Optimal periodic control of a drug delivery system

Administration of certain drugs at a steady rate results in deterioration of drug effect, also known as drug tolerance. Periodic delivery is an attractive option for minimizing tolerance and maximizing the desired effect of such drugs. In this paper, periodic drug infusion strategies for maximizing a time averaged measure of drug effect are investigated. A simple pharmacokinetic-pharmacodynamic (PKPD) model of a system exhibiting tolerance is considered and optimal periodic control theory is employed. First, regions of PKPD parameter space in which periodic infusion provides a locally improved average effect compared to steady infusion are characterized using the so-called π test. Then, optimal drug delivery strategies, obtained using two different computational approaches, are presented for a representative set of parameter values, and insight is provided into the results. The first method, proposed by the authors, is based on the notion of differential flatness, while the second is based on the standard shooting method for dynamic optimization problems.