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−ln2) and (1−β/α) (CV=(1−ln2)/(1−β/α)=0.307/(1−β/α)) has been derived and was compared with the fraction ( f 1 ) of drug elimination or AUC (AUC‐area under C vs t curve) associated with the first exponential term of the two‐compartment equation (f 1 =A/α/AUC). Following i.v. bolus, CV ranges between a minimal value of 0.307 (1−ln2) and infinity. As long as f 1 t 1/2 and vice versa, and when f 1 =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) (T‐infusion 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 f 1 <0.307, then f 1 t 1/2 . (b) When β/α>ln2, then CV>1>f 1 and thus , MRT>t 1/2 . (c) When ln2>β/α>(ln4−1), then 1>CV>0.5 and thus, in order for t 1/2 >MRT, f 1 has to be greater than its complementary fraction f 2 (f 1 >f 2 ). (d) When β/α<(ln4−1), it is possible that t 1/2 >MRT even when f 2 >f 1 , as long as f 1 >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. Copyright © 2004 John Wiley & Sons, Ltd.