<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : van_capelle_durrer_model_1980.xml
CREATED : 28th December 2001
LAST MODIFIED : 9th April 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 van Capelle and
Durrer's 1980 simplified model of cardiac myocytes.
CHANGES:
21/01/2002 - AAC - Updated metadata to conform to the 16/1/02 CellML Metadata
1.0 Specification.
22/07/2002 - CML - Added more metadata.
09/04/2003 - AAC - Added publication date information.
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="vancapelle_durrer_1980_version02" name="vancapelle_durrer_1980_version02">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>The van Capelle-Durrer 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 model created by van Capelle and Durrer (1980) follows the same general form as the FitzHugh-Nagumo model (see <ulink url="${HTML_EXMPL_FN_SIMPLE}">The FitzHugh-Nagumo Model, 1961</ulink>), with a single activation variable and a single recovery variable. It also includes the ability to add more complex parameter representations.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://circres.ahajournals.org/cgi/content/abstract/47/3/454">Computer simulation of arrhythmias in a network of coupled excitable elements</ulink>, van Capelle, F.J.L., Durrer, D., 1980, <ulink url="http://circres.ahajournals.org/">
<emphasis>Circ. Res.</emphasis>
</ulink>, 47, 454-466. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=7408126&dopt=Abstract">PubMed ID: 7408126</ulink>
</para>
<para>
The raw CellML description of the simplified cardiac myocyte models can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>. For an example of a more complete documentation for an electrophysiological model, see <ulink url="${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="per_millivolt">
<unit units="millivolt" exponent="-1"/>
</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="microF_per_mm2" name="C" initial_value="0.01"/>
<variable units="per_millisecond" name="T" initial_value="50.0"/>
<variable units="dimensionless" name="Y" initial_value="0.07"/>
<variable units="dimensionless" name="Y_infinity_Vm"/>
<variable units="millivolt" name="Vm" initial_value="-78.6"/>
<variable units="microA_per_mm2" name="I_ion"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="microA_per_mm2" name="i1_Vm"/>
<variable units="microA_per_mm2" name="i0_Vm"/>
<variable units="microA_per_mm2" name="f_Vm"/>
<variable units="dimensionless" name="af" initial_value="0.00003837854"/>
<variable units="dimensionless" name="bf" initial_value="0.00584649"/>
<variable units="dimensionless" name="cf" initial_value="0.2531834"/>
<variable units="dimensionless" name="df" initial_value="2.356256"/>
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<apply>
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<apply>
<times/>
<apply>
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<ci> i1_Vm </ci>
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<apply>
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<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> Y </ci>
</apply>
<ci> i0_Vm </ci>
</apply>
</apply>
</apply>
<apply id="Y_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Y </ci>
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<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> T </ci>
</apply>
<apply>
<minus/>
<ci> Y_infinity_Vm </ci>
<ci> Y </ci>
</apply>
</apply>
</apply>
<apply id="Y_infinity_Vm_calculation">
<eq/>
<ci> Y_infinity_Vm </ci>
<piecewise>
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<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
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<cn cellml:units="millivolt"> -60.0 </cn>
</apply>
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<otherwise>
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<divide/>
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<ci> Vm </ci>
<cn cellml:units="millivolt"> 80.0 </cn>
</apply>
<cn cellml:units="millivolt"> 20.0 </cn>
</apply>
</otherwise>
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</apply>
<apply id="i1_Vm_calculation">
<eq/>
<ci> i1_Vm </ci>
<piecewise>
<piece>
<apply>
<plus/>
<cn cellml:units="microA_per_mm2"> 0.05 </cn>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.005 </cn>
<apply>
<plus/>
<ci> Vm </ci>
<cn cellml:units="millivolt"> 70.0 </cn>
</apply>
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<apply>
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<ci> Vm </ci>
<cn cellml:units="millivolt"> -70.0 </cn>
</apply>
</piece>
<piece>
<apply>
<plus/>
<cn cellml:units="microA_per_mm2"> 0.06 </cn>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.00425 </cn>
<ci> Vm </ci>
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<apply>
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<ci> Vm </ci>
<cn cellml:units="millivolt"> 0.0 </cn>
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<apply>
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<apply>
<plus/>
<ci> Vm </ci>
<cn cellml:units="millivolt"> 70.0 </cn>
</apply>
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<cn cellml:units="millivolt"> 70.0 </cn>
</apply>
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<apply id="i0_Vm_calculation">
<eq/>
<ci> i0_Vm </ci>
<apply>
<plus/>
<ci> i1_Vm </ci>
<ci> f_Vm </ci>
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<apply id="f_Vm_calculation">
<eq/>
<ci> f_Vm </ci>
<piecewise>
<piece>
<apply>
<plus/>
<cn cellml:units="microA_per_mm2"> 0.0784 </cn>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.02 </cn>
<apply>
<plus/>
<ci> Vm </ci>
<cn cellml:units="millivolt"> 74.3 </cn>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci> Vm </ci>
<cn cellml:units="millivolt"> -74.3 </cn>
</apply>
</piece>
<piece>
<apply>
<plus/>
<cn cellml:units="microA_per_mm2"> -0.9884 </cn>
<apply>
<times/>
<cn cellml:units="per_millivolt"> 0.0171 </cn>
<apply>
<plus/>
<ci> Vm </ci>
<cn cellml:units="per_millivolt"> 27.8 </cn>
</apply>
</apply>
</apply>
<apply>
<gt/>
<ci> Vm </ci>
<cn cellml:units="millivolt"> -27.8 </cn>
</apply>
</piece>
<otherwise>
<apply>
<plus/>
<apply>
<times/>
<ci> af </ci>
<apply>
<power/>
<ci> Vm </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> bf </ci>
<apply>
<power/>
<ci> Vm </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<times/>
<ci> cf </ci>
<ci> Vm </ci>
</apply>
<ci> df </ci>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<connection>
<map_components component_2="environment" component_1="membrane"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<rdf:RDF>
<rdf:Bag rdf:about="rdf:#4862b4d1-0a3b-499c-a1fa-fea1e409ebad">
<rdf:li>Cardiac Myocyte</rdf:li>
<rdf:li>simplified model</rdf:li>
<rdf:li>cardiac myocyte</rdf:li>
<rdf:li>electrophysiology</rdf:li>
<rdf:li>arrythmia</rdf:li>
<rdf:li>cardiac</rdf:li>
<rdf:li>minimal model</rdf:li>
</rdf:Bag>
<rdf:Seq rdf:about="rdf:#citationAuthorsSeq">
<rdf:li rdf:resource="rdf:#author1Vcard"/>
<rdf:li rdf:resource="rdf:#author2Vcard"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#6c6847d6-6088-451e-ac80-fda7ce727465">
<vCard:Given>Autumn</vCard:Given>
<vCard:Family>Cuellar</vCard:Family>
<vCard:Other>A</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8b1feecd-1bbc-4794-b74f-924380ab7196">
<vCard:FN>Catherine Lloyd</vCard:FN>
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<rdf:Description rdf:about="rdf:#fd25311d-9ed8-4ae9-b0dd-873b248c9d6b">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Research Group</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7380b16d-df01-4801-89d9-2a3f634ce3f3">
<dcterms:W3CDTF>1980-09-01</dcterms:W3CDTF>
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<dc:creator rdf:resource="rdf:#8b1feecd-1bbc-4794-b74f-924380ab7196"/>
<rdf:value>This is the CellML description of the van Capelle-Durrer 1980 simplified model of a cardiac myocyte. It follows the same general form as the FitzHugh-Nagumo model with a single activation variable and a single recovery variable. The model also includes the ability to add more complex parameter representations.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0dc1ba35-f8bc-4029-b13c-c47212d2d9cb">
<dcterms:W3CDTF>2002-07-22</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="">
<dc:publisher>
The University of Auckland, Bioengineering Research Group
</dc:publisher>
<cmeta:modification rdf:resource="rdf:#a6ff1681-e4e1-44c2-b53d-2ffed66bbf71"/>
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Added publication date information.
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<vCard:Given>D</vCard:Given>
<vCard:Family>Durrer</vCard:Family>
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<rdf:Description rdf:about="rdf:#be767b20-b3e9-4115-83c4-9a8b81b1948d">
<dcterms:W3CDTF>2003-04-09</dcterms:W3CDTF>
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<rdf:Description rdf:about="rdf:#e7732613-2857-4596-9edf-02023dc00985">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
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<dcterms:W3CDTF>2001-12-28</dcterms:W3CDTF>
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<rdf:value>
Updated metadata to conform to the 16/1/02 CellML Metadata 1.0
Specification.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#2fc41385-c677-4554-8cce-df55d2020cb8"/>
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<dc:title>Circulation Research</dc:title>
</rdf:Description>
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<dcterms:W3CDTF>2002-01-21</dcterms:W3CDTF>
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<rdf:Description rdf:about="#vancapelle_durrer_1980_version02">
<dc:title>
The van Capelle-Durrer Simplified Model of a Cardiac Myocyte
</dc:title>
<cmeta:bio_entity>Cardiac Myocyte</cmeta:bio_entity>
<cmeta:comment rdf:resource="rdf:#da66cf3f-c58f-4df2-a447-a7eabaafc468"/>
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<dc:creator rdf:resource="rdf:#citationAuthorsSeq"/>
<dc:title>Computer simulation of arrhythmias in a network of coupled excitable elements</dc:title>
<bqs:volume>47</bqs:volume>
<bqs:first_page>454</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#273e640d-2e6f-4a25-aed5-9bd5787affbd"/>
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<vCard:Given>F</vCard:Given>
<vCard:Family>van Capelle</vCard:Family>
<vCard:Other>J</vCard:Other>
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<vCard:Given>Catherine</vCard:Given>
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<vCard:Given>Autumn</vCard:Given>
<vCard:Family>Cuellar</vCard:Family>
<vCard:Other>A.</vCard:Other>
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Added more metadata.
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<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
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</model>
