Analysis of Heterogeneous Cardiac Pacemaker Network Models and Traveling Wave Dynamics

The sinoatrial-node (SAN) is a complex heterogeneous network that generates a stable rhythm in healthy hearts, yet a general mechanistic explanation for when and how these networks remain stable is lacking. Although computational and theoretical analyses could elucidate this phenomena, such methods have rarely been used in realistic (large-dimensional) gap-junction coupled heterogeneous pacemaker cell models. In this study, we adapt a recent model of pacemaker cells (Severi et al., 2012), incorporating biophysical representations of ion channel and intracellular calcium dynamics, to capture physiological features of a heterogeneous population of pacemaker cells; in particular “center” and “peripheral” cells with distinct intrinsic frequencies and action potential morphology. Large-scale simulations of the SAN tissue, represented by heterogeneous networks of pacemaker cells, exhibit a rich repertoire of behaviors, including complete synchrony, traveling waves of activity originating from periphery to center, and transient traveling waves originating from the center. We use phase reduction methods that do not require fully simulating the large-scale model to capture these observations. Moreover, the phase reduced models accurately predicts key properties of the tissue electrical dynamics, including wave frequencies when synchronization occurs, and wave propagation direction in a variety of network models. Further, with the reduced phase models, we analyze the relationship between cell distributions and coupling strengths and the resulting transient dynamics. Thus, we demonstrate that phase reduced oscillator models applied to realistic pacemaker networks provide novel insights into the spatial-temporal dynamics of cardiac pacemaker activity.