Volume of Distribution at Pseudo‐distribution Equilibrium: Relationship between Physiologically Based Pharmacokinetic Parameters and Terminal Half‐life of Drug

The terminal half-life, t 1/2, is proportional to the ratio of the volume of distribution at pseudo-equilibrium (Vdβ) and systemic clearance, when the plasma concentration-time profile of a drug exhibits a biphasic decline. As there is little known about the effects of various physiologically based pharmacokinetic parameters of the drug on t 1/2, due to a limited understanding of the relationship between Vdβ and those parameters, it was considered that Vdβ, a ratio between clearance and slope of terminal phase, can only serve as a proportionality constant to relate plasma concentration to the total amount of drug present in the body during the terminal phase, and it is difficult to make an explicit description of the relationship between Vdβ and physiologically based pharmacokinetic parameters, other than by numerical approximation. A simple equation describing Vdβ as a function of elimination (CL) and distributional (CLd) clearances, volume of distribution in the central compartment (Vc) and volume of distribution at steady state (Vdss) was derived for a two-compartment model. The equation indicated that Vdβ and Vdss of drug can be significantly different, when there is a large difference between CL and CLd, or Vc and Vdss. Significant differences in t 1/2 of drugs exhibiting similar CL and Vdss, therefore, could be due to differences in CLd or Vc between those drugs. The new equations can be useful for a better understanding of various pharmacokinetic parameters important in determining t 1/2 values.