Location: Guccione, Mcculloch, Waldman, 1991 @ 02d64dcabbdd / guccione.cellml

Author:
David Nickerson <nickerso@users.sourceforge.net>
Date:
2015-11-09 11:54:02+13:00
Desc:
adding version of the Guccione model updated by Vicky Wang to simplify the math and change parameter values to match some data from a rat trabecula
Permanent Source URI:
https://models.cellml.org/workspace/guccione_mcculloch_waldman_1991/rawfile/02d64dcabbdd24c22e66e0667eda3460c67e75dd/guccione.cellml

<?xml version="1.0" encoding="iso-8859-1"?>

<model
    name="Guccione"
    cmeta:id="Guccione"
    xmlns="http://www.cellml.org/cellml/1.0#"
    xmlns:cellml="http://www.cellml.org/cellml/1.0#"
    xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
  <!-- 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 name="E11" units="strain"  private_interface="out"/>
    <variable name="E22" units="strain"  private_interface="out"/>
    <variable name="E33" units="strain"  private_interface="out"/>
    <variable name="E12" units="strain"  private_interface="out"/>
    <variable name="E13" units="strain"  private_interface="out"/>
    <variable name="E23" units="strain"  private_interface="out"/>
    <variable name="c1" units="strain"  initial_value="0" private_interface="out"/>
    <variable name="c2" units="strain"  initial_value="0" private_interface="out"/>
    <variable name="c3" units="strain"  initial_value="0" private_interface="out"/>
    <variable name="c4" units="strain"  initial_value="0" private_interface="out"/>
    <variable name="c5" units="strain"  initial_value="0" private_interface="out"/>
    
    <!-- Variables we want to make available externally -->
    <variable name="Tdev11" units="stress" public_interface="out" private_interface="in"/>
    <variable name="Tdev22" units="stress" public_interface="out" private_interface="in"/>
    <variable name="Tdev33" units="stress" public_interface="out" private_interface="in"/>
    <variable name="Tdev12" units="stress" public_interface="out" private_interface="in"/>
    <variable name="Tdev13" units="stress" public_interface="out" private_interface="in"/>
    <variable name="Tdev23" units="stress" public_interface="out" private_interface="in"/>

  </component> <!--interface-->

  <component name="equations" cmeta:id="equations">

    <!-- Inputs -->
    <variable name="E11" units="strain"  public_interface="in"/>
    <variable name="E22" units="strain"  public_interface="in"/>
    <variable name="E33" units="strain"  public_interface="in"/>
    <variable name="E12" units="strain"  public_interface="in"/>
    <variable name="E13" units="strain"  public_interface="in"/>
    <variable name="E23" units="strain"  public_interface="in"/>
    <variable name="c1" units="strain"  public_interface="in"/>
    <variable name="c2" units="strain"  public_interface="in"/>
    <variable name="c3" units="strain"  public_interface="in"/>
    <variable name="c4" units="strain"  public_interface="in"/>
    <variable name="c5" units="strain"  public_interface="in"/>
    
    <!-- Outputs computed here -->
    <variable name="Tdev11" units="stress" public_interface="out"/>
    <variable name="Tdev22" units="stress" public_interface="out"/>
    <variable name="Tdev33" units="stress" public_interface="out"/>
    <variable name="Tdev12" units="stress" public_interface="out"/>
    <variable name="Tdev13" units="stress" public_interface="out"/>
    <variable name="Tdev23" units="stress" public_interface="out"/>

    <!-- Temporary variables -->
    <variable name="Q" units="strain"  public_interface="none" private_interface="none"/>

    <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/>
            <cn cellml:units="strain">2</cn>
            <ci>c2</ci>
            <apply><plus/>
              <ci>E11</ci>
              <ci>E22</ci>
              <ci>E33</ci>
            </apply>
          </apply>
          <apply><times/> 
            <ci>c3</ci>
            <apply><power/>
              <ci>E11</ci>
              <cn cellml:units="strain">2</cn>
            </apply>
          </apply>
          <apply><times/>
            <ci>c4</ci>
            <apply><plus/>
              <apply><power/>
                <ci>E33</ci>
                <cn cellml:units="strain">2</cn>
              </apply>
              <apply><power/>
                <ci>E22</ci>
                <cn cellml:units="strain">2</cn>
              </apply>
              <apply><times/>
                <apply><power/>
                  <ci>E23</ci>
                  <cn cellml:units="strain">2</cn>
                </apply>
                <cn cellml:units="strain">2</cn>
              </apply>
            </apply>
          </apply>
          <apply><times/>
            <cn cellml:units="strain">2</cn>
            <ci>c5</ci>
            <apply><plus/>
              <apply><power/>
                <ci>E13</ci>
                <cn cellml:units="strain">2</cn>
              </apply>
              <apply><power/>
                <ci>E12</ci>
                <cn cellml:units="strain">2</cn>
              </apply>
            </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/>
          <cn cellml:units="strain">0.5</cn>
          <ci>c1</ci>
          <apply><exp/>
            <ci>Q</ci>
          </apply>
          <apply><plus/>
            <apply><times/>
              <cn cellml:units="strain">2</cn>
              <ci>c2</ci>
            </apply>
            <apply><times/>
              <cn cellml:units="strain">2</cn>
              <ci>c3</ci>
              <ci>E11</ci>
            </apply>
          </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/>
          <cn cellml:units="strain">0.5</cn>
          <ci>c1</ci>
          <apply><exp/>
            <ci>Q</ci>
          </apply>
          <apply><plus/>
            <apply><times/>
              <cn cellml:units="strain">2</cn>
              <ci>c2</ci>
            </apply>
            <apply><times/>
              <cn cellml:units="strain">2</cn>
              <ci>c4</ci>
              <ci>E22</ci>
            </apply>
          </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/>
          <cn cellml:units="strain">0.5</cn>
          <ci>c1</ci>
          <apply><exp/>
            <ci>Q</ci>
          </apply>
          <apply><plus/>
            <apply><times/>
              <cn cellml:units="strain">2</cn>
              <ci>c2</ci>
            </apply>
            <apply><times/>
              <cn cellml:units="strain">2</cn>
              <ci>c4</ci>
              <ci>E33</ci>
            </apply>
          </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/>
          <cn cellml:units="strain">0.5</cn>
          <ci>c1</ci>
          <apply><exp/>
            <ci>Q</ci>
          </apply>
          <apply><times/>
            <cn cellml:units="strain">2</cn>
            <ci>c5</ci>
            <ci>E12</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/>
          <cn cellml:units="strain">0.5</cn>
          <ci>c1</ci>
          <apply><exp/>
            <ci>Q</ci>
          </apply>
          <apply><times/>
            <cn cellml:units="strain">2</cn>
            <ci>c5</ci>
            <ci>E13</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/>
          <cn cellml:units="strain">0.5</cn>
          <ci>c1</ci>
          <apply><exp/>
            <ci>Q</ci>
          </apply>
          <apply><times/>
            <cn cellml:units="strain">2</cn>
            <ci>c5</ci>
            <ci>E23</ci>
          </apply>
        </apply>
      </apply>
    </math>

  </component><!--membrane-->

  <connection>
    <map_components component_1="interface" component_2="equations"/>
    <map_variables variable_1="E11" variable_2="E11"/>
    <map_variables variable_1="E22" variable_2="E22"/>
    <map_variables variable_1="E33" variable_2="E33"/>
    <map_variables variable_1="E12" variable_2="E12"/>
    <map_variables variable_1="E13" variable_2="E13"/>
    <map_variables variable_1="E23" variable_2="E23"/>
    <map_variables variable_1="Tdev11" variable_2="Tdev11"/>
    <map_variables variable_1="Tdev22" variable_2="Tdev22"/>
    <map_variables variable_1="Tdev33" variable_2="Tdev33"/>
    <map_variables variable_1="Tdev12" variable_2="Tdev12"/>
    <map_variables variable_1="Tdev13" variable_2="Tdev13"/>
    <map_variables variable_1="Tdev23" variable_2="Tdev23"/>
    <map_variables variable_1="c1" variable_2="c1"/>
    <map_variables variable_1="c2" variable_2="c2"/>
    <map_variables variable_1="c3" variable_2="c3"/>
    <map_variables variable_1="c4" variable_2="c4"/>
    <map_variables variable_1="c5" variable_2="c5"/>
  </connection>
  
  <group>
    <relationship_ref relationship="encapsulation"/>
    <component_ref component="interface">
      <component_ref component="equations"/>
    </component_ref>
  </group>
  
  
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
  <rdf:Description rdf:about="">
    <dc:creator rdf:parseType="Resource">
      <vCard:N rdf:parseType="Resource">
        <vCard:Family>Rajgopal</vCard:Family>
        <vCard:Given>Vijayaraghavan</vCard:Given>
      </vCard:N>
      <vCard:ORG rdf:parseType="Resource">
        <vCard:Orgname>The University of Auckland</vCard:Orgname>
        <vCard:Orgunit>Auckland Bioengineering Institute</vCard:Orgunit>
      </vCard:ORG>
    </dc:creator>
    <dcterms:created rdf:parseType="Resource">
        <dcterms:W3CDTF>2003-12-28</dcterms:W3CDTF>
    </dcterms:created>
  </rdf:Description>

  <rdf:Description rdf:about="">
    <bqs:reference rdf:parseType="Resource">
      <dc:subject rdf:parseType="Resource">
        <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>
      </dc:subject>
    </bqs:reference>
  </rdf:Description>
  
</rdf:RDF>

</model>