The Dynamics of Sustained Reentry in a Loop Model with Discrete Gap Junction Resistance

TL;DR

This study investigates how discrete gap junction resistance affects reentry dynamics in a loop model of cardiac cells, revealing critical length changes and bifurcation behavior linked to restitution curve properties.

Contribution

It introduces a detailed loop model with variable gap junction resistance, analyzing how it influences reentry stability, bifurcations, and the critical loop length for cardiac arrhythmias.

Findings

Reentry transitions from period-1 to quasi-periodic at a critical loop length.

Critical length decreases as gap junction resistance increases.

Bifurcation points can be predicted from restitution curve slopes.

Abstract

Dynamics of reentry are studied in a one dimensional loop of model cardiac cells with discrete intercellular gap junction resistance ($R$). Each cell is represented by a continuous cable with ionic current given by a modified Beeler-Reuter formulation. For $R$ below a limiting value, propagation is found to change from period-1 to quasi-periodic ($QP$) at a critical loop length ($L_{crit}$) that decreases with $R$. Quasi-periodic reentry exists from $L_{crit}$ to a minimum length ($L_{min}$) that is also shortening with $R$. The decrease of $L_{crit}(R)$ is not a simple scaling, but the bifurcation can still be predicted from the slope of the restitution curve giving the duration of the action potential as a function of the diastolic interval. However, the shape of the restitution curve changes with $R$.