The operational multiple dosing half-life: a key to defining drug accumulation in patients and to designing extended release dosage forms

Abstract

Half-life (t (1/2)) is the oldest but least well understood pharmacokinetic parameter, because most definitions are related to hypothetical 1-compartment body models that don't describe most drugs in humans. Alternatively, terminal half-life (t (1/2,z)) is utilized as the single defining t (1/2) for most drugs. However, accumulation at steady state may be markedly over predicted utilizing t (1/2, z). An apparent multiple dosing half-life (t (1/2, app)) was determined from peak and trough steady-state ratios and found to be significantly less than reported terminal t (1/2)s for eight orally dosed drugs with t (1/2,z) values longer than one day. We define a new parameter, "operational multiple dosing half-life" (t (1/2, op)), as equal to the dosing interval at steady-state where the maximum concentration at steady-state is twice the maximum concentration found for the first dose. We demonstrate for diazepam that the well-accepted concept that t (1/2,z) representing the great majority of the AUC will govern accumulation can be incorrect. Using oral diazepam, we demonstrate that t (1/2, op) is remarkably sensitive to the absorption t (1/2), even when this absorption t (1/2) is much less than t (1/2,z,) and describe the relevance of this in designing extended release dosage forms. The t (1/2, op) is compared with previously proposed half-lives for predicting accumulation.

Fig. 1

A The ratio (black diamonds) of maximum to minimum concentration at steady-state (C_max,ss/C_min,ss) and the ratio (grey squares) of maximum concentration at steady-state to the maximum concentration for a single dose (C_max,ss/C_max,sd) calculated for 4 h, 8 h, 12 h and 24 h dosing intervals for two-compartment i.v. doses of diazepam. B The ratio (black diamonds) of maximum to minimum concentration at steady-state (C_max,ss/C_min,ss) and the ratio (grey squares) of maximum concentration at steady-state to the maximum concentration ratio for a single dose (C_max,ss/C_max,sd) calculated for 4 h, 8 h, 12 h and 24 h dosing intervals for two-compartment oral data using k_a value of 1.92 h⁻¹ (14).