A mathematical model of automaticity in the sinus node and AV junction based on weakly coupled relaxation oscillators

Abstract

A general mathematical model is proposed for the study of the effects of changes in two interacting pacemaker rates on the nature of cardiac rhythms. The model is based on the weak interaction of two systems of differential equations each of which is capable of self-perpetuating oscillations. Some results of computer experimentation with the model are presented for one simple system of coupling the oscillators. The mathematical model reproduces satisfactorily the physiological results of experiments previously performed on dogs in this laboratory. The model is useful in both the design and analysis of biologic experiments to define most known determinants of either normal or abnormal cardiac rhythm.