Location: Zager, Schlosser, Tran, 2007 @ 248df9f7c507 / zager_schlosser_tran_2007.cellml

Author:
Tommy Yu <tommy.yu@auckland.ac.nz>
Date:
2010-08-26 12:17:41+12:00
Desc:
xml:base fix
Permanent Source URI:
https://models.physiomeproject.org/workspace/zager_schlosser_tran_2007/rawfile/248df9f7c5072e210267eb2b3a09b51606ea364c/zager_schlosser_tran_2007.cellml

<?xml version="1.0" encoding="utf-8"?>
<!--  FILE :  zager_model_2007.xml

CREATED :  2nd July 2007

LAST MODIFIED : 2nd 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 Zager, Schlosser and Tran's 2007 delayed nonlinear PBPK model for genistein dosimetry.

CHANGES:  
  
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#"  cmeta:id="zager_model_2007" name="zager_model_2007">

<documentation xmlns="http://cellml.org/tmp-documentation">

<article>
  <articleinfo>
  <title>A delayed nonlinear PBPK model for genistein dosimetry in rats</title>
  <author>
    <firstname>Catherine</firstname>
          <surname>Lloyd</surname>
    <affiliation>
      <shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
    </affiliation>
  </author>
</articleinfo>
  <section id="sec_status">
    <title>Model Status</title>
    <para>
        This CellML version of the model has been checked in COR and OpenCell and the model runs to 'almost' recreate the published results.  The only difference is the CellML model is missing the time delays.  Although it is possible to express time delays in the CellML language, the software tools PCEnv and COR are currently unable to handle time delays.  The units have been checked and are consistent.  The author of the original model was involved in the process of translating the model into CellML and his help has been invaluable.
          </para>
  </section>
  <sect1 id="sec_structure">
  <title>Model Structure</title>

<para>
Abstract: Genistein is an endocrine-active compound (EAC) found in soy products. It has been linked to beneficial effects such as mammary tumor growth suppression and adverse endocrine-related effects such as reduced birth weight in rats and humans. In its conjugated form, genistein is excreted in the bile, which is a significant factor in its pharmacokinetics. Experimental data suggest that genistein induces a concentration-dependent suppression of biliary excretion. In this article, we describe a physiologically based pharmacokinetic (PBPK) model that focuses on biliary excretion with the goal of accurately simulating the observed suppression. The mathematical model is a system of nonlinear differential equations with state-dependent delay to describe biliary excretion. The model was analyzed to examine local existence and uniqueness of a solution to the equations. Furthermore, unknown parameters were estimated, and the mathematical model was compared against published experimental data.
</para>

<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>model diagram</title>
    </objectinfo>
    <imagedata fileref="zager_2007.png"/>
  </imageobject>
</mediaobject>
<caption>Schematic diagram of the genistein PBPK model.  The upper components represent compartments containing the pure genistein (gen) while the lower components contain genistein that has undergone conjugation in the liver (con).  B - plasma, rp - richly perfused tissues, pp - poorly perfused tissues, l - liver, GI - gastrointestinal tract, ROB - rest of body, Ab - bile-delayed compartment.  The arrows represent genistein transfer as blood flows between the organs and the systemic circulation, and also genistein elimination in the urine (out of Ccon_ROB); these are all linear with the exception of the conversion of pure to conjugated genistein in the liver which follows Michaelis-Menton kinetics.</caption>
</informalfigure>

<para>
A delayed nonlinear PBPK model for genistein dosimetry in rats, Michael G. Zager, Paul M. Schlosser and Hien T. Tran, 2007, <emphasis>Bulletin of Mathematical Biology</emphasis>, 69, 93-117.  <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/17024552">PubMed ID: 17024552</ulink>
</para>

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



  
  
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    <variable name="d_t_Cgen_l" units="hour"/>
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          <ci> H_Ccon_l </ci>
          <ci> Ccon_l </ci>
          <ci> Vl </ci>
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        <apply>
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                  <ci> time </ci>
                  <ci> ct </ci>
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    <variable name="H_Cgen_B" public_interface="out" units="dimensionless"/>
    
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    <variable name="Qt" public_interface="in" units="litre_hour"/>
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    <variable name="G" units="dimensionless"/>
    <variable name="H" units="dimensionless"/>
    <variable name="I" units="dimensionless"/>
    <variable initial_value="0.1" name="epsilon" units="hour"/>
    <variable initial_value="0.25" name="m_rat" units="dimensionless"/>

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                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless"> 60.0 </cn>
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        <ci> I </ci> 
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        <ci> Qt </ci> 
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        </apply>
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    </math> 
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"><rdf:Description rdf:about="#zager_model_2007"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">
        Zager, Schlosser and Tran's 2007 delayed nonlinear PBPK model for genistein dosimetry.
      </title><cmeta:comment><rdf:Description rdf:about="rdf:#b0e35253-b608-4089-94bb-4c05714b0984"/></cmeta:comment><reference xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:about="rdf:#38772a96-6246-4237-8abd-03b6cf2da71d"/></reference><reference xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:about="rdf:#650bf107-c41b-4c1d-9bf4-600d9aed0e69"/></reference><simulation xmlns="http://www.cellml.org/metadata/simulation/1.0#"><rdf:Description rdf:nodeID="n1"/></simulation></rdf:Description><rdf:Description rdf:about="rdf:#737d6301-2936-4336-acf8-4a529166d187"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#dffd8e0d-c7d1-484b-bd8c-600fa8fbb5df"/></N><rdf:type><rdf:Description rdf:about="http://www.cellml.org/bqs/1.0#Person"/></rdf:type></rdf:Description><rdf:Description rdf:about="rdf:#38772a96-6246-4237-8abd-03b6cf2da71d"><subject xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:about="rdf:#79eafc7e-f74a-4b2b-b69e-a74f83c721d8"/></subject></rdf:Description><rdf:Description rdf:about=""><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:about="rdf:#6c6defbf-af67-4ae7-8068-0b2d8de69343"/></creator><cmeta:comment><rdf:Description rdf:about="rdf:#ba88c7b2-a764-430c-881a-c27b763d6c91"/></cmeta:comment><created xmlns="http://purl.org/dc/terms/"><rdf:Description rdf:about="rdf:#68409981-0b15-481f-909e-a39301c602b1"/></created><publisher xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">The University of Auckland, Auckland Bioengineering Institute</publisher><cmeta:modification><rdf:Description rdf:about="rdf:#beb0c910-d86c-404b-88ad-4b2702f6e17b"/></cmeta:modification></rdf:Description><rdf:Description rdf:about="rdf:#dc5b669e-9bfa-4c47-871a-6f5f6467f61a"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#559e0019-cb47-4c69-bc59-914c5674cf08"/></N></rdf:Description><rdf:Description rdf:about="rdf:#ba88c7b2-a764-430c-881a-c27b763d6c91"><rdf:value xml:lang="en">The original model author has worked with us to get the CellML version of his model running in PCEnv to replicate the published results.</rdf:value><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:about="rdf:#e2c681e0-ab84-4b52-b7e5-04a6db02cb10"/></creator></rdf:Description><rdf:Description rdf:about="rdf:#e2c681e0-ab84-4b52-b7e5-04a6db02cb10"><FN xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Catherine Lloyd</FN></rdf:Description><rdf:Description rdf:about="rdf:#534bf4be-85a2-406a-a43c-6eaedff90b4a"><rdf:_3 xml:lang="en">pharmacokinetics</rdf:_3><rdf:_1 xml:lang="en">endocrine</rdf:_1><rdf:_2 xml:lang="en">genistein</rdf:_2><rdf:_4 xml:lang="en">biliary excretion</rdf:_4><rdf:type><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#Bag"/></rdf:type></rdf:Description><rdf:Description rdf:about="#Ccon_ROB"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">Ccon_ROB</title><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">concentration of genistein conjugates in rest-of-body</alternative></rdf:Description><rdf:Description rdf:nodeID="n2"><rdf:rest><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/></rdf:rest><rdf:first><rdf:Description rdf:nodeID="n3"/></rdf:first></rdf:Description><rdf:Description rdf:about="#Cgen_pp"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">Cgen_pp</title><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">concentration of pure genistein in poorly perfused tissues</alternative></rdf:Description><rdf:Description rdf:nodeID="n1"><boundIntervals xmlns="http://www.cellml.org/metadata/simulation/1.0#"><rdf:Description rdf:nodeID="n2"/></boundIntervals></rdf:Description><rdf:Description rdf:about="rdf:#c743caa7-182a-4e53-b508-7f17550be65e"><Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">G</Other><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Zager</Family><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Michael</Given></rdf:Description><rdf:Description rdf:about="rdf:#68409981-0b15-481f-909e-a39301c602b1"><W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en">2007-07-02T00:00:00+00:00</W3CDTF></rdf:Description><rdf:Description rdf:about="#Cgen_B"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">Cgen_B</title><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">concentration of pure genistein in plasma</alternative></rdf:Description><rdf:Description rdf:about="rdf:#eadf1609-cc71-4466-b1d5-5fd558d0b9ca"><Orgname xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">The University of Auckland</Orgname><Orgunit xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Auckland Bioengineering Institute</Orgunit></rdf:Description><rdf:Description rdf:about="rdf:#be67f8a9-91a4-43b6-942b-3ce5ab5929a4"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#c743caa7-182a-4e53-b508-7f17550be65e"/></N><rdf:type><rdf:Description rdf:about="http://www.cellml.org/bqs/1.0#Person"/></rdf:type></rdf:Description><rdf:Description rdf:about="rdf:#056bce3e-c7dd-4585-bbaa-91f85ed61247"><W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en">2007-10-03T13:25:05+13:00</W3CDTF></rdf:Description><rdf:Description rdf:about="rdf:#a681f8fc-89c0-45eb-a4f2-66a60678ad4b"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#74cbce47-4dd7-4bf9-a212-43a8674f9e4b"/></N><rdf:type><rdf:Description rdf:about="http://www.cellml.org/bqs/1.0#Person"/></rdf:type></rdf:Description><rdf:Description rdf:about="rdf:#79eafc7e-f74a-4b2b-b69e-a74f83c721d8"><rdf:value><rdf:Description rdf:about="rdf:#534bf4be-85a2-406a-a43c-6eaedff90b4a"/></rdf:value><subject_type xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">keyword</subject_type></rdf:Description><rdf:Description rdf:about="rdf:#b53a2127-862e-44db-9b54-cfa15e513ffa"><W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en">2007-01</W3CDTF></rdf:Description><rdf:Description rdf:about="#Cgen_rp"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">Cgen_rp</title><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">concentration of pure genistein in richly perfused tissues</alternative></rdf:Description><rdf:Description rdf:about="rdf:#beb0c910-d86c-404b-88ad-4b2702f6e17b"><rdf:value xml:lang="en">The original model author contacted me and gave me an updated equation to calculate &quot;H&quot; (used in the equation to calculate Vinf).  This fixed the units issue (inconsistency) and also fixed the model such that it now recreates the published results.</rdf:value><cmeta:modifier><rdf:Description rdf:about="rdf:#dc5b669e-9bfa-4c47-871a-6f5f6467f61a"/></cmeta:modifier><modified xmlns="http://purl.org/dc/terms/"><rdf:Description rdf:about="rdf:#056bce3e-c7dd-4585-bbaa-91f85ed61247"/></modified></rdf:Description><rdf:Description rdf:about="rdf:#e99737a5-4053-4931-b718-a7a5d8ad461f"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">Bulletin of Mathematical Biology</title></rdf:Description><rdf:Description rdf:about="rdf:#631e9d2e-1867-497d-a186-c6b5b179682b"><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="rdf:#650bf107-c41b-4c1d-9bf4-600d9aed0e69"><Pubmed_id xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">17024552</Pubmed_id><JournalArticle xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:about="rdf:#1e5cac47-7842-42e5-8cd3-eae8a5ded492"/></JournalArticle></rdf:Description><rdf:Description rdf:about="rdf:#1e5cac47-7842-42e5-8cd3-eae8a5ded492"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">A delayed nonlinear PBPK model for genistein dosimetry in rats</title><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:about="rdf:#d0844ee5-1d36-47fe-a8da-cda60a0ab5e5"/></creator><first_page xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">93</first_page><issued xmlns="http://purl.org/dc/terms/"><rdf:Description rdf:about="rdf:#b53a2127-862e-44db-9b54-cfa15e513ffa"/></issued><volume xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">69</volume><last_page xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">117</last_page><Journal xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:about="rdf:#e99737a5-4053-4931-b718-a7a5d8ad461f"/></Journal></rdf:Description><rdf:Description rdf:about="#Ccon_l"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">Ccon_l</title><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">concentration of genistein conjugates in liver</alternative></rdf:Description><rdf:Description rdf:about="#Cgen_l"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">Cgen_l</title><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">concentration of pure genistein in liver</alternative></rdf:Description><rdf:Description rdf:about="rdf:#dffd8e0d-c7d1-484b-bd8c-600fa8fbb5df"><Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">M</Other><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Schlosser</Family><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Paul</Given></rdf:Description><rdf:Description rdf:about="rdf:#74cbce47-4dd7-4bf9-a212-43a8674f9e4b"><Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">T</Other><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Tran</Family><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Hien</Given></rdf:Description><rdf:Description rdf:about="rdf:#3a9b6bc4-d4d0-4969-90c8-8f25057c55d8"><FN xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Catherine Lloyd</FN></rdf:Description><rdf:Description rdf:about="#Cgen_GI"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">Cgen_GI</title><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">concentration of pure genistein in gastrointestinal tract lumen</alternative></rdf:Description><rdf:Description rdf:about="rdf:#559e0019-cb47-4c69-bc59-914c5674cf08"><Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">May</Other><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Lloyd</Family><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Catherine</Given></rdf:Description><rdf:Description rdf:about="rdf:#d0844ee5-1d36-47fe-a8da-cda60a0ab5e5"><rdf:_3><rdf:Description rdf:about="rdf:#a681f8fc-89c0-45eb-a4f2-66a60678ad4b"/></rdf:_3><rdf:_1><rdf:Description rdf:about="rdf:#be67f8a9-91a4-43b6-942b-3ce5ab5929a4"/></rdf:_1><rdf:_2><rdf:Description rdf:about="rdf:#737d6301-2936-4336-acf8-4a529166d187"/></rdf:_2><rdf:type><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#Seq"/></rdf:type></rdf:Description><rdf:Description rdf:about="rdf:#f7b991c6-f4dc-4064-933f-c037a219d513"><Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">May</Other><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Lloyd</Family><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Catherine</Given></rdf:Description><rdf:Description rdf:nodeID="n3"><maximumStepSize xmlns="http://www.cellml.org/metadata/simulation/1.0#" xml:lang="en">0.1</maximumStepSize><endingValue xmlns="http://www.cellml.org/metadata/simulation/1.0#" xml:lang="en">1.1</endingValue></rdf:Description><rdf:Description rdf:about="rdf:#6c6defbf-af67-4ae7-8068-0b2d8de69343"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#f7b991c6-f4dc-4064-933f-c037a219d513"/></N><EMAIL xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#631e9d2e-1867-497d-a186-c6b5b179682b"/></EMAIL><ORG xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#eadf1609-cc71-4466-b1d5-5fd558d0b9ca"/></ORG></rdf:Description><rdf:Description rdf:about="#Acon_b"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">Acon_b</title><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">amount of genistein conjugates in bile-delayed compartment</alternative></rdf:Description><rdf:Description rdf:about="rdf:#b0e35253-b608-4089-94bb-4c05714b0984"><rdf:value xml:lang="en">This is the CellML description of Zager, Schlosser and Tran's 2007 delayed nonlinear PBPK model for genistein dosimetry.</rdf:value><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:about="rdf:#3a9b6bc4-d4d0-4969-90c8-8f25057c55d8"/></creator></rdf:Description></rdf:RDF></model>