Dynamical Theory of Elastic Synchronization of Cardiomyocytes

TL;DR

This paper develops a dynamical model for how cardiomyocytes synchronize their beating through elastic interactions with the substrate, revealing geometry-dependent synchronization states and times.

Contribution

It introduces a phase reduction framework for elastic cardiomyocyte synchronization, linking energetic and dynamical theories with new predictions.

Findings

Cells synchronize in-phase or anti-phase depending on orientation.

Synchronization time varies with distance and orientation.

The model bridges energetic and dynamical synchronization theories.

Abstract

We study synchronization of two cardiomyocytes mediated by elastic interactions through the substrate. Modeling each cell as an oscillating force dipole governed by a Rayleigh-type equation, we derive an effective mechanical coupling from the elastic response of the surrounding medium. Using phase reduction theory, supported by direct numerical simulations, we obtain a dynamical phase description for two cardiomyocytes that predicts geometry-dependent selection of synchronized states. Depending on the mutual orientation, the cells robustly converge to either in-phase or anti-phase beating, yielding an orientation-dependent state map with a nontrivial state boundary. The synchronization time also depends strongly on the distance and mutual orientation of the cells. These results bridge earlier energetic two-body theory and dynamical single-cell theory, and provide a dynamical framework for elastic synchronization of cardiomyocytes.