/*
 * The FitzHugh-Nagumo Simplified Cardiac Myocyte Model
 * 
 * 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.
 */

import nsrunit;
unit conversion on;
// unit millisecond predefined
unit per_millisecond=1E3 second^(-1);

math main {
	realDomain t millisecond;
	t.min=0;
	extern t.max;
	extern t.delta;
	real v(t) dimensionless;
	when(t=t.min) v=0;
	real w(t) dimensionless;
	when(t=t.min) w=0;
	real alpha dimensionless;
	alpha=-0.08;
	real gamma dimensionless;
	gamma=3;
	real epsilon dimensionless;
	epsilon=0.005;
	real I(t) dimensionless;

	// <component name="Main">
	I=(if ((t>=(0 millisecond)) and (t<=(.5 millisecond))) (-1)*80 else 0);
	v:t=((1 per_millisecond)*(v*(v-alpha)*(1-v)-w+I));
	w:t=((1 per_millisecond)*epsilon*(v-gamma*w));
}