Period-doubling bifurcation in Beeler-Reuter model and its relation to ventricular fibrillation

Xiaoqin Zou; Herbert Levine; Alain Karma

doi:10.1117/12.162717

5 November 1993 Period-doubling bifurcation in Beeler-Reuter model and its relation to ventricular fibrillation

Xiaoqin Zou, Herbert Levine, Alain Karma

Proceedings Volume 2036, Chaos in Biology and Medicine; (1993) https://doi.org/10.1117/12.162717
Event: SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, 1993, San Diego, CA, United States

Abstract

We have investigated the dynamics of electrical wave propagation in a ring of excitable cardiac tissue modeled by the Beeler-Reuter membrane equations. By adiabatically eliminating the fast ionic channel variables, we reduce this electrophysiological partial differential equation (PDE) model to a single-front free-boundary problem in which the dynamics is solely determined by the `slow' variables. This free-boundary problem is further reduced to a 3D coupled map by using the intensity of wavefront velocity. Stability analysis of this discrete map shows the existence of a period doubling bifurcation at a certain wave period. The critical period, below which there occurs an alternation in action potential duration, depends sensitively on the dynamics of the calcium channel. These results are in good agreement with finding from direct PDE simulations. Our work supports the hypothesis that electrical alternans result in spiral breakup, which might be one possible mechanism for the transition from ventricular tachycardia to fibrillation.

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Xiaoqin Zou, Herbert Levine, and Alain Karma "Period-doubling bifurcation in Beeler-Reuter model and its relation to ventricular fibrillation", Proc. SPIE 2036, Chaos in Biology and Medicine, (5 November 1993); https://doi.org/10.1117/12.162717

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KEYWORDS

Calcium

Wavefronts

Action potentials

Sodium

Wave propagation

3D modeling

Biology

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