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 T is usually determined in the terminal phase after drug administration, which is readily calculated from the relationship T = ln2/λ where λ is the terminal-phase slope obtainable from non-compartmental analysis (NCA). Since kinetic understanding of λ has been limited to the theory of a one-compartment model, this study seeks kinetic determinants of λ 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 λ and disposition kinetic parameters of PBPK models. In a mammillary form of PBPK models, the two boundary conditions of λ are the inverses of the mean residence time in the body (1/MRT = CL/V) and the mean transit time through the kinetically largest tissue (1/MTT = QfR/VK). Importantly, the limiting conditions of λ between 1/MRT and 1/MTT are dependent on a simple product MRTλ (P) and a simple ratio MTT/MRT (K), leading to introduction of the unitless product-ratio plot for determination of the limiting condition of λ in linear PK. We found that the MRTλ value of 0.5 serves as a practical threshold determining whether λ is more closely associated with 1/MRT or 1/MTT. The current theory was applied for assessment of the terminal slope λ for observed PK data of various compounds in man and rat.