PHYSIOLOGICALLY-BASED PHARMACOKINETIC MODELING OF A HOMOLOGOUS SERIESOF BARBITURATES IN THE RAT - A SENSITIVITY ANALYSIS

Sensitivity analysis studies the effects of the inherent variability a nd uncertainty in model parameters on the model outputs a,td may be a useful tool at all stages of the pharmacokinetic modeling process. The present study examined the sensitivity of a whole-body physiologicall y based pharmacokinetic (PBPK) model for the distribution kinetics of nine 5-n-alkyl-5-ethyl barbituric acids in arterial blood and 14 tissu es (lung, liver, kidney,, stomach, pancreas, spleen, gut, muscle, adip ose, skin, bone, heart, brain, testes) after iv bolus administration t o rats. The aims were to obtain new insights into the model used, to r ank the model parameters involved according to their impact on the mod el outputs and to study the changes in the sensitivity induced by the increase in the lipophilicity of the homologues on ascending the serie s. Two approaches for sensitivity analysis have been implemented. The first, based on the Matrix Perturbation Theory, uses a sensitivity ind ex defined as the normalized sensitivity of the 2-norm of the model co mpartmental matrix to perturbations in its entries. The second approac h uses the traditional definition of the normalized sensitivity functi on as the relative change in a model stare (a tissue concentration) co rresponding to a relative change in a model parameter. Autosensitivity has been defined as sensitivity of a state to any of its parameters; cross-sensitivity as the sensitivity of a state to any other states' p arameters. Using the two approaches, the sensitivity of representative tissue concentrations (lung, liver, kidney, stomach, gut, adipose, he art, and brain) to the following model parameters: tissue-to-unbound p lasma partition coefficients, tissue blood flows, unbound renal and in trinsic hepatic clearance, permeability surface area product of the br ain, have been analyzed. Both the tissues and the parameters were rank ed according to their sensitivity and impact. The following general co nclusions were drawn: (i) the overall sensitivity of the system to all parameters involved is small due to the weak connectivity of the syst em structure; (ii) the time course of both the auto- and cross-sensiti vity functions for all tissues depends on the dynamics of the tissues themselves, e.g., the higher the perfusion of a tissue, the higher are both its cross-sensitivity to other tissues' parameters and the cross -sensitivities of other tissues to its parameters; and (iii) with a fe w exceptions, there is not a marked influence of the lipophilicity of the homologues on either the pattern or the values of the sensitivity functions. The estimates of the sensitivity and the subsequent tissue and parameter rankings may be extended to other drugs, sharing the sam e common structure of the whole body PBPK model, and having similar mo del parameters. Results show also that the computationally simple Matr ix Perturbation Analysis should be used only when an initial idea abou t the sensitivity of a system is required. If comprehensive informatio n regarding the sensitivity is needed, the numerically expensive Direc t Sensitivity Analysis should be used.