Bond graph modelling of the cardiac action potential

Implications for drift and non-unique steady states

Michael Pan, Peter J. Gawthrop, Kenneth Tran, Joseph Cursons, Edmund J. Crampin

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

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, generalizing 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.

Original languageEnglish
Article number20180106
Number of pages27
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume474
Issue number2214
DOIs
Publication statusPublished - 30 Jun 2018
Externally publishedYes

Keywords

  • Bond graph
  • Cardiac electrophysiology
  • Conservation law

Cite this

@article{b035d37ee8fc4337b522e40d9f76de16,
title = "Bond graph modelling of the cardiac action potential: Implications for drift and non-unique steady states",
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, generalizing 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.",
keywords = "Bond graph, Cardiac electrophysiology, Conservation law",
author = "Michael Pan and Gawthrop, {Peter J.} and Kenneth Tran and Joseph Cursons and Crampin, {Edmund J.}",
year = "2018",
month = "6",
day = "30",
doi = "10.1098/rspa.2018.0106",
language = "English",
volume = "474",
journal = "Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences",
issn = "1364-5021",
publisher = "Royal Society, The",
number = "2214",

}

Bond graph modelling of the cardiac action potential : Implications for drift and non-unique steady states. / Pan, Michael; Gawthrop, Peter J.; Tran, Kenneth; Cursons, Joseph; Crampin, Edmund J.

In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 474, No. 2214, 20180106, 30.06.2018.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Bond graph modelling of the cardiac action potential

T2 - Implications for drift and non-unique steady states

AU - Pan, Michael

AU - Gawthrop, Peter J.

AU - Tran, Kenneth

AU - Cursons, Joseph

AU - Crampin, Edmund J.

PY - 2018/6/30

Y1 - 2018/6/30

N2 - 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. 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.

AB - 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. 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.

KW - Bond graph

KW - Cardiac electrophysiology

KW - Conservation law

UR - http://www.scopus.com/inward/record.url?scp=85049624584&partnerID=8YFLogxK

U2 - 10.1098/rspa.2018.0106

DO - 10.1098/rspa.2018.0106

M3 - Article

VL - 474

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 1364-5021

IS - 2214

M1 - 20180106

ER -