Critical analysis of the discrepancy between V_β and V_ss for drugs exhibiting different two-compartment disposition profiles

It is well known that in the two-compartment open body model the values of apparent volume of distribution (V_β) and volume of distribution at steady state (V_ss) are never identical. There are at least two conditions when V_β significantly overestimates V_ss. The first is when most of a drug is eliminated relatively rapidly but a small fraction of the dose persists and gives rise to an extremely long half-life. The second is when a drug is rapidly cleared from the central compartment with a short half-life. The primary purpose of the current paper was to investigate how different two-compartment disposition profiles affect the magnitude of difference between V_β and V_ss. Novel equations have been developed that relate the V_β/V_ss ratio to f₁ (fraction of drug elimination associated with the distributive phase) and to β/α (ratio of the exponential coefficients). This paper demonstrates mathematically that an increasing value of f₁ is associated with a greater divergence between V_β and V_ss. A similar relationship was also found for the divergence between the terminal half-life (t_1/2β) and the mean residence time (MRT). An increase in the β/α ratio results in a substantial decrease of this discrepancy and provides a maximal possible value, or an upper limit to the V_β/V_ss ratio. The newly derived equations along with their graphical presentation may serve as an excellent predictive tool for checking the accuracy of the experimentally obtained values of V_β and V_ss.