Abstract
Extremely complex frequency-dependent patterns of excitation and impulse propagation can be shown in cardiac tissues. Such complex behaviour can be analysed using methods derived from chaos theory1–4, which is concerned with the non-linear dynamics of deterministic systems that have irregular periodicities as well as an exquisite sensitivity to the initial conditions. We report here that the general response patterns of non-oscillatory cardiac conducting tissues, when driven rhythmically by repetitive stimuli from their surroundings, are similar to those of other deterministic systems showing chaotic dynamics. Such patterns include phase locking, period-doubling bifurcation and irregular activity. We have used electrophysiological techniques and analytical arguments to explain this unforeseen behaviour and to provide some key information about its mechanisms. The study of these dynamics is of general application to the understanding of disordered phenomena in excitable media, and may provide new insight about the origin of fatal cardiac arrhythmias.
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References
1. Holden, A. V. Chaos (Princeton University Press, 1986). 2. Cvitanovic, P. Universality in Chaos (Hilges, Bristol, 1984). 3. Hao, B.-L. Chaos (World Scientific, Singapore, 1984). 4. Devaney, R. L. An Introduction to Chaotic Dynamical Systems (Benjamin Cummings, Menlo Park, 1986). 5. Moe, G. K., Rheinboldt, W. C. & Abildskov, J. A. Am. Heart J. 67, 200-220 (1964). 6. Guevara, M. R., Glass, L. & Schrier, A. Science 214, 1350-1353 (1981). 7. Simoyi, R. H., Wolf, A. & Swinney, H. L. Phys. Rev. Lett. 49, 245-248 (1982). 8. Gollub, J. P. & Benson, S. V. / Fluid Mech. 100, 449-470 (1980). 9. Testa, J., Perez, J. & Jeffries, C. Phys. Rev. Lett. 48, 714-717 (1982). 10. Glass, L., Shrier, A. & Belair, J. in Chaos (ed. Holden, A.) 237-256 (Princeton University Press, 1986). 11. Zipes, D. P. Circulation 60, 465-472 (1979). 12. Arnold, V. I. Geometrical Methods in the Theory of Ordinary Differential Equations. Section II (Springer, New York, 1983). 13. Glass, L. & Perez, R. Phys. Rev. Lett. 48, 1772-1775 (1982). 14. Guevara, M. R., Ward, G., Shrier, A. & Glass, L. Comp. Cardiol. 11, 167-170 (1984). 15. Feingold, M., Gonzalez, D., Piro, O. & Viturro, H. Phys. Rev. Lett, (submitted). 16. Harmon, L. P. Kybernetik 1, 89-101 (1961). 17. Guttman, R., Feldman, L. & Jakobsson, E. /. Membrane Biol. 56, 9-18 (1980). 18. Glass, L., Guevara, M. R. & Shrier, A. Ann. N.Y. Acad. Sci. 584, 168-178 (1987). 19. Matsumoto, G. et al. Phys. Lett. A 123, 162-166 (1987). 20. Sato, S. Kybernetik 11, 208-216 (1972). 21. Nagumo, J. & Sato, S. Kybernetik 10, 155-164 (1972). 22. Yoshizawa, S., Osada, H. & Nagumo, J. Biol. Cybern. 45, 23-33 (1982). 23. Mandelbrot, B. B. The Fractal Geometry of Nature (Freeman, San Francisco, 1982). 24. Kaneko, K. Collapse of Tori and Genesis of Chaos in Dissipative Systems (World Scientific, Singapore, 1986). 25. Spear, J. F. & Moore, E. N. Circulation Res. 35, 782-792 (1974). 26. Gonzalez, D. & Piro, O. Phys. Rev. Lett. 50, 870-872 (1983). 27. Guevara, M. R. & Glass, L. J. Math. Biol. 14, 1-23 (1982). 28. Jalife, J. & Moe, G. K. Circulation Res. 39, 801-808 (1976). 29. Johnston, M. F., Simon, S. A. & Ramon, F. Nature 286, 498-500 (1980). 30. Rapp, P. E. et al. in Lecture Notes in Biomathematics 66. Nonlinear Oscillations in Biology and Chemistry 175-205 (1986). 31. Vidal, C. in Nonlinear Phenomena in Chemical Dynamics (eds Vidal, C. & Pacault, A.) 49-62 (Springer, Berlin, 1981). 32. Guckenheimer, J. IEEE Trans. Circuits and Systems 30, 586-591 (1983). 33. Borenblatt, G. I., loos, G. & Joseph, D. Nonlinear Dynamics and Turbulence (Pitman, London, 1983). 34. Ritzenberg, A., Adam, D. & Cohen, R. Nature 307, 159-161 (1984). 35. Winfree, A. T. When Time Breaks Down. The Three-Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias (Princeton University Press, 1987). 36. Rosenbaum, M. B., Elizari, M. V., Levi, R. J. & Nau, G. J. Chest 63, 678-688 (1973). 37. Halpern, M. S., Nau, G. J., Chiale, P. A., Elizari, M. V. & Rosenbaum, M. B. in Frontiers of Cardiac Electrophysiology (eds Rosenbaum, M. B. & Elizari, M. V.) 465-487 (Nijhoff, The Hague, 1983).
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Chialvo, D., Jalife, J. Non-linear dynamics of cardiac excitation and impulse propagation. Nature 330, 749–752 (1987). https://doi.org/10.1038/330749a0
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DOI: https://doi.org/10.1038/330749a0
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