Stochastic interpretation of linear pharmacokinetics: a linear system analysis approach.
Linear drug disposition is most generally defined in terms of the superposition principle. This principle is explained on the molecular level by probability principles involving stochastic, independent kinetic behavior of drug molecules. A stochastic modeling approach is presented that is more general than pharmacokinetic models typically employed in stochastic approaches. First-order microscopic transfer rate constants (Kij) are not employed or assumed in the analysis. The approach is a linear system analysis approach that makes use of the simplest possible kinetic structure that enables a differentiation of the drug disposition into elimination and distribution components. This is done by applying stochastic principles in the context of the disposition decomposition analysis (DDA). The DDA approach in its linear form is a generalization of linear pharmacokinetic systems that assume a homogeneous sampling space. Disposition kinetics is partitioned into two kinetic spaces, a homogeneous sampling space, and a heterogeneous peripheral kinetic space. A structure differentiation beyond this is difficult to justify in common situations when only the parent drug is determined from a single iv sampling site. A stochastic independent molecule (SIM) model is formulated in the structure context of DDA. The model is employed to identify core relationships by isolating elementary stochastic building blocks of the disposition kinetics and absorption kinetics. It is shown how the stochastic building blocks of the SIM-DDA model are related to various mean time parameters. Residence probability functions and drug delivery probability functions provided by the approach appear useful for extending kinetic bioavailability concepts into a purely stochastic realm. The emphasis on transit time concepts enables a kinetic differentiation and a more intrinsic characterization than possible by the use of common residence time principles. Relationships are presented that link stochastic and kinetic elements. Formulas are presented for the practical calculations of the mean time parameters and stochastic functions presented. Practical examples are given of the concepts presented using data from several drugs.
Veng-Pedersen
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College of Pharmacy, University of Iowa, Iowa City 52242.
D001682:Biological Availability; D002927:Cimetidine / Q000493:pharmacokinetics; D005772:Gastrointestinal Transit; D006801:Humans; D008954:Models, Biological; D010599:Pharmacokinetics; D012984:Software
D002927:Cimetidine