Excitability and Repolarization in an Ionic Model of the Cardiac Cell Membrane

The main objective of this study was to investigate the possibility of expressing the activation and repolarization processes of a realistic ionic model of the myocyte membrane in terms of simplified dynamic equivalents. The modified Beeler-Reuter model (MBR) of the ventricular membrane was selected for this purpose because its action potential upstroke, plateau and repolarization phase occur along sufficiently well separated timescales. The information on the MBR model dynamics was obtained by premature stimulation at various coupling intervals, under stable conditions of regular pacing at different cycle lengths. A general method was developed to study the threshold behavior of the system. As a first step, a pair of complementary threshold criteria was defined in terms of peak ionic current and time to repolarization in order to reliably distinguish between classes of sub-threshold and supra-threshold responses. One of the main conclusions is that the activation of the MBR model by short-duration stimuli (< 5 msec) can be accurately represented by a one-variable or a two-variable dynamic equivalent. In addition, because of the large surge of Na+ current at threshold, the recovery of excitability is essentially independent of the conditioning action potential waveform (no threshold-memory effect). Another major result pertains to the higher complexity of the repolarization process, stressing the critical role played by the activation dynamics of the secondary inward current. There is a substantial dependence of the action potential duration (APD) on the conditioning action potential waveform (APD-memory effect), and at least a three-variable model is necessary for a reasonable approximation.