Bond graph modelling of the cardiac action potential: Implications for drift and non-unique steady states

TL;DR

This paper introduces a systematic bond graph modeling approach to identify conservation laws in cardiac electrophysiology models, addressing issues like drift and non-unique steady states, and enhancing robustness in long-term simulations.

Contribution

It presents a general method using bond graphs to uncover conservation laws, including conserved moieties, in cardiac action potential models, improving analysis of model stability.

Findings

Charge conservation laws are specific cases of conserved moieties.

Bond graph models reveal the origins of drift and steady state issues.

The approach can be extended to other excitable systems.

Abstract

Mathematical models of cardiac action potentials have become increasingly important in the study of heart disease and pharmacology, but concerns linger over their robustness during long periods of simulation, in particular due to issues such as model drift and non-unique steady states. Previous studies have linked these to violation of conservation laws, but only explored those issues with respect to charge conservation in specific models. Here, we propose a general and systematic method of identifying conservation laws hidden in models of cardiac electrophysiology by using bond graphs, and develop a bond graph model of the cardiac action potential to study long-term behaviour. Bond graphs provide an explicit energy-based framework for modelling physical systems, which makes them well-suited for examining conservation within electrophysiological models. We find that the charge conservation laws derived in previous studies are examples of the more general concept of a "conserved moiety". Conserved moieties explain model drift and non-unique steady states, generalising the results from previous studies. The bond graph approach provides a rigorous method to check for drift and non-unique steady states in a wide range of cardiac action potential models, and can be extended to examine behaviours of other excitable systems.