Analysis of information content of pharmacokinetic data using generalized sensitivity functions

Abstract

Generalized Sensitivity Functions (GSF) have been recently introduced to overcome the limitation of traditional sensitivity analysis to reveal the information content about estimated model parameters of observations collected during an experiment. This aspect is relevant in mathematical modelling of physiological systems because understanding how the estimation of individual model parameters is related to observed system output patterns gives indications about the effective role of parameters in describing different physiological processes. GSF functions have been initially proposed with reference to continuous-time or frequently sampled data. In this study the common situation encountered in pharmacokinetic (PK) and metabolic studies of discrete-time, sparse data is considered. In this case GSF become staircase functions with step changes at each new data point, and with zero initial condition and final unit value after all data have been collected. The most informative data for a particular parameter are those that produce a major variation in the transition from 0 to 1 of the corresponding GSF. Correlation between parameter estimates causes nonmonotonic oscillatory patterns in GSF. The authors' results show that GSF are a useful tool in the analysis of PK data.