Location: Bueno, 2007 @ 981197b9cf2c / bueno_2007.cellml

Author:
Catherine Lloyd <c.lloyd@auckland.ac.nz>
Date:
2010-05-13 21:14 +1200
Desc:
Added keywords to the model metadata.
Permanent Source URI:
http://models.cellml.org/workspace/bueno_2007/rawfile/981197b9cf2cb0f3e0c2861b89942341cbd47c97/bueno_2007.cellml

<?xml version='1.0' encoding='utf-8'?>
<!--
This CellML file was generated on 25/02/2008 at 13:56:30 using:

COR (0.9.31.873)
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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<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <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 CellML model is known to run in both COR and OpenCell to recreate the results of the original model. The units have been checked and they are consistent. 
</para>
  </section>
  <sect1 id="sec_structure">
  <title>Model Structure</title>
<para>
The applicability and usefulness of the new model have been proved by addressing the study of the Brugada syndrome, an important hereditary genetic disease able to cause sudden cardiac death in human patients even without identifiable structural abnormalities. Despite not incorporating independent descriptions for each of the known currents measured through the cell membrane, the model is however capable to correctly reproduce both the healthy and pathological conditions of the epicardial tissue layer, the latter being characterized by the presence of a much deeper notch in the cardiac action potential as a result of a loss of functionality of sodium channels which leaves unopposed the transient outward potassium current.
</para>

<para>
Despite being able of reproducing a great amount of available experimental data, one important limitation of the proposed minimal model is that it lacks of a complete description of intracellular calcium dynamics. Hence, the model cannot be used to study particular conditions of importance in the generation and development of arrhythmias, such as calcium overload, spontaneous calcium release or calcium-induced alternans. This limitation could be overcome however by coupling our simplified model of the cardiac transmembrane potential to a reduced model of the intracellular calcium cycling of the ventricular myocyte, such as the one suggested by Shiferaw et al. (2003), therefore yielding the first implementation of a second-generation simplified ionic model of the cardiac myocyte.
</para>

<para>
This model was taken from the PhD thesis of Alfonso Bueno:
</para>

<para>
Mathematical modeling and spectral simulation of genetic diseases in the human heart, Alfonso Bueno, Department of Mathematics, University of Castilla-La Mancha, Ciudad Real, May 2007.
</para>

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

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            <ci>tau_so</ci>
            <apply>
               <plus/>
               <ci>tau_so1</ci>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <apply>
                        <minus/>
                        <ci>tau_so2</ci>
                        <ci>tau_so1</ci>
                     </apply>
                     <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <tanh/>
                           <apply>
                              <times/>
                              <ci>k_so</ci>
                              <apply>
                                 <minus/>
                                 <ci>u</ci>
                                 <ci>u_so</ci>
                              </apply>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
                  <cn cellml:units="dimensionless">2</cn>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>J_so</ci>
            <apply>
               <plus/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <ci>u</ci>
                     <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <ci>p</ci>
                     </apply>
                  </apply>
                  <ci>tau_o</ci>
               </apply>
               <apply>
                  <divide/>
                  <ci>p</ci>
                  <ci>tau_so</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="slow_inward_current">
      <variable units="per_ms" public_interface="out" name="J_si"/>
      <variable units="dimensionless" public_interface="in" private_interface="out" name="epi"/>
      <variable units="dimensionless" public_interface="in" private_interface="out" name="endo"/>
      <variable units="dimensionless" public_interface="in" private_interface="out" name="mcell"/>
      <variable units="ms" name="tau_si"/>
      <variable units="dimensionless" public_interface="in" private_interface="out" name="p"/>
      <variable units="dimensionless" public_interface="in" private_interface="out" name="r"/>
      <variable units="ms" public_interface="in" private_interface="out" name="time"/>
      <variable units="dimensionless" public_interface="in" private_interface="out" name="u"/>
      <variable units="dimensionless" private_interface="in" name="w"/>
      <variable units="dimensionless" private_interface="in" name="s"/>
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         <apply>
            <eq/>
            <ci>tau_si</ci>
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               <piece>
                  <cn cellml:units="ms">1.8875</cn>
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                     <eq/>
                     <ci>epi</ci>
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               <piece>
                  <cn cellml:units="ms">2.9013</cn>
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                     <eq/>
                     <ci>endo</ci>
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                  <cn cellml:units="ms">3.3849</cn>
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         <apply>
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            <ci>J_si</ci>
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               <divide/>
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                  <times/>
                  <apply>
                     <minus/>
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                  <ci>w</ci>
                  <ci>s</ci>
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               <ci>tau_si</ci>
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         </apply>
      </math>
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   <component name="slow_inward_current_w_gate">
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      <variable units="dimensionless" public_interface="in" name="epi"/>
      <variable units="dimensionless" public_interface="in" name="endo"/>
      <variable units="dimensionless" public_interface="in" name="mcell"/>
      <variable units="dimensionless" name="w_inf"/>
      <variable units="ms" name="tau_winf"/>
      <variable units="dimensionless" name="wstar_inf"/>
      <variable units="ms" name="tau_w_minus"/>
      <variable units="ms" name="tau_w1_minus"/>
      <variable units="ms" name="tau_w2_minus"/>
      <variable units="dimensionless" name="k_w_minus"/>
      <variable units="dimensionless" name="u_w_minus"/>
      <variable units="ms" name="tau_w_plus"/>
      <variable units="dimensionless" public_interface="in" name="r"/>
      <variable units="dimensionless" public_interface="in" name="u"/>
      <variable units="ms" public_interface="in" name="time"/>
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            <eq/>
            <ci>tau_winf</ci>
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                     <eq/>
                     <ci>epi</ci>
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               <piece>
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                     <eq/>
                     <ci>endo</ci>
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            <ci>wstar_inf</ci>
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               <piece>
                  <cn cellml:units="dimensionless">0.94</cn>
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                     <eq/>
                     <ci>epi</ci>
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               <piece>
                  <cn cellml:units="dimensionless">0.78</cn>
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                     <eq/>
                     <ci>endo</ci>
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               </piece>
               <otherwise>
                  <cn cellml:units="dimensionless">0.5</cn>
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            <eq/>
            <ci>tau_w1_minus</ci>
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               <piece>
                  <cn cellml:units="ms">60</cn>
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                     <eq/>
                     <ci>epi</ci>
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               </piece>
               <piece>
                  <cn cellml:units="ms">6</cn>
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                     <eq/>
                     <ci>endo</ci>
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               </piece>
               <otherwise>
                  <cn cellml:units="ms">70</cn>
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         </apply>
         <apply>
            <eq/>
            <ci>tau_w2_minus</ci>
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               <piece>
                  <cn cellml:units="ms">15</cn>
                  <apply>
                     <eq/>
                     <ci>epi</ci>
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               </piece>
               <piece>
                  <cn cellml:units="ms">140</cn>
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                     <eq/>
                     <ci>endo</ci>
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               </piece>
               <otherwise>
                  <cn cellml:units="ms">8</cn>
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         <apply>
            <eq/>
            <ci>k_w_minus</ci>
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               <piece>
                  <cn cellml:units="dimensionless">65</cn>
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                     <eq/>
                     <ci>epi</ci>
                     <cn cellml:units="dimensionless">1</cn>
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               </piece>
               <piece>
                  <cn cellml:units="dimensionless">200</cn>
                  <apply>
                     <eq/>
                     <ci>endo</ci>
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                  </apply>
               </piece>
               <otherwise>
                  <cn cellml:units="dimensionless">200</cn>
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         <apply>
            <eq/>
            <ci>u_w_minus</ci>
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               <piece>
                  <cn cellml:units="dimensionless">0.03</cn>
                  <apply>
                     <eq/>
                     <ci>epi</ci>
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               </piece>
               <piece>
                  <cn cellml:units="dimensionless">0.016</cn>
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                     <eq/>
                     <ci>endo</ci>
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               <otherwise>
                  <cn cellml:units="dimensionless">0.016</cn>
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         </apply>
         <apply>
            <eq/>
            <ci>tau_w_plus</ci>
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               <piece>
                  <cn cellml:units="ms">200</cn>
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                     <eq/>
                     <ci>epi</ci>
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               </piece>
               <piece>
                  <cn cellml:units="ms">280</cn>
                  <apply>
                     <eq/>
                     <ci>endo</ci>
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                  </apply>
               </piece>
               <otherwise>
                  <cn cellml:units="ms">280</cn>
               </otherwise>
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         </apply>
         <apply>
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            <ci>w_inf</ci>
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               <plus/>
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                  <times/>
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                     <minus/>
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                           <times/>
                           <ci>u</ci>
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                        </apply>
                        <ci>tau_winf</ci>
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                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>r</ci>
                  <ci>wstar_inf</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>tau_w_minus</ci>
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               <plus/>
               <ci>tau_w1_minus</ci>
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                  <divide/>
                  <apply>
                     <times/>
                     <apply>
                        <minus/>
                        <ci>tau_w2_minus</ci>
                        <ci>tau_w1_minus</ci>
                     </apply>
                     <apply>
                        <plus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <apply>
                           <tanh/>
                           <apply>
                              <times/>
                              <ci>k_w_minus</ci>
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                                 <minus/>
                                 <ci>u</ci>
                                 <ci>u_w_minus</ci>
                              </apply>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
                  <cn cellml:units="dimensionless">2</cn>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>w</ci>
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            <apply>
               <minus/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <apply>
                        <minus/>
                        <cn cellml:units="dimensionless">1</cn>
                        <ci>r</ci>
                     </apply>
                     <apply>
                        <minus/>
                        <ci>w_inf</ci>
                        <ci>w</ci>
                     </apply>
                  </apply>
                  <ci>tau_w_minus</ci>
               </apply>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <ci>r</ci>
                     <ci>w</ci>
                  </apply>
                  <ci>tau_w_plus</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
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      <variable units="dimensionless" public_interface="out" name="s" initial_value="0"/>
      <variable units="dimensionless" public_interface="in" name="epi"/>
      <variable units="dimensionless" public_interface="in" name="endo"/>
      <variable units="dimensionless" public_interface="in" name="mcell"/>
      <variable units="ms" name="tau_s"/>
      <variable units="ms" name="tau_s1" initial_value="2.7342"/>
      <variable units="ms" name="tau_s2"/>
      <variable units="dimensionless" name="k_s" initial_value="2.0994"/>
      <variable units="dimensionless" name="u_s" initial_value="0.9087"/>
      <variable units="dimensionless" public_interface="in" name="p"/>
      <variable units="dimensionless" public_interface="in" name="u"/>
      <variable units="ms" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>tau_s2</ci>
            <piecewise>
               <piece>
                  <cn cellml:units="ms">16</cn>
                  <apply>
                     <eq/>
                     <ci>epi</ci>
                     <cn cellml:units="dimensionless">1</cn>
                  </apply>
               </piece>
               <piece>
                  <cn cellml:units="ms">2</cn>
                  <apply>
                     <eq/>
                     <ci>endo</ci>
                     <cn cellml:units="dimensionless">1</cn>
                  </apply>
               </piece>
               <otherwise>
                  <cn cellml:units="ms">4</cn>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>tau_s</ci>
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               <plus/>
               <apply>
                  <times/>
                  <apply>
                     <minus/>
                     <cn cellml:units="dimensionless">1</cn>
                     <ci>p</ci>
                  </apply>
                  <ci>tau_s1</ci>
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               <apply>
                  <times/>
                  <ci>p</ci>
                  <ci>tau_s2</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
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               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>s</ci>
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            <apply>
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                  <minus/>
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                     <divide/>
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                        <plus/>
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                           <tanh/>
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                              <times/>
                              <ci>k_s</ci>
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                                 <minus/>
                                 <ci>u</ci>
                                 <ci>u_s</ci>
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                           </apply>
                        </apply>
                     </apply>
                     <cn cellml:units="dimensionless">2</cn>
                  </apply>
                  <ci>s</ci>
               </apply>
               <ci>tau_s</ci>
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         </apply>
      </math>
   </component>
   <group>
      <relationship_ref relationship="containment"/>
      <component_ref component="membrane">
         <component_ref component="fast_inward_current">
            <component_ref component="fast_inward_current_v_gate"/>
         </component_ref>
         <component_ref component="slow_outward_current"/>
         <component_ref component="slow_inward_current">
            <component_ref component="slow_inward_current_w_gate"/>
            <component_ref component="slow_inward_current_s_gate"/>
         </component_ref>
         <component_ref component="m"/>
         <component_ref component="p"/>
         <component_ref component="q"/>
         <component_ref component="r"/>
      </component_ref>
   </group>
   <group>
      <relationship_ref relationship="encapsulation"/>
      <component_ref component="fast_inward_current">
         <component_ref component="fast_inward_current_v_gate"/>
      </component_ref>
      <component_ref component="slow_inward_current">
         <component_ref component="slow_inward_current_w_gate"/>
         <component_ref component="slow_inward_current_s_gate"/>
      </component_ref>
   </group>
   <connection>
      <map_components component_2="environment" component_1="membrane"/>
      <map_variables variable_2="time" variable_1="time"/>
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   <connection>
      <map_components component_2="environment" component_1="m"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="p"/>
      <map_variables variable_2="time" variable_1="time"/>
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   <connection>
      <map_components component_2="environment" component_1="q"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="epi" variable_1="epi"/>
      <map_variables variable_2="endo" variable_1="endo"/>
      <map_variables variable_2="mcell" variable_1="mcell"/>
   </connection>
   <connection>
      <map_components component_2="environment" component_1="r"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="epi" variable_1="epi"/>
      <map_variables variable_2="endo" variable_1="endo"/>
      <map_variables variable_2="mcell" variable_1="mcell"/>
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   <connection>
      <map_components component_2="environment" component_1="fast_inward_current"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="epi" variable_1="epi"/>
      <map_variables variable_2="endo" variable_1="endo"/>
      <map_variables variable_2="mcell" variable_1="mcell"/>
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   <connection>
      <map_components component_2="environment" component_1="slow_outward_current"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="epi" variable_1="epi"/>
      <map_variables variable_2="endo" variable_1="endo"/>
      <map_variables variable_2="mcell" variable_1="mcell"/>
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   <connection>
      <map_components component_2="environment" component_1="slow_inward_current"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="epi" variable_1="epi"/>
      <map_variables variable_2="endo" variable_1="endo"/>
      <map_variables variable_2="mcell" variable_1="mcell"/>
   </connection>
   <connection>
      <map_components component_2="fast_inward_current" component_1="membrane"/>
      <map_variables variable_2="u" variable_1="u"/>
      <map_variables variable_2="J_fi" variable_1="J_fi"/>
   </connection>
   <connection>
      <map_components component_2="slow_outward_current" component_1="membrane"/>
      <map_variables variable_2="u" variable_1="u"/>
      <map_variables variable_2="J_so" variable_1="J_so"/>
   </connection>
   <connection>
      <map_components component_2="slow_inward_current" component_1="membrane"/>
      <map_variables variable_2="u" variable_1="u"/>
      <map_variables variable_2="J_si" variable_1="J_si"/>
   </connection>
   <connection>
      <map_components component_2="m" component_1="membrane"/>
      <map_variables variable_2="u" variable_1="u"/>
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   <connection>
      <map_components component_2="p" component_1="membrane"/>
      <map_variables variable_2="u" variable_1="u"/>
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   <connection>
      <map_components component_2="q" component_1="membrane"/>
      <map_variables variable_2="u" variable_1="u"/>
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   <connection>
      <map_components component_2="r" component_1="membrane"/>
      <map_variables variable_2="u" variable_1="u"/>
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   <connection>
      <map_components component_2="fast_inward_current" component_1="m"/>
      <map_variables variable_2="m" variable_1="m"/>
      <map_variables variable_2="u_m" variable_1="u_m"/>
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   <connection>
      <map_components component_2="fast_inward_current" component_1="p"/>
      <map_variables variable_2="u_p" variable_1="u_p"/>
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      <map_variables variable_2="p" variable_1="p"/>
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   <connection>
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      <map_variables variable_2="r" variable_1="r"/>
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   <connection>
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      <map_variables variable_2="p" variable_1="p"/>
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   <connection>
      <map_components component_2="slow_inward_current" component_1="r"/>
      <map_variables variable_2="r" variable_1="r"/>
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   <connection>
      <map_components component_2="fast_inward_current" component_1="q"/>
      <map_variables variable_2="q" variable_1="q"/>
      <map_variables variable_2="u_q" variable_1="u_q"/>
   </connection>
   <connection>
      <map_components component_2="fast_inward_current_v_gate" component_1="fast_inward_current"/>
      <map_variables variable_2="v" variable_1="v"/>
      <map_variables variable_2="q" variable_1="q"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="epi" variable_1="epi"/>
      <map_variables variable_2="endo" variable_1="endo"/>
      <map_variables variable_2="mcell" variable_1="mcell"/>
      <map_variables variable_2="m" variable_1="m"/>
      <map_variables variable_2="u" variable_1="u"/>
      <map_variables variable_2="u_q" variable_1="u_q"/>
   </connection>
   <connection>
      <map_components component_2="slow_inward_current_w_gate" component_1="slow_inward_current"/>
      <map_variables variable_2="w" variable_1="w"/>
      <map_variables variable_2="r" variable_1="r"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="epi" variable_1="epi"/>
      <map_variables variable_2="endo" variable_1="endo"/>
      <map_variables variable_2="mcell" variable_1="mcell"/>
      <map_variables variable_2="u" variable_1="u"/>
   </connection>
   <connection>
      <map_components component_2="slow_inward_current_s_gate" component_1="slow_inward_current"/>
      <map_variables variable_2="s" variable_1="s"/>
      <map_variables variable_2="p" variable_1="p"/>
      <map_variables variable_2="u" variable_1="u"/>
      <map_variables variable_2="time" variable_1="time"/>
      <map_variables variable_2="epi" variable_1="epi"/>
      <map_variables variable_2="endo" variable_1="endo"/>
      <map_variables variable_2="mcell" variable_1="mcell"/>
   </connection>



<rdf:RDF>
  <rdf:Seq rdf:about="rdf:#679f10ee-12d7-4474-ad1d-8685b5aab3e9">
    <rdf:li rdf:resource="rdf:#927faa0c-8772-4c18-baec-973b868c6ce4"/>
  </rdf:Seq>
  <rdf:Description rdf:about="rdf:#f3061df5-2fd2-4f4c-a840-4c8cbf3c99b4">
    <dcterms:modified rdf:resource="rdf:#acd5ae7b-56ad-43e5-841e-3e1b69b05f73"/>
    <rdf:value>updated curation status</rdf:value>
    <cmeta:modifier rdf:resource="rdf:#1eed0db6-d2ea-43dc-948b-e0f048014981"/>
  </rdf:Description>
  <rdf:Description rdf:about="">
    <dc:publisher/>
    <cmeta:comment rdf:resource="rdf:#30daf8a5-05a4-4492-9dea-3cf509e5072d"/>
    <dcterms:created rdf:resource="rdf:#2ab16259-22dd-467a-8d88-da85a853cb66"/>
    <dc:creator rdf:resource="rdf:#b3ec4e5a-01ac-4f03-a847-efbdc8809aaa"/>
    <cmeta:modification rdf:resource="rdf:#f3061df5-2fd2-4f4c-a840-4c8cbf3c99b4"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#fa433c77-a70b-477b-81b6-0121d11471b1">
    <dc:creator rdf:resource="rdf:#b21c1c2f-13f1-4e89-b2da-d0ece71736da"/>
    <rdf:value>This model of a ventricular cell was taken from Alfonso Bueno's 2007 PhD thesis, which can be found at http://matematicas.uclm.es/abueno/webpdfs/abueno_thesis.pdf (as of 2008-06-16)</rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#b21c1c2f-13f1-4e89-b2da-d0ece71736da">
    <vCard:FN>Catherine Lloyd</vCard:FN>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#4c0b675b-b50c-40de-8026-022a54b4ecf7">
    <vCard:Given>Alfonso</vCard:Given>
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    <dcterms:W3CDTF>2009-05-28T16:10:40+12:00</dcterms:W3CDTF>
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    <vCard:FN>Catherine Lloyd</vCard:FN>
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    <rdf:value>penny.noble@dpag.ox.ac.uk</rdf:value>
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    <dcterms:W3CDTF>2008-02-28T00:00:00+00:00</dcterms:W3CDTF>
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              <rdf:li>electrophysiology</rdf:li>
			  <rdf:li>cardiac</rdf:li>
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    <vCard:Given>James</vCard:Given>
    <vCard:Family>Lawson</vCard:Family>
    <vCard:Other>Richard</vCard:Other>
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    <dc:title>Mathematical modeling and spectral simulation of genetic diseases in the human heart</dc:title>
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    <vCard:Orgname>The University of Oxford</vCard:Orgname>
    <vCard:Orgunit>Department of Physiology, Anatomy and Genetics</vCard:Orgunit>
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    <vCard:Given>Penny</vCard:Given>
    <vCard:Family>Noble</vCard:Family>
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    <dcterms:W3CDTF>2007-05-00 00:00</dcterms:W3CDTF>
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    <rdf:value>This CellML model is known to run in both COR and PCEnv to recreate the results of the original model.  The units have been checked and are consistent. Model has been curated using Bueno 2007 thesis.</rdf:value>
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