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

作者：Pan Michael; Gawthrop Peter J; Tran Kenneth; Cursons Joseph; Crampin Edmund J^*

来源：Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2018, 474(2214): 20180106.

DOI：10.1098/rspa.2018.0106

• bond graph
• cardiac electrophysiology
• conservation law

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, generalizing the results from previous studies.

• 出版日期2018-6