Phase resetting and annihilation in a mathematical model of sinus node.

A mathematical model of primary sinoatrial pacemaker activity was developed using modifications of Hodgkin-Huxley type equations of voltage- and time-dependent membrane currents. The computer simulation of action potential activity incorporates the results of several existing cardiac models and recent biological data in an attempt to generate a model that more closely approximates the phase-resetting behavior of sinoatrial pacemakers observed biologically in response to subthreshold or electrotonic stimuli. The model was also used to study annihilation, i.e., the cessation of rhythmic activity induced by a critically timed subthreshold stimulus. Perturbation analysis performed by scanning the pacemaker cycle with 50-ms subthreshold current pulses yielded biphasic phase-response relationships that closely resembled the biological data. The pacemaker current, although relatively unimportant in determining the degree of phase 4 depolarization in the simulated sinus nodal pacemaker, was nevertheless prominent in determining phase-resetting behavior. The characteristics of annihilation were studied in normal, "depressed," and hyperpolarized states. In all cases, successful annihilation depended in large part on the dynamic interaction between the slow inward and delayed rectifier outward currents. The annihilation point was found to be an unstable singularity point in which a critical combination of stimulus intensity and timing could cause the pacemaker to approach but never achieve a state of complete quiescence. The model provides the basis for further investigation of complex arrhythmias that may arise as a consequence of multiple-pacemaker interaction within the heart.