# Fast-slow asymptotics for a Markov chain model of fast sodium current

## TL;DR

This paper investigates the use of fast-slow asymptotic methods to reduce computational stiffness in Markov chain models of cardiac sodium channels, aiming to improve simulation efficiency.

## Contribution

It introduces a novel application of asymptotic analysis to simplify Markov chain models of ionic channels in cardiac electrophysiology.

## Key findings

- Demonstrates feasibility of asymptotic reduction
- Reduces computational stiffness in models
- Provides insights into sodium channel dynamics

## Abstract

We explore the feasibility of using fast-slow asymptotic to eliminate the computational stiffness of the discrete-state, continuous-time deterministic Markov chain models of ionic channels underlying cardiac excitability. We focus on a Markov chain model of the fast sodium current, and investigate its asymptotic behaviour with respect to small parameters identified in different ways.