Determinants of Biological Half-Lives and Terminal Slopes in Physiologically Based Pharmacokinetic Systems: Assessment of Limiting Conditions.

In pharmacokinetic (PK) analyses, the biological half-life T1/2 is usually determined in the terminal phase after drug administration, which is readily calculated from the relationship T1/2 = ln2/λz where λz is the terminal-phase slope obtainable from non-compartmental analysis (NCA). Since kinetic understanding of λz has been limited to the theory of a one-compartment model, this study seeks kinetic determinants of λz in more complex plasma concentration-time profiles. We utilized physiologically based pharmacokinetic (PBPK) systems that are consistent with the assumptions of NCA (e.g., linear PK and elimination occurring from plasma) to interrelate λz and disposition kinetic parameters of PBPK models. In a mammillary form of PBPK models, the two boundary conditions of λz are the inverses of the mean residence time in the body (1/MRTB = CL/VSS) and the mean transit time through the kinetically largest tissue (1/MTTmax = QTfdRb/VTKp). Importantly, the limiting conditions of λz between 1/MRTB and 1/MTTmax are dependent on a simple product MRTBλz (Pdet) and a simple ratio MTTmax/MRTB (Kdet), leading to introduction of the unitless product-ratio plot for determination of the limiting condition of λz in linear PK. We found that the MRTBλz value of 0.5 serves as a practical threshold determining whether λz is more closely associated with 1/MRTB or 1/MTTmax. The current theory was applied for assessment of the terminal slope λz for observed PK data of various compounds in man and rat.