Bifurcations and Intrinsic Chaotic and 1/f Dynamics in an Isolated Perfused Rat Heart

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Abstract
The application of the theory of chaotic dynamical systems has gradually evolved from computer simulations to assessment of erratic behavior of physical, chemical, and biological systems. Whereas physical and chemical systems lend themselves to fairly good experimental control, biologic systems, because of their inherent complexity, are limited in this respect. This has not, however, prevented a number of investigators from attempting to understand many biologic periodicities. This has been especially true regarding cardiac dynamics: the spontaneous beating of coupled and non-coupled cardiac pacemakers provides a convenient comparison to the dynamics of oscillating systems of the physical sciences. One potentially important hypothesis regarding cardiac dynamics put forth by Goldberger and colleagues, is that normal heart beat fluctuations are chaotic, and are characterized by a 1/f-like power spectrum. To evaluate these conjectures, we studied the heart beat intervals (R wave toR wave of the electocardiogram) of isolated, perfused rat hearts and their response to a variety of external perturbations. The results indicate bifurcations between complex patterns, states with positive dynamical entropies, and low values of fractal dimensions frequently seen in physical, chemical and cellular systems, as well as power law scaling of the spectrum. Additionally, these dynamics can be modeled by a simple, discrete map, which has been used to describe the dynamics of the Belousov-Zhabotinsky reaction.

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