Vagal entrainment of heart rate is simulated by an integrator with feedback

Abstract

Paradoxical stable entrainment of heart rate to inhibitory vagal impulses can be simulated with two distinct mathematical models; a complex ionic current model of sinoatrial node pacemaker activity, as well as a simple integrator with non-linear feedback. We show that both models exhibit similar entrainment characteristics to repetitive vagal stimuli. By applying a sharp disturbance to each model whilst entrained, the subsequent path of cycle length recovery can be described by dynamic phase response curves and phase-phase plots, the properties of which dictate whether stable entrainment is possible.