I. Gueorguieva, L. Aarons, T. Rodgers and M. Rowland
Centre for Applied Pharmacokinetic Research, School of Pharmacy and Pharmaceutical Sciences, University of Manchester, U.K.
Objective: To suggest optimal sampling times for an iv bolus experiment to study the tissue disposition kinetics of eight beta-blockers in rat.
Methods: A tissue perfusion-rate limited whole body physiologically based (WBPBPK) model was assumed to predict beta-blocker disposition. We aim to plan experiments for efficient estimation of drug- dependent parameters (tissue-to-blood partition coefficients) by employing a D- optimal design criterion. This criterion minimises the volume of the joint confidence region by maximising the determinant of the Fisher information matrix (FIM) (inverse of variance-covariance matrix). It was further assumed that measurements made at distinct times are independent, but measurements made of each drug tissue concentrations are correlated with a constant variance- covariance matrix. These variance-covariance matrices of response for two of the eight beta-blockers were available from a previous iv bolus study. Initial parameter estimates were also obtained from a previous experiment carried out under steady-state conditions. As the assumptions for homoscedasticity and normality of the residuals are often violated in mechanistic models this was taken into account when designing the experiment. In this multivariate response (WBPBPK) model, model parameters were shared between response components. Additionally, the beta-blockers are intended to be cassette dosed and hence the same design needs to be applied to all the drugs in the same cassette. This leads to a compromise design among the separate drug’s optimal sampling times. To determine the D-optimal design the determinant of the FIM has to be maximised over the whole design space. Unfortunately the surface of this determinant is very convoluted which places additional requirements on any optimiser. The selection of an appropriate optimiser involved comparison of the performances of several optimisation methods (downhill simplex, simulated annealing, adaptive random search, Fedorov) to a number of simpler pharmacokinetic models, including a multivariate response for a parent drug and metabolite.
Results: A hybrid scheme consisting of simulated annealing followed by downhill simplex performed the most consistently well. Using this optimisation procedure D-optimal sampling times for each of the beta-blockers were obtained. These were compared to several practically feasible designs and D-efficiency was computed. Average efficiencies of the cassette for each of the practical designs were compared. Based on that, the most efficient design was suggested for implementation.
Conclusions: The proposed hybrid optimisation scheme, although involving high computational costs, proved to be a robust and efficient approach.This technique for multivariate response optimal design can be readily implemented in other similar situations, such as parent drug and metabolites and pharmacokinetic/pharmacodynamic models.
References: Draper and Hunter (1966) Biometrika 53: 525- 533.
Corana (1987) ACM Transactions on mathematical software 13(3): 262-280.
Reference: PAGE 12 () Abstr 400 [www.page-meeting.org/?abstract=400]
Poster: poster