Location: Luo, Rudy, 1991 @ ea7cd8ef7491 / luo_rudy_1991.cellml

Author:

rcai987 <devnull@localhost>

Date:

2014-12-03 14:17:41+13:00

Desc:

Added a few additional annotations to 1991 luo ruddy model

Permanent Source URI:

https://models.cellml.org/workspace/luo_rudy_1991/rawfile/ea7cd8ef7491c78b504ea81d0693c574675d3c9b/luo_rudy_1991.cellml

<?xml version="1.0"?>
<!--
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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<documentation xmlns="http://cellml.org/tmp-documentation">
<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>
  <imageobject>
    <objectinfo>
      <title>cell diagram of the LR-I model showing ionic currents, pumps and exchangers within the sarcolemma</title>
    </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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               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>i_si</ci>
            <apply>
               <times/>
               <cn cellml:units="milliS_per_cm2">0.09</cn>
               <ci>d</ci>
               <ci>f</ci>
               <apply>
                  <minus/>
                  <ci>V</ci>
                  <ci>E_si</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component cmeta:id="id_00026" name="slow_inward_current_d_gate">
      <variable initial_value="0.00302126301779861" name="d" public_interface="out" units="dimensionless"/>
      <variable name="alpha_d" units="per_millisecond"/>
      <variable name="beta_d" units="per_millisecond"/>
      <variable name="V" public_interface="in" units="millivolt"/>
      <variable name="time" public_interface="in" units="millisecond"/>
      <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 cmeta:id="id_00027" name="slow_inward_current_f_gate">
      <variable initial_value="0.999967936476325" name="f" public_interface="out" units="dimensionless"/>
      <variable name="alpha_f" units="per_millisecond"/>
      <variable name="beta_f" units="per_millisecond"/>
      <variable name="V" public_interface="in" units="millivolt"/>
      <variable name="time" public_interface="in" units="millisecond"/>
      <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 cmeta:id="id_00007" name="time_dependent_potassium_current">
      <variable cmeta:id="id_00034" name="i_K" public_interface="out" units="microA_per_cm2"/>
      <variable cmeta:id="id_00033" name="g_K" units="milliS_per_cm2"/>
      <variable cmeta:id="id_00032" name="E_K" units="millivolt"/>
      <variable initial_value="0.01833" name="PR_NaK" units="dimensionless"/>
      <variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
      <variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
      <variable name="R" public_interface="in" units="joule_per_kilomole_kelvin"/>
      <variable name="T" public_interface="in" units="kelvin"/>
      <variable name="F" public_interface="in" units="coulomb_per_mole"/>
      <variable cmeta:id="id_00035" name="Ko" public_interface="in" units="millimolar"/>
      <variable cmeta:id="id_00036" name="Ki" public_interface="in" units="millimolar"/>
      <variable cmeta:id="id_00037" name="Nao" public_interface="in" units="millimolar"/>
      <variable cmeta:id="id_00038" name="Nai" public_interface="in" units="millimolar"/>
      <variable name="X" private_interface="in" units="dimensionless"/>
      <variable name="Xi" private_interface="in" units="dimensionless"/>
      <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 cmeta:id="id_00008" name="time_dependent_potassium_current_X_gate">
      <variable initial_value="0.0417603108167287" name="X" public_interface="out" units="dimensionless"/>
      <variable name="alpha_X" units="per_millisecond"/>
      <variable name="beta_X" units="per_millisecond"/>
      <variable name="V" public_interface="in" units="millivolt"/>
      <variable name="time" public_interface="in" units="millisecond"/>
      <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 cmeta:id="id_00009" name="time_dependent_potassium_current_Xi_gate">
      <variable name="Xi" public_interface="out" units="dimensionless"/>
      <variable name="V" public_interface="in" units="millivolt"/>
      <variable name="time" public_interface="in" units="millisecond"/>
      <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 cmeta:id="id_00010" name="time_independent_potassium_current">
      <variable cmeta:id="id_00039" name="i_K1" public_interface="out" units="microA_per_cm2"/>
      <variable cmeta:id="id_00040" name="E_K1" private_interface="out" public_interface="out" units="millivolt"/>
      <variable cmeta:id="id_00041" name="g_K1" units="milliS_per_cm2"/>
      <variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
      <variable name="Ko" public_interface="in" units="millimolar"/>
      <variable name="Ki" public_interface="in" units="millimolar"/>
      <variable name="R" public_interface="in" units="joule_per_kilomole_kelvin"/>
      <variable name="T" public_interface="in" units="kelvin"/>
      <variable name="F" public_interface="in" units="coulomb_per_mole"/>
      <variable cmeta:id="id_00047" name="K1_infinity" private_interface="in" units="dimensionless"/>
      <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 cmeta:id="id_00011" name="time_independent_potassium_current_K1_gate">
      <variable name="K1_infinity" public_interface="out" units="dimensionless"/>
      <variable name="alpha_K1" units="per_millisecond"/>
      <variable name="beta_K1" units="per_millisecond"/>
      <variable name="V" public_interface="in" units="millivolt"/>
      <variable cmeta:id="id_00042" name="E_K1" public_interface="in" units="millivolt"/>
      <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 cmeta:id="id_00022" name="plateau_potassium_current">
      <variable cmeta:id="id_00023" name="i_Kp" public_interface="out" units="microA_per_cm2"/>
      <variable cmeta:id="id_00043" name="E_Kp" units="millivolt"/>
      <variable cmeta:id="id_00044" initial_value="0.0183" name="g_Kp" units="milliS_per_cm2"/>
      <variable name="Kp" units="dimensionless"/>
      <variable name="V" public_interface="in" units="millivolt"/>
      <variable cmeta:id="id_00046" name="E_K1" public_interface="in" units="millivolt"/>
      <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 cmeta:id="id_00018" name="background_current">
      <variable cmeta:id="id_00019" name="i_b" public_interface="out" units="microA_per_cm2"/>
      <variable cmeta:id="id_00020" initial_value="-59.87" name="E_b" units="millivolt"/>
      <variable cmeta:id="id_00021" initial_value="0.03921" name="g_b" units="milliS_per_cm2"/>
      <variable name="V" public_interface="in" units="millivolt"/>
      <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 cmeta:id="id_00014" initial_value="140" name="Nao" public_interface="out" units="millimolar"/>
      <variable cmeta:id="id_00015" initial_value="18" name="Nai" public_interface="out" units="millimolar"/>
      <variable cmeta:id="id_00016" initial_value="145" name="Ki" public_interface="out" units="millimolar"/>
      <variable cmeta:id="id_00017" initial_value="5.4" name="Ko" public_interface="out" units="millimolar"/>
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      <variable name="time" public_interface="in" units="millisecond"/>
      <variable cmeta:id="id_00045" name="i_si" public_interface="in" units="microA_per_cm2"/>
      <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"/>
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         <component_ref component="slow_inward_current">
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         </component_ref>
         <component_ref component="time_dependent_potassium_current">
            <component_ref component="time_dependent_potassium_current_X_gate"/>
            <component_ref component="time_dependent_potassium_current_Xi_gate"/>
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         <component_ref component="time_independent_potassium_current">
            <component_ref component="time_independent_potassium_current_K1_gate"/>
         </component_ref>
         <component_ref component="plateau_potassium_current"/>
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         <component_ref component="intracellular_calcium_concentration"/>
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   </group>
   <group>
      <relationship_ref relationship="encapsulation"/>
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      <component_ref component="time_dependent_potassium_current">
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      </component_ref>
      <component_ref component="time_independent_potassium_current">
         <component_ref component="time_independent_potassium_current_K1_gate"/>
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      <map_components component_1="membrane" component_2="environment"/>
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   <connection>
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   <connection>
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   <connection>
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   <connection>
      <map_components component_1="intracellular_calcium_concentration" component_2="environment"/>
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   <connection>
      <map_components component_1="membrane" component_2="fast_sodium_current"/>
      <map_variables variable_1="V" variable_2="V"/>
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   </connection>
   <connection>
      <map_components component_1="membrane" component_2="slow_inward_current"/>
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   </connection>
   <connection>
      <map_components component_1="membrane" component_2="time_dependent_potassium_current"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="i_K" variable_2="i_K"/>
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   </connection>
   <connection>
      <map_components component_1="membrane" component_2="time_independent_potassium_current"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="i_K1" variable_2="i_K1"/>
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   </connection>
   <connection>
      <map_components component_1="membrane" component_2="plateau_potassium_current"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="i_Kp" variable_2="i_Kp"/>
   </connection>
   <connection>
      <map_components component_1="membrane" component_2="background_current"/>
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      <map_variables variable_1="i_b" variable_2="i_b"/>
   </connection>
   <connection>
      <map_components component_1="slow_inward_current" component_2="intracellular_calcium_concentration"/>
      <map_variables variable_1="i_si" variable_2="i_si"/>
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   </connection>
   <connection>
      <map_components component_1="fast_sodium_current" component_2="ionic_concentrations"/>
      <map_variables variable_1="Nao" variable_2="Nao"/>
      <map_variables variable_1="Nai" variable_2="Nai"/>
   </connection>
   <connection>
      <map_components component_1="time_dependent_potassium_current" component_2="ionic_concentrations"/>
      <map_variables variable_1="Ko" variable_2="Ko"/>
      <map_variables variable_1="Ki" variable_2="Ki"/>
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   </connection>
   <connection>
      <map_components component_1="time_independent_potassium_current" component_2="plateau_potassium_current"/>
      <map_variables variable_1="E_K1" variable_2="E_K1"/>
   </connection>
   <connection>
      <map_components component_1="time_independent_potassium_current" component_2="ionic_concentrations"/>
      <map_variables variable_1="Ko" variable_2="Ko"/>
      <map_variables variable_1="Ki" variable_2="Ki"/>
   </connection>
   <connection>
      <map_components component_1="fast_sodium_current" component_2="fast_sodium_current_m_gate"/>
      <map_variables variable_1="m" variable_2="m"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V" variable_2="V"/>
   </connection>
   <connection>
      <map_components component_1="fast_sodium_current" component_2="fast_sodium_current_h_gate"/>
      <map_variables variable_1="h" variable_2="h"/>
      <map_variables variable_1="time" variable_2="time"/>
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   </connection>
   <connection>
      <map_components component_1="fast_sodium_current" component_2="fast_sodium_current_j_gate"/>
      <map_variables variable_1="j" variable_2="j"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V" variable_2="V"/>
   </connection>
   <connection>
      <map_components component_1="slow_inward_current" component_2="slow_inward_current_d_gate"/>
      <map_variables variable_1="d" variable_2="d"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V" variable_2="V"/>
   </connection>
   <connection>
      <map_components component_1="slow_inward_current" component_2="slow_inward_current_f_gate"/>
      <map_variables variable_1="f" variable_2="f"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V" variable_2="V"/>
   </connection>
   <connection>
      <map_components component_1="time_dependent_potassium_current" component_2="time_dependent_potassium_current_X_gate"/>
      <map_variables variable_1="X" variable_2="X"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="V" variable_2="V"/>
   </connection>
   <connection>
      <map_components component_1="time_dependent_potassium_current" component_2="time_dependent_potassium_current_Xi_gate"/>
      <map_variables variable_1="Xi" variable_2="Xi"/>
      <map_variables variable_1="time" variable_2="time"/>
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   </connection>
   <connection>
      <map_components component_1="time_independent_potassium_current" component_2="time_independent_potassium_current_K1_gate"/>
      <map_variables variable_1="K1_infinity" variable_2="K1_infinity"/>
      <map_variables variable_1="V" variable_2="V"/>
      <map_variables variable_1="E_K1" variable_2="E_K1"/>
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