Determining Critical Coupling Thresholds for Stable Synchronization in Heterogeneous 2D Cardiac Pacemaker Networks Netriani Veminsyah Ahda
Bengkulu University
Abstract
The heart maintains its function through precise electrical coordination among pacemaker cells in the sinoatrial (SA) node, mediated by gap junction coupling. Disruption of cellular synchronization is a key precursor to arrhythmia- however, the minimum coupling threshold required to sustain stable rhythms in heterogeneous two-dimensional (2D) networks remains unclear. This study investigated pacemaker cell synchronization dynamics in the SA node using 2D heterogeneous network simulations based on the Morris-Lecar model, with the aim of identifying the critical coupling strength for rhythm stability. Cell-to-cell interactions were modelled as discrete diffusion coupling representing gap junction conductance, implemented using fourth-fifth order Runge-Kutta integration, with heterogeneous input currents applied to capture intrinsic variability. Synchronization was quantified using the Kuramoto order parameter (R) across a range of coupling conductance values (gcouple). The results showed that increasing coupling strength reduced membrane potential disparities and enhanced phase coherence, driving a transition from desynchronization to globally synchronized states. A critical transition was consistently observed at R ≈- 0.9, indicating the emergence of stable rhythmic activity. These findings provide quantitative insight into the coupling-dependent mechanisms underlying rhythm stabilization in excitable cardiac tissue and may inform strategies for preventing arrhythmogenic behavior.
Keywords: Cardiac pacemaker cells, Sinoatrial node, Gap junction coupling, Synchronization dynamics, Morris-Lecar model
