Mitchell, Schaeffer, 2003
Model Status
This version of this model is known to run in both PCEnv and COR. The units have been checked and are consistent. A generic stimulus protocol has been added to allow the model to simulate trains of action potentials. Although the model does run, the simulation output is still not quite the same as the original published model. The original model authors have been contacted and we will continue to curate the CellML model.
Model Structure
Over the past 30 to 35 years, mathematical models that describe ventricular action potential have become increasingly complex as new experimental data has become available and has been incorporated into the mathematical equations. Although these complex models are more realistic, they are also computationally expensive to run, and isolating subsets of essential parameters from the model is difficult. One traditional method for avoiding this complexity is to use simplified models such as the FitzHugh-Nagumo model, 1961. However, these simplified models have been criticised as being too simple and as not having the capacity to fully capture certain important features of the ventricular action potential.
The modelling approach that Mitchell and Schaeffer take is based on a similar approach to that of Fenton and Karma (1998). While the Fenton and Karma model is a simplified ionic model of ventricular action potential with three membrane currents, Mitchell and Schaeffer reduce this further to create a model with just two currents. This model retains enough detail to quantitatively reproduce the behaviour of the ventricular action potential captured by the more complex ionic models of cardiac action potential (such as the Beeler-Reuter 1977 model, and the original Luo-Rudy 1991 model), but it is less computationally expensive than these other models.
The two currents in the Michell-Schaeffer model are:
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Jin , an inward current which is a combination of all the currents which raise the voltage across the membrane (primarily sodium and calcium)
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Jout , an outward current which is a combination of all the currents which decrease the membrane voltage (primarily potassium)
The complete original paper reference is cited below:
A two-current model for the dynamics of cardiac membrane, Colleen C. Mitchell, David G. Schaeffer, 2003, Bulletin of Mathematical Biology , 65, (5), 767-793. (A PDF version of the article is available to subscribers on the Bulletin of Mathematical Biology website.) PubMed ID: 12909250
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| A schematic diagram of the two ionic currents described by the Mitchell-Schaeffer model of a ventricular myocyte. |