Location: Tentusscher, Noble, Noble, Panfilov, 2004 @ 941ec8e54e46 / tentusscher_noble_noble_panfilov_2004_c.cellml

Author:
Dougal Cowan <devnull@localhost>
Date:
2010-10-11 09:30:00+13:00
Desc:
removed the file system references from URLs
Permanent Source URI:
https://models.cellml.org/workspace/tentusscher_noble_noble_panfilov_2004/rawfile/941ec8e54e46e6fe82765c17f1d47582169baac2/tentusscher_noble_noble_panfilov_2004_c.cellml

<?xml version="1.0" encoding="utf-8"?>
<!--
This CellML file was generated on 05/11/2007 at 17:00:27 using:

COR (0.9.31.801)
Copyright 2002-2007 Dr Alan Garny
http://COR.physiol.ox.ac.uk/ - COR@physiol.ox.ac.uk

CellML 1.0 was used to generate this cellular model
http://www.CellML.org/
-->
<model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:ns7="http://www.cellml.org/metadata/simulation/1.0#" cmeta:id="tentusscher_2004_endo_cell" name="tentusscher_2004_endo_cell">

<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>A Model For Human Ventricular Tissue</title>
  <author>
    <firstname>Catherine</firstname>
          <surname>Lloyd</surname>
    <affiliation>
      <shortaffil>Auckland Bioengineering Institute, University of Auckland</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 endocardial 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. This file is known to run in OpenCell and COR to recreate the published results. The units have been checked and they are consistent. 
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
ABSTRACT: The experimental and clinical possibilities for studying cardiac arrhythmias in human ventricular myocardium are very limited. Therefore, the use of alternative methods such as computer simulations is of great importance. In this article we introduce a mathematical model of the action potential of human ventricular cells that, while including a high level of electrophysiological detail, is computationally cost-effective enough to be applied in large-scale spatial simulations for the study of reentrant arrhythmias. The model is based on recent experimental data on most of the major ionic currents: the fast sodium, L-type calcium, transient outward, rapid and slow delayed rectifier, and inward rectifier currents. The model includes a basic calcium dynamics, allowing for the realistic modeling of calcium transients, calcium current inactivation, and the contraction staircase. We are able to reproduce human epicardial, endocardial, and M cell action potentials and show that differences can be explained by differences in the transient outward and slow delayed rectifier currents. Our model reproduces the experimentally observed data on action potential duration restitution, which is an important characteristic for reentrant arrhythmias. The conduction velocity restitution of our model is broader than in other models and agrees better with available data. Finally, we model the dynamics of spiral wave rotation in a two-dimensional sheet of human ventricular tissue and show that the spiral wave follows a complex meandering pattern and has a period of 265 ms. We conclude that the proposed model reproduces a variety of electrophysiological behaviors and provides a basis for studies of reentrant arrhythmias in human ventricular tissue.
</para>

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

<para>
A model for human ventricular tissue, K.H.W.J. ten Tusscher, D. Noble, P.J. Noble, and A.V. Panfilov, 2004, 
            <emphasis>American Journal of Physiology</emphasis>
          , 286, H1573-H1589. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/14656705">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 of the Ten Tusscher <emphasis>et al.</emphasis> 2004 mathematical model of the human ventricular myocyte.</caption>
</informalfigure>

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


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      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <variable name="xr2_inf" units="dimensionless"/>
      <variable name="alpha_xr2" units="dimensionless"/>
      <variable name="beta_xr2" units="dimensionless"/>
      <variable name="tau_xr2" units="millisecond"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>xr2_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">88</cn>
                        </apply>
                        <cn cellml:units="millivolt">24</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>alpha_xr2</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">3</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">20</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_xr2</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">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/>
               <cn cellml:units="millisecond">1</cn>
               <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 name="i_Ks" units="picoA_per_picoF" public_interface="out"/>
      <variable name="g_Ks" units="nanoS_per_picoF" initial_value="0.245"/>
      <variable name="E_Ks" units="millivolt" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in" private_interface="out"/>
      <variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
      <variable name="Xs" units="dimensionless" private_interface="in"/>
      <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 name="Xs" units="dimensionless" initial_value="0" public_interface="out"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <variable name="xs_inf" units="dimensionless"/>
      <variable name="alpha_xs" units="dimensionless"/>
      <variable name="beta_xs" units="dimensionless"/>
      <variable name="tau_xs" units="millisecond"/>
      <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="dimensionless">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="dimensionless">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/>
               <cn cellml:units="millisecond">1</cn>
               <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 name="i_Na" units="picoA_per_picoF" public_interface="out"/>
      <variable name="g_Na" units="nanoS_per_picoF" initial_value="14.838"/>
      <variable name="E_Na" units="millivolt" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in" private_interface="out"/>
      <variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
      <variable name="m" units="dimensionless" private_interface="in"/>
      <variable name="h" units="dimensionless" private_interface="in"/>
      <variable name="j" units="dimensionless" private_interface="in"/>
      <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 name="m" units="dimensionless" initial_value="0" public_interface="out"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <variable name="m_inf" units="dimensionless"/>
      <variable name="alpha_m" units="dimensionless"/>
      <variable name="beta_m" units="dimensionless"/>
      <variable name="tau_m" units="millisecond"/>
      <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="dimensionless">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="dimensionless">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="dimensionless">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/>
               <cn cellml:units="millisecond">1</cn>
               <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 name="h" units="dimensionless" initial_value="0.75" public_interface="out"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <variable name="h_inf" units="dimensionless"/>
      <variable name="alpha_h" units="per_millisecond"/>
      <variable name="beta_h" units="per_millisecond"/>
      <variable name="tau_h" units="millisecond"/>
      <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="per_millivolt">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="per_millivolt">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 name="j" units="dimensionless" initial_value="0.75" public_interface="out"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <variable name="j_inf" units="dimensionless"/>
      <variable name="alpha_j" units="per_millisecond"/>
      <variable name="beta_j" units="per_millisecond"/>
      <variable name="tau_j" units="millisecond"/>
      <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>
                        <divide/>
                        <apply>
                           <times/>
                           <apply>
                              <minus/>
                              <apply>
                                 <times/>
                                 <apply>
                                    <minus/>
                                    <cn cellml:units="per_millisecond">25428</cn>
                                 </apply>
                                 <apply>
                                    <exp/>
                                    <apply>
                                       <times/>
                                       <cn cellml:units="per_millivolt">0.2444</cn>
                                       <ci>V</ci>
                                    </apply>
                                 </apply>
                              </apply>
                              <apply>
                                 <times/>
                                 <cn type="e-notation" cellml:units="per_millisecond">6.948   <sep/>
                                 -6</cn>
                                 <apply>
                                    <exp/>
                                    <apply>
                                       <times/>
                                       <apply>
                                          <minus/>
                                          <cn cellml:units="per_millivolt">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>
                        <cn cellml:units="millivolt">1</cn>
                     </apply>
                     <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <times/>
                              <cn cellml:units="per_millivolt">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="per_millivolt">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="per_millivolt">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="per_millivolt">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="per_millivolt">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 name="i_b_Na" units="picoA_per_picoF" public_interface="out"/>
      <variable name="g_bna" units="nanoS_per_picoF" initial_value="0.00029"/>
      <variable name="E_Na" units="millivolt" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <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 name="i_CaL" units="picoA_per_picoF" public_interface="out"/>
      <variable name="g_CaL" units="litre_per_farad_second" initial_value="0.000175"/>
      <variable name="Ca_o" units="millimolar" public_interface="in"/>
      <variable name="Ca_i" units="millimolar" public_interface="in" private_interface="out"/>
      <variable name="R" units="joule_per_mole_kelvin" public_interface="in"/>
      <variable name="F" units="coulomb_per_millimole" public_interface="in"/>
      <variable name="T" units="kelvin" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in" private_interface="out"/>
      <variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
      <variable name="d" units="dimensionless" public_interface="out" private_interface="in"/>
      <variable name="f" units="dimensionless" private_interface="in"/>
      <variable name="fCa" units="dimensionless" private_interface="in"/>
      <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 name="d" units="dimensionless" initial_value="0" public_interface="out"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <variable name="d_inf" units="dimensionless"/>
      <variable name="alpha_d" units="dimensionless"/>
      <variable name="beta_d" units="dimensionless"/>
      <variable name="gamma_d" units="millisecond"/>
      <variable name="tau_d" units="millisecond"/>
      <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="dimensionless">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="dimensionless">0.25</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_d</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">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="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/>
                  <cn cellml:units="millisecond">1</cn>
                  <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 name="f" units="dimensionless" initial_value="1" public_interface="out"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <variable name="f_inf" units="dimensionless"/>
      <variable name="tau_f" units="millisecond"/>
      <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_square">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 name="fCa" units="dimensionless" initial_value="1" public_interface="out"/>
      <variable name="Ca_i" units="millimolar" public_interface="in"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <variable name="alpha_fCa" units="dimensionless"/>
      <variable name="beta_fCa" units="dimensionless"/>
      <variable name="gama_fCa" units="dimensionless"/>
      <variable name="fCa_inf" units="dimensionless"/>
      <variable name="tau_fCa" units="millisecond"/>
      <variable name="d_fCa" units="per_millisecond"/>
      <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="per_millisecond">0</cn>
                  <apply>
                     <and/>
                     <apply>
                        <gt/>
                        <ci>fCa_inf</ci>
                        <ci>fCa</ci>
                     </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 name="i_b_Ca" units="picoA_per_picoF" public_interface="out"/>
      <variable name="g_bca" units="nanoS_per_picoF" initial_value="0.000592"/>
      <variable name="E_Ca" units="millivolt" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <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 name="i_to" units="picoA_per_picoF" public_interface="out"/>
      <variable name="g_to" units="nanoS_per_picoF" initial_value="0.073"/>
      <variable name="E_K" units="millivolt" public_interface="in"/>
      <variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
      <variable name="time" units="millisecond" public_interface="in" private_interface="out"/>
      <variable name="s" units="dimensionless" private_interface="in"/>
      <variable name="r" units="dimensionless" private_interface="in"/>
      <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 name="s" units="dimensionless" initial_value="1" public_interface="out"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <variable name="s_inf" units="dimensionless"/>
      <variable name="tau_s" units="millisecond"/>
      <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">28</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">1000</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <minus/>
                           <apply>
                              <power/>
                              <apply>
                                 <plus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">67</cn>
                              </apply>
                              <cn cellml:units="dimensionless">2</cn>
                           </apply>
                        </apply>
                        <cn cellml:units="millivolt_square">1000</cn>
                     </apply>
                  </apply>
               </apply>
               <cn cellml:units="millisecond">8</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 name="r" units="dimensionless" initial_value="0" public_interface="out"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <variable name="r_inf" units="dimensionless"/>
      <variable name="tau_r" units="millisecond"/>
      <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_square">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 name="i_NaK" units="picoA_per_picoF" public_interface="out"/>
      <variable name="P_NaK" units="picoA_per_picoF" initial_value="1.362"/>
      <variable name="K_mk" units="millimolar" initial_value="1"/>
      <variable name="K_mNa" units="millimolar" initial_value="40"/>
      <variable name="K_o" units="millimolar" public_interface="in"/>
      <variable name="Na_i" units="millimolar" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <variable name="R" units="joule_per_mole_kelvin" public_interface="in"/>
      <variable name="F" units="coulomb_per_millimole" public_interface="in"/>
      <variable name="T" units="kelvin" public_interface="in"/>
      <variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
      <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 name="i_NaCa" units="picoA_per_picoF" public_interface="out"/>
      <variable name="K_NaCa" units="picoA_per_picoF" initial_value="1000"/>
      <variable name="K_sat" units="dimensionless" initial_value="0.1"/>
      <variable name="alpha" units="dimensionless" initial_value="2.5"/>
      <variable name="gamma" units="dimensionless" initial_value="0.35"/>
      <variable name="Km_Ca" units="millimolar" initial_value="1.38"/>
      <variable name="Km_Nai" units="millimolar" initial_value="87.5"/>
      <variable name="Na_i" units="millimolar" public_interface="in"/>
      <variable name="Na_o" units="millimolar" public_interface="in"/>
      <variable name="Ca_i" units="millimolar" public_interface="in"/>
      <variable name="Ca_o" units="millimolar" public_interface="in"/>
      <variable name="R" units="joule_per_mole_kelvin" public_interface="in"/>
      <variable name="F" units="coulomb_per_millimole" public_interface="in"/>
      <variable name="T" units="kelvin" public_interface="in"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <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 name="i_p_Ca" units="picoA_per_picoF" public_interface="out"/>
      <variable name="g_pCa" units="picoA_per_picoF" initial_value="0.825"/>
      <variable name="K_pCa" units="millimolar" initial_value="0.0005"/>
      <variable name="Ca_i" units="millimolar" public_interface="in"/>
      <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 name="i_p_K" units="picoA_per_picoF" public_interface="out"/>
      <variable name="g_pK" units="nanoS_per_picoF" initial_value="0.0146"/>
      <variable name="E_K" units="millivolt" public_interface="in"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <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 name="Ca_i" units="millimolar" initial_value="0.0002" public_interface="out"/>
      <variable name="Ca_o" units="millimolar" initial_value="2" public_interface="out"/>
      <variable name="Ca_SR" units="millimolar" initial_value="0.2"/>
      <variable name="i_rel" units="millimolar_per_millisecond"/>
      <variable name="i_up" units="millimolar_per_millisecond"/>
      <variable name="i_leak" units="millimolar_per_millisecond"/>
      <variable name="g" units="dimensionless" initial_value="1"/>
      <variable name="tau_g" units="millisecond" initial_value="2"/>
      <variable name="g_inf" units="dimensionless"/>
      <variable name="a_rel" units="millimolar_per_millisecond" initial_value="0.016464"/>
      <variable name="b_rel" units="millimolar" initial_value="0.25"/>
      <variable name="c_rel" units="millimolar_per_millisecond" initial_value="0.008232"/>
      <variable name="K_up" units="millimolar" initial_value="0.00025"/>
      <variable name="V_leak" units="per_millisecond" initial_value="8e-5"/>
      <variable name="Vmax_up" units="millimolar_per_millisecond" initial_value="0.000425"/>
      <variable name="Ca_i_bufc" units="dimensionless"/>
      <variable name="Ca_sr_bufsr" units="dimensionless"/>
      <variable name="Buf_c" units="millimolar" initial_value="0.15"/>
      <variable name="K_buf_c" units="millimolar" initial_value="0.001"/>
      <variable name="Buf_sr" units="millimolar" initial_value="10"/>
      <variable name="K_buf_sr" units="millimolar" initial_value="0.3"/>
      <variable name="V_sr" units="micrometre3" initial_value="0.001094"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="V_c" units="micrometre3" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <variable name="d" units="dimensionless" public_interface="in"/>
      <variable name="F" units="coulomb_per_millimole" public_interface="in"/>
      <variable name="Cm" units="microF" public_interface="in"/>
      <variable name="i_CaL" units="picoA_per_picoF" public_interface="in"/>
      <variable name="i_NaCa" units="picoA_per_picoF" public_interface="in"/>
      <variable name="i_p_Ca" units="picoA_per_picoF" public_interface="in"/>
      <variable name="i_b_Ca" units="picoA_per_picoF" public_interface="in"/>
      <variable name="d_g" units="per_millisecond"/>
      <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="per_millisecond">0</cn>
                  <apply>
                     <and/>
                     <apply>
                        <gt/>
                        <ci>g_inf</ci>
                        <ci>g</ci>
                     </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>
                           <times/>
                           <cn cellml:units="mA_pA">1</cn>
                           <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>
                        <apply>
                           <times/>
                           <cn cellml:units="dimensionless">2</cn>
                           <cn cellml:units="litre_micrometre3">1</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 name="Na_i" units="millimolar" initial_value="11.6" public_interface="out"/>
      <variable name="Na_o" units="millimolar" initial_value="140" public_interface="out"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <variable name="F" units="coulomb_per_millimole" public_interface="in"/>
      <variable name="Cm" units="microF" public_interface="in"/>
      <variable name="V_c" units="micrometre3" public_interface="in"/>
      <variable name="i_Na" units="picoA_per_picoF" public_interface="in"/>
      <variable name="i_NaCa" units="picoA_per_picoF" public_interface="in"/>
      <variable name="i_NaK" units="picoA_per_picoF" public_interface="in"/>
      <variable name="i_b_Na" units="picoA_per_picoF" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Na_i</ci>
            </apply>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <apply>
                        <minus/>
                        <cn cellml:units="mA_pA">1</cn>
                     </apply>
                     <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>
                  <apply>
                     <times/>
                     <cn cellml:units="litre_micrometre3">1</cn>
                     <ci>V_c</ci>
                     <ci>F</ci>
                  </apply>
               </apply>
               <ci>Cm</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="potassium_dynamics">
      <variable name="K_i" units="millimolar" initial_value="138.3" public_interface="out"/>
      <variable name="K_o" units="millimolar" initial_value="5.4" public_interface="out"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <variable name="F" units="coulomb_per_millimole" public_interface="in"/>
      <variable name="Cm" units="microF" public_interface="in"/>
      <variable name="V_c" units="micrometre3" public_interface="in"/>
      <variable name="i_K1" units="picoA_per_picoF" public_interface="in"/>
      <variable name="i_to" units="picoA_per_picoF" public_interface="in"/>
      <variable name="i_NaK" units="picoA_per_picoF" public_interface="in"/>
      <variable name="i_Kr" units="picoA_per_picoF" public_interface="in"/>
      <variable name="i_Ks" units="picoA_per_picoF" public_interface="in"/>
      <variable name="i_p_K" units="picoA_per_picoF" public_interface="in"/>
      <variable name="i_Stim" units="picoA_per_picoF" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>K_i</ci>
            </apply>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <apply>
                        <minus/>
                        <cn cellml:units="mA_pA">1</cn>
                     </apply>
                     <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>
                  <apply>
                     <times/>
                     <cn cellml:units="litre_micrometre3">1</cn>
                     <ci>V_c</ci>
                     <ci>F</ci>
                  </apply>
               </apply>
               <ci>Cm</ci>
            </apply>
         </apply>
      </math>
   </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="inward_rectifier_potassium_current"/>
         <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>
      <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">
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    <dc:title>A model for human ventricular tissue</dc:title>
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    <rdf:value>This variant of the model was created by Penny Noble of Oxford University, and represents the parameters given for the endocardial 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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