Rendering of the source text

<?xml version='1.0' encoding='utf-8'?>
<!--
This CellML file was generated on 01/04/2005 at 14:28:13 using:

COR (0.9.31.48)
Copyright 2002-2005 Oxford Cardiac Electrophysiology Group
http://COR.physiol.ox.ac.uk/ - COR@physiol.ox.ac.uk

CellML 1.0 was used to generate this cellular model
http://www.CellML.org/
-->

<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="vanderpol_vandermark_1928_version01" name="vanderpol_vandermark_1928_version01">
   
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>The Heartbeat Considered as a Relaxation Oscillation, and an Electrical Model of the Heart</title>
  <author>
    <firstname>Penny</firstname>
          <surname>Noble</surname>
    <affiliation>
      <shortaffil>Oxford University</shortaffil>
    </affiliation>
  </author>
</articleinfo>
  <section id="sec_status">
    <title>Model Status</title>
    <para>
This version of the model has been curated by Penny Noble using COR and is known to read in to JSim. The model is also known to run in PCEnv.
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
The original paper reference is cited below:
				</para>
				
				<para>
					The heartbeat considered as a relaxation oscillation and an electrical model of the heart, B. van der Pol and J. van der Mark, 1928, <emphasis>The London, Edinburgh and Dublin Physiological Magazine and Journal of Science</emphasis>, 6, 763-775.
				</para>

<para>
This paper is a classic in the field and a Google search will yield plenty of information regarding the model (such as the <ulink url="http://en.wikipedia.org/wiki/Van_der_Pol_oscillator">Wikipedia entry</ulink>).
</para>

</sect1>
</article>
</documentation>


  


   <units name="per_second">
      <unit units="second" exponent="-1"/>
   </units>
   <component name="Main">
      <variable units="second" name="time"/>
      <variable units="dimensionless" name="x" initial_value="-2"/>
      <variable units="dimensionless" name="y" initial_value="0"/>
      <variable units="dimensionless" name="epsilon" initial_value="1"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>x</ci>
            </apply>
            <apply>
              <times/>
              <ci>y</ci>
              <cn cellml:units="per_second">1</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>y</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                 <minus/>
                 <apply>
                    <times/>
                    <ci>epsilon</ci>
                    <apply>
                       <minus/>
                       <cn cellml:units="dimensionless">1</cn>
                       <apply>
                          <power/>
                          <ci>x</ci>
                          <cn cellml:units="dimensionless">2</cn>
                       </apply>
                    </apply>
                    <ci>y</ci>
                 </apply>
                 <ci>x</ci>
               </apply>
               <cn cellml:units="second">1</cn>
            </apply> 
         </apply>
      </math>
   </component>





<rdf:RDF>
  <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:#author2VcardN">
    <vCard:Given>J</vCard:Given>
    <vCard:Family>Van der Mark</vCard:Family>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#8dd43368-8917-4a9c-a7d5-a9670a19c162">
    <bqs:JournalArticle rdf:resource="rdf:#c54da9b9-bd7c-45a4-977e-043e3b8786ac"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#af8f5b2c-82a5-4d13-8a5e-f9d6df459857">
    <vCard:ORG rdf:resource="rdf:#dd43054b-e1d5-4394-88a4-bd769a92050e"/>
    <vCard:EMAIL rdf:resource="rdf:#12ef5d76-7c57-4629-baf7-20790a61b682"/>
    <vCard:N rdf:resource="rdf:#79545738-bf24-4ac9-b9f7-af4645e3762e"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#c54da9b9-bd7c-45a4-977e-043e3b8786ac">
    <dc:creator rdf:resource="rdf:#citationAuthorsSeq"/>
    <dc:title>The Heartbeat Considered as a Relaxation Oscillation, and an Electrical Model of the Heart.</dc:title>
    <bqs:volume>6</bqs:volume>
    <bqs:first_page>763</bqs:first_page>
    <bqs:Journal rdf:resource="rdf:#0c2ebad6-7c08-4052-b739-e681d56d30e9"/>
    <dcterms:issued rdf:resource="rdf:#7dc83f84-0eb0-4946-a3fb-d2cbf933f62d"/>
    <bqs:last_page>775</bqs:last_page>
  </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:#ac52e806-0307-46e0-ba6b-9a811cf6ba71">
    <vCard:N rdf:resource="rdf:#40ec0d5e-fe26-4d1e-8f68-5a4b6ee66f5f"/>
  </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="">
    <cmeta:modification rdf:resource="rdf:#542a4135-7251-448b-b316-4e1415c847c8"/>
    <dcterms:created rdf:resource="rdf:#08adc06b-9fed-4282-a08d-b7975cd2133c"/>
    <dc:creator rdf:resource="rdf:#af8f5b2c-82a5-4d13-8a5e-f9d6df459857"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#79545738-bf24-4ac9-b9f7-af4645e3762e">
    <vCard:Given>Penny</vCard:Given>
    <vCard:Family>Noble</vCard:Family>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#dd43054b-e1d5-4394-88a4-bd769a92050e">
    <vCard:Orgname>Oxford University</vCard:Orgname>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#12ef5d76-7c57-4629-baf7-20790a61b682">
    <rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
    <rdf:value>penny.noble@physiol.ox.ac.uk</rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="#vanderpol_vandermark_1928_version01">
    <bqs:reference rdf:resource="rdf:#8dd43368-8917-4a9c-a7d5-a9670a19c162"/>
<bqs:reference rdf:parseType="Resource">
  <dc:subject rdf:parseType="Resource">
    <bqs:subject_type>keyword</bqs:subject_type>
    <rdf:value>
      <rdf:Bag>
        <rdf:li>cardiac</rdf:li>
        <rdf:li>heartbeat</rdf:li>
        <rdf:li>electrophysiology</rdf:li>
        <rdf:li>relaxation oscillation</rdf:li>
      </rdf:Bag>
    </rdf:value>
  </dc:subject>
</bqs:reference>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#author1VcardN">
    <vCard:Given>B</vCard:Given>
    <vCard:Family>Van der Pol</vCard:Family>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#40ec0d5e-fe26-4d1e-8f68-5a4b6ee66f5f">
    <vCard:Given>Peter</vCard:Given>
    <vCard:Family>Villiger</vCard:Family>
    <vCard:Other>J</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#542a4135-7251-448b-b316-4e1415c847c8">
    <dcterms:modified rdf:resource="rdf:#5e0600bb-559e-4bad-b946-2e81bae29e74"/>
    <rdf:value>
          added metadata
        </rdf:value>
    <cmeta:modifier rdf:resource="rdf:#ac52e806-0307-46e0-ba6b-9a811cf6ba71"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#08adc06b-9fed-4282-a08d-b7975cd2133c">
    <dcterms:W3CDTF>2005-04-01</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#0c2ebad6-7c08-4052-b739-e681d56d30e9">
    <dc:title>The London, Edinburgh and Dublin Physiological Magazine and Journal of Science</dc:title>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#7dc83f84-0eb0-4946-a3fb-d2cbf933f62d">
    <dcterms:W3CDTF>1928-01-01</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#5e0600bb-559e-4bad-b946-2e81bae29e74">
    <dcterms:W3CDTF>2006-03-31</dcterms:W3CDTF>
  </rdf:Description>
</rdf:RDF>
</model>