The relationships between half-life (t_1/2) and mean residence time (MRT) in the two-compartment open body model

Rationale. In the one-compartment model following i.v. administration the mean residence time (MRT) of a drug is always greater than its half-life (t_1/2). However, following i.v. administration, drug plasma concentration (C) versus time (t) is best described by a two-compartment model or a two exponential equation: C = Ae^-αt + Be^-βt, where A and B are concentration unit-coefficients and α and β are exponential coefficients. The relationships between t_1/2 and MRT in the two-compartment model have not been explored and it is not clear whether in this model too MRT is always greater than t_1/2. Methods. In the current paper new equations have been developed that describe the relationships between the terminal t_1/2 (or t_1/2β) and MRT in the two-compartment model following administration of i.v. bolus, i.v. infusion (zero order input) and oral administration (first order input). Results. A critical value (CV) equals to the quotient of (1-ln 2) and (1-β/α) (CV = (1-ln 2)/(1-β/α)=0.307/(1-β /α)) has been derived and was compared with the fraction (f₁) of drug elimination or AUC (AUC-area under C vs t curve) associated with the first exponential term of the two-compartment equation (f₁=A/α/AUQ. Following i.v. bolus, CV ranges between a minimal value of 0.307 (1-ln 2) and infinity. As long as f₁ < CV, MRT > t_1/2 and vice versa, and when f₁=CV, then MRT=t_1/2. Following i.v. infusion and oral administration the denominator of the CV equation does not change but its numerator increases to (0.307 + βT/2) (Tinfusion duration) and (0.307 + β/ka) (ka-absorption rate constant), respectively. Examples of various drugs are provided. Conclusions. For every drug that after i.v. bolus shows two-compartment disposition kinetics the following conclusions can be drawn (a) When f₁ <0.307, then f₁ <CV and thus, MRT> t_1/2. (b) When β/α> ln 2, then CV > 1 > f₁ and thus, MRT > t_1/2. (c) When ln 2 > β/α > (ln 4-1), then 1> CV > 0.5 and thus, in order for t_1/2 > MRT, f₁ has to be greater than its complementary fraction f₂ (f₁ > f₂). (d) When α/α < (ln 4-1), it is possible that t_1/2 > MRT even when f₂ > f₁, as long as f₁ > CV. (e) As β gets closer to α, CV approaches its maximal value (infinity) and therefore, the chances of MRT > t_1/2 are growing. (f) As β becomes smaller compared with α, β/α approaches zero, the denominator approaches unity and consequently, CV gets its minimal value and thus, the chances of t_1/2 > MRT are growing. (g) Following zero and first order input MRT increases compared with i.v. bolus and so does CV and thus, the chances of MRT > t_1/2 are growing.