- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2007-12-04 00:26:00+13:00
- Desc:
- committing version01 of costa_holmes_mcculloch_2001
- Permanent Source URI:
- https://models.cellml.org/workspace/costa_holmes_mcculloch_2001/rawfile/995069385782dd16bc2df762fbb717f56176dda7/costa_holmes_mcculloch_2001.cellml
<?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" name="guccione_mcculloch_waldman_1991_version02">
<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>Bioengineering Institute, 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>
The mechanics of the heart are multi-dimensional by nature, the constitutive properties of myocardium are three dimensional; anisotropic, nonlinear
and time dependent. The significance of this is that the forces generated by the ventricular sarcomeres (basic functional units of muscle) are converted
to chamber pressures in the heart. These forces and chamber pressures are in turn dependant on the three-dimensional geometry and myofibre architecture
of the ventricular myocardium.
</para>
<para>
One of the main problems in modeling the heart and its mechanical properties is its inherent multi-dimensional nature; the foremost issues of concern
include identifying functional forms and parameters of the constitutive equations, which describe the material properties of the resting and active,
normal and diseased myocardium.
</para>
<para>
Formulating useful constitutive laws are the key to solving the problem of modelling cardiac mechanics, and requires a combination of things.
Such as multi-axial tissue testing in vitro, microstructural modelling based on quantitative morphology, statistical parameter estimation, and validation
with measurements from intact hearts.
</para>
<para>
The inability to simplify myocardium mechanics to a 2D level requires a more rigorous approach, and so mathematical models are needed to interpret
experimental and clinical observations on regional myocardial deformations.
</para>
<para>
Because the problem of modelling cardiac mechanics is nonlinear, dynamic and three-dimensional, numerical methods are essential for accurate
quantitative analysis. Many aspects of the problem are covered elsewhere: LeGrice <emphasis>et al.</emphasis> (2001) and <ulink url="http://www.cellml.org/models/guccione_mcculloch_waldman_1991_version01">
Guccione <emphasis>et al.</emphasis> (1991) </ulink>.
</para>
<para>
In the paper described here, Kevin Costa, Jeffrey Holmes and Andrew McCulloch review a critical challenge in myocardial mechanics: developing accurate
constitutive models that describe how the structure and biophysics of the normal and diseased myocardium give rise to the mechanical responses of the
intact tissue.
</para>
<para>
While much of the work in this field builds on uniaxial and two-dimensional studies, the authors focus primarily on three-dimensional measurements and
models.
</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 Bioengineering Institute, 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 complete 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. <ulink url="http://www.journals.royalsoc.ac.uk/content/c53h9ljv7m7yqd96/">
<emphasis>Philosophical Transactions of The Royal Society</emphasis>
</ulink>, 359, 1233-1250. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/">PubMed ID: Unknown</ulink> </para>
</sect1>
</article>
</documentation>
<!-- Global units -->
<units name="strain">
<unit units="dimensionless"/>
</units>
<units name="stress">
<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="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 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="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 -->
<variable units="strain" public_interface="none" private_interface="none" name="q"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="q_calculation_eq">
<apply id="q_calculation">
<eq/>
<ci>q</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>bff</ci>
<apply>
<power/>
<ci>E11</ci>
<cn cellml:units="strain">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>bss</ci>
<apply>
<power/>
<ci>E22</ci>
<cn cellml:units="strain">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>bnn</ci>
<apply>
<power/>
<ci>E33</ci>
<cn cellml:units="strain">2</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>bfn</ci>
<apply>
<power/>
<ci>E13</ci>
<cn cellml:units="strain">2</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>bfs</ci>
<apply>
<power/>
<ci>E12</ci>
<cn cellml:units="strain">2</cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>bns</ci>
<apply>
<power/>
<ci>E23</ci>
<cn cellml:units="strain">2</cn>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev11_calculation_eq">
<apply id="Tdev11_calculation">
<eq/>
<ci>Tdev11</ci>
<apply>
<times/>
<ci>a</ci>
<ci>bff</ci>
<ci>E11</ci>
<apply>
<exp/>
<ci>q</ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev22_calculation_eq">
<apply id="Tdev22_calculation">
<eq/>
<ci>Tdev22</ci>
<apply>
<times/>
<ci>a</ci>
<ci>bss</ci>
<ci>E22</ci>
<apply>
<exp/>
<ci>q</ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdev33_calculation_eq">
<apply id="Tdev33_calculation">
<eq/>
<ci>Tdev33</ci>
<apply>
<times/>
<ci>a</ci>
<ci>bnn</ci>
<ci>E33</ci>
<apply>
<exp/>
<ci>q</ci>
</apply>
</apply>
</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"/>
<map_variables variable_2="E13" variable_1="E13"/>
<map_variables variable_2="E22" variable_1="E22"/>
<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"/>
<map_variables variable_2="Tdev33" variable_1="Tdev33"/>
<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:#f1c834a2-6dc6-4cf1-93e9-30206d356e10">
<rdf:li rdf:resource="rdf:#10822813-74dc-4d81-90e5-e9a5174bb797"/>
<rdf:li rdf:resource="rdf:#8a035e6d-0a15-47a9-be87-dd8fd2d4e83c"/>
<rdf:li rdf:resource="rdf:#61a89d0c-3018-4181-99b6-f377d15264f9"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#eb1345ea-01bd-4d91-891f-090c5fa76181">
<dc:creator rdf:resource="rdf:#f1c834a2-6dc6-4cf1-93e9-30206d356e10"/>
<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:#23069cb9-04a8-4519-96f0-f3733e5d8e2d"/>
<dcterms:issued rdf:resource="rdf:#d9941717-8d2d-4319-9042-971c7903da0c"/>
<bqs:last_page>1250</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="">
<dc:publisher>Auckland Bioengineering Institute</dc:publisher>
<cmeta:comment rdf:resource="rdf:#7ee5a233-7c07-4af5-b809-3b84fa5e4657"/>
<dcterms:created rdf:resource="rdf:#aa45e684-d78c-43f7-8d44-b9cdccde138f"/>
<dc:creator rdf:resource="rdf:#64fd00c6-ccab-495f-8f43-85d5b458fb80"/>
<cmeta:modification rdf:resource="rdf:#b0e5b22d-7491-43fd-a2c9-1284ed3eb292"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#2d57d210-da3a-4428-bca3-ddb07a574084">
<dc:creator rdf:resource="rdf:#01079ddd-2e96-48e7-80d5-834ac32a1a2b"/>
<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:#01079ddd-2e96-48e7-80d5-834ac32a1a2b">
<vCard:FN>Vignesh Kumar</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#b8ae16d3-009e-43ff-acb9-d87d7d91da54">
<vCard:Given>Holger </vCard:Given>
<vCard:Family>Schmid</vCard:Family>
<vCard:Other/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7ee5a233-7c07-4af5-b809-3b84fa5e4657">
<dc:creator rdf:resource="rdf:#bea2f43f-e804-426e-ad4e-d7117f60c50a"/>
<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:#5985b015-7251-495f-b81b-37c50f9f0123">
<vCard:Given>K</vCard:Given>
<vCard:Family>Costa</vCard:Family>
<vCard:Other>D</vCard:Other>
</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:#ed9145c2-293b-40a9-b8a9-4e63f0dd7af9">
<vCard:Given>Holger</vCard:Given>
<vCard:Family>Schmid</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8a035e6d-0a15-47a9-be87-dd8fd2d4e83c">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#c9db32d4-338e-47ad-bc52-3ad367e8200d"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#bea2f43f-e804-426e-ad4e-d7117f60c50a">
<vCard:FN>Vignesh Kumar</vCard:FN>
</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:#64fd00c6-ccab-495f-8f43-85d5b458fb80">
<vCard:ORG rdf:resource="rdf:#91bd472d-9342-4b7a-9174-8128db006887"/>
<vCard:EMAIL rdf:resource="rdf:#45751053-958f-4441-8c6b-8bc3c2eb0113"/>
<vCard:N rdf:resource="rdf:#b8ae16d3-009e-43ff-acb9-d87d7d91da54"/>
</rdf:Description>
<rdf:Description rdf:about="#Costa">
<bqs:reference rdf:resource="rdf:#6e07caa2-07fe-4b5e-8c3b-6d35910c66dc"/>
<bqs:reference rdf:resource="rdf:#d78a8c7b-45b4-44e4-b8df-768b34b08881"/>
<cmeta:comment rdf:resource="rdf:#2d57d210-da3a-4428-bca3-ddb07a574084"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d78a8c7b-45b4-44e4-b8df-768b34b08881">
<dc:subject rdf:resource="rdf:#5c9d91ac-ba89-4597-9268-5598f295bbf7"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#10822813-74dc-4d81-90e5-e9a5174bb797">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#5985b015-7251-495f-b81b-37c50f9f0123"/>
</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:#91bd472d-9342-4b7a-9174-8128db006887">
<vCard:Orgname>University of Auckland</vCard:Orgname>
<vCard:Orgunit>Auckland Bioengineering Institute</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#45751053-958f-4441-8c6b-8bc3c2eb0113">
<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:#61a89d0c-3018-4181-99b6-f377d15264f9">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#9f56ad89-9a4e-4865-8613-9947cf01fc6f"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a2e191e5-52de-4cf2-ac23-c26d1d98e4f9">
<dcterms:W3CDTF>2003-12-28</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7346b5b0-9ffb-4cd4-944d-97fa3e6e15ef">
<vCard:Given>Vignesh</vCard:Given>
<vCard:Family>Kumar</vCard:Family>
<vCard:Other/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9f56ad89-9a4e-4865-8613-9947cf01fc6f">
<vCard:Given>A</vCard:Given>
<vCard:Family>McCulloch</vCard:Family>
<vCard:Other>D</vCard:Other>
</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:#5c9d91ac-ba89-4597-9268-5598f295bbf7">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value>constitutive material law</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c9db32d4-338e-47ad-bc52-3ad367e8200d">
<vCard:Given>J</vCard:Given>
<vCard:Family>Holmes</vCard:Family>
<vCard:Other>W</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="#equations">
<cmeta:comment rdf:resource="rdf:#d51cfa53-0aad-4d27-9227-1b78b0b293d9"/>
</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="rdf:#d9941717-8d2d-4319-9042-971c7903da0c">
<dcterms:W3CDTF>2001-06-15 00:00</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:#b0e5b22d-7491-43fd-a2c9-1284ed3eb292">
<dcterms:modified rdf:resource="rdf:#1454180c-72cb-4ead-a564-d7b88c4c948d"/>
<rdf:value>Updated documentation</rdf:value>
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