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<!--
This CellML file was generated on 17/12/2009 at 3:28:21 at p.m. using:
COR (0.9.31.1333)
Copyright 2002-2009 Dr Alan Garny
http://cor.physiol.ox.ac.uk/ - cor@physiol.ox.ac.uk
CellML 1.0 was used to generate this model
http://www.cellml.org/
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<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>
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<section id="sec_status">
<title>Model Status</title>
<para>
This model is valid CellML but can not be integrated as it is overconstrained. Some variables are not initialised but more importantly the model contains time delays, making it unsuitable for description using CellML.
</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>
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<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>
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<para>finally, viral loads continue to decrease, but at a slower rate.</para>
</listitem>
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<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 complete original paper reference is cited below:
</para>
<para>
Complex patterns of viral load decay under antiretroviral therapy: influence of pharmacokinetics and intracelllar delay, Narendra M. Dixit and Alan S. Perelson, 2004,
<emphasis>Journal of Theoretical Biology</emphasis>
, 226, 95-109. <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>
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<title>cell diagram</title>
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<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>
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<title>reaction diagram1</title>
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<caption>Pharmacokinetics - the two compartment model for protease inhibitors.</caption>
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<title>reaction diagram2</title>
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<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>
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<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="VNI" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Cb" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Cc" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="T" component_2="T_"/>
<map_variables variable_1="T" variable_2="T"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="T" component_2="VI"/>
<map_variables variable_1="VI" variable_2="VI"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="T_" component_2="VI"/>
<map_variables variable_1="VI" variable_2="VI"/>
<map_variables variable_1="T_" variable_2="T_"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="T_" component_2="VNI"/>
<map_variables variable_1="T_" variable_2="T_"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="T" component_2="kinetic_parameters"/>
<map_variables variable_1="k" variable_2="k"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="T_" component_2="kinetic_parameters"/>
<map_variables variable_1="delta" variable_2="delta"/>
<map_variables variable_1="k" variable_2="k"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="VI" component_2="kinetic_parameters"/>
<map_variables variable_1="delta" variable_2="delta"/>
<map_variables variable_1="c" variable_2="c"/>
<map_variables variable_1="N" variable_2="N"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="VI" component_2="epsilon_PI"/>
<map_variables variable_1="epsilon_PI" variable_2="epsilon_PI"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="VNI" component_2="kinetic_parameters"/>
<map_variables variable_1="delta" variable_2="delta"/>
<map_variables variable_1="c" variable_2="c"/>
<map_variables variable_1="N" variable_2="N"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="VNI" component_2="epsilon_PI"/>
<map_variables variable_1="epsilon_PI" variable_2="epsilon_PI"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="epsilon_PI" component_2="Cc"/>
<map_variables variable_1="Cc" variable_2="Cc"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Cb" component_2="kinetic_parameters"/>
<map_variables variable_1="ka" variable_2="ka"/>
<map_variables variable_1="ke" variable_2="ke"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Cc" component_2="Cx"/>
<map_variables variable_1="Cx" variable_2="Cx"/>
<map_variables variable_1="Cc" variable_2="Cc"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Cx" component_2="Cb"/>
<map_variables variable_1="Cb" variable_2="Cb"/>
</connection>
</model>
