On the volume of distribution at steady state and its relationship with two-compartmental models

The volume of distribution at steady state is considered to be one of the primary pharmacokinetic measurements obtained from in vivo experiments. This quantity is quite commonly calculated using moments of the observed concentration curve, the process being referred to as noncompartmental analysis. In this paper the underlying assumptions of noncompartmental analysis are analysed with regard to the observed behaviour of models with two compartments: one of which has elimination from the central compartment, the other from the peripheral tissue compartment. This is in order to clarify the relationship between volume of distribution and clearance. It is shown that these two models are indistinguishable from measurements in blood. Furthermore relationships between the parameter values for the two models are given so that they produce the same observed profile. Expressions are derived in a novel way that relates the volume of distribution to these model rate constants. The definitions of clearance and volume of distribution at steady state are investigated using several different mathematical techniques, demonstrating the consistency of the derived expressions. It is shown, in a manner that the authors believe is a new approach, that when the assumption of central elimination does not apply, noncompartmental analysis will under estimate the volume of distribution, whereas clearance remains unchanged. This is compared quantitatively with respect to the volume predicted where central elimination holds, and is a result of an extended mean residence time.