Ionic basis and analytical solution of the wenckebach phenomenon in guinea pig ventricular myocytes

The ionic mechanisms of slow recovery of cardiac excitability and rate-dependent activation failure were studied in single, enzymatically dissociated guinea pig ventricular myocytes and in computer simulations using a modified version of the Beeler and Reuter model for the ventricular cell. On the basis of our results, we developed a simplified analytical model for recovery of cell excitability during diastole. This model was based on the equations for current distribution in a resistive-capacitive circuit. A critical assumption in the model is that, in the voltage domain of the subthreshold responses, the sodium and calcium inward currents do not play a significant role, and only the two potassium outward currents, the delayed rectifier (IK) and the inward rectifier, are operative. The appropriate parameters needed to numerically solve the analytical model were measured in the guinea pig ventricular myocyte, as well as in the Beeler and Reuter cell. The curves of recovery of excitability and the rate-dependent activation patterns generated by numerical iteration of the analytical model equations closely reproduced the experimental results. Our analysis demonstrates that slow deactivation of the delayed rectifier current determines the observed variations in excitability during diastole, whereas the inward rectifier current determines the amplitude and shape of the subthreshold response. Both currents combined are responsible for the development of Wenckebach periodicities in the ventricular cell. The overall study provides new insight into the ionic mechanisms of rate-dependent conduction block processes and may have important clinical implications as well.