Related Experiment Video
Updated: Feb 8, 2026
A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
Published on: May 25, 2019
Bond graph modelling of the cardiac action potential: implications for drift and non-unique steady states
Michael Pan1, Peter J Gawthrop1, Kenneth Tran2
1Systems Biology Laboratory, School of Mathematics and Statistics, and Department of Biomedical Engineering, Melbourne School of Engineering, University of Melbourne, Parkville, Victoria 3010, Australia.
Insights
Mathematical models of cardiac action potentials can drift over time. This study introduces bond graphs to identify hidden conservation laws, explaining and preventing model drift in cardiac electrophysiology simulations.
Area of Science:
- Computational Biology
- Physiology
- Mathematical Modeling
Background:
- Cardiac action potential models are crucial for studying heart disease and pharmacology.
- Long-term simulations face challenges like model drift and non-unique steady states.
- Previous research linked these issues to conservation law violations, specifically charge conservation.
Purpose of the Study:
- To develop a general method for identifying hidden conservation laws in cardiac electrophysiology models.
- To investigate the long-term behavior of cardiac action potential models using bond graphs.
- To explain and generalize the causes of model drift and non-unique steady states.
Main Methods:
- Utilized bond graphs, an energy-based modeling framework, to analyze cardiac electrophysiology models.
- Developed a specific bond graph model for the cardiac action potential.
- Systematically identified conservation laws within the bond graph framework.
Main Results:
- Charge conservation laws are specific instances of a more general concept: 'conserved moieties'.
- Conserved moieties provide a unified explanation for model drift and non-unique steady states in cardiac models.
- The bond graph approach rigorously identifies these issues, generalizing previous findings.
Conclusions:
- Bond graphs offer a robust method for detecting and understanding model drift and non-unique steady states in cardiac electrophysiology.
- This approach enhances the reliability of long-term simulations.
- The methodology can be extended to analyze 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, 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.
Related Concept Videos
01:30Cardiac Action Potential
The cardiac action potential process involves a series of phases characterized by the movement of ions across the cardiac cell membranes, leading to the depolarization and repolarization of the cardiac myocytes.
Ionic Basis of Cardiac Action Potentials
01:41Action Potentials
01:31Action Potential
Membrane potential in neurons
Neurons typically have a resting membrane potential of about -70 millivolts (mV). When they receive...
01:14Action Potential
Membrane potential in neurons
Neurons typically have a resting membrane potential of about -70 millivolts (mV). When they receive...
01:23Propagation of Action Potentials
Neurons (nerve cells) have a resting membrane potential, with a slightly negative charge inside compared to outside. This is maintained by ion channels, such as sodium (Na+) and potassium (K+) channels, which control the flow of ions. When a stimulus, like a touch or a signal from another neuron, triggers the neuron, sodium channels open, allowing sodium ions to...
02:32Bonding in Metals