NASPE young investigator awardee-1990. Complex rhythms resulting from overdrive suppression in electrically stimulated heart cell aggregates

Spontaneous Initiation and Termination of Complex Rhythms in Cardiac Cell Culture

INTRODUCTION

Complex cardiac arrhythmias often start and stop spontaneously. These poorly understood behaviors frequently are associated with pathologic modification of the structural heterogeneity and functional connectivity of the myocardium. To evaluate underlying mechanisms, we modify heterogeneity by varying the confluence of embryonic chick monolayer cultures that display complex bursting behaviors. A simple mathematical model was developed that reproduces the experimental behaviors and reveals possible generic mechanisms for bursting dynamics in heterogeneous excitable systems.

METHODS AND RESULTS

Wave propagation was mapped in embryonic chick myocytes monolayers using calcium-sensitive dyes. Monolayer confluence was varied by plating cultures with different cell densities and by varying times in culture. At high plating densities, waves propagate without breaks, whereas monolayers plated at low densities display spirals with frequent breaks and irregular activation fronts. Monolayers at intermediate densities display bursting rhythms in which there is paroxysmal starting and stopping of spiral waves of activity. Similar spatiotemporal patterns of activity were also observed as a function of the time in culture; irregular activity dominates the first 30 hours, followed by repetitive bursting dynamics until 54 hours, after which periodic target patterns or stable spirals prevail. In some quiescent cultures derived from older embryos, it was possible to trigger pacemaker activity following a single activation. We are able to reproduce all of these behaviors by introducing spatial heterogeneity and varying neighborhood size, equivalent to cell connectivity, in a spontaneous cellular automaton model containing a rate-dependent fatigue term.

CONCLUSION

We observe transitions from irregular propagating waves, to spiral waves that spontaneously start and stop, to target waves originating from localized pacemakers in cell culture and a simple theoretical model of heterogeneous excitable media. The results show how physiologic properties of spontaneous activity, heterogeneity, and fatigue can give rise to a wide range of different complex dynamic behaviors similar to clinically observed cardiac arrhythmias.

Bursting behavior during fixed-delay stimulation of spontaneously beating chick heart cell aggregates

Spontaneously beating embryonic chick atrial heart cell aggregates were stimulated with depolarizing current pulses delivered at a fixed delay after each action potential. This preparation is an experimental model of a reentrant tachycardia. During fixed-delay stimulation, bursting behavior was typically observed for a wide range of delays. Episodes of bursting at a rate faster (slower) than control were followed by overdrive suppression (underdrive acceleration). We use a simple nonlinear model, based on the interaction between excitability and overdrive suppression, to describe these dynamics. A modified version of the Shrier-Clay ionic model of electrical activity of the embryonic chick heart cell aggregates that includes a simplified Na+ pump term is also presented. We show that the complex patterns during fixed-delay stimulation arise as a result of delicate interactions between overdrive suppression and phase resetting, which can be described in terms of the underlying ionic mechanisms. This study may provide a basis for understanding incessant tachycardias in the intact heart, as well as an alternative mechanism for the emergence of bursting activity in other biologic tissue.

The topology of phase response curves induced by single and paired stimuli in spontaneously oscillating chick heart cell aggregates

The topological properties of the phase resetting of biological oscillators by an isolated stimulus delivered at various phases of the cycle depend on whether the stimulus is "weak" or "strong." When multiple stimuli are delivered to the oscillator, the response to stimulation also depends on the time between the stimuli, and the rate at which the oscillator returns to an underlying limit cycle attractor. If the time between two consecutive "weak" stimuli is sufficiently short, the effects produced by the pair of stimuli may be characteristic of a single "strong" stimulus. These results are demonstrated in a model experimental system, spontaneously beating aggregates of cells derived from embryonic chick heart, and are illustrated by consideration of a simple theoretical model of nonlinear oscillators, the Poincaré oscillator.

Evolution of rhythms during periodic stimulation of embryonic chick heart cell aggregates

During periodic stimulation of spontaneously beating chick heart cell aggregates, there is often an evolution of coupling patterns between the stimulator and the aggregate action potential. For example, at rapid stimulation frequencies, a rhythm that is initially 1:1 (stimulus frequency:aggregate frequency) can evolve to other rhythms such as 5:4 and 4:3. Time-dependent effects generated during periodic stimulation are characterized by three types of experiments to determine 1) the effect of periodic stimulation on the intrinsic cardiac beat rate (overdrive suppression), 2) the effect of periodic stimulation on the phase resetting properties of the aggregate, and 3) the time-dependent changes in the coupling patterns between the stimulator and the aggregate during periodic stimulation. The protocols involved variations in the duration and rate of periodic stimulation. A mathematical model is developed in the form of a two-dimensional finite difference equation based on the data from experiments 1 and 2. The model is used to predict the data generated by experiment 3. There is good correspondence with the experiments in that the theory reproduces complex transitions between various rhythms and displays irregular rhythms similar to those observed experimentally. These results have implications for the evolution of cardiac arrhythmias such as atrioventricular heart block and modulated parasystole.

Cardiac arrhythmias and circle maps-A classical problem

The periodic forcing of nonlinear oscillations can often be cast as a problem involving self-maps of the circle. Consideration of the effects of changes in the frequency and amplitude of the periodic forcing leads to a problem involving the bifurcations of circle maps in a two-dimensional parameter space. The global bifurcations in this two-dimensional parameter space is described for periodic forcing of several simple theoretical models of nonlinear oscillations. As was originally recognized by Arnold, one motivation for the formulation of these models is their connection with theoretical models of cardiac arrhythmias originating from the competition and interaction between two pacemakers for the control of the heart.