<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : costa_law_1991.xml
CREATED : 308th July 2005
LAST MODIFIED : 18th February 2004
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 Orthotropic Exponential Constitutive relationship proposed by Costa et. al. (2001), it deals with the situation of modelling the three dimensional mechanical properties of cardiac tissue.
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="costa_2001" name="costa_2001">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>The Guccione Constitutive Material Law</title>
<author>
<firstname>Vijayaraghavan</firstname>
<surname>Rajagopal</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
ValidateCellML verifies this model as valid CellML with consistent units.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: The central problem in modelling the multi-dimensional mechanics of the heart is in identifying functional forms and parameters of the constitutive equations, which describe the material properties of the resting and active, normal and diseased myocardium. The constitutive properties of myocardium are three dimensional, anisotropic, nonlinear and time dependent. Formulating useful constitutive laws requires a combination of multi-axial tissue testing in vitro, microstructural modelling based on quantitative morphology, statistical parameter estimation, and validation with measurements from intact hearts. Recent models capture some important properties of healthy and diseased myocardium including: the nonlinear interactions between the responses to different loading patterns; the influence of the laminar myofibre sheet architecture; the effects of transverse stresses developed by the myocytes; and the relationship between collagen fibre architecture and mechanical properties in healing scar tissue after myocardial infarction.
</para>
<para>
The model was implemented in a manner that could be used for peforming finite element model simulations on the CMISS software program developed at the Auckland Bioengineering Institute, The University of Auckland.
</para>
<para>
For additional information on implementation of cellML files in CMISS, please refer to the following <ulink url="http://www.bioeng.auckland.ac.nz/people/nickerso/cmiss/help.html">Link</ulink>.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
Modelling cardiac mechanical properties in three dimensions, K.D. Costa, J.W. Holmes and A. D. McCulloch, 2001.
<emphasis>Philosophical Transactions of The Royal Society</emphasis>
, 359, 1233-1250. (no PubMed ID)</para>
</sect1>
</article>
</documentation>
<!-- Global units -->
<units name="strain">
<unit units="dimensionless"/>
</units>
<units name="stress">
<unit units="dimensionless"/>
</units>
<component name="interface" cmeta:id="interface">
<!-- Variables we expect to be set/controlled externally -->
<variable units="strain" private_interface="out" name="E11"/>
<variable units="strain" private_interface="out" name="E12"/>
<variable units="strain" private_interface="out" name="E13"/>
<variable units="strain" private_interface="out" name="E22"/>
<variable units="strain" private_interface="out" name="E23"/>
<variable units="strain" private_interface="out" name="E33"/>
<variable units="strain" private_interface="out" name="a" initial_value="0"/>
<variable units="strain" private_interface="out" name="bff" initial_value="0"/>
<variable units="strain" private_interface="out" name="bfn" initial_value="0"/>
<variable units="strain" private_interface="out" name="bfs" initial_value="0"/>
<variable units="strain" private_interface="out" name="bnn" initial_value="0"/>
<variable units="strain" private_interface="out" name="bns" initial_value="0"/>
<variable units="strain" private_interface="out" name="bss" 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="Tdev12"/>
<variable units="stress" public_interface="out" private_interface="in" name="Tdev13"/>
<variable units="stress" public_interface="out" private_interface="in" name="Tdev22"/>
<variable units="stress" public_interface="out" private_interface="in" name="Tdev23"/>
<variable units="stress" public_interface="out" private_interface="in" name="Tdev33"/>
</component> <!--interface-->
<component name="equations" cmeta:id="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="strain" public_interface="in" name="a"/>
<variable units="strain" public_interface="in" name="bff"/>
<variable units="strain" public_interface="in" name="bfn"/>
<variable units="strain" public_interface="in" name="bfs"/>
<variable units="strain" public_interface="in" name="bnn"/>
<variable units="strain" public_interface="in" name="bns"/>
<variable units="strain" public_interface="in" name="bss"/>
<!-- 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 -->
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<power/>
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</apply>
</apply>
<apply>
<times/>
<ci>bss</ci>
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<power/>
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</apply>
</apply>
<apply>
<times/>
<ci>bnn</ci>
<apply>
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</apply>
</apply>
<apply>
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<apply>
<power/>
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</apply>
</apply>
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<ci>bfs</ci>
<apply>
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<apply>
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<ci>E11</ci>
<apply>
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</apply>
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<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev22_calculation_eq">
<apply id="Tdev22_calculation">
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<ci>bss</ci>
<ci>E22</ci>
<apply>
<exp/>
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</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev33_calculation_eq">
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<ci>bnn</ci>
<ci>E33</ci>
<apply>
<exp/>
<ci>q</ci>
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</apply>
</math>
<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>a</ci>
<ci>bfs</ci>
<ci>E12</ci>
<apply>
<exp/>
<ci>q</ci>
</apply>
</apply>
</apply>
</math>
<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>a</ci>
<ci>bfn</ci>
<ci>E13</ci>
<apply>
<exp/>
<ci>q</ci>
</apply>
</apply>
</apply>
</math>
<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>a</ci>
<ci>bns</ci>
<ci>E23</ci>
<apply>
<exp/>
<ci>q</ci>
</apply>
</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="E12" variable_1="E12"/>
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<map_variables variable_2="E23" variable_1="E23"/>
<map_variables variable_2="E33" variable_1="E33"/>
<map_variables variable_2="Tdev11" variable_1="Tdev11"/>
<map_variables variable_2="Tdev12" variable_1="Tdev12"/>
<map_variables variable_2="Tdev13" variable_1="Tdev13"/>
<map_variables variable_2="Tdev22" variable_1="Tdev22"/>
<map_variables variable_2="Tdev23" variable_1="Tdev23"/>
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<map_variables variable_2="a" variable_1="a"/>
<map_variables variable_2="bff" variable_1="bff"/>
<map_variables variable_2="bfn" variable_1="bfn"/>
<map_variables variable_2="bfs" variable_1="bfs"/>
<map_variables variable_2="bnn" variable_1="bnn"/>
<map_variables variable_2="bns" variable_1="bns"/>
<map_variables variable_2="bss" variable_1="bss"/>
</connection>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="interface">
<component_ref component="equations"/>
</component_ref>
</group>
<rdf:RDF>
<rdf:Seq rdf:about="rdf:#7ef5ce85-51ec-41c6-812b-2e66a652bc3f">
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<dc:publisher>Auckland Bioengineering Institute</dc:publisher>
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<vCard:Orgname>University of Auckland</vCard:Orgname>
<vCard:Orgunit>Auckland Bioengineering Institute</vCard:Orgunit>
</rdf:Description>
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<vCard:Given>Holger</vCard:Given>
<vCard:Family>Schmid</vCard:Family>
<vCard:Other/>
</rdf:Description>
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<rdf:Description rdf:about="rdf:#244dbd03-fd51-48dd-a09f-76f177e53b64">
<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:#c2519afa-641b-4776-a56e-7405564b8740">
<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:#d51cfa53-0aad-4d27-9227-1b78b0b293d9">
<rdf:value>
In this simple model we only have one component, which holds the
six equations.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a9cf18ec-ed50-48ec-9181-0633ff354212">
<dc:creator rdf:resource="rdf:#7ef5ce85-51ec-41c6-812b-2e66a652bc3f"/>
<dc:title>Modelling Cardiac Mechanical Properties In Three Dimensions</dc:title>
<bqs:volume>359</bqs:volume>
<bqs:first_page>1233</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#3f3ac4a8-146d-42c5-aef1-536072f938f4"/>
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<bqs:last_page>1250</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#bbe33cd3-2e24-4934-9a2d-4e39e8fe7985">
<vCard:Given>James</vCard:Given>
<vCard:Family>Lawson</vCard:Family>
<vCard:Other>Richard </vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#2f33cb9b-6bc9-46ab-a22a-0e7d37dc90b5">
<vCard:Given>A</vCard:Given>
<vCard:Family>McCulloch</vCard:Family>
<vCard:Other>D</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6fd4e976-f1f9-4229-95d5-9bb35c36ac98">
<dc:creator rdf:resource="rdf:#932f2311-0c49-4f26-b00d-a94de75f2e27"/>
<rdf:value>This file contains a CellML description of the Orthotropic Exponential Constitutive relationship proposed by Costa et. al. (2001), it deals with the situation of modelling the three dimensional mechanical properties of cardiac tissue.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b0e5b22d-7491-43fd-a2c9-1284ed3eb292">
<dcterms:modified rdf:resource="rdf:#1454180c-72cb-4ead-a564-d7b88c4c948d"/>
<rdf:value>Updated documentation</rdf:value>
<cmeta:modifier rdf:resource="rdf:#0a7580b5-952c-46f5-996f-489f77658a29"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#559f3d7a-c25e-4d68-b37a-65a71a449f7f">
<dcterms:W3CDTF>2005-07-30T00:00:00+00:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3bed5515-7c47-4b46-bf0b-b123df93a5d9">
<dc:creator rdf:resource="rdf:#e663a7e0-5c28-4ca6-8a4a-f5c5777a8c2c"/>
<rdf:value>This is a CellML version of the Costa 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>
<rdf:Description rdf:about="rdf:#e663a7e0-5c28-4ca6-8a4a-f5c5777a8c2c">
<vCard:FN>Vignesh Kumar</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="#costa_2001">
<bqs:reference rdf:resource="rdf:#d78a8c7b-45b4-44e4-b8df-768b34b08881"/>
<bqs:reference rdf:resource="rdf:#ddacfa1b-045b-48de-8759-fd85f68d19c6"/>
<cmeta:comment rdf:resource="rdf:#3bed5515-7c47-4b46-bf0b-b123df93a5d9"/>
</rdf:Description>
<rdf:Description rdf:about="">
<dcterms:created rdf:resource="rdf:#a2e191e5-52de-4cf2-ac23-c26d1d98e4f9"/>
<dc:creator rdf:resource="rdf:#20c32c6d-6c4f-4d2e-aad8-ab21aa4be2d6"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#fc485da5-46f1-4856-8617-b6251ca9fb47">
<vCard:Given>J</vCard:Given>
<vCard:Family>Holmes</vCard:Family>
<vCard:Other>W</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#57d78bca-38c6-465d-b8b4-03ba7792bb09">
<vCard:N rdf:resource="rdf:#bbe33cd3-2e24-4934-9a2d-4e39e8fe7985"/>
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<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#fc485da5-46f1-4856-8617-b6251ca9fb47"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#30800923-8f37-4fac-8217-0135e03f1e7a">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>M</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8748152d-ce84-488e-9709-7b35f8b3b4a3">
<dcterms:W3CDTF>2009-06-08T12:51:49+12:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ca1b35ee-2b31-4dc6-8be0-f7f1446aa05d">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#2f33cb9b-6bc9-46ab-a22a-0e7d37dc90b5"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#932f2311-0c49-4f26-b00d-a94de75f2e27">
<vCard:FN>Vignesh Kumar</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7cc96552-018c-4d10-8b1f-89ff59031d0e">
<vCard:Given>K</vCard:Given>
<vCard:Family>Costa</vCard:Family>
<vCard:Other>D</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7346b5b0-9ffb-4cd4-944d-97fa3e6e15ef">
<vCard:Given>Vignesh</vCard:Given>
<vCard:Family>Kumar</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ed9145c2-293b-40a9-b8a9-4e63f0dd7af9">
<vCard:Given>Holger</vCard:Given>
<vCard:Family>Schmid</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1454180c-72cb-4ead-a564-d7b88c4c948d">
<dcterms:W3CDTF>2007-12-04T12:21:03+13:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0a7580b5-952c-46f5-996f-489f77658a29">
<vCard:N rdf:resource="rdf:#7346b5b0-9ffb-4cd4-944d-97fa3e6e15ef"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3f3ac4a8-146d-42c5-aef1-536072f938f4">
<dc:title>Philosophical Transactions of The Royal Society</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5c9d91ac-ba89-4597-9268-5598f295bbf7">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value>
<rdf:Bag>
<rdf:li>costa law</rdf:li>
<rdf:li>mechanical constitutive laws</rdf:li>
<rdf:li>cardiac mechanics</rdf:li>
</rdf:Bag>
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#equations">
<cmeta:comment rdf:resource="rdf:#d51cfa53-0aad-4d27-9227-1b78b0b293d9"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#77e5557f-2366-48f1-b852-8b1500e34bbb">
<dcterms:modified rdf:resource="rdf:#d197e273-dc68-4f63-9ecc-02acf35c415e"/>
<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:#24f91ec0-4edb-4259-b0b9-09351c59eede"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c902de92-6f02-4768-abfb-828b4671d605">
<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="rdf:#d197e273-dc68-4f63-9ecc-02acf35c415e">
<dcterms:W3CDTF>2004-02-18</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="#interface">
<cmeta:comment rdf:resource="rdf:#c902de92-6f02-4768-abfb-828b4671d605"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ddacfa1b-045b-48de-8759-fd85f68d19c6">
<bqs:Pubmed_id/>
<bqs:JournalArticle rdf:resource="rdf:#a9cf18ec-ed50-48ec-9181-0633ff354212"/>
</rdf:Description>
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<vCard:Orgname>The University of Auckland</vCard:Orgname>
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