- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2010-03-17 13:42:59+13:00
- Desc:
- Fix broken rdf, corrected some units, and separated out the equations for I and I_0.
- Permanent Source URI:
- https://models.cellml.org/workspace/mittler_sulzer_neumann_perelson_1998/rawfile/41a3b72cac7f2fd53dc63446c23e5ccf0593bada/mittler_sulzer_neumann_perelson_1998.cellml
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<!--
This CellML file was generated on 11/02/2010 at 2:44:42 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>Influence of Delayed Viral Production on Viral Dynamics in HIV-1 Infected Patients</title>
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<title>Model Status</title>
<para>
This CellML model runs in both OpenCell and COR however we are uncertain as to whether or not the CellML model replicates the original model from the published paper as there are no validation figures to compare it against. The CellML model is based on equatiosn 10a to 10e. Parameter values for the variables k and p are not stated in the paper so in the CellML model these were taken from a previously published model by the same author (Perelson et al. 1996). The units have been checked and they are consistent. Note that while the model does run in COR, since the unit of time is days the model is not ideally suited for running in COR.
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<para> ABSTRACT: We present and analyze a model for the interaction of human immunodeficiency virus type 1 (HIV-1) with target cells that includes a time delay between initial infection and the formation of productively infected cells. Assuming that the variation among cells with respect to this 'intracellular' delay can be approximated by a gamma distribution, a high flexible distribution that can mimic a variety of biologically plausible delays, we provide analytical solutions for the expected decline in plasma virus concentration after the initiation of antiretroviral therapy with one or more protease inhibitors. We then use the model to investigate whether the parameters that characterize viral dynamics can be identified from biological data. Using non-linear least-squares regression to fit the model to simulated data in which the delays conform to a gamma distribution, we show that good estimates for free viral clearance rates, infected cell death rates, and parameters characterizing the gamma distribution can be obtained. For simulated data sets in which the delays were generated using other biologically plausible distributions, reasonably good estimates for viral clearance rates, infected cell death rates, and mean delay times can be obtained using the gamma-delay model. For simulated data sets that include added simulated noise, viral clearance rate estimates are not as reliable. If the mean intracellular delay is known, however, we show that reasonable estimates for the viral clearance rate can be obtained by taking the harmonic mean of viral clearance rate estimates from a group of patients. These results demonstrate that it is possible to incorporate distributed intracellular delays into existing models for HIV dynamics and to use these refined models to estimate the half-life of free virus from data on the decline in HIV-1 RNA following treatment.
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<para>
The original paper reference is cited below:
</para>
<para>
Influence of Delayed Viral Production on Viral Dynamics in HIV-1 Infected Patients, John E. Mittler, Bernhard Sulzer, Avidan U. Neumann, and Alan S. Perelson, 1998, <emphasis>Mathematical Biosciences</emphasis>
, 152, 143-163. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/9780612">PubMed ID: 9780612</ulink>
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<caption>Schematic summary of the dynamics of HIV-1 infection <emphasis>in vivo</emphasis> captured by the Perelson <emphasis>et al.</emphasis> 1996 model.</caption>
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<caption>Schematic summary of the dynamics of viral infection <emphasis>in vivo</emphasis> captured by the <ulink url="${HTML_EXMPL_HERZ_MODEL}">Herz <emphasis>et al.</emphasis> 1996 model</ulink>.</caption>
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<component xmlns="http://www.cellml.org/cellml/1.0#" name="kinetic_parameters">
<variable name="c" units="first_order_rate_constant" initial_value="3" public_interface="out"/>
<variable name="delta" units="first_order_rate_constant" initial_value="0.5" public_interface="out"/>
<variable name="p" units="first_order_rate_constant" initial_value="774" public_interface="out"/>
<variable name="b_" units="day" public_interface="out"/>
<variable name="k_" units="ml_per_day" public_interface="out"/>
<variable name="k" units="ml_per_day" initial_value="2.4e-5" public_interface="out"/>
<variable name="b" units="day" initial_value="0.25"/>
<variable name="m" units="first_order_rate_constant" initial_value="0.01"/>
<variable name="n" units="dimensionless" initial_value="4"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>b_</ci>
<apply>
<divide/>
<ci>b</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>m</ci>
<ci>b</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k_</ci>
<apply>
<divide/>
<ci>k</ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>m</ci>
<ci>b</ci>
</apply>
</apply>
<ci>n</ci>
</apply>
</apply>
</apply>
</math>
</component>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="I" 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="E1" 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="E2" 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="E3" 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="E4" 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="VI" 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="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="Heavyside_function" 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="I" 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="I" component_2="E4"/>
<map_variables variable_1="E4" variable_2="E4"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="E1" 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="E2" component_2="E1"/>
<map_variables variable_1="E1" variable_2="E1"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="E3" component_2="E2"/>
<map_variables variable_1="E2" variable_2="E2"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="E4" component_2="E3"/>
<map_variables variable_1="E3" variable_2="E3"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="VI" component_2="I"/>
<map_variables variable_1="I" variable_2="I"/>
<map_variables variable_1="VI_0" variable_2="VI_0"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="VNI" component_2="I"/>
<map_variables variable_1="I" variable_2="I"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="VNI" component_2="virus_total"/>
<map_variables variable_1="VNI" variable_2="VNI"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="VI" component_2="virus_total"/>
<map_variables variable_1="VI" variable_2="VI"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Heavyside_function" component_2="VI"/>
<map_variables variable_1="h" variable_2="h"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="Heavyside_function" component_2="VNI"/>
<map_variables variable_1="h" variable_2="h"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="T" component_2="kinetic_parameters"/>
<map_variables variable_1="c" variable_2="c"/>
<map_variables variable_1="p" variable_2="p"/>
<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="I" component_2="kinetic_parameters"/>
<map_variables variable_1="k_" variable_2="k_"/>
<map_variables variable_1="delta" variable_2="delta"/>
<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="E1" component_2="kinetic_parameters"/>
<map_variables variable_1="b_" variable_2="b_"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="E2" component_2="kinetic_parameters"/>
<map_variables variable_1="b_" variable_2="b_"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="E3" component_2="kinetic_parameters"/>
<map_variables variable_1="b_" variable_2="b_"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="E4" component_2="kinetic_parameters"/>
<map_variables variable_1="b_" variable_2="b_"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="VI" component_2="kinetic_parameters"/>
<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="VNI" component_2="kinetic_parameters"/>
<map_variables variable_1="p" variable_2="p"/>
<map_variables variable_1="c" variable_2="c"/>
</connection>
</model>
