Characterization of drug efficacy regions based on dosage and frequency schedules.

This paper proposes a framework to study the drug effect at the molecular level in order to address the following question of current interest in the drug community: Given a fixed total delivered drug, which is better, frequent small or infrequent large drug dosages? A hybrid system model is proposed to link the drug's pharmacokinetic and pharmacodynamic information, and allows the drug effects for different dosages and treatment schedules to be compared. A hybrid model facilitates the modeling of continuous quantitative changes that leads to discrete transitions. An optimal dosage-frequency regimen and the necessary and sufficient conditions for the drug to be effective are obtained analytically when the drug is designed to control a target gene. Then, we extend the analysis to the case where the target gene is part of a genetic regulatory network. A crucial observation is that there exists a "sweet spot," defined as the "drug efficacy region (DER)" in this paper, for certain dosage and frequency arrangements given the total delivered drug. This paper quantifies the therapeutic benefits of dosage regimen lying within the DER. Simulations are performed using MATLAB/SIMULINK to validate the analytical results.