Dynamics of spatially nonuniform patterning in the model of blood coagulation

Chaos

Volumn 11, Issue 1, 2001, Pages 57-70

  Zarnitsina, V I ^a   Ataullakhanov, F I ^a   Lobanov, A I ^b   Morozova, O L ^c  

^a NATIONAL RESEARCH CENTER FOR HEMATOLOGY   (Russian Federation)

^b MOSCOW INSTITUTE OF PHYSICS AND TECHNOLOGY   (Russian Federation)

^c TRAPEZNIKOV INSTITUTE OF CONTROL SCIENCES   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002556664     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1345728     Document Type: Article

References (37)

1. A. M. Turing, " The chemical basis of morphogenesis, " Philos. Trans. R. Soc. London, Ser. B 237, 37-42 (1952).
2. G. Nicolis and I. Prigogine, Self-Organization in Non-Equilibrium Systems (Wiley, New York, 1977).
3. Oscillation and Traveling Waves in Chemical Systems, edited by R. J. Field and M. Burger (Wiley, New York, 1985).
4. H. Meinhardt, " Dynamics of stripe formation, " Nature (London) 376, 722-723 (1995).
5. A. J. Koch and H. Meinhardt, " Biological pattern formation: From basic mechanisms to complex structures, " Rev. Mod. Phys. 66, 1481-1507 (1994).
6. K. J. Lee, W. D. McCormick, Q. Quyang, and H. L. Swinney, " Pattern formation by interacting chemical fronts, " Science 261, 192-194 (1993).
7. A. De Wit, " Spatial patterns and spatiotemporal dynamics in chemical systems, " Adv. Chem. Eng. 109, 435-513 (1999).
8. I. S. Lendyel and I. R. Epstein, " Transient Turing structures in a gradient-free closed system, " Science 259, 493-495 (1993).
9. J. Ross, A. Arkin, and S. C. Mueller, " Experimental evidence of Turing structures, " J. Phys. Chem. 99, 10417-10419 (1995).
10. F. I. Ataullakhanov and G. T. Guriya, " Spatial aspects of the dynamics of blood clotting - I. Hypothesis, " Biophysics (Engl. Transl.) 39, 91-97 (1994).
11. F. I. Ataullakhanov, G. T. Guriya, V. I. Sarbash, and R. I. Volkova, " Spatio-temporal dynamics of clotting and pattern formation in human blood, " Biochim. Biophys. Acta. 1425, 453-468 (1998).
12. F. I. Ataullakhanov, G. T. Guriya, and A. Yu. Safroshkina, " Spatial aspects of the dynamics of blood clotting - II. Phenomenological model, " Biophysics (Engl. Transl.) 39, 99-108 (1994).
13. A. I. Lobanov, T. K. Starozhilova, and G. T. Guria, " Numerical investigation of pattern formation processes in blood coagulation, " Matematicheskoe modelirovanie 9, 83-95 (1997); in Russian.
14. 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, " Thrombosis Research 84, 225-236 (1996).
15. V. I. Zarnitsina, A. V. Pokhilko, and F. I. Ataullakhanov, " A mathematical model for the spatio-temporal dynamics of intrinsic pathway of blood coagulation. II. Results, " Thrombosis Research 84, 333-344 (1996).
16. B. S. Kerner and V. V. Osipov, Autosolitons (Moscow, Nauka, 1991), in Russian.
17. A. N. Zaikin, "Generation, propagation, and interaction of excitons (autowave-particles) in an active medium," Preprint, Pushino (1993), in Russian.
18. W. N. Reynolds, J. E. Pearson, and S. Ponce-Dawson, " Dynamics of self-replicating patterns in reaction-diffusion systems, " Phys. Rev. Lett. 72, 2797-2800 (1994).
19. K. J. Lee, W. D. McCormick, J. E. Pearson, and H. L. Swinney, " Experimental observation of self-replicating spots in a reaction-diffusion system, " Nature (London) 369, 215-218 (1994).
20. K. Krischer and A. Mikhailov, " Bifurcation to travelling spots in reaction-diffusion system, " Phys. Rev. Lett. 73, 3165-3168 (1994).
21. C. P. Schenk, M. Or-Guil, M. Bode, and H.-G. Purwins, " Interacting pulses in three-component reaction-diffusion systems on two-dimensional domains, " Phys. Rev. Lett. 78, 3781-3784 (1997).
22. D. T. Berg, M. R. Wileyand, and B. W. Grinnell, " Enhanced protein C activation and inhibition of fibrinogen cleavage by a thrombin modulator, " Science 273, 1389-1391 (1996).
23. Q. D. Dang, A. Vindigni, and E. Di Cera, " Identification of residues linked to the slow-fast transition of thrombin, " Proc. Natl. Acad. Sci. U.S.A. 91, 11185-11189 (1995).
24. J. W. Fenton, Jr., " Regulation of thrombin generation and functions, " Semin. Thromb. Hemost. 14, 234-240 (1988).
25. E. Hairer, S. P. Norsett, and G. Wanner, Solving Ordinary Differential Equations. Nonstiff Problems, Springer Series in Computational Mathematics 8 (Springer, Berlin, 1987).
26. A. I. Tolstykh, Compact Difference Schemes and Their Applications to Fluid Dynamics Problems (Moscow, Nauka, 1990), in Russian.
27. A. I. Khibnik, Yu. A. Kuznetsov, V. V. Levitin, and E. V. Nikolaev, 1993, LocBif, Version2: Interactive LOCal BIFurcation Analyzer, CAN Expertise Centre, Amsterdam, 1-148.
28. B. N. Belintzev, B. F. Dibrov, M. A. Lifshitz, and M. V. Volkenshtein, " Nonlinear stability in distributed trigger type system. Biological threshold, " Biofizika 23, 864-869 (1978), in Russian.
29. Y. Oono and M. Kohmoto, " Discrete model of chemical turbulence, " Phys. Rev. Lett. 55, 2927-2931 (1985).
30. D. Feinn and P. Ortoleva, " Catastrophe and propagation in chemical reactions, " J. Chem. Phys. 67, 2119 (1977).
31. P. Ortoleva, " J. Ross theory of propagation of discontinuities in kinetic systems with multiple time scales: Fronts, front multiplicity and pulses, " J. Chem. Phys. 63, 3398 (1975).
32. G. I. Marchuk, " Perturbation theory and the statement of inverse problems, " Lect. Notes Comput. Sci. 4, 159-166 (1973).
33. G. I. Marchuk, V. I. Agoshkov, and V. P. Shutyaev, Conjugated Equations and Perturbation Methods in Nonlinear Problems of Mathematical Physics (Moscow, Fizmatlit, 1993), in Russian.
34. G. I. Marchuk and V. I. Agoshkov, " Conjugated operators and algorithms of perturbation in nonlinear problems. 1. Principles of construction of conjugated operators, " Sov. J. Numerical Analysis Mathematical Modeling 1, 21-46 (1988).
35. G. I. Marchuk and V. I. Agoshkov, " Conjugated operators and algorithms of perturbation in nonlinear problems. 2. Perturbation algorithms, " Sov. J. Numerical Analysis Mathematical Modeling 2, 115-136 (1988).
36. ′), " Proc. Phys. Math. Soc. Jpn. 19, 861-866 (1937).
37. K. W. Chang and F. A. Howes, Nonlinear Singular Perturbation Phenomena: Theory and Applications (Springer, New York, 1984), Vol. 56.