Mathematical comparison between volume of distribution (V) and volume of distribution at steady-state (V_SS) utilizing model-indepent approach

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.