- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2010-01-28 14:25:32+13:00
- Desc:
- Removed redundant model file (an older version of the model). Also updated documentation and corrected broken RDF.
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/lenbury_ruktamatakul_amornsamarnkul_2001/rawfile/fd486bef34328be6944d99c9c0144f1c1b5ce41a/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>Modeling insulin kinetics: responses to a single oral glucose administration or ambulatory-fed conditions</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>
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>
ABSTRACT: This paper presents a nonlinear mathematical model of the glucose-insulin feedback system, which has been extended to incorporate the beta-cells' function on maintaining and regulating plasma insulin level in man. Initially, a gastrointestinal absorption term for glucose is utilized to effect the glucose absorption by the intestine and the subsequent release of glucose into the bloodstream, taking place at a given initial rate and falling off exponentially with time. An analysis of the model is carried out by the singular perturbation technique in order to derive boundary conditions on the system parameters which identify, in particular, the existence of limit cycles in our model system consistent with the oscillatory patterns often observed in clinical data. We then utilize a sinusoidal term to incorporate the temporal absorption of glucose in order to study the responses in the patients under ambulatory-fed conditions. A numerical investigation is carried out in this case to construct a bifurcation diagram to identify the ranges of parametric values for which chaotic behavior can be expected, leading to interesting biological interpretations.
</para>
<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 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/pubmed/11226623">PubMed ID: 11226623</ulink>
</para>
</sect1>
</article>
</documentation>
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<cn cellml:units="dimensionless">1e-7</cn>
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<rdf:RDF>
<rdf:Bag rdf:about="rdf:#82ed34fd-8b77-4472-bd7f-67b5e15fadb2">
<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">
<rdf:li rdf:resource="rdf:#f526d346-fb5a-46c3-855e-383227f54203"/>
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<dc:publisher>The University of Auckland, Bioengineering Institute</dc:publisher>
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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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<dc:title>Modeling insulin kinetics: responses to a single oral glucose administration or ambulatory-fed conditions</dc:title>
<bqs:volume>59</bqs:volume>
<bqs:first_page>15</bqs:first_page>
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<vCard:Given>Somkid</vCard:Given>
<vCard:Family>Amornsamarnkul</vCard:Family>
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<dcterms:W3CDTF>2001-00-00 00:00</dcterms:W3CDTF>
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<dc:creator rdf:resource="rdf:#3aeec9d9-c567-40ab-955a-3c0af3ae3626"/>
<rdf:value>This is the CellML description of Lenbury et al.'s 2001 mathematical model of insulin kinetics.</rdf:value>
</rdf:Description>
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<vCard:N rdf:resource="rdf:#001c3f2b-48ce-45f8-9e0b-da511ac60b9e"/>
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<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"/>
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<bqs:Pubmed_id>11226623</bqs:Pubmed_id>
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</rdf:Description>
<rdf:Description rdf:about="rdf:#578ea9ef-2951-4988-97e0-35b6d6a5bc8d">
<dcterms:W3CDTF>2007-09-03T13:56:05+12:00</dcterms:W3CDTF>
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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>
<rdf:Description rdf:about="rdf:#9af5a991-26ce-45b0-8fd4-78c99af62827">
<vCard:ORG rdf:resource="rdf:#7b2b843b-f70a-4c86-ab96-b5247c02367e"/>
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<dc:title>BioSystems</dc:title>
</rdf:Description>
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<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"/>
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<rdf:Description rdf:about="rdf:#64f9f981-44fe-4a42-8244-293a01fd7f47">
<vCard:Given>Sitipong</vCard:Given>
<vCard:Family>Ruktamatakul</vCard:Family>
</rdf:Description>
<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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<dc:subject rdf:resource="rdf:#55539d48-6d75-4109-ba6e-f3ffa4b06250"/>
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</model>
