Difference equation model of the entrainment of myocardial pacemaker cells based on the phase response curve

As a method for investigating entrainment phenomena found in biological oscillations, a model is presented which is formulated as a set of difference equations on the basis of "phase response curves" of biological oscillators. Properties of the model are discussed and synchronization of cardiac pacemaker cells to the external periodic stimuli is analyzed by use of the model. It is shown that the model is reducible to an equivalent system to the mathematical neuron model of Nagumo et al. under a specific parametric condition of the phase response curve. As an application to the cardiac arrhythmias, the model of ventricular parasystoles studied by Moe et al. is described mathematically in terms of a system of difference equations. In addition, a more comprehensive model of ventricular parasystoles is proposed.