Rendering of the source text

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This CellML file was generated on 16/01/2008 at 16:52:25 using:

COR (0.9.31.857)
Copyright 2002-2008 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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<article>
  <articleinfo>
  <title>Mathematical Model Of An Adult Human Atrial Cell, 1998</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 has been curated and unit checked and is known to run and produce the correct output in PCEnv and COR.
          </para>

  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
Over the past decade, extensive voltage-clamp and action potential data from human atrial myocytes have been published from a number of laboratories.  Based on these experimental data, A. Nygren, C. Fiset, L. Firek, J.W. Clark, D.S. Lindblad, R.B. Clark and W.R. Giles have published a mathematical model of the electrophysiological responses of a representative human atrial cell.  Their model is sufficiently accurate to have predictive capabilities for selected aspects of the electrophysiological responses in the human atrium.  Emphasis has been placed on the functional roles of the K<superscript>+</superscript> currents during repolarisation.
</para>

<para>
The mathematical model is based on the classical formulation of Hodgkin and Huxley (see <ulink url="${HTML_EXMPL_HHSA_INTRO}">The Hodgkin-Huxley Squid Axon Model, 1952</ulink>).  Ionic currents through the sarcolemma are coupled with a fluid compartment model (see the figure below), which accounts for changes in ionic concentrations in the cytoplasm and sarcoplasmic reticulum.
</para>

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

<para>
<ulink url="http://circres.ahajournals.org/cgi/content/abstract/82/1/63">Mathematical Model of an Adult Human Atrial Cell: The Role of K<superscript>+</superscript> Currents in Repolarization,</ulink> A Nygren, C. Fiset, L. Firek, J.W. Clark, D.S. Lindblad, R.B. Clark and W.R. Giles, 1998, <ulink url="http://circres.ahajournals.org/">
            <emphasis>Circulation Research</emphasis>
          </ulink>, 82, 63-81.  (<ulink url="http://circres.ahajournals.org/cgi/content/full/82/1/63">Full text</ulink> and <ulink url="http://circres.ahajournals.org/cgi/reprint/82/1/63.pdf">PDF</ulink> versions of the article are available for Journal Members on the Circulation Research website.)  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=9440706&amp;dopt=Abstract">PubMed ID: 9440706</ulink> 
</para>

<informalfigure float="0" id="fig_fluid_compartment_model">
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    <objectinfo>
      <title>fluid compartment model of a human atrial cell</title>
    </objectinfo>
    <imagedata fileref="nygren_1998.png"/>
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<caption>A fluid compartment model of the human atrial cell, including intracellular, cleft and extracellular spaces.</caption>
</informalfigure>

</sect1>
</article>
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                           <cn cellml:units="dimensionless">2</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <cn cellml:units="second">0.002</cn>
            </apply>
         </apply>
      </math>
   </component>
   <component name="L_type_Ca_channel_f_L1_gate">
      <variable units="dimensionless" public_interface="out" name="f_L_1" initial_value="0.9986"/>
      <variable units="dimensionless" public_interface="out" name="f_L_infinity"/>
      <variable units="second" name="tau_f_L1"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>f_L_1</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>f_L_infinity</ci>
                  <ci>f_L_1</ci>
               </apply>
               <ci>tau_f_L1</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>f_L_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">27.4</cn>
                        </apply>
                        <cn cellml:units="millivolt">7.1</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_f_L1</ci>
            <apply>
               <plus/>
               <apply>
                  <times/>
                  <cn cellml:units="second">0.161</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <minus/>
                        <apply>
                           <power/>
                           <apply>
                              <divide/>
                              <apply>
                                 <plus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">40</cn>
                              </apply>
                              <cn cellml:units="millivolt">14.4</cn>
                           </apply>
                           <cn cellml:units="dimensionless">2</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <cn cellml:units="second">0.01</cn>
            </apply>
         </apply>
      </math>
   </component>
   <component name="L_type_Ca_channel_f_L2_gate">
      <variable units="dimensionless" public_interface="out" name="f_L_2" initial_value="0.9986"/>
      <variable units="second" name="tau_f_L2"/>
      <variable units="dimensionless" public_interface="in" name="f_L_infinity"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>f_L_2</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>f_L_infinity</ci>
                  <ci>f_L_2</ci>
               </apply>
               <ci>tau_f_L2</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_f_L2</ci>
            <apply>
               <plus/>
               <apply>
                  <times/>
                  <cn cellml:units="second">1.3323</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <minus/>
                        <apply>
                           <power/>
                           <apply>
                              <divide/>
                              <apply>
                                 <plus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">40</cn>
                              </apply>
                              <cn cellml:units="millivolt">14.2</cn>
                           </apply>
                           <cn cellml:units="dimensionless">2</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <cn cellml:units="second">0.0626</cn>
            </apply>
         </apply>
      </math>
   </component>
   <component name="Ca_independent_transient_outward_K_current">
      <variable units="picoA" public_interface="out" name="i_t"/>
      <variable units="millivolt" public_interface="out" name="E_K"/>
      <variable units="nanoS" name="g_t" initial_value="7.5"/>
      <variable units="second" public_interface="in" private_interface="out" name="time"/>
      <variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
      <variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
      <variable units="coulomb_per_mole" public_interface="in" name="F"/>
      <variable units="kelvin" public_interface="in" name="T"/>
      <variable units="millimolar" public_interface="in" name="K_c"/>
      <variable units="millimolar" public_interface="in" name="K_i"/>
      <variable units="dimensionless" private_interface="in" name="r"/>
      <variable units="dimensionless" private_interface="in" name="s"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_t</ci>
            <apply>
               <times/>
               <ci>g_t</ci>
               <ci>r</ci>
               <ci>s</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_K</ci>
               </apply>
            </apply>
         </apply>
         <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_c</ci>
                     <ci>K_i</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="Ca_independent_transient_outward_K_current_r_gate">
      <variable units="dimensionless" public_interface="out" name="r" initial_value="0.0010678"/>
      <variable units="second" name="tau_r"/>
      <variable units="dimensionless" name="r_infinity"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>r</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>r_infinity</ci>
                  <ci>r</ci>
               </apply>
               <ci>tau_r</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>r_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">1</cn>
                        </apply>
                        <apply>
                           <minus/>
                           <cn cellml:units="millivolt">11</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_r</ci>
            <apply>
               <plus/>
               <apply>
                  <times/>
                  <cn cellml:units="second">0.0035</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <minus/>
                        <apply>
                           <power/>
                           <apply>
                              <divide/>
                              <ci>V</ci>
                              <cn cellml:units="millivolt">30</cn>
                           </apply>
                           <cn cellml:units="dimensionless">2</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <cn cellml:units="second">0.0015</cn>
            </apply>
         </apply>
      </math>
   </component>
   <component name="Ca_independent_transient_outward_K_current_s_gate">
      <variable units="dimensionless" public_interface="out" name="s" initial_value="0.949"/>
      <variable units="second" name="tau_s"/>
      <variable units="dimensionless" name="s_infinity"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>s</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>s_infinity</ci>
                  <ci>s</ci>
               </apply>
               <ci>tau_s</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>s_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">40.5</cn>
                        </apply>
                        <cn cellml:units="millivolt">11.5</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_s</ci>
            <apply>
               <plus/>
               <apply>
                  <times/>
                  <cn cellml:units="second">0.4812</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <minus/>
                        <apply>
                           <power/>
                           <apply>
                              <divide/>
                              <apply>
                                 <plus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">52.45</cn>
                              </apply>
                              <cn cellml:units="millivolt">14.97</cn>
                           </apply>
                           <cn cellml:units="dimensionless">2</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <cn cellml:units="second">0.01414</cn>
            </apply>
         </apply>
      </math>
   </component>
   <component name="sustained_outward_K_current">
      <variable units="picoA" public_interface="out" name="i_sus"/>
      <variable units="nanoS" name="g_sus" initial_value="2.75"/>
      <variable units="second" 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="r_sus"/>
      <variable units="dimensionless" private_interface="in" name="s_sus"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_sus</ci>
            <apply>
               <times/>
               <ci>g_sus</ci>
               <ci>r_sus</ci>
               <ci>s_sus</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_K</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="sustained_outward_K_current_r_sus_gate">
      <variable units="dimensionless" public_interface="out" name="r_sus" initial_value="0.00015949"/>
      <variable units="second" name="tau_r_sus"/>
      <variable units="dimensionless" name="r_sus_infinity"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>r_sus</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>r_sus_infinity</ci>
                  <ci>r_sus</ci>
               </apply>
               <ci>tau_r_sus</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>r_sus_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">4.3</cn>
                        </apply>
                        <apply>
                           <minus/>
                           <cn cellml:units="millivolt">8</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_r_sus</ci>
            <apply>
               <plus/>
               <apply>
                  <divide/>
                  <cn cellml:units="second">0.009</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">12</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <cn cellml:units="second">0.0005</cn>
            </apply>
         </apply>
      </math>
   </component>
   <component name="sustained_outward_K_current_s_sus_gate">
      <variable units="dimensionless" public_interface="out" name="s_sus" initial_value="0.9912"/>
      <variable units="second" name="tau_s_sus"/>
      <variable units="dimensionless" name="s_sus_infinity"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>s_sus</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>s_sus_infinity</ci>
                  <ci>s_sus</ci>
               </apply>
               <ci>tau_s_sus</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>s_sus_infinity</ci>
            <apply>
               <plus/>
               <apply>
                  <divide/>
                  <cn cellml:units="dimensionless">0.4</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">10</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <cn cellml:units="dimensionless">0.6</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_s_sus</ci>
            <apply>
               <plus/>
               <apply>
                  <divide/>
                  <cn cellml:units="second">0.047</cn>
                  <apply>
                     <plus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <divide/>
                           <apply>
                              <plus/>
                              <ci>V</ci>
                              <cn cellml:units="millivolt">60</cn>
                           </apply>
                           <cn cellml:units="millivolt">10</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <cn cellml:units="second">0.3</cn>
            </apply>
         </apply>
      </math>
   </component>
   <component name="delayed_rectifier_K_currents">
      <variable units="picoA" public_interface="out" name="i_Ks"/>
      <variable units="picoA" public_interface="out" name="i_Kr"/>
      <variable units="nanoS" name="g_Ks" initial_value="1"/>
      <variable units="nanoS" name="g_Kr" initial_value="0.5"/>
      <variable units="second" 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="n"/>
      <variable units="dimensionless" private_interface="in" name="p_a"/>
      <variable units="dimensionless" private_interface="in" name="p_i"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_Ks</ci>
            <apply>
               <times/>
               <ci>g_Ks</ci>
               <ci>n</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_K</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_Kr</ci>
            <apply>
               <times/>
               <ci>g_Kr</ci>
               <ci>p_a</ci>
               <ci>p_i</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_K</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="delayed_rectifier_K_currents_n_gate">
      <variable units="dimensionless" public_interface="out" name="n" initial_value="0.0048357"/>
      <variable units="second" name="tau_n"/>
      <variable units="dimensionless" name="n_infinity"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>n</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>n_infinity</ci>
                  <ci>n</ci>
               </apply>
               <ci>tau_n</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>n_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">19.9</cn>
                        </apply>
                        <apply>
                           <minus/>
                           <cn cellml:units="millivolt">12.7</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_n</ci>
            <apply>
               <plus/>
               <cn cellml:units="second">0.7</cn>
               <apply>
                  <times/>
                  <cn cellml:units="second">0.4</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <minus/>
                        <apply>
                           <power/>
                           <apply>
                              <divide/>
                              <apply>
                                 <minus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">20</cn>
                              </apply>
                              <cn cellml:units="millivolt">20</cn>
                           </apply>
                           <cn cellml:units="dimensionless">2</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="delayed_rectifier_K_currents_pa_gate">
      <variable units="dimensionless" public_interface="out" name="p_a" initial_value="0.0001"/>
      <variable units="second" name="tau_p_a"/>
      <variable units="dimensionless" name="p_a_infinity"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>p_a</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>p_a_infinity</ci>
                  <ci>p_a</ci>
               </apply>
               <ci>tau_p_a</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>p_a_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">15</cn>
                        </apply>
                        <apply>
                           <minus/>
                           <cn cellml:units="millivolt">6</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_p_a</ci>
            <apply>
               <plus/>
               <cn cellml:units="second">0.03118</cn>
               <apply>
                  <times/>
                  <cn cellml:units="second">0.21718</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <minus/>
                        <apply>
                           <power/>
                           <apply>
                              <divide/>
                              <apply>
                                 <plus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">20.1376</cn>
                              </apply>
                              <cn cellml:units="millivolt">22.1996</cn>
                           </apply>
                           <cn cellml:units="dimensionless">2</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="delayed_rectifier_K_currents_pi_gate">
      <variable units="dimensionless" public_interface="out" name="p_i"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>p_i</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">55</cn>
                        </apply>
                        <cn cellml:units="millivolt">24</cn>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="inward_rectifier">
      <variable units="picoA" public_interface="out" name="i_K1"/>
      <variable units="nanoS" name="g_K1" initial_value="3"/>
      <variable units="second" public_interface="in" name="time"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
      <variable units="coulomb_per_mole" public_interface="in" name="F"/>
      <variable units="kelvin" public_interface="in" name="T"/>
      <variable units="millimolar" public_interface="in" name="K_c"/>
      <variable units="millivolt" public_interface="in" name="E_K"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_K1</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>g_K1</ci>
                  <apply>
                     <power/>
                     <apply>
                        <divide/>
                        <ci>K_c</ci>
                        <cn cellml:units="millimolar">1</cn>
                     </apply>
                     <cn cellml:units="dimensionless">0.4457</cn>
                  </apply>
                  <apply>
                     <minus/>
                     <ci>V</ci>
                     <ci>E_K</ci>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <divide/>
                        <apply>
                           <times/>
                           <cn cellml:units="dimensionless">1.5</cn>
                           <apply>
                              <plus/>
                              <apply>
                                 <minus/>
                                 <ci>V</ci>
                                 <ci>E_K</ci>
                              </apply>
                              <cn cellml:units="millivolt">3.6</cn>
                           </apply>
                           <ci>F</ci>
                        </apply>
                        <apply>
                           <times/>
                           <ci>R</ci>
                           <ci>T</ci>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="background_currents">
      <variable units="picoA" public_interface="out" name="i_B_Na"/>
      <variable units="picoA" public_interface="out" name="i_B_Ca"/>
      <variable units="nanoS" name="g_B_Na" initial_value="0.060599"/>
      <variable units="nanoS" name="g_B_Ca" initial_value="0.078681"/>
      <variable units="millivolt" name="E_Ca"/>
      <variable units="millivolt" public_interface="in" name="E_Na"/>
      <variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
      <variable units="coulomb_per_mole" public_interface="in" name="F"/>
      <variable units="kelvin" public_interface="in" name="T"/>
      <variable units="millimolar" public_interface="in" name="Ca_c"/>
      <variable units="millimolar" public_interface="in" name="Ca_i"/>
      <variable units="second" public_interface="in" name="time"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_B_Na</ci>
            <apply>
               <times/>
               <ci>g_B_Na</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_Na</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_B_Ca</ci>
            <apply>
               <times/>
               <ci>g_B_Ca</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_Ca</ci>
               </apply>
            </apply>
         </apply>
         <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_c</ci>
                     <ci>Ca_i</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="sodium_potassium_pump">
      <variable units="picoA" public_interface="out" name="i_NaK"/>
      <variable units="millimolar" name="k_NaK_K" initial_value="1"/>
      <variable units="millimolar" name="k_NaK_Na" initial_value="11"/>
      <variable units="picoA" name="i_NaK_max" initial_value="70.8253"/>
      <variable units="millimolar" public_interface="in" name="K_c"/>
      <variable units="millimolar" public_interface="in" name="Na_i"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_NaK</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <ci>i_NaK_max</ci>
                              <ci>K_c</ci>
                           </apply>
                           <apply>
                              <plus/>
                              <ci>K_c</ci>
                              <ci>k_NaK_K</ci>
                           </apply>
                        </apply>
                        <apply>
                           <power/>
                           <ci>Na_i</ci>
                           <cn cellml:units="dimensionless">1.5</cn>
                        </apply>
                     </apply>
                     <apply>
                        <plus/>
                        <apply>
                           <power/>
                           <ci>Na_i</ci>
                           <cn cellml:units="dimensionless">1.5</cn>
                        </apply>
                        <apply>
                           <power/>
                           <ci>k_NaK_Na</ci>
                           <cn cellml:units="dimensionless">1.5</cn>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <plus/>
                     <ci>V</ci>
                     <cn cellml:units="millivolt">150</cn>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <ci>V</ci>
                  <cn cellml:units="millivolt">200</cn>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="sarcolemmal_calcium_pump_current">
      <variable units="picoA" public_interface="out" name="i_CaP"/>
      <variable units="picoA" name="i_CaP_max" initial_value="4"/>
      <variable units="millimolar" name="k_CaP" initial_value="0.0002"/>
      <variable units="millimolar" public_interface="in" name="Ca_i"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_CaP</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>i_CaP_max</ci>
                  <ci>Ca_i</ci>
               </apply>
               <apply>
                  <plus/>
                  <ci>Ca_i</ci>
                  <ci>k_CaP</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="Na_Ca_ion_exchanger_current">
      <variable units="picoA" public_interface="out" name="i_NaCa"/>
      <variable units="picoA_per_millimolar_4" name="k_NaCa" initial_value="0.0374842"/>
      <variable units="per_millimolar_4" name="d_NaCa" initial_value="0.0003"/>
      <variable units="dimensionless" name="gamma" initial_value="0.45"/>
      <variable units="millimolar" public_interface="in" name="Na_i"/>
      <variable units="millimolar" public_interface="in" name="Na_c"/>
      <variable units="millimolar" public_interface="in" name="Ca_i"/>
      <variable units="millimolar" public_interface="in" name="Ca_c"/>
      <variable units="millijoule_per_mole_kelvin" public_interface="in" name="R"/>
      <variable units="coulomb_per_mole" public_interface="in" name="F"/>
      <variable units="kelvin" public_interface="in" name="T"/>
      <variable units="millivolt" public_interface="in" name="V"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_NaCa</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>k_NaCa</ci>
                  <apply>
                     <minus/>
                     <apply>
                        <times/>
                        <apply>
                           <power/>
                           <ci>Na_i</ci>
                           <cn cellml:units="dimensionless">3</cn>
                        </apply>
                        <ci>Ca_c</ci>
                        <apply>
                           <exp/>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <ci>gamma</ci>
                                 <ci>F</ci>
                                 <ci>V</ci>
                              </apply>
                              <apply>
                                 <times/>
                                 <ci>R</ci>
                                 <ci>T</ci>
                              </apply>
                           </apply>
                        </apply>
                     </apply>
                     <apply>
                        <times/>
                        <apply>
                           <power/>
                           <ci>Na_c</ci>
                           <cn cellml:units="dimensionless">3</cn>
                        </apply>
                        <ci>Ca_i</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>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <times/>
                     <ci>d_NaCa</ci>
                     <apply>
                        <plus/>
                        <apply>
                           <times/>
                           <apply>
                              <power/>
                              <ci>Na_c</ci>
                              <cn cellml:units="dimensionless">3</cn>
                           </apply>
                           <ci>Ca_i</ci>
                        </apply>
                        <apply>
                           <times/>
                           <apply>
                              <power/>
                              <ci>Na_i</ci>
                              <cn cellml:units="dimensionless">3</cn>
                           </apply>
                           <ci>Ca_c</ci>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="intracellular_ion_concentrations">
      <variable units="millimolar" public_interface="out" name="Na_i" initial_value="8.5547"/>
      <variable units="millimolar" public_interface="out" name="Ca_i" initial_value="6.729e-5"/>
      <variable units="millimolar" public_interface="out" name="K_i" initial_value="129.435"/>
      <variable units="millimolar" public_interface="out" name="Ca_d" initial_value="7.2495e-5"/>
      <variable units="picoA" public_interface="out" name="phi_Na_en" initial_value="-1.68"/>
      <variable units="nanolitre" public_interface="out" name="Vol_i" initial_value="0.005884"/>
      <variable units="nanolitre" name="Vol_d"/>
      <variable units="picoA" name="i_di"/>
      <variable units="second" name="tau_di" initial_value="0.01"/>
      <variable units="second" public_interface="in" name="time"/>
      <variable units="coulomb_per_mole" public_interface="in" name="F"/>
      <variable units="picoA" public_interface="in" name="i_Na"/>
      <variable units="picoA" public_interface="in" name="i_Ca_L"/>
      <variable units="picoA" public_interface="in" name="i_B_Na"/>
      <variable units="picoA" public_interface="in" name="i_NaCa"/>
      <variable units="picoA" public_interface="in" name="i_NaK"/>
      <variable units="picoA" public_interface="in" name="i_Ks"/>
      <variable units="picoA" public_interface="in" name="i_Kr"/>
      <variable units="picoA" public_interface="in" name="i_K1"/>
      <variable units="picoA" public_interface="in" name="i_t"/>
      <variable units="picoA" public_interface="in" name="i_sus"/>
      <variable units="picoA" public_interface="in" name="i_CaP"/>
      <variable units="picoA" public_interface="in" name="i_B_Ca"/>
      <variable units="picoA" public_interface="in" name="i_up"/>
      <variable units="picoA" public_interface="in" name="i_rel"/>
      <variable units="per_second" public_interface="in" name="dOCdt"/>
      <variable units="per_second" public_interface="in" name="dOTCdt"/>
      <variable units="per_second" public_interface="in" name="dOTMgCdt"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>Vol_d</ci>
            <apply>
               <times/>
               <cn cellml:units="dimensionless">0.02</cn>
               <ci>Vol_i</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Na_i</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <apply>
                     <plus/>
                     <ci>i_Na</ci>
                     <ci>i_B_Na</ci>
                     <apply>
                        <times/>
                        <cn cellml:units="dimensionless">3</cn>
                        <ci>i_NaK</ci>
                     </apply>
                     <apply>
                        <times/>
                        <cn cellml:units="dimensionless">3</cn>
                        <ci>i_NaCa</ci>
                     </apply>
                     <ci>phi_Na_en</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>Vol_i</ci>
                  <ci>F</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>K_i</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <apply>
                     <minus/>
                     <apply>
                        <plus/>
                        <ci>i_t</ci>
                        <ci>i_sus</ci>
                        <ci>i_K1</ci>
                        <ci>i_Kr</ci>
                        <ci>i_Ks</ci>
                     </apply>
                     <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>i_NaK</ci>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>Vol_i</ci>
                  <ci>F</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ca_i</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <divide/>
                  <apply>
                     <minus/>
                     <apply>
                        <minus/>
                        <apply>
                           <plus/>
                           <apply>
                              <minus/>
                              <apply>
                                 <plus/>
                                 <apply>
                                    <minus/>
                                    <ci>i_di</ci>
                                 </apply>
                                 <ci>i_B_Ca</ci>
                                 <ci>i_CaP</ci>
                              </apply>
                              <apply>
                                 <times/>
                                 <cn cellml:units="dimensionless">2</cn>
                                 <ci>i_NaCa</ci>
                              </apply>
                           </apply>
                           <ci>i_up</ci>
                        </apply>
                        <ci>i_rel</ci>
                     </apply>
                  </apply>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">2</cn>
                     <ci>Vol_i</ci>
                     <ci>F</ci>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <apply>
                     <times/>
                     <cn cellml:units="millimolar">0.08</cn>
                     <ci>dOTCdt</ci>
                  </apply>
                  <apply>
                     <times/>
                     <cn cellml:units="millimolar">0.16</cn>
                     <ci>dOTMgCdt</ci>
                  </apply>
                  <apply>
                     <times/>
                     <cn cellml:units="millimolar">0.045</cn>
                     <ci>dOCdt</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ca_d</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <apply>
                     <plus/>
                     <ci>i_Ca_L</ci>
                     <ci>i_di</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <cn cellml:units="dimensionless">2</cn>
                  <ci>Vol_d</ci>
                  <ci>F</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_di</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <apply>
                     <minus/>
                     <ci>Ca_d</ci>
                     <ci>Ca_i</ci>
                  </apply>
                  <cn cellml:units="dimensionless">2</cn>
                  <ci>F</ci>
                  <ci>Vol_d</ci>
               </apply>
               <ci>tau_di</ci>
            </apply>
         </apply>
      </math>
   </component>
   <component name="intracellular_Ca_buffering">
      <variable units="dimensionless" name="O_C" initial_value="0.0275"/>
      <variable units="per_second" public_interface="out" name="dOCdt"/>
      <variable units="dimensionless" name="O_TC" initial_value="0.0133"/>
      <variable units="per_second" public_interface="out" name="dOTCdt"/>
      <variable units="dimensionless" name="O_TMgC" initial_value="0.1961"/>
      <variable units="per_second" public_interface="out" name="dOTMgCdt"/>
      <variable units="dimensionless" name="O_TMgMg" initial_value="0.7094"/>
      <variable units="millimolar" name="Mg_i" initial_value="2.5"/>
      <variable units="millimolar" public_interface="in" name="Ca_i"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>O_C</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <cn cellml:units="per_millimolar_second">200000</cn>
                  <ci>Ca_i</ci>
                  <apply>
                     <minus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <ci>O_C</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <cn cellml:units="per_second">476</cn>
                  <ci>O_C</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>dOCdt</ci>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>O_C</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>O_TC</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <cn cellml:units="per_millimolar_second">78400</cn>
                  <ci>Ca_i</ci>
                  <apply>
                     <minus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <ci>O_TC</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <cn cellml:units="per_second">392</cn>
                  <ci>O_TC</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>dOTCdt</ci>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>O_TC</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>O_TMgC</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <cn cellml:units="per_millimolar_second">200000</cn>
                  <ci>Ca_i</ci>
                  <apply>
                     <minus/>
                     <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <ci>O_TMgC</ci>
                     </apply>
                     <ci>O_TMgMg</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <cn cellml:units="per_second">6.6</cn>
                  <ci>O_TMgC</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>dOTMgCdt</ci>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>O_TMgC</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>O_TMgMg</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <cn cellml:units="per_millimolar_second">2000</cn>
                  <ci>Mg_i</ci>
                  <apply>
                     <minus/>
                     <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <ci>O_TMgC</ci>
                     </apply>
                     <ci>O_TMgMg</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <cn cellml:units="per_second">666</cn>
                  <ci>O_TMgMg</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="cleft_space_ion_concentrations">
      <variable units="millimolar" public_interface="out" name="Na_c" initial_value="130.011"/>
      <variable units="millimolar" public_interface="out" name="Ca_c" initial_value="1.8147"/>
      <variable units="millimolar" public_interface="out" name="K_c" initial_value="5.3581"/>
      <variable units="nanolitre" public_interface="in" name="Vol_i"/>
      <variable units="nanolitre" name="Vol_c"/>
      <variable units="second" name="tau_Na" initial_value="14.3"/>
      <variable units="second" name="tau_K" initial_value="10"/>
      <variable units="second" name="tau_Ca" initial_value="24.7"/>
      <variable units="millimolar" name="Na_b" initial_value="130"/>
      <variable units="millimolar" name="Ca_b" initial_value="1.8"/>
      <variable units="millimolar" name="K_b" initial_value="5.4"/>
      <variable units="second" public_interface="in" name="time"/>
      <variable units="coulomb_per_mole" public_interface="in" name="F"/>
      <variable units="picoA" public_interface="in" name="i_Na"/>
      <variable units="picoA" public_interface="in" name="i_Ca_L"/>
      <variable units="picoA" public_interface="in" name="i_B_Na"/>
      <variable units="picoA" public_interface="in" name="i_NaCa"/>
      <variable units="picoA" public_interface="in" name="i_NaK"/>
      <variable units="picoA" public_interface="in" name="i_Ks"/>
      <variable units="picoA" public_interface="in" name="i_Kr"/>
      <variable units="picoA" public_interface="in" name="i_K1"/>
      <variable units="picoA" public_interface="in" name="i_t"/>
      <variable units="picoA" public_interface="in" name="i_sus"/>
      <variable units="picoA" public_interface="in" name="i_CaP"/>
      <variable units="picoA" public_interface="in" name="i_B_Ca"/>
      <variable units="picoA" public_interface="in" name="phi_Na_en"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>Vol_c</ci>
            <apply>
               <times/>
               <cn cellml:units="dimensionless">0.136</cn>
               <ci>Vol_i</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Na_c</ci>
            </apply>
            <apply>
               <plus/>
               <apply>
                  <divide/>
                  <apply>
                     <minus/>
                     <ci>Na_b</ci>
                     <ci>Na_c</ci>
                  </apply>
                  <ci>tau_Na</ci>
               </apply>
               <apply>
                  <divide/>
                  <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>
                     <ci>phi_Na_en</ci>
                  </apply>
                  <apply>
                     <times/>
                     <ci>Vol_c</ci>
                     <ci>F</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>K_c</ci>
            </apply>
            <apply>
               <plus/>
               <apply>
                  <divide/>
                  <apply>
                     <minus/>
                     <ci>K_b</ci>
                     <ci>K_c</ci>
                  </apply>
                  <ci>tau_K</ci>
               </apply>
               <apply>
                  <divide/>
                  <apply>
                     <minus/>
                     <apply>
                        <plus/>
                        <ci>i_t</ci>
                        <ci>i_sus</ci>
                        <ci>i_K1</ci>
                        <ci>i_Kr</ci>
                        <ci>i_Ks</ci>
                     </apply>
                     <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>i_NaK</ci>
                     </apply>
                  </apply>
                  <apply>
                     <times/>
                     <ci>Vol_c</ci>
                     <ci>F</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ca_c</ci>
            </apply>
            <apply>
               <plus/>
               <apply>
                  <divide/>
                  <apply>
                     <minus/>
                     <ci>Ca_b</ci>
                     <ci>Ca_c</ci>
                  </apply>
                  <ci>tau_Ca</ci>
               </apply>
               <apply>
                  <divide/>
                  <apply>
                     <minus/>
                     <apply>
                        <plus/>
                        <ci>i_Ca_L</ci>
                        <ci>i_B_Ca</ci>
                        <ci>i_CaP</ci>
                     </apply>
                     <apply>
                        <times/>
                        <cn cellml:units="dimensionless">2</cn>
                        <ci>i_NaCa</ci>
                     </apply>
                  </apply>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">2</cn>
                     <ci>Vol_c</ci>
                     <ci>F</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="Ca_handling_by_the_SR">
      <variable units="picoA" public_interface="out" name="i_rel"/>
      <variable units="picoA" public_interface="out" name="i_up"/>
      <variable units="picoA" name="i_tr"/>
      <variable units="picoA" name="I_up_max" initial_value="2800"/>
      <variable units="millimolar" name="k_cyca" initial_value="0.0003"/>
      <variable units="millimolar" name="k_srca" initial_value="0.5"/>
      <variable units="dimensionless" name="k_xcs" initial_value="0.4"/>
      <variable units="picoA_per_millimolar" name="alpha_rel" initial_value="200000"/>
      <variable units="millimolar" name="Ca_rel" initial_value="0.6465"/>
      <variable units="millimolar" name="Ca_up" initial_value="0.6646"/>
      <variable units="nanolitre" name="Vol_up" initial_value="0.0003969"/>
      <variable units="nanolitre" name="Vol_rel" initial_value="4.41e-5"/>
      <variable units="per_second" name="r_act"/>
      <variable units="per_second" name="r_inact"/>
      <variable units="per_second" name="r_recov" initial_value="0.815"/>
      <variable units="dimensionless" name="O_Calse" initial_value="0.4369"/>
      <variable units="dimensionless" name="F1" initial_value="0.4284"/>
      <variable units="dimensionless" name="F2" initial_value="0.0028"/>
      <variable units="second" name="tau_tr" initial_value="0.01"/>
      <variable units="millimolar" name="k_rel_i" initial_value="0.0003"/>
      <variable units="millimolar" name="k_rel_d" initial_value="0.003"/>
      <variable units="second" public_interface="in" name="time"/>
      <variable units="millimolar" public_interface="in" name="Ca_i"/>
      <variable units="millimolar" public_interface="in" name="Ca_d"/>
      <variable units="coulomb_per_mole" public_interface="in" name="F"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_up</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>I_up_max</ci>
                  <apply>
                     <minus/>
                     <apply>
                        <divide/>
                        <ci>Ca_i</ci>
                        <ci>k_cyca</ci>
                     </apply>
                     <apply>
                        <divide/>
                        <apply>
                           <times/>
                           <apply>
                              <power/>
                              <ci>k_xcs</ci>
                              <cn cellml:units="dimensionless">2</cn>
                           </apply>
                           <ci>Ca_up</ci>
                        </apply>
                        <ci>k_srca</ci>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <apply>
                     <divide/>
                     <apply>
                        <plus/>
                        <ci>Ca_i</ci>
                        <ci>k_cyca</ci>
                     </apply>
                     <ci>k_cyca</ci>
                  </apply>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <ci>k_xcs</ci>
                        <apply>
                           <plus/>
                           <ci>Ca_up</ci>
                           <ci>k_srca</ci>
                        </apply>
                     </apply>
                     <ci>k_srca</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_tr</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <apply>
                     <minus/>
                     <ci>Ca_up</ci>
                     <ci>Ca_rel</ci>
                  </apply>
                  <cn cellml:units="dimensionless">2</cn>
                  <ci>F</ci>
                  <ci>Vol_rel</ci>
               </apply>
               <ci>tau_tr</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_rel</ci>
            <apply>
               <times/>
               <ci>alpha_rel</ci>
               <apply>
                  <power/>
                  <apply>
                     <divide/>
                     <ci>F2</ci>
                     <apply>
                        <plus/>
                        <ci>F2</ci>
                        <cn cellml:units="dimensionless">0.25</cn>
                     </apply>
                  </apply>
                  <cn cellml:units="dimensionless">2</cn>
               </apply>
               <apply>
                  <minus/>
                  <ci>Ca_rel</ci>
                  <ci>Ca_i</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>O_Calse</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <cn cellml:units="per_millimolar_second">480</cn>
                  <ci>Ca_rel</ci>
                  <apply>
                     <minus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <ci>O_Calse</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <cn cellml:units="per_second">400</cn>
                  <ci>O_Calse</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ca_rel</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <divide/>
                  <apply>
                     <minus/>
                     <ci>i_tr</ci>
                     <ci>i_rel</ci>
                  </apply>
                  <apply>
                     <times/>
                     <cn cellml:units="dimensionless">2</cn>
                     <ci>Vol_rel</ci>
                     <ci>F</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <cn cellml:units="millimolar">31</cn>
                  <apply>
                     <diff/>
                     <bvar>
                        <ci>time</ci>
                     </bvar>
                     <ci>O_Calse</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ca_up</ci>
            </apply>
            <apply>
               <divide/>
               <apply>
                  <minus/>
                  <ci>i_up</ci>
                  <ci>i_tr</ci>
               </apply>
               <apply>
                  <times/>
                  <cn cellml:units="dimensionless">2</cn>
                  <ci>Vol_up</ci>
                  <ci>F</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>F1</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>r_recov</ci>
                  <apply>
                     <minus/>
                     <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <ci>F1</ci>
                     </apply>
                     <ci>F2</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>r_act</ci>
                  <ci>F1</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>F2</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>r_act</ci>
                  <ci>F1</ci>
               </apply>
               <apply>
                  <times/>
                  <ci>r_inact</ci>
                  <ci>F2</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>r_act</ci>
            <apply>
               <times/>
               <cn cellml:units="per_second">203.8</cn>
               <apply>
                  <plus/>
                  <apply>
                     <power/>
                     <apply>
                        <divide/>
                        <ci>Ca_i</ci>
                        <apply>
                           <plus/>
                           <ci>Ca_i</ci>
                           <ci>k_rel_i</ci>
                        </apply>
                     </apply>
                     <cn cellml:units="dimensionless">4</cn>
                  </apply>
                  <apply>
                     <power/>
                     <apply>
                        <divide/>
                        <ci>Ca_d</ci>
                        <apply>
                           <plus/>
                           <ci>Ca_d</ci>
                           <ci>k_rel_d</ci>
                        </apply>
                     </apply>
                     <cn cellml:units="dimensionless">4</cn>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>r_inact</ci>
            <apply>
               <plus/>
               <cn cellml:units="per_second">33.96</cn>
               <apply>
                  <times/>
                  <cn cellml:units="per_second">339.6</cn>
                  <apply>
                     <power/>
                     <apply>
                        <divide/>
                        <ci>Ca_i</ci>
                        <apply>
                           <plus/>
                           <ci>Ca_i</ci>
                           <ci>k_rel_i</ci>
                        </apply>
                     </apply>
                     <cn cellml:units="dimensionless">4</cn>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <group>
      <relationship_ref relationship="containment"/>
      <component_ref component="membrane">
         <component_ref component="sodium_current">
            <component_ref component="sodium_current_m_gate"/>
            <component_ref component="sodium_current_h1_gate"/>
            <component_ref component="sodium_current_h2_gate"/>
         </component_ref>
         <component_ref component="L_type_Ca_channel">
            <component_ref component="L_type_Ca_channel_d_L_gate"/>
            <component_ref component="L_type_Ca_channel_f_L1_gate"/>
            <component_ref component="L_type_Ca_channel_f_L2_gate"/>
         </component_ref>
         <component_ref component="Ca_independent_transient_outward_K_current">
            <component_ref component="Ca_independent_transient_outward_K_current_r_gate"/>
            <component_ref component="Ca_independent_transient_outward_K_current_s_gate"/>
         </component_ref>
         <component_ref component="sustained_outward_K_current">
            <component_ref component="sustained_outward_K_current_r_sus_gate"/>
            <component_ref component="sustained_outward_K_current_s_sus_gate"/>
         </component_ref>
         <component_ref component="delayed_rectifier_K_currents">
            <component_ref component="delayed_rectifier_K_currents_n_gate"/>
            <component_ref component="delayed_rectifier_K_currents_pa_gate"/>
            <component_ref component="delayed_rectifier_K_currents_pi_gate"/>
         </component_ref>
         <component_ref component="inward_rectifier"/>
         <component_ref component="background_currents"/>
         <component_ref component="sodium_potassium_pump"/>
         <component_ref component="sarcolemmal_calcium_pump_current"/>
         <component_ref component="Na_Ca_ion_exchanger_current"/>
         <component_ref component="Ca_handling_by_the_SR"/>
         <component_ref component="intracellular_ion_concentrations"/>
         <component_ref component="intracellular_Ca_buffering"/>
         <component_ref component="cleft_space_ion_concentrations"/>
      </component_ref>
   </group>
   <group>
      <relationship_ref relationship="encapsulation"/>
      <component_ref component="sodium_current">
         <component_ref component="sodium_current_m_gate"/>
         <component_ref component="sodium_current_h1_gate"/>
         <component_ref component="sodium_current_h2_gate"/>
      </component_ref>
      <component_ref component="L_type_Ca_channel">
         <component_ref component="L_type_Ca_channel_d_L_gate"/>
         <component_ref component="L_type_Ca_channel_f_L1_gate"/>
         <component_ref component="L_type_Ca_channel_f_L2_gate"/>
      </component_ref>
      <component_ref component="Ca_independent_transient_outward_K_current">
         <component_ref component="Ca_independent_transient_outward_K_current_r_gate"/>
         <component_ref component="Ca_independent_transient_outward_K_current_s_gate"/>
      </component_ref>
      <component_ref component="sustained_outward_K_current">
         <component_ref component="sustained_outward_K_current_r_sus_gate"/>
         <component_ref component="sustained_outward_K_current_s_sus_gate"/>
      </component_ref>
      <component_ref component="delayed_rectifier_K_currents">
         <component_ref component="delayed_rectifier_K_currents_n_gate"/>
         <component_ref component="delayed_rectifier_K_currents_pa_gate"/>
         <component_ref component="delayed_rectifier_K_currents_pi_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="sodium_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="L_type_Ca_channel"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="Ca_independent_transient_outward_K_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="sustained_outward_K_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="delayed_rectifier_K_currents"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="inward_rectifier"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="background_currents"/>
      <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_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="Na_Ca_ion_exchanger_current"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="Ca_handling_by_the_SR"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="intracellular_Ca_buffering"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="intracellular_ion_concentrations"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="cleft_space_ion_concentrations"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="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="L_type_Ca_channel" component_1="membrane"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_Ca_L" variable_1="i_Ca_L"/>
   </connection>
   <connection>
      <map_components component_2="Ca_independent_transient_outward_K_current" component_1="membrane"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_t" variable_1="i_t"/>
      <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="sustained_outward_K_current" component_1="membrane"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_sus" variable_1="i_sus"/>
   </connection>
   <connection>
      <map_components component_2="inward_rectifier" 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="delayed_rectifier_K_currents" 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="i_Ks" variable_1="i_Ks"/>
   </connection>
   <connection>
      <map_components component_2="background_currents" component_1="membrane"/>
      <map_variables variable_2="V" variable_1="V"/>
      <map_variables variable_2="i_B_Na" variable_1="i_B_Na"/>
      <map_variables variable_2="i_B_Ca" variable_1="i_B_Ca"/>
      <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"/>
   </connection>
   <connection>
      <map_components component_2="sarcolemmal_calcium_pump_current" component_1="membrane"/>
      <map_variables variable_2="i_CaP" variable_1="i_CaP"/>
   </connection>
   <connection>
      <map_components component_2="Na_Ca_ion_exchanger_current" 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="intracellular_ion_concentrations" component_1="membrane"/>
      <map_variables variable_2="F" variable_1="F"/>
   </connection>
   <connection>
      <map_components component_2="cleft_space_ion_concentrations" component_1="membrane"/>
      <map_variables variable_2="F" variable_1="F"/>
   </connection>
   <connection>
      <map_components component_2="Ca_handling_by_the_SR" component_1="membrane"/>
      <map_variables variable_2="F" variable_1="F"/>
   </connection>
   <connection>
      <map_components component_2="intracellular_ion_concentrations" component_1="sodium_current"/>
      <map_variables variable_2="i_Na" variable_1="i_Na"/>
      <map_variables variable_2="Na_i" variable_1="Na_i"/>
   </connection>
   <connection>
      <map_components component_2="background_currents" component_1="sodium_current"/>
      <map_variables variable_2="E_Na" variable_1="E_Na"/>
   </connection>
   <connection>
      <map_components component_2="cleft_space_ion_concentrations" component_1="sodium_current"/>
      <map_variables variable_2="i_Na" variable_1="i_Na"/>
      <map_variables variable_2="Na_c" variable_1="Na_c"/>
   </connection>
   <connection>
      <map_components component_2="intracellular_ion_concentrations" component_1="L_type_Ca_channel"/>
      <map_variables variable_2="i_Ca_L" variable_1="i_Ca_L"/>
      <map_variables variable_2="Ca_d" variable_1="Ca_d"/>
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