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Mathematical comparison between volume of distribution (V) and volume of distribution at steady‐state (V ss ) utilizing model‐independent approach
Author(s) -
Sobol Eyal,
Bialer Meir
Publication year - 2004
Publication title -
biopharmaceutics and drug disposition
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.419
H-Index - 58
eISSN - 1099-081X
pISSN - 0142-2782
DOI - 10.1002/bdd.372
Subject(s) - volume of distribution , mathematical model , distribution (mathematics) , constant (computer programming) , reaction rate constant , distribution volume , volume (thermodynamics) , thermodynamics , chemistry , mathematics , pharmacokinetics , kinetics , computer science , mathematical analysis , physics , statistics , bioinformatics , classical mechanics , biology , programming language
Pharmacokinetic textbooks state that the (apparent) volume of distribution based on drug concentration in plasma ( V or V β ) is always greater than the volume of distribution (apparent) under steady state conditions ( V ss ), but do not provide a general model‐independent mathematical proof. Wagner's mathematical comparison between V β and V ss is based on microscopic rate constants of either specific models and is restricted solely to the two‐compartment open body model. Nakashima and Benet utilizing a model‐dependent approach showed a mathematical relationship between V β and V ss for a multicompartment model, but again by using microscopic model constants. The limitation of these two above mentioned mathematical comparisons is the necessity of knowledge of the model's structure and its microscopic rate constants. The present article describes a new non‐compartmental, model‐independent, general mathematical proof for V β to be always greater than V ss . This new method does not require any knowledge of microscopical rate constants and is based solely on an exponentially decreasing function, which is the common way to describe drug disposition following i.v. bolus. Copyright © 2004 John Wiley & Sons, Ltd.