Optimal design of dose and drug pharmacokinetic characteristics to achieve the desired pharmacodynamic profile in repeated drug dosing

Oral drug therapy requires achieving a delicate balance between therapeutic efficacy and patient safety, yet current dosing strategies often rely on empirical trial-and-error methods that overlook the complex nonlinear dynamic nature of drug behavior in the human body. Conventional pharmacokinetic/pharmacodynamic (PK-PD) approaches provide valuable insights but lack a systematic method for designing dose sequences and formulations that achieve an optimal therapeutic response. This work introduces a structured optimization framework that combines PK-PD modeling, impulsive dosing concepts, and nonlinear optimization to determine optimal repeated oral dosing regimens. We model each orally administered dose as an impulsive input in a linear compartmental PK system and couple the resulting drug concentration profile with a nonlinear Hill-type PD model. To enable efficient optimization, we derive sensitivity functions describing how the therapeutic effect depends on dose size and adjustable drug-formulation parameters, allowing to construct the Jacobian required by the Gauss-Newton nonlinear least-squares algorithm. The proposed method jointly optimizes dose magnitude and formulation-dependent liberation (release) rate to match a clinically meaningful therapeutic effect trajectory. Using a four-compartment pharmacokinetic model, we demonstrate in silico that the method achieves rapid onset, stable long-term therapeutic effect, and reduced fluctuations of the therapeutic effect across repeated dosing cycles.