A PHASE RESPONSE CURVE BASED MODEL - EFFECT OF VAGAL AND SYMPATHETIC-STIMULATION AND INTERACTION ON A PACEMAKER CELL

This study introduces a simple mathematical model for a pacemaker cell affected by an external parasympathetic and/or sympathetic input. The model presented is based on the two most important functional propert ies of the cardiac pacemaker cells. The first property is the intrinsi c pacemaker cycle length, an ''internal'' parameter of the cell. The s econd basic property is the phase response curve (PRC), a function whi ch reflects the various interactions of the pacemaker cell with the ou tside world (i.e. interaction with surrounding cells, external stimulu s). The vagal stimulus is simulated as affecting the pacemaker cycle l ength via a PRC, while the sympathetic input is expressed in the model as a continuous reduction in the pacemaker cycle length. When combine d vagal and sympathetic activation is allowed, our model shows that au tonomic systems are also capable of interacting. First, we studied the entrainment phenomena resulting from a repetitively applied vagal sti mulus. Various complex patterns of dynamic interaction between the pac emaker cell and the vagal input were simulated. The PRC parameters app ear to be an important factor in the prediction of the entrainment phe nomena. Specifically, they permit a quantitative description of the li mits of a 1:1 synchronization zone. Next, we apply this model to quali tatively investigate the phenomenon of ''accentuated antagonism'' betw een parasympathetic and sympathetic autonomic branches. We examined th e various options for this interaction in regulating the pacemaker per iodicity. Although this model is a simplified reflection of the biolog ical system, we conclude that it can mimic many aspects of the dynamic autonomic control and of the possible interactions between vagal and sympathetic stimulation of a pacemaker cell. (C) 1998 Academic Press.