<?xml version='1.0' encoding='utf-8'?>
<!-- FILE :topp_model_2000.xml
CREATED : 7th November 2002
LAST MODIFIED : 9th April 2003
AUTHOR : Catherine Lloyd
Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/01/2002 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Topp et al.s 2000 model of beta-cell mass, insulin, and glucose dynamics.
CHANGES:
09/04/2003 - AAC - Added publication date information.
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="topp_promislow_devries_miura_finegood_2000_version01" name="topp_promislow_devries_miura_finegood_2000_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>A Model of Beta-cell Mass, Insulin, and Glucose Kinetics</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>
This is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Diabetes is a disease of the glucose regulatory system that is associated with increased morbidity and premature mortality. There are two main types of diabetes. Type 1 diabetes (also called juvenile onset or insulin-dependent diabetes) is due to an autoimmune attack on the insulin secreting pancreatic beta-cell. Type 2 diabetes (also called adult onset or non-insulin-dependent diabetes) is characterised by a reduced mass of beta-cells, reduced insulin secretion and resistance to the action of insulin (elevated concentrations of glucose in the blood). In healthy individuals, blood glucose levels are controlled by two negative feedback loops. In the short term hyperglycemia (high blood glucose levels) stimulates insulin secretion from the pancreatic beta-cells. This then induces increased glucose uptake and decreased glucose production, leading to a decrease in blood glucose levels. Prolonged hyperglycemia may induce a second negative feedback loop by increasing the rate of beta-cell replication and thus the mass of beta-cells. An increased beta-cell mass represents an increased potential for insulin secretion, which in turn leads to a decrease in blood glucose. Type 2 diabetes has been associated with defects in both the short-term and long-term feedback loops.
</para>
<para>
The mathematical models produced as part of diabetes research have predominantly concentrated on the dynamics of a single variable, namely blood glucose level, insulin concentration or beta-cell mass. In their 2000 study, Brian Topp, Keith Promislow, Gerda de Vries, Robert M. Miura and Diane T. Finegood combine all three variables in a coupled model of beta-cell mass, insulin and glucose dynamics (see the figure below). They used their model to investigate both the normal behaviour of the glucose regulatory system, and to investigate the effects of defects on the behaviour of the system.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WMD-45CWWRD-1X&_user=140507&_coverDate=10%2F21%2F2000&_alid=62947438&_rdoc=1&_fmt=summary&_orig=search&_qd=1&_cdi=6932&_sort=d&_docanchor=&wchp=dGLbVzz-lSztz&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=47912bb7c34edff047f33b09feaa95fa">A Model of Beta-cell Mass, Insulin, and Glucose Kinetics: Pathways to Diabetes</ulink>, Brian Topp, Keith Promislow, Gerda de Vries, Robert M. Miura and Diane T. Finegood, 2000, <ulink url="http://www.sciencedirect.com/science?_ob=JournalURL&_cdi=6932&_auth=y&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=c8e64d20ff203cda2255f4b6b7affe4f">
<emphasis>Journal of Theoretical Biology</emphasis>
</ulink>, 206, 605-619. (<ulink url="http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6WMD-45CWWRD-1X-1&_cdi=6932&_orig=search&_coverDate=10%2F21%2F2000&_qd=1&_sk=997939995&wchp=dGLbVzz-lSztz&_acct=C000011498&_version=1&_userid=140507&md5=75820029209e99ebe40219330500b3da&ie=f.pdf">A PDF</ulink> version of the article is available for Journal Members on the Journal of Theoretical Biology website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11013117&dopt=Abstract">PubMed ID: 11013117</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell schematic for the model</title>
</objectinfo>
<imagedata fileref="topp_2000a.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>
</sect1>
</article>
</documentation>
<!--
Below, we define some additional units for association with variables and
constants within the model. The identifiers are fairly self-explanatory.
-->
<units name="day">
<unit units="second" multiplier="86400.0"/>
</units>
<units name="per_day">
<unit units="day" exponent="-1"/>
</units>
<units name="mg_per_dl">
<unit units="gram" prefix="milli"/>
<unit units="litre" prefix="deci" exponent="-1"/>
</units>
<units name="mg2_per_dl2">
<unit units="gram" prefix="milli" exponent="2"/>
<unit units="litre" prefix="deci" exponent="-2"/>
</units>
<units name="mg_per_dl_per_day">
<unit units="gram" prefix="milli"/>
<unit units="litre" prefix="deci" exponent="-1"/>
<unit units="day" exponent="-1"/>
</units>
<units name="U">
<unit units="gram" multiplier="1.6605402E-24"/>
</units>
<units name="microU_per_ml_per_day">
<unit units="U" prefix="micro"/>
<unit units="litre" prefix="milli" exponent="-1"/>
<unit units="day" exponent="-1"/>
</units>
<units name="ml_per_microU_per_day">
<unit units="litre" prefix="milli"/>
<unit units="U" prefix="micro" exponent="-1"/>
<unit units="day" exponent="-1"/>
</units>
<units name="dl_per_mg_per_day">
<unit units="litre" prefix="deci"/>
<unit units="gram" prefix="milli" exponent="-1"/>
<unit units="day" exponent="-1"/>
</units>
<units name="dl2_per_mg2_per_day">
<unit units="litre" prefix="deci" exponent="2"/>
<unit units="gram" prefix="milli" exponent="-2"/>
<unit units="day" exponent="-1"/>
</units>
<!--
The "environment" component is used to declare variables that are used by
all or most of the other components, in this case just "time".
-->
<component name="environment">
<variable units="day" public_interface="out" name="time"/>
</component>
<component name="glucose_dynamics">
<variable units="mg_per_dl" public_interface="out" name="G"/>
<variable units="mg_per_dl_per_day" name="R0" initial_value="846.0"/>
<variable units="ml_per_microU_per_day" name="SI" initial_value="0.72"/>
<variable units="per_day" name="EG0" initial_value="1.44"/>
<variable units="day" public_interface="in" name="time"/>
<variable units="mg_per_dl" public_interface="in" name="I"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="G_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> G </ci>
</apply>
<apply>
<minus/>
<ci> R0 </ci>
<apply>
<times/>
<apply>
<plus/>
<ci> EG0 </ci>
<apply>
<times/>
<ci> SI </ci>
<ci> I </ci>
</apply>
</apply>
<ci> G </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="insulin_dynamics">
<variable units="mg_per_dl" public_interface="out" name="I"/>
<variable units="mg2_per_dl2" name="alpha" initial_value="2000.0"/>
<variable units="microU_per_ml_per_day" name="sigma" initial_value="43.2"/>
<variable units="per_day" name="k" initial_value="432.0"/>
<variable units="day" public_interface="in" name="time"/>
<variable units="mg_per_dl" public_interface="in" name="G"/>
<variable units="mg_per_dl" public_interface="in" name="beta"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="I_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> I </ci>
</apply>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci> beta </ci>
<ci> sigma </ci>
<apply>
<power/>
<ci> G </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
<apply>
<plus/>
<ci> alpha </ci>
<apply>
<power/>
<ci> G </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> k </ci>
<ci> I </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="beta_cell_dynamics">
<variable units="mg_per_dl" public_interface="out" name="beta"/>
<variable units="per_day" name="d0" initial_value="0.06"/>
<variable units="dl_per_mg_per_day" name="r1" initial_value="0.84E-3"/>
<variable units="dl2_per_mg2_per_day" name="r2" initial_value="0.24E-5"/>
<variable units="day" public_interface="in" name="time"/>
<variable units="mg_per_dl" public_interface="in" name="G"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="beta_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> beta </ci>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci> r1 </ci>
<ci> G </ci>
</apply>
<apply>
<minus/>
<ci> d0 </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> r2 </ci>
<apply>
<power/>
<ci> G </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
<ci> beta </ci>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_2="environment" component_1="glucose_dynamics"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="insulin_dynamics"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="beta_cell_dynamics"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="insulin_dynamics" component_1="glucose_dynamics"/>
<map_variables variable_2="G" variable_1="G"/>
<map_variables variable_2="I" variable_1="I"/>
</connection>
<connection>
<map_components component_2="beta_cell_dynamics" component_1="glucose_dynamics"/>
<map_variables variable_2="G" variable_1="G"/>
</connection>
<connection>
<map_components component_2="insulin_dynamics" component_1="beta_cell_dynamics"/>
<map_variables variable_2="beta" variable_1="beta"/>
</connection>
<rdf:RDF>
<rdf:Bag rdf:about="rdf:#9caa8dd9-292c-4f82-b3ca-975b4a4662c6">
<rdf:li>insulin-glucose dynamics</rdf:li>
<rdf:li>signal transduction</rdf:li>
<rdf:li>Pancreatic Beta-Cell</rdf:li>
<rdf:li>calcium dynamics</rdf:li>
<rdf:li>beta cell</rdf:li>
<rdf:li>diabetes</rdf:li>
<rdf:li>metabolism</rdf:li>
<rdf:li>pancreas</rdf:li>
</rdf:Bag>
<rdf:Seq rdf:about="rdf:#019e0bc0-4312-4319-baa6-5cebff15a4f1">
<rdf:li rdf:resource="rdf:#18b78bea-1d9f-46cd-853b-0e8b894d4b20"/>
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</rdf:Seq>
<rdf:Description rdf:about="#topp_promislow_devries_miura_finegood_2000_version01">
<dc:title>
Topp et al.s 2000 model of beta-cell mass, insulin, and glucose
dynamics.
</dc:title>
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<rdf:value>
Added publication date information.
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<vCard:Given>Catherine</vCard:Given>
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<vCard:Other>May</vCard:Other>
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<rdf:Description rdf:about="">
<dc:publisher>
The University of Auckland, Bioengineering Institute
</dc:publisher>
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<dcterms:W3CDTF>2002-11-07</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#dc5cdc00-6d18-4881-8b39-cac587abab23">
<vCard:Given>Keith</vCard:Given>
<vCard:Family>Promislow</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#1376ab3b-0d5c-40d3-9d53-419ee7cc6d38">
<vCard:Given>Gerda</vCard:Given>
<vCard:Family>de Vries</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4aaa3012-fbfe-4a7f-8e90-9c036a30f1ae">
<dc:title>Journal of Theoretical Biology</dc:title>
</rdf:Description>
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<vCard:Given>Brian</vCard:Given>
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<bqs:Pubmed_id>11013117</bqs:Pubmed_id>
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<vCard:Orgname>The University of Auckland</vCard:Orgname>
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<dc:creator rdf:resource="rdf:#019e0bc0-4312-4319-baa6-5cebff15a4f1"/>
<dc:title>
A Model of Beta-Cell Mass, Insulin, and Glucose Kinetics: Paythways
to Diabetes
</dc:title>
<bqs:volume>206</bqs:volume>
<bqs:first_page>605</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#4aaa3012-fbfe-4a7f-8e90-9c036a30f1ae"/>
<dcterms:issued rdf:resource="rdf:#bb96d5d3-f4e2-45e3-bd78-63b1b2b1a809"/>
<bqs:last_page>619</bqs:last_page>
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<dcterms:W3CDTF>2003-04-09</dcterms:W3CDTF>
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<dcterms:W3CDTF>2000-10-21</dcterms:W3CDTF>
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<vCard:Given>Diane</vCard:Given>
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<vCard:Other>T</vCard:Other>
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<vCard:Given>Robert</vCard:Given>
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<vCard:Given>Autumn</vCard:Given>
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This is the CellML descripition of Topp et al.s 2000 model of
beta-cell mass, insulin, and glucose dynamics.
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