# Analytical Insights into Ephaptic Coupling and Its Effect on Conduction Velocity

## TL;DR

This paper explores how ephaptic coupling, a contactless form of cell communication, affects the speed of electrical signals in heart tissue, offering new insights into cardiac conduction.

## Contribution

The study introduces analytical models using asymptotic theory to calculate conduction velocity in the presence of weak ephaptic coupling.

## Key findings

- An analytical expression for conduction velocity was derived for both continuous and discrete models with weak ephaptic coupling.
- Numerical simulations validated the analytical results, confirming the models' accuracy.
- Conduction velocity can increase under weak ephaptic coupling if sodium current is concentrated on the end membrane.

## Abstract

Cardiovascular disease continues to be the leading cause of death in the United States. A major contributing factor is cardiac arrhythmia, which results from irregular electrical activity in the heart. On a tissue level, cardiac conduction involves the spread of action potentials (AP) across the heart, enabling coordinated contraction of the myocardium. On a cellular level, the transmission of signals between cells is facilitated by low-resistance pathways formed by gap junctions (GJs). Recent experimental studies have sparked discussion on whether GJs play a dominant role in cell communication. Interestingly, research has revealed that GJ knockout mice can still demonstrate signal propagation in the heart, albeit more slowly and discontinuously, indicating the presence of an alternative mechanism for cardiac conduction. Unlike GJ-mediated propagation, ephaptic coupling (EpC) has emerged as a distinct form of electrical transmission, characterized by contactless electrochemical signaling across the narrow intercalated discs (IDs) between cardiomyocytes. Advancements in cardiac research have highlighted the crucial role of EpC in restoring conduction by increasing conduction velocity (CV), reducing conduction block (CB), and terminating reentry arrhythmias, particularly when GJs are impaired. However, most EpC studies are either numerical or experimental, while analytical studies on ephaptic conduction–an equally important aspect of understanding EpC–remain extremely limited. In this paper, we applied asymptotic theory to calculate the CV in the presence of weak EpC. To achieve this, we developed both continuous and discrete models to describe ephaptic conduction along a strand of cells. Ionic dynamics were modeled using the piecewise linear and cubic functions. The resulting system represents a bistable system with weak EpC. We calculated an expression for CV in the presence of weak EpC for both models, and validated our analytical results with numerical simulations. Additionally, we showed that under weak EpC, CV can increase if the distribution of INa is more prominent on the end membrane.