Depot-central synchronization of a pharmacokinetic model with capacity-limited saturable absorption

Nonlinear drug absorption, driven by saturable transport or enzyme-mediated processes, significantly impacts drug disposition, yet its theoretical framework remains underdeveloped. This study investigates a one-compartment pharmacokinetic (PK) model featuring nonlinear saturable absorption and linear elimination under single- and multiple-dose regimens. We derive mathematical solutions for the concentration-time profiles in both scenarios. For multiple-dose administration, we identify a critical threshold where steady-state concentrations ([Formula: see text]) transition between constant and non-constant periodic solutions depending on the dosing regimen. Our analysis reveals that the Hill or Michaelis-Menten exponent α directly modulates oscillation amplitude, with higher values increasing plasma variability. Furthermore, we mathematically characterize key PK metrics, such as the Area Under the Concentration-time Curve (AUC) and the Fluctuation Index (FI), demonstrating that the relationship between single- and multiple-dose AUC is regimen-dependent, while the FI exhibits a dose-dependency that contrasts with classical first-order kinetics. These theoretical results are validated using clinical data for Cefatrizine. Overall, this work elucidates the intrinsic properties of nonlinear Hill-type or Michaelis-Menten absorption, providing a robust mathematical foundation for optimizing dosage regimen design.