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,
<i>Journal of Elasticity</i> 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">
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  </units>

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    <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"/>
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    <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"/>
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    <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-->

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    <variable units="strain" public_interface="in" name="E22"/>
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    <variable units="stress" public_interface="out" name="Tdev33"/>
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Source
Derived from workspace Hunter, Smaill, Hunter, 1995 at changeset 0e03251c9546.
This exposure was expired.
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License

This work is licensed under a Creative Commons Attribution 3.0 Unported License.