Determination of volume of distribution at steady state with complete consideration of the kinetics of protein and tissue binding in linear pharmacokinetics

The assumption of an instant equilibrium between bound and unbound drug fractions is commonly applied in pharmacokinetic calculations. The equation for the calculation of the steady-state volume of distribution V(ss) from the time curve of drug concentration in plasma after intravenous bolus dose administration, which does not assume an immediate equilibrium and thus incorporates dissociation and association rates of protein and tissue binding, is presented. The equation obtained V(ss) = (Dose/AUC)*MRT(u) looks like the traditional equation, but instead of mean residence time MRT calculated using the total drug concentration in plasma, it contains mean residence time MRT(u) calculated using the plasma concentration of the unbound drug. The equation connecting MRT(u) and MRT is derived. If an immediate equilibrium between bound and unbound drug fractions occurs, MRT(u) and MRT are the same, but in general, MRT(u) is always smaller than MRT. For drugs with high protein affinity and slow dissociation rate MRT(u) may be of an order of several hours smaller than MRT, so that V(ss) can be considerably overestimated in the traditional calculation.