Location: Hunter, Mcculloch, Terkeurs, 1998 @ 1becea7999ac / hunter_mcculloch_terkeurs_1998.cellml

Author:
pmr2.import <nobody@models.cellml.org>
Date:
2006-07-09 07:39:15+12:00
Desc:
committing version01 of hunter_mcculloch_terkeurs_1998
Permanent Source URI:
http://models.cellml.org/workspace/hunter_mcculloch_terkeurs_1998/rawfile/1becea7999ac106e7cf27771642257757ac3060a/hunter_mcculloch_terkeurs_1998.cellml

<?xml version='1.0' encoding='utf-8'?>
<!--  FILE :  HMT_model_1998.xml

CREATED :  15th March 2002

LAST MODIFIED :  20th August 2002

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

DESCRIPTION :  This file contains a CellML description of Hunter, McCulloch and ter Keurs's 1998 mathematical model of the mechanical properties of cardiac muscle.

CHANGES: 
  16/04/2002 - CML - Corrected the name of the model, from HMK to HMT.  Merged 
                     the two equations for T_11 into one, piecewise equation.
  18/07/2002 - CML - Added more metadata.
  20/08/2002 - AAC - Removed the 'passive_elasticity' component.
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:ns8="http://www.rddl.org//" xmlns:ns9="http://www.rddl.org///" 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:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:rddl="http://www.rddl.org/" xmlns:ns7="http://www.w3.org/1999/" cmeta:id="hunter_mcculloch_terkeurs_1998_version01" name="hunter_mcculloch_terkeurs_1998_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>The Mechanical Properties of Cardiac Muscle, 1998</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 model is not currently functional (overconstrained).
          </para>
  </section>
  <sect1 id="sec_structure">
<title>Model Structure</title>

<para> 
Finite element models of the electrical and mechanical behaviour of the whole heart are well established.  At the cellular level, there are several models published which describe the changes in ion concentrations and membrane ionic currents underlying the cardiac cell action potential.  However, the Hunter-McCulloch-ter Keurs 1998 model is the first to capture the mechanical properties of actively contracting cardiac muscle.  The model is based on an extensive review of experimental data from a variety of preparations and species.  These experiments are interpreted with a four state variable model which includes i) the passive elasticity of myocardial tissue, ii) the rapid binding of Ca<superscript>2+</superscript> to troponin C, iii) the kinetics of tropomyosin movement and iv) the kinetics of crossbridge tension development.   
</para>

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

<para>
<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&amp;_udi=B6TBN-3V3YR56-B&amp;_user=140507&amp;_handle=B-WA-A-A-WC-MsSAYWA-UUA-AUEWCYYWWE-AUEUAZEUWE-CWBYCADUE-WC-U&amp;_fmt=summary&amp;_coverDate=03%2F05%2F1998&amp;_rdoc=10&amp;_orig=browse&amp;_srch=%23toc%235147%231998%23999309997%2329171!&amp;_cdi=5147&amp;view=c&amp;_acct=C000011498&amp;_version=1&amp;_urlVersion=0&amp;_userid=140507&amp;md5=5533102f7cfadc6100d342bb5f784bcb">Modelling the mechanical properties of cardiac muscle</ulink>, P.J. Hunter, A.D. McCulloch and H.E.D.J. ter Keurs, 1998, <ulink url="http://www.sciencedirect.com/science/journal/00796107">
            <emphasis>Progress in Biophysics and Molecular Biology</emphasis>
          </ulink>, 69, 289-331.  (A PDF version of the article is available to <emphasis>Science Direct</emphasis> subscribers.)  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=9785944&amp;dopt=Abstract">PubMed ID: 9785944</ulink> 
</para>

<para>
The raw CellML description of the Hunter-McCulloch-ter Keurs model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>.  For an example of a more complete documentation for an electrophysiological model, see <ulink url="${HTML_EXMPL_HHSA_INTRO}">The Hodgkin-Huxley Squid Axon Model, 1952</ulink>. 
</para>

</sect1>
</article>
</documentation>
  
  
  <!--
    Below, we define some additional units for association with variables and
    constants within the model. The identifiers are fairly self-explanatory.
  -->
  
  <units name="micromolar">
    <unit units="mole" prefix="micro"/>
    <unit units="litre" 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>
  
  <units name="kilopascal">
    <unit units="pascal" prefix="kilo"/>
  </units>
  
  <units name="per_kilopascal">
    <unit units="kilopascal" exponent="-1"/>
  </units>
 
  <!--
    The "environment" component is used to declare variables that are used by
    all or most of the other components, in this case just "time".
  -->
  <component name="environment">
    <variable units="second" public_interface="out" name="time"/>
  </component>
  
  <component name="calcium_transient">
  <variable units="micromolar" public_interface="out" name="Ca_i" initial_value="10.0"/>
              
  <variable units="micromolar" name="Ca_max" initial_value="1.0"/>
  <variable units="second" name="tau_Ca" initial_value="0.06"/>
  <variable units="micromolar" name="Ca_o" initial_value="0.01"/>
  
  <variable units="second" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="dCa_i_dt">
        <eq/>
        <apply>
          <diff/>
          <bvar>
            <ci> time </ci>
          </bvar>
          <ci> Ca_i </ci>
        </apply>
        <apply>
          <plus/>
          <ci> Ca_o </ci>
          <apply>
            <times/>
            <apply>
              <minus/>
              <ci> Ca_max </ci>
              <ci> Ca_o </ci>
            </apply>
            <apply>
              <divide/>
              <ci> time </ci>
              <ci> tau_Ca </ci>
            </apply>
            <apply>
              <exp/>
              <apply>
                <divide/>
                <apply>
                  <minus/>
                  <cn cellml:units="dimensionless"> 1.0 </cn>
                  <ci> time </ci>
                </apply>
                <ci> tau_Ca </ci>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component> 
  
  <component name="TnC_Ca_binding_kinetics">
    <variable units="micromolar" public_interface="out" name="Ca_b"/>
    <variable units="dimensionless" public_interface="out" name="lambda" initial_value="2.6"/>
   
    <variable units="micromolar" name="Ca_b_max" initial_value="2.26"/>
    <variable units="second_order_rate_constant" name="rho_0" initial_value="100.0"/>
    <variable units="first_order_rate_constant" name="rho_1" initial_value="163.0"/>
    
    <variable units="second" public_interface="in" name="time"/>
    <variable units="micromolar" public_interface="in" name="Ca_i"/>
    <variable units="kilopascal" public_interface="in" name="To"/>
    <variable units="kilopascal" public_interface="in" name="T"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
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        <eq/>
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            <ci> time </ci>
          </bvar>
          <ci> Ca_b </ci>
        </apply>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> rho_0 </ci>
            <ci> Ca_i </ci>
            <apply>
              <minus/>
              <ci> Ca_b_max </ci>
              <ci> Ca_b </ci>
            </apply>
          </apply>
          <apply>
            <times/>
            <ci> rho_1 </ci>
            <ci> Ca_b </ci>
            <apply>
              <minus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <divide/>
                <ci> T </ci>
                <apply>
                  <times/>
                  <ci> lambda </ci>
                  <ci> To </ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </math>
  </component>
  
  <component name="thin_filament_kinetics">
    <variable units="kilopascal" public_interface="out" name="To"/>
    
    <variable units="dimensionless" name="z"/>
    <variable units="micromolar" name="C_50" initial_value="1.0"/>
    <variable units="micromolar" name="pC_50"/>
    <variable units="micromolar" name="pC_50_ref" initial_value="6.2"/>
    <variable units="dimensionless" name="n" initial_value="4.5"/>
    <variable units="dimensionless" name="n_ref" initial_value="6.9"/>
    <variable units="first_order_rate_constant" name="alpha_0" initial_value="2.0"/>
    <variable units="kilopascal" name="T_ref" initial_value="100.0"/>
    <variable units="per_kilopascal" name="beta_0" initial_value="1.45"/>
    <variable units="per_kilopascal" name="beta_1" initial_value="1.95"/>
    <variable units="per_kilopascal" name="beta_2" initial_value="0.31"/>
     
    <variable units="second" public_interface="in" name="time"/>
    <variable units="micromolar" public_interface="in" name="Ca_b"/>
    <variable units="dimensionless" public_interface="in" name="lambda"/>
              
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="dz_dt">
        <eq/>
        <apply>
          <diff/>
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            <ci> time </ci>
          </bvar>
          <ci> z </ci>
        </apply>
        <apply>
          <times/>
          <ci> alpha_0 </ci>
          <apply>
            <minus/>
            <apply>
              <times/>
              <apply>
                <power/>
                <apply>
                  <divide/>
                  <ci> Ca_b </ci>
                  <ci> C_50 </ci>
                </apply>
                <ci> n </ci>
              </apply>
              <apply>
                <minus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <ci> z </ci>
              </apply>
            </apply>
            <ci> z </ci>
          </apply>
        </apply>
      </apply>
      
      <apply id="To_calculation">
        <eq/>
        <ci> To </ci>
        <apply>
          <times/>
          <ci> T_ref </ci>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <times/>
              <ci> beta_0 </ci>
              <apply>
                <minus/>
                <ci> lambda </ci>
                <cn cellml:units="dimensionless"> 1.0 </cn>
              </apply>
            </apply>
          </apply>
          <ci> z </ci>
        </apply>
      </apply>
      
      <apply id="n_calculation">
        <eq/>
        <ci> n </ci>
        <apply>
          <times/>
          <ci> n_ref </ci>
          <apply>
            <plus/>
            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
              <times/>
              <ci> beta_1 </ci>
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                <ci> lambda </ci>
                <cn cellml:units="dimensionless"> 1.0 </cn>
              </apply>
            </apply>
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      <apply id="pC_50_calculation">
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          <times/>
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            <cn cellml:units="dimensionless"> 1.0 </cn>
            <apply>
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                <minus/>
                <ci> lambda </ci>
                <cn cellml:units="dimensionless"> 1.0 </cn>
              </apply>
            </apply>
          </apply>
        </apply>
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    </math>
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  <component name="crossbridge_kinetics">
    <variable units="kilopascal" public_interface="out" name="T"/>
   
    <variable units="dimensionless" name="a" initial_value="0.5"/> 
    <variable units="dimensionless" name="Q"/>
    <variable units="dimensionless" name="A1" initial_value="50.0"/>
    <variable units="dimensionless" name="A2" initial_value="175.0"/>
    <variable units="dimensionless" name="A3" initial_value="175.0"/>
    <variable units="first_order_rate_constant" name="alpha_1" initial_value="33.0"/>
    <variable units="first_order_rate_constant" name="alpha_2" initial_value="2850.0"/>
    <variable units="first_order_rate_constant" name="alpha_3" initial_value="2850.0"/>
    <variable units="second" name="tau"/>
    <variable units="first_order_rate_constant" name="dlambda_dt"/>
     
    <variable units="second" public_interface="in" name="time"/>
    <variable units="kilopascal" public_interface="in" name="To"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML">
      <apply id="dlambda_dt_calculation">
        <eq/>
        <ci> dlambda_dt </ci>
        <apply>
          <times/>
          <apply>
            <divide/>
            <ci> alpha_1 </ci>
            <ci> A1 </ci>
          </apply>
          <apply>
            <divide/>
            <apply>
              <minus/>
              <apply>
                <divide/>
                <ci> T </ci>
                <ci> To </ci>
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                <ci> T </ci>
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              <ci> a </ci>
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      <apply id="T_calculation">
        <eq/>
        <ci> T </ci>
        <apply>
          <times/>
          <ci> To </ci>
          <apply>
            <divide/>
            <apply>
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                <ci> a </ci>
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        <ci> Q </ci>
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          <plus/>
          <apply>
            <times/>
            <ci> A1 </ci>
            <apply>
              <times/>
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                <apply>
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                    <ci> tau </ci>
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              <ci> dlambda_dt </ci>
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          <apply>
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            <ci> A2 </ci>
            <apply>
              <times/>
              <apply>
                <exp/>
                <apply>
                  <times/>
                  <apply>
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                    <ci> alpha_2 </ci>
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                  <apply>
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                    <ci> time </ci>
                    <ci> tau </ci>
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              <ci> dlambda_dt </ci>
              <ci> tau </ci>
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          <apply>
            <times/>
            <ci> A3 </ci>
            <apply>
              <times/>
              <apply>
                <exp/>
                <apply>
                  <times/>
                  <apply>
                    <minus/>
                    <ci> alpha_3 </ci>
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                    <ci> tau </ci>
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              <ci> dlambda_dt </ci>
              <ci> tau </ci>
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        </apply>
      </apply>
    </math>
  </component>
  
  <connection>
    <map_components component_2="environment" component_1="calcium_transient"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="TnC_Ca_binding_kinetics"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="thin_filament_kinetics"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="crossbridge_kinetics"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="TnC_Ca_binding_kinetics" component_1="calcium_transient"/>
    <map_variables variable_2="Ca_i" variable_1="Ca_i"/>
  </connection>
  
  <connection>
    <map_components component_2="thin_filament_kinetics" component_1="TnC_Ca_binding_kinetics"/>
    <map_variables variable_2="Ca_b" variable_1="Ca_b"/>
    <map_variables variable_2="lambda" variable_1="lambda"/>
    <map_variables variable_2="To" variable_1="To"/>
  </connection>
  
  <connection>
    <map_components component_2="TnC_Ca_binding_kinetics" component_1="crossbridge_kinetics"/>
    <map_variables variable_2="T" variable_1="T"/>
  </connection>
  
  <connection>
    <map_components component_2="thin_filament_kinetics" component_1="crossbridge_kinetics"/>
    <map_variables variable_2="To" variable_1="To"/>
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    <vCard:Given>H</vCard:Given>
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          mathematical model of the mechanical properties of passive and active 
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