Volume of Distribution at Steady State for a Linear Pharmacokinetic System with Peripheral Elimination

Abstract

The problem of finding the steady-state volume of distribution Vss for a linear pharmacokinetic system with peripheral drug elimination is considered. A commonly used equation Vss = (D/AUC)*MRT is applicable only for the systems with central (plasma) drug elimination. The following equation, Vss = (D/AUC)*MRTint, was obtained, where AUC is the commonly calculated area under the time curve of the total drug concentration in plasma after intravenous (iv) administration of bolus drug dose, D, and MRTint is the intrinsic mean residence time, which is the average time the drug spends in the body (system) after entering the systemic circulation (plasma). The value of MRTint cannot be found from a drug plasma concentration profile after an iv bolus drug input if a peripheral drug exit occurs. The obtained equation does not contain the assumption of an immediate equilibrium of protein and tissue binding in plasma and organs, and thus incorporates the rates of all possible reactions. If drug exits the system only through central compartment (plasma) and there is an instant equilibrium between bound and unbound drug fractions in plasma, then MRTint becomes equal to MRT = AUMC/AUC, which is calculated using the time course of the total drug concentration in plasma after an iv bolus injection. Thus, the obtained equation coincides with the traditional one, Vss = (D/AUC)*MRT, if the assumptions for validity of this equation are met. Experimental methods for determining the steady-state volume of distribution and MRTint, as well as the problem of determining whether peripheral drug elimination occurs, are considered. The equation for calculation of the tissue–plasma partition coefficient with the account of peripheral elimination is obtained. The difference between traditionally calculated Vss = (D/AUC)*MRT and the true value given by (D/AUC)*MRTint is discussed. © 2004 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 93:1628–1640, 2004