Wave propagation in an excitable medium with a negatively sloped restitution curve

Chaos

Volumn 12, Issue 3, 2002, Pages 800-806

  Panfilov, A V ^a   Zemlin, C W ^b  

^a UTRECHT UNIVERSITY   (Netherlands)

^b Innovationskolleg Theoretische Biologie   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036711447     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1493095     Document Type: Article

References (23)

1. R.J. Myerburg, K.M. Kessler, A. Interian, Jr., P. Fernandez, S. Kimura, P.L. Kozlovskis, T. Furukawa, A.L. Bassett, and A. Castellanos, in Cardiac Electrophysiology. From Cell to Bedside, edited by D.P. Zipes and J. Jalife (Saunders, Philadelphia, 1990), p. 666.
2. J. Nolasco and R. Dahlen, "A graphic method for the study of alternation in cardiac action potentials," J. Appl. Physiol. 25, 191-196 (1968).
3. M. Guevara, A. Ward, A. Shrier, and L. Glass, "Electrical alternans and period doubling bifurcations," IEEE Comp. Cardiol. 562, 167-170 (1984).
4. A.V. Panfilov and A.V. Holden, "Self-generation of turbulent vortices in a two-dimensional model of cardiac tissue," Phys. Lett. A 147, 463-466 (1990).
5. M. Gerhard, H. Schuster, and J.J. Tyson, "A cellular automaton model of excitable media including curvature and dispersion," Science 247, 1563-1566 (1990).
6. M. Courtemanche and A.T. Winfree, "Re-entrant rotating waves in a Beeler-Reuter based model of two-dimensional cardiac activity," Int. J. Bifurcation Chaos Appl. Sci. Eng. 1, 431-444 (1991).
7. H. Ito and L. Glass, "Spiral breakup in a new model of discrete excitable media," Phys. Rev. Lett. 66, 671-674 (1991).
8. A. Karma, "Electrical alternans and spiral wave breakup in cardiac tissue," Chaos 4, 461-472 (1994).
9. M. Wijffels, C. Kirchhof, R. Dorland, and M.A. Allessie, "Atrical fibrillation begets atrical fibrillation, a study in awake chronically instrumented goats," Circulation 92, 1954-1968 (1995).
10. M. Franz, J. Schaefer, M, Schóttler, W. Seed, and M. Noble, "Electrical and mechanical restitution of the human heart at different rates of stimulation," Circ. Res. 53, 815-822 (1983).
11. J. Morgan, D. Cunninggham, and E. Rowland, "Electrical restitution in the endocardium of the intact human right ventricule," Br. Heart J. 67, 42-46 (1992).
12. Z. Qu, J. Weiss, and A. Garfinkel, "Spatiotemporal chaos in a simulated ring of cardiac cells," Phys. Rev. Lett. 78, 1387-1390 (1997).
13. J. Weiss, A. Garfinkel, H. Karagueuzian, Z. Qu, and P. Chen, "Chaos and transition to ventricular fibrillation," Circulation 99, 2819-2826 (1999).
14. K. Wenckebach, "Zur analyze des unregelmassigen pulses, II. Ueber den regelmassig intermittirenden puls," Z. Klin. Med. 37, 475-488 (1899).
15. M. Courtemanche, J.P. Keener, and L. Glass, "A delay equation representation of pulse circulation on a ring of excitable media," SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 56, 119-142 (1996).
16. C. Zemlin and A.V. Panfilov, "Spiral waves in excitable media with negative restitution," Phys. Rev. E 63, 041912 (2001).
17. A.V. Panfilov and A.M. Pertsov, "Vortex ring in three-dimensional active medium in reaction-diffusion system," Dokl. Akad. Nauk SSSR 274, 1500-1503 (1984) (in Russian).
18. R. Khramov, "Circulation of a pulse in an excitable medium," Biofizika 23, 871-876 (1978) (in Russian).
19. A.V. Panfilov and J.P. Keener, "Dynamics of dissipative structures in reaction-diffusion equations," SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 55, 205-219 (1995).
20. P.S. Chen, P. Wolf, E.G. Dixon, N.D. Danieley, D.W. Frazier, W.M. Smith, and R.E. Ideker, "Mechanism of ventricular vulnerability to single premature stimuli in open-chest dogs," Circ. Res. 62, 1191-1209 (1988).
21. V.S. Zykov, Simulation of Wave Processes in Excitable Media (Manchester University Press, Manchester, 1987).
22. A.V. Panfilov and P. Hogeweg, "Spiral break-up in a modified FitzHugh-Nagumo model," Phys. Lett. A 176, 295-299 (1993).
23. A.V. Panfilov, "Spiral breakup as a model of ventricular fibrillation," Chaos 8, 57-64 (1998).