- Author:
- Hanne <Hanne@hanne-nielsens-macbook.local>
- Date:
- 2009-11-05 12:33:29+13:00
- Desc:
- Added keyword, removed non pub med link
- Permanent Source URI:
- https://models.cellml.org/workspace/lenbury_ruktamatakul_amornsamarnkul_2001/rawfile/fa1a05be28285f23a434495a0b92af666f26bbe1/lenbury_ruktamatakul_amornsamarnkul_2001_a.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : lenbury_model_2001.xml
CREATED : 18th June 2007
LAST MODIFIED : 18th June 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 Lenbury et al.'s 2001 mathematical model of insulin kinetics.
CHANGES:
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<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modelling insulin kinetics in response to oral glucose administration</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
Please note that this particular variant of the model is the basic core model which includes three main variables : plasma insulin concentration (x), glucose concentration (y), and the density of the pancreatic beta cells (z).</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
The secretion of insulin, and its biological effectiveness in reducing blood glucose levels, is mainly dependent on the number and functional efficiency of the pancreatic beta-cells, and also the degree of peripheral insulin resistance. Diabetes can arise from either a deficiency in insulin secretion or from a resistance to insulin. Several mathematical models have been proposed to try and describe the relationships between the plasma concentrations of glucose and insulin. However, these models are often too complex for the available clinical data; which is usually based on glucose alone and is only for a relatively short time period. The current model described here in CellML is based on the published model of Lenbury <emphasis>et al.</emphasis> (2001) and involves just four variables:
</para>
<itemizedlist>
<listitem>
<para>Plasma insulin concentration;</para>
</listitem>
<listitem>
<para>Plasma glucose concentration;</para>
</listitem>
<listitem>
<para>Pancreatic beta-cell density; and</para>
</listitem>
<listitem>
<para>A term to define gastrointestinal glucose absorption.</para>
</listitem>
</itemizedlist>
<para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="lenbury_2001a.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of the pancreatic beta-cells. Glucose is taken up and produced in response to insulin secretion and clearance. Beta-cell formation and loss represent the rates at which beta-cells replicate and die.</caption>
</informalfigure>
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
Modeling insulin kinetics: responses to a single oral glucose administration or ambulatory-fed conditions. Yongwimon Lenbury, Sitipong Ruktamatakul, and Somkid Amornsamarnkul, 2001, <emphasis>Mathematical Biosciences</emphasis>, 59, 15-25. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=11226623&query_hl=1&itool=pubmed_docsum">PubMed ID: 11226623</ulink>
</para>
</sect1>
</article>
</documentation>
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<variable units="dimensionless" name="z_" initial_value="2.0"/>
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<cn cellml:units="dimensionless">1e-7</cn>
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<rdf:li>endocrine</rdf:li>
<rdf:li>beta cell</rdf:li>
<rdf:li>insulin</rdf:li>
<rdf:li>pancreas</rdf:li>
</rdf:Bag>
<rdf:Seq rdf:about="rdf:#08530b50-a2c5-4d7b-a763-cf27ef2da63d">
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<dc:publisher>The University of Auckland, Bioengineering Institute</dc:publisher>
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<dc:creator rdf:resource="rdf:#9af5a991-26ce-45b0-8fd4-78c99af62827"/>
<cmeta:modification rdf:resource="rdf:#308c7ac7-b1c9-4616-870b-1ca26a50e38f"/>
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<rdf:Description rdf:about="rdf:#2590dd26-8318-49ab-ac5e-d11d0d74ce10">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
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<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#64f9f981-44fe-4a42-8244-293a01fd7f47"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#108f985c-ec1f-485f-b0ee-36c1a85fb6fc">
<dc:creator rdf:resource="rdf:#08530b50-a2c5-4d7b-a763-cf27ef2da63d"/>
<dc:title>Mathematical modeling of the hypothalamic-pituitary-adrenal system activity</dc:title>
<bqs:volume>59</bqs:volume>
<bqs:first_page>15</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#96608990-f07c-46f8-9f39-50a8c205f213"/>
<dcterms:issued rdf:resource="rdf:#28431c4e-a8e5-4ca4-b5c0-2fe28afa34af"/>
<bqs:last_page>25</bqs:last_page>
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<rdf:Description rdf:about="rdf:#f6649729-2654-4dd6-b4cf-077364afaa1d">
<vCard:Given>Somkid</vCard:Given>
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</rdf:Description>
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<dcterms:W3CDTF>2001-00-00 00:00</dcterms:W3CDTF>
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<rdf:value>This is the CellML description of Lenbury et al.'s 2001 mathematical model of insulin kinetics.</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#a8338d58-ba45-4ed8-b630-9e8e2980b1dc">
<vCard:N rdf:resource="rdf:#001c3f2b-48ce-45f8-9e0b-da511ac60b9e"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7b2b843b-f70a-4c86-ab96-b5247c02367e">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="#lenbury_model_2001">
<dc:title>
Lenbury et al.'s 2001 mathematical model of insulin kinetics.
</dc:title>
<cmeta:bio_entity>pacreatic beta cell</cmeta:bio_entity>
<cmeta:comment rdf:resource="rdf:#f9453d70-81aa-48c7-ad47-181dd54cb9f1"/>
<bqs:reference rdf:resource="rdf:#039df862-4049-4dd4-bf40-580c4e7f1a29"/>
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<bqs:Pubmed_id>11226623</bqs:Pubmed_id>
<bqs:JournalArticle rdf:resource="rdf:#108f985c-ec1f-485f-b0ee-36c1a85fb6fc"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#578ea9ef-2951-4988-97e0-35b6d6a5bc8d">
<dcterms:W3CDTF>2007-09-03T13:56:05+12:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f526d346-fb5a-46c3-855e-383227f54203">
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<rdf:Description rdf:about="rdf:#edeab1d6-9125-4410-b274-e2dc5ecea537">
<vCard:FN>Catherine Lloyd</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9514e30c-c130-4ba9-86f4-d2c02d18f638">
<vCard:Given>Yongwimon</vCard:Given>
<vCard:Family>Lenbury</vCard:Family>
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<dcterms:W3CDTF>2007-06-18T00:00:00+00:00</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="/z">
<dcterms:alternative>pancreatic beta cell density</dcterms:alternative>
<dc:title>z</dc:title>
</rdf:Description>
<rdf:Description rdf:about="/x">
<dcterms:alternative>insulin</dcterms:alternative>
<dc:title>x</dc:title>
</rdf:Description>
<rdf:Description rdf:about="/y">
<dcterms:alternative>glucose</dcterms:alternative>
<dc:title>y</dc:title>
</rdf:Description>
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<vCard:ORG rdf:resource="rdf:#7b2b843b-f70a-4c86-ab96-b5247c02367e"/>
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<rdf:Description rdf:about="rdf:#96608990-f07c-46f8-9f39-50a8c205f213">
<dc:title>BioSystems</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#35362bf9-16a9-4d0f-86f8-f09638f28327">
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
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<rdf:Description rdf:about="rdf:#308c7ac7-b1c9-4616-870b-1ca26a50e38f">
<dcterms:modified rdf:resource="rdf:#578ea9ef-2951-4988-97e0-35b6d6a5bc8d"/>
<rdf:value>I've added a piecewise equation for "z" such that it can never equal zero. This now solves the NaN problem generated by having a zero as a denominator.</rdf:value>
<cmeta:modifier rdf:resource="rdf:#a8338d58-ba45-4ed8-b630-9e8e2980b1dc"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#001c3f2b-48ce-45f8-9e0b-da511ac60b9e">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#55539d48-6d75-4109-ba6e-f3ffa4b06250">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value rdf:resource="rdf:#82ed34fd-8b77-4472-bd7f-67b5e15fadb2"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#64f9f981-44fe-4a42-8244-293a01fd7f47">
<vCard:Given>Sitipong</vCard:Given>
<vCard:Family>Ruktamatakul</vCard:Family>
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<rdf:Description rdf:about="rdf:#2b7202ed-91eb-4e83-9746-1798c5d07337">
<dc:creator rdf:resource="rdf:#edeab1d6-9125-4410-b274-e2dc5ecea537"/>
<rdf:value>Model now runs in PCEnv without generating NaNs - but I'm still not sure it can generate the published results!</rdf:value>
</rdf:Description>
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<vCard:FN>Catherine Lloyd</vCard:FN>
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</model>
