Stochastic Chiral Pharmacokinetics: Dynamics with Dual Randomized Dosing Regimens

Medication non-adherence is recognized as a critical determinant of therapeutic efficacy and safety. However, its specific impact on the concentration fluctuations of chiral drugs remains poorly understood. By incorporating dual stochasticity in dosing intervals and dosages, we developed a stochastic pharmacokinetic model for chiral drugs comprising bio-active and bio-inactive enantiomers under multiple intravenous bolus administrations. Utilizing characteristic functions and second-type Volterra integral equations, we derived explicit expressions for the expectation and variance of both the active moiety and total measured concentrations, as well as their discrepancy. Moreover, leveraging Kesten theorem and ergodic theory, the existence and the geometric ergodicity of the stationary probability distribution were mathematically demonstrated. Taking ibuprofen as a case study, we simulated various medication non-adherence scenarios to quantify the enantiomeric randomness. The results demonstrated that stochastic concentrations not only cause significant deviation from the ideal levels under perfect adherence, but also induce non-negligible discrepancy between the effective and total measured concentrations. These findings of the work provide a rigorous theoretical guidance for the characterization of two enantiomers variability of chiral drugs induced by medication non-adherence, offering new insights for enhancing therapeutic efficacy and safety.