<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : tangent_law_1991.xml
CREATED : 1st July 2003
LAST MODIFIED : 1st July 2003
AUTHOR : Holger Schmid
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 Taylor series expansion of the Tangent Law, defining the relation between the six independent strain components and the stress components.
CHANGES:
18/02/04 - CML - Completed the Metadata.
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="Tangent" name="schmid_2006">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>The Taylor Series Expansion of the Tangent Law</title>
<author>
<firstname>Holger</firstname>
<surname>Schmid</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This CellML model was implemented in a manner that could be used for performing finite element model simulations on the CMISS software program developed at the Auckland Bioengineering Institute, The University of Auckland.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: The study of ventricular mechanics-analyzing the distribution of strain and stress in myocardium throughout the cardiac cycle-is crucially dependent on the accuracy of the constitutive law chosen to represent the highly nonlinear and anisotropic properties of passive cardiac muscle. A number of such laws have been proposed and fitted to experimental measurements of stress-strain behavior. Here we examine five of these laws and compare them on the basis of (i) "goodness of fit:" How well they fit a set of six shear deformation tests, (ii) "determinability:" How well determined the objective function is at the optimal parameter fit, and (iii) "variability:" How well determined the material parameters are over the range of experiments. These criteria are utilized to discuss the advantages and disadvantages of the constitutive laws.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
Myocardial Material Parameter Estimation - A Comparative Study for Simple Shear, H. Schmid, M. P. Nash, A. A. Young and P. J. Hunter, 2006. <emphasis>Journal of Biomechanical Engineering</emphasis>, 128(5), 742-750. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/16995761">PubMed ID: 16995761</ulink> </para>
</sect1>
</article>
</documentation>
<!-- Global units -->
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<unit units="dimensionless"/>
</units>
<units name="stress">
<unit units="dimensionless"/>
</units>
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<!-- Variables we expect to be set/controlled externally -->
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<!-- 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"/>
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<!-- Outputs computed here -->
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<component_ref component="interface">
<component_ref component="equations"/>
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<rdf:RDF>
<rdf:Seq rdf:about="rdf:#9920f12b-4aa1-401d-81a0-929a42b42243">
<rdf:li rdf:resource="rdf:#4f5a9ee4-7c52-481b-b0ef-21010e839fc2"/>
<rdf:li rdf:resource="rdf:#69059ab1-1387-4a04-9419-52d1ff37c978"/>
<rdf:li rdf:resource="rdf:#81eaa51d-1059-4691-bb88-977f878fd923"/>
<rdf:li rdf:resource="rdf:#90651551-6cb9-4f69-b0d6-33e01618acfe"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#e010ab9b-1428-46f1-a264-2f572dac4921">
<vCard:FN>Vignesh Kumar</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="">
<dc:title>Myocardial Material Parameter Estimation - A Comparative Study for Simple Shear (Taylor Series Expansion of the Tangent Law)</dc:title>
<dc:publisher>Auckland Bioengineering Institute</dc:publisher>
<cmeta:comment rdf:resource="rdf:#0135fcc9-d708-4e22-aa3a-486f468bb985"/>
<dcterms:created rdf:resource="rdf:#585ba385-3b15-4c60-b143-0319e1d71c30"/>
<dc:creator rdf:resource="rdf:#0f4ab691-7ed8-469e-bf6b-33848837d039"/>
<cmeta:modification rdf:resource="rdf:#fe4404d5-d1dd-46dd-912d-ebf7fb98ad60"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#faa9e00f-8285-42e1-a58e-6ae319f92afa">
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
<rdf:value>h.schmid@auckland.ac.nz</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3f2c22f0-64d5-4270-a4c4-4818e5db6396">
<rdf:value>
We'll use this component as the "interface" to the model, all
other components are hidden via encapsulation in this component.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#interface">
<cmeta:comment rdf:resource="rdf:#3f2c22f0-64d5-4270-a4c4-4818e5db6396"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#63bd398d-67fe-485a-996e-a08014602bf6">
<bqs:Pubmed_id>16995761</bqs:Pubmed_id>
<bqs:JournalArticle rdf:resource="rdf:#edbb0a72-e609-490a-a972-1e4b13449211"/>
</rdf:Description>
<rdf:Description rdf:about="#Tangent">
<bqs:reference rdf:resource="rdf:#19ea753c-a022-425c-be0f-c39bbca9d1d2"/>
<bqs:reference rdf:resource="rdf:#63bd398d-67fe-485a-996e-a08014602bf6"/>
<cmeta:comment rdf:resource="rdf:#eab6e4fc-e864-4b12-bbfc-d682e0dc5d17"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0135fcc9-d708-4e22-aa3a-486f468bb985">
<dc:creator rdf:resource="rdf:#e010ab9b-1428-46f1-a264-2f572dac4921"/>
<rdf:value>This file contains a CellML description of the Taylor series expansion of the Tangent Law, defining the relation between the six independent strain components and the stress components.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#fe4404d5-d1dd-46dd-912d-ebf7fb98ad60">
<dcterms:modified rdf:resource="rdf:#715df17f-ead9-4d0b-b1ae-5bf26bf11bfd"/>
<rdf:value>Updated documentation</rdf:value>
<cmeta:modifier rdf:resource="rdf:#e8ccc2e0-c663-4c48-aaa2-5f35dfe722ab"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#be7b5494-0b8d-46c1-ae5c-e078f99ed234">
<dcterms:W3CDTF>2003-12-28</dcterms:W3CDTF>
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<dc:title>Myocardial Material Parameter Estimation - A Comparative Study for Simple Shear</dc:title>
<bqs:volume>128(5)</bqs:volume>
<bqs:first_page>742</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#cfd782bc-d053-4d74-95dd-a93ac8036b75"/>
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<bqs:last_page>750</bqs:last_page>
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<vCard:Given>Holger</vCard:Given>
<vCard:Family>Schmid</vCard:Family>
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<vCard:Given>P</vCard:Given>
<vCard:Family>Hunter</vCard:Family>
<vCard:Other>J</vCard:Other>
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<dcterms:W3CDTF>2004-02-18</dcterms:W3CDTF>
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<rdf:value>h.schmid@auckland.ac.nz</rdf:value>
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<rdf:Description rdf:about="rdf:#7dcc2646-fc15-4c0d-bf3e-b4bf39c3561d">
<vCard:Given>A</vCard:Given>
<vCard:Family>Young</vCard:Family>
<vCard:Other>A</vCard:Other>
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<rdf:Description rdf:about="rdf:#1ad97bec-06ac-4334-931e-6c924d186116">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
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<rdf:Description rdf:about="rdf:#585ba385-3b15-4c60-b143-0319e1d71c30">
<dcterms:W3CDTF>2003-07-01T00:00:00+12:00</dcterms:W3CDTF>
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<vCard:Given>M</vCard:Given>
<vCard:Family>Nash</vCard:Family>
<vCard:Other>P</vCard:Other>
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<rdf:Description rdf:about="rdf:#e102e6e7-2056-4eac-93a1-fa4679056cc5">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>M</vCard:Other>
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<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>Auckland Bioengineering Institute</vCard:Orgunit>
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<dcterms:W3CDTF>2007-12-05T13:49:01+13:00</dcterms:W3CDTF>
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<rdf:Description rdf:about="rdf:#fa6a7584-bdfd-407a-9128-13eb1af85592">
<rdf:value>
In this simple model we only have one component, which holds the
six equations.
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<dcterms:modified rdf:resource="rdf:#e4829a26-7ce9-4e60-95d5-e73482a4b348"/>
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Added metadata to the model.
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<cmeta:modifier rdf:resource="rdf:#3e8884cb-8235-47af-875b-1c5af10c93d8"/>
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<vCard:Given>H</vCard:Given>
<vCard:Family>Schmid</vCard:Family>
<vCard:Other/>
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<vCard:FN>Vignesh Kumar</vCard:FN>
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<vCard:ORG rdf:resource="rdf:#d97ba06e-ef1c-48d5-829b-1543e1e8049f"/>
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<dc:title>Journal of Biomechanical Engineering</dc:title>
</rdf:Description>
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<bqs:subject_type>keyword</bqs:subject_type>
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<rdf:li>tangent law</rdf:li>
<rdf:li>mechanical constitutive laws</rdf:li>
<rdf:li>cardiac mechanics</rdf:li>
<rdf:li>constitutive material law</rdf:li>
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<vCard:Given>Holger</vCard:Given>
<vCard:Family>Schmid</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="#equations">
<cmeta:comment rdf:resource="rdf:#fa6a7584-bdfd-407a-9128-13eb1af85592"/>
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<dc:creator rdf:resource="rdf:#fdc97d7e-d815-4e1e-96ce-0da4bf02bfdd"/>
<rdf:value>This is a CellML version of the Tangent constitutive material law,
defining the relation between the six independent strain components
and the stress components. It is assumed that the strain components
will be controlled externally by the application using this CellML
model.</rdf:value>
</rdf:Description>
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<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
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<rdf:Description rdf:about="rdf:#73e77a38-e951-4227-a3ca-be372da37bb0">
<vCard:Given>Vignesh</vCard:Given>
<vCard:Family>Kumar</vCard:Family>
<vCard:Other/>
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<dcterms:W3CDTF>2006-10-01 00:00</dcterms:W3CDTF>
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