Location: Kyrylov, Severyanova, Vieira, 2005 @ 0847e01840ff / kyrylov_severyanova_vieira_2005.cellml

Author:
pmr2.import <nobody@models.cellml.org>
Date:
2007-07-12 01:12:40+12:00
Desc:
committing version01 of kyrylov_severyanova_vieira_2005
Permanent Source URI:
https://models.cellml.org/workspace/kyrylov_severyanova_vieira_2005/rawfile/0847e01840ff8f7bb711cbe0f11b4bb7ba8578c4/kyrylov_severyanova_vieira_2005.cellml

<?xml version='1.0' encoding='utf-8'?>
<!--  FILE :  kyrylov_model_2005.xml

CREATED :  11th July 2007

LAST MODIFIED : 11th July 2007

AUTHOR :  Catherine Lloyd
          Bioengineering Institute
          The University of Auckland
          
MODEL STATUS :  This model conforms to the CellML 1.1 Specification.

DESCRIPTION :  This file contains a CellML description of Kyrylov et al's 2005 mathematical model of oscillatory behaviour of the hypothalamic-pituitary-adrenal axis.

CHANGES:  
  
--><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="kyrylov_severyanova_vieira_model_2005_version01" name="kyrylov_severyanova_vieira_model_2005_version01">

<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>Modeling robust oscillatory behavior of the hypothalamic-pituitary-adrenal axis</title>
  <author>
    <firstname>Catherine</firstname>
          <surname>Lloyd</surname>
    <affiliation>
      <shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
    </affiliation>
  </author>
</articleinfo>
  <sect1 id="sec_structure">
  <title>Model Structure</title>

<para>
The hypothalamus-pituitary-adrenal (HPA) axis forms part of the endocrine system and it plays an essential role in the coordination of physiological processes in mammals.  As its name suggests it comprises three glands; the hypothalamus, anterior pituitary and adrenal cortex.  These glands function together by synthesising and secreting, or sensing and responding to, hormones such as corticotropin-releasing hormone (CRH), corticotropin (ACTH), and cortisol.  Typically CRH is produced and secreted by the hypothalamus, stimulating the synthesis and secretion of ACTH by the anterior pituitary, in turn activating the adrenal cortex to produce and release cortisol.  Cortisol has a negative feedback effect on CRH and ACTH production by the hypothalamus and anterior pituitary respectively (see figure below).  The free cortisol in the plasma is bound by two proteins; corticosteroid-binding globulin (CBG) and albumin. 
</para>

<para>
The hypothalamus effectively acts as an interface between the central nervous system (CNS) and the endocrine system.  CNS activity affects the diurnal and circadian patterns of the HPA axis, and under conditions of stress the CNS increases its stimulation of the hypothalamus leading to a higher concentration of CRH and subsequently, significantly increased production of cortisol.
</para>

<para>
In the paper described here, Kyrylov <emphasis>et al.</emphasis> present a mathematical model of the HPA axis.  Five system state variables were used to represent the circulatory concentrations of CRH, ACTH, free cortisol, CBG-bound cortisol and albumin-bound cortisol.  Their model is based on the mathematical model published by Liu <emphasis>et al.</emphasis> in 1999 (which has also been described in CellML and can be found in the model repository), and further builds on this model by stabilising it and making it more robust to perturbations in certain parameter values.  In addition, this new version of the model provides circadian rhythms, stress responses, and the ability to modulate gland size parameters, while retaining simplicity, and physiological relevance in terms of the hormone concentrations. 
</para>

<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>model diagram</title>
    </objectinfo>
    <imagedata fileref="kyrylov_2005.png"/>
  </imageobject>
</mediaobject>
<caption>Schematic diagram of the hypothalamus-pituitary-adrenal (HPA) axis.  Stimulatory and inhibitory paths are indicated by the arrows and + or - signs respectively.  CRH represents corticotropin-releasing hormone, ACTH is corticotropin, and CBG represents corticosteroid-binding globulin.</caption>
</informalfigure>

<para>
The complete original paper reference is cited below:
</para>

<para>
<ulink url="http://ieeexplore.ieee.org/search/srchabstract.jsp?arnumber=1542449&amp;isnumber=32944&amp;punumber=10&amp;k2dockey=1542449@ieeejrns&amp;query=%28%28kyrylov%29%3Cin%3Emetadata%29&amp;pos=0">Modeling robust oscillatory behavior of the hypothalamic-pituitary-adrenal axis</ulink>, Vadim Kyrylov, Liudmila A. Severyanova, and Amandio Vieira, 2005, <ulink url="http://www.ieee.org/portal/site/mainsite/menuitem.818c0c39e85ef176fb2275875bac26c8/index.jsp?&amp;pName=corp_level1&amp;path=pubs/transactions&amp;file=tbe.xml&amp;xsl=generic.xsl">
            <emphasis>IEEE Transactions on Biomedical Engineering</emphasis>
          </ulink>, 52, 1977-1983.  (A <ulink url="http://ieeexplore.ieee.org/iel5/10/32944/01542449.pdf">PDF</ulink> version of the article is available to journal subscribers on the <emphasis>IEEE Transactions on Biomedical Engineering</emphasis> website.)  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&amp;cmd=Retrieve&amp;dopt=AbstractPlus&amp;list_uids=16366221&amp;query_hl=1&amp;itool=pubmed_docsum">PubMed ID: 16366221</ulink>
</para>

</sect1>
</article>
</documentation> 


<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#">
    <!--
      The following RDF block contains metadata that applies to this document
      as a whole, as indicated by the empty about attribute on the 
      <rdf:Description> element.
    -->
    <rdf:Description rdf:about="">
      <!--
        The Model Builder Metadata.  The Dublin Core "creator" element is used  
        to indicate the person who translated the model into CellML.
      -->
      <dc:creator rdf:parseType="Resource">
        <vCard:N rdf:parseType="Resource">
          <vCard:Family>Lloyd</vCard:Family>
          <vCard:Given>Catherine</vCard:Given>
          <vCard:Other>May</vCard:Other>
        </vCard:N>
        <vCard:EMAIL rdf:parseType="Resource">
          <rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
          <rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
        </vCard:EMAIL>
        <vCard:ORG rdf:parseType="Resource">
          <vCard:Orgname>The University of Auckland</vCard:Orgname>
          <vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
        </vCard:ORG>
      </dc:creator>
      
      <!--
        The Creation Date metadata. This is the date on which the model
        was translated into CellML.
      -->
      <dcterms:created rdf:parseType="Resource">
        <dcterms:W3CDTF>2007-07-11</dcterms:W3CDTF>
      </dcterms:created>
      
      <!--
        The Modification History metadata. This lists the changes that have been
        made to the document, who made the changes, and when they were made.
      -->
      
      <!-- The Publisher metadata. -->
      <dc:publisher>
        The University of Auckland, Bioengineering Institute
      </dc:publisher>
    </rdf:Description>
    
    <!--
      The following metadata refers to the model itself, as indicated by the
      reference to the ID "kyrylov_model_2005", which is declared   
    on the <model> element.
    -->
    <rdf:Description rdf:about="#kyrylov_model_2005">
      <!-- A human readable name for the model. -->
      <dc:title>
        Kyrylov et al's 2005 mathematical model of oscillatory behaviour of the hypothalamic-pituitary-adrenal axis.
      </dc:title>
      
      <!-- A comment regarding the model. -->
      <cmeta:comment rdf:parseType="Resource">
        <rdf:value>
          This is a CellML description of Kyrylov et al's 2005 mathematical model of oscillatory behaviour of the hypothalamic-pituitary-adrenal axis.
        </rdf:value>
        <!-- The creator of the comment. -->
        <dc:creator rdf:parseType="Resource">
          <vCard:FN>Catherine Lloyd</vCard:FN>
        </dc:creator>
      </cmeta:comment>
      
      <!--  Keyword(s) -->
      <bqs:reference rdf:parseType="Resource">
        <dc:subject rdf:parseType="Resource">
          <bqs:subject_type>keyword</bqs:subject_type>
          <rdf:value>
            <rdf:Bag>
              <rdf:li>HPA axis</rdf:li>
              <rdf:li>cortisol</rdf:li>
              <rdf:li>hypothalamus</rdf:li>
              <rdf:li>adrenal cortex</rdf:li>
              <rdf:li>anterior pituitary</rdf:li>
            </rdf:Bag>
          </rdf:value>
        </dc:subject>
      </bqs:reference>
      
      <!-- 
        The CellML Metadata Specification recommends that bibliographic metadata
        is used to provide information about the original model reference.  The 
        "identifier" attribute on the "BibliographicReference" class provides an
        elegant way to identify a cited reference using a database identifier   
        such as Pubmed.  All associated data such as author, journal title,     
        date, etc can be looked up on the database.
      -->
      <bqs:reference rdf:parseType="Resource">
        <bqs:Pubmed_id>16366221</bqs:Pubmed_id>
        <bqs:JournalArticle rdf:parseType="Resource">
          <dc:creator>
            <rdf:Seq>
              <rdf:li rdf:parseType="Resource">
                <bqs:Person rdf:parseType="Resource">
                  <vCard:N rdf:parseType="Resource">
                    <vCard:Family>Kyrylov</vCard:Family>
                    <vCard:Given>Vadim</vCard:Given>
                  </vCard:N>
                </bqs:Person>
              </rdf:li>
              <rdf:li rdf:parseType="Resource">
                <bqs:Person rdf:parseType="Resource">
                  <vCard:N rdf:parseType="Resource">
                    <vCard:Family>Severyanova</vCard:Family>
                    <vCard:Given>Liudmila</vCard:Given>
                    <vCard:Other>A</vCard:Other>
                  </vCard:N>
                </bqs:Person>
              </rdf:li>
              <rdf:li rdf:parseType="Resource">
                <bqs:Person rdf:parseType="Resource">
                  <vCard:N rdf:parseType="Resource">
                    <vCard:Family>Vieira</vCard:Family>
                    <vCard:Given>Amandio</vCard:Given>
                  </vCard:N>
                </bqs:Person>
              </rdf:li>
            </rdf:Seq>
          </dc:creator>
          <dc:title>
            Modeling robust oscillatory behavior of the hypothalamic-pituitary-adrenal axis
          </dc:title>
          <dcterms:issued rdf:parseType="Resource">
            <dcterms:W3CDTF>2005-12</dcterms:W3CDTF>
          </dcterms:issued>
          <bqs:Journal rdf:parseType="Resource">
            <dc:title>
              IEEE Transactions on Biomedical Engineering
            </dc:title>
          </bqs:Journal>
          <bqs:volume>52</bqs:volume>
          <bqs:first_page>1977</bqs:first_page>
          <bqs:last_page>1983</bqs:last_page>
        </bqs:JournalArticle>
      </bqs:reference>
    </rdf:Description>
  </rdf:RDF>

  
  <units name="minute">
    <unit multiplier="60.0" units="second"/>
  </units>

  <units name="microg_l">
    <unit prefix="micro" units="gram"/>
    <unit units="litre" exponent="-1"/>
  </units>

  <units name="microg_l_min">
    <unit units="microg_l"/>
    <unit units="minute" exponent="-1"/>
  </units>

  <units name="first_order_rate_constant">
    <unit units="minute" exponent="-1"/>
  </units>
  
  
  <component name="environment">
    <variable name="time" public_interface="out" units="minute"/>
  </component>
  
  <component name="y0" cmeta:id="y0">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
      <rdf:Description rdf:about="y0">
        <dc:title>y0</dc:title>
        <dcterms:alternative>CRH</dcterms:alternative>
        <dcterms:alternative>corticotropin-releasing hormone</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF>  
    <variable name="y0" public_interface="out" units="microg_l"/>
    
    <variable name="g0" units="microg_l_min"/>
    <variable name="r0" units="microg_l_min"/>
    <variable name="h0" units="microg_l_min"/>
    <variable name="S0" initial_value="0.010" units="dimensionless"/>
    
    <variable name="y2" public_interface="in" units="microg_l"/>
    <variable name="a00" public_interface="in" units="first_order_rate_constant"/>
    <variable name="a02" public_interface="in" units="first_order_rate_constant"/>
    <variable name="c0" public_interface="in" units="first_order_rate_constant"/>
    <variable name="e0" public_interface="in" units="first_order_rate_constant"/>
    <variable name="epsilon" public_interface="in" units="dimensionless"/>
    <variable name="time" public_interface="in" units="minute"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply><eq/> 
        <apply><diff/> 
          <bvar><ci>time</ci></bvar> 
          <ci> y0 </ci> 
        </apply>
        <apply><plus/>
          <ci> g0 </ci>
          <ci> c0 </ci>
          <ci> e0 </ci>
        </apply>
      </apply>

      <apply><eq/> 
        <ci> g0 </ci> 
        <apply><times/>
          <ci> h0 </ci>
          <ci> r0 </ci>
        </apply>
      </apply>
          
      <apply><eq/> 
        <ci> h0 </ci>   
        <piecewise>
          <piece>
            <apply><divide/>
              <apply><plus/>
                <apply><times/>
                  <ci> a00 </ci>
                  <ci> y0 </ci>
                </apply>
                <apply><times/>
                  <ci> a02 </ci>
                  <ci> y2 </ci>
                </apply>
              </apply>
              <apply><plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply><times/>
                  <apply><divide/>
                    <apply><plus/>
                      <apply><times/>
                        <ci> a00 </ci>
                        <ci> y0 </ci>
                      </apply>
                      <apply><times/>
                        <ci> a02 </ci>
                        <ci> y2 </ci>
                      </apply>
                    </apply>
                    <ci> S0 </ci>
                  </apply>
                  <apply><minus/>
                    <cn cellml:units="dimensionless"> 1.0 </cn>
                    <apply><exp/>
                      <apply><minus/>
                        <apply><divide/>
                          <apply><plus/>
                            <apply><times/>
                              <ci> a00 </ci>
                              <ci> y0 </ci>
                            </apply>
                            <apply><times/>
                              <ci> a02 </ci>
                              <ci> y2 </ci>
                            </apply>
                          </apply>
                          <ci> S0 </ci>
                        </apply>
                      </apply>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
            <apply><gt/>
              <apply><plus/>
                <apply><times/>
                  <ci> a00 </ci>
                  <ci> y0 </ci>
                </apply>
                <apply><times/>
                  <ci> a02 </ci>
                  <ci> y2 </ci>
                </apply>
              </apply>
              <cn cellml:units="dimensionless"> 0.0 </cn>
            </apply>
          </piece>
          <piece>
            <apply><plus/>
              <apply><times/>
                <ci> a00 </ci>
                <ci> y0 </ci>
              </apply>
              <apply><times/>
                <ci> a02 </ci>
                <ci> y2 </ci>
              </apply>
            </apply>
            <apply><leq/>
              <apply><plus/>
                <apply><times/>
                  <ci> a00 </ci>
                  <ci> y0 </ci>
                </apply>
                <apply><times/>
                  <ci> a02 </ci>
                  <ci> y2 </ci>
                </apply>
              </apply>
              <cn cellml:units="dimensionless"> 0.0 </cn>
            </apply>
          </piece>
        </piecewise>
      </apply>

      <apply><eq/> 
        <ci> r0 </ci>   
        <piecewise>
          <piece>
            <apply><minus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply><exp/>
                <apply><divide/>
                  <apply><times/>
                    <ci> S0 </ci>
                    <apply><power/>
                      <ci> y0 </ci>
                      <cn cellml:units="dimensionless"> 2.0 </cn>
                    </apply>
                  </apply>
                  <apply><times/>
                    <apply><plus/>
                      <apply><times/>
                        <ci> a00 </ci>
                        <ci> y0 </ci>
                      </apply>
                      <apply><times/>
                        <ci> a02 </ci>
                        <ci> y2 </ci>
                      </apply>
                    </apply>
                    <apply><power/>
                      <apply><minus/>
                        <ci> epsilon </ci>
                        <ci> y0 </ci>
                      </apply>
                      <cn cellml:units="dimensionless"> 2.0 </cn>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
            <apply><and/>
              <apply><lt/>
                <ci> y0 </ci>
                <ci> epsilon </ci>
              </apply>
              <apply><lt/>
                <apply><plus/>
                  <apply><times/>
                    <ci> a00 </ci>
                    <ci> y0 </ci>
                  </apply>
                  <apply><times/>
                    <ci> a02 </ci>
                    <ci> y2 </ci>
                  </apply>
                </apply>
                <cn cellml:units="dimensionless"> 0.0 </cn>
              </apply>
            </apply>
          </piece>
          <otherwise>
            <cn cellml:units="dimensionless"> 1.0 </cn>
          </otherwise>
        </piecewise>
      </apply>        
    </math>
  </component>

  <component name="y1" cmeta:id="y1">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
      <rdf:Description rdf:about="y1">
        <dc:title>y1</dc:title>
        <dcterms:alternative>ACTH</dcterms:alternative>
        <dcterms:alternative>corticotropin</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF>  
    <variable name="y1" public_interface="out" units="microg_l"/>
    
    <variable name="g1" units="microg_l_min"/>
    <variable name="r1" units="microg_l_min"/>
    <variable name="h1" units="microg_l_min"/>
    <variable name="S1" initial_value="0.010" units="dimensionless"/>
    
    <variable name="y0" public_interface="in" units="microg_l"/>
    <variable name="a10" public_interface="in" units="first_order_rate_constant"/>
    <variable name="y2" public_interface="in" units="microg_l"/>
    <variable name="a12" public_interface="in" units="first_order_rate_constant"/>
    <variable name="a11" public_interface="in" units="first_order_rate_constant"/>
    <variable name="e1" public_interface="in" units="first_order_rate_constant"/>
    <variable name="epsilon" public_interface="in" units="dimensionless"/>
    <variable name="time" public_interface="in" units="minute"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply><eq/> 
        <apply><diff/> 
          <bvar><ci>time</ci></bvar> 
          <ci> y1 </ci> 
        </apply>
        <apply><plus/>
          <ci> g1 </ci>
          <ci> e1 </ci>
        </apply>
      </apply>

      <apply><eq/> 
        <ci> g1 </ci> 
        <apply><times/>
          <ci> h1 </ci>
          <ci> r1 </ci>
        </apply>
      </apply>
          
      <apply><eq/> 
        <ci> h1 </ci>   
        <piecewise>
          <piece>
            <apply><divide/>
              <apply><plus/>
                <apply><times/>
                  <ci> a10 </ci>
                  <ci> y0 </ci>
                </apply>
                <apply><times/>
                  <ci> a11 </ci>
                  <ci> y1 </ci>
                </apply>
                <apply><times/>
                  <ci> a12 </ci>
                  <ci> y2 </ci>
                </apply>
              </apply>
              <apply><plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply><times/>
                  <apply><divide/>
                    <apply><plus/>
                      <apply><times/>
                        <ci> a10 </ci>
                        <ci> y0 </ci>
                      </apply>
                      <apply><times/>
                        <ci> a11 </ci>
                        <ci> y1 </ci>
                      </apply>
                      <apply><times/>
                        <ci> a12 </ci>
                        <ci> y2 </ci>
                      </apply>
                    </apply>
                    <ci> S1 </ci>
                  </apply>
                  <apply><minus/>
                    <cn cellml:units="dimensionless"> 1.0 </cn>
                    <apply><exp/>
                      <apply><minus/>
                        <apply><divide/>
                          <apply><plus/>
                            <apply><times/>
                              <ci> a10 </ci>
                              <ci> y0 </ci>
                            </apply>
                            <apply><times/>
                              <ci> a11 </ci>
                              <ci> y1 </ci>
                            </apply>
                            <apply><times/>
                              <ci> a12 </ci>
                              <ci> y2 </ci>
                            </apply>
                          </apply>
                          <ci> S1 </ci>
                        </apply>
                      </apply>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
            <apply><gt/>
              <apply><plus/>
                <apply><times/>
                  <ci> a10 </ci>
                  <ci> y0 </ci>
                </apply>
                <apply><times/>
                  <ci> a11 </ci>
                  <ci> y1 </ci>
                </apply>
                <apply><times/>
                  <ci> a12 </ci>
                  <ci> y2 </ci>
                </apply>
              </apply>
              <cn cellml:units="dimensionless"> 0.0 </cn>
            </apply>
          </piece>
          <piece>
            <apply><plus/>
              <apply><times/>
                <ci> a10 </ci>
                <ci> y0 </ci>
              </apply>
              <apply><times/>
                <ci> a11 </ci>
                <ci> y1 </ci>
              </apply>
              <apply><times/>
                <ci> a12 </ci>
                <ci> y2 </ci>
              </apply>
            </apply>
            <apply><leq/>
              <apply><plus/>
                <apply><times/>
                  <ci> a10 </ci>
                  <ci> y0 </ci>
                </apply>
                <apply><times/>
                  <ci> a11 </ci>
                  <ci> y1 </ci>
                </apply>
                <apply><times/>
                  <ci> a12 </ci>
                  <ci> y2 </ci>
                </apply>
              </apply>
              <cn cellml:units="dimensionless"> 0.0 </cn>
            </apply>
          </piece>
        </piecewise>
      </apply>

      <apply><eq/> 
        <ci> r1 </ci>   
        <piecewise>
          <piece>
            <apply><minus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply><exp/>
                <apply><divide/>
                  <apply><times/>
                    <ci> S1 </ci>
                    <apply><power/>
                      <ci> y1 </ci>
                      <cn cellml:units="dimensionless"> 2.0 </cn>
                    </apply>
                  </apply>
                  <apply><times/>
                    <apply><plus/>
                      <apply><times/>
                        <ci> a10 </ci>
                        <ci> y0 </ci>
                      </apply>
                      <apply><times/>
                        <ci> a11 </ci>
                        <ci> y1 </ci>
                      </apply>
                      <apply><times/>
                        <ci> a12 </ci>
                        <ci> y2 </ci>
                      </apply>
                    </apply>
                    <apply><power/>
                      <apply><minus/>
                        <ci> epsilon </ci>
                        <ci> y1 </ci>
                      </apply>
                      <cn cellml:units="dimensionless"> 2.0 </cn>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
            <apply><and/>
              <apply><lt/>
                <ci> y1 </ci>
                <ci> epsilon </ci>
              </apply>
              <apply><lt/>
                <apply><plus/>
                  <apply><times/>
                    <ci> a10 </ci>
                    <ci> y0 </ci>
                  </apply>
                  <apply><times/>
                    <ci> a11 </ci>
                    <ci> y1 </ci>
                  </apply>
                  <apply><times/>
                    <ci> a12 </ci>
                    <ci> y2 </ci>
                  </apply>
                </apply>
                <cn cellml:units="dimensionless"> 0.0 </cn>
              </apply>
            </apply>
          </piece>
          <otherwise>
            <cn cellml:units="dimensionless"> 1.0 </cn>
          </otherwise>
        </piecewise>
      </apply>            
    </math>
  </component>

  <component name="y2" cmeta:id="y2">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
      <rdf:Description rdf:about="y2">
        <dc:title>y2</dc:title>
        <dcterms:alternative>free cortisol</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF>  
    <variable name="y2" public_interface="out" units="microg_l"/>
    
    <variable name="g2" units="microg_l_min"/>
    <variable name="r2" units="microg_l_min"/>
    <variable name="h2" units="microg_l_min"/>
    <variable name="S2" initial_value="0.010" units="dimensionless"/>
    
    <variable name="y0" public_interface="in" units="microg_l"/>
    <variable name="y1" public_interface="in" units="microg_l"/>
    <variable name="y3" public_interface="in" units="microg_l"/>
    <variable name="y4" public_interface="in" units="microg_l"/>
    <variable name="a23" public_interface="in" units="first_order_rate_constant"/>
    <variable name="a24" public_interface="in" units="first_order_rate_constant"/>
    <variable name="a20" public_interface="in" units="first_order_rate_constant"/>
    <variable name="a21" public_interface="in" units="first_order_rate_constant"/>
    <variable name="a22" public_interface="in" units="first_order_rate_constant"/>
    <variable name="e2" public_interface="in" units="first_order_rate_constant"/>
    <variable name="epsilon" public_interface="in" units="dimensionless"/>
    <variable name="time" public_interface="in" units="minute"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply><eq/> 
        <apply><diff/> 
          <bvar><ci>time</ci></bvar> 
          <ci> y2 </ci> 
        </apply>
        <apply><plus/>
          <ci> g2 </ci>
          <ci> e2 </ci>
        </apply>
      </apply>

      <apply><eq/> 
        <ci> g2 </ci> 
        <apply><times/>
          <ci> h2 </ci>
          <ci> r2 </ci>
        </apply>
      </apply>
          
      <apply><eq/> 
        <ci> h2 </ci>   
        <piecewise>
          <piece>
            <apply><divide/>
              <apply><plus/>
                <apply><times/>
                  <ci> a20 </ci>
                  <ci> y0 </ci>
                </apply>
                <apply><times/>
                  <ci> a21 </ci>
                  <ci> y1 </ci>
                </apply>
                <apply><times/>
                  <ci> a22 </ci>
                  <ci> y2 </ci>
                </apply>
                <apply><times/>
                  <ci> a23 </ci>
                  <ci> y3 </ci>
                </apply>
                <apply><times/>
                  <ci> a24 </ci>
                  <ci> y4 </ci>
                </apply>
              </apply>
              <apply><plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply><times/>
                  <apply><divide/>
                    <apply><plus/>
                      <apply><times/>
                        <ci> a20 </ci>
                        <ci> y0 </ci>
                      </apply>
                      <apply><times/>
                        <ci> a21 </ci>
                        <ci> y1 </ci>
                      </apply>
                      <apply><times/>
                        <ci> a22 </ci>
                        <ci> y2 </ci>
                      </apply>
                      <apply><times/>
                        <ci> a23 </ci>
                        <ci> y3 </ci>
                      </apply>
                      <apply><times/>
                        <ci> a24 </ci>
                        <ci> y4 </ci>
                      </apply>
                    </apply>
                    <ci> S2 </ci>
                  </apply>
                  <apply><minus/>
                    <cn cellml:units="dimensionless"> 1.0 </cn>
                    <apply><exp/>
                      <apply><minus/>
                        <apply><divide/>
                          <apply><plus/>
                            <apply><times/>
                              <ci> a20 </ci>
                              <ci> y0 </ci>
                            </apply>
                            <apply><times/>
                              <ci> a21 </ci>
                              <ci> y1 </ci>
                            </apply>
                            <apply><times/>
                              <ci> a22 </ci>
                              <ci> y2 </ci>
                            </apply>
                            <apply><times/>
                              <ci> a23 </ci>
                              <ci> y3 </ci>
                            </apply>
                            <apply><times/>
                              <ci> a24 </ci>
                              <ci> y4 </ci>
                            </apply>
                          </apply>
                          <ci> S2 </ci>
                        </apply>
                      </apply>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
            <apply><gt/>
              <apply><plus/>
                <apply><times/>
                  <ci> a20 </ci>
                  <ci> y0 </ci>
                </apply>
                <apply><times/>
                  <ci> a21 </ci>
                  <ci> y1 </ci>
                </apply>
                <apply><times/>
                  <ci> a22 </ci>
                  <ci> y2 </ci>
                </apply>
                <apply><times/>
                  <ci> a23 </ci>
                  <ci> y3 </ci>
                </apply>
                <apply><times/>
                  <ci> a24 </ci>
                  <ci> y4 </ci>
                </apply>
              </apply>
              <cn cellml:units="dimensionless"> 0.0 </cn>
            </apply>
          </piece>
          <piece>
            <apply><plus/>
              <apply><times/>
                <ci> a20 </ci>
                <ci> y0 </ci>
              </apply>
              <apply><times/>
                <ci> a21 </ci>
                <ci> y1 </ci>
              </apply>
              <apply><times/>
                <ci> a22 </ci>
                <ci> y2 </ci>
              </apply>
              <apply><times/>
                <ci> a23 </ci>
                <ci> y3 </ci>
              </apply>
              <apply><times/>
                <ci> a24 </ci>
                <ci> y4 </ci>
              </apply>
            </apply>
            <apply><leq/>
              <apply><plus/>
                <apply><times/>
                  <ci> a20 </ci>
                  <ci> y0 </ci>
                </apply>
                <apply><times/>
                  <ci> a21 </ci>
                  <ci> y1 </ci>
                </apply>
                <apply><times/>
                  <ci> a22 </ci>
                  <ci> y2 </ci>
                </apply>
                <apply><times/>
                  <ci> a23 </ci>
                  <ci> y3 </ci>
                </apply>
                <apply><times/>
                  <ci> a24 </ci>
                  <ci> y4 </ci>
                </apply>
              </apply>
              <cn cellml:units="dimensionless"> 0.0 </cn>
            </apply>
          </piece>
        </piecewise>
      </apply>

      <apply><eq/> 
        <ci> r2 </ci>   
        <piecewise>
          <piece>
            <apply><minus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply><exp/>
                <apply><divide/>
                  <apply><times/>
                    <ci> S2 </ci>
                    <apply><power/>
                      <ci> y2 </ci>
                      <cn cellml:units="dimensionless"> 2.0 </cn>
                    </apply>
                  </apply>
                  <apply><times/>
                    <apply><plus/>
                      <apply><times/>
                        <ci> a20 </ci>
                        <ci> y0 </ci>
                      </apply>
                      <apply><times/>
                        <ci> a21 </ci>
                        <ci> y1 </ci>
                      </apply>
                      <apply><times/>
                        <ci> a22 </ci>
                        <ci> y2 </ci>
                      </apply>
                      <apply><times/>
                        <ci> a23 </ci>
                        <ci> y3 </ci>
                      </apply>
                      <apply><times/>
                        <ci> a24 </ci>
                        <ci> y4 </ci>
                      </apply>
                    </apply>
                    <apply><power/>
                      <apply><minus/>
                        <ci> epsilon </ci>
                        <ci> y2 </ci>
                      </apply>
                      <cn cellml:units="dimensionless"> 2.0 </cn>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
            <apply><and/>
              <apply><lt/>
                <ci> y2 </ci>
                <ci> epsilon </ci>
              </apply>
              <apply><lt/>
                <apply><plus/>
                  <apply><times/>
                    <ci> a20 </ci>
                    <ci> y0 </ci>
                  </apply>
                  <apply><times/>
                    <ci> a21 </ci>
                    <ci> y1 </ci>
                  </apply>
                  <apply><times/>
                    <ci> a22 </ci>
                    <ci> y2 </ci>
                  </apply>
                  <apply><times/>
                    <ci> a23 </ci>
                    <ci> y3 </ci>
                  </apply>
                  <apply><times/>
                    <ci> a24 </ci>
                    <ci> y4 </ci>
                  </apply>
                </apply>
                <cn cellml:units="dimensionless"> 0.0 </cn>
              </apply>
            </apply>
          </piece>
          <otherwise>
            <cn cellml:units="dimensionless"> 1.0 </cn>
          </otherwise>
        </piecewise>
      </apply>            
    </math>
  </component>
  
  <component name="y3" cmeta:id="y3">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
      <rdf:Description rdf:about="y3">
        <dc:title>y3</dc:title>
        <dcterms:alternative>albumin-bound cortisol</dcterms:alternative>
      </rdf:Description>
    </rdf:RDF>  
    <variable name="y3" public_interface="out" units="microg_l"/>
    
    <variable name="g3" units="microg_l_min"/>
    <variable name="r3" units="microg_l_min"/>
    <variable name="h3" units="microg_l_min"/>
    <variable name="S3" initial_value="0.010" units="dimensionless"/>
    
    <variable name="y2" public_interface="in" units="microg_l"/>
    <variable name="a32" public_interface="in" units="first_order_rate_constant"/>
    <variable name="a33" public_interface="in" units="first_order_rate_constant"/>
    <variable name="epsilon" public_interface="in" units="dimensionless"/>
    <variable name="time" public_interface="in" units="minute"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply><eq/> 
        <apply><diff/> 
          <bvar><ci>time</ci></bvar> 
          <ci> y3 </ci> 
        </apply>
        <ci> g3 </ci>
      </apply>

      <apply><eq/> 
        <ci> g3 </ci> 
        <apply><times/>
          <ci> h3 </ci>
          <ci> r3 </ci>
        </apply>
      </apply>
          
      <apply><eq/> 
        <ci> h3 </ci>   
        <piecewise>
          <piece>
            <apply><divide/>
              <apply><plus/>
                <apply><times/>
                  <ci> a32 </ci>
                  <ci> y2 </ci>
                </apply>
                <apply><times/>
                  <ci> a33 </ci>
                  <ci> y3 </ci>
                </apply>
              </apply>
              <apply><plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply><times/>
                  <apply><divide/>
                    <apply><plus/>
                      <apply><times/>
                        <ci> a32 </ci>
                        <ci> y2 </ci>
                      </apply>
                      <apply><times/>
                        <ci> a33 </ci>
                        <ci> y3 </ci>
                      </apply>
                    </apply>
                    <ci> S3 </ci>
                  </apply>
                  <apply><minus/>
                    <cn cellml:units="dimensionless"> 1.0 </cn>
                    <apply><exp/>
                      <apply><minus/>
                        <apply><divide/>
                          <apply><plus/>
                            <apply><times/>
                              <ci> a32 </ci>
                              <ci> y2 </ci>
                            </apply>
                            <apply><times/>
                              <ci> a33 </ci>
                              <ci> y3 </ci>
                            </apply>
                          </apply>
                          <ci> S3 </ci>
                        </apply>
                      </apply>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
            <apply><gt/>
              <apply><plus/>
                <apply><times/>
                  <ci> a32 </ci>
                  <ci> y2 </ci>
                </apply>
                <apply><times/>
                  <ci> a33 </ci>
                  <ci> y3 </ci>
                </apply>
              </apply>
              <cn cellml:units="dimensionless"> 0.0 </cn>
            </apply>
          </piece>
          <piece>
            <apply><plus/>
              <apply><times/>
                <ci> a32 </ci>
                <ci> y2 </ci>
              </apply>
              <apply><times/>
                <ci> a33 </ci>
                <ci> y3 </ci>
              </apply>
            </apply>
            <apply><leq/>
              <apply><plus/>
                <apply><times/>
                  <ci> a32 </ci>
                  <ci> y2 </ci>
                </apply>
                <apply><times/>
                  <ci> a33 </ci>
                  <ci> y3 </ci>
                </apply>
              </apply>
              <cn cellml:units="dimensionless"> 0.0 </cn>
            </apply>
          </piece>
        </piecewise>
      </apply>

      <apply><eq/> 
        <ci> r3 </ci>   
        <piecewise>
          <piece>
            <apply><minus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply><exp/>
                <apply><divide/>
                  <apply><times/>
                    <ci> S3 </ci>
                    <apply><power/>
                      <ci> y3 </ci>
                      <cn cellml:units="dimensionless"> 2.0 </cn>
                    </apply>
                  </apply>
                  <apply><times/>
                    <apply><plus/>
                      <apply><times/>
                        <ci> a32 </ci>
                        <ci> y2 </ci>
                      </apply>
                      <apply><times/>
                        <ci> a33 </ci>
                        <ci> y3 </ci>
                      </apply>
                    </apply>
                    <apply><power/>
                      <apply><minus/>
                        <ci> epsilon </ci>
                        <ci> y3 </ci>
                      </apply>
                      <cn cellml:units="dimensionless"> 2.0 </cn>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
            <apply><and/>
              <apply><lt/>
                <ci> y3 </ci>
                <ci> epsilon </ci>
              </apply>
              <apply><lt/>
                <apply><plus/>
                  <apply><times/>
                    <ci> a32 </ci>
                    <ci> y2 </ci>
                  </apply>
                  <apply><times/>
                    <ci> a33 </ci>
                    <ci> y3 </ci>
                  </apply>
                </apply>
                <cn cellml:units="dimensionless"> 0.0 </cn>
              </apply>
            </apply>
          </piece>
          <otherwise>
            <cn cellml:units="dimensionless"> 1.0 </cn>
          </otherwise>
        </piecewise>
      </apply>        
    </math>
  </component>

  <component name="y4" cmeta:id="y4">
    <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
      <rdf:Description rdf:about="y4">
        <dc:title>y4</dc:title>
        <dcterms:alternative>CBG-bound cortisol</dcterms:alternative>
      </rdf:Description>
    </rdf:RDF>  
    <variable name="y4" public_interface="out" units="microg_l"/>
    
    <variable name="g4" units="microg_l_min"/>
    <variable name="r4" units="microg_l_min"/>
    <variable name="h4" units="microg_l_min"/>
    <variable name="S4" initial_value="0.010" units="dimensionless"/>
    
    <variable name="y2" public_interface="in" units="microg_l"/>
    <variable name="a42" public_interface="in" units="first_order_rate_constant"/>
    <variable name="a44" public_interface="in" units="first_order_rate_constant"/>
    <variable name="epsilon" public_interface="in" units="dimensionless"/>
    <variable name="time" public_interface="in" units="minute"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply><eq/> 
        <apply><diff/> 
          <bvar><ci>time</ci></bvar> 
          <ci> y4 </ci> 
        </apply>
        <ci> g4 </ci>
      </apply>

      <apply><eq/> 
        <ci> g4 </ci> 
        <apply><times/>
          <ci> h4 </ci>
          <ci> r4 </ci>
        </apply>
      </apply>
          
      <apply><eq/> 
        <ci> h4 </ci>   
        <piecewise>
          <piece>
            <apply><divide/>
              <apply><plus/>
                <apply><times/>
                  <ci> a42 </ci>
                  <ci> y2 </ci>
                </apply>
                <apply><times/>
                  <ci> a44 </ci>
                  <ci> y4 </ci>
                </apply>
              </apply>
              <apply><plus/>
                <cn cellml:units="dimensionless"> 1.0 </cn>
                <apply><times/>
                  <apply><divide/>
                    <apply><plus/>
                      <apply><times/>
                        <ci> a42 </ci>
                        <ci> y2 </ci>
                      </apply>
                      <apply><times/>
                        <ci> a44 </ci>
                        <ci> y4 </ci>
                      </apply>
                    </apply>
                    <ci> S4 </ci>
                  </apply>
                  <apply><minus/>
                    <cn cellml:units="dimensionless"> 1.0 </cn>
                    <apply><exp/>
                      <apply><minus/>
                        <apply><divide/>
                          <apply><plus/>
                            <apply><times/>
                              <ci> a42 </ci>
                              <ci> y2 </ci>
                            </apply>
                            <apply><times/>
                              <ci> a44 </ci>
                              <ci> y4 </ci>
                            </apply>
                          </apply>
                          <ci> S4 </ci>
                        </apply>
                      </apply>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
            <apply><gt/>
              <apply><plus/>
                <apply><times/>
                  <ci> a42 </ci>
                  <ci> y2 </ci>
                </apply>
                <apply><times/>
                  <ci> a44 </ci>
                  <ci> y4 </ci>
                </apply>
              </apply>
              <cn cellml:units="dimensionless"> 0.0 </cn>
            </apply>
          </piece>
          <piece>
            <apply><plus/>
              <apply><times/>
                <ci> a42 </ci>
                <ci> y2 </ci>
              </apply>
              <apply><times/>
                <ci> a44 </ci>
                <ci> y4 </ci>
              </apply>
            </apply>
            <apply><leq/>
              <apply><plus/>
                <apply><times/>
                  <ci> a42 </ci>
                  <ci> y2 </ci>
                </apply>
                <apply><times/>
                  <ci> a44 </ci>
                  <ci> y4 </ci>
                </apply>
              </apply>
              <cn cellml:units="dimensionless"> 0.0 </cn>
            </apply>
          </piece>
        </piecewise>
      </apply>

      <apply><eq/> 
        <ci> r4 </ci>   
        <piecewise>
          <piece>
            <apply><minus/>
              <cn cellml:units="dimensionless"> 1.0 </cn>
              <apply><exp/>
                <apply><divide/>
                  <apply><times/>
                    <ci> S4 </ci>
                    <apply><power/>
                      <ci> y4 </ci>
                      <cn cellml:units="dimensionless"> 2.0 </cn>
                    </apply>
                  </apply>
                  <apply><times/>
                    <apply><plus/>
                      <apply><times/>
                        <ci> a42 </ci>
                        <ci> y2 </ci>
                      </apply>
                      <apply><times/>
                        <ci> a44 </ci>
                        <ci> y4 </ci>
                      </apply>
                    </apply>
                    <apply><power/>
                      <apply><minus/>
                        <ci> epsilon </ci>
                        <ci> y4 </ci>
                      </apply>
                      <cn cellml:units="dimensionless"> 2.0 </cn>
                    </apply>
                  </apply>
                </apply>
              </apply>
            </apply>
            <apply><and/>
              <apply><lt/>
                <ci> y4 </ci>
                <ci> epsilon </ci>
              </apply>
              <apply><lt/>
                <apply><plus/>
                  <apply><times/>
                    <ci> a42 </ci>
                    <ci> y2 </ci>
                  </apply>
                  <apply><times/>
                    <ci> a44 </ci>
                    <ci> y4 </ci>
                  </apply>
                </apply>
                <cn cellml:units="dimensionless"> 0.0 </cn>
              </apply>
            </apply>
          </piece>
          <otherwise>
            <cn cellml:units="dimensionless"> 1.0 </cn>
          </otherwise>
        </piecewise>
      </apply>        
    </math>
  </component>

  <component name="model_parameters"> 
    <variable name="a00" public_interface="out" initial_value="-0.00843" units="first_order_rate_constant"/>
    <variable name="a02" public_interface="out" initial_value="-0.440" units="first_order_rate_constant"/>
    <variable name="a10" public_interface="out" initial_value="0.082" units="first_order_rate_constant"/>
    <variable name="a11" public_interface="out" initial_value="-0.0040" units="first_order_rate_constant"/>
    <variable name="a12" public_interface="out" initial_value="-0.0668" units="first_order_rate_constant"/>
    <variable name="a20" public_interface="out" initial_value="0.0" units="first_order_rate_constant"/>
    <variable name="a21" public_interface="out" initial_value="0.0310" units="first_order_rate_constant"/>
    <variable name="a22" public_interface="out" initial_value="-0.0957" units="first_order_rate_constant"/>
    <variable name="a23" public_interface="out" initial_value="0.0576" units="first_order_rate_constant"/>
    <variable name="a24" public_interface="out" initial_value="3.25E-4" units="first_order_rate_constant"/>
    <variable name="a32" public_interface="out" initial_value="0.00869" units="first_order_rate_constant"/>
    <variable name="a33" public_interface="out" initial_value="-0.00857" units="first_order_rate_constant"/>
    <variable name="a42" public_interface="out" initial_value="1.39E-4" units="first_order_rate_constant"/>
    <variable name="a44" public_interface="out" initial_value="-1.43E-4" units="first_order_rate_constant"/>
    <variable name="c0" public_interface="out" initial_value="0.443" units="first_order_rate_constant"/>
    <variable name="e0" public_interface="out" initial_value="0.0" units="first_order_rate_constant"/>
    <variable name="e1" public_interface="out" initial_value="0.0" units="first_order_rate_constant"/>
    <variable name="e2" public_interface="out" initial_value="0.0" units="first_order_rate_constant"/>
    <variable name="epsilon" public_interface="out" initial_value="0.50" units="first_order_rate_constant"/>
  </component>
  
  <connection>
    <map_components component_1="y0" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="y1" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>

  <connection>
    <map_components component_1="y2" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="y3" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>

  <connection>
    <map_components component_1="y4" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>
  
  <connection>
    <map_components component_1="y0" component_2="y2"/>
    <map_variables variable_1="y0" variable_2="y0"/>
    <map_variables variable_1="y2" variable_2="y2"/>
  </connection> 

  <connection>
    <map_components component_1="y0" component_2="y1"/>
    <map_variables variable_1="y0" variable_2="y0"/>
  </connection>

  <connection>
    <map_components component_1="y0" component_2="model_parameters"/>
    <map_variables variable_1="a00" variable_2="a00"/>
    <map_variables variable_1="a02" variable_2="a02"/>
    <map_variables variable_1="c0" variable_2="c0"/>
    <map_variables variable_1="e0" variable_2="e0"/>
    <map_variables variable_1="epsilon" variable_2="epsilon"/>
  </connection>

  <connection>
    <map_components component_1="y1" component_2="y2"/>
    <map_variables variable_1="y1" variable_2="y1"/>
    <map_variables variable_1="y2" variable_2="y2"/>
  </connection> 

  <connection>
    <map_components component_1="y1" component_2="model_parameters"/>
    <map_variables variable_1="a10" variable_2="a10"/>
    <map_variables variable_1="a12" variable_2="a12"/>
    <map_variables variable_1="a11" variable_2="a11"/>
    <map_variables variable_1="e1" variable_2="e1"/>
    <map_variables variable_1="epsilon" variable_2="epsilon"/>
  </connection>

  <connection>
    <map_components component_1="y3" component_2="y2"/>
    <map_variables variable_1="y3" variable_2="y3"/>
    <map_variables variable_1="y2" variable_2="y2"/>
  </connection>

  <connection>
    <map_components component_1="y4" component_2="y2"/>
    <map_variables variable_1="y4" variable_2="y4"/>
    <map_variables variable_1="y2" variable_2="y2"/>
  </connection>  

  <connection>
    <map_components component_1="y2" component_2="model_parameters"/>
    <map_variables variable_1="a20" variable_2="a20"/>
    <map_variables variable_1="a22" variable_2="a22"/>
    <map_variables variable_1="a21" variable_2="a21"/>
    <map_variables variable_1="a23" variable_2="a23"/>
    <map_variables variable_1="a24" variable_2="a24"/>
    <map_variables variable_1="e2" variable_2="e2"/>
    <map_variables variable_1="epsilon" variable_2="epsilon"/>
  </connection>

  <connection>
    <map_components component_1="y3" component_2="model_parameters"/>
    <map_variables variable_1="a32" variable_2="a32"/>
    <map_variables variable_1="a33" variable_2="a33"/>
    <map_variables variable_1="epsilon" variable_2="epsilon"/>
  </connection>

  <connection>
    <map_components component_1="y4" component_2="model_parameters"/>
    <map_variables variable_1="a42" variable_2="a42"/>
    <map_variables variable_1="a44" variable_2="a44"/>
    <map_variables variable_1="epsilon" variable_2="epsilon"/>
  </connection>


<rdf:RDF 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:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
  <rdf:Bag rdf:about="rdf:#3220e680-747a-456f-baad-adb42187f19c">
    <rdf:li>HPA axis</rdf:li>
    <rdf:li>cortisol</rdf:li>
    <rdf:li>hypothalamus</rdf:li>
    <rdf:li>adrenal cortex</rdf:li>
    <rdf:li>anterior pituitary</rdf:li>
  </rdf:Bag>
  <rdf:Seq rdf:about="rdf:#c3eb7ef4-132c-42fb-846d-b236e357f6c3">
    <rdf:li rdf:resource="rdf:#0a78b029-57e0-42b7-9eda-acfe91a01a01"/>
    <rdf:li rdf:resource="rdf:#fb99f707-231f-41d7-84a0-fb7f826e1988"/>
    <rdf:li rdf:resource="rdf:#439fa823-48da-4203-952f-87a038f6dec5"/>
  </rdf:Seq>
  <rdf:Description rdf:about="rdf:#1939baf4-ce7a-42ed-842b-10130c08add9">
    <bqs:subject_type>keyword</bqs:subject_type>
    <rdf:value rdf:resource="rdf:#3220e680-747a-456f-baad-adb42187f19c"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#1001d67f-fb21-423a-bad6-061d113e20cf">
    <dc:creator rdf:resource="rdf:#f36baf50-7dbc-4cd4-898c-b2a92233a9e2"/>
    <rdf:value>
          This is a CellML description of Kyrylov et al's 2005 mathematical model of oscillatory behaviour of the hypothalamic-pituitary-adrenal axis.
        </rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#1cc93614-ba6a-4be3-9da7-2545f59eeb8f">
    <bqs:Pubmed_id>16366221</bqs:Pubmed_id>
    <bqs:JournalArticle rdf:resource="rdf:#8ed14ff9-30ef-4573-b15c-9ec974a46d91"/>
  </rdf:Description>
  <rdf:Description rdf:about="">
    <dc:publisher>
        The University of Auckland, Bioengineering Institute
      </dc:publisher>
    <dcterms:created rdf:resource="rdf:#0897aa66-8388-4c29-af7f-7363f15ce9fa"/>
    <dc:creator rdf:resource="rdf:#0e5cd1eb-eb95-474b-b08d-f3bd25206cd6"/>
  </rdf:Description>
  <rdf:Description rdf:about="#kyrylov_model_2005">
    <dc:title>
        Kyrylov et al's 2005 mathematical model of oscillatory behaviour of the hypothalamic-pituitary-adrenal axis.
      </dc:title>
    <cmeta:comment rdf:resource="rdf:#1001d67f-fb21-423a-bad6-061d113e20cf"/>
    <bqs:reference rdf:resource="rdf:#10e2d932-c4c2-432c-8486-94aaea9aeae0"/>
    <bqs:reference rdf:resource="rdf:#1cc93614-ba6a-4be3-9da7-2545f59eeb8f"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#51135672-1173-40b5-b7bb-bf36f18ec89b">
    <vCard:Given>Vadim</vCard:Given>
    <vCard:Family>Kyrylov</vCard:Family>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#e5300184-3c95-43b2-ba97-ab771c574526">
    <dcterms:W3CDTF>2005-12</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#8ed14ff9-30ef-4573-b15c-9ec974a46d91">
    <dc:creator rdf:resource="rdf:#c3eb7ef4-132c-42fb-846d-b236e357f6c3"/>
    <dc:title>
            Modeling robust oscillatory behavior of the hypothalamic-pituitary-adrenal axis
          </dc:title>
    <bqs:volume>52</bqs:volume>
    <bqs:first_page>1977</bqs:first_page>
    <bqs:Journal rdf:resource="rdf:#98f3b603-06de-4894-a04d-9c23b3cb5469"/>
    <dcterms:issued rdf:resource="rdf:#e5300184-3c95-43b2-ba97-ab771c574526"/>
    <bqs:last_page>1983</bqs:last_page>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#6636887e-4f1b-4735-8053-e755bdefdaa0">
    <vCard:Given>Catherine</vCard:Given>
    <vCard:Family>Lloyd</vCard:Family>
    <vCard:Other>May</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#439fa823-48da-4203-952f-87a038f6dec5">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N rdf:resource="rdf:#66a8ad16-6d9d-4837-a346-9310871beb29"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#98f3b603-06de-4894-a04d-9c23b3cb5469">
    <dc:title>
              IEEE Transactions on Biomedical Engineering
            </dc:title>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#10e2d932-c4c2-432c-8486-94aaea9aeae0">
    <dc:subject rdf:resource="rdf:#1939baf4-ce7a-42ed-842b-10130c08add9"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#fb99f707-231f-41d7-84a0-fb7f826e1988">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N rdf:resource="rdf:#599bbab0-262c-4a59-bd09-f2a99b7570b9"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#0897aa66-8388-4c29-af7f-7363f15ce9fa">
    <dcterms:W3CDTF>2007-07-11</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#13a129d5-a433-4ef3-95d3-180df07c259f">
    <rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
    <rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#f36baf50-7dbc-4cd4-898c-b2a92233a9e2">
    <vCard:FN>Catherine Lloyd</vCard:FN>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#0e5cd1eb-eb95-474b-b08d-f3bd25206cd6">
    <vCard:ORG rdf:resource="rdf:#77d5b480-41b5-4e5c-8e71-a81efacb397c"/>
    <vCard:EMAIL rdf:resource="rdf:#13a129d5-a433-4ef3-95d3-180df07c259f"/>
    <vCard:N rdf:resource="rdf:#6636887e-4f1b-4735-8053-e755bdefdaa0"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#0a78b029-57e0-42b7-9eda-acfe91a01a01">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N rdf:resource="rdf:#51135672-1173-40b5-b7bb-bf36f18ec89b"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#599bbab0-262c-4a59-bd09-f2a99b7570b9">
    <vCard:Given>Liudmila</vCard:Given>
    <vCard:Family>Severyanova</vCard:Family>
    <vCard:Other>A</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#77d5b480-41b5-4e5c-8e71-a81efacb397c">
    <vCard:Orgname>The University of Auckland</vCard:Orgname>
    <vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#66a8ad16-6d9d-4837-a346-9310871beb29">
    <vCard:Given>Amandio</vCard:Given>
    <vCard:Family>Vieira</vCard:Family>
  </rdf:Description>
</rdf:RDF>
</model>