Nickerson
David
d.nickerson@auckland.ac.nz
The University of Auckland
The Bioengineering Institute
2004-07-15
This is a CellML version of the modified FitzHugh-Nagumo model,
published by Aliev and Panfilov in 1996. While the
original two-variable model described a non-dimensional activation
variable (u) and a non-dimensional recovery variable (v),
here we formulate the model in terms of the `real' action potential
given by the time course of the transmembrane potential (Vm). In so
doing, the time rate of change of the activation variable describes
the total `ionic current' through the membrane with the original
model parameters adjusted to give the correct dimensionality.
This model has been further modified by Nash and Panfilov 2004 to
include active tension development.
Nash
M
P
Panfilov
A
V
Electromechanical model of excitable tissue to study reentrant
cardiac arrhythmias
2004
Prog. Biophys. Molec. Biol.
85
501
522
We'll use this component as the "interface" to the model, all
other components are hidden via encapsulation in this component.
This is a dummy equation that we simply use to make grabbing the
value in CMISS much easier.
$\mathrm{IStimC}=\mathrm{Istim}$
The component which defines the kinetics of the transmembrane potential.
This equation describes the kinetics of the transmembrane,
potential - the action potential.
$\frac{d \mathrm{Vm}}{d t}=\frac{\mathrm{Istim}-\mathrm{Iion}}{\mathrm{Cm}}$
The non-dimensional and scaled potential value.
$u=\frac{\mathrm{Vm}-\mathrm{Vr}}{\mathrm{Vp}-\mathrm{Vr}}$
Here we define the total ionic current through the cellular
membrane - equivalent to the temporal derivative of the original
activation variable. One modification of Aliev and Panfilov is
in this equation, with the additional multiplication of the recovery
variable with the normalised potential and removal of the scalar
multiplier.
The calcuation of the total ionic current.
$\mathrm{Iion}=\mathrm{c1}u(u-\frac{\mathrm{Vth}-\mathrm{Vr}}{\mathrm{Vp}-\mathrm{Vr}})(u-1.0)+uv$
Here we define the non-dimensional recovery variable, v. The kinetics
of the recovery variable have been reworked by Aliev and Panfilov to
provide more realistic restitution properties.
The kinetics of the recovery variable.
$\frac{d v}{d t}=\mathrm{eps}(-v-\mathrm{rate}\mathrm{vstar}(\mathrm{Vm}-\mathrm{Vr}))$
$\mathrm{eps}=b+\frac{dv}{u+\mathrm{mu2}}$
$\mathrm{rate}=\frac{\mathrm{c1}}{(\mathrm{Vp}-\mathrm{Vr})^{2.0}}$
$\mathrm{vstar}=\mathrm{Vm}+\mathrm{Vr}-\mathrm{Vp}-\mathrm{Vth}$
This is the active tension relation from the Nash and Panfilov
article.
The kinetics of the active tension.
$\frac{d \mathrm{Ta}}{d t}=e(\mathrm{kTa}u-\mathrm{Ta})$
$e=\begin{cases}100.0\mathrm{e0} & \text{if $u< 0.05$}\\ 10.0\mathrm{e0} & \text{otherwise}\end{cases}$