A model is constructed for cardiac rhythmic response to stimulation via a family of continuous time dynamical systems. Starting with experimentally observed properties common to the kinetics of both repolarizing membrane currents and cardiac action potential responses to sudden changes in cycle length, extremely elementary dynamical assumptions are made concerning current activation and decay, and repolarization threshold. A two-parameter family of one-dimensional dynamical systems emerges. The resulting systems are analytically tractable in considerable detail generating restitution curves, bifurcation schemes, rhythmic responses and chaotic behavior for a representative cardiac cell. The excellent qualitative and quantitative agreement with experimental data reported for several cardiac preparations is discussed. The two-dimensional analog produces unexpected basin behavior which could be of clinical significance in explaining how a single extra beat or a pause could alter subsequent action potential behavior and cause dispersion of refractoriness across the ventricle increasing the risks for arrhythmias. By having a manageable number of parameters, analytically defined patterns of behavior, and computational ease, this dynamical system has the potential to be used in computer simulations to study the effects of antiarrhythmic drugs on complex two- and three-dimensional reentrant substrates, or used on line by an interactive pacemaker.
An on-line approach in coordination of dynamical systems
