Location: Fox, Mcharg, Gilmour, 2002 @ 320ccf2dea5e / fox_mcharg_gilmour_2002.cellml

Author:
Hanne <Hanne@hanne-nielsens-macbook.local>
Date:
2009-12-07 12:52:26+13:00
Desc:
Added images in ai and svg format
Permanent Source URI:
https://staging.physiomeproject.org/workspace/fox_mcharg_gilmour_2002/rawfile/320ccf2dea5ef6ad7834f9ea002ef499db37ec4e/fox_mcharg_gilmour_2002.cellml

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<!--
This CellML file was generated on 30/10/2007 at 17:49:22 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/
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<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>Ionic mechanism of electrical alternans</title>
  <author>
    <firstname>Catherine</firstname>
          <surname>Lloyd</surname>
    <affiliation>
      <shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
    </affiliation>
  </author>
</articleinfo>
  <section id="sec_status">
    <title>Model Status</title>
    <para>
            This model is known to run in PCEnv 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>
The duration of a cardiac action potential is largely dependent on the length of the preceding diastolic interval.  This relationship is called the action potential duration restitution relation, and if its slope is equal to or greater than 1, and alternation of action potential duration, or electrical alternans, often develops during high frequency pacing.  Such rate-dependent electrical alternans may be a precursor to the development of ventricular arrhythmias, especially ventricular fibrillation.  In support of this theory, several experiments have demonstrated that when the slope of the restitution relation is greater than 1, rapid pacing induces both alternans and fibrillation in isolated ventricles.  However, to date, attempts to intervene with this process have been limited, and alternative, more effective, methods of suppressing alternans need to be identified.
</para>

<para>
To this end, mathematical models of the ventricular myocyte have been developed, with the ultimate aim of facilitating the discovery of new therapeutic targets.  In the model described here in CellML, Jeffrey Fox <emphasis>et al.</emphasis> (2001) have developed a mathematical model of the canine ventricular myocyte.  This model was, at least in part, based on the model published by Winslow <emphasis>et al.</emphasis> (1999) (also described in CellML), and it extends this model to reproduce sustained alternans at rapid pacing rates. 
</para>

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

<para>
Ionic mechanism of electrical alternans, Jeffrey J. Fox, Jennifer L. McHarg, and Robert F. Gilmour Jr, 2001,
            <emphasis>American Journal of Physiology: Heart and Circulatory Physiology</emphasis>
           <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&amp;cmd=Retrieve&amp;dopt=AbstractPlus&amp;list_uids=11788399&amp;query_hl=1&amp;itool=pubmed_docsum">PubMed ID: 11788399</ulink>
</para>

<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>cell diagram</title>
    </objectinfo>
    <imagedata fileref="fox_2001.png"/>
  </imageobject>
</mediaobject>
<caption>A schematic diagram describing the current flows across the cell membrane and the calcium fluxes between the cytoplasm and the sarcoplasmic reticulum that are captured in the Fox <emphasis>et al.</emphasis> canine ventricular cell model.</caption>
</informalfigure>


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

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      <variable units="millimolar" public_interface="in" name="K_i"/>
      <variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
      <variable units="kelvin" public_interface="in" name="T"/>
      <variable units="coulomb_per_millimole" public_interface="in" name="F"/>
      <variable units="dimensionless" private_interface="in" name="X_kr"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>E_K</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <ci>R</ci>
                     <ci>T</ci>
                  </apply>
                  <ci>F</ci>
               </apply>
               <apply>
                  <ln/>
                  <apply>
                     <divide/>
                     <ci>K_o</ci>
                     <ci>K_i</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>R_V</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">1</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">2.5</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <times/>
                           <cn cellml:units="per_millivolt">0.1</cn>
                           <apply>
                              <plus/>
                              <ci>V</ci>
                              <cn cellml:units="millivolt">28</cn>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_Kr</ci>
            <apply>
               <times/>
               <ci>g_Kr</ci>
               <ci>R_V</ci>
               <ci>X_kr</ci>
               <apply>
                  <root/>
                  <apply>
                     <divide/>
                     <ci>K_o</ci>
                     <cn cellml:units="millimolar">4</cn>
                  </apply>
               </apply>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_K</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="rapid_activating_delayed_rectifiyer_K_current_X_kr_gate">
      <variable units="dimensionless" public_interface="out" name="X_kr" initial_value="0.229"/>
      <variable units="dimensionless" name="X_kr_inf"/>
      <variable units="millisecond" name="tau_X_kr"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>X_kr_inf</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">1</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <minus/>
                        <apply>
                           <minus/>
                           <cn cellml:units="dimensionless">2.182</cn>
                        </apply>
                        <apply>
                           <times/>
                           <cn cellml:units="per_millivolt">0.1819</cn>
                           <ci>V</ci>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_X_kr</ci>
            <apply>
               <plus/>
               <cn cellml:units="millisecond">43</cn>
               <apply>
                  <divide/>
                  <cn cellml:units="millisecond">1</cn>
                  <apply>
                     <plus/>
                     <apply>
                        <exp/>
                        <apply>
                           <plus/>
                           <apply>
                              <minus/>
                              <cn cellml:units="dimensionless">5.495</cn>
                           </apply>
                           <apply>
                              <times/>
                              <cn cellml:units="per_millivolt">0.1691</cn>
                              <ci>V</ci>
                           </apply>
                        </apply>
                     </apply>
                     <apply>
                        <exp/>
                        <apply>
                           <minus/>
                           <apply>
                              <minus/>
                              <cn cellml:units="dimensionless">7.677</cn>
                           </apply>
                           <apply>
                              <times/>
                              <cn cellml:units="per_millivolt">0.0128</cn>
                              <ci>V</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>X_kr</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>X_kr_inf</ci>
                  <ci>X_kr</ci>
               </apply>
               <ci>tau_X_kr</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="slow_activating_delayed_rectifiyer_K_current">
      <variable units="microA_per_microF" public_interface="out" name="i_Ks"/>
      <variable units="milliS_per_microF" name="g_Ks" initial_value="0.0245"/>
      <variable units="millivolt" name="E_Ks"/>
      <variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
      <variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
      <variable units="millimolar" public_interface="in" name="K_o"/>
      <variable units="millimolar" public_interface="in" name="K_i"/>
      <variable units="millimolar" public_interface="in" name="Na_o"/>
      <variable units="millimolar" public_interface="in" name="Na_i"/>
      <variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
      <variable units="kelvin" public_interface="in" name="T"/>
      <variable units="coulomb_per_millimole" public_interface="in" name="F"/>
      <variable units="dimensionless" private_interface="in" name="X_ks"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>E_Ks</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <ci>R</ci>
                     <ci>T</ci>
                  </apply>
                  <ci>F</ci>
               </apply>
               <apply>
                  <ln/>
                  <apply>
                     <divide/>
                     <apply>
                        <plus/>
                        <ci>K_o</ci>
                        <apply>
                           <times/>
                           <cn cellml:units="dimensionless">0.01833</cn>
                           <ci>Na_o</ci>
                        </apply>
                     </apply>
                     <apply>
                        <plus/>
                        <ci>K_i</ci>
                        <apply>
                           <times/>
                           <cn cellml:units="dimensionless">0.01833</cn>
                           <ci>Na_i</ci>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_Ks</ci>
            <apply>
               <times/>
               <ci>g_Ks</ci>
               <apply>
                  <power/>
                  <ci>X_ks</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_activating_delayed_rectifiyer_K_current_X_ks_gate">
      <variable units="dimensionless" public_interface="out" name="X_ks" initial_value="0.0001"/>
      <variable units="millisecond" name="tau_X_ks"/>
      <variable units="dimensionless" name="X_ks_infinity"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>X_ks_infinity</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">16</cn>
                        </apply>
                        <apply>
                           <minus/>
                           <cn cellml:units="millivolt">13.6</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_X_ks</ci>
            <apply>
               <divide/>
               <cn cellml:units="millisecond">1</cn>
               <apply>
                  <plus/>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <cn cellml:units="per_millivolt">0.0000719</cn>
                        <apply>
                           <minus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">10</cn>
                        </apply>
                     </apply>
                     <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <cn cellml:units="per_millivolt">0.148</cn>
                              </apply>
                              <apply>
                                 <minus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">10</cn>
                              </apply>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <cn cellml:units="per_millivolt">0.000131</cn>
                        <apply>
                           <minus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">10</cn>
                        </apply>
                     </apply>
                     <apply>
                        <minus/>
                        <apply>
                           <exp/>
                           <apply>
                              <times/>
                              <cn cellml:units="per_millivolt">0.0687</cn>
                              <apply>
                                 <minus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">10</cn>
                              </apply>
                           </apply>
                        </apply>
                        <cn cellml:units="dimensionless">1</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>X_ks</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>X_ks_infinity</ci>
                  <ci>X_ks</ci>
               </apply>
               <ci>tau_X_ks</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="transient_outward_potassium_current">
      <variable units="microA_per_microF" public_interface="out" name="i_to"/>
      <variable units="milliS_per_microF" name="g_to" initial_value="0.23815"/>
      <variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
      <variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
      <variable units="millivolt" public_interface="in" name="E_K"/>
      <variable units="dimensionless" private_interface="in" name="X_to"/>
      <variable units="dimensionless" private_interface="in" name="Y_to"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_to</ci>
            <apply>
               <times/>
               <ci>g_to</ci>
               <ci>X_to</ci>
               <ci>Y_to</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_K</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="transient_outward_potassium_current_X_to_gate">
      <variable units="dimensionless" public_interface="out" name="X_to" initial_value="0.00003742"/>
      <variable units="per_millisecond" name="alpha_X_to"/>
      <variable units="per_millisecond" name="beta_X_to"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>alpha_X_to</ci>
            <apply>
               <times/>
               <cn cellml:units="per_millisecond">0.04516</cn>
               <apply>
                  <exp/>
                  <apply>
                     <times/>
                     <cn cellml:units="per_millivolt">0.03577</cn>
                     <ci>V</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_X_to</ci>
            <apply>
               <times/>
               <cn cellml:units="per_millisecond">0.0989</cn>
               <apply>
                  <exp/>
                  <apply>
                     <times/>
                     <apply>
                        <minus/>
                        <cn cellml:units="per_millivolt">0.06237</cn>
                     </apply>
                     <ci>V</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>X_to</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>alpha_X_to</ci>
                  <apply>
                     <minus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <ci>X_to</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>beta_X_to</ci>
                  <ci>X_to</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="transient_outward_potassium_current_Y_to_gate">
      <variable units="dimensionless" public_interface="out" name="Y_to" initial_value="1"/>
      <variable units="per_millisecond" name="alpha_Y_to"/>
      <variable units="per_millisecond" name="beta_Y_to"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>alpha_Y_to</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn cellml:units="per_millisecond">0.005415</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <plus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">33.5</cn>
                        </apply>
                        <apply>
                           <minus/>
                           <cn cellml:units="millivolt">5</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">0.051335</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <plus/>
                              <ci>V</ci>
                              <cn cellml:units="millivolt">33.5</cn>
                           </apply>
                           <apply>
                              <minus/>
                              <cn cellml:units="millivolt">5</cn>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_Y_to</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn cellml:units="per_millisecond">0.005415</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <plus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">33.5</cn>
                        </apply>
                        <cn cellml:units="millivolt">5</cn>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">0.051335</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <plus/>
                              <ci>V</ci>
                              <cn cellml:units="millivolt">33.5</cn>
                           </apply>
                           <cn cellml:units="millivolt">5</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Y_to</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>alpha_Y_to</ci>
                  <apply>
                     <minus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <ci>Y_to</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>beta_Y_to</ci>
                  <ci>Y_to</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="plateau_potassium_current">
      <variable units="microA_per_microF" public_interface="out" name="i_Kp"/>
      <variable units="milliS_per_microF" name="g_Kp" initial_value="0.002216"/>
      <variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
      <variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
      <variable units="millivolt" public_interface="in" name="E_K"/>
      <variable units="dimensionless" private_interface="in" name="Kp_V"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_Kp</ci>
            <apply>
               <times/>
               <ci>g_Kp</ci>
               <ci>Kp_V</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_K</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="plateau_potassium_current_Kp_gate">
      <variable units="dimensionless" public_interface="out" name="Kp_V"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>Kp_V</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">7.488</cn>
                           <ci>V</ci>
                        </apply>
                        <cn cellml:units="millivolt">5.98</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="sodium_potassium_pump">
      <variable units="microA_per_microF" public_interface="out" name="i_NaK"/>
      <variable units="microA_per_microF" name="i_NaK_max" initial_value="0.693"/>
      <variable units="dimensionless" name="f_NaK"/>
      <variable units="millimolar" name="K_mNai" initial_value="10"/>
      <variable units="millimolar" name="K_mKo" initial_value="1.5"/>
      <variable units="dimensionless" name="sigma"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
      <variable units="kelvin" public_interface="in" name="T"/>
      <variable units="coulomb_per_millimole" public_interface="in" name="F"/>
      <variable units="millimolar" public_interface="in" name="Na_i"/>
      <variable units="millimolar" public_interface="in" name="Na_o"/>
      <variable units="millimolar" public_interface="in" name="K_o"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>f_NaK</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">1</cn>
               <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">0.0365</cn>
                     <ci>sigma</ci>
                     <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>
         <apply>
            <eq/>
            <ci>sigma</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <cn cellml:units="dimensionless">1</cn>
                  <cn cellml:units="dimensionless">7</cn>
               </apply>
               <apply>
                  <minus/>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <ci>Na_o</ci>
                        <cn cellml:units="millimolar">67.3</cn>
                     </apply>
                  </apply>
                  <cn cellml:units="dimensionless">1</cn>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_NaK</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <ci>i_NaK_max</ci>
                        <ci>f_NaK</ci>
                     </apply>
                     <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <power/>
                           <apply>
                              <divide/>
                              <ci>K_mNai</ci>
                              <ci>Na_i</ci>
                           </apply>
                           <cn cellml:units="dimensionless">1.5</cn>
                        </apply>
                     </apply>
                  </apply>
                  <ci>K_o</ci>
               </apply>
               <apply>
                  <plus/>
                  <ci>K_o</ci>
                  <ci>K_mKo</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="Na_Ca_exchanger">
      <variable units="microA_per_microF" public_interface="out" name="i_NaCa"/>
      <variable units="micromolar" name="K_mCa" initial_value="1380"/>
      <variable units="millimolar" name="K_mNa" initial_value="87.5"/>
      <variable units="microA_per_microF" name="K_NaCa" initial_value="1500"/>
      <variable units="dimensionless" name="K_sat" initial_value="0.2"/>
      <variable units="dimensionless" name="eta" initial_value="0.35"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
      <variable units="kelvin" public_interface="in" name="T"/>
      <variable units="coulomb_per_millimole" public_interface="in" name="F"/>
      <variable units="millimolar" public_interface="in" name="Na_i"/>
      <variable units="millimolar" public_interface="in" name="Na_o"/>
      <variable units="micromolar" public_interface="in" name="Ca_i"/>
      <variable units="micromolar" public_interface="in" name="Ca_o"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_NaCa</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <ci>K_NaCa</ci>
                  <apply>
                     <times/>
                     <apply>
                        <plus/>
                        <apply>
                           <power/>
                           <ci>K_mNa</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>K_mCa</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>eta</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>
                  <minus/>
                  <apply>
                     <times/>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <ci>eta</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>eta</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>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="sarcolemmal_calcium_pump">
      <variable units="microA_per_microF" public_interface="out" name="i_p_Ca"/>
      <variable units="micromolar" name="K_mpCa" initial_value="0.05"/>
      <variable units="microA_per_microF" name="i_pCa_max" initial_value="0.05"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="micromolar" public_interface="in" name="Ca_i"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_p_Ca</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>i_pCa_max</ci>
                  <ci>Ca_i</ci>
               </apply>
               <apply>
                  <plus/>
                  <ci>K_mpCa</ci>
                  <ci>Ca_i</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="calcium_background_current">
      <variable units="microA_per_microF" public_interface="out" name="i_Ca_b"/>
      <variable units="milliS_per_microF" name="g_Cab" initial_value="0.0003842"/>
      <variable units="millivolt" name="E_Ca"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
      <variable units="kelvin" public_interface="in" name="T"/>
      <variable units="coulomb_per_millimole" public_interface="in" name="F"/>
      <variable units="micromolar" public_interface="in" name="Ca_i"/>
      <variable units="micromolar" public_interface="in" name="Ca_o"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>E_Ca</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <ci>R</ci>
                     <ci>T</ci>
                  </apply>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">2</cn>
                     <ci>F</ci>
                  </apply>
               </apply>
               <apply>
                  <ln/>
                  <apply>
                     <divide/>
                     <ci>Ca_o</ci>
                     <ci>Ca_i</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_Ca_b</ci>
            <apply>
               <times/>
               <ci>g_Cab</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_Ca</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="sodium_background_current">
      <variable units="microA_per_microF" public_interface="out" name="i_Na_b"/>
      <variable units="milliS_per_microF" name="g_Nab" initial_value="0.0031"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millivolt" public_interface="in" name="E_Na"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_Na_b</ci>
            <apply>
               <times/>
               <ci>g_Nab</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_Na</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   
   <component name="L_type_Ca_current">
      <variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
      <variable units="microA_per_microF" public_interface="out" name="i_Ca"/>
      <variable units="microA_per_microF" public_interface="out" name="i_CaK"/>
      <variable units="cm_per_millisecond" name="P_Ca" initial_value="0.0000226"/>
      <variable units="cm_per_millisecond" name="P_CaK" initial_value="0.000000579"/>
      <variable units="microA_per_microF" name="i_Ca_half" initial_value="-0.265"/>
      <variable units="microA_per_microF" name="i_Ca_max"/>
      <variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
      <variable units="microF_per_cm2" public_interface="out" name="C_sc" initial_value="1"/>
      <variable units="micromolar" public_interface="in" name="Ca_o"/>
      <variable units="millimolar" public_interface="in" name="K_o"/>
      <variable units="millimolar" public_interface="in" name="K_i"/>
      <variable units="micromolar" public_interface="in" private_interface="out" name="Ca_i"/>
      <variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
      <variable units="kelvin" public_interface="in" name="T"/>
      <variable units="coulomb_per_millimole" public_interface="in" name="F"/>
      
	  <variable units="dimensionless" public_interface="out" private_interface="in" name="f"/>
      <variable units="dimensionless" public_interface="out" private_interface="in" name="d"/>
      <variable units="dimensionless" public_interface="out" private_interface="in" name="f_Ca"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_Ca</ci>
            <apply>
               <times/>
               <ci>i_Ca_max</ci>
               <ci>f</ci>
               <ci>d</ci>
               <ci>f_Ca</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_Ca_max</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <apply>
                           <divide/>
                           <ci>P_Ca</ci>
                           <ci>C_sc</ci>
                        </apply>
                        <cn cellml:units="uM_mM">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>
         <apply>
            <eq/>
            <ci>i_CaK</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <apply>
                                 <divide/>
                                 <ci>P_CaK</ci>
                                 <ci>C_sc</ci>
                              </apply>
                              <ci>f</ci>
                              <ci>d</ci>
                              <ci>f_Ca</ci>
                           </apply>
                           <apply>
                              <plus/>
                              <cn cellml:units="dimensionless">1</cn>
                              <apply>
                                 <divide/>
                                 <ci>i_Ca_max</ci>
                                 <ci>i_Ca_half</ci>
                              </apply>
                           </apply>
                        </apply>
                        <cn cellml:units="nM_mM">1000</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>K_i</ci>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <ci>V</ci>
                                 <ci>F</ci>
                              </apply>
                              <apply>
                                 <times/>
                                 <ci>R</ci>
                                 <ci>T</ci>
                              </apply>
                           </apply>
                        </apply>
                     </apply>
                     <ci>K_o</ci>
                  </apply>
               </apply>
               <apply>
                  <minus/>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <times/>
                           <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_f_gate">
      <variable units="dimensionless" public_interface="out" name="f" initial_value="0.983"/>
      <variable units="dimensionless" name="f_infinity"/>
      <variable units="millisecond" name="tau_f"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>f_infinity</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">12.5</cn>
                        </apply>
                        <cn cellml:units="millivolt">5</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_f</ci>
            <apply>
               <plus/>
               <cn cellml:units="millisecond">30</cn>
               <apply>
                  <divide/>
                  <cn cellml:units="millisecond">200</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">9.5</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_infinity</ci>
                  <ci>f</ci>
               </apply>
               <ci>tau_f</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="L_type_Ca_current_d_gate">
      <variable units="dimensionless" public_interface="out" name="d" initial_value="0.0001"/>
      <variable units="dimensionless" name="d_infinity"/>
      <variable units="millisecond" name="tau_d"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="millivolt" name="E0_m"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>d_infinity</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">10</cn>
                        </apply>
                        <apply>
                           <minus/>
                           <cn cellml:units="millivolt">6.24</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>E0_m</ci>
            <apply>
               <plus/>
               <ci>V</ci>
               <cn cellml:units="millivolt">40</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_d</ci>
            <apply>
               <divide/>
               <cn cellml:units="millisecond">1</cn>
               <apply>
                  <plus/>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <cn cellml:units="dimensionless">0.25</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <cn cellml:units="per_millivolt">0.01</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">0.07</cn>
                              </apply>
                              <ci>V</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <cn cellml:units="dimensionless">0.07</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <cn cellml:units="per_millivolt">0.05</cn>
                              </apply>
                              <ci>E0_m</ci>
                           </apply>
                        </apply>
                     </apply>
                     <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <times/>
                              <cn cellml:units="per_millivolt">0.05</cn>
                              <ci>E0_m</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>d</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>d_infinity</ci>
                  <ci>d</ci>
               </apply>
               <ci>tau_d</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="L_type_Ca_current_f_Ca_gate">
      <variable units="dimensionless" public_interface="out" name="f_Ca" initial_value="0.942"/>
      <variable units="millisecond" name="tau_f_Ca"/>
      <variable units="dimensionless" name="f_Ca_infinity"/>
      <variable units="micromolar" name="K_mfCa" initial_value="0.18"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="micromolar" public_interface="in" name="Ca_i"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>f_Ca_infinity</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>
                        <ci>K_mfCa</ci>
                     </apply>
                     <cn cellml:units="dimensionless">3</cn>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_f_Ca</ci>
            <cn cellml:units="millisecond">30</cn>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>f_Ca</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>f_Ca_infinity</ci>
                  <ci>f_Ca</ci>
               </apply>
               <ci>tau_f_Ca</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="calcium_dynamics">
      <variable units="micromolar" public_interface="out" name="Ca_i" initial_value="0.0472"/>
      <variable units="dimensionless" name="beta_i"/>
      <variable units="micromolar" name="K_mCMDN" initial_value="2"/>
      <variable units="micromolar" name="CMDN_tot" initial_value="10"/>
      <variable units="microlitre" name="V_myo" initial_value="0.00002584"/>
      <variable units="coulomb_per_millimole" public_interface="in" name="F"/>
      <variable units="microF_per_cm2" public_interface="in" name="C_sc"/>
      <variable units="cm2" name="A_Cap" initial_value="0.0001534"/>
      <variable units="micromolar_per_millisecond" name="J_rel"/>
      <variable units="micromolar_per_millisecond" name="J_leak"/>
      <variable units="micromolar_per_millisecond" name="J_up"/>
      <variable units="microA_per_microF" public_interface="in" name="i_Ca"/>
      <variable units="microA_per_microF" public_interface="in" name="i_Ca_b"/>
      <variable units="microA_per_microF" public_interface="in" name="i_p_Ca"/>
      <variable units="microA_per_microF" public_interface="in" name="i_NaCa"/>
      <variable units="micromolar" name="Ca_SR" initial_value="320"/>
      <variable units="per_millisecond" name="P_rel" initial_value="6"/>
      <variable units="per_millisecond" name="P_leak" initial_value="0.000001"/>
      <variable units="micromolar" name="K_mCSQN" initial_value="600"/>
      <variable units="micromolar" name="CSQN_tot" initial_value="10000"/>
      <variable units="microlitre" name="V_SR" initial_value="0.000002"/>
      <variable units="micromolar_per_millisecond" name="V_up" initial_value="0.1"/>
      <variable units="micromolar" name="K_mup" initial_value="0.32"/>
      <variable units="dimensionless" name="gamma"/>
      <variable units="dimensionless" public_interface="in" name="f_Ca"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millisecond" public_interface="in" name="time"/>
      <variable units="dimensionless" public_interface="in" name="f"/>
      <variable units="dimensionless" public_interface="in" name="d"/>
      <variable units="dimensionless" name="beta_SR"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>J_up</ci>
            <apply>
               <divide/>
               <ci>V_up</ci>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <power/>
                     <apply>
                        <divide/>
                        <ci>K_mup</ci>
                        <ci>Ca_i</ci>
                     </apply>
                     <cn cellml:units="dimensionless">2</cn>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>gamma</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">1</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <power/>
                     <apply>
                        <divide/>
                        <cn cellml:units="micromolar">2000</cn>
                        <ci>Ca_SR</ci>
                     </apply>
                     <cn cellml:units="dimensionless">3</cn>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>J_rel</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>P_rel</ci>
                  <ci>f</ci>
                  <ci>d</ci>
                  <ci>f_Ca</ci>
                  <apply>
                     <minus/>
                     <apply>
                        <times/>
                        <ci>gamma</ci>
                        <ci>Ca_SR</ci>
                     </apply>
                     <ci>Ca_i</ci>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">1.65</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">20</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>J_leak</ci>
            <apply>
               <times/>
               <ci>P_leak</ci>
               <apply>
                  <minus/>
                  <ci>Ca_SR</ci>
                  <ci>Ca_i</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_SR</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">1</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <ci>CSQN_tot</ci>
                        <ci>K_mCSQN</ci>
                     </apply>
                     <apply>
                        <power/>
                        <apply>
                           <plus/>
                           <ci>K_mCSQN</ci>
                           <ci>Ca_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_SR</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>beta_SR</ci>
                  <apply>
                     <minus/>
                     <apply>
                        <minus/>
                        <ci>J_up</ci>
                        <ci>J_leak</ci>
                     </apply>
                     <ci>J_rel</ci>
                  </apply>
                  <ci>V_myo</ci>
               </apply>
               <ci>V_SR</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_i</ci>
            <apply>
               <divide/>
               <cn cellml:units="dimensionless">1</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <ci>CMDN_tot</ci>
                        <ci>K_mCMDN</ci>
                     </apply>
                     <apply>
                        <power/>
                        <apply>
                           <plus/>
                           <ci>K_mCMDN</ci>
                           <ci>Ca_i</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>beta_i</ci>
               <apply>
                  <minus/>
                  <apply>
                     <minus/>
                     <apply>
                        <plus/>
                        <ci>J_rel</ci>
                        <ci>J_leak</ci>
                     </apply>
                     <ci>J_up</ci>
                  </apply>
                  <apply>
                     <times/>
                     <apply>
                        <divide/>
                        <apply>
                           <times/>
                           <ci>A_Cap</ci>
                           <ci>C_sc</ci>
                        </apply>
                        <apply>
                           <times/>
                           <cn cellml:units="dimensionless">2</cn>
                           <ci>F</ci>
                           <ci>V_myo</ci>
                        </apply>
                     </apply>
                     <apply>
                        <minus/>
                        <apply>
                           <plus/>
                           <ci>i_Ca</ci>
                           <ci>i_Ca_b</ci>
                           <ci>i_p_Ca</ci>
                        </apply>
                        <apply>
                           <times/>
                           <cn cellml:units="dimensionless">2</cn>
                           <ci>i_NaCa</ci>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="standard_ionic_concentrations">
      <variable units="millimolar" public_interface="out" name="Na_i" initial_value="10"/>
      <variable units="millimolar" public_interface="out" name="Na_o" initial_value="138"/>
      <variable units="micromolar" public_interface="out" name="Ca_o" initial_value="2000"/>
      <variable units="millimolar" public_interface="out" name="K_i" initial_value="149.4"/>
      <variable units="millimolar" public_interface="out" name="K_o" initial_value="4"/>
   </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="rapid_activating_delayed_rectifiyer_K_current">
            <component_ref component="rapid_activating_delayed_rectifiyer_K_current_X_kr_gate"/>
         </component_ref>
         <component_ref component="slow_activating_delayed_rectifiyer_K_current">
            <component_ref component="slow_activating_delayed_rectifiyer_K_current_X_ks_gate"/>
         </component_ref>
         <component_ref component="transient_outward_potassium_current">
            <component_ref component="transient_outward_potassium_current_X_to_gate"/>
            <component_ref component="transient_outward_potassium_current_Y_to_gate"/>
         </component_ref>
         <component_ref component="time_independent_potassium_current">
            <component_ref component="time_independent_potassium_current_K1_gate"/>
         </component_ref>
         <component_ref component="plateau_potassium_current">
            <component_ref component="plateau_potassium_current_Kp_gate"/>
         </component_ref>
         <component_ref component="Na_Ca_exchanger"/>
         <component_ref component="sodium_potassium_pump"/>
         <component_ref component="sarcolemmal_calcium_pump"/>
         <component_ref component="calcium_background_current"/>
         <component_ref component="sodium_background_current"/>
         <component_ref component="L_type_Ca_current">
            <component_ref component="L_type_Ca_current_f_gate"/>
            <component_ref component="L_type_Ca_current_d_gate"/>
            <component_ref component="L_type_Ca_current_f_Ca_gate"/>
         </component_ref>
         <component_ref component="calcium_dynamics"/>
         <component_ref component="standard_ionic_concentrations"/>
      </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="rapid_activating_delayed_rectifiyer_K_current">
         <component_ref component="rapid_activating_delayed_rectifiyer_K_current_X_kr_gate"/>
      </component_ref>
      <component_ref component="slow_activating_delayed_rectifiyer_K_current">
         <component_ref component="slow_activating_delayed_rectifiyer_K_current_X_ks_gate"/>
      </component_ref>
      <component_ref component="transient_outward_potassium_current">
         <component_ref component="transient_outward_potassium_current_X_to_gate"/>
         <component_ref component="transient_outward_potassium_current_Y_to_gate"/>
      </component_ref>
      <component_ref component="time_independent_potassium_current">
         <component_ref component="time_independent_potassium_current_K1_gate"/>
      </component_ref>
      <component_ref component="plateau_potassium_current">
         <component_ref component="plateau_potassium_current_Kp_gate"/>
      </component_ref>
      <component_ref component="L_type_Ca_current">
         <component_ref component="L_type_Ca_current_f_gate"/>
         <component_ref component="L_type_Ca_current_d_gate"/>
         <component_ref component="L_type_Ca_current_f_Ca_gate"/>
      </component_ref>
   </group>
   <connection>
      <map_components component_2="environment" component_1="membrane"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="fast_sodium_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="rapid_activating_delayed_rectifiyer_K_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="slow_activating_delayed_rectifiyer_K_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="transient_outward_potassium_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="time_independent_potassium_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="plateau_potassium_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="Na_Ca_exchanger"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="sodium_potassium_pump"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="sarcolemmal_calcium_pump"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="calcium_background_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="sodium_background_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="calcium_dynamics"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="fast_sodium_current" component_1="membrane"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="R" variable_1="R"/>
      <map_variables variable_2="T" variable_1="T"/>
      <map_variables variable_2="F" variable_1="F"/>
      <map_variables variable_2="i_Na" variable_1="i_Na"/>
   </connection>
   <connection>
      <map_components component_2="rapid_activating_delayed_rectifiyer_K_current" component_1="membrane"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_Kr" variable_1="i_Kr"/>
      <map_variables variable_2="R" variable_1="R"/>
      <map_variables variable_2="T" variable_1="T"/>
      <map_variables variable_2="F" variable_1="F"/>
   </connection>
   <connection>
      <map_components component_2="slow_activating_delayed_rectifiyer_K_current" component_1="membrane"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_Ks" variable_1="i_Ks"/>
      <map_variables variable_2="R" variable_1="R"/>
      <map_variables variable_2="T" variable_1="T"/>
      <map_variables variable_2="F" variable_1="F"/>
   </connection>
   <connection>
      <map_components component_2="transient_outward_potassium_current" component_1="membrane"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_to" variable_1="i_to"/>
   </connection>
   <connection>
      <map_components component_2="time_independent_potassium_current" component_1="membrane"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_K1" variable_1="i_K1"/>
      <map_variables variable_2="R" variable_1="R"/>
      <map_variables variable_2="T" variable_1="T"/>
      <map_variables variable_2="F" variable_1="F"/>
   </connection>
   <connection>
      <map_components component_2="plateau_potassium_current" component_1="membrane"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_Kp" variable_1="i_Kp"/>
   </connection>
   <connection>
      <map_components component_2="Na_Ca_exchanger" component_1="membrane"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
      <map_variables variable_2="R" variable_1="R"/>
      <map_variables variable_2="T" variable_1="T"/>
      <map_variables variable_2="F" variable_1="F"/>
   </connection>
   <connection>
      <map_components component_2="sodium_potassium_pump" component_1="membrane"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_NaK" variable_1="i_NaK"/>
      <map_variables variable_2="R" variable_1="R"/>
      <map_variables variable_2="T" variable_1="T"/>
      <map_variables variable_2="F" variable_1="F"/>
   </connection>
   <connection>
      <map_components component_2="sarcolemmal_calcium_pump" component_1="membrane"/>
      <map_variables variable_2="i_p_Ca" variable_1="i_p_Ca"/>
   </connection>
   <connection>
      <map_components component_2="calcium_background_current" component_1="membrane"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_Ca_b" variable_1="i_Ca_b"/>
      <map_variables variable_2="R" variable_1="R"/>
      <map_variables variable_2="T" variable_1="T"/>
      <map_variables variable_2="F" variable_1="F"/>
   </connection>
   <connection>
      <map_components component_2="sodium_background_current" component_1="membrane"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_Na_b" variable_1="i_Na_b"/>
   </connection>
   <connection>
      <map_components component_2="L_type_Ca_current" component_1="membrane"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_Ca" variable_1="i_Ca"/>
      <map_variables variable_2="i_CaK" variable_1="i_CaK"/>
      <map_variables variable_2="R" variable_1="R"/>
      <map_variables variable_2="T" variable_1="T"/>
      <map_variables variable_2="F" variable_1="F"/>
   </connection>
   <connection>
      <map_components component_2="sodium_background_current" component_1="fast_sodium_current"/>
      <map_variables variable_2="E_Na" variable_1="E_Na"/>
   </connection>
   <connection>
      <map_components component_2="rapid_activating_delayed_rectifiyer_K_current" component_1="transient_outward_potassium_current"/>
      <map_variables variable_2="E_K" variable_1="E_K"/>
   </connection>
   <connection>
      <map_components component_2="rapid_activating_delayed_rectifiyer_K_current" component_1="time_independent_potassium_current"/>
      <map_variables variable_2="E_K" variable_1="E_K"/>
   </connection>
   <connection>
      <map_components component_2="rapid_activating_delayed_rectifiyer_K_current" component_1="plateau_potassium_current"/>
      <map_variables variable_2="E_K" variable_1="E_K"/>
   </connection>
   <connection>
      <map_components component_2="standard_ionic_concentrations" component_1="time_independent_potassium_current"/>
      <map_variables variable_2="K_o" variable_1="K_o"/>
   </connection>
   <connection>
      <map_components component_2="fast_sodium_current_m_gate" component_1="fast_sodium_current"/>
      <map_variables variable_2="m" variable_1="m"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="V" variable_1="V"/>
   </connection>
   <connection>
      <map_components component_2="fast_sodium_current_h_gate" component_1="fast_sodium_current"/>
      <map_variables variable_2="h" variable_1="h"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="V" variable_1="V"/>
   </connection>
   <connection>
      <map_components component_2="fast_sodium_current_j_gate" component_1="fast_sodium_current"/>
      <map_variables variable_2="j" variable_1="j"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="V" variable_1="V"/>
   </connection>
   <connection>
      <map_components component_2="rapid_activating_delayed_rectifiyer_K_current_X_kr_gate" component_1="rapid_activating_delayed_rectifiyer_K_current"/>
      <map_variables variable_2="X_kr" variable_1="X_kr"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="V" variable_1="V"/>
   </connection>
   <connection>
      <map_components component_2="slow_activating_delayed_rectifiyer_K_current_X_ks_gate" component_1="slow_activating_delayed_rectifiyer_K_current"/>
      <map_variables variable_2="X_ks" variable_1="X_ks"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="V" variable_1="V"/>
   </connection>
   <connection>
      <map_components component_2="transient_outward_potassium_current_X_to_gate" component_1="transient_outward_potassium_current"/>
      <map_variables variable_2="X_to" variable_1="X_to"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="V" variable_1="V"/>
   </connection>
   <connection>
      <map_components component_2="transient_outward_potassium_current_Y_to_gate" component_1="transient_outward_potassium_current"/>
      <map_variables variable_2="Y_to" variable_1="Y_to"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="V" variable_1="V"/>
   </connection>
   <connection>
      <map_components component_2="time_independent_potassium_current_K1_gate" component_1="time_independent_potassium_current"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="R" variable_1="R"/>
      <map_variables variable_2="T" variable_1="T"/>
      <map_variables variable_2="F" variable_1="F"/>
      <map_variables variable_2="E_K" variable_1="E_K"/>
      <map_variables variable_2="K1_infinity" variable_1="K1_infinity"/>
   </connection>
   <connection>
      <map_components component_2="plateau_potassium_current_Kp_gate" component_1="plateau_potassium_current"/>
      <map_variables variable_2="Kp_V" variable_1="Kp_V"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="V" variable_1="V"/>
   </connection>
   <connection>
      <map_components component_2="L_type_Ca_current_f_gate" component_1="L_type_Ca_current"/>
      <map_variables variable_2="f" variable_1="f"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="V" variable_1="V"/>
   </connection>
   <connection>
      <map_components component_2="L_type_Ca_current_d_gate" component_1="L_type_Ca_current"/>
      <map_variables variable_2="d" variable_1="d"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="V" variable_1="V"/>
   </connection>
   <connection>
      <map_components component_2="L_type_Ca_current_f_Ca_gate" component_1="L_type_Ca_current"/>
      <map_variables variable_2="f_Ca" variable_1="f_Ca"/>
      <map_variables variable_2="Ca_i" variable_1="Ca_i"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="V" variable_1="V"/>
   </connection>
   <connection>
      <map_components component_2="calcium_dynamics" component_1="membrane"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="F" variable_1="F"/>
   </connection>
   <connection>
      <map_components component_2="standard_ionic_concentrations" component_1="fast_sodium_current"/>
      <map_variables variable_2="Na_i" variable_1="Na_i"/>
      <map_variables variable_2="Na_o" variable_1="Na_o"/>
   </connection>
   <connection>
      <map_components component_2="standard_ionic_concentrations" component_1="rapid_activating_delayed_rectifiyer_K_current"/>
      <map_variables variable_2="K_i" variable_1="K_i"/>
      <map_variables variable_2="K_o" variable_1="K_o"/>
   </connection>
   <connection>
      <map_components component_2="standard_ionic_concentrations" component_1="slow_activating_delayed_rectifiyer_K_current"/>
      <map_variables variable_2="K_i" variable_1="K_i"/>
      <map_variables variable_2="K_o" variable_1="K_o"/>
      <map_variables variable_2="Na_i" variable_1="Na_i"/>
      <map_variables variable_2="Na_o" variable_1="Na_o"/>
   </connection>
   <connection>
      <map_components component_2="standard_ionic_concentrations" component_1="Na_Ca_exchanger"/>
      <map_variables variable_2="Ca_o" variable_1="Ca_o"/>
      <map_variables variable_2="Na_i" variable_1="Na_i"/>
      <map_variables variable_2="Na_o" variable_1="Na_o"/>
   </connection>
   <connection>
      <map_components component_2="standard_ionic_concentrations" component_1="sodium_potassium_pump"/>
      <map_variables variable_2="Na_i" variable_1="Na_i"/>
      <map_variables variable_2="Na_o" variable_1="Na_o"/>
      <map_variables variable_2="K_o" variable_1="K_o"/>
   </connection>
   <connection>
      <map_components component_2="standard_ionic_concentrations" component_1="calcium_background_current"/>
      <map_variables variable_2="Ca_o" variable_1="Ca_o"/>
   </connection>
   <connection>
      <map_components component_2="standard_ionic_concentrations" component_1="L_type_Ca_current"/>
      <map_variables variable_2="Ca_o" variable_1="Ca_o"/>
      <map_variables variable_2="K_i" variable_1="K_i"/>
      <map_variables variable_2="K_o" variable_1="K_o"/>
   </connection>
   <connection>
      <map_components component_2="L_type_Ca_current" component_1="environment"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="calcium_dynamics" component_1="Na_Ca_exchanger"/>
      <map_variables variable_2="Ca_i" variable_1="Ca_i"/>
      <map_variables variable_2="i_NaCa" variable_1="i_NaCa"/>
   </connection>
   <connection>
      <map_components component_2="calcium_dynamics" component_1="sarcolemmal_calcium_pump"/>
      <map_variables variable_2="Ca_i" variable_1="Ca_i"/>
      <map_variables variable_2="i_p_Ca" variable_1="i_p_Ca"/>
   </connection>
   <connection>
      <map_components component_2="calcium_dynamics" component_1="calcium_background_current"/>
      <map_variables variable_2="Ca_i" variable_1="Ca_i"/>
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