Location: Mlcek, Neumann, Kittnar, Novak, 2001 @ 98af4be61d7a / mlcek_neumann_kittnar_novak_2001.cellml

Author:
pmr2.import <nobody@models.cellml.org>
Date:
2006-07-09 07:25:44+12:00
Desc:
committing version01 of mlcek_neumann_kittnar_novak_2001
Permanent Source URI:
https://staging.physiomeproject.org/workspace/mlcek_neumann_kittnar_novak_2001/rawfile/98af4be61d7ab1e2229119d3d7b00a3139607415/mlcek_neumann_kittnar_novak_2001.cellml

<?xml version='1.0' encoding='utf-8'?>
<!--  FILE :  mlcek_model_2001_raw.xml

CREATED :  19th June 2002

LAST MODIFIED : 18th July 2002

AUTHOR :  Catherine Lloyd
          The Bioengineering Institute
          The University of Auckland
          
MODEL STATUS :  This model conforms to the CellML 1.0 Specification released on
                10th August 2001, and the 16/01/2002 CellML Metadata 1.0
                Specification.

DESCRIPTION :  This file contains a CellML description of Mlcek et al's
               mathematical model of the electromechanical heart contractile
               system.

CHANGES:  
   18/07/2002 - CML - Added more metadata.
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:pathway_editor="http://www.physiome.com/pathway_editor/1.0#" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" pathway_editor:rendering_config_file="mlcek_model_2001_CellMLrender.xml" cmeta:id="mlcek_neumann_kittnar_novak_2001_version01" name="mlcek_neumann_kittnar_novak_2001_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>Mathematical Model of the Electromechanical Heart Contractile System</title>
  <author>
    <firstname>Catherine</firstname>
          <surname>Lloyd</surname>
    <affiliation>
      <shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
    </affiliation>
  </author>
</articleinfo>
  <section id="sec_status">
    <title>Model Status</title>
    <para>
            This is the original unchecked version of the model imported from the previous
            CellML model repository, 24-Jan-2006.
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para>
Computational modelling in molecular cardiology has recently focused on simulating subsets of myocardial excitation-contraction processes.  As people try to improve their understanding of myocardial function, there is an increasing interest in excitation-contraction coupling and mechanical events in cardiac muscle.  It is hoped that these computer simulations will also help explain the pathophysiological mechanisms of heart failure.
</para>

<para>
In their 2001 paper, Mlcek, Neumann, Kittnar and Novak concentrate on the molecular level of electromechanical events in cardiac muscle.  They introduce an actomyosin subsystem accompanied by a simple regulatory subsystem involving calcium binding to troponin C (see <xref linkend="fig_reaction_diagram"/> below).  They performed many simulations to prove the stability of their model and they then used the simulation results to help interpret experimental and clinical data.     
</para>

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

<para>
<ulink url="http://www.biomed.cas.cz/physiolres/2001/issue4/mlcek.htm">Mathematical Model of the Electromechanical Heart Contractile System - Regulatory Subsystem Physiological Considerations</ulink>, M. Mlcek, J. Neumann, O. Kittnar and V. Novak, 2001, <ulink url="http://www.biomed.cas.cz/physiolres/">
            <emphasis>Physiological Research</emphasis>
          </ulink>, 50, 425-432. (A PDF version of the article is also available on the Physiological Research journal website.)  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=11551150&amp;dopt=Abstract">PubMed ID: 11551150</ulink> 
</para>

<para>
The raw CellML descriptions of the model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>.
</para>

<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>reaction_diagram</title>
    </objectinfo>
    <imagedata fileref="mlcek_2001.png"/>
  </imageobject>
</mediaobject>
<caption>Diagram of the regulatory subsystem scheme and the actomyosin subsystem scheme.</caption>
</informalfigure>

</sect1>
</article>
</documentation>
  
  
  <!--
    We start the model definition with a definition of some named
    sets of units for use throughout the model.
  -->
   
   <units name="micromolar">
     <unit units="mole" prefix="micro"/>
     <unit units="litre" exponent="-1"/>
   </units>
   
   <units name="flux">
      <unit units="micromolar"/>
      <unit units="second" exponent="-1"/>
   </units>
   
   <units name="first_order_rate_constant">
     <unit units="second" exponent="-1"/>
   </units>
   
   <units name="second_order_rate_constant">
     <unit units="micromolar" exponent="-1"/>
     <unit units="second" exponent="-1"/>
   </units>
   
  <!--  
    The following component is defined for modelling convenience.  It contains 
    all the universal variables, in this case, only time.
  -->
   <component name="global_variables">
      <variable units="second" public_interface="out" name="time"/>
   </component>
  
  <!--  
    The following components describe all the metabolites - both reactants and 
    products - involved in the elctromechanical heart contractile system.
   -->
   
   <component cmeta:id="Actin" name="Actin">
      <variable units="micromolar" public_interface="out" name="Actin" initial_value="1.0"/>
      <variable units="flux" public_interface="in" name="delta_Actin_rxn1"/>
      <variable units="flux" public_interface="in" name="delta_Actin_rxn5"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Actin</ci>
            </apply>
            <apply>
               <plus/>
               <ci>delta_Actin_rxn1</ci>
               <ci>delta_Actin_rxn5</ci>
            </apply>
         </apply>
      </math>
   </component>
   
   <component cmeta:id="Myosin" name="Myosin">
      <variable units="micromolar" public_interface="out" name="Myosin" initial_value="1.0"/>
      <variable units="flux" public_interface="in" name="delta_Myosin_rxn0"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Myosin</ci>
            </apply>
            <ci>delta_Myosin_rxn0</ci>
         </apply>
      </math>
   </component>
  
   <component cmeta:id="ATP" name="ATP">
      <variable units="micromolar" public_interface="out" name="ATP" initial_value="1.0"/>
      <variable units="flux" public_interface="in" name="delta_ATP_rxn0"/>
      <variable units="flux" public_interface="in" name="delta_ATP_rxn2"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>ATP</ci>
            </apply>
            <apply>
               <plus/>
               <ci>delta_ATP_rxn0</ci>
               <ci>delta_ATP_rxn2</ci>
            </apply>
         </apply>
      </math>
   </component>
   
   <component cmeta:id="ADP" name="ADP">
      <variable units="micromolar" public_interface="out" name="ADP" initial_value="1.0"/>
      <variable units="flux" public_interface="in" name="delta_ADP_rxn3"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>ADP</ci>
            </apply>
            <ci>delta_ADP_rxn3</ci>
         </apply>
      </math>
   </component>
  
   <component cmeta:id="Myosin_ATP" name="Myosin_ATP">
      <variable units="micromolar" public_interface="out" name="Myosin_ATP" initial_value="1.0"/>
      <variable units="flux" public_interface="in" name="delta_Myosin_ATP_rxn0"/>
      <variable units="flux" public_interface="in" name="delta_Myosin_ATP_rxn1"/>
      <variable units="flux" public_interface="in" name="delta_Myosin_ATP_rxn7"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Myosin_ATP</ci>
            </apply>
            <apply>
               <plus/>
               <ci>delta_Myosin_ATP_rxn0</ci>
               <ci>delta_Myosin_ATP_rxn1</ci>
               <ci>delta_Myosin_ATP_rxn7</ci>
            </apply>
         </apply>
      </math>
   </component>
  
   <component cmeta:id="Actomyosin_ATP" name="Actomyosin_ATP">
      <variable units="micromolar" public_interface="out" name="Actomyosin_ATP" initial_value="1.0"/>
      <variable units="flux" public_interface="in" name="delta_Actomyosin_ATP_rxn1"/>
      <variable units="flux" public_interface="in" name="delta_Actomyosin_ATP_rxn2"/>
      <variable units="flux" public_interface="in" name="delta_Actomyosin_ATP_rxn6"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Actomyosin_ATP</ci>
            </apply>
            <apply>
               <plus/>
               <ci>delta_Actomyosin_ATP_rxn1</ci>
               <ci>delta_Actomyosin_ATP_rxn2</ci>
               <ci>delta_Actomyosin_ATP_rxn6</ci>
            </apply>
         </apply>
      </math>
   </component>

   <component cmeta:id="Actomyosin" name="Actomyosin">
      <variable units="micromolar" public_interface="out" name="Actomyosin" initial_value="1.0"/>
      <variable units="flux" public_interface="in" name="delta_Actomyosin_rxn3"/>
      <variable units="flux" public_interface="in" name="delta_Actomyosin_rxn2"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Actomyosin</ci>
            </apply>
            <apply>
               <plus/>
               <ci>delta_Actomyosin_rxn3</ci>
               <ci>delta_Actomyosin_rxn2</ci>
            </apply>
         </apply>
      </math>
   </component>
  
   <component cmeta:id="Actomyosin_ADP" name="Actomyosin_ADP">
      <variable units="micromolar" public_interface="out" name="Actomyosin_ADP" initial_value="1.0"/>
      <variable units="flux" public_interface="in" name="delta_Actomyosin_ADP_rxn4"/>
      <variable units="flux" public_interface="in" name="delta_Actomyosin_ADP_rxn3"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Actomyosin_ADP</ci>
            </apply>
            <apply>
               <plus/>
               <ci>delta_Actomyosin_ADP_rxn4</ci>
               <ci>delta_Actomyosin_ADP_rxn3</ci>
            </apply>
         </apply>
      </math>
   </component>
 
   <component cmeta:id="Pi" name="Pi">
      <variable units="micromolar" public_interface="out" name="Pi" initial_value="1.0"/>
      <variable units="flux" public_interface="in" name="delta_Pi_rxn4"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Pi</ci>
            </apply>
            <ci>delta_Pi_rxn4</ci>
         </apply>
      </math>
   </component>
  
   <component cmeta:id="Actomyosin_ADP_Pi" name="Actomyosin_ADP_Pi">
      <variable units="micromolar" public_interface="out" name="Actomyosin_ADP_Pi" initial_value="1.0"/>
      <variable units="flux" public_interface="in" name="delta_Actomyosin_ADP_Pi_rxn5"/>
      <variable units="flux" public_interface="in" name="delta_Actomyosin_ADP_Pi_rxn6"/>
      <variable units="flux" public_interface="in" name="delta_Actomyosin_ADP_Pi_rxn4"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Actomyosin_ADP_Pi</ci>
            </apply>
            <apply>
               <plus/>
               <ci>delta_Actomyosin_ADP_Pi_rxn5</ci>
               <ci>delta_Actomyosin_ADP_Pi_rxn6</ci>
               <ci>delta_Actomyosin_ADP_Pi_rxn4</ci>
            </apply>
         </apply>
      </math>
   </component>
  
   <component cmeta:id="Myosin_ADP_Pi" name="Myosin_ADP_Pi">
      <variable units="micromolar" public_interface="out" name="Myosin_ADP_Pi" initial_value="1.0"/>
      <variable units="flux" public_interface="in" name="delta_Myosin_ADP_Pi_rxn7"/>
      <variable units="flux" public_interface="in" name="delta_Myosin_ADP_Pi_rxn5"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Myosin_ADP_Pi</ci>
            </apply>
            <apply>
               <plus/>
               <ci>delta_Myosin_ADP_Pi_rxn7</ci>
               <ci>delta_Myosin_ADP_Pi_rxn5</ci>
            </apply>
         </apply>
      </math>
   </component>
  
   <component cmeta:id="Troponin_C" name="Troponin_C">
      <variable units="micromolar" public_interface="out" name="Troponin_C" initial_value="1.0"/>
      <variable units="flux" public_interface="in" name="delta_Troponin_C_rxn8"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Troponin_C</ci>
            </apply>
            <ci>delta_Troponin_C_rxn8</ci>
         </apply>
      </math>
   </component>
 
   <component cmeta:id="Troponin_C_Ca" name="Troponin_C_Ca">
      <variable units="micromolar" public_interface="out" name="Troponin_C_Ca" initial_value="1.0"/>
      <variable units="flux" public_interface="in" name="delta_Troponin_C_Ca_rxn8"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Troponin_C_Ca</ci>
            </apply>
            <ci>delta_Troponin_C_Ca_rxn8</ci>
         </apply>
      </math>
   </component>
  
   <component cmeta:id="Ca_i" name="Ca_i">
      <variable units="micromolar" public_interface="out" name="Ca_i" initial_value="1.0"/>
      <variable units="flux" public_interface="in" name="kr"/>
      <variable units="flux" public_interface="in" name="delta_Ca_i_rxn8"/>
      <variable units="flux" public_interface="in" name="delta_Ca_F"/>
      <variable units="second" public_interface="in" name="time"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ca_i</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <plus/>
                  <ci>delta_Ca_i_rxn8</ci>
                  <ci>delta_Ca_F</ci>
               </apply>
               <apply>
                  <times/>
                  <ci>kr</ci>
                  <ci>Ca_i</ci>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   
   <component cmeta:id="delta_Ca_F" name="delta_Ca_F">
      <variable units="flux" public_interface="out" name="delta_Ca_F" initial_value="480.0"/>
      <variable units="second" public_interface="in" name="time"/>
   </component>
   
   <!--
    The following component represents a calcium pump in the sarcoplasmic 
    reticulum.
   -->
   
   <component cmeta:id="Ca_pump" name="Ca_pump">
      <variable units="flux" public_interface="out" name="kr" initial_value="1.0"/>
      
      <variable units="micromolar" name="Ca_SR" initial_value="1.0"/>
      <variable units="second" name="tau_kr" initial_value="1.0"/>
      
      <variable units="micromolar" public_interface="in" name="Ca_i"/>
      <variable units="second" public_interface="in" name="time"/>
      
      <math xmlns="http://www.w3.org/1998/Math/MathML">    
         <apply id="kr_calculation">
        <eq/>
           <ci> kr </ci>
           <apply>
          <divide/>
              <apply>
            <minus/>
                 <ci> Ca_i </ci>
                 <ci> Ca_SR </ci>
              </apply>
              <ci> tau_kr </ci>
           </apply>
        </apply>
      </math>
   </component>
   
   <!--
    The following components represent the reaction steps of the 
    elctromechanical heart contractile system.
   -->
  
   <component name="reaction0">
      <variable units="micromolar" public_interface="in" name="Myosin"/>
      <variable units="micromolar" public_interface="in" name="ATP"/>
      <variable units="micromolar" public_interface="in" name="Myosin_ATP"/>
      <variable units="flux" public_interface="out" name="delta_Myosin_rxn0"/>
      <variable units="flux" public_interface="out" name="delta_ATP_rxn0"/>
      <variable units="flux" public_interface="out" name="delta_Myosin_ATP_rxn0"/>
      <variable units="second_order_rate_constant" name="k0" initial_value="1.0"/>
      <variable units="first_order_rate_constant" name="k0_" initial_value="1.0"/>
      <variable units="flux" name="rate"/>
      <reaction reversible="yes">
         <variable_ref variable="Myosin">
            <role stoichiometry="1" direction="forward" delta_variable="delta_Myosin_rxn0" role="reactant"/>
         </variable_ref>
         <variable_ref variable="ATP">
            <role stoichiometry="1" direction="forward" delta_variable="delta_ATP_rxn0" role="reactant"/>
         </variable_ref>
         <variable_ref variable="Myosin_ATP">
            <role stoichiometry="1" direction="forward" delta_variable="delta_Myosin_ATP_rxn0" role="product"/>
         </variable_ref>
         <variable_ref variable="rate">
            <role role="rate">
               <math xmlns="http://www.w3.org/1998/Math/MathML">
                  <apply>
                     <eq/>
                     <ci>rate</ci>
                     <apply>
                        <plus/>
                        <apply>
                           <times/>
                           <ci>k0</ci>
                           <ci>Myosin</ci>
                           <ci>ATP</ci>
                        </apply>
                        <apply>
                           <minus/>
                           <apply>
                              <times/>
                              <ci>k0_</ci>
                              <ci>Myosin_ATP</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </math>
            </role>
         </variable_ref>
      </reaction>
   </component>
  
   <component name="reaction1">
      <variable units="micromolar" public_interface="in" name="Actin"/>
      <variable units="micromolar" public_interface="in" name="Myosin_ATP"/>
      <variable units="micromolar" public_interface="in" name="Actomyosin_ATP"/>
      <variable units="flux" public_interface="out" name="delta_Actin_rxn1"/>
      <variable units="flux" public_interface="out" name="delta_Myosin_ATP_rxn1"/>
      <variable units="flux" public_interface="out" name="delta_Actomyosin_ATP_rxn1"/>
      <variable units="second_order_rate_constant" name="k1" initial_value="1.0"/>
      <variable units="first_order_rate_constant" name="k1_" initial_value="1.0"/>
      <variable units="flux" name="rate"/>
      <reaction reversible="yes">
         <variable_ref variable="Actin">
            <role stoichiometry="1" direction="forward" delta_variable="delta_Actin_rxn1" role="reactant"/>
         </variable_ref>
         <variable_ref variable="Myosin_ATP">
            <role stoichiometry="1" direction="forward" delta_variable="delta_Myosin_ATP_rxn1" role="reactant"/>
         </variable_ref>
         <variable_ref variable="Actomyosin_ATP">
            <role stoichiometry="1" direction="forward" delta_variable="delta_Actomyosin_ATP_rxn1" role="product"/>
         </variable_ref>
         <variable_ref variable="rate">
            <role role="rate">
               <math xmlns="http://www.w3.org/1998/Math/MathML">
                  <apply>
                     <eq/>
                     <ci>rate</ci>
                     <apply>
                        <plus/>
                        <apply>
                           <times/>
                           <ci>k1</ci>
                           <ci>Actin</ci>
                           <ci>Myosin_ATP</ci>
                        </apply>
                        <apply>
                           <minus/>
                           <apply>
                              <times/>
                              <ci>k1_</ci>
                              <ci>Actomyosin_ATP</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </math>
            </role>
         </variable_ref>
      </reaction>
   </component>
  
   <component name="reaction2">
      <variable units="micromolar" public_interface="in" name="ATP"/>
      <variable units="micromolar" public_interface="in" name="Actomyosin"/>
      <variable units="micromolar" public_interface="in" name="Actomyosin_ATP"/>
      <variable units="flux" public_interface="out" name="delta_ATP_rxn2"/>
      <variable units="flux" public_interface="out" name="delta_Actomyosin_rxn2"/>
      <variable units="flux" public_interface="out" name="delta_Actomyosin_ATP_rxn2"/>
      <variable units="second_order_rate_constant" name="k2" initial_value="1.0"/>
      <variable units="first_order_rate_constant" name="k2_" initial_value="1.0"/>
      <variable units="flux" name="rate"/>
      <reaction reversible="yes">
         <variable_ref variable="ATP">
            <role stoichiometry="1" direction="forward" delta_variable="delta_ATP_rxn2" role="reactant"/>
         </variable_ref>
         <variable_ref variable="Actomyosin">
            <role stoichiometry="1" direction="forward" delta_variable="delta_Actomyosin_rxn2" role="reactant"/>
         </variable_ref>
         <variable_ref variable="Actomyosin_ATP">
            <role stoichiometry="1" direction="forward" delta_variable="delta_Actomyosin_ATP_rxn2" role="product"/>
         </variable_ref>
         <variable_ref variable="rate">
            <role role="rate">
               <math xmlns="http://www.w3.org/1998/Math/MathML">
                  <apply>
                     <eq/>
                     <ci>rate</ci>
                     <apply>
                        <plus/>
                        <apply>
                           <times/>
                           <ci>k2</ci>
                           <ci>ATP</ci>
                           <ci>Actomyosin</ci>
                        </apply>
                        <apply>
                           <minus/>
                           <apply>
                              <times/>
                              <ci>k2_</ci>
                              <ci>Actomyosin_ATP</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </math>
            </role>
         </variable_ref>
      </reaction>
   </component>
  
   <component name="reaction3">
      <variable units="micromolar" public_interface="in" name="Actomyosin_ADP"/>
      <variable units="micromolar" public_interface="in" name="ADP"/>
      <variable units="micromolar" public_interface="in" name="Actomyosin"/>
      <variable units="flux" public_interface="out" name="delta_Actomyosin_ADP_rxn3"/>
      <variable units="flux" public_interface="out" name="delta_ADP_rxn3"/>
      <variable units="flux" public_interface="out" name="delta_Actomyosin_rxn3"/>
      <variable units="first_order_rate_constant" name="k3" initial_value="1.0"/>
      <variable units="flux" name="rate"/>
      <reaction reversible="no">
         <variable_ref variable="Actomyosin_ADP">
            <role stoichiometry="1" delta_variable="delta_Actomyosin_ADP_rxn3" role="reactant"/>
         </variable_ref>
         <variable_ref variable="ADP">
            <role stoichiometry="1" delta_variable="delta_ADP_rxn3" role="product"/>
         </variable_ref>
         <variable_ref variable="Actomyosin">
            <role stoichiometry="1" delta_variable="delta_Actomyosin_rxn3" role="product"/>
         </variable_ref>
         <variable_ref variable="rate">
            <role role="rate">
               <math xmlns="http://www.w3.org/1998/Math/MathML">
                  <apply>
                     <eq/>
                     <ci>rate</ci>
                     <apply>
                        <times/>
                        <ci>k3</ci>
                        <ci>Actomyosin_ADP</ci>
                     </apply>
                  </apply>
               </math>
            </role>
         </variable_ref>
      </reaction>
   </component>
 
   <component name="reaction4">
      <variable units="micromolar" public_interface="in" name="Actomyosin_ADP_Pi"/>
      <variable units="micromolar" public_interface="in" name="Pi"/>
      <variable units="micromolar" public_interface="in" name="Actomyosin_ADP"/>
      <variable units="flux" public_interface="out" name="delta_Actomyosin_ADP_Pi_rxn4"/>
      <variable units="flux" public_interface="out" name="delta_Pi_rxn4"/>
      <variable units="flux" public_interface="out" name="delta_Actomyosin_ADP_rxn4"/>
      <variable units="first_order_rate_constant" name="k4" initial_value="1.0"/>
      <variable units="flux" name="rate"/>
      <reaction reversible="no">
         <variable_ref variable="Actomyosin_ADP_Pi">
            <role stoichiometry="1" delta_variable="delta_Actomyosin_ADP_Pi_rxn4" role="reactant"/>
         </variable_ref>
         <variable_ref variable="Pi">
            <role stoichiometry="1" delta_variable="delta_Pi_rxn4" role="product"/>
         </variable_ref>
         <variable_ref variable="Actomyosin_ADP">
            <role stoichiometry="1" delta_variable="delta_Actomyosin_ADP_rxn4" role="product"/>
         </variable_ref>
         <variable_ref variable="rate">
            <role role="rate">
               <math xmlns="http://www.w3.org/1998/Math/MathML">
                  <apply>
                     <eq/>
                     <ci>rate</ci>
                     <apply>
                        <times/>
                        <ci>k4</ci>
                        <ci>Actomyosin_ADP_Pi</ci>
                     </apply>
                  </apply>
               </math>
            </role>
         </variable_ref>
      </reaction>
   </component>
  
   <component name="reaction5">
      <variable units="micromolar" public_interface="in" name="Myosin_ADP_Pi"/>
      <variable units="micromolar" public_interface="in" name="Actin"/>
      <variable units="micromolar" public_interface="in" name="Actomyosin_ADP_Pi"/>
      <variable units="flux" public_interface="out" name="delta_Myosin_ADP_Pi_rxn5"/>
      <variable units="flux" public_interface="out" name="delta_Actin_rxn5"/>
      <variable units="flux" public_interface="out" name="delta_Actomyosin_ADP_Pi_rxn5"/>
      <variable units="second_order_rate_constant" name="k5" initial_value="1.0"/>
      <variable units="first_order_rate_constant" name="k5_" initial_value="1.0"/>
      <variable units="flux" name="rate"/>
      <reaction reversible="yes">
         <variable_ref variable="Myosin_ADP_Pi">
            <role stoichiometry="1" direction="forward" delta_variable="delta_Myosin_ADP_Pi_rxn5" role="reactant"/>
         </variable_ref>
         <variable_ref variable="Actin">
            <role stoichiometry="1" direction="forward" delta_variable="delta_Actin_rxn5" role="reactant"/>
         </variable_ref>
         <variable_ref variable="Actomyosin_ADP_Pi">
            <role stoichiometry="1" direction="forward" delta_variable="delta_Actomyosin_ADP_Pi_rxn5" role="product"/>
         </variable_ref>
         <variable_ref variable="rate">
            <role role="rate">
               <math xmlns="http://www.w3.org/1998/Math/MathML">
                  <apply>
                     <eq/>
                     <ci>rate</ci>
                     <apply>
                        <plus/>
                        <apply>
                           <times/>
                           <ci>k5</ci>
                           <ci>Myosin_ADP_Pi</ci>
                           <ci>Actin</ci>
                        </apply>
                        <apply>
                           <minus/>
                           <apply>
                              <times/>
                              <ci>k5_</ci>
                              <ci>Actomyosin_ADP_Pi</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </math>
            </role>
         </variable_ref>
      </reaction>
   </component>
 
   <component name="reaction6">
      <variable units="micromolar" public_interface="in" name="Actomyosin_ATP"/>
      <variable units="micromolar" public_interface="in" name="Actomyosin_ADP_Pi"/>
      <variable units="flux" public_interface="out" name="delta_Actomyosin_ATP_rxn6"/>
      <variable units="flux" public_interface="out" name="delta_Actomyosin_ADP_Pi_rxn6"/>
      <variable units="first_order_rate_constant" name="k6" initial_value="1.0"/>
      <variable units="first_order_rate_constant" name="k6_" initial_value="1.0"/>
      <variable units="flux" name="rate"/>
      <reaction reversible="yes">
         <variable_ref variable="Actomyosin_ATP">
            <role stoichiometry="1" direction="forward" delta_variable="delta_Actomyosin_ATP_rxn6" role="reactant"/>
         </variable_ref>
         <variable_ref variable="Actomyosin_ADP_Pi">
            <role stoichiometry="1" direction="forward" delta_variable="delta_Actomyosin_ADP_Pi_rxn6" role="product"/>
         </variable_ref>
         <variable_ref variable="rate">
            <role role="rate">
               <math xmlns="http://www.w3.org/1998/Math/MathML">
                  <apply>
                     <eq/>
                     <ci>rate</ci>
                     <apply>
                        <plus/>
                        <apply>
                           <times/>
                           <ci>k6</ci>
                           <ci>Actomyosin_ATP</ci>
                        </apply>
                        <apply>
                           <minus/>
                           <apply>
                              <times/>
                              <ci>k6_</ci>
                              <ci>Actomyosin_ADP_Pi</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </math>
            </role>
         </variable_ref>
      </reaction>
   </component>
  
   <component name="reaction7">
      <variable units="micromolar" public_interface="in" name="Myosin_ATP"/>
      <variable units="micromolar" public_interface="in" name="Myosin_ADP_Pi"/>
      <variable units="flux" public_interface="out" name="delta_Myosin_ATP_rxn7"/>
      <variable units="flux" public_interface="out" name="delta_Myosin_ADP_Pi_rxn7"/>
      <variable units="first_order_rate_constant" name="k7" initial_value="1.0"/>
      <variable units="first_order_rate_constant" name="k7_" initial_value="1.0"/>
      <variable units="flux" name="rate"/>
      <reaction reversible="yes">
         <variable_ref variable="Myosin_ATP">
            <role stoichiometry="1" direction="forward" delta_variable="delta_Myosin_ATP_rxn7" role="reactant"/>
         </variable_ref>
         <variable_ref variable="Myosin_ADP_Pi">
            <role stoichiometry="1" direction="forward" delta_variable="delta_Myosin_ADP_Pi_rxn7" role="product"/>
         </variable_ref>
         <variable_ref variable="rate">
            <role role="rate">
               <math xmlns="http://www.w3.org/1998/Math/MathML">
                  <apply>
                     <eq/>
                     <ci>rate</ci>
                     <apply>
                        <plus/>
                        <apply>
                           <times/>
                           <ci>k7</ci>
                           <ci>Myosin_ATP</ci>
                        </apply>
                        <apply>
                           <minus/>
                           <apply>
                              <times/>
                              <ci>k7_</ci>
                              <ci>Myosin_ADP_Pi</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </math>
            </role>
         </variable_ref>
      </reaction>
   </component>
  
   <component name="reaction8">
      <variable units="micromolar" public_interface="in" name="Troponin_C"/>
      <variable units="micromolar" public_interface="in" name="Ca_i"/>
      <variable units="micromolar" public_interface="in" name="Troponin_C_Ca"/>
      <variable units="flux" public_interface="out" name="delta_Troponin_C_rxn8"/>
      <variable units="flux" public_interface="out" name="delta_Ca_i_rxn8"/>
      <variable units="flux" public_interface="out" name="delta_Troponin_C_Ca_rxn8"/>
      <variable units="second_order_rate_constant" name="k8" initial_value="1.0"/>
      <variable units="first_order_rate_constant" name="k8_" initial_value="1.0"/>
      <variable units="flux" name="rate"/>
      <reaction reversible="yes">
         <variable_ref variable="Troponin_C">
            <role stoichiometry="1" direction="forward" delta_variable="delta_Troponin_C_rxn8" role="reactant"/>
         </variable_ref>
         <variable_ref variable="Ca_i">
            <role stoichiometry="1" direction="forward" delta_variable="delta_Ca_i_rxn8" role="reactant"/>
         </variable_ref>
         <variable_ref variable="Troponin_C_Ca">
            <role stoichiometry="1" direction="forward" delta_variable="delta_Troponin_C_Ca_rxn8" role="product"/>
         </variable_ref>
         <variable_ref variable="rate">
            <role role="rate">
               <math xmlns="http://www.w3.org/1998/Math/MathML">
                  <apply>
                     <eq/>
                     <ci>rate</ci>
                     <apply>
                        <plus/>
                        <apply>
                           <times/>
                           <ci>k8</ci>
                           <ci>Troponin_C</ci>
                           <ci>Ca_i</ci>
                        </apply>
                        <apply>
                           <minus/>
                           <apply>
                              <times/>
                              <ci>k8_</ci>
                              <ci>Troponin_C_Ca</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </math>
            </role>
         </variable_ref>
      </reaction>
   </component>
 
   <connection>
      <map_components component_2="reaction1" component_1="Actin"/>
      <map_variables variable_2="Actin" variable_1="Actin"/>
      <map_variables variable_2="delta_Actin_rxn1" variable_1="delta_Actin_rxn1"/>
   </connection>
 
   <connection>
      <map_components component_2="reaction5" component_1="Actin"/>
      <map_variables variable_2="Actin" variable_1="Actin"/>
      <map_variables variable_2="delta_Actin_rxn5" variable_1="delta_Actin_rxn5"/>
   </connection>
 
   <connection>
      <map_components component_2="reaction0" component_1="Myosin"/>
      <map_variables variable_2="Myosin" variable_1="Myosin"/>
      <map_variables variable_2="delta_Myosin_rxn0" variable_1="delta_Myosin_rxn0"/>
   </connection>
  
   <connection>
      <map_components component_2="reaction0" component_1="ATP"/>
      <map_variables variable_2="ATP" variable_1="ATP"/>
      <map_variables variable_2="delta_ATP_rxn0" variable_1="delta_ATP_rxn0"/>
   </connection>
  
   <connection>
      <map_components component_2="reaction2" component_1="ATP"/>
      <map_variables variable_2="ATP" variable_1="ATP"/>
      <map_variables variable_2="delta_ATP_rxn2" variable_1="delta_ATP_rxn2"/>
   </connection>
   
   <connection>
      <map_components component_2="reaction3" component_1="ADP"/>
      <map_variables variable_2="ADP" variable_1="ADP"/>
      <map_variables variable_2="delta_ADP_rxn3" variable_1="delta_ADP_rxn3"/>
   </connection>
  
   <connection>
      <map_components component_2="reaction0" component_1="Myosin_ATP"/>
      <map_variables variable_2="Myosin_ATP" variable_1="Myosin_ATP"/>
      <map_variables variable_2="delta_Myosin_ATP_rxn0" variable_1="delta_Myosin_ATP_rxn0"/>
   </connection>
  
   <connection>
      <map_components component_2="reaction1" component_1="Myosin_ATP"/>
      <map_variables variable_2="Myosin_ATP" variable_1="Myosin_ATP"/>
      <map_variables variable_2="delta_Myosin_ATP_rxn1" variable_1="delta_Myosin_ATP_rxn1"/>
   </connection>
  
   <connection>
      <map_components component_2="reaction7" component_1="Myosin_ATP"/>
      <map_variables variable_2="Myosin_ATP" variable_1="Myosin_ATP"/>
      <map_variables variable_2="delta_Myosin_ATP_rxn7" variable_1="delta_Myosin_ATP_rxn7"/>
   </connection>
 
   <connection>
      <map_components component_2="reaction1" component_1="Actomyosin_ATP"/>
      <map_variables variable_2="Actomyosin_ATP" variable_1="Actomyosin_ATP"/>
      <map_variables variable_2="delta_Actomyosin_ATP_rxn1" variable_1="delta_Actomyosin_ATP_rxn1"/>
   </connection>
   
   <connection>
      <map_components component_2="reaction2" component_1="Actomyosin_ATP"/>
      <map_variables variable_2="Actomyosin_ATP" variable_1="Actomyosin_ATP"/>
      <map_variables variable_2="delta_Actomyosin_ATP_rxn2" variable_1="delta_Actomyosin_ATP_rxn2"/>
   </connection>
  
   <connection>
      <map_components component_2="reaction6" component_1="Actomyosin_ATP"/>
      <map_variables variable_2="Actomyosin_ATP" variable_1="Actomyosin_ATP"/>
      <map_variables variable_2="delta_Actomyosin_ATP_rxn6" variable_1="delta_Actomyosin_ATP_rxn6"/>
   </connection>
 
   <connection>
      <map_components component_2="reaction3" component_1="Actomyosin"/>
      <map_variables variable_2="Actomyosin" variable_1="Actomyosin"/>
      <map_variables variable_2="delta_Actomyosin_rxn3" variable_1="delta_Actomyosin_rxn3"/>
   </connection>
  
   <connection>
      <map_components component_2="reaction2" component_1="Actomyosin"/>
      <map_variables variable_2="Actomyosin" variable_1="Actomyosin"/>
      <map_variables variable_2="delta_Actomyosin_rxn2" variable_1="delta_Actomyosin_rxn2"/>
   </connection>
  
   <connection>
      <map_components component_2="reaction4" component_1="Actomyosin_ADP"/>
      <map_variables variable_2="Actomyosin_ADP" variable_1="Actomyosin_ADP"/>
      <map_variables variable_2="delta_Actomyosin_ADP_rxn4" variable_1="delta_Actomyosin_ADP_rxn4"/>
   </connection>
 
   <connection>
      <map_components component_2="reaction3" component_1="Actomyosin_ADP"/>
      <map_variables variable_2="Actomyosin_ADP" variable_1="Actomyosin_ADP"/>
      <map_variables variable_2="delta_Actomyosin_ADP_rxn3" variable_1="delta_Actomyosin_ADP_rxn3"/>
   </connection>
  
   <connection>
      <map_components component_2="reaction4" component_1="Pi"/>
      <map_variables variable_2="Pi" variable_1="Pi"/>
      <map_variables variable_2="delta_Pi_rxn4" variable_1="delta_Pi_rxn4"/>
   </connection>
  
   <connection>
      <map_components component_2="reaction5" component_1="Actomyosin_ADP_Pi"/>
      <map_variables variable_2="Actomyosin_ADP_Pi" variable_1="Actomyosin_ADP_Pi"/>
      <map_variables variable_2="delta_Actomyosin_ADP_Pi_rxn5" variable_1="delta_Actomyosin_ADP_Pi_rxn5"/>
   </connection>
  
   <connection>
      <map_components component_2="reaction6" component_1="Actomyosin_ADP_Pi"/>
      <map_variables variable_2="Actomyosin_ADP_Pi" variable_1="Actomyosin_ADP_Pi"/>
      <map_variables variable_2="delta_Actomyosin_ADP_Pi_rxn6" variable_1="delta_Actomyosin_ADP_Pi_rxn6"/>
   </connection>
  
   <connection>
      <map_components component_2="reaction4" component_1="Actomyosin_ADP_Pi"/>
      <map_variables variable_2="Actomyosin_ADP_Pi" variable_1="Actomyosin_ADP_Pi"/>
      <map_variables variable_2="delta_Actomyosin_ADP_Pi_rxn4" variable_1="delta_Actomyosin_ADP_Pi_rxn4"/>
   </connection>
   
   <connection>
      <map_components component_2="reaction7" component_1="Myosin_ADP_Pi"/>
      <map_variables variable_2="Myosin_ADP_Pi" variable_1="Myosin_ADP_Pi"/>
      <map_variables variable_2="delta_Myosin_ADP_Pi_rxn7" variable_1="delta_Myosin_ADP_Pi_rxn7"/>
   </connection>
  
   <connection>
      <map_components component_2="reaction5" component_1="Myosin_ADP_Pi"/>
      <map_variables variable_2="Myosin_ADP_Pi" variable_1="Myosin_ADP_Pi"/>
      <map_variables variable_2="delta_Myosin_ADP_Pi_rxn5" variable_1="delta_Myosin_ADP_Pi_rxn5"/>
   </connection>
  
   <connection>
      <map_components component_2="reaction8" component_1="Troponin_C"/>
      <map_variables variable_2="Troponin_C" variable_1="Troponin_C"/>
      <map_variables variable_2="delta_Troponin_C_rxn8" variable_1="delta_Troponin_C_rxn8"/>
   </connection>
   
   <connection>
      <map_components component_2="reaction8" component_1="Troponin_C_Ca"/>
      <map_variables variable_2="Troponin_C_Ca" variable_1="Troponin_C_Ca"/>
      <map_variables variable_2="delta_Troponin_C_Ca_rxn8" variable_1="delta_Troponin_C_Ca_rxn8"/>
   </connection>
  
   <connection>
      <map_components component_2="reaction8" component_1="Ca_i"/>
      <map_variables variable_2="Ca_i" variable_1="Ca_i"/>
      <map_variables variable_2="delta_Ca_i_rxn8" variable_1="delta_Ca_i_rxn8"/>
   </connection>
   
   <connection>
      <map_components component_2="global_variables" component_1="Actin"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   
   <connection>
      <map_components component_2="global_variables" component_1="Myosin"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   
   <connection>
      <map_components component_2="global_variables" component_1="ATP"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   
   <connection>
      <map_components component_2="global_variables" component_1="ADP"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
  
   <connection>
      <map_components component_2="global_variables" component_1="Myosin_ATP"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
  
   <connection>
      <map_components component_2="global_variables" component_1="Actomyosin_ATP"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   
   <connection>
      <map_components component_2="global_variables" component_1="Actomyosin"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
 
   <connection>
      <map_components component_2="global_variables" component_1="Actomyosin_ADP"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
  
   <connection>
      <map_components component_2="global_variables" component_1="Pi"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   
   <connection>
      <map_components component_2="global_variables" component_1="Actomyosin_ADP_Pi"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   
   <connection>
      <map_components component_2="global_variables" component_1="Myosin_ADP_Pi"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
  
   <connection>
      <map_components component_2="global_variables" component_1="Troponin_C"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
  
   <connection>
      <map_components component_2="global_variables" component_1="Troponin_C_Ca"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
  
   <connection>
      <map_components component_2="global_variables" component_1="Ca_i"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   
   <connection>
      <map_components component_2="Ca_pump" component_1="Ca_i"/>
      <map_variables variable_2="kr" variable_1="kr"/>
      <map_variables variable_2="Ca_i" variable_1="Ca_i"/>
   </connection>
   
   <connection>
      <map_components component_2="delta_Ca_F" component_1="Ca_i"/>
      <map_variables variable_2="delta_Ca_F" variable_1="delta_Ca_F"/>
   </connection>
   
   <connection>
      <map_components component_2="global_variables" component_1="delta_Ca_F"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>
   
   <connection>
      <map_components component_2="global_variables" component_1="Ca_pump"/>
      <map_variables variable_2="time" variable_1="time"/>
   </connection>


<rdf:RDF>
  <rdf:Bag rdf:about="rdf:#30ee0e52-f40c-4d2c-87f1-2c570dc4d6a9">
    <rdf:li>Cardiac Myocyte</rdf:li>
    <rdf:li>Molecular Mechanisms</rdf:li>
  </rdf:Bag>
  <rdf:Seq rdf:about="rdf:#397f8ce4-bccc-4f79-8d45-d1a70e4ab8f2">
    <rdf:li rdf:resource="rdf:#91a5b11c-40fc-4d90-a001-908daaac5f9c"/>
    <rdf:li rdf:resource="rdf:#aa83c3a2-e8b0-446c-aad5-4ac00f1d21ae"/>
    <rdf:li rdf:resource="rdf:#e03ad4ff-ba20-405f-9eeb-bcaebb24b0e3"/>
    <rdf:li rdf:resource="rdf:#fd6dfca4-c034-4c14-990c-5a555bdc0d36"/>
  </rdf:Seq>
  <rdf:Description rdf:about="rdf:#b4904208-3e10-4e23-8997-b40dba5708e7">
    <dc:subject rdf:resource="rdf:#fb7d123a-023b-4739-81fe-d0bdcb53fa62"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#0a2d830e-978f-452d-9bec-6d650779a44d">
    <vCard:Given>O</vCard:Given>
    <vCard:Family>Kittnar</vCard:Family>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#d044b95c-0485-43d7-9f26-3ee48e864acf">
    <vCard:Given>M</vCard:Given>
    <vCard:Family>Mlcek</vCard:Family>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#dac69bf8-b86a-467a-bb89-a5ffe769607e">
    <vCard:Given>Catherine</vCard:Given>
    <vCard:Family>Lloyd</vCard:Family>
    <vCard:Other>May</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#ab2eb79b-e12c-4d5c-85cd-a113865ec2ad">
    <vCard:N rdf:resource="rdf:#dac69bf8-b86a-467a-bb89-a5ffe769607e"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#1150a657-330d-4e41-8988-803ef02600a2">
    <dc:creator rdf:resource="rdf:#397f8ce4-bccc-4f79-8d45-d1a70e4ab8f2"/>
    <dc:title>
            Mathematical Model of the Electromechanical Heart Contractile System             - Regulatory Subsystem Physiological Considerations
          </dc:title>
    <bqs:volume>50</bqs:volume>
    <bqs:first_page>425</bqs:first_page>
    <bqs:Journal rdf:resource="rdf:#66deb655-fb61-4e9c-82e2-b18f284a3bde"/>
    <dcterms:issued rdf:resource="rdf:#3dc20cc2-35ba-42cc-a029-1a349f6a4ff7"/>
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        Mlcek et al's 2001 mathematical model of the elctromechanical heart 
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