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Optimizing antimicrobial treatment schedules: some fundamental analytical results

Guy Katriel
Mar 2023
摘要
This work studies fundamental questions regarding the optimal design ofantimicrobial treatment protocols, using standard pharmacodynamic andpharmacokinetic mathematical models. We consider the problem of designing anantimicrobial treatment schedule to achieve eradication of a microbialinfection, while minimizing the area under the time-concentration curve (AUC).We first solve this problem under the assumption that an arbitraryantimicrobial concentration profile may be chosen, and prove that the 'ideal'concentration profile consists of a constant concentration over a finite timeduration, where explicit expressions for the optimal concentration and the timeduration are given in terms of the pharmacodynamic parameters. Sinceantimicrobial concentration profiles are induced by a dosing schedule and theantimicrobial pharmacokinetics, the ideal concentration profile is not strictlyfeasible. We therefore also investigate the possibility of achieving outcomeswhich are close to those provided by the ideal concentration profile,using abolus+continuous dosing schedule, which consists of a loading dose followed byinfusion of the antimicrobial at a constant rate. We explicitly find theoptimal bolus+continuous dosing schedule, and show that, for realisticparameter ranges, this schedule achieves results which are nearly as efficientas those attained by the ideal concentration profile. The optimality resultsobtained here provide a baseline and reference point for comparison andevaluation of antimicrobial treatment plans.
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