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 a standard shooting method for dynamic optimization problems.
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Periodic operation has the potential to provide significantly better performance over optimum steady state for some systems, as is demonstrated for the drug delivery application here. In general, this is feasible when there are admissible regions of the state space away from the steady-state manifold with a favorable objective function value and by suitable forcing of the dynamics of the system, these regions become accessible and enable a better time-average performance. The vast literature on optimal periodic control reveals a gap in our understanding of the physical mechanisms which allow an advantage to be gained by periodic control. We hope that the present work will inspire further research in this direction. This research was supported in part by the National Science Foundation.
- Differential flatness
- Drug delivery
- Optimal periodic control