Rendering of the source text

<?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&amp;db=PubMed&amp;list_uids=7408126&amp;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"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="I_ion_calculation">
        <eq/>
        <ci> I_ion </ci>
        <apply>
          <minus/>
          <apply>
            <times/>
            <apply>
              <minus/>
              <ci> Y </ci>
            </apply>
            <ci> i1_Vm </ci>
          </apply>
          <apply>
            <times/>
            <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>
        </apply>
        <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>
          <piece>
            <cn cellml:units="dimensionless"> 0.0 </cn>
            <apply>
              <lt/>
              <ci> Vm </ci>
              <cn cellml:units="millivolt"> -80.0 </cn>
            </apply>
          </piece>
          <piece>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <gt/>
              <ci> Vm </ci>
              <cn cellml:units="millivolt"> -60.0 </cn>
            </apply>
          </piece>
          <otherwise>
            <apply>
              <divide/>
              <apply>
                <plus/>
                <ci> Vm </ci>
                <cn cellml:units="millivolt"> 80.0 </cn>
              </apply>
              <cn cellml:units="millivolt"> 20.0 </cn>
            </apply>
          </otherwise>
        </piecewise>
      </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>
              </apply>
            </apply>
            <apply>
              <lt/>
              <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>
              </apply>
            </apply>
            <apply>
              <gt/>
              <ci> Vm </ci>
              <cn cellml:units="millivolt"> 0.0 </cn>
            </apply>
          </piece>
          <otherwise>
            <apply>
              <plus/>
              <cn cellml:units="microA_per_mm2"> 0.05 </cn>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <cn cellml:units="dimensionless"> 0.01 </cn>
                  <apply>
                    <plus/>
                    <ci> Vm </ci>
                    <cn cellml:units="millivolt"> 70.0 </cn>
                  </apply>
                </apply>
                <cn cellml:units="millivolt"> 70.0 </cn>
              </apply>
            </apply>
          </otherwise>
        </piecewise>
      </apply>
      
      <apply id="i0_Vm_calculation">
        <eq/>
        <ci> i0_Vm </ci>
        <apply>
          <plus/>
          <ci> i1_Vm </ci>
          <ci> f_Vm </ci>
        </apply>        
      </apply>
        
      <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>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#2fc41385-c677-4554-8cce-df55d2020cb8">
    <vCard:N rdf:resource="rdf:#7b2d6089-76d6-4211-a855-0d4391379052"/>
  </rdf:Description>
  <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>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#ab3a6583-b5ce-467c-aad4-48aca484485a">
    <vCard:N rdf:resource="rdf:#6c6847d6-6088-451e-ac80-fda7ce727465"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#da66cf3f-c58f-4df2-a447-a7eabaafc468">
    <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"/>
    <cmeta:modification rdf:resource="rdf:#e1e8bdc8-2392-4f6b-85f3-534f28037187"/>
    <cmeta:modification rdf:resource="rdf:#f0fe7c4c-c1e8-4cbc-87e9-996f31be62ff"/>
    <dcterms:created rdf:resource="rdf:#5ce66f22-e0cb-4ad1-97a7-66d9c246abe2"/>
    <dc:creator rdf:resource="rdf:#6e59d209-dce4-4ce0-b4cc-f5e368e28959"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#a6ff1681-e4e1-44c2-b53d-2ffed66bbf71">
    <dcterms:modified rdf:resource="rdf:#be767b20-b3e9-4115-83c4-9a8b81b1948d"/>
    <rdf:value>
          Added publication date information.
        </rdf:value>
    <cmeta:modifier rdf:resource="rdf:#ab3a6583-b5ce-467c-aad4-48aca484485a"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#6e59d209-dce4-4ce0-b4cc-f5e368e28959">
    <vCard:ORG rdf:resource="rdf:#fd25311d-9ed8-4ae9-b0dd-873b248c9d6b"/>
    <vCard:EMAIL rdf:resource="rdf:#ca0c4189-c161-45e6-bfed-857ec2e92d82"/>
    <vCard:N rdf:resource="rdf:#e7732613-2857-4596-9edf-02023dc00985"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#8c57b67e-71d1-4fa4-9eb4-8751ba044215">
    <dc:subject rdf:resource="rdf:#1e2a5d00-3d83-4be1-8f45-e11923dc04a7"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#author2Vcard">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N rdf:resource="rdf:#author2VcardN"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#author2VcardN">
    <vCard:Given>D</vCard:Given>
    <vCard:Family>Durrer</vCard:Family>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#be767b20-b3e9-4115-83c4-9a8b81b1948d">
    <dcterms:W3CDTF>2003-04-09</dcterms:W3CDTF>
  </rdf:Description>
  <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>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#5ce66f22-e0cb-4ad1-97a7-66d9c246abe2">
    <dcterms:W3CDTF>2001-12-28</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#f0fe7c4c-c1e8-4cbc-87e9-996f31be62ff">
    <dcterms:modified rdf:resource="rdf:#2599c7be-418a-4b8b-8f73-ce1a9624faef"/>
    <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"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#414c20f6-2666-4f8e-a510-abd852c76a7f">
    <bqs:Pubmed_id>7408126</bqs:Pubmed_id>
    <bqs:JournalArticle rdf:resource="rdf:#e13f1b9d-c1c7-4782-a91a-217ec13daa9d"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#1e2a5d00-3d83-4be1-8f45-e11923dc04a7">
    <bqs:subject_type>keyword</bqs:subject_type>
    <rdf:value rdf:resource="rdf:#4862b4d1-0a3b-499c-a1fa-fea1e409ebad"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#273e640d-2e6f-4a25-aed5-9bd5787affbd">
    <dc:title>Circulation Research</dc:title>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#2599c7be-418a-4b8b-8f73-ce1a9624faef">
    <dcterms:W3CDTF>2002-01-21</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#38680ce2-4663-43a0-9659-7d332ac98a52">
    <vCard:N rdf:resource="rdf:#05522898-a7fe-46d5-b3e3-ddba3da3ffd4"/>
  </rdf:Description>
  <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"/>
    <bqs:reference rdf:resource="rdf:#414c20f6-2666-4f8e-a510-abd852c76a7f"/>
    <bqs:reference rdf:resource="rdf:#8c57b67e-71d1-4fa4-9eb4-8751ba044215"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#author1Vcard">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N rdf:resource="rdf:#author1VcardN"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#e13f1b9d-c1c7-4782-a91a-217ec13daa9d">
    <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"/>
    <dcterms:issued rdf:resource="rdf:#7380b16d-df01-4801-89d9-2a3f634ce3f3"/>
    <bqs:last_page>466</bqs:last_page>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#author1VcardN">
    <vCard:Given>F</vCard:Given>
    <vCard:Family>van Capelle</vCard:Family>
    <vCard:Other>J</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#05522898-a7fe-46d5-b3e3-ddba3da3ffd4">
    <vCard:Given>Catherine</vCard:Given>
    <vCard:Family>Lloyd</vCard:Family>
    <vCard:Other>May</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#7b2d6089-76d6-4211-a855-0d4391379052">
    <vCard:Given>Autumn</vCard:Given>
    <vCard:Family>Cuellar</vCard:Family>
    <vCard:Other>A.</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#e1e8bdc8-2392-4f6b-85f3-534f28037187">
    <dcterms:modified rdf:resource="rdf:#0dc1ba35-f8bc-4029-b13c-c47212d2d9cb"/>
    <rdf:value>
          Added more metadata.
        </rdf:value>
    <cmeta:modifier rdf:resource="rdf:#38680ce2-4663-43a0-9659-7d332ac98a52"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#ca0c4189-c161-45e6-bfed-857ec2e92d82">
    <rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
    <rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
  </rdf:Description>
</rdf:RDF>
</model>