- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2009-06-17 15:02:19+12:00
- Desc:
- committing version01 of liu_hu_peng_liu_1999
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/liu_hu_peng_liu_1999/rawfile/8b72fdfcd8488da3dbcd622cb8f6e1e754b105cc/liu_hu_peng_liu_1999.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : liu_model_1999.xml
CREATED : 13th July 2007
LAST MODIFIED : 13th 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 Liu et al's 1999 mathematical model for the pulsatile secretion 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="liu_model_1999" name="liu_hu_peng_liu_model_1999_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Mathematical modeling and qualitative analysis of insulin therapies</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>
Many hormones are secreted pulsatilely with periods of about one hour. These rhythms are on a different timescale to circadian rhythms, suggesting they are regulated by distinct mechanisms. Neither does it seem likely these hormone oscillations are completely controlled at the molecular or cellular level. Instead, the authors of the model described here suggest they probably originate from system dynamics. They propose a dynamical model for the secretory system of the hypothalamic-pituitary-adrenal (HPA) axis (see the figure below). Comparison of model simulation results with experimental data demonstrate the mathematical model captures the essence of the hormone dynamics.
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="liu_1999.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of the hormone flow and interactions between the different components of the hypothalamic-pituitary-adrenal (HPA) axis which are described by the mathematical model. CRH represents corticotropin releasing hormone, ACTH represents corticotropin, and CBG is corticosteroid binding globulin. Red arrows represent hormone disposal, while black arrows represent flow between the different glands and plasma. + represents a stimulatory effect while - represents an inhibitory effect.</caption>
</informalfigure>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V0V-3WHKW87-9&_user=140507&_coverDate=02%2F28%2F1999&_rdoc=9&_fmt=summary&_orig=browse&_srch=doc-info(%23toc%235656%231999%23999709995%2398249%23FLP%23display%23Volume)&_cdi=5656&_sort=d&_docanchor=&view=c&_ct=10&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=6946dd0053a249aa4173d761a73a7ab5">A dynamical model for the pulsatile secretion of the hypothalamo-pituitary-adrenal axis</ulink>, Yi-Wei Liu, Zhi-Hong Hu, Jian-Hua Peng, and Bing-Zheng Liu, 1999, <ulink url="http://www.sciencedirect.com/science/journal/08957177">
<emphasis>Mathematical and Computer Modelling</emphasis>
</ulink>, 29, 103-110. (A PDF version of the article is available to journal subscribers on the <emphasis>Mathematical and Computer Modelling</emphasis> website.)
</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>2007-07-13</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 "liu_model_1999", which is declared
on the <model> element.
-->
<rdf:Description rdf:about="#liu_model_1999">
<!-- A human readable name for the model. -->
<dc:title>
Liu et al's 1999 mathematical model for the pulsatile secretion 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 Liu et al's 1999 mathematical model for the pulsatile secretion 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>cortisol</rdf:li>
<rdf:li>endocrine</rdf:li>
<rdf:li>adrenal cortex</rdf:li>
<rdf:li>HPA axis</rdf:li>
<rdf:li>hypothalamus</rdf:li>
<rdf:li>hpa axis</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: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>Liu</vCard:Family>
<vCard:Given>Yi-Wei</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>Hu</vCard:Family>
<vCard:Given>Zhi-Hong</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>Peng</vCard:Family>
<vCard:Given>Jian-Hua</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>Liu</vCard:Family>
<vCard:Given>Bing-Zheng</vCard:Given>
</vCard:N>
</bqs:Person>
</rdf:li>
</rdf:Seq>
</dc:creator>
<dc:title>
A dynamical model for the pulsatile secretion of the hypothalamo-pituitary-adrenal axis
</dc:title>
<dcterms:issued rdf:parseType="Resource">
<dcterms:W3CDTF>1999-02</dcterms:W3CDTF>
</dcterms:issued>
<bqs:Journal rdf:parseType="Resource">
<dc:title>
Mathematical and Computer Modelling
</dc:title>
</bqs:Journal>
<bqs:volume>29</bqs:volume>
<bqs:first_page>103</bqs:first_page>
<bqs:last_page>110</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="first_order_rate_constant">
<unit units="minute" exponent="-1"/>
</units>
<component name="environment">
<variable name="time" public_interface="out" units="minute"/>
</component>
<component name="x1" cmeta:id="x1">
<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="x1">
<dc:title>x1</dc:title>
<dcterms:alternative>CRH</dcterms:alternative>
<dcterms:alternative>corticotropin-releasing hormone</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="x1" public_interface="out" units="microg_l"/>
<variable name="lambda1" public_interface="in" units="first_order_rate_constant"/>
<variable name="x3" public_interface="in" units="microg_l"/>
<variable name="a1" public_interface="in" units="first_order_rate_constant"/>
<variable name="a2" public_interface="in" units="first_order_rate_constant"/>
<variable name="a3" public_interface="in" units="first_order_rate_constant"/>
<variable name="a4" public_interface="in" units="first_order_rate_constant"/>
<variable name="a5" public_interface="in" units="first_order_rate_constant"/>
<variable name="a6" public_interface="in" units="first_order_rate_constant"/>
<variable name="a7" public_interface="in" units="first_order_rate_constant"/>
<variable name="a8" public_interface="in" units="first_order_rate_constant"/>
<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> x1 </ci>
</apply>
<apply><minus/>
<apply><plus/>
<ci> a1 </ci>
<apply><divide/>
<apply><plus/>
<ci> a2 </ci>
<apply><times/>
<ci> a3 </ci>
<ci> x1 </ci>
</apply>
<apply><times/>
<ci> a4 </ci>
<apply><power/>
<ci> x1 </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<apply><plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><times/>
<ci> a5 </ci>
<ci> x1 </ci>
</apply>
<apply><times/>
<ci> a6 </ci>
<apply><power/>
<ci> x1 </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply><times/>
<ci> a7 </ci>
<ci> x3 </ci>
</apply>
<apply><times/>
<ci> a8 </ci>
<apply><power/>
<ci> x3 </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply><times/>
<ci> lambda1 </ci>
<ci> x1 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="x2" cmeta:id="x2">
<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="x2">
<dc:title>x2</dc:title>
<dcterms:alternative>ACTH</dcterms:alternative>
<dcterms:alternative>corticotropin</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="x2" public_interface="out" units="microg_l"/>
<variable name="lambda2" public_interface="in" units="first_order_rate_constant"/>
<variable name="x1" public_interface="in" units="microg_l"/>
<variable name="x3" public_interface="in" units="microg_l"/>
<variable name="a9" public_interface="in" units="first_order_rate_constant"/>
<variable name="a10" public_interface="in" units="first_order_rate_constant"/>
<variable name="a11" public_interface="in" units="first_order_rate_constant"/>
<variable name="a12" public_interface="in" units="first_order_rate_constant"/>
<variable name="a13" public_interface="in" units="first_order_rate_constant"/>
<variable name="a14" public_interface="in" units="first_order_rate_constant"/>
<variable name="a15" public_interface="in" units="first_order_rate_constant"/>
<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> x2 </ci>
</apply>
<apply><minus/>
<apply><divide/>
<apply><plus/>
<ci> a9 </ci>
<apply><times/>
<ci> a10 </ci>
<ci> x1 </ci>
</apply>
<apply><times/>
<ci> a11 </ci>
<apply><power/>
<ci> x1 </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<apply><plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><times/>
<ci> a12 </ci>
<ci> x1 </ci>
</apply>
<apply><times/>
<ci> a13 </ci>
<apply><power/>
<ci> x1 </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply><times/>
<ci> a14 </ci>
<ci> x3 </ci>
</apply>
<apply><times/>
<ci> a15 </ci>
<apply><power/>
<ci> x3 </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply><times/>
<ci> lambda2 </ci>
<ci> x2 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="x3" cmeta:id="x3">
<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="x3">
<dc:title>x3</dc:title>
<dcterms:alternative>free cortisol</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="x3" public_interface="out" units="microg_l"/>
<variable name="lambda3_" public_interface="in" units="first_order_rate_constant"/>
<variable name="x1" public_interface="in" units="microg_l"/>
<variable name="x2" public_interface="in" units="microg_l"/>
<variable name="x4" public_interface="in" units="microg_l"/>
<variable name="x5" public_interface="in" units="microg_l"/>
<variable name="a16" public_interface="in" units="first_order_rate_constant"/>
<variable name="a17" public_interface="in" units="first_order_rate_constant"/>
<variable name="a18" public_interface="in" units="first_order_rate_constant"/>
<variable name="a19" 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="a23" public_interface="in" units="first_order_rate_constant"/>
<variable name="a24" public_interface="in" units="first_order_rate_constant"/>
<variable name="a25" public_interface="in" units="first_order_rate_constant"/>
<variable name="a26" public_interface="in" units="first_order_rate_constant"/>
<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> x3 </ci>
</apply>
<apply><minus/>
<apply><plus/>
<ci> a16 </ci>
<apply><divide/>
<apply><plus/>
<apply><times/>
<ci> a17 </ci>
<ci> x1 </ci>
</apply>
<apply><times/>
<ci> a18 </ci>
<apply><power/>
<ci> x1 </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply><times/>
<ci> a19 </ci>
<ci> x2 </ci>
</apply>
<apply><times/>
<ci> a20 </ci>
<apply><power/>
<ci> x2 </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<apply><plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply><times/>
<ci> a21 </ci>
<ci> x1 </ci>
</apply>
<apply><times/>
<ci> a22 </ci>
<apply><power/>
<ci> x1 </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply><times/>
<ci> a23 </ci>
<ci> x2 </ci>
</apply>
<apply><times/>
<ci> a24 </ci>
<apply><power/>
<ci> x2 </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply><times/>
<ci> a25 </ci>
<ci> x4 </ci>
</apply>
<apply><times/>
<ci> a26 </ci>
<ci> x5 </ci>
</apply>
</apply>
<apply><times/>
<ci> lambda3_ </ci>
<ci> x3 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="x4" cmeta:id="x4">
<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="x4">
<dc:title>x4</dc:title>
<dcterms:alternative>CBG-bound cortisol</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="x4" public_interface="out" units="microg_l"/>
<variable name="lambda4_" public_interface="in" units="first_order_rate_constant"/>
<variable name="x3" public_interface="in" units="microg_l"/>
<variable name="a27" public_interface="in" units="first_order_rate_constant"/>
<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> x4 </ci>
</apply>
<apply><minus/>
<apply><times/>
<ci> a27 </ci>
<ci> x3 </ci>
</apply>
<apply><times/>
<ci> lambda4_ </ci>
<ci> x4 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="x5" cmeta:id="x5">
<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="x5">
<dc:title>x5</dc:title>
<dcterms:alternative>albumin-bound cortisol</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable name="x5" public_interface="out" units="microg_l"/>
<variable name="lambda5_" public_interface="in" units="first_order_rate_constant"/>
<variable name="x3" public_interface="in" units="microg_l"/>
<variable name="a28" public_interface="in" units="first_order_rate_constant"/>
<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> x5 </ci>
</apply>
<apply><minus/>
<apply><times/>
<ci> a28 </ci>
<ci> x3 </ci>
</apply>
<apply><times/>
<ci> lambda5_ </ci>
<ci> x5 </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="model_parameters">
<variable name="a1" public_interface="out" initial_value="0.000017" units="first_order_rate_constant"/>
<variable name="a2" public_interface="out" initial_value="0.0023" units="first_order_rate_constant"/>
<variable name="a3" public_interface="out" initial_value="0.6" units="first_order_rate_constant"/>
<variable name="a4" public_interface="out" initial_value="45.0" units="first_order_rate_constant"/>
<variable name="a5" public_interface="out" initial_value="36.0" units="first_order_rate_constant"/>
<variable name="a6" public_interface="out" initial_value="216.0" units="first_order_rate_constant"/>
<variable name="a7" public_interface="out" initial_value="0.28" units="first_order_rate_constant"/>
<variable name="a8" public_interface="out" initial_value="0.36" units="first_order_rate_constant"/>
<variable name="a9" public_interface="out" initial_value="0.0003" units="first_order_rate_constant"/>
<variable name="a10" public_interface="out" initial_value="0.18" units="first_order_rate_constant"/>
<variable name="a11" public_interface="out" initial_value="150.0" units="first_order_rate_constant"/>
<variable name="a12" public_interface="out" initial_value="18.0" units="first_order_rate_constant"/>
<variable name="a13" public_interface="out" initial_value="460.0" units="first_order_rate_constant"/>
<variable name="a14" public_interface="out" initial_value="0.46" units="first_order_rate_constant"/>
<variable name="a15" public_interface="out" initial_value="0.10" units="first_order_rate_constant"/>
<variable name="a16" public_interface="out" initial_value="0.04" units="first_order_rate_constant"/>
<variable name="a17" public_interface="out" initial_value="150.0" units="first_order_rate_constant"/>
<variable name="a18" public_interface="out" initial_value="3800.0" units="first_order_rate_constant"/>
<variable name="a19" public_interface="out" initial_value="57.0" units="first_order_rate_constant"/>
<variable name="a20" public_interface="out" initial_value="2600.0" units="first_order_rate_constant"/>
<variable name="a21" public_interface="out" initial_value="200.0" units="first_order_rate_constant"/>
<variable name="a22" public_interface="out" initial_value="9400.0" units="first_order_rate_constant"/>
<variable name="a23" public_interface="out" initial_value="10.0" units="first_order_rate_constant"/>
<variable name="a24" public_interface="out" initial_value="320.0" units="first_order_rate_constant"/>
<variable name="a25" public_interface="out" initial_value="0.04" units="first_order_rate_constant"/>
<variable name="a26" public_interface="out" initial_value="0.00097" units="first_order_rate_constant"/>
<variable name="a27" public_interface="out" initial_value="0.57" units="first_order_rate_constant"/>
<variable name="a28" public_interface="out" initial_value="0.0017" units="first_order_rate_constant"/>
<variable name="lambda1" public_interface="out" initial_value="0.059" units="first_order_rate_constant"/>
<variable name="lambda2" public_interface="out" initial_value="0.028" units="first_order_rate_constant"/>
<variable name="lambda3_" public_interface="out" initial_value="0.67" units="first_order_rate_constant"/>
<variable name="lambda4_" public_interface="out" initial_value="0.06" units="first_order_rate_constant"/>
<variable name="lambda5_" public_interface="out" initial_value="0.001" units="first_order_rate_constant"/>
</component>
<connection>
<map_components component_1="x1" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="x2" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="x3" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="x4" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="x5" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="x1" component_2="x3"/>
<map_variables variable_1="x1" variable_2="x1"/>
<map_variables variable_1="x3" variable_2="x3"/>
</connection>
<connection>
<map_components component_1="x1" component_2="x2"/>
<map_variables variable_1="x1" variable_2="x1"/>
</connection>
<connection>
<map_components component_1="x1" component_2="model_parameters"/>
<map_variables variable_1="a1" variable_2="a1"/>
<map_variables variable_1="a2" variable_2="a2"/>
<map_variables variable_1="a3" variable_2="a3"/>
<map_variables variable_1="a4" variable_2="a4"/>
<map_variables variable_1="a5" variable_2="a5"/>
<map_variables variable_1="a6" variable_2="a6"/>
<map_variables variable_1="a7" variable_2="a7"/>
<map_variables variable_1="a8" variable_2="a8"/>
<map_variables variable_1="lambda1" variable_2="lambda1"/>
</connection>
<connection>
<map_components component_1="x2" component_2="x3"/>
<map_variables variable_1="x2" variable_2="x2"/>
<map_variables variable_1="x3" variable_2="x3"/>
</connection>
<connection>
<map_components component_1="x2" component_2="model_parameters"/>
<map_variables variable_1="a9" variable_2="a9"/>
<map_variables variable_1="a10" variable_2="a10"/>
<map_variables variable_1="a11" variable_2="a11"/>
<map_variables variable_1="a12" variable_2="a12"/>
<map_variables variable_1="a13" variable_2="a13"/>
<map_variables variable_1="a14" variable_2="a14"/>
<map_variables variable_1="a15" variable_2="a15"/>
<map_variables variable_1="lambda2" variable_2="lambda2"/>
</connection>
<connection>
<map_components component_1="x4" component_2="x3"/>
<map_variables variable_1="x4" variable_2="x4"/>
<map_variables variable_1="x3" variable_2="x3"/>
</connection>
<connection>
<map_components component_1="x5" component_2="x3"/>
<map_variables variable_1="x5" variable_2="x5"/>
<map_variables variable_1="x3" variable_2="x3"/>
</connection>
<connection>
<map_components component_1="x3" component_2="model_parameters"/>
<map_variables variable_1="a16" variable_2="a16"/>
<map_variables variable_1="a17" variable_2="a17"/>
<map_variables variable_1="a18" variable_2="a18"/>
<map_variables variable_1="a19" variable_2="a19"/>
<map_variables variable_1="a20" variable_2="a20"/>
<map_variables variable_1="a21" variable_2="a21"/>
<map_variables variable_1="a22" variable_2="a22"/>
<map_variables variable_1="a23" variable_2="a23"/>
<map_variables variable_1="a24" variable_2="a24"/>
<map_variables variable_1="a25" variable_2="a25"/>
<map_variables variable_1="a26" variable_2="a26"/>
<map_variables variable_1="lambda3_" variable_2="lambda3_"/>
</connection>
<connection>
<map_components component_1="x4" component_2="model_parameters"/>
<map_variables variable_1="a27" variable_2="a27"/>
<map_variables variable_1="lambda4_" variable_2="lambda4_"/>
</connection>
<connection>
<map_components component_1="x5" component_2="model_parameters"/>
<map_variables variable_1="a28" variable_2="a28"/>
<map_variables variable_1="lambda5_" variable_2="lambda5_"/>
</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:#335c5ce3-7f8b-4c8a-8352-18eec06e0d40">
<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:#a8c4aedd-1935-4541-87aa-2087d146ef1d">
<rdf:li rdf:resource="rdf:#ac4c6fac-d59d-487f-9b57-61a379c30143"/>
<rdf:li rdf:resource="rdf:#e5ac2e0c-41d7-4c7e-aac2-38952283e88f"/>
<rdf:li rdf:resource="rdf:#992d45ad-ac20-4fbe-b414-13f5f6fd0f54"/>
<rdf:li rdf:resource="rdf:#3b8f3c3d-ac87-43fa-87d1-7103f2b60bf2"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#b83f229e-bed6-4197-b785-cc2b14cac841">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="">
<dc:publisher>
The University of Auckland, Bioengineering Institute
</dc:publisher>
<dcterms:created rdf:resource="rdf:#de29f83e-c481-4b30-a4f2-982bbc498213"/>
<dc:creator rdf:resource="rdf:#6508c9ad-0f6c-4b2b-a12c-37de8814d1e0"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f438e448-6599-4ae3-9121-60a0b3e70c64">
<vCard:Given>Bing-Zheng</vCard:Given>
<vCard:Family>Liu</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#cd5cca94-cacf-43a3-a54b-f5f3365aeba6">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value rdf:resource="rdf:#335c5ce3-7f8b-4c8a-8352-18eec06e0d40"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#14e96501-0e28-4598-87fd-efe45f6eacfd">
<vCard:Given>Yi-Wei</vCard:Given>
<vCard:Family>Liu</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#992d45ad-ac20-4fbe-b414-13f5f6fd0f54">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#54b94b21-e7c3-487c-944e-34cfd55b6260"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#830be75c-ae0b-44c1-9449-a678f96e3a3c">
<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:#54b94b21-e7c3-487c-944e-34cfd55b6260">
<vCard:Given>Jian-Hua</vCard:Given>
<vCard:Family>Peng</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ac4c6fac-d59d-487f-9b57-61a379c30143">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#14e96501-0e28-4598-87fd-efe45f6eacfd"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#2529fcf0-9919-4a66-915a-f983223c99f8">
<vCard:Given>Zhi-Hong</vCard:Given>
<vCard:Family>Hu</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e481ed33-251b-4140-907e-3df2c8de13f5">
<dc:subject rdf:resource="rdf:#cd5cca94-cacf-43a3-a54b-f5f3365aeba6"/>
</rdf:Description>
<rdf:Description rdf:about="#liu_model_1999">
<dc:title>
Liu et al's 1999 mathematical model for the pulsatile secretion of the hypothalamic-pituitary-adrenal axis.
</dc:title>
<cmeta:comment rdf:resource="rdf:#84b6dc03-46b0-490c-b4d1-49cee1d718e8"/>
<bqs:reference rdf:resource="rdf:#e481ed33-251b-4140-907e-3df2c8de13f5"/>
<bqs:reference rdf:resource="rdf:#f71e5251-06d3-45e9-98b0-67fd6ae40520"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e5ac2e0c-41d7-4c7e-aac2-38952283e88f">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#2529fcf0-9919-4a66-915a-f983223c99f8"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#60591c01-f510-4524-8564-e5425c703ac1">
<dc:title>
Mathematical and Computer Modelling
</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c06bf733-353b-46b9-971f-c51484557112">
<dcterms:W3CDTF>1999-02</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#84b6dc03-46b0-490c-b4d1-49cee1d718e8">
<dc:creator rdf:resource="rdf:#789647a5-7a91-4e51-a79f-74a8420bd13a"/>
<rdf:value>
This is a CellML description of Liu et al's 1999 mathematical model for the pulsatile secretion of the hypothalamic-pituitary-adrenal axis.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f71e5251-06d3-45e9-98b0-67fd6ae40520">
<bqs:JournalArticle rdf:resource="rdf:#872e30ca-b525-43b2-ad61-7b6de9ec3dca"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#3b8f3c3d-ac87-43fa-87d1-7103f2b60bf2">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#f438e448-6599-4ae3-9121-60a0b3e70c64"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#789647a5-7a91-4e51-a79f-74a8420bd13a">
<vCard:FN>Catherine Lloyd</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6ce84c97-8085-4d48-abd0-a51f08677cdf">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#872e30ca-b525-43b2-ad61-7b6de9ec3dca">
<dc:creator rdf:resource="rdf:#a8c4aedd-1935-4541-87aa-2087d146ef1d"/>
<dc:title>
A dynamical model for the pulsatile secretion of the hypothalamo-pituitary-adrenal axis
</dc:title>
<bqs:volume>29</bqs:volume>
<bqs:first_page>103</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#60591c01-f510-4524-8564-e5425c703ac1"/>
<dcterms:issued rdf:resource="rdf:#c06bf733-353b-46b9-971f-c51484557112"/>
<bqs:last_page>110</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#6508c9ad-0f6c-4b2b-a12c-37de8814d1e0">
<vCard:ORG rdf:resource="rdf:#6ce84c97-8085-4d48-abd0-a51f08677cdf"/>
<vCard:EMAIL rdf:resource="rdf:#830be75c-ae0b-44c1-9449-a678f96e3a3c"/>
<vCard:N rdf:resource="rdf:#b83f229e-bed6-4197-b785-cc2b14cac841"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#de29f83e-c481-4b30-a4f2-982bbc498213">
<dcterms:W3CDTF>2007-07-13</dcterms:W3CDTF>
</rdf:Description>
</rdf:RDF>
</model>
