Rendering of the source text

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

CREATED :  3rd May 2004

LAST MODIFIED : 3rd May 2004

AUTHOR :  Espen Remme
          Bioengineering Institute
          The University of Auckland
          
MODEL STATUS :  This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/1/02 CellML Metadata 1.0 Specification.

DESCRIPTION :  This file contains a CellML description of the Pole-Zero constitutive material law, defining the relation between the six independent strain components and the stress components.

  
--><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:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="PoleZero" name="hunter_1995">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>The Pole-Zero Constitutive Material Law</title>
  <author>
    <firstname>Catherine</firstname>
          <surname>Lloyd</surname>
    <affiliation>
      <shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
    </affiliation>
  </author>
</articleinfo>
  <section id="sec_status">
    <title>Model Status</title>
    <para>
            This 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>
Myocardial tissue consists of layers of interconnected sheets of tissue, separated by cleavage planes.  The muscle fibres lie in the plane of a sheet, and adjacent fibres are coupled more strongly in the plane of the sheet than traverse to it.  This results in three microstructural axes:
</para>
<itemizedlist>
  <listitem>
            <para>one along the fibre direction called the fibre axis;</para>
          </listitem>
  <listitem>
            <para>one orthogonal to the fibre axis but also in the plane of the sheet called the sheet axis; and</para>
          </listitem>
  <listitem>
            <para>one which is orthogonal to these two, directed across the cleavage planes called the sheet normal.</para>
          </listitem>
</itemizedlist>  

<para>
The most obvious difference in the material behaviour of the myocardial tisue along these three axes is the limiting strain for an elastic response.  Another feature of the biaxial tests is that the stress-strain curve along one axis is almost independent of the degree of lateral stretch.  To account for these microstructural properties, a strain energy function called the pole-zero law has been proposed (see <xref linkend="fig_reaction_diagram"/> below).  By using a separate pole for each microstructurally defined axis, the different strain limiting behaviour along each axis is accounted for without the need for numerically unstable, large exponents which are needed in exponential or power law expressions.
</para>


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

<para>
Computational mechanics of the heart: from tissue structure to 
ventricular function,
M P Nash and P J Hunter,
<em>Journal of Elasticity</em> 61(1/3): 113-141, 2000.

</para>


</sect1>
</article>
</documentation>
    
    
    
  <!-- Global units -->
  <units name="strain">
    <unit units="dimensionless"/>
  </units>
  <units name="stress">
    <unit units="dimensionless"/>
  </units>
  <units name="pole">
    <unit units="dimensionless"/>
  </units>
  <units name="curvature">
    <unit units="dimensionless"/>
  </units>
  <units name="scale">
    <unit units="dimensionless"/>
  </units>

  <component cmeta:id="interface" name="interface">

 
    <!-- Variables we expect to be set/controlled externally -->
    <variable units="strain" private_interface="out" name="E11"/>
    <variable units="strain" private_interface="out" name="E22"/>
    <variable units="strain" private_interface="out" name="E33"/>
    <variable units="strain" private_interface="out" name="E12"/>
    <variable units="strain" private_interface="out" name="E13"/>
    <variable units="strain" private_interface="out" name="E23"/>
    <variable units="scale" private_interface="out" name="k11" initial_value="0"/>
    <variable units="pole" private_interface="out" name="a11" initial_value="0"/>
    <variable units="curvature" private_interface="out" name="b11" initial_value="0"/>
    <variable units="scale" private_interface="out" name="k22" initial_value="0"/>
    <variable units="pole" private_interface="out" name="a22" initial_value="0"/>
    <variable units="curvature" private_interface="out" name="b22" initial_value="0"/>
    <variable units="scale" private_interface="out" name="k33" initial_value="0"/>
    <variable units="pole" private_interface="out" name="a33" initial_value="0"/>
    <variable units="curvature" private_interface="out" name="b33" initial_value="0"/>
    <variable units="scale" private_interface="out" name="k12" initial_value="0"/>
    <variable units="pole" private_interface="out" name="a12" initial_value="0"/>
    <variable units="curvature" private_interface="out" name="b12" initial_value="0"/>
    <variable units="scale" private_interface="out" name="k13" initial_value="0"/>
    <variable units="pole" private_interface="out" name="a13" initial_value="0"/>
    <variable units="curvature" private_interface="out" name="b13" initial_value="0"/>
    <variable units="scale" private_interface="out" name="k23" initial_value="0"/>
    <variable units="pole" private_interface="out" name="a23" initial_value="0"/>
    <variable units="curvature" private_interface="out" name="b23" initial_value="0"/>
    
    <!-- Variables we want to make available externally -->
    <variable units="stress" public_interface="out" private_interface="in" name="Tdev11"/>
    <variable units="stress" public_interface="out" private_interface="in" name="Tdev22"/>
    <variable units="stress" public_interface="out" private_interface="in" name="Tdev33"/>
    <variable units="stress" public_interface="out" private_interface="in" name="Tdev12"/>
    <variable units="stress" public_interface="out" private_interface="in" name="Tdev13"/>
    <variable units="stress" public_interface="out" private_interface="in" name="Tdev23"/>
    
  </component> <!--interface-->

  <component cmeta:id="equations" name="equations">

    <!-- Inputs -->
    <variable units="strain" public_interface="in" name="E11"/>
    <variable units="strain" public_interface="in" name="E22"/>
    <variable units="strain" public_interface="in" name="E33"/>
    <variable units="strain" public_interface="in" name="E12"/>
    <variable units="strain" public_interface="in" name="E13"/>
    <variable units="strain" public_interface="in" name="E23"/>
    <variable units="scale" public_interface="in" name="k11"/>
    <variable units="pole" public_interface="in" name="a11"/>
    <variable units="curvature" public_interface="in" name="b11"/>
    <variable units="scale" public_interface="in" name="k22"/>
    <variable units="pole" public_interface="in" name="a22"/>
    <variable units="curvature" public_interface="in" name="b22"/>
    <variable units="scale" public_interface="in" name="k33"/>
    <variable units="pole" public_interface="in" name="a33"/>
    <variable units="curvature" public_interface="in" name="b33"/>
    <variable units="scale" public_interface="in" name="k12"/>
    <variable units="pole" public_interface="in" name="a12"/>
    <variable units="curvature" public_interface="in" name="b12"/>
    <variable units="scale" public_interface="in" name="k13"/>
    <variable units="pole" public_interface="in" name="a13"/>
    <variable units="curvature" public_interface="in" name="b13"/>
    <variable units="scale" public_interface="in" name="k23"/>
    <variable units="pole" public_interface="in" name="a23"/>
    <variable units="curvature" public_interface="in" name="b23"/>
    
    <!-- Outputs computed here -->
    <variable units="stress" public_interface="out" name="Tdev11"/>
    <variable units="stress" public_interface="out" name="Tdev22"/>
    <variable units="stress" public_interface="out" name="Tdev33"/>
    <variable units="stress" public_interface="out" name="Tdev12"/>
    <variable units="stress" public_interface="out" name="Tdev13"/>
    <variable units="stress" public_interface="out" name="Tdev23"/>
    
    <!-- Temporary variables -->
    <variable units="strain" name="Elim11"/>
    <variable units="strain" name="Elim22"/>
    <variable units="strain" name="Elim33"/>
    <variable units="strain" name="Elim12"/>
    <variable units="strain" name="Elim13"/>
    <variable units="strain" name="Elim23"/>
    <variable units="dimensionless" name="Tol" initial_value="0.9"/>
    <variable units="dimensionless" name="Sign12"/>
    <variable units="dimensionless" name="Sign13"/>
    <variable units="dimensionless" name="Sign23"/>
    <variable units="strain" name="Eabs12"/>
    <variable units="strain" name="Eabs13"/>
    <variable units="strain" name="Eabs23"/>
    
    <!-- Calculating strain limits  for where the slope-extrapolation starts-->

    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Elim11_calculation_eq">
      <apply id="Elim11_calculation">
        <eq/>
        <ci>Elim11</ci>
        <apply>
          <times/>
          <ci>Tol</ci>
          <ci>a11</ci>
        </apply>
      </apply>
    </math>
    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Elim22_calculation_eq">
      <apply id="Elim22_calculation">
        <eq/>
        <ci>Elim22</ci>
        <apply>
          <times/>
          <ci>Tol</ci>
          <ci>a22</ci>
        </apply>
      </apply>
    </math>
    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Elim33_calculation_eq">
      <apply id="Elim33_calculation">
        <eq/>
        <ci>Elim33</ci>
        <apply>
          <times/>
          <ci>Tol</ci>
          <ci>a33</ci>
        </apply>
      </apply>
    </math>
    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Elim12_calculation_eq">
      <apply id="Elim12_calculation">
        <eq/>
        <ci>Elim12</ci>
        <apply>
          <times/>
          <ci>Tol</ci>
          <ci>a12</ci>
        </apply>
      </apply>
    </math>
    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Elim13_calculation_eq">
      <apply id="Elim13_calculation">
        <eq/>
        <ci>Elim13</ci>
        <apply>
          <times/>
          <ci>Tol</ci>
          <ci>a13</ci>
        </apply>
      </apply>
    </math>
    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Elim23_calculation_eq">
      <apply id="Elim23_calculation">
        <eq/>
        <ci>Elim23</ci>
        <apply>
          <times/>
          <ci>Tol</ci>
          <ci>a23</ci>
        </apply>
      </apply>
    </math>

    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Sign12_calculation_eq">
      <apply id="Sign12_calculation">
        <eq/>
        <ci>Sign12</ci>
        <piecewise>
          <piece>
            <cn cellml:units="dimensionless">1.0</cn>
            <apply>
              <geq/>
              <ci>E12</ci>
              <cn cellml:units="strain">0.0</cn>
            </apply>
          </piece>
          <otherwise>
            <cn cellml:units="dimensionless">-1.0</cn>
          </otherwise>
        </piecewise>
      </apply>
    </math>
    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Sign13_calculation_eq">
      <apply id="Sign13_calculation">
        <eq/>
        <ci>Sign13</ci>
        <piecewise>
          <piece>
            <cn cellml:units="dimensionless">1.0</cn>
            <apply>
              <geq/>
              <ci>E13</ci>
              <cn cellml:units="strain">0.0</cn>
            </apply>
          </piece>
          <otherwise>
            <cn cellml:units="dimensionless">-1.0</cn>
          </otherwise>
        </piecewise>
      </apply>
    </math>
    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Sign23_calculation_eq">
      <apply id="Sign23_calculation">
        <eq/>
        <ci>Sign23</ci>
        <piecewise>
          <piece>
            <cn cellml:units="dimensionless">1.0</cn>
            <apply>
              <geq/>
              <ci>E23</ci>
              <cn cellml:units="strain">0.0</cn>
            </apply>
          </piece>
          <otherwise>
            <cn cellml:units="dimensionless">-1.0</cn>
          </otherwise>
        </piecewise>
      </apply>
    </math>

    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Eabs12_calculation_eq">
      <apply id="Eabs12_calculation">
        <eq/>
        <ci>Eabs12</ci>
        <piecewise>
          <piece>
            <ci>E12</ci>
            <apply>
              <geq/>
              <ci>E12</ci>
              <cn cellml:units="strain">0.0</cn>
            </apply>
          </piece>
          <otherwise>
            <apply>
              <times/>
              <cn cellml:units="dimensionless">-1.0</cn>
              <ci>E12</ci>
            </apply>
          </otherwise>
        </piecewise>
      </apply>
    </math>
    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Eabs13_calculation_eq">
      <apply id="Eabs13_calculation">
        <eq/>
        <ci>Eabs13</ci>
        <piecewise>
          <piece>
            <ci>E13</ci>
            <apply>
              <geq/>
              <ci>E13</ci>
              <cn cellml:units="strain">0.0</cn>
            </apply>
          </piece>
          <otherwise>
            <apply>
              <times/>
              <cn cellml:units="dimensionless">-1.0</cn>
              <ci>E13</ci>
            </apply>
          </otherwise>
        </piecewise>
      </apply>
    </math>
    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Eabs23_calculation_eq">
      <apply id="Eabs23_calculation">
        <eq/>
        <ci>Eabs23</ci>
        <piecewise>
          <piece>
            <ci>E23</ci>
            <apply>
              <geq/>
              <ci>E23</ci>
              <cn cellml:units="strain">0.0</cn>
            </apply>
          </piece>
          <otherwise>
            <apply>
              <times/>
              <cn cellml:units="dimensionless">-1.0</cn>
              <ci>E23</ci>
            </apply>
          </otherwise>
        </piecewise>
      </apply>
    </math>

    <!-- 11 direction -->

    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev11_calculation_eq">
      <apply id="Tdev11_calculation">
        <eq/>
        <ci>Tdev11</ci>
        <piecewise>
          <piece>
            <apply>
              <divide/>
              <apply>
                <times/>
                <cn cellml:units="dimensionless">2.0</cn>
                <ci>k11</ci>
                <ci>E11</ci>
              </apply>
              <apply>
                <power/>
                <ci>a11</ci>
                <ci>b11</ci>
              </apply>
            </apply>
            <apply>
              <leq/>
              <ci>E11</ci>
              <cn cellml:units="strain">0.0</cn>
            </apply>
          </piece>
          <piece>
            <apply>
              <plus/>
              <apply>
                <times/>
                <apply>
                  <divide/>
                  <apply>
                    <times/>
                    <ci>k11</ci>
                    <ci>Elim11</ci>
                  </apply>
                  <apply>
                    <power/>
                    <apply>
                      <minus/>
                      <ci>a11</ci>
                      <ci>Elim11</ci>
                    </apply>
                    <ci>b11</ci>
                  </apply>
                </apply>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">2.0</cn>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci>b11</ci>
                      <ci>Elim11</ci>
                    </apply>
                    <apply>
                      <minus/>
                      <ci>a11</ci>
                      <ci>Elim11</ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
              <apply>
                <times/>
                <apply>
                  <times/>
                  <apply>
                    <divide/>
                    <ci>k11</ci>
                    <apply>
                      <power/>
                      <apply>
                        <minus/>
                        <ci>a11</ci>
                        <ci>Elim11</ci>
                      </apply>
                      <ci>b11</ci>
                    </apply>
                  </apply>
                  <apply>
                    <plus/>
                    <cn cellml:units="dimensionless">2.0</cn>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <cn cellml:units="dimensionless">4.0</cn>
                        <ci>b11</ci>
                        <ci>Elim11</ci>
                      </apply>
                      <apply>
                        <minus/>
                        <ci>a11</ci>
                        <ci>Elim11</ci>
                      </apply>
                    </apply>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <ci>b11</ci>
                        <apply>
                          <power/>
                          <ci>Elim11</ci>
                          <cn cellml:units="dimensionless">2.0</cn>
                        </apply>
                        <apply>
                          <plus/>
                          <ci>b11</ci>
                          <cn cellml:units="curvature">1.0</cn>
                        </apply>
                      </apply>
                      <apply>
                        <power/>
                        <apply>
                          <minus/>
                          <ci>a11</ci>
                          <ci>Elim11</ci>
                        </apply>
                        <cn cellml:units="dimensionless">2.0</cn>
                      </apply>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <minus/>
                  <ci>E11</ci>
                  <ci>Elim11</ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <gt/>
              <ci>E11</ci>
              <ci>Elim11</ci>
            </apply>  
          </piece>
          <otherwise>
            <apply>
              <times/>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <ci>k11</ci>
                  <ci>E11</ci>
                </apply>
                <apply>
                  <power/>
                  <apply>
                    <minus/>
                    <ci>a11</ci>
                    <ci>E11</ci>
                  </apply>
                  <ci>b11</ci>
                </apply>
              </apply>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless">2.0</cn>
                <apply>
                  <divide/>
                  <apply>
                    <times/>
                    <ci>b11</ci>
                    <ci>E11</ci>
                  </apply>
                  <apply>
                    <minus/>
                    <ci>a11</ci>
                    <ci>E11</ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </otherwise>          
        </piecewise>
      </apply>
    </math>
    

    <!-- 22 direction -->
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev22_calculation_eq">
      <apply id="Tdev22_calculation">
        <eq/>
        <ci>Tdev22</ci>
        <piecewise>
          <piece>
            <apply>
              <divide/>
              <apply>
                <times/>
                <cn cellml:units="dimensionless">2.0</cn>
                <ci>k22</ci>
                <ci>E22</ci>
              </apply>
              <apply>
                <power/>
                <ci>a22</ci>
                <ci>b22</ci>
              </apply>
            </apply>
            <apply>
              <leq/>
              <ci>E22</ci>
              <cn cellml:units="strain">0.0</cn>
            </apply>
          </piece>
          <piece>
            <apply>
              <plus/>
              <apply>
                <times/>
                <apply>
                  <divide/>
                  <apply>
                    <times/>
                    <ci>k22</ci>
                    <ci>Elim22</ci>
                  </apply>
                  <apply>
                    <power/>
                    <apply>
                      <minus/>
                      <ci>a22</ci>
                      <ci>Elim22</ci>
                    </apply>
                    <ci>b22</ci>
                  </apply>
                </apply>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">2.0</cn>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci>b22</ci>
                      <ci>Elim22</ci>
                    </apply>
                    <apply>
                      <minus/>
                      <ci>a22</ci>
                      <ci>Elim22</ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
              <apply>
                <times/>
                <apply>
                  <times/>
                  <apply>
                    <divide/>
                    <ci>k22</ci>
                    <apply>
                      <power/>
                      <apply>
                        <minus/>
                        <ci>a22</ci>
                        <ci>Elim22</ci>
                      </apply>
                      <ci>b22</ci>
                    </apply>
                  </apply>
                  <apply>
                    <plus/>
                    <cn cellml:units="dimensionless">2.0</cn>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <cn cellml:units="dimensionless">4.0</cn>
                        <ci>b22</ci>
                        <ci>Elim22</ci>
                      </apply>
                      <apply>
                        <minus/>
                        <ci>a22</ci>
                        <ci>Elim22</ci>
                      </apply>
                    </apply>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <ci>b22</ci>
                        <apply>
                          <power/>
                          <ci>Elim22</ci>
                          <cn cellml:units="dimensionless">2.0</cn>
                        </apply>
                        <apply>
                          <plus/>
                          <ci>b22</ci>
                          <cn cellml:units="curvature">1.0</cn>
                        </apply>
                      </apply>
                      <apply>
                        <power/>
                        <apply>
                          <minus/>
                          <ci>a22</ci>
                          <ci>Elim22</ci>
                        </apply>
                        <cn cellml:units="dimensionless">2.0</cn>
                      </apply>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <minus/>
                  <ci>E22</ci>
                  <ci>Elim22</ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <gt/>
              <ci>E22</ci>
              <ci>Elim22</ci>
            </apply>  
          </piece>
          <otherwise>
            <apply>
              <times/>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <ci>k22</ci>
                  <ci>E22</ci>
                </apply>
                <apply>
                  <power/>
                  <apply>
                    <minus/>
                    <ci>a22</ci>
                    <ci>E22</ci>
                  </apply>
                  <ci>b22</ci>
                </apply>
              </apply>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless">2.0</cn>
                <apply>
                  <divide/>
                  <apply>
                    <times/>
                    <ci>b22</ci>
                    <ci>E22</ci>
                  </apply>
                  <apply>
                    <minus/>
                    <ci>a22</ci>
                    <ci>E22</ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </otherwise>          
        </piecewise>
      </apply>
    </math>
    

    <!-- 33 direction -->
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev33_calculation_eq">
      <apply id="Tdev33_calculation">
        <eq/>
        <ci>Tdev33</ci>
        <piecewise>
          <piece>
            <apply>
              <divide/>
              <apply>
                <times/>
                <cn cellml:units="dimensionless">2.0</cn>
                <ci>k33</ci>
                <ci>E33</ci>
              </apply>
              <apply>
                <power/>
                <ci>a33</ci>
                <ci>b33</ci>
              </apply>
            </apply>
            <apply>
              <leq/>
              <ci>E33</ci>
              <cn cellml:units="strain">0.0</cn>
            </apply>
          </piece>
          <piece>
            <apply>
              <plus/>
              <apply>
                <times/>
                <apply>
                  <divide/>
                  <apply>
                    <times/>
                    <ci>k33</ci>
                    <ci>Elim33</ci>
                  </apply>
                  <apply>
                    <power/>
                    <apply>
                      <minus/>
                      <ci>a33</ci>
                      <ci>Elim33</ci>
                    </apply>
                    <ci>b33</ci>
                  </apply>
                </apply>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">2.0</cn>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci>b33</ci>
                      <ci>Elim33</ci>
                    </apply>
                    <apply>
                      <minus/>
                      <ci>a33</ci>
                      <ci>Elim33</ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
              <apply>
                <times/>
                <apply>
                  <times/>
                  <apply>
                    <divide/>
                    <ci>k33</ci>
                    <apply>
                      <power/>
                      <apply>
                        <minus/>
                        <ci>a33</ci>
                        <ci>Elim33</ci>
                      </apply>
                      <ci>b33</ci>
                    </apply>
                  </apply>
                  <apply>
                    <plus/>
                    <cn cellml:units="dimensionless">2.0</cn>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <cn cellml:units="dimensionless">4.0</cn>
                        <ci>b33</ci>
                        <ci>Elim33</ci>
                      </apply>
                      <apply>
                        <minus/>
                        <ci>a33</ci>
                        <ci>Elim33</ci>
                      </apply>
                    </apply>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <ci>b33</ci>
                        <apply>
                          <power/>
                          <ci>Elim33</ci>
                          <cn cellml:units="dimensionless">2.0</cn>
                        </apply>
                        <apply>
                          <plus/>
                          <ci>b33</ci>
                          <cn cellml:units="curvature">1.0</cn>
                        </apply>
                      </apply>
                      <apply>
                        <power/>
                        <apply>
                          <minus/>
                          <ci>a33</ci>
                          <ci>Elim33</ci>
                        </apply>
                        <cn cellml:units="dimensionless">2.0</cn>
                      </apply>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <minus/>
                  <ci>E33</ci>
                  <ci>Elim33</ci>
                </apply>
              </apply>
            </apply>
            <apply>
              <gt/>
              <ci>E33</ci>
              <ci>Elim33</ci>
            </apply>  
          </piece>
          <otherwise>
            <apply>
              <times/>
              <apply>
                <divide/>
                <apply>
                  <times/>
                  <ci>k33</ci>
                  <ci>E33</ci>
                </apply>
                <apply>
                  <power/>
                  <apply>
                    <minus/>
                    <ci>a33</ci>
                    <ci>E33</ci>
                  </apply>
                  <ci>b33</ci>
                </apply>
              </apply>
              <apply>
                <plus/>
                <cn cellml:units="dimensionless">2.0</cn>
                <apply>
                  <divide/>
                  <apply>
                    <times/>
                    <ci>b33</ci>
                    <ci>E33</ci>
                  </apply>
                  <apply>
                    <minus/>
                    <ci>a33</ci>
                    <ci>E33</ci>
                  </apply>
                </apply>
              </apply>
            </apply>
          </otherwise>          
        </piecewise>
      </apply>
    </math>
    
    <!-- 12 direction -->
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev12_calculation_eq">
      <apply id="Tdev12_calculation">
        <eq/>
        <ci>Tdev12</ci>
        <apply>
          <times/>
          <ci>Sign12</ci>
          <piecewise>
            <piece>
              <apply>
                <plus/>
                <apply>
                  <times/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci>k12</ci>
                      <ci>Elim12</ci>
                    </apply>
                    <apply>
                      <power/>
                      <apply>
                        <minus/>
                        <ci>a12</ci>
                        <ci>Elim12</ci>
                      </apply>
                      <ci>b12</ci>
                    </apply>
                  </apply>
                  <apply>
                    <plus/>
                    <cn cellml:units="dimensionless">2.0</cn>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <ci>b12</ci>
                        <ci>Elim12</ci>
                      </apply>
                      <apply>
                        <minus/>
                        <ci>a12</ci>
                        <ci>Elim12</ci>
                      </apply>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <times/>
                  <apply>
                    <times/>
                    <apply>
                      <divide/>
                      <ci>k12</ci>
                      <apply>
                        <power/>
                        <apply>
                          <minus/>
                          <ci>a12</ci>
                          <ci>Elim12</ci>
                        </apply>
                        <ci>b12</ci>
                      </apply>
                    </apply>
                    <apply>
                      <plus/>
                      <cn cellml:units="dimensionless">2.0</cn>
                      <apply>
                        <divide/>
                        <apply>
                          <times/>
                          <cn cellml:units="dimensionless">4.0</cn>
                          <ci>b12</ci>
                          <ci>Elim12</ci>
                        </apply>
                        <apply>
                          <minus/>
                          <ci>a12</ci>
                          <ci>Elim12</ci>
                        </apply>
                      </apply>
                      <apply>
                        <divide/>
                        <apply>
                          <times/>
                          <ci>b12</ci>
                          <apply>
                            <power/>
                            <ci>Elim12</ci>
                            <cn cellml:units="dimensionless">2.0</cn>
                          </apply>
                          <apply>
                            <plus/>
                            <ci>b12</ci>
                            <cn cellml:units="curvature">1.0</cn>
                          </apply>
                        </apply>
                        <apply>
                          <power/>
                          <apply>
                            <minus/>
                            <ci>a12</ci>
                            <ci>Elim12</ci>
                          </apply>
                          <cn cellml:units="dimensionless">2.0</cn>
                        </apply>
                      </apply>
                    </apply>
                  </apply>
                  <apply>
                    <minus/>
                    <ci>Eabs12</ci>
                    <ci>Elim12</ci>
                  </apply>
                </apply>
              </apply>
              <apply>
                <gt/>
                <ci>Eabs12</ci>
                <ci>Elim12</ci>
              </apply>  
              </piece>
              <otherwise>
              <apply>
                <times/>
                <apply>
                  <divide/>
                  <apply>
                    <times/>
                    <ci>k12</ci>
                    <ci>Eabs12</ci>
                  </apply>
                  <apply>
                    <power/>
                    <apply>
                      <minus/>
                      <ci>a12</ci>
                      <ci>Eabs12</ci>
                    </apply>
                    <ci>b12</ci>
                  </apply>
                </apply>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">2.0</cn>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci>b12</ci>
                      <ci>Eabs12</ci>
                    </apply>
                    <apply>
                      <minus/>
                      <ci>a12</ci>
                      <ci>Eabs12</ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </otherwise>          
          </piecewise>
        </apply>
      </apply>
    </math>
    
    
    <!-- 13 direction -->
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev13_calculation_eq">
      <apply id="Tdev13_calculation">
        <eq/>
        <ci>Tdev13</ci>
        <apply>
          <times/>
          <ci>Sign13</ci>
          <piecewise>
            <piece>
              <apply>
                <plus/>
                <apply>
                  <times/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci>k13</ci>
                      <ci>Elim13</ci>
                    </apply>
                    <apply>
                      <power/>
                      <apply>
                        <minus/>
                        <ci>a13</ci>
                        <ci>Elim13</ci>
                      </apply>
                      <ci>b13</ci>
                    </apply>
                  </apply>
                  <apply>
                    <plus/>
                    <cn cellml:units="dimensionless">2.0</cn>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <ci>b13</ci>
                        <ci>Elim13</ci>
                      </apply>
                      <apply>
                        <minus/>
                        <ci>a13</ci>
                        <ci>Elim13</ci>
                      </apply>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <times/>
                  <apply>
                    <times/>
                    <apply>
                      <divide/>
                      <ci>k13</ci>
                      <apply>
                        <power/>
                        <apply>
                          <minus/>
                          <ci>a13</ci>
                          <ci>Elim13</ci>
                        </apply>
                        <ci>b13</ci>
                      </apply>
                    </apply>
                    <apply>
                      <plus/>
                      <cn cellml:units="dimensionless">2.0</cn>
                      <apply>
                        <divide/>
                        <apply>
                          <times/>
                          <cn cellml:units="dimensionless">4.0</cn>
                          <ci>b13</ci>
                          <ci>Elim13</ci>
                        </apply>
                        <apply>
                          <minus/>
                          <ci>a13</ci>
                          <ci>Elim13</ci>
                        </apply>
                      </apply>
                      <apply>
                        <divide/>
                        <apply>
                          <times/>
                          <ci>b13</ci>
                          <apply>
                            <power/>
                            <ci>Elim13</ci>
                            <cn cellml:units="dimensionless">2.0</cn>
                          </apply>
                          <apply>
                            <plus/>
                            <ci>b13</ci>
                            <cn cellml:units="curvature">1.0</cn>
                          </apply>
                        </apply>
                        <apply>
                          <power/>
                          <apply>
                            <minus/>
                            <ci>a13</ci>
                            <ci>Elim13</ci>
                          </apply>
                          <cn cellml:units="dimensionless">2.0</cn>
                        </apply>
                      </apply>
                    </apply>
                  </apply>
                  <apply>
                    <minus/>
                    <ci>Eabs13</ci>
                    <ci>Elim13</ci>
                  </apply>
                </apply>
              </apply>
              <apply>
                <gt/>
                <ci>Eabs13</ci>
                <ci>Elim13</ci>
              </apply>  
              </piece>
              <otherwise>
              <apply>
                <times/>
                <apply>
                  <divide/>
                  <apply>
                    <times/>
                    <ci>k13</ci>
                    <ci>Eabs13</ci>
                  </apply>
                  <apply>
                    <power/>
                    <apply>
                      <minus/>
                      <ci>a13</ci>
                      <ci>Eabs13</ci>
                    </apply>
                    <ci>b13</ci>
                  </apply>
                </apply>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">2.0</cn>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci>b13</ci>
                      <ci>Eabs13</ci>
                    </apply>
                    <apply>
                      <minus/>
                      <ci>a13</ci>
                      <ci>Eabs13</ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </otherwise>          
          </piecewise>
        </apply>
      </apply>
    </math>


    <!-- 23 direction -->
    
    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev23_calculation_eq">
      <apply id="Tdev23_calculation">
        <eq/>
        <ci>Tdev23</ci>
        <apply>
          <times/>
          <ci>Sign23</ci>
          <piecewise>
            <piece>
              <apply>
                <plus/>
                <apply>
                  <times/>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci>k23</ci>
                      <ci>Elim23</ci>
                    </apply>
                    <apply>
                      <power/>
                      <apply>
                        <minus/>
                        <ci>a23</ci>
                        <ci>Elim23</ci>
                      </apply>
                      <ci>b23</ci>
                    </apply>
                  </apply>
                  <apply>
                    <plus/>
                    <cn cellml:units="dimensionless">2.0</cn>
                    <apply>
                      <divide/>
                      <apply>
                        <times/>
                        <ci>b23</ci>
                        <ci>Elim23</ci>
                      </apply>
                      <apply>
                        <minus/>
                        <ci>a23</ci>
                        <ci>Elim23</ci>
                      </apply>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <times/>
                  <apply>
                    <times/>
                    <apply>
                      <divide/>
                      <ci>k23</ci>
                      <apply>
                        <power/>
                        <apply>
                          <minus/>
                          <ci>a23</ci>
                          <ci>Elim23</ci>
                        </apply>
                        <ci>b23</ci>
                      </apply>
                    </apply>
                    <apply>
                      <plus/>
                      <cn cellml:units="dimensionless">2.0</cn>
                      <apply>
                        <divide/>
                        <apply>
                          <times/>
                          <cn cellml:units="dimensionless">4.0</cn>
                          <ci>b23</ci>
                          <ci>Elim23</ci>
                        </apply>
                        <apply>
                          <minus/>
                          <ci>a23</ci>
                          <ci>Elim23</ci>
                        </apply>
                      </apply>
                      <apply>
                        <divide/>
                        <apply>
                          <times/>
                          <ci>b23</ci>
                          <apply>
                            <power/>
                            <ci>Elim23</ci>
                            <cn cellml:units="dimensionless">2.0</cn>
                          </apply>
                          <apply>
                            <plus/>
                            <ci>b23</ci>
                            <cn cellml:units="curvature">1.0</cn>
                          </apply>
                        </apply>
                        <apply>
                          <power/>
                          <apply>
                            <minus/>
                            <ci>a23</ci>
                            <ci>Elim23</ci>
                          </apply>
                          <cn cellml:units="dimensionless">2.0</cn>
                        </apply>
                      </apply>
                    </apply>
                  </apply>
                  <apply>
                    <minus/>
                    <ci>Eabs23</ci>
                    <ci>Elim23</ci>
                  </apply>
                </apply>
              </apply>
              <apply>
                <gt/>
                <ci>Eabs23</ci>
                <ci>Elim23</ci>
              </apply>  
              </piece>
              <otherwise>
              <apply>
                <times/>
                <apply>
                  <divide/>
                  <apply>
                    <times/>
                    <ci>k23</ci>
                    <ci>Eabs23</ci>
                  </apply>
                  <apply>
                    <power/>
                    <apply>
                      <minus/>
                      <ci>a23</ci>
                      <ci>Eabs23</ci>
                    </apply>
                    <ci>b23</ci>
                  </apply>
                </apply>
                <apply>
                  <plus/>
                  <cn cellml:units="dimensionless">2.0</cn>
                  <apply>
                    <divide/>
                    <apply>
                      <times/>
                      <ci>b23</ci>
                      <ci>Eabs23</ci>
                    </apply>
                    <apply>
                      <minus/>
                      <ci>a23</ci>
                      <ci>Eabs23</ci>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </otherwise>          
          </piecewise>
        </apply>
      </apply>
    </math>
    
    
    
    
    
  </component>
  <!--membrane-->

  <connection>
    <map_components component_2="equations" component_1="interface"/>
    <map_variables variable_2="E11" variable_1="E11"/>
    <map_variables variable_2="E22" variable_1="E22"/>
    <map_variables variable_2="E33" variable_1="E33"/>
    <map_variables variable_2="E12" variable_1="E12"/>
    <map_variables variable_2="E13" variable_1="E13"/>
    <map_variables variable_2="E23" variable_1="E23"/>
    <map_variables variable_2="Tdev11" variable_1="Tdev11"/>
    <map_variables variable_2="Tdev22" variable_1="Tdev22"/>
    <map_variables variable_2="Tdev33" variable_1="Tdev33"/>
    <map_variables variable_2="Tdev12" variable_1="Tdev12"/>
    <map_variables variable_2="Tdev13" variable_1="Tdev13"/>
    <map_variables variable_2="Tdev23" variable_1="Tdev23"/>
    <map_variables variable_2="k11" variable_1="k11"/>
    <map_variables variable_2="a11" variable_1="a11"/>
    <map_variables variable_2="b11" variable_1="b11"/>
    <map_variables variable_2="k22" variable_1="k22"/>
    <map_variables variable_2="a22" variable_1="a22"/>
    <map_variables variable_2="b22" variable_1="b22"/>
    <map_variables variable_2="k33" variable_1="k33"/>
    <map_variables variable_2="a33" variable_1="a33"/>
    <map_variables variable_2="b33" variable_1="b33"/>
    <map_variables variable_2="k12" variable_1="k12"/>
    <map_variables variable_2="a12" variable_1="a12"/>
    <map_variables variable_2="b12" variable_1="b12"/>
    <map_variables variable_2="k13" variable_1="k13"/>
    <map_variables variable_2="a13" variable_1="a13"/>
    <map_variables variable_2="b13" variable_1="b13"/>
    <map_variables variable_2="k23" variable_1="k23"/>
    <map_variables variable_2="a23" variable_1="a23"/>
    <map_variables variable_2="b23" variable_1="b23"/>

  </connection>
  
  <group>
    <relationship_ref relationship="encapsulation"/>
    <component_ref component="interface">
      <component_ref component="equations"/>
    </component_ref>
  </group>




<rdf:RDF>
  <rdf:Seq rdf:about="rdf:#41087a2a-a1ea-4150-b0fd-21c42afb506d">
    <rdf:li rdf:resource="rdf:#53a1e0d8-4549-4ab4-aa80-011aa775c086"/>
    <rdf:li rdf:resource="rdf:#a950a822-9675-40b2-93f6-df22468dc13b"/>
    <rdf:li rdf:resource="rdf:#bed8498d-4eda-4121-be6e-8aed1c031b34"/>
  </rdf:Seq>
  <rdf:Seq rdf:about="rdf:#9078d897-ee88-409d-8f5a-e562bf62e995">
    <rdf:li rdf:resource="rdf:#02f447ba-c4ae-44ef-9677-4a26d6c07b63"/>
    <rdf:li rdf:resource="rdf:#490a92a0-8902-4656-bf53-0243b1fcb91e"/>
    <rdf:li rdf:resource="rdf:#403b25a0-597f-48fc-8146-541c66d60ab0"/>
  </rdf:Seq>
  <rdf:Description rdf:about="">
    <dc:publisher/>
    <cmeta:comment rdf:resource="rdf:#b3a2c496-b66a-434e-ae4e-d9edffcdf606"/>
    <dcterms:created rdf:resource="rdf:#f235e100-243d-4a7b-a396-0a61a19d3c91"/>
    <dc:creator rdf:resource="rdf:#3c0b8bf0-03c8-4182-a64a-ff3613054f4e"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#403b25a0-597f-48fc-8146-541c66d60ab0">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N rdf:resource="rdf:#c4e46faa-8d34-45a9-8a1b-f13184a68753"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#b3a2c496-b66a-434e-ae4e-d9edffcdf606">
    <dc:creator rdf:resource="rdf:#08806110-3eaf-4c59-80ee-678c597fbbb9"/>
    <rdf:value/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#3ad6aef4-979d-4e05-a0e1-62f9ec31261e">
    <vCard:Given>P</vCard:Given>
    <vCard:Family>Hunter</vCard:Family>
    <vCard:Other>J</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#30f05dd3-5c3e-4dd8-90d5-be8e80138601">
    <vCard:Orgname>The University of Auckland</vCard:Orgname>
    <vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#1ec66dc7-a0af-4feb-9c0d-95618d4393b6">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#JournalArticle"/>
    <dc:creator rdf:resource="rdf:#41087a2a-a1ea-4150-b0fd-21c42afb506d"/>
    <dc:title>
            A pole-zero constitutive law for myocardium
          </dc:title>
    <bqs:volume>382</bqs:volume>
    <bqs:first_page>303</bqs:first_page>
    <bqs:Journal rdf:resource="rdf:#fd9c9326-1a0e-40cd-aa0a-02d4d39479b8"/>
    <dcterms:issued rdf:resource="rdf:#af7a8725-60d3-4d4c-984b-816d74ea5aaf"/>
    <bqs:last_page>318</bqs:last_page>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#b2bda3c8-e1b0-40ed-90f3-be8409d07730">
    <dcterms:W3CDTF>2004-08-10</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#26b68cc7-e522-4989-9da0-7eabbd986a07">
    <rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
    <rdf:value>e.remme@auckland.ac.nz</rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#af7a8725-60d3-4d4c-984b-816d74ea5aaf">
    <dcterms:W3CDTF>1995</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#16dda939-0d4c-4ecd-bad0-768515d1125d">
    <bqs:subject_type>keyword</bqs:subject_type>
    <rdf:value>
      <rdf:Bag>
        <rdf:li>myocardium</rdf:li>
        <rdf:li>pole-zero</rdf:li>
        <rdf:li>mechanical constitutive laws</rdf:li>
      </rdf:Bag>
    </rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#490a92a0-8902-4656-bf53-0243b1fcb91e">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N rdf:resource="rdf:#4180fd36-b724-4c99-8552-d946e7bf345d"/>
  </rdf:Description>
  <rdf:Description rdf:about="#PoleZero">
    <bqs:reference rdf:resource="rdf:#1ec66dc7-a0af-4feb-9c0d-95618d4393b6"/>
    <bqs:reference rdf:resource="rdf:#989a71d9-b3d6-45ce-9650-2a9fd5b3283e"/>
    <bqs:reference rdf:resource="rdf:#bb02f8eb-951d-4246-9045-f5f9bf477bba"/>
    <cmeta:comment rdf:resource="rdf:#78dcdb91-07ea-47bb-a9b3-6af726652a51"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#53a1e0d8-4549-4ab4-aa80-011aa775c086">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N rdf:resource="rdf:#3ad6aef4-979d-4e05-a0e1-62f9ec31261e"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#c40d2ebe-af1f-41df-a9b0-6c96eae223ab">
    <dc:creator rdf:resource="rdf:#9078d897-ee88-409d-8f5a-e562bf62e995"/>
    <dc:title>A pole-zero constitutive law for myocardium</dc:title>
    <bqs:volume>382</bqs:volume>
    <bqs:first_page>303</bqs:first_page>
    <bqs:Journal rdf:resource="rdf:#01243918-f2bc-465d-8a3f-9f1df8b91708"/>
    <dcterms:issued rdf:resource="rdf:#20e8b53b-8f84-4f70-a95c-892a2c952996"/>
    <bqs:last_page>318</bqs:last_page>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#20e8b53b-8f84-4f70-a95c-892a2c952996">
    <dcterms:W3CDTF>1995-00-00 00:00</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#19a8dcac-6553-4f3c-8000-a02d0009bdb2">
    <dcterms:modified rdf:resource="rdf:#b2bda3c8-e1b0-40ed-90f3-be8409d07730"/>
    <rdf:value>
          Added metadata to the model.
        </rdf:value>
    <rdf:type rdf:resource="http://www.cellml.org/metadata/1.0#modification"/>
    <cmeta:modifier rdf:resource="rdf:#23f55ee3-5a78-4b0f-b9e7-9a4fdc4b3009"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#d2daa757-b1a9-44a3-9f04-7cd1d8bf2d43">
    <vCard:Given>P</vCard:Given>
    <vCard:Family>Hunter</vCard:Family>
    <vCard:Other>J</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#23f55ee3-5a78-4b0f-b9e7-9a4fdc4b3009">
    <vCard:N rdf:resource="rdf:#162565bd-237f-4589-8c4d-f4f8048856d3"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#fd9c9326-1a0e-40cd-aa0a-02d4d39479b8">
    <dc:title>Journal of Biomechanical Engineering</dc:title>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#3c0b8bf0-03c8-4182-a64a-ff3613054f4e">
    <vCard:ORG rdf:resource="rdf:#30f05dd3-5c3e-4dd8-90d5-be8e80138601"/>
    <vCard:EMAIL rdf:resource="rdf:#26b68cc7-e522-4989-9da0-7eabbd986a07"/>
    <vCard:N rdf:resource="rdf:#eac5760f-3919-43b5-bbcf-10a834de15ee"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#4180fd36-b724-4c99-8552-d946e7bf345d">
    <vCard:Given>B</vCard:Given>
    <vCard:Family>Smaill</vCard:Family>
    <vCard:Other>H</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#01243918-f2bc-465d-8a3f-9f1df8b91708">
    <dc:title>Journal of Biomechanical Engineering</dc:title>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#27a147ee-6f1f-438c-8a45-c032d5c09e88">
    <vCard:Given>I</vCard:Given>
    <vCard:Family>Hunter</vCard:Family>
    <vCard:Other>W</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#bed8498d-4eda-4121-be6e-8aed1c031b34">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N rdf:resource="rdf:#27a147ee-6f1f-438c-8a45-c032d5c09e88"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#c4e46faa-8d34-45a9-8a1b-f13184a68753">
    <vCard:Given>I</vCard:Given>
    <vCard:Family>Hunter</vCard:Family>
    <vCard:Other>W</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#08806110-3eaf-4c59-80ee-678c597fbbb9">
    <vCard:FN/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#bb02f8eb-951d-4246-9045-f5f9bf477bba">
    <bqs:Pubmed_id/>
    <bqs:JournalArticle rdf:resource="rdf:#c40d2ebe-af1f-41df-a9b0-6c96eae223ab"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#eac5760f-3919-43b5-bbcf-10a834de15ee">
    <vCard:Given>Espen</vCard:Given>
    <vCard:Family>Remme</vCard:Family>
    <vCard:Other/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#162565bd-237f-4589-8c4d-f4f8048856d3">
    <vCard:Given>Catherine</vCard:Given>
    <vCard:Family>Lloyd</vCard:Family>
    <vCard:Other>M</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#f235e100-243d-4a7b-a396-0a61a19d3c91">
    <dcterms:W3CDTF>2004-05-03T00:00:00+00:00</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#989a71d9-b3d6-45ce-9650-2a9fd5b3283e">
    <dc:subject rdf:resource="rdf:#16dda939-0d4c-4ecd-bad0-768515d1125d"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#a950a822-9675-40b2-93f6-df22468dc13b">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N rdf:resource="rdf:#9eabdff1-c043-4209-8072-5ada71dab522"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#78dcdb91-07ea-47bb-a9b3-6af726652a51">
    <dc:creator rdf:resource="rdf:#6a22a7d7-0ac1-431d-bc92-e7f95ce95ce8"/>
    <rdf:value>This is a CellML version of the pole-zero law.  CellML is being used to define passive material laws for use in solving finite elasticity problems.</rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#9eabdff1-c043-4209-8072-5ada71dab522">
    <vCard:Given>B</vCard:Given>
    <vCard:Family>Smaill</vCard:Family>
    <vCard:Other>H</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#02f447ba-c4ae-44ef-9677-4a26d6c07b63">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N rdf:resource="rdf:#d2daa757-b1a9-44a3-9f04-7cd1d8bf2d43"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#6a22a7d7-0ac1-431d-bc92-e7f95ce95ce8">
    <vCard:FN/>
  </rdf:Description>
</rdf:RDF>
</model>