Impulses and Physiological States in Theoretical Models of Nerve Membrane

Model Status

This version of the model has been curated by Penny Noble using COR and is also known to read in to JSim and PCEnv. There is also a PCEnv session file associated with this model.

Model Structure

Often it is not necessary to model the ionic currents of a cell with the accuracy and complexity inherent in the biophysically based models. With a view to investigating phenomena on a larger spatial and temporal scale, several ionic current models have been developed that do not seek to model subcellular processes but only to provide an action potential at a minimal computational cost.

The FitzHugh-Nagumo model (1961) is based on the cubic excitation model (see The Polynomial Model, 1975), but it also includes a recovery variable so both depolarisation and repolarisation can be modelled. In 1994, Rogers and McCulloch modified the original model to generate a more realistic action potential. The velocity of the upstroke was increased and the large hyperpolarisation at the end of the recovery phase was removed. The model parameters were also updated. In 1996, this form of the already modified FitzHugh_Nagumo model was further updated by Aliev and Panfilov. They altered the equation which modelled the change of the recovery variable to provide a more realistic restitution period and to allow for reentrant phenomena.

The complete original paper references are cited below:

Impulses and physiological states in theoretical models of nerve membrane, FitzHugh, R.A., 1961, Biophys. J. , 1, 445-466.

An active pulse transmission line simulating nerve axon, Nagumo, J., Animoto, S., Yoshizawa, S., 1962, Proc. Inst. Radio Engineers, 50, 2061-2070.

A collocation-Galerkin finite element model of cardiac action potential propagation, Rogers, J.M., McCulloch, A.D., 1994a, IEEE Trans. Biomed. Eng. , 41, 743-757.

A simple two-variable model of cardiac excitation, Aliev, R.R. and Panfilov, A.V., 1996, Chaos, Solitons and Fractals , 7, 293-301. PubMed ID: 8796189

The raw CellML description of the simplified cardiac myocyte models can be downloaded in various formats as described in . For an example of a more complete documentation for an electrophysiological model, see The Hodgkin-Huxley Squid Axon Model, 1952.