Location: Kyrylov, Severyanova, Vieira, 2005 @ 03ca86f8fd33 / kyrylov_severyanova_vieira_2005.cellml

Author:
Hanne <Hanne@hanne-nielsens-macbook.local>
Date:
2010-01-28 09:50:30+13:00
Desc:
Added cmeta:ids to CellML and added session file
Permanent Source URI:
https://models.cellml.org/workspace/kyrylov_severyanova_vieira_2005/rawfile/03ca86f8fd33bb8b633566d7be8d4ed975f313af/kyrylov_severyanova_vieira_2005.cellml

<?xml version="1.0"?>
<!--  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:  
  
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<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>
Modeling robust oscillatory behavior of the hypothalamic-pituitary-adrenal axis, Vadim Kyrylov, Liudmila A. Severyanova, and Amandio Vieira, 2005, <emphasis>IEEE Transactions on Biomedical Engineering</emphasis>, 52, 1977-1983.   <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> 




  
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                    </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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless"> 0.0 </cn>
            </apply>
          </piece>
        </piecewise>
      </apply>

      <apply>
        <eq/> 
        <ci> r2 </ci>   
        <piecewise>
          <piece>
            <apply>
              <minus/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <exp/>
                <apply>
                  <divide/>
                  <apply>
                    <times/>
                    <ci> S2 </ci>
                    <apply>
                      <power/>
                      <ci> y2 </ci>
                      <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless"> 0.0 </cn>
              </apply>
            </apply>
          </piece>
          <otherwise>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless"> 1.0 </cn>
          </otherwise>
        </piecewise>
      </apply>            
    </math>
  </component>
  
  <component cmeta:id="y3" name="y3">
      
    <variable cmeta:id="y3_y3" initial_value="0.95" 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 initial_value="0.010" name="S3" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless"> 0.0 </cn>
            </apply>
          </piece>
        </piecewise>
      </apply>

      <apply>
        <eq/> 
        <ci> r3 </ci>   
        <piecewise>
          <piece>
            <apply>
              <minus/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <exp/>
                <apply>
                  <divide/>
                  <apply>
                    <times/>
                    <ci> S3 </ci>
                    <apply>
                      <power/>
                      <ci> y3 </ci>
                      <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless"> 0.0 </cn>
              </apply>
            </apply>
          </piece>
          <otherwise>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless"> 1.0 </cn>
          </otherwise>
        </piecewise>
      </apply>        
    </math>
  </component>

  <component cmeta:id="y4" name="y4">
      
    <variable cmeta:id="y4_y4" initial_value="0.65" 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 initial_value="0.010" name="S4" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless"> 0.0 </cn>
            </apply>
          </piece>
        </piecewise>
      </apply>

      <apply>
        <eq/> 
        <ci> r4 </ci>   
        <piecewise>
          <piece>
            <apply>
              <minus/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <exp/>
                <apply>
                  <divide/>
                  <apply>
                    <times/>
                    <ci> S4 </ci>
                    <apply>
                      <power/>
                      <ci> y4 </ci>
                      <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" 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 xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless"> 0.0 </cn>
              </apply>
            </apply>
          </piece>
          <otherwise>
            <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless"> 1.0 </cn>
          </otherwise>
        </piecewise>
      </apply>        
    </math>
  </component>

  <component name="model_parameters"> 
    <variable initial_value="-0.00843" name="a00" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="-0.440" name="a02" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="0.082" name="a10" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="-0.0040" name="a11" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="-0.0668" name="a12" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="0.0" name="a20" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="0.0310" name="a21" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="-0.0957" name="a22" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="0.0576" name="a23" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="3.25E-4" name="a24" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="0.00869" name="a32" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="-0.00857" name="a33" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="1.39E-4" name="a42" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="-1.43E-4" name="a44" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="0.443" name="c0" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="0.0" name="e0" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="0.0" name="e1" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="0.0" name="e2" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="0.50" name="epsilon" public_interface="out" units="dimensionless"/>
  </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"/>
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        Kyrylov et al's 2005 mathematical model of oscillatory behaviour of the hypothalamic-pituitary-adrenal axis.
      </title></rdf:Description><rdf:Description rdf:about="rdf:#6f70947a-2cea-442a-bdc7-1877f985b19b"><rdf:value xml:lang="en">c.lloyd@auckland.ac.nz</rdf:value><rdf:type><rdf:Description rdf:about="http://imc.org/vCard/3.0#internet"/></rdf:type></rdf:Description><rdf:Description rdf:about="/y4"><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">CBG-bound cortisol</alternative><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">y4</title></rdf:Description><rdf:Description rdf:about="/y3"><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">albumin-bound cortisol</alternative><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">y3</title></rdf:Description><rdf:Description rdf:nodeID="n2"><boundIntervals xmlns="http://www.cellml.org/metadata/simulation/1.0#"><rdf:Description rdf:nodeID="n3"/></boundIntervals></rdf:Description><rdf:Description rdf:about="rdf:#52328131-a68d-42d1-b7b5-faa5e2a53fc3"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">IEEE Transactions on Biomedical Engineering</title></rdf:Description><rdf:Description rdf:nodeID="n3"><rdf:first><rdf:Description rdf:nodeID="n1"/></rdf:first><rdf:rest><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/></rdf:rest></rdf:Description><rdf:Description rdf:about="rdf:#4fcf1924-7987-409a-aa2d-a046e2512720"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#632de3c2-4cec-4702-b755-98e9c9450fe2"/></N><rdf:type><rdf:Description rdf:about="http://www.cellml.org/bqs/1.0#Person"/></rdf:type></rdf:Description><rdf:Description rdf:about="rdf:#c110f01e-3453-48fe-92d1-c20e7e005150"><subject xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:about="rdf:#ae459f0c-9ee3-471d-a5d1-1fd22bf5e70b"/></subject></rdf:Description><rdf:Description rdf:about="rdf:#1c65ddcf-ea9e-4c7b-8e52-5500eb2db2bf"><Orgunit xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">The Bioengineering Institute</Orgunit><Orgname xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">The University of Auckland</Orgname></rdf:Description><rdf:Description rdf:about="rdf:#b27724a7-f898-44c2-8d20-d5c2fcf76043"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#2569a5cd-ef52-4d96-8269-c2bf6bf9ab63"/></N><rdf:type><rdf:Description rdf:about="http://www.cellml.org/bqs/1.0#Person"/></rdf:type></rdf:Description><rdf:Description rdf:about="rdf:#c1d6204d-5fe7-4ed0-8aee-720c58192cf2"><rdf:value xml:lang="en">This version of the HPA axis model runs in PCEnv to recreate the results published in the paper.</rdf:value><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:about="rdf:#6f6bf0cd-1d85-42f4-85dd-f5ccbdf0cc75"/></creator></rdf:Description><rdf:Description rdf:about="rdf:#075e657b-1e64-4650-b701-19347fdf2123"><W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en">2005-12-00 00:00</W3CDTF></rdf:Description></rdf:RDF></model>