- Author:
- Tessa Paris <tpar054@aucklanduni.ac.nz>
- Date:
- 2010-02-19 15:08:31+13:00
- Desc:
- Changed parameter values. Integration fails
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/neumann_lam_dahari_gretch_wiley_layden_perelson_1998/rawfile/a34cf7bf6436104ab27aa246f836f4203a09ecd1/neumann_lam_dahari_gretch_wiley_layden_perelson_1998.cellml
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<!--
This CellML file was generated on 12/02/2010 at 2:55:04 at p.m. using:
COR (0.9.31.1333)
Copyright 2002-2010 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 Hepatitis C Viral Dynamics <emphasis>in Vivo</emphasis> and investigating the Antiviral Efficacy of Interferon-alpha Therapy</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
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<section id="sec_status">
<title>Model Status</title>
<para>
This model is valid CellML except for a unit warning. The integration fails so the model is unable to produce the same output as in the paper.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>ABSTRACT:
</para>
<para>
To better understand the dynamics of hepatitis C virus and the antiviral effect of interferon-alpha-2b (IFN), viral decline in 23 patients during therapy was analyzed with a mathematical model. The analysis indicates that the major initial effect of IFN is to block virion production or release, with blocking efficacies of 81, 95, and 96% for daily doses of 5, 10, and 15 million international units, respectively. The estimated virion half-life (t1/2) was, on average, 2.7 hours, with pretreatment production and clearance of 10(12) virions per day. The estimated infected cell death rate exhibited large interpatient variation (corresponding t1/2 = 1.7 to 70 days), was inversely correlated with baseline viral load, and was positively correlated with alanine aminotransferase levels. Fast death rates were predictive of virus being undetectable by polymerase chain reaction at 3 months. These findings show that infection with hepatitis C virus is highly dynamic and that early monitoring of viral load can help guide therapy.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
Hepatitis C Viral Dynamics in Vivo and the Antiviral Efficacy of Interferon-alpha Therapy, Avidan U. Neumann, Nancy P. Lam, Harel Dahari, David R. Gretch, Thelma E. Wiley, Thomas J. Layden, and Alan S. Perelson, 1998, <emphasis>Science</emphasis>, 282, 103-107. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/9756471?dopt=Abstract">PubMed ID: 9756471</ulink>
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>reaction diagram</title>
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<imagedata fileref="neumann_1998.png"/>
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<caption>Schematic diagram of the viral dynamics of Hepatitis C <emphasis>in vivo</emphasis>.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
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Neumann et al's 1998 mathematical model of hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-alpha therapy.
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<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>I</ci>
</apply>
<piecewise>
<piece>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>eta</ci>
</apply>
<ci>beta</ci>
<ci>V</ci>
<ci>T</ci>
<cn cellml:units="first_order_rate_constant">1</cn>
</apply>
<apply>
<times/>
<ci>delta</ci>
<ci>I</ci>
</apply>
</apply>
<apply>
<gt/>
<ci>time</ci>
<cn cellml:units="day">0</cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<times/>
<ci>c</ci>
<ci>V</ci>
<cn cellml:units="cell_per_ml">1</cn>
</apply>
<ci>p</ci>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="Viral_load">
<variable name="V" units="virons_per_ml" initial_value="9.4e6" public_interface="out"/>
<variable name="epsilon" units="dimensionless" initial_value="0.96"/>
<variable name="p" units="virons_per_day" initial_value="1276e9" public_interface="out"/>
<variable name="c" units="first_order_rate_constant" initial_value="6.2" public_interface="out"/>
<variable name="I" units="cell" public_interface="in"/>
<variable name="time" units="day" public_interface="in"/>
<variable name="log_V" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>V</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>epsilon</ci>
</apply>
<ci>p</ci>
<ci>I</ci>
<cn cellml:units="per_ml_per_cell">1</cn>
</apply>
<apply>
<times/>
<ci>c</ci>
<ci>V</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>log_V</ci>
<apply>
<log/>
<apply>
<times/>
<ci>V</ci>
<cn cellml:units="ml_per_viron">1</cn>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="kinetic_parameters">
<variable name="beta" units="ml_per_viron" initial_value="3e-7" public_interface="out"/>
<variable name="eta" units="dimensionless" initial_value="0.8" public_interface="out"/>
</component>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Target_cells" 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="Infected_cells" 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="Viral_load" 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="Target_cells" component_2="Viral_load"/>
<map_variables variable_1="c" variable_2="c"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Infected_cells" component_2="Target_cells"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="delta" variable_2="delta"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Infected_cells" component_2="Viral_load"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="I" variable_2="I"/>
<map_variables variable_1="p" variable_2="p"/>
<map_variables variable_1="c" variable_2="c"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Target_cells" component_2="kinetic_parameters"/>
<map_variables variable_1="beta" variable_2="beta"/>
<map_variables variable_1="eta" variable_2="eta"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Infected_cells" component_2="kinetic_parameters"/>
<map_variables variable_1="beta" variable_2="beta"/>
<map_variables variable_1="eta" variable_2="eta"/>
</connection>
</model>
