Optimal experiment design with applications to Pharmacokinetic modeling

We study the problem of designing an input to a dynamical system that is optimal at estimating unknown parameters in the system’s model. We take the A and D optimality criteria on the Fisher Information Matrix associated with the estimation problem as our optimization objective. Our main motivation is the estimation of the physiological parameters that appear in pharmacokinetic dynamics using a relatively short set of measurements. In this context, model inputs correspond to the intravenous injection of drugs and input selection needs to consider safety constraints that include max-min instantaneous injection rates and total dosage amount. We divide the time interval available for the experiment into learning and optimization stages. We use the initial learning stage to obtain a preliminary estimate for the system’s model. Then we find an optimal input for the optimization stage so that we can improve upon this initial estimate.

I. INTRODUCTION

Learning system dynamics from measured data can be a significant challenge when long time series of measurements are difficult to obtain. This challenge is especially important in biology-related fields such as pharmacokinetics, where subject-to-subject variability is large and time-series of measurements can be difficult to collect. In such systems, it is crucial to maximize the information content of the limited data that can be collected.