- 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_b.cellml
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<!-- 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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<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>
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<section id="sec_status">
<title>Model Status</title>
<para>
Please note that this particular variant of the model is an extension of the basic core model. To the three variables described in the core model: plasma insulin concentration (x), glucose concentration (y) and the density of the pancreatic beta cells (z), we are adding a forth variable (u) which describes the temporal glucose absorption by the gastrointestinal tract.
</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">
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<title>model diagram</title>
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<caption>Schematic diagram of the pancreatic beta-cells. Glucose production is by beta-cells and uptake is by gastrointestinal cells. 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>
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<rdf:li>insulin</rdf:li>
<rdf:li>pancreas</rdf:li>
<rdf:li>beta cell</rdf:li>
<rdf:li>endocrine</rdf:li>
</rdf:Bag>
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<dcterms:W3CDTF>2001-00-00 00:00</dcterms:W3CDTF>
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<dc:publisher>The University of Auckland, Bioengineering Institute</dc:publisher>
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<dcterms:modified rdf:resource="rdf:#fad7737a-fc0d-4daa-ab48-f692f62d1701"/>
<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>
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<vCard:FN>Catherine Lloyd</vCard:FN>
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<dc:title>
Lenbury et al.'s 2001 mathematical model of insulin kinetics.
</dc:title>
<cmeta:bio_entity>pacreatic beta cell</cmeta:bio_entity>
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<rdf:value>The model now runs in PCEnv without producing "NaNs" but I'm still not sure it can recreate the published results.
Also, please note that this particular variant of the model is an extension of the basic core model. To the three variables described in the core model: plasma insulin concentration (x), glucose concentration (y) and the density of the pancreatic beta cells (z), we are adding a forth variable (u) which describes the temporal glucose absorption by the gastrointestinal tract.</rdf:value>
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<dc:title>BioSystems</dc:title>
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<dcterms:W3CDTF>2007-09-03T13:59:03+12:00</dcterms:W3CDTF>
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<dcterms:alternative>glucose absorption</dcterms:alternative>
<dc:title>u</dc:title>
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<dcterms:alternative>pancreatic beta cell density</dcterms:alternative>
<dc:title>z</dc:title>
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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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<dcterms:alternative>insulin</dcterms:alternative>
<dc:title>x</dc:title>
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<dcterms:alternative>glucose</dcterms:alternative>
<dc:title>y</dc:title>
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<rdf:value>This is the CellML description of Lenbury et al.'s 2001 mathematical model of insulin kinetics.</rdf:value>
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<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
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<vCard:FN>Catherine Lloyd</vCard:FN>
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<vCard:Given>Somkid</vCard:Given>
<vCard:Family>Amornsamarnkul</vCard:Family>
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<vCard:Given>Catherine</vCard:Given>
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<dcterms:W3CDTF>2007-06-18T00:00:00+00:00</dcterms:W3CDTF>
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