Dosage regimen calculations with optimal control theory

In clinical pharmacokinetics, dosage regimen calculation involves determination of either: (1) the drug amount to be administered according to a set time schedule, or (2) the time schedule to be used for appropriate drug amounts. The goal is to guarantee that the time profile of circulating drug levels is between the thresholds of toxicity and efficacy. For the first case, solutions are obtained by using the property of linearity when it holds. Herein, we present several results concerning the second case. The optimal control theory allows determination of switching times between the minimal and maximal input rates in order to ensure the fastest transition from an initial state to the therapeutic levels. Fundamental results are reported and the approach is developed for drugs administered by intravenous infusion. By means of the phase trajectories, general graphical rules are presented to design the optimal control and to determine the reachable areas. A numerical example is given, comparisons of the method with others are attempted and potential developments are pointed out.