<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : FiberDispersion_law_2468.xml
CREATED : 30th July 2005
LAST MODIFIED : 1st January 2007
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.
The model represented here focuses on the combination 2,4,6,8 of the fibre dispersion law.
With '2' representing the isotropic component of the functional form and
'4', '6' and '8' representing the anisotropic components of the functional form.
DESCRIPTION : This file contains a CellML description of the Guccione constitutive material 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="FiberDispersion" name="gasser_2006">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Fibre Dispersion 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 peforming finite element model simulations on the CMISS software program developed at the Auckland Bioengineering Institute, The University of Auckland. The model file presented here focuses on the functional form of the fibre dispersion law corresponding to the the combination 2,4,6,8 <emphasis>(FiberDispersion_law_2468)</emphasis>, with 2 representing the isotropic component of the functional form, and 4, 6 and 8 representing the anisotropic components of the fucntional form. 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>. This file has not been recently checked for compatibility within CMISS, any feedback regarding this and any other issues would be appreciated.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Constitutive relations are fundamental to the solution of problems in continuum mechanics, and are required in the study of, for example, mechanically dominated clinical interventions involving soft biological tissues. Structural continuum constitutive models of arterial layers integrate information about the tissue morphology and therefore allow investigation of the interrelation between structure and function in response to mechanical loading. Collagen fibres are key ingredients in the structure of arteries. In the media (the middle layer of the artery wall) they are arranged in two helically distributed families with a small pitch and very little dispersion in their orientation (i.e. they are aligned quite close to the circumferential direction). By contrast, in the adventitial and intimal layers, the orientation of the collagen fibres is dispersed, as shown by polarized light microscopy of stained arterial tissue. As a result, continuum models that do not account for the dispersion are not able to capture accurately the stress-strain response of these layers. The purpose of this paper, therefore, is to develop a structural continuum framework that is able to represent the dispersion of the collagen fibre orientation. This then allows the development of a new hyperelastic free-energy function that is particularly suited for representing the anisotropic elastic properties of adventitial and intimal layers of arterial walls, and is a generalization of the fibre-reinforced structural model introduced by Holzapfel and Gasser (Holzapfel and Gasser 2001 Comput. Meth. Appl. Mech. Eng. 190, 4379-4403) and Holzapfel et al. (Holzapfel et al. 2000 J. Elast. 61, 1-48). The model incorporates an additional scalar structure parameter that characterizes the dispersed collagen orientation. An efficient finite element implementation of the model is then presented and numerical examples show that the dispersion of the orientation of collagen fibres in the adventitia of human iliac arteries has a significant effect on their mechanical response.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
Hyperelastic modelling of arterial layers with distributed collagen fibre orientations, T.C. Gasser, R.W. Ogden and G.A. Holzapfel, 2006, <emphasis>Journal of the Royal Society</emphasis>, 3(6), 15-35. <ulink url="http://www.ncbi.nlm.nih.gov/sites/entrez?cmd=Retrieve&db=PubMed&dopt=AbstractPlus&list_uids=16849214">PubMed ID: 16849214</ulink> </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="Emm"/>
<variable units="strain" private_interface="out" name="Emn"/>
<variable units="strain" private_interface="out" name="Ems"/>
<variable units="strain" private_interface="out" name="Enn"/>
<variable units="strain" private_interface="out" name="Ens"/>
<variable units="strain" private_interface="out" name="Ess"/>
<variable units="strain" private_interface="out" name="c21" initial_value="0"/>
<variable units="strain" private_interface="out" name="c22" initial_value="0"/>
<variable units="strain" private_interface="out" name="c41" initial_value="0"/>
<variable units="strain" private_interface="out" name="c42" initial_value="0"/>
<variable units="strain" private_interface="out" name="c61" initial_value="0"/>
<variable units="strain" private_interface="out" name="c62" initial_value="0"/>
<variable units="strain" private_interface="out" name="c81" initial_value="0"/>
<variable units="strain" private_interface="out" name="c82" initial_value="0"/>
<variable units="strain" private_interface="out" name="kappa1" initial_value="0"/>
<variable units="strain" private_interface="out" name="kappa2" initial_value="0"/>
<variable units="strain" private_interface="out" name="kappa3" initial_value="0"/>
<!-- Variables we want to make available externally -->
<variable units="stress" public_interface="out" private_interface="in" name="Tdevmm"/>
<variable units="stress" public_interface="out" private_interface="in" name="Tdevmn"/>
<variable units="stress" public_interface="out" private_interface="in" name="Tdevms"/>
<variable units="stress" public_interface="out" private_interface="in" name="Tdevnn"/>
<variable units="stress" public_interface="out" private_interface="in" name="Tdevns"/>
<variable units="stress" public_interface="out" private_interface="in" name="Tdevss"/>
</component> <!--interface-->
<component name="equations" cmeta:id="equations">
<!-- Inputs -->
<variable units="strain" public_interface="in" name="Emm"/>
<variable units="strain" public_interface="in" name="Enn"/>
<variable units="strain" public_interface="in" name="Ess"/>
<variable units="strain" public_interface="in" name="Emn"/>
<variable units="strain" public_interface="in" name="Ems"/>
<variable units="strain" public_interface="in" name="Ens"/>
<variable units="strain" public_interface="in" name="c21"/>
<variable units="strain" public_interface="in" name="c22"/>
<variable units="strain" public_interface="in" name="c41"/>
<variable units="strain" public_interface="in" name="c42"/>
<variable units="strain" public_interface="in" name="c61"/>
<variable units="strain" public_interface="in" name="c62"/>
<variable units="strain" public_interface="in" name="c81"/>
<variable units="strain" public_interface="in" name="c82"/>
<variable units="strain" public_interface="in" name="kappa1"/>
<variable units="strain" public_interface="in" name="kappa2"/>
<variable units="strain" public_interface="in" name="kappa3"/>
<!-- Outputs computed here -->
<variable units="stress" public_interface="out" name="Tdevmm"/>
<variable units="stress" public_interface="out" name="Tdevnn"/>
<variable units="stress" public_interface="out" name="Tdevss"/>
<variable units="stress" public_interface="out" name="Tdevmn"/>
<variable units="stress" public_interface="out" name="Tdevms"/>
<variable units="stress" public_interface="out" name="Tdevns"/>
<!-- Temporary variables -->
<variable units="strain" public_interface="none" private_interface="none" name="I1"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="I1_calculation_eq">
<apply id="I1_calculation">
<eq/>
<ci>I1</ci>
<apply>
<plus/>
<cn cellml:units="strain">3</cn>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>Emm</ci>
</apply>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>Enn</ci>
</apply>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>Ess</ci>
</apply>
</apply>
</apply>
</math>
<variable units="strain" public_interface="none" private_interface="none" name="I2"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="I2_calculation_eq">
<apply id="I2_calculation">
<eq/>
<ci>I2</ci>
<apply>
<plus/>
<cn cellml:units="strain">3</cn>
<apply>
<times/>
<cn cellml:units="strain">-4</cn>
<ci>Emn</ci>
<ci>Emn</ci>
</apply>
<apply>
<times/>
<cn cellml:units="strain">4</cn>
<ci>Enn</ci>
</apply>
<apply>
<times/>
<cn cellml:units="strain">-4</cn>
<ci>Ems</ci>
<ci>Ems</ci>
</apply>
<apply>
<times/>
<cn cellml:units="strain">-4</cn>
<ci>Ens</ci>
<ci>Ens</ci>
</apply>
<apply>
<times/>
<cn cellml:units="strain">4</cn>
<apply>
<plus/>
<cn cellml:units="strain">1</cn>
<ci>Enn</ci>
</apply>
<ci>Ess</ci>
</apply>
<apply>
<times/>
<cn cellml:units="strain">4</cn>
<apply>
<plus/>
<cn cellml:units="strain">1</cn>
<ci>Enn</ci>
</apply>
<ci>Ess</ci>
</apply>
<apply>
<times/>
<cn cellml:units="strain">4</cn>
<apply>
<plus/>
<cn cellml:units="strain">1</cn>
<ci>Enn</ci>
<ci>Ess</ci>
</apply>
<ci>Emm</ci>
</apply>
</apply>
</apply>
</math>
<variable units="strain" public_interface="none" private_interface="none" name="I4"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="I4_calculation_eq">
<apply id="I4_calculation">
<eq/>
<ci>I4</ci>
<apply>
<plus/>
<cn cellml:units="strain">1</cn>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>Emm</ci>
</apply>
</apply>
</apply>
</math>
<variable units="strain" public_interface="none" private_interface="none" name="I6"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="I6_calculation_eq">
<apply id="I6_calculation">
<eq/>
<ci>I6</ci>
<apply>
<plus/>
<cn cellml:units="strain">1</cn>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>Enn</ci>
</apply>
</apply>
</apply>
</math>
<variable units="strain" public_interface="none" private_interface="none" name="I8"/>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="I8_calculation_eq">
<apply id="I8_calculation">
<eq/>
<ci>I8</ci>
<apply>
<plus/>
<cn cellml:units="strain">1</cn>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>Ess</ci>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdevmm_calculation_eq">
<apply id="Tdevmm_calculation">
<eq/>
<ci>Tdevmm</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="strain">4</cn>
<ci>c21</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>c22</ci>
<apply>
<power/>
<apply>
<minus/>
<ci>I2</ci>
<cn cellml:units="strain">3</cn>
</apply>
<cn cellml:units="strain">2</cn>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci>I2</ci>
<cn cellml:units="strain">3</cn>
</apply>
<apply>
<plus/>
<cn cellml:units="strain">1</cn>
<ci>Enn</ci>
<ci>Ess</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>c41</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>c42</ci>
<apply>
<power/>
<apply>
<minus/>
<apply>
<times/>
<ci>I4</ci>
<apply>
<minus/>
<cn cellml:units="strain">1</cn>
<apply>
<times/>
<cn cellml:units="strain">3</cn>
<ci>kappa1</ci>
</apply>
</apply>
</apply>
<cn cellml:units="strain">1</cn>
</apply>
<cn cellml:units="strain">2</cn>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>I4</ci>
<apply>
<minus/>
<cn cellml:units="strain">1</cn>
<apply>
<times/>
<cn cellml:units="strain">3</cn>
<ci>kappa1</ci>
</apply>
</apply>
</apply>
<cn cellml:units="strain">1</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="strain">1</cn>
<apply>
<times/>
<cn cellml:units="strain">3</cn>
<ci>kappa1</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdevmn_calculation_eq">
<apply id="Tdevmn_calculation">
<eq/>
<ci>Tdevmn</ci>
<apply>
<times/>
<cn cellml:units="strain">-4</cn>
<ci>c21</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>c22</ci>
<apply>
<power/>
<apply>
<minus/>
<ci>I2</ci>
<cn cellml:units="strain">3</cn>
</apply>
<cn cellml:units="strain">2</cn>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci>I2</ci>
<cn cellml:units="strain">3</cn>
</apply>
<ci>Emn</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdevms_calculation_eq">
<apply id="Tdevms_calculation">
<eq/>
<ci>Tdevms</ci>
<apply>
<times/>
<cn cellml:units="strain">-4</cn>
<ci>c21</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>c22</ci>
<apply>
<power/>
<apply>
<minus/>
<ci>I2</ci>
<cn cellml:units="strain">3</cn>
</apply>
<cn cellml:units="strain">2</cn>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci>I2</ci>
<cn cellml:units="strain">3</cn>
</apply>
<ci>Ems</ci>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdevnn_calculation_eq">
<apply id="Tdevnn_calculation">
<eq/>
<ci>Tdevnn</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="strain">4</cn>
<ci>c21</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>c22</ci>
<apply>
<power/>
<apply>
<minus/>
<ci>I2</ci>
<cn cellml:units="strain">3</cn>
</apply>
<cn cellml:units="strain">2</cn>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci>I2</ci>
<cn cellml:units="strain">3</cn>
</apply>
<apply>
<plus/>
<cn cellml:units="strain">1</cn>
<ci>Emm</ci>
<ci>Ess</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>c61</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>c62</ci>
<apply>
<power/>
<apply>
<minus/>
<apply>
<times/>
<ci>I6</ci>
<apply>
<minus/>
<cn cellml:units="strain">1</cn>
<apply>
<times/>
<cn cellml:units="strain">3</cn>
<ci>kappa2</ci>
</apply>
</apply>
</apply>
<cn cellml:units="strain">1</cn>
</apply>
<cn cellml:units="strain">2</cn>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>I6</ci>
<apply>
<minus/>
<cn cellml:units="strain">1</cn>
<apply>
<times/>
<cn cellml:units="strain">3</cn>
<ci>kappa2</ci>
</apply>
</apply>
</apply>
<cn cellml:units="strain">1</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="strain">1</cn>
<apply>
<times/>
<cn cellml:units="strain">3</cn>
<ci>kappa2</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdevss_calculation_eq">
<apply id="Tdevss_calculation">
<eq/>
<ci>Tdevss</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="strain">4</cn>
<ci>c21</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>c22</ci>
<apply>
<power/>
<apply>
<minus/>
<ci>I2</ci>
<cn cellml:units="strain">3</cn>
</apply>
<cn cellml:units="strain">2</cn>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci>I2</ci>
<cn cellml:units="strain">3</cn>
</apply>
<apply>
<plus/>
<cn cellml:units="strain">1</cn>
<ci>Emm</ci>
<ci>Enn</ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="strain">2</cn>
<ci>c81</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>c82</ci>
<apply>
<power/>
<apply>
<minus/>
<apply>
<times/>
<ci>I8</ci>
<apply>
<minus/>
<cn cellml:units="strain">1</cn>
<apply>
<times/>
<cn cellml:units="strain">3</cn>
<ci>kappa3</ci>
</apply>
</apply>
</apply>
<cn cellml:units="strain">1</cn>
</apply>
<cn cellml:units="strain">2</cn>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>I8</ci>
<apply>
<minus/>
<cn cellml:units="strain">1</cn>
<apply>
<times/>
<cn cellml:units="strain">3</cn>
<ci>kappa3</ci>
</apply>
</apply>
</apply>
<cn cellml:units="strain">1</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="strain">1</cn>
<apply>
<times/>
<cn cellml:units="strain">3</cn>
<ci>kappa3</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
<math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="Tdevns_calculation_eq">
<apply id="Tdevns_calculation">
<eq/>
<ci>Tdevns</ci>
<apply>
<times/>
<cn cellml:units="strain">-4</cn>
<ci>c21</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>c22</ci>
<apply>
<power/>
<apply>
<minus/>
<ci>I2</ci>
<cn cellml:units="strain">3</cn>
</apply>
<cn cellml:units="strain">2</cn>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci>I2</ci>
<cn cellml:units="strain">3</cn>
</apply>
<ci>Ens</ci>
</apply>
</apply>
</math>
</component>
<!--membrane-->
<connection>
<map_components component_2="equations" component_1="interface"/>
<map_variables variable_2="Emm" variable_1="Emm"/>
<map_variables variable_2="Emn" variable_1="Emn"/>
<map_variables variable_2="Ems" variable_1="Ems"/>
<map_variables variable_2="Enn" variable_1="Enn"/>
<map_variables variable_2="Ens" variable_1="Ens"/>
<map_variables variable_2="Ess" variable_1="Ess"/>
<map_variables variable_2="Tdevmm" variable_1="Tdevmm"/>
<map_variables variable_2="Tdevmn" variable_1="Tdevmn"/>
<map_variables variable_2="Tdevms" variable_1="Tdevms"/>
<map_variables variable_2="Tdevnn" variable_1="Tdevnn"/>
<map_variables variable_2="Tdevns" variable_1="Tdevns"/>
<map_variables variable_2="Tdevss" variable_1="Tdevss"/>
<map_variables variable_2="c21" variable_1="c21"/>
<map_variables variable_2="c22" variable_1="c22"/>
<map_variables variable_2="c41" variable_1="c41"/>
<map_variables variable_2="c42" variable_1="c42"/>
<map_variables variable_2="c61" variable_1="c61"/>
<map_variables variable_2="c62" variable_1="c62"/>
<map_variables variable_2="c81" variable_1="c81"/>
<map_variables variable_2="c82" variable_1="c82"/>
<map_variables variable_2="kappa1" variable_1="kappa1"/>
<map_variables variable_2="kappa2" variable_1="kappa2"/>
<map_variables variable_2="kappa3" variable_1="kappa3"/>
</connection>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="interface">
<component_ref component="equations"/>
</component_ref>
</group>
<rdf:RDF>
<rdf:Seq rdf:about="rdf:#e4ef94ce-9957-42e5-9c46-0bf030533ca8">
<rdf:li rdf:resource="rdf:#7aa3af00-4cd2-4550-8810-61b39649d66e"/>
<rdf:li rdf:resource="rdf:#1ab3e26d-10fb-4312-9357-78c49fd7b9a1"/>
<rdf:li rdf:resource="rdf:#d39ec8d7-be96-45e4-b0ac-bb31483568e2"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#38dc4538-87e9-480d-9569-c6f9a058fa22">
<vCard:Given>G</vCard:Given>
<vCard:Family>Holzapfel</vCard:Family>
<vCard:Other>A</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#d39ec8d7-be96-45e4-b0ac-bb31483568e2">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#38dc4538-87e9-480d-9569-c6f9a058fa22"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5d57bddd-ed77-4dc6-9f90-12f08adf9c76">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#b1328599-e0b0-4c87-8097-6e35eb0dff5d"/>
</rdf:Description>
<rdf:Description rdf:about="">
<dc:title>Fibre Dispersion Law (Version A)</dc:title>
<dc:publisher>University of Auckland</dc:publisher>
<cmeta:comment rdf:resource="rdf:#ea2607e5-05cd-4db8-a943-2445bfb463a7"/>
<dcterms:created rdf:resource="rdf:#ae19039d-e31b-4a02-82d2-394029aca202"/>
<dc:creator rdf:resource="rdf:#783bb21e-8f74-4df7-8e99-626421372cd8"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#2790987a-685a-4d78-b1e1-55860a7f4df4">
<vCard:Given>Yikan</vCard:Given>
<vCard:Family>Wang</vCard:Family>
<vCard:Other>M</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="#equations">
<cmeta:comment rdf:resource="rdf:#372f2282-d4d4-4c1e-8ef7-b7bab086e255"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#964ac2eb-90f5-47b3-bad6-51607493beb5">
<dc:subject rdf:resource="rdf:#9630c5b4-5556-4962-8d78-99c32c777a72"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1ab3e26d-10fb-4312-9357-78c49fd7b9a1">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#726e2df2-38c9-4f72-aeee-c9bf61c62c05"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9630c5b4-5556-4962-8d78-99c32c777a72">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value>
<rdf:Bag>
<rdf:li>constitutive material law</rdf:li>
<rdf:li>mechanical constitutive laws</rdf:li>
</rdf:Bag>
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0dd3c3b2-c2ce-4c90-ba9d-1daa0a756ed1">
<dcterms:W3CDTF>2007-02-01</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4501e271-14d1-46c9-875e-1c51afc93ce1">
<vCard:Given>T</vCard:Given>
<vCard:Family>Gasser</vCard:Family>
<vCard:Other>C</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#61ea5d63-3eef-4e5c-a891-2b17d0ceb8c0">
<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:#f5b358db-26e9-4a4d-a08a-01eb9c7a202c">
<vCard:FN>Vignesh Kumar</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#783bb21e-8f74-4df7-8e99-626421372cd8">
<vCard:ORG rdf:resource="rdf:#9cb6e1e4-03ed-47b1-bde8-e268f5c904e9"/>
<vCard:EMAIL rdf:resource="rdf:#bbce8543-bf62-4380-bcd3-b7af3b67b92e"/>
<vCard:N rdf:resource="rdf:#546d8c82-a87f-43a8-8e9d-5728e758d4ce"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#edcd2699-3109-4b84-900f-ae77d63b4bda">
<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:#23421562-a0f4-4883-b6b7-a8a2e3ffefe2">
<vCard:FN>Vignesh Kumar</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#564ac71d-ae7d-4be9-b617-f423e3c6cee4">
<dc:creator rdf:resource="rdf:#f5b358db-26e9-4a4d-a08a-01eb9c7a202c"/>
<rdf:value>This is a CellML version of the Fibre Dispersion 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:#53a8d901-6a41-46d8-9d9a-f7389064acc0">
<vCard:Given>Holger</vCard:Given>
<vCard:Family>Schmid</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#07382a71-66fd-4692-8d69-ab257ca24bc6">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#c2e5692a-5861-4c33-8427-6ca65a10106a"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0aa62278-0265-4231-9113-c5f20670dce4">
<dcterms:W3CDTF>2003-12-28</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ea2607e5-05cd-4db8-a943-2445bfb463a7">
<dc:creator rdf:resource="rdf:#23421562-a0f4-4883-b6b7-a8a2e3ffefe2"/>
<rdf:value>This CellML file focuses on the development and introduction of a structural continuum framework that is able to represent the dispersion of
collagen fibres orientation within arterial walls. Thus allowing the development of a new hyperelastic free-energy function
that is well suited for representing the anisotropic elastic properties of adventitial and intimal layers of arterial walls. This file focuses on the combination 2,4,6,8 of the fibre dispersion law. With '2' representing the isotropic component of the functional form and '4', '6' and '8' representing the anisotropic component of the functional form.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#726e2df2-38c9-4f72-aeee-c9bf61c62c05">
<vCard:Given>R</vCard:Given>
<vCard:Family>Ogden</vCard:Family>
<vCard:Other>W</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#19668794-7948-4d11-a559-c3b8c4c7d88d">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#7e862b0c-16e0-42ff-a430-8f99c269455b"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#372f2282-d4d4-4c1e-8ef7-b7bab086e255">
<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:#8fa00cc1-fa7f-4d8a-a5f0-1a720c15452b">
<dcterms:modified rdf:resource="rdf:#0dd3c3b2-c2ce-4c90-ba9d-1daa0a756ed1"/>
<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:#ab9f7c80-defd-4d08-9232-620f905cbc6b"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ee79ad3a-ab00-453b-951a-9488a0610204">
<bqs:Pubmed_id>16849214</bqs:Pubmed_id>
<bqs:JournalArticle rdf:resource="rdf:#0051a138-3b8a-4b77-9c7e-364fde8fd2a8"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a7988c5d-8599-4518-87fa-7a1be4964ec2">
<vCard:ORG rdf:resource="rdf:#7ac2ec8f-7faf-4e69-82d5-ee28cd92d43f"/>
<vCard:EMAIL rdf:resource="rdf:#61ea5d63-3eef-4e5c-a891-2b17d0ceb8c0"/>
<vCard:N rdf:resource="rdf:#53a8d901-6a41-46d8-9d9a-f7389064acc0"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7aa3af00-4cd2-4550-8810-61b39649d66e">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#4501e271-14d1-46c9-875e-1c51afc93ce1"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ae19039d-e31b-4a02-82d2-394029aca202">
<dcterms:W3CDTF>2005-07-30T00:00:00+12:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0b1d33be-0de0-4058-a7a0-6583be4cd5a2">
<dc:title>Journal of The Royal Society Interface</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#bbce8543-bf62-4380-bcd3-b7af3b67b92e">
<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="#FiberDispersion">
<bqs:reference rdf:resource="rdf:#964ac2eb-90f5-47b3-bad6-51607493beb5"/>
<bqs:reference rdf:resource="rdf:#ee79ad3a-ab00-453b-951a-9488a0610204"/>
<cmeta:comment rdf:resource="rdf:#564ac71d-ae7d-4be9-b617-f423e3c6cee4"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7e81774f-5fb6-49f1-abc9-ffea399d1aca">
<dcterms:W3CDTF>2006-02-22 00:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="#interface">
<cmeta:comment rdf:resource="rdf:#edcd2699-3109-4b84-900f-ae77d63b4bda"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7ac2ec8f-7faf-4e69-82d5-ee28cd92d43f">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0051a138-3b8a-4b77-9c7e-364fde8fd2a8">
<dc:creator rdf:resource="rdf:#e4ef94ce-9957-42e5-9c46-0bf030533ca8"/>
<dc:title>Hyperelastic modelling of arterial layers with distributed collagen fibre orientations</dc:title>
<bqs:volume>3(6)</bqs:volume>
<bqs:first_page>15</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#0b1d33be-0de0-4058-a7a0-6583be4cd5a2"/>
<dcterms:issued rdf:resource="rdf:#7e81774f-5fb6-49f1-abc9-ffea399d1aca"/>
<bqs:last_page>35</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ab9f7c80-defd-4d08-9232-620f905cbc6b">
<vCard:N rdf:resource="rdf:#2790987a-685a-4d78-b1e1-55860a7f4df4"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#546d8c82-a87f-43a8-8e9d-5728e758d4ce">
<vCard:Given>Holger</vCard:Given>
<vCard:Family>Schmid</vCard:Family>
<vCard:Other/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9cb6e1e4-03ed-47b1-bde8-e268f5c904e9">
<vCard:Orgname>Auckland Bioengineering Institute</vCard:Orgname>
<vCard:Orgunit>The University of Auckland</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="">
<dcterms:created rdf:resource="rdf:#0aa62278-0265-4231-9113-c5f20670dce4"/>
<dc:creator rdf:resource="rdf:#a7988c5d-8599-4518-87fa-7a1be4964ec2"/>
</rdf:Description>
</rdf:RDF>
</model>
