Abstract
The interaction between two nonlinear oscillators is discussed, each one representing a region of the heart and characterized by a specific type of phase transition curve (PTC) which has been derived from human ECG-recordings. Besides the normal conduction a tachycardia mode is studied where the excitation is reflected by each oscillator (reentry). It turns out that under specific physiologically plausible conditions this tachycardia mode cannot be terminated by an external stimulus. Under periodic stimulation the response of the tachycardia mode is chaotic. Within a sheet of nonlinear oscillators the tachycardia mode serves as an ectopic focus or a region of reentry which induces fibrillation of the whole tissue.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Guevara, M. R., Glass, L.: Phase locking, period doubling bifurcations and chaos in a mathematical model of a periodically driven oscillator: A theory for the entrainment of biological oscillators and the generation of cardiac dysrhythmias. J. Math. Biology 14, 1–23 (1982)
Honerkamp, J.: The heart as a system of coupled nonlinear oscillators. J. Math. Biology 18, 69–88 (1983)
Keener, J. P.: Chaotic behavior in piecewise continuous difference equations. Trans. Am. Math. Soc. 261, 589–604 (1980)
Keener, J. P.: Chaotic Cardiac Dynamics. Lect. Appl. Math. 19, 229–325 (1981a)
Keener, J. P.: On Cardiac Arrythmias: AV Conduction Block. J. Math. Biology 12, 215–225 (1981b)
Mandel, W. J.: Cardiac Arrhythmias. Philadelphia, Toronto: J. B. Lippincott Comp. 1980
Ott, E.: Strange attractors and chaotic motions of dynamical systems. Rev. Mod. Phys. 53, 655–671 (1981)
Pavlidis, Th.: Biological Oscillators: Their Mathematical Analysis. New York: Academic Press 1973
Schamroth, L.: The Disorders of Cardiac Rhythm. Vol. I, II. Oxford, London, Edinburgh, Melbourne: Blackwell Scient. Publ. 1980
Strittmatter, W.: Diploma thesis, University of Freiburg 1984
Van der Pol, D. Sc., Van der Mark, J.: Phil. Magazine 6, 763–775 (1928)
Winfree, A. T.: The Geometry of Biological Time. New York-Heidelberg-Berlin: Springer 1980
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Strittmatter, W., Honerkamp, J. Fibrillation of a cardiac region and the tachycardia mode of a two-oscillator system. J. Math. Biology 20, 171–184 (1984). https://doi.org/10.1007/BF00285345
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00285345