 96–105 | MR

[28] T. Pedli, Gidrodinamika krupnykh krovenosnykh sosudov, Mir, M., 1983, 290 pp.

[29] A. I. Zhurov, “Obtekanie poristogo tsilindra sdvigovym potokom”, Teoreticheskie osnovy khimicheskoi tekhnologii, 1995, no. 2, 213–216