Location: Luo, Rudy, 1991 @ 88c466ea509f / luo_rudy_1991.cellml

Author:
Catherine Lloyd <c.lloyd@auckland.ac.nz>
Date:
2010-07-14 05:26:33+12:00
Desc:
Model changed to one which is at steady state.
Permanent Source URI:
https://models.cellml.org/workspace/luo_rudy_1991/rawfile/88c466ea509fa9d83741b89def0bdb4208c3fde7/luo_rudy_1991.cellml

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<!--
This CellML file was generated on 06/11/2007 at 17:08:44 using:

COR (0.9.31.807)
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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<article>
  <articleinfo>
  <title>Luo-Rudy Mammalian Ventricular Model I 1991</title>
  <author>
    <firstname>Catherine</firstname>
          <surname>Lloyd</surname>
    <affiliation>
      <shortaffil>Auckland Bioengineering Institute, The 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 replicate the published results in OpenCell and COR.
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
In 1991, Ching-hsing Luo and Yoram Rudy published a mathematical model of the ventricular cardiac action potential.  This original model is the first of the two Luo-Rudy models, and it has subsequently come to be known as the Luo-Rudy I model.  It is a significant update of the Beeler-Reuter mammalian ventricular model (1977) (see the figure below), and like the the Beeler-Reuter model, the Luo-Rudy I model uses Hodgkin-Huxley type equations to calculate ionic currents.
</para>

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

<para>
A Model of the Ventricular Cardiac Action Potential - Depolarisation, Repolarisation and Their Interaction, Ching-hsing Luo and Yoram Rudy, 1991 <emphasis>Circulation Research</emphasis>, 68, 1501-1526.  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=1709839&amp;dopt=Abstract">PubMed ID: 1709839</ulink> 
</para>

<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
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    <objectinfo>
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    </objectinfo>
    <imagedata fileref="luo_rudy_i_1991.png"/>
  </imageobject>
</mediaobject>
<caption>A schematic diagram describing the current flows across the cell membrane that are captured in the LR-I model.</caption>
</informalfigure>

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

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      <variable name="d" units="dimensionless" initial_value="0.00302126301779861" public_interface="out"/>
      <variable name="alpha_d" units="per_millisecond"/>
      <variable name="beta_d" units="per_millisecond"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>alpha_d</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn cellml:units="per_millisecond">0.095</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <times/>
                        <apply>
                           <minus/>
                           <cn cellml:units="per_millivolt">0.01</cn>
                        </apply>
                        <apply>
                           <minus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">5</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <times/>
                        <apply>
                           <minus/>
                           <cn cellml:units="per_millivolt">0.072</cn>
                        </apply>
                        <apply>
                           <minus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">5</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_d</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn cellml:units="per_millisecond">0.07</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <times/>
                        <apply>
                           <minus/>
                           <cn cellml:units="per_millivolt">0.017</cn>
                        </apply>
                        <apply>
                           <plus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">44</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <times/>
                        <cn cellml:units="per_millivolt">0.05</cn>
                        <apply>
                           <plus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">44</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>d</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>alpha_d</ci>
                  <apply>
                     <minus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <ci>d</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>beta_d</ci>
                  <ci>d</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="slow_inward_current_f_gate">
      <variable name="f" units="dimensionless" initial_value="0.999967936476325" public_interface="out"/>
      <variable name="alpha_f" units="per_millisecond"/>
      <variable name="beta_f" units="per_millisecond"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>alpha_f</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn cellml:units="per_millisecond">0.012</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <times/>
                        <apply>
                           <minus/>
                           <cn cellml:units="per_millivolt">0.008</cn>
                        </apply>
                        <apply>
                           <plus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">28</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <times/>
                        <cn cellml:units="per_millivolt">0.15</cn>
                        <apply>
                           <plus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">28</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_f</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn cellml:units="per_millisecond">0.0065</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <times/>
                        <apply>
                           <minus/>
                           <cn cellml:units="per_millivolt">0.02</cn>
                        </apply>
                        <apply>
                           <plus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">30</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <times/>
                        <apply>
                           <minus/>
                           <cn cellml:units="per_millivolt">0.2</cn>
                        </apply>
                        <apply>
                           <plus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">30</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>f</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>alpha_f</ci>
                  <apply>
                     <minus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <ci>f</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>beta_f</ci>
                  <ci>f</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="time_dependent_potassium_current">
      <variable name="i_K" units="microA_per_cm2" public_interface="out"/>
      <variable name="g_K" units="milliS_per_cm2"/>
      <variable name="E_K" units="millivolt"/>
      <variable name="PR_NaK" units="dimensionless" initial_value="0.01833"/>
      <variable name="time" units="millisecond" public_interface="in" private_interface="out"/>
      <variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
      <variable name="R" units="joule_per_kilomole_kelvin" public_interface="in"/>
      <variable name="T" units="kelvin" public_interface="in"/>
      <variable name="F" units="coulomb_per_mole" public_interface="in"/>
      <variable name="Ko" units="millimolar" public_interface="in"/>
      <variable name="Ki" units="millimolar" public_interface="in"/>
      <variable name="Nao" units="millimolar" public_interface="in"/>
      <variable name="Nai" units="millimolar" public_interface="in"/>
      <variable name="X" units="dimensionless" private_interface="in"/>
      <variable name="Xi" units="dimensionless" private_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>g_K</ci>
            <apply>
               <times/>
               <cn cellml:units="milliS_per_cm2">0.282</cn>
               <apply>
                  <root/>
                  <apply>
                     <divide/>
                     <ci>Ko</ci>
                     <cn cellml:units="millimolar">5.4</cn>
                  </apply>
               </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/>
                     <apply>
                        <plus/>
                        <ci>Ko</ci>
                        <apply>
                           <times/>
                           <ci>PR_NaK</ci>
                           <ci>Nao</ci>
                        </apply>
                     </apply>
                     <apply>
                        <plus/>
                        <ci>Ki</ci>
                        <apply>
                           <times/>
                           <ci>PR_NaK</ci>
                           <ci>Nai</ci>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_K</ci>
            <apply>
               <times/>
               <ci>g_K</ci>
               <ci>X</ci>
               <ci>Xi</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_K</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="time_dependent_potassium_current_X_gate">
      <variable name="X" units="dimensionless" initial_value="0.0417603108167287" public_interface="out"/>
      <variable name="alpha_X" units="per_millisecond"/>
      <variable name="beta_X" units="per_millisecond"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>alpha_X</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn cellml:units="per_millisecond">0.0005</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <times/>
                        <cn cellml:units="per_millivolt">0.083</cn>
                        <apply>
                           <plus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">50</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <times/>
                        <cn cellml:units="per_millivolt">0.057</cn>
                        <apply>
                           <plus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">50</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_X</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <cn cellml:units="per_millisecond">0.0013</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <times/>
                        <apply>
                           <minus/>
                           <cn cellml:units="per_millivolt">0.06</cn>
                        </apply>
                        <apply>
                           <plus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">20</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <times/>
                        <apply>
                           <minus/>
                           <cn cellml:units="per_millivolt">0.04</cn>
                        </apply>
                        <apply>
                           <plus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">20</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>X</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>alpha_X</ci>
                  <apply>
                     <minus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <ci>X</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>beta_X</ci>
                  <ci>X</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="time_dependent_potassium_current_Xi_gate">
      <variable name="Xi" units="dimensionless" public_interface="out"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>Xi</ci>
            <piecewise>
               <piece>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <cn cellml:units="millivolt">2.837</cn>
                        <apply>
                           <minus/>
                           <apply>
                              <exp/>
                              <apply>
                                 <times/>
                                 <cn cellml:units="per_millivolt">0.04</cn>
                                 <apply>
                                    <plus/>
                                    <ci>V</ci>
                                    <cn cellml:units="millivolt">77</cn>
                                 </apply>
                              </apply>
                           </apply>
                           <cn cellml:units="dimensionless">1</cn>
                        </apply>
                     </apply>
                     <apply>
                        <times/>
                        <apply>
                           <plus/>
                           <ci>V</ci>
                           <cn cellml:units="millivolt">77</cn>
                        </apply>
                        <apply>
                           <exp/>
                           <apply>
                              <times/>
                              <cn cellml:units="per_millivolt">0.04</cn>
                              <apply>
                                 <plus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">35</cn>
                              </apply>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <gt/>
                     <ci>V</ci>
                     <apply>
                        <minus/>
                        <cn cellml:units="millivolt">100</cn>
                     </apply>
                  </apply>
               </piece>
               <otherwise>
                  <cn cellml:units="dimensionless">1</cn>
               </otherwise>
            </piecewise>
         </apply>
      </math>
   </component>
   <component name="time_independent_potassium_current">
      <variable name="i_K1" units="microA_per_cm2" public_interface="out"/>
      <variable name="E_K1" units="millivolt" public_interface="out" private_interface="out"/>
      <variable name="g_K1" units="milliS_per_cm2"/>
      <variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
      <variable name="Ko" units="millimolar" public_interface="in"/>
      <variable name="Ki" units="millimolar" public_interface="in"/>
      <variable name="R" units="joule_per_kilomole_kelvin" public_interface="in"/>
      <variable name="T" units="kelvin" public_interface="in"/>
      <variable name="F" units="coulomb_per_mole" public_interface="in"/>
      <variable name="K1_infinity" units="dimensionless" private_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>g_K1</ci>
            <apply>
               <times/>
               <cn cellml:units="milliS_per_cm2">0.6047</cn>
               <apply>
                  <root/>
                  <apply>
                     <divide/>
                     <ci>Ko</ci>
                     <cn cellml:units="millimolar">5.4</cn>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>E_K1</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <ci>R</ci>
                     <ci>T</ci>
                  </apply>
                  <ci>F</ci>
               </apply>
               <apply>
                  <ln/>
                  <apply>
                     <divide/>
                     <ci>Ko</ci>
                     <ci>Ki</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_K1</ci>
            <apply>
               <times/>
               <ci>g_K1</ci>
               <ci>K1_infinity</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_K1</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="time_independent_potassium_current_K1_gate">
      <variable name="K1_infinity" units="dimensionless" public_interface="out"/>
      <variable name="alpha_K1" units="per_millisecond"/>
      <variable name="beta_K1" units="per_millisecond"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="E_K1" units="millivolt" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>alpha_K1</ci>
            <apply>
               <divide/>
               <cn cellml:units="per_millisecond">1.02</cn>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <times/>
                        <cn cellml:units="per_millivolt">0.2385</cn>
                        <apply>
                           <minus/>
                           <apply>
                              <minus/>
                              <ci>V</ci>
                              <ci>E_K1</ci>
                           </apply>
                           <cn cellml:units="millivolt">59.215</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>beta_K1</ci>
            <apply>
               <divide/>
               <apply>
                  <plus/>
                  <apply>
                     <times/>
                     <cn cellml:units="per_millisecond">0.49124</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <times/>
                           <cn cellml:units="per_millivolt">0.08032</cn>
                           <apply>
                              <minus/>
                              <apply>
                                 <plus/>
                                 <ci>V</ci>
                                 <cn cellml:units="millivolt">5.476</cn>
                              </apply>
                              <ci>E_K1</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <times/>
                     <cn cellml:units="per_millisecond">1</cn>
                     <apply>
                        <exp/>
                        <apply>
                           <times/>
                           <cn cellml:units="per_millivolt">0.06175</cn>
                           <apply>
                              <minus/>
                              <ci>V</ci>
                              <apply>
                                 <plus/>
                                 <ci>E_K1</ci>
                                 <cn cellml:units="millivolt">594.31</cn>
                              </apply>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">1</cn>
                  <apply>
                     <exp/>
                     <apply>
                        <times/>
                        <apply>
                           <minus/>
                           <cn cellml:units="per_millivolt">0.5143</cn>
                        </apply>
                        <apply>
                           <plus/>
                           <apply>
                              <minus/>
                              <ci>V</ci>
                              <ci>E_K1</ci>
                           </apply>
                           <cn cellml:units="millivolt">4.753</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>K1_infinity</ci>
            <apply>
               <divide/>
               <ci>alpha_K1</ci>
               <apply>
                  <plus/>
                  <ci>alpha_K1</ci>
                  <ci>beta_K1</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="plateau_potassium_current">
      <variable name="i_Kp" units="microA_per_cm2" public_interface="out"/>
      <variable name="E_Kp" units="millivolt"/>
      <variable name="g_Kp" units="milliS_per_cm2" initial_value="0.0183"/>
      <variable name="Kp" units="dimensionless"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <variable name="E_K1" units="millivolt" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>E_Kp</ci>
            <ci>E_K1</ci>
         </apply>
         <apply>
            <eq/>
            <ci>Kp</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>
         <apply>
            <eq/>
            <ci>i_Kp</ci>
            <apply>
               <times/>
               <ci>g_Kp</ci>
               <ci>Kp</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_Kp</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="background_current">
      <variable name="i_b" units="microA_per_cm2" public_interface="out"/>
      <variable name="E_b" units="millivolt" initial_value="-59.87"/>
      <variable name="g_b" units="milliS_per_cm2" initial_value="0.03921"/>
      <variable name="V" units="millivolt" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>i_b</ci>
            <apply>
               <times/>
               <ci>g_b</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_b</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="ionic_concentrations">
      <variable name="Nao" units="millimolar" initial_value="140" public_interface="out"/>
      <variable name="Nai" units="millimolar" initial_value="18" public_interface="out"/>
      <variable name="Ki" units="millimolar" initial_value="145" public_interface="out"/>
      <variable name="Ko" units="millimolar" initial_value="5.4" public_interface="out"/>
   </component>
   <component name="intracellular_calcium_concentration">
      <variable name="Cai" units="millimolar" initial_value="0.00017948816388306" public_interface="out"/>
      <variable name="time" units="millisecond" public_interface="in"/>
      <variable name="i_si" units="microA_per_cm2" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Cai</ci>
            </apply>
            <apply>
               <plus/>
               <apply>
                  <times/>
                  <apply>
                     <divide/>
                     <apply>
                        <minus/>
                        <cn cellml:units="per_1000_centimetre">0.0001</cn>
                     </apply>
                     <cn cellml:units="coulomb_per_mole">1</cn>
                  </apply>
                  <ci>i_si</ci>
               </apply>
               <apply>
                  <times/>
                  <cn cellml:units="per_millisecond">0.07</cn>
                  <apply>
                     <minus/>
                     <cn cellml:units="millimolar">0.0001</cn>
                     <ci>Cai</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <group>
      <relationship_ref relationship="containment"/>
      <component_ref component="membrane">
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