Complex patterns of viral load decay under antiretroviral therapy: influence of pharmacokinetics and intracellular delay
Model Status
This is the original unchecked version of the model imported from the previous CellML model repository, 24-Jan-2006.
Model Structure
When treated with antiretroviral therapy, the plasma viral loads in HIV patients decline in three distinct phases:
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When the treatment is initially administered there is a 6 to 72 hour delay before the viral loads begin to decline;
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following this shoulder period viral load decline rapidly for about one week;
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finally, viral loads continue to decrease, but at a slower rate.
Mathematical models which describe this process have been developed. For more details please see:
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Nowak and Bangham, Modelling the Population Dynamics of Immune Responses to Persistent Viruses, 1996;
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Grossman et al., Modelling the Kinetics of Plasma Virus Following the Initiation of Therapy, 1998;
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Wodarz and Nowak, Modelling the Interaction Between HIV and the Immune System, 1999; and
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Bonhoeffer et al. Modelling the Population Dynamics of Virus Infected Cells, 2000.
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.
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 Perelson et al. (see the figure 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 and ).
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 ).
The complete original paper reference is cited below:
Complex patterns of viral load decay under antiretroviral therapy: influence of pharmacokinetics and intracelllar delay, Narendra M. Dixit and Alan S. Perelson, 2004, Journal of Theoretical Biology , 226, 95-109. (Full text (HTML) and PDF versions of the article are available on the Journal of Theoretical Biology website.) PubMed ID: 14637059
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Schematic summary of the dynamics of HIV-1 infection in vivo. This model is based on that published by Perelson et al. in 1996. |
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Pharmacokinetics - the two compartment model for protease inhibitors. |
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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. |