- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-09-03 23:51:32+12:00
- Desc:
- committing version01 of fitzhugh_1961
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/fitzhugh_1961/rawfile/b55d5d4140431f1c097c3b6f7a951aaaab0d32a5/fitzhugh_1961.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : fitzhugh_nagumo_model_1961.xml
CREATED : 28th December 2001
LAST MODIFIED : 11th August 2003
AUTHOR : Catherine Lloyd
Department of Engineering Science
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/01/2002 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of FitzHugh and Nagumo's
1961 simplified model of cardiac myocytes.
CHANGES:
03/01/2002 - CML - Added Aliev and Panfilov (1996) modifications.
21/01/2002 - AAC - Updated metadata to conform to the 16/1/02 CellML Metadata
1.0 Specification.
25/02/2002 - CML - Corrected an equation.
10/07/2002 - CML - Removed modifications component - as this is not the
original model.
11/08/2003 - CML - Separated out equations into different components.
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<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>The FitzHugh-Nagumo Simplified Cardiac Myocyte Model</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
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.
</para>
<para>
The FitzHugh-Nagumo model (1961) is based on the cubic excitation model (see <ulink url="${HTML_EXMPL_HMN_SIMPLE}">The Polynomial Model, 1975</ulink>), 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.
</para>
<para>
The complete original paper references are cited below:
</para>
<para>
Impulses and physiological states in theoretical models of nerve membrane, FitzHugh, R.A., 1961, <ulink url="http://www.biophysj.org/">
<emphasis>Biophys. J.</emphasis>
</ulink>, 1, 445-466.
</para>
<para>
An active pulse transmission line simulating nerve axon, Nagumo, J., Animoto, S., Yoshizawa, S., 1962, <emphasis>Proc. Inst. Radio Engineers</emphasis>, 50, 2061-2070.
</para>
<para>
A collocation-Galerkin finite element model of cardiac action potential propagation, Rogers, J.M., McCulloch, A.D., 1994a, <ulink url="http://www.ieee.org/organizations/pubs/pub_preview/bme_toc.html">
<emphasis>IEEE Trans. Biomed. Eng.</emphasis>
</ulink>, 41, 743-757.
</para>
<para>
A simple two-variable model of cardiac excitation, Aliev, R.R. and Panfilov, A.V., 1996, <ulink url="http://www.theo-physik.uni-kiel.de/theo-physik/schuster/contents/csf95.html#7_2">
<emphasis>Chaos, Solitons and Fractals</emphasis>
</ulink>, 7, 293-301. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=8796189&dopt=Abstract">PubMed ID: 8796189</ulink>
</para>
<para>
The raw CellML description of the simplified cardiac myocyte models can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>. For an example of a more complete documentation for an electrophysiological model, see <ulink url="${HTML_EXMPL_HHSA_INTRO}">The Hodgkin-Huxley Squid Axon Model, 1952</ulink>.
</para>
</sect1>
</article>
</documentation>
<!--
Below, we define some additional units for association with variables and
constants within the model. The identifiers are fairly self-explanatory.
-->
<units name="millisecond">
<unit units="second" prefix="milli"/>
</units>
<units name="per_millisecond">
<unit units="second" prefix="milli" exponent="-1"/>
</units>
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units name="microA_per_mm2">
<unit units="ampere" prefix="micro"/>
<unit units="metre" prefix="milli" exponent="-2"/>
</units>
<units name="microF_per_mm2">
<unit units="farad" prefix="micro"/>
<unit units="metre" prefix="milli" exponent="-2"/>
</units>
<!--
The "environment" component is used to declare variables that are used by
all or most of the other components, in this case just "time".
-->
<component name="environment">
<variable units="millisecond" public_interface="out" name="time"/>
</component>
<component name="membrane">
<variable units="dimensionless" public_interface="out" name="u"/>
<variable units="millivolt" public_interface="out" name="Vr" initial_value="-85.0"/>
<variable units="millivolt" public_interface="out" name="Vth" initial_value="-75.0"/>
<variable units="millivolt" public_interface="out" name="Vp" initial_value="15.0"/>
<variable units="microF_per_mm2" name="Cm" initial_value="0.01"/>
<variable units="millivolt" name="Vm"/>
<variable units="microA_per_mm2" public_interface="in" name="I_ion"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Vm_diff_eq">
<eq/>
<apply>
<diff/>
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</bvar>
<ci> Vm </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> I_ion </ci>
</apply>
<ci> Cm </ci>
</apply>
</apply>
<apply id="u_calculation">
<eq/>
<ci> u </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> Vm </ci>
<ci> Vr </ci>
</apply>
<apply>
<minus/>
<ci> Vp </ci>
<ci> Vr </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="ionic_current">
<variable units="microA_per_mm2" public_interface="out" name="I_ion"/>
<variable units="dimensionless" name="alpha"/>
<variable units="microA_per_mm2" name="c1" initial_value="0.175"/>
<variable units="microA_per_mm2" name="c2" initial_value="0.03"/>
<variable units="dimensionless" public_interface="in" name="v"/>
<variable units="dimensionless" public_interface="in" name="u"/>
<variable units="millivolt" public_interface="in" name="Vr"/>
<variable units="millivolt" public_interface="in" name="Vth"/>
<variable units="millivolt" public_interface="in" name="Vp"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_calculation">
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<apply>
<divide/>
<apply>
<minus/>
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<ci> Vr </ci>
</apply>
<apply>
<minus/>
<ci> Vp </ci>
<ci> Vr </ci>
</apply>
</apply>
</apply>
<apply id="I_ion_calculation">
<eq/>
<ci> I_ion </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> c1 </ci>
<ci> u </ci>
<apply>
<minus/>
<ci> u </ci>
<ci> alpha </ci>
</apply>
<apply>
<minus/>
<ci> u </ci>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> c2 </ci>
<ci> v </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="recovery_variable">
<variable units="dimensionless" public_interface="out" name="v"/>
<variable units="per_millisecond" name="b" initial_value="0.011"/>
<variable units="dimensionless" name="d" initial_value="0.55"/>
<variable units="dimensionless" public_interface="in" name="u"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="v_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> v </ci>
</apply>
<apply>
<times/>
<ci> b </ci>
<apply>
<minus/>
<ci> u </ci>
<apply>
<times/>
<ci> d </ci>
<ci> v </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_2="environment" component_1="membrane"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="ionic_current"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="recovery_variable"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="ionic_current" component_1="membrane"/>
<map_variables variable_2="u" variable_1="u"/>
<map_variables variable_2="Vr" variable_1="Vr"/>
<map_variables variable_2="Vth" variable_1="Vth"/>
<map_variables variable_2="Vp" variable_1="Vp"/>
<map_variables variable_2="I_ion" variable_1="I_ion"/>
</connection>
<connection>
<map_components component_2="recovery_variable" component_1="membrane"/>
<map_variables variable_2="u" variable_1="u"/>
</connection>
<connection>
<map_components component_2="recovery_variable" component_1="ionic_current"/>
<map_variables variable_2="v" variable_1="v"/>
</connection>
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<rdf:Bag rdf:about="rdf:#97980b62-d44e-4009-b240-a1a1951f67c2">
<rdf:li>Myocyte</rdf:li>
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<dcterms:W3CDTF>2002-07-10</dcterms:W3CDTF>
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<dc:title>Biophysical Journal</dc:title>
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The FitzHugh-Nagumo 1961 Simplified Model of a Cardiac Myocyte
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