This equation describes the kinetics of the transmembrane
potential - the action potential.
d.nickerson@auckland.ac.nz
Here we define the ionic current through the cellular
membrane, defined as the summation of the two component
currents weighted by the excitability variable.
This is a CellML version of the 1980 van Capelle & Durrer activation model. This model was designed to be used in simulations of arrhythmias in a network of coupled excitable elements. They developed a membrane kinetics model with two variables of state: the transmembrane potential, V; and a generalised excitability parameter, Y.
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The component which defines the kinetics of the transmembrane potential.
The function f, used to define the i0 component current, consists
of three sections: two linear components joined by a cubic
component. The function was fitted such that both the function
value and its derivative df/dVm were continuous.
The current-voltage relation for when the membrane is
completely inexcitable. van Capelle & Durrer used a
simple three segment piecewise linear function to
represent this component of the total current.
D
Durrer
We'll use this component as the "interface" to the model, all
other components are hidden via encapsulation in this component.
The calcuation of the total ionic current.
The kinetics of the excitability variable. The time constant, T,
can be used to scale the duration of the action potential.
Circulation Research
Computer Simulation of Arrhythmias in a Network of Coupled Excitable Elements
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454
466
This is a dummy equation that we simply use to make grabbing the
value in CMISS much easier.
Here we define the kinetics of the non-dimensional excitability
variable.
The current-voltage relation for when the membrane
is maximally excitable. This is defined as the addition
of a piecewise function, f, to the i1 component current.
van Capelle & Durrer defined i0 as this to improve
the efficiency of their algorithm.
David
Nickerson
N
F
van Capelle
J. L
1980-01-01
2003-06-10
The voltage dependent steady-state value for the excitability
variable. Must be an S-shaped function, increasing from zero
when Vm is more negative than the resting potential to 1 at more
positive values of Vm.
The University of Auckland
The Bioengineering Institute