Stochastic interpretation of linear pharmacokinetics: a linear system analysis approach

Area of Science:

• Pharmacokinetics and Pharmacodynamics
• Stochastic Modeling
• Systems Biology

Background:

• Linear drug disposition is typically defined by the superposition principle.
• This principle is molecularly explained by stochastic, independent kinetic behavior of drug molecules.
• Current stochastic approaches often rely on first-order microscopic transfer rate constants (Kij).

Purpose of the Study:

• To present a more general stochastic modeling approach for drug disposition.
• To differentiate drug disposition into elimination and distribution components using stochastic principles.
• To formulate a stochastic independent molecule (SIM) model within the disposition decomposition analysis (DDA) framework.

Main Methods:

• Employed a linear system analysis approach without assuming first-order rate constants.
• Utilized disposition decomposition analysis (DDA) to partition disposition kinetics into homogeneous and heterogeneous spaces.
• Formulated a stochastic independent molecule (SIM) model to isolate elementary stochastic building blocks.

Main Results:

• Demonstrated relationships between stochastic building blocks and mean time parameters.
• Introduced residence probability functions and drug delivery probability functions.
• Showcased practical calculations and examples using data from several drugs.

Conclusions:

• The proposed stochastic modeling approach offers a more general framework than traditional pharmacokinetic models.
• The SIM-DDA model provides intrinsic characterization of drug disposition and absorption kinetics.
• The approach extends kinetic bioavailability concepts into a stochastic realm using transit time principles.