  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.
