The Polynomial Model
Catherine
Lloyd
Bioengineering Institute, University of Auckland
Model Status
This is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
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 simplest of these models is a polynomial model that just uses one variable. It was developed by Hunter, McNaughton and Noble in 1975 and it is commonly used to track cellular depolarisation. However, it does not attempt to model repolarisation. The lowest order polynomial model is the cubic model which can be extended to use a higher order polynomial. As there is only a single variable, the model is very fast to calculate and therefore it may be used on large geometries.
The complete original paper reference is cited below:
Analytical models of propagation in excitable cells, Hunter, P.J., McNaughton, P.A. and Noble, D., 1975,
Prog. Biophys. molec. Biol.
, 30, 99-144. PubMed ID: 792954
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.
$\frac{d \mathrm{Vm}}{d t}=\frac{\mathrm{Istim}-I}{\mathrm{Cm}}$
$\mathrm{plateau}=\mathrm{Vm\_plateau}-\mathrm{Vm\_rest}$
$\mathrm{threshold}=\mathrm{Vm\_threshold}-\mathrm{Vm\_rest}$
$\mathrm{phi}=\mathrm{Vm}-\mathrm{Vm\_rest}$
$I=\mathrm{membrane\_conductance}\mathrm{phi}(1.0-\frac{\mathrm{phi}}{\mathrm{threshold}})(1.0-\frac{\mathrm{phi}}{\mathrm{plateau}})$
Analytical models of propagation in excitable cells
30
99
144
d.nickerson@auckland.ac.nz
Evaluation of the membrane potential ODE.
keyword
Cardiac Myocyte
simplified model
electrophysiology
excitable tissue
propagation
Progress in Biophysics and Molecular Biology
D
Noble
We'll use this component as the "interface" to the model, all
other components are hidden via encapsulation in this component.
P
McNaughton
A
The single current calculation.
792954
1975-01-01
The University of Auckland
The Bioengineering Institute
This is the main equation for the model, describing the dependency
of the time course of transmembrane potential on the single ionic
current plus any applied stimulus current.
This is a CellML version of the cubic polynomial model of activation from the 1975 paper by Hunter et. al.
P
Hunter
J
This is the calculation of the single current in this model, and where
the model name comes from.
David
Nickerson
P
2005-01-06