Location: Hund, Rudy, 2004 @ 6785825aeb7b / hund_rudy_2004_a.cellml

Author:
Hanne <Hanne@hanne-nielsens-macbook.local>
Date:
2009-12-09 10:47:48+13:00
Desc:
Added images in ai and svg fomrat, removed non pub med references
Permanent Source URI:
https://models.fieldml.org/workspace/hund_rudy_2004/rawfile/6785825aeb7b31a34854bfc24a31b7cfedeee176/hund_rudy_2004_a.cellml

<?xml version="1.0"?>
<!--
This CellML file was generated on 28/01/2008 at 16:45:18 using:

COR (0.9.31.863)
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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        <author>
          <firstname>Penny</firstname>
          <surname>Noble</surname>
          <affiliation>
            <shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
          </affiliation>
        </author>
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      <section id="sec_status">
        <title>Model Status</title>
        <para>
        This CellML version of the model has been checked in COR and PCEnv. A stimulus protocol has been added to allow the model to simulate action potentials for 5 seconds. The units are consistent and the model runs to recreate the published results. The parameter 'tissue' has been added to switch between the original (default value 0) and 'tissue' (any other value, for example 1) models.
          </para>
      </section>
      <sect1 id="sec_structure">
        <title>Model Structure</title>
        <para>
In the paper described here, Thomas Hund and Yoram Rudy present a detailed, and physiologically realistic, mathematical model of a canine ventricular cell.  Model simulations are able to recreate the rate-dependent phenomena associated with ion-channel kinetics, action potential properties, and calcium ion handling.  The model is based on an epicardial myocyte because these cells contain the largest transient outward potassium current (when compared with endocardial or midmyocardial myocytes).  The calcium/calmodulin-dependent protein kinase (CaMKII) regulatory pathway was embedded within the electrophysiological model, incorporating calcium-release formulation, calcium subspace, and dynamic chloride handling.  Results from the model simulations revealed CaMKII is an important determinant of the rate dependence of the calcium transient, but not of the action potential duration, which depends instead on the ion-channel kinetics.
</para>
        <informalfigure float="0" id="fig_reaction_diagram">
          <mediaobject>
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              <objectinfo>
                <title>model diagram</title>
              </objectinfo>
              <imagedata fileref="hund_2004.png"/>
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          <caption>Schematic diagram of the Hund and Rudy 2004 Canine Ventricular Cell Model.</caption>
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        <para>
The complete original paper reference is cited below:
</para>
        <para>
Rate dependence and regulation of action potential and calcium transient in a canine cardiac ventricular cell model, Thomas J. Hund and Yoram Rudy, 2004, 
            <emphasis>Circulation</emphasis>, 
           110, 3168-3174. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&amp;cmd=Retrieve&amp;dopt=AbstractPlus&amp;list_uids=15505083&amp;query_hl=1&amp;itool=pubmed_docsum">PubMed ID: 15505083</ulink>
</para>
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        <eq/>
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          <divide/>
          <apply>
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              <exp/>
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            <ci>K_o</ci>
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          <apply>
            <plus/>
            <ci>K_o</ci>
            <ci>kmko</ci>
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        </apply>
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                <ci>KmCa</ci>
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        <ci>num</ci>
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          <minus/>
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              <power/>
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                <ci>FonRT</ci>
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              <power/>
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            <ci>ca_i_NaCa</ci>
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              <exp/>
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                  <minus/>
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                <ci>V</ci>
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      <apply>
        <eq/>
        <ci>denom1</ci>
        <apply>
          <plus/>
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            <ci>ksat</ci>
            <apply>
              <exp/>
              <apply>
                <times/>
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                  <minus/>
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                <ci>V</ci>
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      <apply>
        <eq/>
        <ci>denom2</ci>
        <apply>
          <plus/>
          <apply>
            <times/>
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            <apply>
              <power/>
              <ci>Na_i</ci>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
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              <power/>
              <ci>KmNao</ci>
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            <ci>ca_i_NaCa</ci>
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            <times/>
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              <power/>
              <ci>KmNai</ci>
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            <ci>Ca_o</ci>
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              <plus/>
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          </apply>
        </apply>
      </apply>
    </math>
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        <eq/>
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          <divide/>
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            <times/>
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          <apply>
            <plus/>
            <ci>kmpca</ci>
            <ci>Ca_i</ci>
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        </apply>
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    </math>
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  <component name="ICab">
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    <variable name="FonRT" public_interface="in" units="per_mV"/>
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    <variable name="Ca_o" public_interface="in" units="mM"/>
    <variable name="ICab" public_interface="out" units="uA_per_uF"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
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        <eq/>
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          <divide/>
          <apply>
            <times/>
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                <times/>
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                  <exp/>
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                    <times/>
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              <apply>
                <times/>
                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.341</cn>
                <ci>Ca_o</ci>
              </apply>
            </apply>
          </apply>
          <apply>
            <minus/>
            <apply>
              <exp/>
              <apply>
                <times/>
                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                <ci>V</ci>
                <ci>FonRT</ci>
              </apply>
            </apply>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="Ito2">
    <variable name="time" public_interface="in" units="ms"/>
    <variable name="V" public_interface="in" units="mV"/>
    <variable name="F" public_interface="in" units="C_per_mole"/>
    <variable name="FonRT" public_interface="in" units="per_mV"/>
    <variable name="Cl_i" public_interface="in" units="mM"/>
    <variable name="Cl_o" public_interface="in" units="mM"/>
    <variable name="Ca_ss" public_interface="in" units="mM"/>
    <variable initial_value="4e-7" name="PCl" units="L_per_F_ms"/>
    <variable initial_value="0.000816605172" name="AA" units="dimensionless"/>
    <variable name="Ito2_max" units="uA_per_uF"/>
    <variable name="AAss" units="dimensionless"/>
    <variable initial_value="0.1502" name="Kmto2" units="mM"/>
    <variable name="Ito2" public_interface="out" units="uA_per_uF"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <ci>Ito2_max</ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci>PCl</ci>
            <ci>V</ci>
            <ci>F</ci>
            <ci>FonRT</ci>
            <apply>
              <minus/>
              <ci>Cl_i</ci>
              <apply>
                <times/>
                <ci>Cl_o</ci>
                <apply>
                  <exp/>
                  <apply>
                    <times/>
                    <ci>V</ci>
                    <ci>FonRT</ci>
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                </apply>
              </apply>
            </apply>
          </apply>
          <apply>
            <minus/>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
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                <ci>V</ci>
                <ci>FonRT</ci>
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        </apply>
      </apply>
      <apply>
        <eq/>
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          <divide/>
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            <plus/>
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            <apply>
              <divide/>
              <ci>Kmto2</ci>
              <ci>Ca_ss</ci>
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          </apply>
        </apply>
      </apply>
      <apply>
        <eq/>
        <ci>Ito2</ci>
        <apply>
          <times/>
          <ci>Ito2_max</ci>
          <ci>AA</ci>
        </apply>
      </apply>
      <apply>
        <eq/>
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          <diff/>
          <bvar>
            <ci>time</ci>
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          <ci>AA</ci>
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        <apply>
          <divide/>
          <apply>
            <minus/>
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            <ci>AA</ci>
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          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1</cn>
        </apply>
      </apply>
    </math>
  </component>
  <component name="IClb">
    <variable name="V" public_interface="in" units="mV"/>
    <variable name="ECl" public_interface="in" units="mV"/>
    <variable initial_value="2.25e-4" name="GClb" units="mS_per_uF"/>
    <variable name="IClb" public_interface="out" units="uA_per_uF"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <ci>IClb</ci>
        <apply>
          <times/>
          <ci>GClb</ci>
          <apply>
            <minus/>
            <ci>V</ci>
            <ci>ECl</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="INal">
    <variable name="time" public_interface="in" units="ms"/>
    <variable name="V" public_interface="in" units="mV"/>
    <variable name="ENa" public_interface="in" units="mV"/>
    <variable initial_value="65e-4" name="GNaL" units="mS_per_uF"/>
    <variable initial_value="0.001356538159" name="mL" units="dimensionless"/>
    <variable initial_value="0.26130711759" name="hL" units="dimensionless"/>
    <variable name="amL" units="per_ms"/>
    <variable name="bmL" units="per_ms"/>
    <variable name="hLss" units="dimensionless"/>
    <variable name="INal" public_interface="out" units="uA_per_uF"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <ci>INal</ci>
        <apply>
          <times/>
          <ci>GNaL</ci>
          <apply>
            <power/>
            <ci>mL</ci>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
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          <ci>hL</ci>
          <apply>
            <minus/>
            <ci>V</ci>
            <ci>ENa</ci>
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        </apply>
      </apply>
      <apply>
        <eq/>
        <ci>amL</ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_ms">0.32</cn>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_mV">1</cn>
            <apply>
              <plus/>
              <ci>V</ci>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mV">47.13</cn>
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          </apply>
          <apply>
            <minus/>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
            <apply>
              <exp/>
              <apply>
                <times/>
                <apply>
                  <minus/>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_mV">0.1</cn>
                </apply>
                <apply>
                  <plus/>
                  <ci>V</ci>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mV">47.13</cn>
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              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq/>
        <ci>bmL</ci>
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          <times/>
          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_ms">0.08</cn>
          <apply>
            <exp/>
            <apply>
              <divide/>
              <apply>
                <minus/>
                <ci>V</ci>
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              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mV">11</cn>
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          </apply>
        </apply>
      </apply>
      <apply>
        <eq/>
        <ci>hLss</ci>
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          <apply>
            <plus/>
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            <apply>
              <exp/>
              <apply>
                <divide/>
                <apply>
                  <plus/>
                  <ci>V</ci>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mV">91</cn>
                </apply>
                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mV">6.1</cn>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>mL</ci>
        </apply>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci>amL</ci>
            <apply>
              <minus/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
              <ci>mL</ci>
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          </apply>
          <apply>
            <times/>
            <ci>bmL</ci>
            <ci>mL</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq/>
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          <diff/>
          <bvar>
            <ci>time</ci>
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          <ci>hL</ci>
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        <apply>
          <divide/>
          <apply>
            <minus/>
            <ci>hLss</ci>
            <ci>hL</ci>
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          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">600</cn>
        </apply>
      </apply>
    </math>
  </component>
  <component name="reversal_potentials">
    <variable name="Na_i" public_interface="in" units="mM"/>
    <variable name="Na_o" public_interface="in" units="mM"/>
    <variable name="K_o" public_interface="in" units="mM"/>
    <variable name="K_i" public_interface="in" units="mM"/>
    <variable name="Cl_o" public_interface="in" units="mM"/>
    <variable name="Cl_i" public_interface="in" units="mM"/>
    <variable name="FonRT" public_interface="in" units="per_mV"/>
    <variable initial_value="0.01833" name="prnak" units="dimensionless"/>
    <variable name="ENa" public_interface="out" units="mV"/>
    <variable name="EK" public_interface="out" units="mV"/>
    <variable name="EKs" public_interface="out" units="mV"/>
    <variable name="ECl" public_interface="out" units="mV"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <ci>ENa</ci>
        <apply>
          <divide/>
          <apply>
            <ln/>
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              <divide/>
              <ci>Na_o</ci>
              <ci>Na_i</ci>
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          </apply>
          <ci>FonRT</ci>
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      <apply>
        <eq/>
        <ci>EK</ci>
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          <divide/>
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            <ln/>
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              <divide/>
              <ci>K_o</ci>
              <ci>K_i</ci>
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          </apply>
          <ci>FonRT</ci>
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      <apply>
        <eq/>
        <ci>EKs</ci>
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          <divide/>
          <apply>
            <ln/>
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              <divide/>
              <apply>
                <plus/>
                <ci>K_o</ci>
                <apply>
                  <times/>
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                  <ci>Na_o</ci>
                </apply>
              </apply>
              <apply>
                <plus/>
                <ci>K_i</ci>
                <apply>
                  <times/>
                  <ci>prnak</ci>
                  <ci>Na_i</ci>
                </apply>
              </apply>
            </apply>
          </apply>
          <ci>FonRT</ci>
        </apply>
      </apply>
      <apply>
        <eq/>
        <ci>ECl</ci>
        <apply>
          <divide/>
          <apply>
            <minus/>
            <apply>
              <ln/>
              <apply>
                <divide/>
                <ci>Cl_o</ci>
                <ci>Cl_i</ci>
              </apply>
            </apply>
          </apply>
          <ci>FonRT</ci>
        </apply>
      </apply>
    </math>
  </component>
  <component name="Irel">
    <variable name="time" public_interface="in" units="ms"/>
    <variable name="tissue" public_interface="in" units="dimensionless"/>
    <variable name="Ca_ss" public_interface="in" units="mM"/>
    <variable name="Ca_jsr" public_interface="in" units="mM"/>
    <variable name="ibarca" public_interface="in" units="uA_per_uF"/>
    <variable name="ICaL" public_interface="in" units="uA_per_uF"/>
    <variable name="Grel" units="per_ms"/>
    <variable name="dro_inf" units="dimensionless"/>
    <variable initial_value="10" name="dtau_rel_max" units="ms"/>
    <variable name="dtau_rel" units="ms"/>
    <variable name="ross" units="dimensionless"/>
    <variable name="riss" units="dimensionless"/>
    <variable name="tauri" units="ms"/>
    <variable name="irelcicr" public_interface="out" units="mM_per_ms"/>
    <variable initial_value="0.05" name="CaMK0" units="dimensionless"/>
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    <variable initial_value="0.15" name="KmCaMK" public_interface="out" units="dimensionless"/>
    <variable name="CaMKbound" units="dimensionless"/>
    <variable name="CaMKactive" public_interface="out" units="dimensionless"/>
    <variable initial_value="0.021123704774" name="CaMKtrap" units="dimensionless"/>
    <variable initial_value="0" name="ro" units="dimensionless"/>
    <variable initial_value="0.862666650318" name="ri" units="dimensionless"/>
    <variable name="vg" units="dimensionless"/>
    <variable name="cafac" units="dimensionless"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <ci>CaMKbound</ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci>CaMK0</ci>
            <apply>
              <minus/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
              <ci>CaMKtrap</ci>
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          </apply>
          <apply>
            <plus/>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
            <apply>
              <divide/>
              <ci>Km</ci>
              <ci>Ca_ss</ci>
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          </apply>
        </apply>
      </apply>
      <apply>
        <eq/>
        <ci>CaMKactive</ci>
        <apply>
          <plus/>
          <ci>CaMKbound</ci>
          <ci>CaMKtrap</ci>
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      </apply>
      <apply>
        <eq/>
        <ci>Grel</ci>
        <apply>
          <times/>
          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_ms">3000</cn>
          <ci>vg</ci>
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      </apply>
      <apply>
        <eq/>
        <ci>vg</ci>
        <piecewise>
          <piece>
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              <apply>
                <plus/>
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                <apply>
                  <exp/>
                  <apply>
                    <divide/>
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                      <plus/>
                      <ci>ibarca</ci>
                      <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="uA_per_uF">13</cn>
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                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="uA_per_uF">5</cn>
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                </apply>
              </apply>
            </apply>
            <apply>
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              <ci>tissue</ci>
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          <otherwise>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
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        </piecewise>
      </apply>
      <apply>
        <eq/>
        <ci>cafac</ci>
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            <apply>
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              <apply>
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                  <plus/>
                  <ci>ICaL</ci>
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                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="uA_per_uF">0.015</cn>
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            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
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        <ci>dro_inf</ci>
        <apply>
          <divide/>
          <apply>
            <power/>
            <ci>Ca_jsr</ci>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.9</cn>
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          <apply>
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            <apply>
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              <ci>Ca_jsr</ci>
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            <apply>
              <power/>
              <apply>
                <divide/>
                <apply>
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                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM">49.28</cn>
                  <ci>Ca_ss</ci>
                </apply>
                <apply>
                  <plus/>
                  <ci>Ca_ss</ci>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM">0.0028</cn>
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              </apply>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.9</cn>
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          </apply>
        </apply>
      </apply>
      <apply>
        <eq/>
        <ci>dtau_rel</ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci>dtau_rel_max</ci>
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          <apply>
            <plus/>
            <ci>KmCaMK</ci>
            <ci>CaMKactive</ci>
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        </apply>
      </apply>
      <apply>
        <eq/>
        <ci>ross</ci>
        <apply>
          <divide/>
          <ci>dro_inf</ci>
          <apply>
            <plus/>
            <apply>
              <power/>
              <apply>
                <divide/>
                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="uA_per_uF">1</cn>
                <ci>ICaL</ci>
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              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
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            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
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        </apply>
      </apply>
      <apply>
        <eq/>
        <ci>riss</ci>
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          <divide/>
          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
          <apply>
            <plus/>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
            <apply>
              <exp/>
              <apply>
                <divide/>
                <apply>
                  <plus/>
                  <apply>
                    <minus/>
                    <ci>Ca_ss</ci>
                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM" type="e-notation">4<sep/>-4</cn>
                  </apply>
                  <apply>
                    <times/>
                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM">0.002</cn>
                    <ci>cafac</ci>
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                </apply>
                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM" type="e-notation">2.5<sep/>-5</cn>
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            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq/>
        <ci>tauri</ci>
        <apply>
          <plus/>
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          <ci>dtau_rel</ci>
          <apply>
            <divide/>
            <apply>
              <minus/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">350</cn>
              <ci>dtau_rel</ci>
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            <apply>
              <plus/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
              <apply>
                <exp/>
                <apply>
                  <divide/>
                  <apply>
                    <plus/>
                    <apply>
                      <minus/>
                      <ci>Ca_ss</ci>
                      <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM">0.003</cn>
                    </apply>
                    <apply>
                      <times/>
                      <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM">0.003</cn>
                      <ci>cafac</ci>
                    </apply>
                  </apply>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM" type="e-notation">2<sep/>-4</cn>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq/>
        <ci>irelcicr</ci>
        <apply>
          <times/>
          <ci>Grel</ci>
          <ci>ro</ci>
          <ci>ri</ci>
          <apply>
            <minus/>
            <ci>Ca_jsr</ci>
            <ci>Ca_ss</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>ro</ci>
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        <apply>
          <divide/>
          <apply>
            <minus/>
            <ci>ross</ci>
            <ci>ro</ci>
          </apply>
          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">3</cn>
        </apply>
      </apply>
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>ri</ci>
        </apply>
        <apply>
          <divide/>
          <apply>
            <minus/>
            <ci>riss</ci>
            <ci>ri</ci>
          </apply>
          <ci>tauri</ci>
        </apply>
      </apply>
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>CaMKtrap</ci>
        </apply>
        <apply>
          <minus/>
          <apply>
            <times/>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_ms">0.05</cn>
            <ci>CaMKactive</ci>
            <apply>
              <minus/>
              <ci>CaMKactive</ci>
              <ci>CaMKtrap</ci>
            </apply>
          </apply>
          <apply>
            <times/>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_ms" type="e-notation">6.8<sep/>-4</cn>
            <ci>CaMKtrap</ci>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="Iup_Ileak">
    <variable initial_value="0.00017" name="dKmPLBmax" units="mM"/>
    <variable initial_value="0.75" name="dJupmax" units="dimensionless"/>
    <variable name="dKmPLB" units="mM"/>
    <variable name="dJup" units="dimensionless"/>
    <variable initial_value="0.004375" name="iupmax" units="mM_per_ms"/>
    <variable initial_value="0.00092" name="Kmup" units="mM"/>
    <variable initial_value="15" name="nsrmax" units="mM"/>
    <variable name="iup" public_interface="out" units="mM_per_ms"/>
    <variable name="ileak" public_interface="out" units="mM_per_ms"/>
    <variable name="KmCaMK" public_interface="in" units="dimensionless"/>
    <variable name="CaMKactive" public_interface="in" units="dimensionless"/>
    <variable name="Ca_i" public_interface="in" units="mM"/>
    <variable name="Ca_nsr" public_interface="in" units="mM"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <ci>dKmPLB</ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci>dKmPLBmax</ci>
            <ci>CaMKactive</ci>
          </apply>
          <apply>
            <plus/>
            <ci>KmCaMK</ci>
            <ci>CaMKactive</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq/>
        <ci>dJup</ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci>dJupmax</ci>
            <ci>CaMKactive</ci>
          </apply>
          <apply>
            <plus/>
            <ci>KmCaMK</ci>
            <ci>CaMKactive</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq/>
        <ci>iup</ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <apply>
              <plus/>
              <ci>dJup</ci>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
            </apply>
            <ci>iupmax</ci>
            <ci>Ca_i</ci>
          </apply>
          <apply>
            <minus/>
            <apply>
              <plus/>
              <ci>Ca_i</ci>
              <ci>Kmup</ci>
            </apply>
            <ci>dKmPLB</ci>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq/>
        <ci>ileak</ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci>iupmax</ci>
            <ci>Ca_nsr</ci>
          </apply>
          <ci>nsrmax</ci>
        </apply>
      </apply>
    </math>
  </component>
  <component name="Idiff_Itr">
    <variable name="idiff" public_interface="out" units="mM_per_ms"/>
    <variable name="itr" public_interface="out" units="mM_per_ms"/>
    <variable name="Ca_ss" public_interface="in" units="mM"/>
    <variable name="Ca_i" public_interface="in" units="mM"/>
    <variable name="Ca_nsr" public_interface="in" units="mM"/>
    <variable name="Ca_jsr" public_interface="in" units="mM"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <ci>idiff</ci>
        <apply>
          <divide/>
          <apply>
            <minus/>
            <ci>Ca_ss</ci>
            <ci>Ca_i</ci>
          </apply>
          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">0.2</cn>
        </apply>
      </apply>
      <apply>
        <eq/>
        <ci>itr</ci>
        <apply>
          <divide/>
          <apply>
            <minus/>
            <ci>Ca_nsr</ci>
            <ci>Ca_jsr</ci>
          </apply>
          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">120</cn>
        </apply>
      </apply>
    </math>
  </component>
  <component name="Na">
    <variable name="time" public_interface="in" units="ms"/>
    <variable initial_value="12.972433387269" name="Na_i" public_interface="out" units="mM"/>
    <variable name="naiont" public_interface="in" units="uA_per_uF"/>
    <variable name="AF" public_interface="in" units="uF_mole_per_C"/>
    <variable name="vmyo" public_interface="in" units="uL"/>
    <variable name="CTNaCl" public_interface="out" units="mM_per_ms"/>
    <variable initial_value="9.8443e-6" name="CTNaClmax" units="mM_per_ms"/>
    <variable name="ENa" public_interface="in" units="mV"/>
    <variable name="ECl" public_interface="in" units="mV"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <ci>CTNaCl</ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci>CTNaClmax</ci>
            <apply>
              <power/>
              <apply>
                <minus/>
                <ci>ENa</ci>
                <ci>ECl</ci>
              </apply>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
            </apply>
          </apply>
          <apply>
            <plus/>
            <apply>
              <power/>
              <apply>
                <minus/>
                <ci>ENa</ci>
                <ci>ECl</ci>
              </apply>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
            </apply>
            <apply>
              <power/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mV">87.8251</cn>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>Na_i</ci>
        </apply>
        <apply>
          <plus/>
          <apply>
            <divide/>
            <apply>
              <times/>
              <apply>
                <minus/>
                <ci>naiont</ci>
              </apply>
              <ci>AF</ci>
            </apply>
            <ci>vmyo</ci>
          </apply>
          <ci>CTNaCl</ci>
        </apply>
      </apply>
    </math>
  </component>
  <component name="K">
    <variable name="time" public_interface="in" units="ms"/>
    <variable initial_value="135.469546216758" name="K_i" public_interface="out" units="mM"/>
    <variable name="kiont" public_interface="in" units="uA_per_uF"/>
    <variable name="AF" public_interface="in" units="uF_mole_per_C"/>
    <variable name="vmyo" public_interface="in" units="uL"/>
    <variable name="CTKCl" public_interface="out" units="mM_per_ms"/>
    <variable initial_value="7.0756e-6" name="CTKClmax" units="mM_per_ms"/>
    <variable name="EK" public_interface="in" units="mV"/>
    <variable name="ECl" public_interface="in" units="mV"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <ci>CTKCl</ci>
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci>CTKClmax</ci>
            <apply>
              <minus/>
              <ci>EK</ci>
              <ci>ECl</ci>
            </apply>
          </apply>
          <apply>
            <plus/>
            <apply>
              <minus/>
              <ci>EK</ci>
              <ci>ECl</ci>
            </apply>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mV">87.8251</cn>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>K_i</ci>
        </apply>
        <apply>
          <plus/>
          <apply>
            <divide/>
            <apply>
              <times/>
              <apply>
                <minus/>
                <ci>kiont</ci>
              </apply>
              <ci>AF</ci>
            </apply>
            <ci>vmyo</ci>
          </apply>
          <ci>CTKCl</ci>
        </apply>
      </apply>
    </math>
  </component>
  <component name="Cl">
    <variable name="time" public_interface="in" units="ms"/>
    <variable initial_value="15.59207157178" name="Cl_i" public_interface="out" units="mM"/>
    <variable name="clont" public_interface="in" units="uA_per_uF"/>
    <variable name="AF" public_interface="in" units="uF_mole_per_C"/>
    <variable name="vmyo" public_interface="in" units="uL"/>
    <variable name="CTNaCl" public_interface="in" units="mM_per_ms"/>
    <variable name="CTKCl" public_interface="in" units="mM_per_ms"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
          </bvar>
          <ci>Cl_i</ci>
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        <apply>
          <plus/>
          <apply>
            <divide/>
            <apply>
              <times/>
              <ci>clont</ci>
              <ci>AF</ci>
            </apply>
            <ci>vmyo</ci>
          </apply>
          <ci>CTNaCl</ci>
          <ci>CTKCl</ci>
        </apply>
      </apply>
    </math>
  </component>
  <component name="Ca">
    <variable name="time" public_interface="in" units="ms"/>
    <variable cmeta:id="Ca_Ca_i" initial_value="0.00012131666" name="Ca_i" public_interface="out" units="mM"/>
    <variable initial_value="1.737580994071" name="Ca_jsr" public_interface="out" units="mM"/>
    <variable initial_value="1.832822335168" name="Ca_nsr" public_interface="out" units="mM"/>
    <variable initial_value="0.00012271265" name="Ca_ss" public_interface="out" units="mM"/>
    <variable initial_value="0.5e-3" name="kmt" units="mM"/>
    <variable initial_value="2.38e-3" name="kmc" units="mM"/>
    <variable initial_value="70e-3" name="tbar" units="mM"/>
    <variable initial_value="50e-3" name="cbar" units="mM"/>
    <variable initial_value="0.8" name="kmcsqn" units="mM"/>
    <variable initial_value="10" name="csqnbar" units="mM"/>
    <variable name="bcsqn" units="dimensionless"/>
    <variable name="bmyo" units="dimensionless"/>
    <variable initial_value="0.047" name="BSRmax" units="mM"/>
    <variable initial_value="0.00087" name="KmBSR" units="mM"/>
    <variable initial_value="1.124" name="BSLmax" units="mM"/>
    <variable initial_value="0.0087" name="KmBSL" units="mM"/>
    <variable name="bss" units="dimensionless"/>
    <variable name="ICab" public_interface="in" units="uA_per_uF"/>
    <variable name="ICaL" public_interface="in" units="uA_per_uF"/>
    <variable name="IpCa" public_interface="in" units="uA_per_uF"/>
    <variable name="INaCa" public_interface="in" units="uA_per_uF"/>
    <variable name="vmyo" public_interface="in" units="uL"/>
    <variable name="vsr" public_interface="in" units="uL"/>
    <variable name="vnsr" public_interface="in" units="uL"/>
    <variable name="vjsr" public_interface="in" units="uL"/>
    <variable name="vss" public_interface="in" units="uL"/>
    <variable name="AF" public_interface="in" units="uF_mole_per_C"/>
    <variable name="iup" public_interface="in" units="mM_per_ms"/>
    <variable name="ileak" public_interface="in" units="mM_per_ms"/>
    <variable name="irelcicr" public_interface="in" units="mM_per_ms"/>
    <variable name="idiff" public_interface="in" units="mM_per_ms"/>
    <variable name="itr" public_interface="in" units="mM_per_ms"/>
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
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          <ci>Ca_i</ci>
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        <apply>
          <times/>
          <ci>bmyo</ci>
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            <plus/>
            <apply>
              <divide/>
              <apply>
                <times/>
                <apply>
                  <minus/>
                  <apply>
                    <minus/>
                    <apply>
                      <plus/>
                      <ci>ICab</ci>
                      <ci>IpCa</ci>
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                    <apply>
                      <times/>
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                      <ci>INaCa</ci>
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                  </apply>
                </apply>
                <ci>AF</ci>
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              <apply>
                <times/>
                <ci>vmyo</ci>
                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
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            </apply>
            <apply>
              <divide/>
              <apply>
                <times/>
                <apply>
                  <minus/>
                  <ci>ileak</ci>
                  <ci>iup</ci>
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                <ci>vnsr</ci>
              </apply>
              <ci>vmyo</ci>
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            <apply>
              <divide/>
              <apply>
                <times/>
                <ci>idiff</ci>
                <ci>vss</ci>
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              <ci>vmyo</ci>
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          </apply>
        </apply>
      </apply>
      <apply>
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci>time</ci>
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          <ci>Ca_ss</ci>
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        <apply>
          <times/>
          <ci>bss</ci>
          <apply>
            <minus/>
            <apply>
              <plus/>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <apply>
                    <minus/>
                    <ci>ICaL</ci>
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                  <ci>AF</ci>
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                <apply>
                  <times/>
                  <ci>vss</ci>
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                </apply>
              </apply>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <ci>irelcicr</ci>
                  <ci>vjsr</ci>
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                <ci>vss</ci>
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            </apply>
            <ci>idiff</ci>
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      <apply>
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          <diff/>
          <bvar>
            <ci>time</ci>
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          <ci>Ca_nsr</ci>
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        <apply>
          <minus/>
          <apply>
            <minus/>
            <ci>iup</ci>
            <apply>
              <divide/>
              <apply>
                <times/>
                <ci>itr</ci>
                <ci>vjsr</ci>
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              <ci>vnsr</ci>
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          <ci>ileak</ci>
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      <apply>
        <eq/>
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          <bvar>
            <ci>time</ci>
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          <ci>Ca_jsr</ci>
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        <apply>
          <times/>
          <ci>bcsqn</ci>
          <apply>
            <minus/>
            <ci>itr</ci>
            <ci>irelcicr</ci>
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        </apply>
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      <apply>
        <eq/>
        <ci>bcsqn</ci>
        <apply>
          <divide/>
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            <apply>
              <divide/>
              <apply>
                <times/>
                <ci>kmcsqn</ci>
                <ci>csqnbar</ci>
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              <apply>
                <power/>
                <apply>
                  <plus/>
                  <ci>Ca_jsr</ci>
                  <ci>kmcsqn</ci>
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                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
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            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq/>
        <ci>bmyo</ci>
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          <divide/>
          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
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            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
            <apply>
              <divide/>
              <apply>
                <times/>
                <ci>cbar</ci>
                <ci>kmc</ci>
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              <apply>
                <power/>
                <apply>
                  <plus/>
                  <ci>Ca_i</ci>
                  <ci>kmc</ci>
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                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
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            <apply>
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              <apply>
                <times/>
                <ci>kmt</ci>
                <ci>tbar</ci>
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              <apply>
                <power/>
                <apply>
                  <plus/>
                  <ci>Ca_i</ci>
                  <ci>kmt</ci>
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                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
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            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <eq/>
        <ci>bss</ci>
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          <divide/>
          <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
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            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
            <apply>
              <divide/>
              <apply>
                <times/>
                <ci>BSRmax</ci>
                <ci>KmBSR</ci>
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              <apply>
                <power/>
                <apply>
                  <plus/>
                  <ci>KmBSR</ci>
                  <ci>Ca_ss</ci>
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                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
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            <apply>
              <divide/>
              <apply>
                <times/>
                <ci>BSLmax</ci>
                <ci>KmBSL</ci>
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              <apply>
                <power/>
                <apply>
                  <plus/>
                  <ci>KmBSL</ci>
                  <ci>Ca_ss</ci>
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                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  <component name="intracellular_currents"/>
  <component name="transmembrane_currents"/>
  <component name="Ions_n_reversal_potentials"/>
  <group>
    <relationship_ref relationship="containment"/>
    <component_ref component="cell">
      <component_ref component="transmembrane_currents">
        <component_ref component="INa"/>
        <component_ref component="ICaL"/>
        <component_ref component="IK1"/>
        <component_ref component="IKr"/>
        <component_ref component="IKs"/>
        <component_ref component="Ito"/>
        <component_ref component="INaK"/>
        <component_ref component="INaCa"/>
        <component_ref component="IKp"/>
        <component_ref component="IpCa"/>
        <component_ref component="ICab"/>
        <component_ref component="Ito2"/>
        <component_ref component="IClb"/>
        <component_ref component="INal"/>
      </component_ref>
      <component_ref component="intracellular_currents">
        <component_ref component="Irel"/>
        <component_ref component="Iup_Ileak"/>
        <component_ref component="Idiff_Itr"/>
      </component_ref>
      <component_ref component="Ions_n_reversal_potentials">
        <component_ref component="Ca"/>
        <component_ref component="Na"/>
        <component_ref component="K"/>
        <component_ref component="Cl"/>
        <component_ref component="reversal_potentials"/>
      </component_ref>
    </component_ref>
  </group>
  <connection>
    <map_components component_1="cell" component_2="Environment"/>
    <map_variables variable_1="time" variable_2="time"/>
    <map_variables variable_1="F" variable_2="F"/>
  </connection>
  <connection>
    <map_components component_1="reversal_potentials" component_2="Environment"/>
    <map_variables variable_1="K_o" variable_2="K_o"/>
    <map_variables variable_1="Na_o" variable_2="Na_o"/>
    <map_variables variable_1="Cl_o" variable_2="Cl_o"/>
    <map_variables variable_1="FonRT" variable_2="FonRT"/>
  </connection>
  <connection>
    <map_components component_1="INa" component_2="Environment"/>
    <map_variables variable_1="time" variable_2="time"/>
    <map_variables variable_1="tissue" variable_2="tissue"/>
  </connection>
  <connection>
    <map_components component_1="ICaL" component_2="Environment"/>
    <map_variables variable_1="time" variable_2="time"/>
    <map_variables variable_1="Ca_o" variable_2="Ca_o"/>
    <map_variables variable_1="F" variable_2="F"/>
    <map_variables variable_1="FonRT" variable_2="FonRT"/>
    <map_variables variable_1="tissue" variable_2="tissue"/>
  </connection>
  <connection>
    <map_components component_1="IKr" component_2="Environment"/>
    <map_variables variable_1="time" variable_2="time"/>
    <map_variables variable_1="K_o" variable_2="K_o"/>
  </connection>
  <connection>
    <map_components component_1="IKs" component_2="Environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  <connection>
    <map_components component_1="IK1" component_2="Environment"/>
    <map_variables variable_1="K_o" variable_2="K_o"/>
  </connection>
  <connection>
    <map_components component_1="Ito" component_2="Environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  <connection>
    <map_components component_1="INaK" component_2="Environment"/>
    <map_variables variable_1="K_o" variable_2="K_o"/>
    <map_variables variable_1="Na_o" variable_2="Na_o"/>
    <map_variables variable_1="FonRT" variable_2="FonRT"/>
  </connection>
  <connection>
    <map_components component_1="INaCa" component_2="Environment"/>
    <map_variables variable_1="Ca_o" variable_2="Ca_o"/>
    <map_variables variable_1="Na_o" variable_2="Na_o"/>
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