Location: Tentusscher, Noble, Noble, Panfilov, 2004 @ 5005395a3f3c / tentusscher_noble_noble_panfilov_2004.cellml

Author:
James Lawson <j.lawson@auckland.ac.nz>
Date:
2009-07-20 15:51:26+12:00
Desc:
for a, b, c: fixed e-notation, updated curation status, fixed ten Tusscher > Ten Tusscher in citation metadata
Permanent Source URI:
https://staging.physiomeproject.org/workspace/605/rawfile/5005395a3f3c6d075a7332a2eb7ade87fdbe2bdb/tentusscher_noble_noble_panfilov_2004.cellml

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COR (0.9.31.389)
Copyright 2002-2006 Oxford Cardiac Electrophysiology Group
http://COR.physiol.ox.ac.uk/ - COR@physiol.ox.ac.uk

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http://www.CellML.org/
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<article>
  <articleinfo>
  <title>A Model For Human Ventricular Tissue - M-cell variant</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 variant of the model was created by Penny Noble of Oxford University, and represents the parameters given for the M-cell variant in Ten Tusscher et al. 2004. A stimulus protocol component has been added to the model to allow simulation of trains of action potentials (JL, 18/06/07). This file is known to run in PCEnv and COR. This model is also associated with a PCEnv session file.
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
Cardiac arrhythmias and sudden cardiac death are amongst the most common causes of premature death in the devloped world.  However despite their prevalance, they remain relatively poorly understood.  Mathematical models, which capture the function of the beating human heart, play an important role in cardiac research.  In part this is because practical experiments on human hearts are limited, and animal hearts may differ significantly in their anatomy and physiology relative to the human heart.  In addition, cardiac arrhythmias are three dimensional phenomena, while experimental observations are mainly limited to surface recordings.
</para>

<para>
Existing mathematical models of human ventricular cells include:
</para>
<itemizedlist>
  <listitem>
            <para>
              Priebe and Beuckelmann, Electrophysiological Model of the Human Ventricular Myocyte, 1998; and</para>
          </listitem>
  <listitem>
            <para>
              Bernus <emphasis>et al.</emphasis> A Computationally Efficient Electrophysiological Model of Human Ventricular Cells, 2002.</para>
          </listitem>
</itemizedlist>
<para>
However, these models have their limitations, such as the fact that several of the equations are based on animal data.  The aim of the 2004 study by ten Tusscher <emphasis>et al.</emphasis>, is to develop a new model for human ventricular cells that is based on recent experimetnal data and that is computationally efficient for large-scale spatial simulations.  A schematic diagram of the modl can be seen in the figure below.
</para>

<para>
The complete original paper reference is cited below:
</para>

<para>
<ulink url="http://ajpheart.physiology.org/cgi/content/abstract/286/4/H1573">A model for human ventricular tissue</ulink>, K.H.W.J. ten Tusscher, D. Noble, P.J. Noble, and A.V. Panfilov, 2004, <ulink url="http://ajpheart.physiology.org/">
            <emphasis>American Journal of Physiology</emphasis>
          </ulink>, 286, H1573-H1589.  (<ulink url="http://ajpheart.physiology.org/cgi/content/full/286/4/H1573">Full text (HTML)</ulink> and <ulink url="http://ajpheart.physiology.org/cgi/reprint/286/4/H1573.pdf">PDF</ulink> versions of the article are available to subscribers on the <emphasis>American Journal of Physiology</emphasis> website.)  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=14656705&amp;dopt=Abstract">PubMed ID: 14656705</ulink>
</para>

<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>cell diagram</title>
    </objectinfo>
    <imagedata fileref="ten_tusscher_2004.png"/>
  </imageobject>
</mediaobject>
<caption>A schematic diagram describing the ion movement across the cell surface membrane and the sarcoplasmic reticulum, which are described by the Ten Tusscher <emphasis>et al.</emphasis> 2004 mathematical model of the human ventricular myocyte.</caption>
</informalfigure>

</sect1>
</article>
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            <ci>beta_xr2</ci>
            <apply>
               <divide/>
               <cn cellml:units="per_millisecond">1.12</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">60</cn>
                        </apply>
                        <cn cellml:units="millivolt">20</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_xr2</ci>
            <apply>
               <times/>
               <ci>alpha_xr2</ci>
               <ci>beta_xr2</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Xr2</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>xr2_inf</ci>
                  <ci>Xr2</ci>
               </apply>
               <ci>tau_xr2</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="slow_time_dependent_potassium_current">
      <variable units="picoA_per_picoF" public_interface="out" name="i_Ks" cmeta:id="slow_time_dependent_potassium_current_i_Ks"/>
      <variable units="nanoS_per_picoF" name="g_Ks" initial_value="0.062"/>
      <variable units="millivolt" public_interface="in" name="E_Ks"/>
      <variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
      <variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
      <variable units="dimensionless" private_interface="in" name="Xs"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_Ks</ci>
            <apply>
               <times/>
               <ci>g_Ks</ci>
               <apply>
                  <power/>
                  <ci>Xs</ci>
                  <cn cellml:units="dimensionless">2</cn>
               </apply>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_Ks</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="slow_time_dependent_potassium_current_Xs_gate">
      <variable units="dimensionless" public_interface="out" name="Xs" initial_value="0"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="dimensionless" name="xs_inf"/>
      <variable units="per_millisecond" name="alpha_xs"/>
      <variable units="per_millisecond" name="beta_xs"/>
      <variable units="millisecond" name="tau_xs"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>xs_inf</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">1</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <apply>
                              <minus/>
                              <cn cellml:units="millivolt">5</cn>
                           </apply>
                           <ci>V</ci>
                        </apply>
                        <cn cellml:units="millivolt">14</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>alpha_xs</ci>
            <apply>
               <divide/>
               <cn cellml:units="per_millisecond">1100</cn>
               <apply>
                  <root/>
                  <apply>
                     <plus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <minus/>
                              <apply>
                                 <minus/>
                                 <cn cellml:units="millivolt">10</cn>
                              </apply>
                              <ci>V</ci>
                           </apply>
                           <cn cellml:units="millivolt">6</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_xs</ci>
            <apply>
               <divide/>
               <cn cellml:units="per_millisecond">1</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">60</cn>
                        </apply>
                        <cn cellml:units="millivolt">20</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_xs</ci>
            <apply>
               <times/>
               <ci>alpha_xs</ci>
               <ci>beta_xs</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Xs</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>xs_inf</ci>
                  <ci>Xs</ci>
               </apply>
               <ci>tau_xs</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="fast_sodium_current">
      <variable units="picoA_per_picoF" public_interface="out" name="i_Na"/>
      <variable units="nanoS_per_picoF" name="g_Na" initial_value="14.838"/>
      <variable units="millivolt" public_interface="in" name="E_Na"/>
      <variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
      <variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
      <variable units="dimensionless" private_interface="in" name="m"/>
      <variable units="dimensionless" private_interface="in" name="h"/>
      <variable units="dimensionless" private_interface="in" name="j"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_Na</ci>
            <apply>
               <times/>
               <ci>g_Na</ci>
               <apply>
                  <power/>
                  <ci>m</ci>
                  <cn cellml:units="dimensionless">3</cn>
               </apply>
               <ci>h</ci>
               <ci>j</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_Na</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="fast_sodium_current_m_gate">
      <variable units="dimensionless" public_interface="out" name="m" initial_value="0"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="dimensionless" name="m_inf"/>
      <variable units="per_millisecond" name="alpha_m"/>
      <variable units="per_millisecond" name="beta_m"/>
      <variable units="millisecond" name="tau_m"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>m_inf</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">1</cn>
               <apply>
                  <power/>
                  <apply>
                     <plus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <minus/>
                              <apply>
                                 <minus/>
                                 <cn cellml:units="millivolt">56.86</cn>
                              </apply>
                              <ci>V</ci>
                           </apply>
                           <cn cellml:units="millivolt">9.03</cn>
                        </apply>
                     </apply>
                  </apply>
                  <cn cellml:units="dimensionless">2</cn>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>alpha_m</ci>
            <apply>
               <divide/>
               <cn cellml:units="per_millisecond">1</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <apply>
                              <minus/>
                              <cn cellml:units="millivolt">60</cn>
                           </apply>
                           <ci>V</ci>
                        </apply>
                        <cn cellml:units="millivolt">5</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_m</ci>
            <apply>
               <plus/>
               <apply>
                  <divide/>
                  <cn cellml:units="per_millisecond">0.1</cn>
                  <apply>
                     <plus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <plus/>
                              <ci>V</ci>
                              <cn cellml:units="millivolt">35</cn>
                           </apply>
                           <cn cellml:units="millivolt">5</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <divide/>
                  <cn cellml:units="per_millisecond">0.1</cn>
                  <apply>
                     <plus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <minus/>
                              <ci>V</ci>
                              <cn cellml:units="millivolt">50</cn>
                           </apply>
                           <cn cellml:units="millivolt">200</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_m</ci>
            <apply>
               <times/>
               <ci>alpha_m</ci>
               <ci>beta_m</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>m</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>m_inf</ci>
                  <ci>m</ci>
               </apply>
               <ci>tau_m</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="fast_sodium_current_h_gate">
      <variable units="dimensionless" public_interface="out" name="h" initial_value="0.75"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="dimensionless" name="h_inf"/>
      <variable units="per_millisecond" name="alpha_h"/>
      <variable units="per_millisecond" name="beta_h"/>
      <variable units="millisecond" name="tau_h"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>h_inf</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">1</cn>
               <apply>
                  <power/>
                  <apply>
                     <plus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <plus/>
                              <ci>V</ci>
                              <cn cellml:units="millivolt">71.55</cn>
                           </apply>
                           <cn cellml:units="millivolt">7.43</cn>
                        </apply>
                     </apply>
                  </apply>
                  <cn cellml:units="dimensionless">2</cn>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>alpha_h</ci>
            <piecewise>
               <piece>
                  <apply>
                     <times/>
                     <cn cellml:units="per_millisecond">0.057</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <minus/>
                              <apply>
                                 <plus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">80</cn>
                              </apply>
                           </apply>
                           <cn cellml:units="millivolt">6.8</cn>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <lt/>
                     <ci>V</ci>
                     <apply>
                        <minus/>
                        <cn cellml:units="millivolt">40</cn>
                     </apply>
                  </apply>
               </piece>
               <otherwise>
                  <cn cellml:units="per_millisecond">0</cn>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>beta_h</ci>
            <piecewise>
               <piece>
                  <apply>
                     <plus/>
                     <apply>
                        <times/>
                        <cn cellml:units="per_millisecond">2.7</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <times/>
                              <cn cellml:units="dimensionless">0.079</cn>
                              <ci>V</ci>
                           </apply>
                        </apply>
                     </apply>
                     <apply>
                        <times/>
                        <cn cellml:units="per_millisecond">310000</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <times/>
                              <cn cellml:units="dimensionless">0.3485</cn>
                              <ci>V</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <lt/>
                     <ci>V</ci>
                     <apply>
                        <minus/>
                        <cn cellml:units="millivolt">40</cn>
                     </apply>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <divide/>
                     <cn cellml:units="per_millisecond">0.77</cn>
                     <apply>
                        <times/>
                        <cn cellml:units="dimensionless">0.13</cn>
                        <apply>
                           <plus/>
                           <cn cellml:units="dimensionless">1</cn>
                           <apply>
                              <exp/>
                              <apply>
                                 <divide/>
                                 <apply>
                                    <plus/>
                                    <ci>V</ci>
                                    <cn cellml:units="millivolt">10.66</cn>
                                 </apply>
                                 <apply>
                                    <minus/>
                                    <cn cellml:units="millivolt">11.1</cn>
                                 </apply>
                              </apply>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>tau_h</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">1</cn>
               <apply>
                  <plus/>
                  <ci>alpha_h</ci>
                  <ci>beta_h</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>h</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>h_inf</ci>
                  <ci>h</ci>
               </apply>
               <ci>tau_h</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="fast_sodium_current_j_gate">
      <variable units="dimensionless" public_interface="out" name="j" initial_value="0.75"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="dimensionless" name="j_inf"/>
      <variable units="per_millisecond" name="alpha_j"/>
      <variable units="per_millisecond" name="beta_j"/>
      <variable units="millisecond" name="tau_j"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>j_inf</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">1</cn>
               <apply>
                  <power/>
                  <apply>
                     <plus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <plus/>
                              <ci>V</ci>
                              <cn cellml:units="millivolt">71.55</cn>
                           </apply>
                           <cn cellml:units="millivolt">7.43</cn>
                        </apply>
                     </apply>
                  </apply>
                  <cn cellml:units="dimensionless">2</cn>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>alpha_j</ci>
            <piecewise>
               <piece>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <apply>
                           <minus/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <cn cellml:units="per_millisecond">25428</cn>
                              </apply>
                              <apply>
                                 <exp/>
                                 <apply>
                                    <times/>
                                    <cn cellml:units="dimensionless">0.2444</cn>
                                    <ci>V</ci>
                                 </apply>
                              </apply>
                           </apply>
                           <apply>
                              <times/>
                              <cn cellml:units="per_millisecond">6.948e-6</cn>
                              <apply>
                                 <exp/>
                                 <apply>
                                    <times/>
                                    <apply>
                                       <minus/>
                                       <cn cellml:units="dimensionless">0.04391</cn>
                                    </apply>
                                    <ci>V</ci>
                                 </apply>
                              </apply>
                           </apply>
                        </apply>
                        <apply>
                           <plus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">37.78</cn>
                        </apply>
                     </apply>
                     <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <times/>
                              <cn cellml:units="dimensionless">0.311</cn>
                              <apply>
                                 <plus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">79.23</cn>
                              </apply>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <lt/>
                     <ci>V</ci>
                     <apply>
                        <minus/>
                        <cn cellml:units="millivolt">40</cn>
                     </apply>
                  </apply>
               </piece>
               <otherwise>
                  <cn cellml:units="per_millisecond">0</cn>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>beta_j</ci>
            <piecewise>
               <piece>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <cn cellml:units="per_millisecond">0.02424</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <cn cellml:units="dimensionless">0.01052</cn>
                              </apply>
                              <ci>V</ci>
                           </apply>
                        </apply>
                     </apply>
                     <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <cn cellml:units="dimensionless">0.1378</cn>
                              </apply>
                              <apply>
                                 <plus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">40.14</cn>
                              </apply>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <lt/>
                     <ci>V</ci>
                     <apply>
                        <minus/>
                        <cn cellml:units="millivolt">40</cn>
                     </apply>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <cn cellml:units="per_millisecond">0.6</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <times/>
                              <cn cellml:units="dimensionless">0.057</cn>
                              <ci>V</ci>
                           </apply>
                        </apply>
                     </apply>
                     <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <cn cellml:units="dimensionless">0.1</cn>
                              </apply>
                              <apply>
                                 <plus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">32</cn>
                              </apply>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>tau_j</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">1</cn>
               <apply>
                  <plus/>
                  <ci>alpha_j</ci>
                  <ci>beta_j</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>j</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>j_inf</ci>
                  <ci>j</ci>
               </apply>
               <ci>tau_j</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="sodium_background_current">
      <variable units="picoA_per_picoF" public_interface="out" name="i_b_Na"/>
      <variable units="nanoS_per_picoF" name="g_bna" initial_value="0.00029"/>
      <variable units="millivolt" public_interface="in" name="E_Na"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_b_Na</ci>
            <apply>
               <times/>
               <ci>g_bna</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_Na</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="L_type_Ca_current">
      <variable units="picoA_per_picoF" public_interface="out" name="i_CaL" cmeta:id="L_type_Ca_current_i_CaL"/>
      <variable units="nanoS_per_picoF" name="g_CaL" initial_value="0.000175"/>
      <variable units="millimolar" public_interface="in" name="Ca_o"/>
      <variable units="millimolar" public_interface="in" private_interface="out" name="Ca_i"/>
      <variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
      <variable units="coulomb_per_millimole" public_interface="in" name="F"/>
      <variable units="kelvin" public_interface="in" name="T"/>
      <variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
      <variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
      <variable units="dimensionless" public_interface="out" private_interface="in" name="d"/>
      <variable units="dimensionless" private_interface="in" name="f"/>
      <variable units="dimensionless" private_interface="in" name="fCa"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_CaL</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <ci>g_CaL</ci>
                        <ci>d</ci>
                        <ci>f</ci>
                        <ci>fCa</ci>
                        <cn cellml:units="dimensionless">4</cn>
                        <ci>V</ci>
                        <apply>
                           <power/>
                           <ci>F</ci>
                           <cn cellml:units="dimensionless">2</cn>
                        </apply>
                     </apply>
                     <apply>
                        <times/>
                        <ci>R</ci>
                        <ci>T</ci>
                     </apply>
                  </apply>
                  <apply>
                     <minus/>
                     <apply>
                        <times/>
                        <ci>Ca_i</ci>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <cn cellml:units="dimensionless">2</cn>
                                 <ci>V</ci>
                                 <ci>F</ci>
                              </apply>
                              <apply>
                                 <times/>
                                 <ci>R</ci>
                                 <ci>T</ci>
                              </apply>
                           </apply>
                        </apply>
                     </apply>
                     <apply>
                        <times/>
                        <cn cellml:units="dimensionless">0.341</cn>
                        <ci>Ca_o</ci>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <minus/>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <times/>
                           <cn cellml:units="dimensionless">2</cn>
                           <ci>V</ci>
                           <ci>F</ci>
                        </apply>
                        <apply>
                           <times/>
                           <ci>R</ci>
                           <ci>T</ci>
                        </apply>
                     </apply>
                  </apply>
                  <cn cellml:units="dimensionless">1</cn>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="L_type_Ca_current_d_gate">
      <variable units="dimensionless" public_interface="out" name="d" initial_value="0"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="dimensionless" name="d_inf"/>
      <variable units="per_millisecond" name="alpha_d"/>
      <variable units="per_millisecond" name="beta_d"/>
      <variable units="per_millisecond" name="gamma_d"/>
      <variable units="millisecond" name="tau_d"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>d_inf</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">1</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <apply>
                              <minus/>
                              <cn cellml:units="millivolt">5</cn>
                           </apply>
                           <ci>V</ci>
                        </apply>
                        <cn cellml:units="millivolt">7.5</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>alpha_d</ci>
            <apply>
               <plus/>
               <apply>
                  <divide/>
                  <cn cellml:units="per_millisecond">1.4</cn>
                  <apply>
                     <plus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <minus/>
                              <apply>
                                 <minus/>
                                 <cn cellml:units="millivolt">35</cn>
                              </apply>
                              <ci>V</ci>
                           </apply>
                           <cn cellml:units="millivolt">13</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <cn cellml:units="per_millisecond">0.25</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_d</ci>
            <apply>
               <divide/>
               <cn cellml:units="per_millisecond">1.4</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <plus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">5</cn>
                        </apply>
                        <cn cellml:units="millivolt">5</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>gamma_d</ci>
            <apply>
               <divide/>
               <cn cellml:units="per_millisecond">1</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <cn cellml:units="millivolt">50</cn>
                           <ci>V</ci>
                        </apply>
                        <cn cellml:units="millivolt">20</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_d</ci>
            <apply>
               <plus/>
               <apply>
                  <times/>
                  <ci>alpha_d</ci>
                  <ci>beta_d</ci>
               </apply>
               <ci>gamma_d</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>d</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>d_inf</ci>
                  <ci>d</ci>
               </apply>
               <ci>tau_d</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="L_type_Ca_current_f_gate">
      <variable units="dimensionless" public_interface="out" name="f" initial_value="1"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="dimensionless" name="f_inf"/>
      <variable units="millisecond" name="tau_f"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>f_inf</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">1</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <plus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">20</cn>
                        </apply>
                        <cn cellml:units="millivolt">7</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_f</ci>
            <apply>
               <plus/>
               <apply>
                  <times/>
                  <cn cellml:units="millisecond">1125</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <apply>
                              <power/>
                              <apply>
                                 <plus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">27</cn>
                              </apply>
                              <cn cellml:units="dimensionless">2</cn>
                           </apply>
                        </apply>
                        <cn cellml:units="millivolt">240</cn>
                     </apply>
                  </apply>
               </apply>
               <cn cellml:units="millisecond">80</cn>
               <apply>
                  <divide/>
                  <cn cellml:units="millisecond">165</cn>
                  <apply>
                     <plus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <minus/>
                              <cn cellml:units="millivolt">25</cn>
                              <ci>V</ci>
                           </apply>
                           <cn cellml:units="millivolt">10</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>f</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>f_inf</ci>
                  <ci>f</ci>
               </apply>
               <ci>tau_f</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="L_type_Ca_current_fCa_gate">
      <variable units="dimensionless" public_interface="out" name="fCa" initial_value="1"/>
      <variable units="millimolar" public_interface="in" name="Ca_i"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="dimensionless" name="alpha_fCa"/>
      <variable units="dimensionless" name="beta_fCa"/>
      <variable units="dimensionless" name="gama_fCa"/>
      <variable units="dimensionless" name="fCa_inf"/>
      <variable units="millisecond" name="tau_fCa"/>
      <variable units="dimensionless" name="d_fCa"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>alpha_fCa</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">1</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <power/>
                     <apply>
                        <divide/>
                        <ci>Ca_i</ci>
                        <cn cellml:units="millimolar">0.000325</cn>
                     </apply>
                     <cn cellml:units="dimensionless">8</cn>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_fCa</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">0.1</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <ci>Ca_i</ci>
                           <cn cellml:units="millimolar">0.0005</cn>
                        </apply>
                        <cn cellml:units="millimolar">0.0001</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>gama_fCa</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">0.2</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <ci>Ca_i</ci>
                           <cn cellml:units="millimolar">0.00075</cn>
                        </apply>
                        <cn cellml:units="millimolar">0.0008</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>fCa_inf</ci>
            <apply>
               <divide/>
               <apply>
                  <plus/>
                  <ci>alpha_fCa</ci>
                  <ci>beta_fCa</ci>
                  <ci>gama_fCa</ci>
                  <cn cellml:units="dimensionless">0.23</cn>
               </apply>
               <cn cellml:units="dimensionless">1.46</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_fCa</ci>
            <cn cellml:units="millisecond">2</cn>
         </apply>
         <apply>
            <eq/>
            <ci>d_fCa</ci>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>fCa_inf</ci>
                  <ci>fCa</ci>
               </apply>
               <ci>tau_fCa</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>fCa</ci>
            </apply>
            <piecewise>
               <piece>
                  <cn cellml:units="dimensionless">0</cn>
                  <apply>
                     <and/>
                     <apply>
                        <gt/>
                        <apply>
                           <times/>
                           <cn cellml:units="millisecond">0.01</cn>
                           <ci>d_fCa</ci>
                        </apply>
                        <cn cellml:units="dimensionless">0</cn>
                     </apply>
                     <apply>
                        <gt/>
                        <ci>V</ci>
                        <apply>
                           <minus/>
                           <cn cellml:units="millivolt">60</cn>
                        </apply>
                     </apply>
                  </apply>
               </piece>
               <otherwise>
                  <ci>d_fCa</ci>
               </otherwise>
            </piecewise>
         </apply>
      </math>
   </component>
   <component name="calcium_background_current">
      <variable units="picoA_per_picoF" public_interface="out" name="i_b_Ca"/>
      <variable units="nanoS_per_picoF" name="g_bca" initial_value="0.000592"/>
      <variable units="millivolt" public_interface="in" name="E_Ca"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_b_Ca</ci>
            <apply>
               <times/>
               <ci>g_bca</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_Ca</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="transient_outward_current">
      <variable units="picoA_per_picoF" public_interface="out" name="i_to"/>
      <variable units="nanoS_per_picoF" name="g_to" initial_value="0.294"/>
      <variable units="millivolt" public_interface="in" name="E_K"/>
      <variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
      <variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
      <variable units="dimensionless" private_interface="in" name="s"/>
      <variable units="dimensionless" private_interface="in" name="r"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_to</ci>
            <apply>
               <times/>
               <ci>g_to</ci>
               <ci>r</ci>
               <ci>s</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_K</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="transient_outward_current_s_gate">
      <variable units="dimensionless" public_interface="out" name="s" initial_value="1"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="dimensionless" name="s_inf"/>
      <variable units="dimensionless" name="tau_s"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>s_inf</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">1</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <plus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">20</cn>
                        </apply>
                        <cn cellml:units="millivolt">5</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_s</ci>
            <apply>
               <plus/>
               <apply>
                  <times/>
                  <cn cellml:units="millisecond">85</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <apply>
                              <power/>
                              <apply>
                                 <plus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">45</cn>
                              </apply>
                              <cn cellml:units="dimensionless">2</cn>
                           </apply>
                        </apply>
                        <cn cellml:units="millivolt">320</cn>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <divide/>
                  <cn cellml:units="millisecond">5</cn>
                  <apply>
                     <plus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <minus/>
                              <ci>V</ci>
                              <cn cellml:units="millivolt">20</cn>
                           </apply>
                           <cn cellml:units="millivolt">5</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <cn cellml:units="millisecond">3</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>s</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>s_inf</ci>
                  <ci>s</ci>
               </apply>
               <ci>tau_s</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="transient_outward_current_r_gate">
      <variable units="dimensionless" public_interface="out" name="r" initial_value="0"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="dimensionless" name="r_inf"/>
      <variable units="millisecond" name="tau_r"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>r_inf</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">1</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <cn cellml:units="millivolt">20</cn>
                           <ci>V</ci>
                        </apply>
                        <cn cellml:units="millivolt">6</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_r</ci>
            <apply>
               <plus/>
               <apply>
                  <times/>
                  <cn cellml:units="millisecond">9.5</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <apply>
                              <power/>
                              <apply>
                                 <plus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">40</cn>
                              </apply>
                              <cn cellml:units="dimensionless">2</cn>
                           </apply>
                        </apply>
                        <cn cellml:units="millivolt">1800</cn>
                     </apply>
                  </apply>
               </apply>
               <cn cellml:units="millisecond">0.8</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>r</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>r_inf</ci>
                  <ci>r</ci>
               </apply>
               <ci>tau_r</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="sodium_potassium_pump_current">
      <variable units="picoA_per_picoF" public_interface="out" name="i_NaK"/>
      <variable units="picoA_per_picoF" name="P_NaK" initial_value="1.362"/>
      <variable units="millimolar" name="K_mk" initial_value="1"/>
      <variable units="millimolar" name="K_mNa" initial_value="40"/>
      <variable units="millimolar" public_interface="in" name="K_o"/>
      <variable units="millimolar" public_interface="in" name="Na_i"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
      <variable units="coulomb_per_millimole" public_interface="in" name="F"/>
      <variable units="kelvin" public_interface="in" name="T"/>
      <variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_NaK</ci>
            <apply>
               <divide/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <apply>
                        <divide/>
                        <apply>
                           <times/>
                           <ci>P_NaK</ci>
                           <ci>K_o</ci>
                        </apply>
                        <apply>
                           <plus/>
                           <ci>K_o</ci>
                           <ci>K_mk</ci>
                        </apply>
                     </apply>
                     <ci>Na_i</ci>
                  </apply>
                  <apply>
                     <plus/>
                     <ci>Na_i</ci>
                     <ci>K_mNa</ci>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">0.1245</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <cn cellml:units="dimensionless">0.1</cn>
                              </apply>
                              <ci>V</ci>
                              <ci>F</ci>
                           </apply>
                           <apply>
                              <times/>
                              <ci>R</ci>
                              <ci>T</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">0.0353</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <ci>V</ci>
                              </apply>
                              <ci>F</ci>
                           </apply>
                           <apply>
                              <times/>
                              <ci>R</ci>
                              <ci>T</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="sodium_calcium_exchanger_current">
      <variable units="picoA_per_picoF" public_interface="out" name="i_NaCa"/>
      <variable units="picoA_per_picoF" name="K_NaCa" initial_value="1000"/>
      <variable units="dimensionless" name="K_sat" initial_value="0.1"/>
      <variable units="dimensionless" name="alpha" initial_value="2.5"/>
      <variable units="dimensionless" name="gamma" initial_value="0.35"/>
      <variable units="millimolar" name="Km_Ca" initial_value="1.38"/>
      <variable units="millimolar" name="Km_Nai" initial_value="87.5"/>
      <variable units="millimolar" public_interface="in" name="Na_i"/>
      <variable units="millimolar" public_interface="in" name="Na_o"/>
      <variable units="millimolar" public_interface="in" name="Ca_i"/>
      <variable units="millimolar" public_interface="in" name="Ca_o"/>
      <variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
      <variable units="coulomb_per_millimole" public_interface="in" name="F"/>
      <variable units="kelvin" public_interface="in" name="T"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_NaCa</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>K_NaCa</ci>
                  <apply>
                     <minus/>
                     <apply>
                        <times/>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <ci>gamma</ci>
                                 <ci>V</ci>
                                 <ci>F</ci>
                              </apply>
                              <apply>
                                 <times/>
                                 <ci>R</ci>
                                 <ci>T</ci>
                              </apply>
                           </apply>
                        </apply>
                        <apply>
                           <power/>
                           <ci>Na_i</ci>
                           <cn cellml:units="dimensionless">3</cn>
                        </apply>
                        <ci>Ca_o</ci>
                     </apply>
                     <apply>
                        <times/>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <apply>
                                    <minus/>
                                    <ci>gamma</ci>
                                    <cn cellml:units="dimensionless">1</cn>
                                 </apply>
                                 <ci>V</ci>
                                 <ci>F</ci>
                              </apply>
                              <apply>
                                 <times/>
                                 <ci>R</ci>
                                 <ci>T</ci>
                              </apply>
                           </apply>
                        </apply>
                        <apply>
                           <power/>
                           <ci>Na_o</ci>
                           <cn cellml:units="dimensionless">3</cn>
                        </apply>
                        <ci>Ca_i</ci>
                        <ci>alpha</ci>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <apply>
                     <plus/>
                     <apply>
                        <power/>
                        <ci>Km_Nai</ci>
                        <cn cellml:units="dimensionless">3</cn>
                     </apply>
                     <apply>
                        <power/>
                        <ci>Na_o</ci>
                        <cn cellml:units="dimensionless">3</cn>
                     </apply>
                  </apply>
                  <apply>
                     <plus/>
                     <ci>Km_Ca</ci>
                     <ci>Ca_o</ci>
                  </apply>
                  <apply>
                     <plus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <apply>
                        <times/>
                        <ci>K_sat</ci>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <apply>
                                    <minus/>
                                    <ci>gamma</ci>
                                    <cn cellml:units="dimensionless">1</cn>
                                 </apply>
                                 <ci>V</ci>
                                 <ci>F</ci>
                              </apply>
                              <apply>
                                 <times/>
                                 <ci>R</ci>
                                 <ci>T</ci>
                              </apply>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="calcium_pump_current">
      <variable units="picoA_per_picoF" public_interface="out" name="i_p_Ca" cmeta:id="calcium_pump_current_i_p_Ca"/>
      <variable units="nanoS_per_picoF" name="g_pCa" initial_value="0.825"/>
      <variable units="millimolar" name="K_pCa" initial_value="0.0005"/>
      <variable units="millimolar" public_interface="in" name="Ca_i"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_p_Ca</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>g_pCa</ci>
                  <ci>Ca_i</ci>
               </apply>
               <apply>
                  <plus/>
                  <ci>Ca_i</ci>
                  <ci>K_pCa</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="potassium_pump_current">
      <variable units="picoA_per_picoF" public_interface="out" name="i_p_K"/>
      <variable units="nanoS_per_picoF" name="g_pK" initial_value="0.0146"/>
      <variable units="millivolt" public_interface="in" name="E_K"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_p_K</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>g_pK</ci>
                  <apply>
                     <minus/>
                     <ci>V</ci>
                     <ci>E_K</ci>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <cn cellml:units="millivolt">25</cn>
                           <ci>V</ci>
                        </apply>
                        <cn cellml:units="millivolt">5.98</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="calcium_dynamics">
      <variable units="millimolar" public_interface="out" name="Ca_i" initial_value="0.0002"/>
      <variable units="millimolar" public_interface="out" name="Ca_o" initial_value="2"/>
      <variable units="millimolar" name="Ca_SR" initial_value="0.2"/>
      <variable units="millimolar_per_millisecond" name="i_rel"/>
      <variable units="millimolar_per_millisecond" name="i_up"/>
      <variable units="millimolar_per_millisecond" name="i_leak"/>
      <variable units="dimensionless" name="g" initial_value="1"/>
      <variable units="millisecond" name="tau_g" initial_value="2"/>
      <variable units="dimensionless" name="g_inf"/>
      <variable units="millimolar_per_millisecond" name="a_rel" initial_value="0.016464"/>
      <variable units="millimolar" name="b_rel" initial_value="0.25"/>
      <variable units="millimolar_per_millisecond" name="c_rel" initial_value="0.008232"/>
      <variable units="millimolar" name="K_up" initial_value="0.00025"/>
      <variable units="per_millisecond" name="V_leak" initial_value="8e-5"/>
      <variable units="millimolar_per_millisecond" name="Vmax_up" initial_value="0.000425"/>
      <variable units="millimolar" name="Ca_i_bufc"/>
      <variable units="millimolar" name="Ca_sr_bufsr"/>
      <variable units="millimolar" name="Buf_c" initial_value="0.15"/>
      <variable units="millimolar" name="K_buf_c" initial_value="0.001"/>
      <variable units="millimolar" name="Buf_sr" initial_value="10"/>
      <variable units="millimolar" name="K_buf_sr" initial_value="0.3"/>
      <variable units="micrometre3" name="V_sr" initial_value="0.001094"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="micrometre3" public_interface="in" name="V_c"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="dimensionless" public_interface="in" name="d"/>
      <variable units="coulomb_per_millimole" public_interface="in" name="F"/>
      <variable units="microF_per_cm2" public_interface="in" name="Cm"/>
      <variable units="picoA_per_picoF" public_interface="in" name="i_CaL"/>
      <variable units="picoA_per_picoF" public_interface="in" name="i_NaCa"/>
      <variable units="picoA_per_picoF" public_interface="in" name="i_p_Ca"/>
      <variable units="picoA_per_picoF" public_interface="in" name="i_b_Ca"/>
      <variable units="dimensionless" name="d_g"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_rel</ci>
            <apply>
               <times/>
               <apply>
                  <plus/>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <ci>a_rel</ci>
                        <apply>
                           <power/>
                           <ci>Ca_SR</ci>
                           <cn cellml:units="dimensionless">2</cn>
                        </apply>
                     </apply>
                     <apply>
                        <plus/>
                        <apply>
                           <power/>
                           <ci>b_rel</ci>
                           <cn cellml:units="dimensionless">2</cn>
                        </apply>
                        <apply>
                           <power/>
                           <ci>Ca_SR</ci>
                           <cn cellml:units="dimensionless">2</cn>
                        </apply>
                     </apply>
                  </apply>
                  <ci>c_rel</ci>
               </apply>
               <ci>d</ci>
               <ci>g</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_up</ci>
            <apply>
               <divide/>
               <ci>Vmax_up</ci>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <divide/>
                     <apply>
                        <power/>
                        <ci>K_up</ci>
                        <cn cellml:units="dimensionless">2</cn>
                     </apply>
                     <apply>
                        <power/>
                        <ci>Ca_i</ci>
                        <cn cellml:units="dimensionless">2</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_leak</ci>
            <apply>
               <times/>
               <ci>V_leak</ci>
               <apply>
                  <minus/>
                  <ci>Ca_SR</ci>
                  <ci>Ca_i</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>g_inf</ci>
            <piecewise>
               <piece>
                  <apply>
                     <divide/>
                     <cn cellml:units="dimensionless">1</cn>
                     <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <power/>
                           <apply>
                              <divide/>
                              <ci>Ca_i</ci>
                              <cn cellml:units="millimolar">0.00035</cn>
                           </apply>
                           <cn cellml:units="dimensionless">6</cn>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <lt/>
                     <ci>Ca_i</ci>
                     <cn cellml:units="millimolar">0.00035</cn>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <divide/>
                     <cn cellml:units="dimensionless">1</cn>
                     <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <power/>
                           <apply>
                              <divide/>
                              <ci>Ca_i</ci>
                              <cn cellml:units="millimolar">0.00035</cn>
                           </apply>
                           <cn cellml:units="dimensionless">16</cn>
                        </apply>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>d_g</ci>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>g_inf</ci>
                  <ci>g</ci>
               </apply>
               <ci>tau_g</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>g</ci>
            </apply>
            <piecewise>
               <piece>
                  <cn cellml:units="dimensionless">0</cn>
                  <apply>
                     <and/>
                     <apply>
                        <gt/>
                        <apply>
                           <times/>
                           <cn cellml:units="millisecond">0.01</cn>
                           <ci>d_g</ci>
                        </apply>
                        <cn cellml:units="dimensionless">0</cn>
                     </apply>
                     <apply>
                        <gt/>
                        <ci>V</ci>
                        <apply>
                           <minus/>
                           <cn cellml:units="millivolt">60</cn>
                        </apply>
                     </apply>
                  </apply>
               </piece>
               <otherwise>
                  <ci>d_g</ci>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>Ca_i_bufc</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">1</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <ci>Buf_c</ci>
                        <ci>K_buf_c</ci>
                     </apply>
                     <apply>
                        <power/>
                        <apply>
                           <plus/>
                           <ci>Ca_i</ci>
                           <ci>K_buf_c</ci>
                        </apply>
                        <cn cellml:units="dimensionless">2</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>Ca_sr_bufsr</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">1</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <ci>Buf_sr</ci>
                        <ci>K_buf_sr</ci>
                     </apply>
                     <apply>
                        <power/>
                        <apply>
                           <plus/>
                           <ci>Ca_SR</ci>
                           <ci>K_buf_sr</ci>
                        </apply>
                        <cn cellml:units="dimensionless">2</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ca_i</ci>
            </apply>
            <apply>
               <times/>
               <ci>Ca_i_bufc</ci>
               <apply>
                  <minus/>
                  <apply>
                     <plus/>
                     <apply>
                        <minus/>
                        <ci>i_leak</ci>
                        <ci>i_up</ci>
                     </apply>
                     <ci>i_rel</ci>
                  </apply>
                  <apply>
                     <times/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <apply>
                              <plus/>
                              <ci>i_CaL</ci>
                              <ci>i_b_Ca</ci>
                              <ci>i_p_Ca</ci>
                           </apply>
                           <apply>
                              <times/>
                              <cn cellml:units="dimensionless">2</cn>
                              <ci>i_NaCa</ci>
                           </apply>
                        </apply>
                        <apply>
                           <times/>
                           <cn cellml:units="dimensionless">2</cn>
                           <ci>V_c</ci>
                           <ci>F</ci>
                        </apply>
                     </apply>
                     <ci>Cm</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ca_SR</ci>
            </apply>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <ci>Ca_sr_bufsr</ci>
                     <ci>V_c</ci>
                  </apply>
                  <ci>V_sr</ci>
               </apply>
               <apply>
                  <minus/>
                  <ci>i_up</ci>
                  <apply>
                     <plus/>
                     <ci>i_rel</ci>
                     <ci>i_leak</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="sodium_dynamics">
      <variable units="millimolar" public_interface="out" name="Na_i" initial_value="11.6"/>
      <variable units="millimolar" public_interface="out" name="Na_o" initial_value="140"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="coulomb_per_millimole" public_interface="in" name="F"/>
      <variable units="microF_per_cm2" public_interface="in" name="Cm"/>
      <variable units="micrometre3" public_interface="in" name="V_c"/>
      <variable units="picoA_per_picoF" public_interface="in" name="i_Na"/>
      <variable units="picoA_per_picoF" public_interface="in" name="i_NaCa"/>
      <variable units="picoA_per_picoF" public_interface="in" name="i_NaK"/>
      <variable units="picoA_per_picoF" public_interface="in" name="i_b_Na"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Na_i</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <apply>
                     <minus/>
                     <apply>
                        <plus/>
                        <ci>i_Na</ci>
                        <ci>i_b_Na</ci>
                        <apply>
                           <times/>
                           <cn cellml:units="dimensionless">3</cn>
                           <ci>i_NaK</ci>
                        </apply>
                        <apply>
                           <times/>
                           <cn cellml:units="dimensionless">3</cn>
                           <ci>i_NaCa</ci>
                        </apply>
                     </apply>
                  </apply>
                  <ci>Cm</ci>
               </apply>
               <apply>
                  <times/>
                  <ci>V_c</ci>
                  <ci>F</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="potassium_dynamics">
      <variable units="millimolar" public_interface="out" name="K_i" initial_value="138.3"/>
      <variable units="millimolar" public_interface="out" name="K_o" initial_value="5.4"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="coulomb_per_millimole" public_interface="in" name="F"/>
      <variable units="microF_per_cm2" public_interface="in" name="Cm"/>
      <variable units="micrometre3" public_interface="in" name="V_c"/>
      <variable units="picoA_per_picoF" public_interface="in" name="i_K1"/>
      <variable units="picoA_per_picoF" public_interface="in" name="i_to"/>
      <variable units="picoA_per_picoF" public_interface="in" name="i_NaK"/>
      <variable units="picoA_per_picoF" public_interface="in" name="i_Kr"/>
      <variable units="picoA_per_picoF" public_interface="in" name="i_Ks"/>
      <variable units="picoA_per_picoF" public_interface="in" name="i_p_K"/>
      <variable units="picoA_per_picoF" public_interface="in" name="i_Stim"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>K_i</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <apply>
                     <minus/>
                     <apply>
                        <minus/>
                        <apply>
                           <plus/>
                           <ci>i_K1</ci>
                           <ci>i_to</ci>
                           <ci>i_Kr</ci>
                           <ci>i_Ks</ci>
                           <ci>i_p_K</ci>
                           <ci>i_Stim</ci>
                        </apply>
                        <apply>
                           <times/>
                           <cn cellml:units="dimensionless">2</cn>
                           <ci>i_NaK</ci>
                        </apply>
                     </apply>
                  </apply>
                  <ci>Cm</ci>
               </apply>
               <apply>
                  <times/>
                  <ci>V_c</ci>
                  <ci>F</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>

<component name="stimulus_protocol">
    <variable units="picoA_per_picoF" public_interface="out" name="Istim" cmeta:id="stimulus_protocol_Istim"/>
    <variable units="millisecond" cmeta:id="stimulus_protocol_IstimStart" name="IstimStart" initial_value="100"/>
    <variable units="millisecond" cmeta:id="stimulus_protocol_IstimEnd" name="IstimEnd" initial_value="50000"/>
    <variable units="picoA_per_picoF" cmeta:id="stimulus_protocol_IstimAmplitude" name="IstimAmplitude" initial_value="-52"/>
    <variable units="millisecond" cmeta:id="stimulus_protocol_IstimPeriod" name="IstimPeriod" initial_value="1000"/>
    <variable units="millisecond" cmeta:id="stimulus_protocol_IstimPulseDuration" name="IstimPulseDuration" initial_value="1"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML" id="Stimulus_Current_Equation">
      <apply>
        <eq/>
        <ci>Istim</ci>
        <piecewise>
          <piece>
            <ci>IstimAmplitude</ci>
            <apply>
              <and/>
              <apply>
                <geq/>
                <ci>time</ci>
                <ci>IstimStart</ci>
              </apply>
              <apply>
                <leq/>
                <ci>time</ci>
                <ci>IstimEnd</ci>
              </apply>
              <apply>
                <leq/>
                <apply>
                  <minus/>
                  <apply>
                    <minus/>
                    <ci>time</ci>
                    <ci>IstimStart</ci>
                  </apply>
                  <apply>
                    <times/>
                    <apply>
                      <floor/>
                      <apply>
                        <divide/>
                        <apply>
                          <minus/>
                          <ci>time</ci>
                          <ci>IstimStart</ci>
                        </apply>
                        <ci>IstimPeriod</ci>
                      </apply>
                    </apply>
                    <ci>IstimPeriod</ci>
                  </apply>
                </apply>
                <ci>IstimPulseDuration</ci>
              </apply>
            </apply>
          </piece>
          <otherwise>
            <cn cellml:units="picoA_per_picoF">0</cn>
          </otherwise>
        </piecewise>
      </apply>
    </math>
    <variable units="millisecond" public_interface="in" name="time"/>
  </component>

   <group>
      <relationship_ref relationship="containment"/>
      <component_ref component="membrane">
         <component_ref component="fast_sodium_current">
            <component_ref component="fast_sodium_current_m_gate"/>
            <component_ref component="fast_sodium_current_h_gate"/>
            <component_ref component="fast_sodium_current_j_gate"/>
         </component_ref>
         <component_ref component="L_type_Ca_current">
            <component_ref component="L_type_Ca_current_d_gate"/>
            <component_ref component="L_type_Ca_current_f_gate"/>
            <component_ref component="L_type_Ca_current_fCa_gate"/>
         </component_ref>
         <component_ref component="rapid_time_dependent_potassium_current">
            <component_ref component="rapid_time_dependent_potassium_current_Xr1_gate"/>
            <component_ref component="rapid_time_dependent_potassium_current_Xr2_gate"/>
         </component_ref>
         <component_ref component="slow_time_dependent_potassium_current">
            <component_ref component="slow_time_dependent_potassium_current_Xs_gate"/>
         </component_ref>
         <component_ref component="sodium_background_current"/>
         <component_ref component="calcium_background_current"/>
         <component_ref component="transient_outward_current">
            <component_ref component="transient_outward_current_s_gate"/>
            <component_ref component="transient_outward_current_r_gate"/>
         </component_ref>
         <component_ref component="sodium_potassium_pump_current"/>
         <component_ref component="sodium_calcium_exchanger_current"/>
         <component_ref component="calcium_pump_current"/>
         <component_ref component="potassium_pump_current"/>
         <component_ref component="calcium_dynamics"/>
         <component_ref component="sodium_dynamics"/>
         <component_ref component="potassium_dynamics"/>
         <component_ref component="reversal_potentials"/>
      </component_ref>
   </group>
   <group>
      <relationship_ref relationship="encapsulation"/>
      <component_ref component="fast_sodium_current">
         <component_ref component="fast_sodium_current_m_gate"/>
         <component_ref component="fast_sodium_current_h_gate"/>
         <component_ref component="fast_sodium_current_j_gate"/>
      </component_ref>
      <component_ref component="L_type_Ca_current">
         <component_ref component="L_type_Ca_current_d_gate"/>
         <component_ref component="L_type_Ca_current_f_gate"/>
         <component_ref component="L_type_Ca_current_fCa_gate"/>
      </component_ref>
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    <vCard:Given>P</vCard:Given>
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    <vCard:Other>J</vCard:Other>
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    <rdf:value>This variant describes the human cardiac M-cell, as described in ten Tusscher et al. 2004 &#13;
&#13;
This is a merge of Version 3 Variant 3 into the trunk so that the main repository listing auto-points to the latest version of the model.</rdf:value>
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    <rdf:value>A stimulus protocol component was added to the model to allow simulation of trains of action potentials. Values for the amplitude (-52 picoA per picoF) and duration (1 ms) of the stimulus were taken from the original single stimulus in the model. The period of 1000 ms is intended to reflect beat period of the human heart, on which this model is based.</rdf:value>
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  <rdf:Description rdf:about="rdf:#0c416269-ddf5-48c9-ab48-916a404ff438">
    <vCard:Given>Tommy</vCard:Given>
    <vCard:Family>Yu</vCard:Family>
    <vCard:Other/>
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  <rdf:Description rdf:about="rdf:#157954b8-18d9-4028-abb6-3050db782c35">
    <vCard:Given>Penny</vCard:Given>
    <vCard:Family>Noble</vCard:Family>
    <vCard:Other>unknown</vCard:Other>
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    <vCard:Orgname>Oxford University</vCard:Orgname>
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    <vCard:Given>A</vCard:Given>
    <vCard:Family>Panfilov</vCard:Family>
    <vCard:Other>V</vCard:Other>
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    <ns7:endingValue>10000</ns7:endingValue>
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  <rdf:Description rdf:about="rdf:#9f0bbf92-7466-42c5-9dc0-2f1470ff6d79">
    <vCard:Given>James</vCard:Given>
    <vCard:Family>Lawson</vCard:Family>
    <vCard:Other>Richard</vCard:Other>
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  <rdf:Description rdf:about="rdf:#318f4370-36df-401f-a5d1-effdc167ae9f">
    <dc:creator rdf:resource="rdf:#a58d18e0-f4a7-4319-9498-6b9f2d5d4785"/>
    <rdf:value>This variant of the model was created by Penny Noble of Oxford University, and represents the parameters given for the M-cell variant in Ten Tusscher et al. 2004. A stimulus protocol component has been added to the model to allow simulation of trains of action potentials (JL, 18/06/07). This file is known to run in PCEnv and COR.</rdf:value>
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  <rdf:Description rdf:about="rdf:#f466f81f-77a6-495a-ad6f-5f56ddc3214d">
    <vCard:Given>James</vCard:Given>
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    <vCard:Other>Richard</vCard:Other>
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    <rdf:value>Version 03 Variant 01 duplicated as version 04 to allow repository main page listing to point straight to latest TT04 version. v3v1 session also duplicated.</rdf:value>
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  <rdf:Description rdf:about="rdf:#8b4426fc-e7b6-4b56-8ae1-6dbccb5d5e47">
    <vCard:N rdf:resource="rdf:#f466f81f-77a6-495a-ad6f-5f56ddc3214d"/>
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  <rdf:Description rdf:about="rdf:#d4afc7e3-b69b-48bc-b422-9a3979e48c6f">
    <dcterms:W3CDTF>2007-06-22T15:51:38+12:00</dcterms:W3CDTF>
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  <rdf:Description rdf:about="rdf:#362ce6ed-17a9-4884-b974-7acf77d8a707">
    <vCard:Orgname>Oxford University</vCard:Orgname>
    <vCard:Orgunit>Department of Physiology, Anatomy &amp; Genetics</vCard:Orgunit>
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  <rdf:Description rdf:about="rdf:#78952b84-f98a-4010-adfd-482b32ad5269">
    <vCard:Given>D</vCard:Given>
    <vCard:Family>Noble</vCard:Family>
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  <rdf:Description rdf:about="rdf:#39ca2adc-1a09-481c-870d-5124f6612865">
    <dcterms:modified rdf:resource="rdf:#bd2eef02-8b67-49c5-85af-e2a1787eafc3"/>
    <rdf:value>Penny's file was modified to allow it to run in PCEnv. This required rearrangement of some differential equations such that the differential was on the left hand side. This modification produces a mathematically equivalent model and the output of the pre-modified model has not been altered in any way.</rdf:value>
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  <rdf:Description rdf:about="rdf:#41d307c2-a4ae-4000-9179-d17c9604da8f">
    <dcterms:W3CDTF>2007-11-26T12:38:03+13:00</dcterms:W3CDTF>
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    <vCard:Given>K</vCard:Given>
    <vCard:Family>ten Tusscher</vCard:Family>
    <vCard:Other>H</vCard:Other>
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    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
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  <rdf:Description rdf:about="rdf:#$5qYgz1">
    <rdf:rest rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/>
    <rdf:first rdf:resource="rdf:#$6qYgz1"/>
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  <rdf:Description rdf:about="rdf:#$TTbci">
    <ns7:endingValue>10000</ns7:endingValue>
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    <ns7:maximumStepSize>0.01</ns7:maximumStepSize>
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  <rdf:Description rdf:about="rdf:#$ozQGz">
    <ns7:endingValue>10000</ns7:endingValue>
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    <ns7:maximumStepSize>0.1</ns7:maximumStepSize>
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  <rdf:Description rdf:about="rdf:#$nzQGz">
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  <rdf:Description rdf:about="rdf:#afe98b15-bc5d-4624-a72a-72be6ca1b507">
    <vCard:Given>James</vCard:Given>
    <vCard:Family>Lawson</vCard:Family>
    <vCard:Other>Richard</vCard:Other>
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  <rdf:Description rdf:about="rdf:#$oZnH.1">
    <ns7:endingValue>10000</ns7:endingValue>
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    <ns7:maximumStepSize>0.1</ns7:maximumStepSize>
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  <rdf:Description rdf:about="rdf:#$RTbci">
    <ns7:boundIntervals rdf:resource="rdf:#$STbci"/>
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  <rdf:Description rdf:about="http://www.cellml.org/people/jlaw060/Desktop/tt05.cellml#tentusscher_noble_noble_panfilov_2006_version02_variant01">
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    <ns7:simulation rdf:resource="rdf:#$+k1WL"/>
    <ns7:simulation rdf:resource="rdf:#$RTbci"/>
    <ns7:simulation rdf:resource="rdf:#$c02cI3"/>
    <ns7:simulation rdf:resource="rdf:#$mZnH.1"/>
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    <dc:title>unknown</dc:title>
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    <vCard:Given>Penny</vCard:Given>
    <vCard:Family>Noble</vCard:Family>
    <vCard:Other>J</vCard:Other>
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  <rdf:Description rdf:about="">
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  <rdf:Description rdf:about="rdf:#$0l1WL">
    <rdf:rest rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/>
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  <rdf:Description rdf:about="rdf:#e93617f8-1c81-4193-8c1e-fec90d70a8f1">
    <dcterms:W3CDTF>2007-10-18T15:39:05+13:00</dcterms:W3CDTF>
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  <rdf:Description rdf:about="rdf:#05914a59-6aaa-42fd-b252-94031d03ca33">
    <dc:title>American Journal of Physiology Heart and Circulatory Physiology</dc:title>
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    <dcterms:modified rdf:resource="rdf:#41d307c2-a4ae-4000-9179-d17c9604da8f"/>
    <rdf:value>Tommy hand-fixed the RDF to get the repository to save the simulation metadata.</rdf:value>
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    <dcterms:W3CDTF>2004-04-01</dcterms:W3CDTF>
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    <ns7:endingValue>10000</ns7:endingValue>
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  <rdf:Description rdf:about="rdf:#10dc27e0-3958-478a-98b3-ce62d8bda228">
    <dcterms:modified rdf:resource="rdf:#d4afc7e3-b69b-48bc-b422-9a3979e48c6f"/>
    <rdf:value>Some variables have been given cmeta:id's to allow a PCEnv session to be created.</rdf:value>
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  <rdf:Description rdf:about="rdf:#62e7f227-da71-4eb6-bc5d-fce425307859">
    <dcterms:W3CDTF>2006-01-01</dcterms:W3CDTF>
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    <vCard:N rdf:resource="rdf:#03ea6587-be02-4ce8-a4a7-d66a8e7ec496"/>
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