Fast simulations of waves in three-dimensional excitable media

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 7, Issue 11, 1997, Pages 2529-2545

  Dowle, Matthew ^a   Mantel, Rolf Martin ^a   Barkley, Dwight ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031278982     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127497001692     Document Type: Article

References (26)

1. Barkley, D. [1991] "A model for fast computer-simulation of waves in excitable media," Physica D49 (1, 2), 61-70.
2. Barkley, D. [1995] "Spiral meandering," in Chemical Waves and Patterns, eds. Kapral, R. & Showalter, K. (Kluwer), pp. 163-190.
3. Barkley, D. & Kevrekidis, I. [1994] "A dynamical systems approach to spiral-wave dynamics," Chaos 4, 453-460.
4. Barkley, D., Kness, M. & Tuckerman, L. [1990] "Spiral-wave dynamics in a simple-model of excitable media - The transition from simple to compound rotation," Phys. Rev. A42(4), 2489-2492.
5. Beeler, G. & Reuter, H. [1977] "Reconstruction of the action potential of ventricular myocardinal fibres," J. Physiol. 268, 177-210.
6. Cline, H., Lorensen, W., Ludke, S., Crawford, C. & Teeter, B. [1988] "2 algorithms for the 3-dimensional reconstruction of tomograms," Med. Phys. 15(3), 320-327.
7. Davidenko, J., Pertsov, A., Salomonsz, R., Baxter, W. & Jalife, J. [1992] "Stationary and drifting spiral waves of excitation in isolated cardiac-muscle," Nature 355(6358), 349-351.
8. Gerhardt, M., Schuster, H. & Tyson, J. [1990a] "A cellular automaton model of excitable media including curvature and dispersion," Science 247(4950), 1563-1566.
9. Gerhardt, M., Schuster, H. & Tyson, J. [1990b] "A cellular automaton model of excitable media. 2. Curvature, dispersion, rotating waves and meandering waves," Physica D46(3), 392-415.
10. Gerhardt, M., Schuster, H. & Tyson, J. [1990c] "A cellular automaton model of excitable media. 3. Fitting the Belousov-Zhabotinskii reaction," Physica D46(3), 416-426.
11. Gerhardt, M., Schuster, H. & Tyson, J. [1991] "A cellular automaton model of excitable media. 4. Untwisted scroll rings," Physica D50(2), 189-206.
12. Gray, R., Jalife, J., Panfilov, A., Baxter, W., Cabo, C. & J. D. [1995] "Mechanisms of cardiac fibrillation," Science 270(5239), 1222-1223.
13. Henze, C. [1993] "Vortex filaments in three dimensional excitable media," PhD thesis, University Arizona.
14. Henze, C. & Tyson, J. [1996] "Cellular-automaton model of three-dimensional excitable media," J. Chem. Soc. - Faraday Trans. 92(16), 2883-2895.
15. Lorensen, W. & Cline, H. [1987] "Marching Cubes: A high resolution 3D surface construction algorithm," Comput. Graph. 21(4), 163-169.
16. Mantel, R. & Barkley, D. [1996] "Periodic forcing of spiral waves in excitable media," Phys. Rev. E54, 4791-4802.
17. Markus, M. & Hess, B. [1990] "Isotropic cellular automaton for modeling excitable media," Nature 347(6288), 56-58.
18. Montani, C., Scateni, R. & Scopigno, R. [1994] "A modified look-up table for implicit disambiguation of Marching Cubes," Visual Comput. 10, 353-355.
19. Panfilov, A. & Hogeweg, P. [1995] "Mechanisms of cardiac fibrillation," Science 270(5239), 1223 and 1224.
20. Panfilov, A. & Keener, J. [1995] "Reentry in three-dimensional Fitzhugh-Nagumo medium with rotational Anisotropy," Physica D84(3, 4), 545-552.
21. Panfilov, A., Rudenko, A. & Krinsky, V. [1986] "Turbulent rings in three-dimensional active media with diffusion by 2 components," Biofizika 31(5), 850-854.
22. Weimar, J., Tyson, J. & Watson, L. [1992a] "3rd generation cellular automaton for modeling excitable media," Physica D55(3, 4), 328-339.
23. Weimar, J., Tyson, J. & Watson, L. [1992b] "Diffusion and wave-propagation in cellular automaton models of excitable media," Physica D55(3, 4), 309-327.
24. Winfree, A. [1987] When Time Breaks Down (Princeton Univ. Press, NJ).
25. Winfree, A. [1994] "Electrical turbulence in three-dimensional heart-muscle," Science 266(5187), 1003-1006.
26. Winfree, A. [1995] "Persistent tangles of vortex rings in excitable media," Physica D84(1, 2), 126-147.