- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2010-05-25 23:04:08+12:00
- Desc:
- Updated citation. Model requires further curation - but I believe the errors may be linked to the CMISS compatibility(?!)
- Permanent Source URI:
- http://models.cellml.org/workspace/hunter_smaill_hunter_1995/rawfile/77edc4109f41f205d401406f6f14ebef147cc8ed/hunter_smaill_hunter_1995.cellml
<?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>
A pole-zero constitutive law for myocardium, P.J. Hunter, B.H. Smaill, and I.W. Hunter, 1995,
<emphasis>ASME J. Biochem. Eng.</emphasis>, 382, 303-318 (no PubMed ID available).
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>reaction diagram</title>
</objectinfo>
<imagedata fileref="hunter_1995.png"/>
</imageobject>
</mediaobject>
<caption>Pole-zero law: three families of muscle fibres oriented about the microstructurally defined tissue axes.</caption>
</informalfigure>
</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 -->
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<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"/>
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<variable units="strain" name="Eabs12"/>
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<variable units="strain" name="Eabs23"/>
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<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Elim33_calculation_eq">
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<ci>a33</ci>
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<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Elim12_calculation_eq">
<apply id="Elim12_calculation">
<eq/>
<ci>Elim12</ci>
<apply>
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<ci>Tol</ci>
<ci>a12</ci>
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<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Elim13_calculation_eq">
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<vCard:Other>W</vCard:Other>
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<vCard:FN/>
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<bqs:Pubmed_id/>
<bqs:JournalArticle rdf:resource="rdf:#c40d2ebe-af1f-41df-a9b0-6c96eae223ab"/>
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<rdf:Description rdf:about="rdf:#eac5760f-3919-43b5-bbcf-10a834de15ee">
<vCard:Given>Espen</vCard:Given>
<vCard:Family>Remme</vCard:Family>
<vCard:Other/>
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<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>
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<dcterms:W3CDTF>2004-05-03T00:00:00+00:00</dcterms:W3CDTF>
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<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#9eabdff1-c043-4209-8072-5ada71dab522"/>
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<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>
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<vCard:Given>B</vCard:Given>
<vCard:Family>Smaill</vCard:Family>
<vCard:Other>H</vCard:Other>
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