Dynamics of pure parasystole.

Abstract

A mathematical model is proposed for ventricular parasystole. In this model, there are two separate rhythms, a sinus rhythm and a ventricular ectopic rhythm. An ectopic beat will occur if the ectopic depolarization falls during a time interval when the ventricles are not refractory. Following an ectopic beat there is a compensatory pause. Analysis of this model, utilizing numerical simulation and techniques in number theory, demonstrates several new rules for parasystole. Specifically, for any set of fixed values for the sinus and ectopic frequencies and the ventricular refractory time, there are at most three different values for the number of sinus beats between ectopic beats. One and only one of these values is odd, and the sum of the two smaller values is one less than the larger value. The variation in the allowed values of the number of sinus beats between ectopic beats, as a function of the parameters of the model, is classified. Clinical cases found in the literature display certain aspects of the predictions of the theoretical model. Theoretical analysis of this kind provides new approaches to assessing the mechanism of complex ventricular arrhythmias.