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 1/2 is usually determined in the terminal phase after drug administration, which is readily calculated from the relationship T 1/2 = ln2/ λ z where λ z is the terminal-phase slope obtainable from non-compartmental analysis (NCA). Since kinetic understanding of λ z has been limited to the theory of a one-compartment model, this study seeks kinetic determinants of λ z 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 z and disposition kinetic parameters of PBPK models. In a mammillary form of PBPK models, the two boundary conditions of λ z are the inverses of the mean residence time in the body (1/ MRT B = CL / V SS ) and the mean transit time through the kinetically largest tissue (1/ MTT max = Q T f d R b / V T K p ). Importantly, the limiting conditions of λ z between 1/ MRT B and 1/ MTT max are dependent on a simple product MRT B λ z ( P det ) and a simple ratio MTT max / MRT B ( K det ), leading to introduction of the unitless product-ratio plot for determination of the limiting condition of λ z in linear PK. We found that the MRT B λ z value of 0.5 serves as a practical threshold determining whether λ z is more closely associated with 1/ MRT B or 1/ MTT max . The current theory was applied for assessment of the terminal slope λ z for observed PK data of various compounds in man and rat. Graphical abstract