Regulated feedback networks with degradation

Abstract

Pharmacokinetic and pharmacodynamic (PK/PD)-models describe and predict the time course of drug effects resulting from a certain dosage administered to an organism. PK/PD models benefit all phases of preclinical and clinical drug development. Their wider application in clinical therapy is to determine the specific dosage for a patient. In this thesis, we review several PK/PD models and investigate the time-to-peak, T, of the models. We state and prove a theorem about the uniqueness of T. The theorem considers PK/PD modes which are linear and nonlinear in the response variable. We show that if the forcing function and the response function satisfy some conditions, then there exists only one peak in the response variable. We apply this theorem to several PK/PD models which have a unique T and show that the condition of the theorem were satisfied. The theorem is also used to investigate how T changes with respect to drug dosage D for the turnover models considered.