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Parsimonious Cardiac Action Potential Model of the Rabbit

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This regulatory science tool presents a computer model of a rabbit action potential derived from a high-fidelity experimental data from the rabbit (both single cells and during propagation in the isolated whole heart).


Technical Description

Cardiac electrophysiological computational models are comprised of numerous complex non-linear equations that predict the action potential in the heart at one or multiple sites. Cardiac electrophysiological modeling is a mature field which has been integrated with experimental studies to develop and test hypotheses for decades. Such models are highly modular, and equations are often reused and/or modified.

This model of the ‘parsimonious’ rabbit action potential is very simple with only two currents and three variables, including a novel non-linear phenomenological model of repolarization. The novelty of this model is that it is mathematically identifiable and extremely simple. The model allows a prediction of the dynamical patterns during ventricular fibrillation in the rabbit.

The tool is entirely self-contained although the cardiac model developer or user can modify the equations representing the cell kinetics, stimulation protocol, and numerical solvers to generate the corresponding output for any cardiac model. This tool presents a standalone model (no user input required) for simulating the rabbit action potential in single cardiac cells and tissue.

Intended Purpose

The model may be appropriate for the design and analysis of device function in experimental studies involving rabbits. The tool is intended to be used by cardiac model developers and users. The simplicity of the model, and the fact that its parameters have physiological meaning, make it ideal for engendering generalizable mechanistic insight and should provide a solid building-block to generate more detailed ionic models to represent complex rabbit electrophysiology.


This tool is an exact copy of the model included in the Supplementary Material for the following manuscript:

Gray RA, Pathmanathan P. A Parsimonious Model of the Rabbit Action Potential Elucidates the Minimal Physiological Requirements for Alternans and Spiral Wave Breakup. PLOS Computational Biology, 2016, 12(10): e1005087. doi:10.1371/journal.pcbi.1005087.

Model calibration and validation is described in detail in this manuscript. Briefly, the model was calibrated using the following well-known and important electro-physiological phenomena measured from rabbit ventricular myocytes/tissue under nearly identical and physiological conditions: 1) steady-state sodium channel inactivation as determined from voltage clamp experiments; 2) action potential depolarization in single cells; 3) recovery of excitability in single cells; 4) action potential depolarization dynamics during propagation in the whole heart; and 5) the action potential shape during repolarization in the whole heart.

The model was validated by comparing simulation results of resting membrane potential, action potential amplitude, (dVm/dt)max, and conduction speed to several experimental datasets from previously published studies: see Table B in Supplement from (Gray and Pathmanathan, 2016), and spiral wave characteristics in Figure 5 (Gray and Pathmanathan, 2016)).

The level of validation required for a model depends on its “context of use” and the consequences of incorrect model predictions; hence further validation is expected to be required for each specific context.


  1. The model assumes that intra- and extracellular concentrations of ions are constant.
  2. The equations are of Hodgkin-Huxley type, Markov models are required to replicate certain features of voltage clamp experiments including drug binding kinetics.
  3. Importantly, the APD in our model is dependent on Vmax, which depends on the magnitude of the stimulus current, which is different in single cells compared to in tissue during propagation. When the model is stimulated to unphysiologically large Vm the action potential duration is unphysiologically long; to avoid this excitation can be initiated we initiated by holding Vm at 0 mV for 2 ms.

Supporting Documentation

A comprehensive explanation and justification of the model as well as validation are provided in the original publication and supplementary material in the manuscript by Gray and Pathmanathan referenced above.

The model is implemented in CellML. The CellML language is an open standard based on the XML markup language. CellML is being developed by the Auckland Bioengineering Institute at the University of Auckland and affiliated research groups (https://cellml.org).

The code itself is provided on GitHub. In two files (representing two types of stimulation: current clamp or voltage clamp):

Relevant FDA guidance documents and FDA-recognized standards include:

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