A PRC based model of a pacemaker cell: effect of vagal activity and investigation of the respiratory sinus arrhythmia.

In this study we present a computer model of a pacemaker cell subjected to vagal stimulation. This model allows us to investigate the entrainment phenomena of the pacemaker cell resulting from its dynamic interaction with a periodic train of vagal bursts. The possibility of entrainment depends mainly on the fact that a vagal stimulation discharge can "correct" the pacemaker rhythm by an amount that depends on its instantaneous relationship to the pacemaker cycle length. This very simple model, is based on the two most important functional properties of the cardiac pacemaker cells. The first property is the intrinsic pacemaker cycle length, which is an "internal" parameter of the cell, describing the most basic feature of a pacemaker cell. The second one is the phase response curve (PRC), which is an "overall collective" function, containing all the "information" about the possible interactions between the pacemaker cell and the outside world (i.e. its interaction with surrounding cells, external stimulus, etc.). A "collective" PRC was reconstructed from the resulting effects of all the pulses composing a burst. It appears that the PRC parameters as well as the vagal burst parameters are important factors in predicting the entrainment phenomena. Specifically, we found that the tendency of the pacemaker cell to become synchronized with bursts of vagal activity is greater, the larger the number of pulses per burst. However, increasing the number of pulses may also increase the tendency of the pacemaker towards instability, which was unveiled as changes in the configuration of the "collective" PRC. We applied the periodic train of vagal bursts so as to simulate the respiratory sinus arrhythmia (RSA) modulation on the pacemaker cell. We included also a modulation of sympathetic origin, represented as periodic changes in the intrinsic pacemaker cycle length. The frequency response of the pacemaker to "autonomic" modulations allowed us to demonstrate that the RSA dynamics can be interpreted in terms of the entrainment of the pacemaker cell by the respiratory modulation of vagal activity.