<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : wang_model_2007.xml
CREATED : 10th July 2007
LAST MODIFIED : 10th 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 Wang, Li, and Kuang's 2007 mathematical model and qualitative analysis of insulin therapies.
CHANGES:
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<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>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. The units are consistent and the model runs to partially recreate the published results. The infusion of glucose and insulin, and the insulin response, are the same as in the paper, but the glucose oscillations are different - this may be because the time delays in the original model can not be included in the CellML model.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Abstract: Several insulin therapies are widely in clinical use with the basic strategy that mimics insulin secretion in a normal glucose-nsulin endocrine metabolic regulatory system. In this paper, we model the insulin therapies using a delay differential equation model. We study the dynamics of the model both qualitatively and quantitatively. The analytical results show the existence and uniqueness of a stable periodic solution that corresponds to ultradian insulin secretion oscillations. Numerically we simulate the insulin administration based on our model. The numerical simulation results are in agreement with findings of clinical studies.
</para>
<informalfigure float="0" id="fig_reaction_diagram">
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</objectinfo>
<imagedata fileref="wang_2007.png"/>
</imageobject>
</mediaobject>
<caption>Glucose (blue solid line) and insulin (red dotted line) concentrations oscillate over time, with a slight time delay between the peaks as insulin spikes in response to elevated glucose levels.</caption>
</informalfigure>
<para>
The complete original paper reference is cited below:
</para>
<para>
Mathematical modeling and qualitative analysis of insulin therapies, Haiyan Wang, Jiaxu Li, and Yang Kuang, 2007, <emphasis>Mathematical Biosciences</emphasis> 210, 17-33. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=17610909&query_hl=1&itool=pubmed_docsum">PubMed ID: 17610909</ulink>
</para>
</sect1>
</article>
</documentation>
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