ArticleProceedings. Mathematical, physical, and engineering sciences2018
Bond graph modelling of the cardiac action potential: implications for drift and non-unique steady states.
Article in Proceedings. Mathematical, physical, and engineering sciences, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 10 papers.
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10 citing papers in PubMed.
- Thermodynamically consistent, reduced models of gene regulatory networks.Royal Society open science · 2025Article
- Energy-based analysis of biochemical oscillators using bond graphs and linear control theory.Royal Society open science · 2025Article
- An arteriovenous mock circulatory loop and accompanying bond graph model for in vitro study of peripheral intravascular bioartificial organs.Artificial organs · 2024Article
- A Parameter Representing Missing Charge Should Be Considered when Calibrating Action Potential Models.Frontiers in physiology · 2022Article
- Analysing and simulating energy-based models in biology using BondGraphTools.The European physical journal. E, Soft matter · 2021Article
- Modular assembly of dynamic models in systems biology.PLoS computational biology · 2021Article
- Modular dynamic biomolecular modelling with bond graphs: the unification of stoichiometry, thermodynamics, kinetics and data.Journal of the Royal Society, Interface · 2021Article
- Hierarchical semantic composition of biosimulation models using bond graphs.PLoS computational biology · 2021Article
- Network Thermodynamical Modeling of Bioelectrical Systems: A Bond Graph Approach.Bioelectricity · 2021Article
- Bond graph modelling of the cardiac action potential: implications for drift and non-unique steady states.Proceedings. Mathematical, physical, and engineering sciences · 2018Article
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5 authors.
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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.
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