Optimal drug dosing via application of the Contraction Mapping Theorem

The problem of determining an oral dose, or schedule of oral doses, that gives rise to an arbitrary area-under-curve or to points on the time-series for a variable of interest in a drug kinetics model is considered. These two measures are considered as surrogates for the particular drug response to the dose. The approach taken is to formulate the problem as a fixed point one to which a version of the Contraction Mapping Theorem can be applied. The results, illustrated for a model for the anti-cancer agent topotecan, demonstrate the applicability of the approach.