Structural Identifiability of PBPK Models: Practical Consequences for Modeling Strategies and Study Designs

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Abstract
Physiologically based pharmacokinetic (PBPK) models usually contain unknown parameters that need to be estimated by calibration to concentration-time profiles from in vivo experiments. However, even with error-free data, the number of parameters that can be estimated in this way is limited, depending on the particular situation. This paper introduces the concept of structural identifiability of a model, a requirement to make the estimation of parameters by calibration a meaningful undertaking. We briefly discuss the techniques-available from systems analysis-for examining the identifiability of models. Two conditions of uniqueness are involved, one relating to the model's equations and its parameters, the other to the number of available observations in time. The assessment of the first uniqueness condition involves rather tedious matrix algebra, requiring the appropriate mathematical expertise. We therefore give some general results for a particular class of PBPK models, indicating in what situations the first uniqueness condition either holds or does not. The assessment of the second uniqueness condition does not require specialized skills, and the minimum number of observations in time necessary can be easily determined for any particular situation. The practical implications for both modeling strategies and experimental protocols are discussed.