  The sinoatrial-node (SAN) is a complex heterogeneous tissue that generates a
stable rhythm in healthy hearts, yet a general mechanistic explanation for when
and how this tissue remains stable is lacking. Although computational and
theoretical analyses could elucidate these phenomena, such methods have rarely
been used in realistic (large-dimensional) gap-junction coupled heterogeneous
pacemaker tissue 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 a
heterogeneous tissue structure 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 predict key properties of the tissue electrical
dynamics, including wave frequencies when synchronization occurs, and wave
propagation direction in a variety of tissue models. With the reduced phase
models, we analyze the relationship between cell distributions and coupling
strengths and the resulting transient dynamics. Further, the reduced phase
model predicts parameter regimes of irregular electrical dynamics. Thus, we
demonstrate that phase reduced oscillator models applied to realistic pacemaker
tissue is a useful tool for investigating the spatial-temporal dynamics of
cardiac pacemaker activity.
