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

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 to R wave of the electrocardiogram) 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.

Complex dynamics underlying the human electrocardiogram

“…The rationale for the dimensional analysis of ECGs relies on a large collection of experimental and simulation results supporting the modelling of cardiac electrical activity as a nonlinear system (Glass et al 1983;Jensen et al 1984;Chialvo and Jalife 1987;Chee et al 1988;Savino et al 1989;Zbilut et al 1989). This approach offers a promising explanation to the intriguing contradiction between the sudden changes in rhythm observed on the ECG and the relatively slow variations in the overall cardiac state.…”

“…Evidence that concepts from nonlinear dynamics are relevant in cardiac physiology comes from both experimental and theoretical studies. Experimental investigations on cardiac preparations of increasing complexity-from single cells to perfused whole heartshave shown, in response to electrical stimulation, the generation of complex patterns, typical of nonlinear systems, such as phase locking, period-doubling bifurcations and chaotic activity (Glass et al 1983;Chialvo and Jalife 1987;Savino et al 1989;Zbilut et al 1989;Chialvo et al 1990). Complex temporal or spatio-temporal patterns have also been described by computer simulations based on either the equations of membrane dynamics (Jensen et al 1984), or a formalized model of excitable medium (Moe et al 1964;Krinsky 1968;Smith and Cohen 1984;Chee et al 1988).…”

A new method for analysis of heart rate variability: counting statistics of 1/f fluctuations

“…It has been shown that conventional statistical measures of this variability, such as the standard deviation, of intervals between normal heart beats have strong prognostic implications in patients with myocardial infarction (Kleiger et al 1987;Bigger et al 1988). Recently, there has been increased interest in more sophisticated ways of analysis of this variability, including methods of nonlinear dynamics (Mayer-Kress et al 1988;Babloyantz and Destexhe 1988;Lipsitz et al 1990) and spectral analysis as obtained by Fast Fourier Transform (FFT) (Kobayashi and Musha 1982;Saul et al 1987;Appel et al 1989;Zbilut et al 1989;Kleiger et al 1991;Bigger et al 1992). However, there are several problems in using FFT for spectral analysis of heart rate variability (HRV).…”

A terminal dynamics model of the heartbeat

“…Our work has indicated that the rat heartbeat has a power law scaling of &2, and correlation dimension of &2 as would be expected of a random walk in time (Zbilut et al 1989). Transplanted human hearts, which do not have nervous system connections, also have power law scaling of &2 and dimensions of &2 (Zbilut et al 1988).…”