  This work studies fundamental questions regarding the optimal design of
antimicrobial treatment protocols, using standard pharmacodynamic and
pharmacokinetic mathematical models. We consider the problem of designing an
antimicrobial treatment schedule to achieve eradication of a microbial
infection, while minimizing the area under the time-concentration curve (AUC).
We first solve this problem under the assumption that an arbitrary
antimicrobial concentration profile may be chosen, and prove that the 'ideal'
concentration profile consists of a constant concentration over a finite time
duration, where explicit expressions for the optimal concentration and the time
duration are given in terms of the pharmacodynamic parameters. Since
antimicrobial concentration profiles are induced by a dosing schedule and the
antimicrobial pharmacokinetics, the ideal concentration profile is not strictly
feasible. We therefore also investigate the possibility of achieving outcomes
which are close to those provided by the ideal concentration profile,using a
bolus+continuous dosing schedule, which consists of a loading dose followed by
infusion of the antimicrobial at a constant rate. We explicitly find the
optimal bolus+continuous dosing schedule, and show that, for realistic
parameter ranges, this schedule achieves results which are nearly as efficient
as those attained by the ideal concentration profile. The optimality results
obtained here provide a baseline and reference point for comparison and
evaluation of antimicrobial treatment plans.
