- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2009-06-17 13:38:06+12:00
- Desc:
- committing version02 of dixit_perelson_2004
- Permanent Source URI:
- https://models.cellml.org/workspace/dixit_perelson_2004/rawfile/dd435250a44f54d0911414d73d074d8296f8afd4/dixit_perelson_2004.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : dixit_model_II_2004.xml
CREATED : 12th December 2003
LAST MODIFIED : 12th December 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 16/1/02 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Dixit and Perelson's 2nd 2004 mathematical model of viral dynamics in the presence of reverse transcriptase inhibitors.
CHANGES:
--><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="dixit_perelson_2004_version02" name="dixit_perelson_2004_version02">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modelling the Complex Patterns of Viral Load Decay under Antiretroviral Therapy</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>
When treated with antiretroviral therapy, the plasma viral loads in HIV patients decline in three distinct phases:
</para>
<itemizedlist>
<listitem>
<para>When the treatment is initially administered there is a 6 to 72 hour delay before the viral loads begin to decline;</para>
</listitem>
<listitem>
<para>following this <emphasis>shoulder</emphasis> period viral load decline rapidly for about one week;</para>
</listitem>
<listitem>
<para>finally, viral loads continue to decrease, but at a slower rate.</para>
</listitem>
</itemizedlist>
<para>
Mathematical models which describe this process have been developed. For more details please see:
</para>
<itemizedlist>
<listitem>
<para>
<ulink url="${HTML_EXMPL_HERZ_MODEL}">Herz <emphasis>et al.</emphasis>, Modelling Viral Dynamics <emphasis>In Vivo</emphasis>, 1996</ulink>;</para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_NOWAK_MODEL}">Nowak and Bangham, Modelling the Population Dynamics of Immune Responses to Persistent Viruses, 1996</ulink>;</para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_PERELSON_MODEL}">Perelson <emphasis>et al.</emphasis>, Modelling HIV-1 Dynamics <emphasis>In Vivo</emphasis>, 1996</ulink>;</para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_GROSSMAN_MODEL}">Grossman <emphasis>et al.</emphasis>, Modelling the Kinetics of Plasma Virus Following the Initiation of Therapy, 1998</ulink>;</para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_MITTLER_MODEL}">Mittler <emphasis>et al.</emphasis>, Influence of Delayed Viral Production on Viral Dynamics in HIV-1 Infected Patients, 1998</ulink>;</para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_WODARZ_MODEL}">Wodarz and Nowak, Modelling the Interaction Between HIV and the Immune System, 1999</ulink>; and </para>
</listitem>
<listitem>
<para>
<ulink url="${HTML_EXMPL_BONHOEFFER_MODEL}">Bonhoeffer <emphasis>et al.</emphasis> Modelling the Population Dynamics of Virus Infected Cells, 2000</ulink>.</para>
</listitem>
</itemizedlist>
<para>
Despite these models the shoulder phase, where viral loads remain virtually unchanged by the drug therapy, is poorly understood. Two factors are known to contribute to this delay: Firstly, a pharmacological delay which is the period between the drug administration and the drug action. This delay is due to the time it takes for the drug to be absorbed from the gut into the blood stream, and then carried to and taken up by the target cells. The second factor is an intracellular delay which is due to the finite time required for an infected cell to replicate the virus.
</para>
<para>
In the Dixit and Perelson 2004 publication described here, the authors present a mathematical model that combines pharmacokinetics and viral dynamics and includes intracellular delay. The model of viral dynamics is based on that published by <ulink url="${HTML_EXMPL_PERELSON_MODEL}">Perelson <emphasis>et al.</emphasis>
</ulink> (see <xref linkend="fig_cell_diagram"/> below). To accurately represent the pharmacokinetics they assume a two compartment model consisting of blood and cells. The models of viral dynamics and pharmacokinetics are connected via a parameter which represents drug specific efficacy. Because reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs) have very different effects on the duration of the intracellular delay, they have been modelled separately (see <xref linkend="fig_reaction_diagram1"/> and <xref linkend="fig_reaction_diagram2"/>). </para>
<para>
The models have been described here in CellML (the raw CellML description of the Dixit and Perelson 2004 models can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>).
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WMD-4B1WXVT-6&_user=140507&_coverDate=01%2F07%2F2004&_alid=134704688&_rdoc=1&_fmt=summary&_orig=search&_qd=1&_cdi=6932&_sort=d&_docanchor=&view=c&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=574df08b1a72cfc52ed9a2bb186e39a5">Complex patterns of viral load decay under antiretroviral therapy: influence of pharmacokinetics and intracelllar delay</ulink>, Narendra M. Dixit and Alan S. Perelson, 2004, <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>, 226, 95-109. (<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WMD-4B1WXVT-6&_coverDate=01%2F07%2F2004&_alid=134704688&_rdoc=1&_fmt=&_orig=search&_qd=1&_cdi=6932&_sort=d&view=c&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=d77dd62b0a4028ce41dd953455d4bf3c">Full text (HTML)</ulink> and PDF versions of the article are available on the <emphasis>Journal of Theoretical Biology</emphasis> website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=14637059&dopt=Abstract">PubMed ID: 14637059</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram</title>
</objectinfo>
<imagedata fileref="dixit_2004a.png"/>
</imageobject>
</mediaobject>
<caption>Schematic summary of the dynamics of HIV-1 infection <emphasis>in vivo</emphasis>. This model is based on that published by Perelson <emphasis>et al.</emphasis> in 1996.</caption>
</informalfigure>
<informalfigure float="0" id="fig_reaction_diagram1">
<mediaobject>
<imageobject>
<objectinfo>
<title>reaction diagram1</title>
</objectinfo>
<imagedata fileref="dixit_2004b.png"/>
</imageobject>
</mediaobject>
<caption>Pharmacokinetics - the two compartment model for protease inhibitors.</caption>
</informalfigure>
<informalfigure float="0" id="fig_reaction_diagram2">
<mediaobject>
<imageobject>
<objectinfo>
<title>reaction diagram2</title>
</objectinfo>
<imagedata fileref="dixit_2004c.png"/>
</imageobject>
</mediaobject>
<caption>Pharmacokinetics - the two compartment model for reverse transcriptase inhibitors. The main difference between the models is that RTIs must be phosphorylated within the cell in order to be in their active form.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<units name="ml">
<unit units="litre" prefix="milli"/>
</units>
<units name="mg">
<unit units="gram" prefix="milli"/>
</units>
<units name="per_ml">
<unit units="litre" prefix="milli" exponent="-1"/>
</units>
<units name="mg_per_ml">
<unit units="gram" prefix="milli"/>
<unit units="litre" prefix="milli" exponent="-1"/>
</units>
<units name="day">
<unit units="second" multiplier="86400.0"/>
</units>
<units name="flux">
<unit units="ml"/>
<unit units="day" exponent="-1"/>
</units>
<units name="first_order_rate_constant">
<unit units="day" exponent="-1"/>
</units>
<units name="second_order_rate_constant">
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<unit units="day" exponent="-1"/>
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<component cmeta:id="T" name="T">
<rdf:RDF>
<rdf:Description rdf:about="T">
<dc:title>T</dc:title>
<dcterms:alternative>uninfected target CD4 cells</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="per_ml" public_interface="out" name="T" initial_value="1E6"/>
<variable units="second_order_rate_constant" name="lamda" initial_value="1E4"/>
<variable units="first_order_rate_constant" name="d" initial_value="0.01"/>
<variable units="flux" public_interface="in" name="k"/>
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</math>
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<rdf:RDF>
<rdf:Description rdf:about="T_">
<dc:title>T_</dc:title>
<dcterms:alternative>productively infected CD4 cells</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="per_ml" public_interface="out" name="T_"/>
<variable units="first_order_rate_constant" name="tau" initial_value="1.5"/>
<variable units="first_order_rate_constant" name="m" initial_value="0.01"/>
<variable units="flux" public_interface="in" name="k"/>
<variable units="per_ml" public_interface="in" name="VI"/>
<variable units="per_ml" public_interface="in" name="T"/>
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<variable units="day" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
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<ci>time</ci>
</bvar>
<ci>T_</ci>
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<ci> tau </ci>
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<rdf:RDF>
<rdf:Description rdf:about="VI">
<dc:title>VI</dc:title>
<dcterms:alternative>infectious viral load</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="per_ml" public_interface="out" name="VI"/>
<variable units="dimensionless" public_interface="in" name="N"/>
<variable units="first_order_rate_constant" public_interface="in" name="c"/>
<variable units="dimensionless" public_interface="in" name="epsilon_PI"/>
<variable units="per_ml" public_interface="in" name="T_"/>
<variable units="first_order_rate_constant" public_interface="in" name="delta"/>
<variable units="day" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
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<ci>time</ci>
</bvar>
<ci>VI</ci>
</apply>
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<minus/>
<apply>
<times/>
<ci> N </ci>
<ci> delta </ci>
<ci> T_ </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> epsilon_PI </ci>
</apply>
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<apply>
<times/>
<ci> c </ci>
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</apply>
</apply>
</math>
</component>
<component cmeta:id="VNI" name="VNI">
<rdf:RDF>
<rdf:Description rdf:about="VNI">
<dc:title>VNI</dc:title>
<dcterms:alternative>non-infectious viral load</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="per_ml" public_interface="out" name="VNI"/>
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<ci> epsilon_PI </ci>
</apply>
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<times/>
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<ci> VNI </ci>
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</apply>
</apply>
</math>
</component>
<component cmeta:id="epsilon_PI" name="epsilon_PI">
<rdf:RDF>
<rdf:Description rdf:about="epsilon_PI">
<dc:title>instantaneous drug efficacy</dc:title>
<dcterms:alternative>non-infectious viral load</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<variable units="dimensionless" public_interface="out" name="epsilon_PI"/>
<variable units="mg_per_ml" name="IC50" initial_value="9.0E-7"/>
<variable units="mg_per_ml" public_interface="in" name="Cc"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>epsilon_PI</ci>
<apply>
<divide/>
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<apply>
<plus/>
<ci> IC50 </ci>
<ci> Cc </ci>
</apply>
</apply>
</apply>
</math>
</component>
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Dixit and Perelson's 2nd 2004 mathematical model of viral dynamics in the presence of reverse transcriptase inhibitors.
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