Action potential restitution and hysteresis in a reaction-diffusion system with pacing rate dependent excitation threshold

TL;DR

This paper demonstrates how rate-dependent restitution and hysteresis phenomena in a reaction-diffusion system can be modeled with a variable excitation threshold, revealing insights into the dynamics of action potential behavior.

Contribution

It introduces a reaction-diffusion model with a variable excitation threshold that reproduces restitution and hysteresis effects, providing analytical insights into wavefront stability and alternans onset.

Findings

Restitution and hysteresis depend on pacing period and excitation threshold dynamics.

The minimal stable wavefront speed predicts the onset of action potential duration alternans.

Analytical critical speed accurately estimates wave stability across various parameters.

Abstract

We have demonstrated that rate dependent restitution and action potential duration-refractory period hysteresis can be reproduced in a one-dimensional two-variable Chernyak-Starobin-Cohen reaction-diffusion medium with variable excitation threshold. We show that restitution and hysteresis depend on the relationship between pacing period and steady state excitation threshold and also on the rate of excitation threshold adaptation after an abrupt change in pacing period. It was also observed that the onset of action potential duration alternans is determined by the minimal stable wavefront speed, which could be approximated by the analytical critical speed of a stable solitary pulse. This approximation was suitably accurate regardless of the adaptation constant of excitation threshold, its dependence on pacing interval, or magnitude of the slopes of restitution curves.