Sensitivity Analysis of Pharmacokinetic and Pharmacodynamic Systems: I. A Structural Approach to Sensitivity Analysis of Physiologically Based Pharmacokinetic Models

Abstract

Based on a frequency response approach to the sensitivity analysis of pharmacokinetic models, the concept of structural sensitivity is introduced. The core of this concept is the factorization of the system sensitivity into two multipliers. The first one, called structural sensitivity index, has an analytical form, which depends solely on the structure and connectivity of the system and does not depend on the drug administered or the factor perturbed. The second multiplier, the parameter sensitivity index, depends on the drug properties, the tissue of interest and the parameter perturbed, but is largely independent of the structure of the system. The structural and parametric sensitivity indices can be evaluated and analyzed separately. The most important feature of the proposed approach is that the conclusions drawn from the analysis of the structural sensitivity index are valid across all mammalian species, as the latter share a common anatomical and physiological structure. The concept of structural sensitivity is illustrated on the commonly used structure of the whole body physiologically based pharmacokinetic models by showing that the factorization of the sensitivity carried out arises naturally from the mechanism of the distribution of perturbations throughout the organism. The concept of structural sensitivity has interesting practical implications. It enables the formal proof of relationships and facts that have been observed previously. Moreover, the conclusions drawn introduce in fact a ranking of the tissues or subsystems with respect to their impact on the model outputs. From this ranking, direct recommendations regarding the design of experiments for whole-body physiologically based pharmacokinetic models are derived.