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Incorporating Uncertainty and Variability in the Physiological Parameters of a PBPK Model

S. Gisbert, I. Gueorguieva, G. Graham, L. Aarons

Centre for Applied Pharmacokinetic Research, University of Manchester

Background: PBPK models are used to scale animal PK to man. However, using average parameters, these models only give rise to mean predictions. As well as the mean result it is important to estimate the variability in predicted concentrations that arises from the existing uncertainty and variability in the model parameters [1]. The parameters of a PBPK model can be described as being either drug dependent (fu, Clint and Kpu) or physiological (tissue volumes and flow rates). Although some work has been done on assessing the contribution of the variability of the drug dependant parameters to the PK variability, little work have been done on the contribution of the uncertainty and variability in the physiological parameters.

Aim: To incorporate uncertainty and variability in physiological parameters taking into account the relationship between tissue volumes and their corresponding flow rates together with constraints for body weight and cardiac output, respectively.

Methods: We initially developed a PBPK model for diazepam in rats. The uncertainty and variability in tissue volumes was assumed to follow a truncated Dirichlet distribution [2, 3]. The flow rates were then functionally related to the volumes. The model was used to predict the variability in human PK. The PBPK analyses were implemented in MATLAB 6.1.

Results and discussion: The incorporation of uncertainty and variability in the physiological parameters accounted for the variability seen in the initial distribution phase, which was not described by the drug dependent parameters.

[1]: T. Yates. Predicting Physiological Variability and their Interaction through Interspecies Scaling. Centre for Applied Pharmacokinetic Research. University of Manchester, UK. Annual report 2001.
[2]: D. Farrar, B. Allen, K. Crump and A. Shipp. Evaluation of uncertainty in input parameters to pharmacokinetic models and the resulting uncertainty in output. Toxicology Letters, 49:371-385, 1989.
[3]: D. Krewski, Y. Wang, S. Bartlett and K. Krishnan. Uncertainty, variability, and sensitivity analysis in physiological pharmacokinetic models. Journal of Biopharmaceutical Statistics, 5(3): 245-271, 1995.