title: The relationships between half-life (t1/2) and mean residence time (MRT) in the two-compartment open body model.
abstract: BACKGROUND
  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(-alpha t)+Be(-beta t), where A and B are concentration unit-coefficients and alpha and beta 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(1/2 beta)) 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-beta/alpha) (CV=(1-ln2)/(1-beta/alpha)=0.307/(1-beta/alpha)) 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/alpha/AUC). Following i.v. bolus, CV ranges between a minimal value of 0.307 (1-ln2) and infinity. As long as f(1)<CV,MRT>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+beta T/2) (T-infusion duration) and (0.307+beta/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)<CV and thus, MRT>t(1/2). (b) When beta/alpha>ln2, then CV>1>f(1) and thus(,) MRT>t(1/2). (c) When ln2>beta/alpha>(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 beta/alpha<(ln4-1), it is possible that t(1/2)>MRT even when f(2)>f(1), as long as f(1)>CV. (e) As beta gets closer to alpha, CV approaches its maximal value (infinity) and therefore, the chances of MRT>t(1/2) are growing. (f) As beta becomes smaller compared with alpha, beta/alpha 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.
authors.affiliation: Department of Pharmaceutics, School of Pharmacy, Faculty of Medicine, The Hebrew University of Jerusalem, Jerusalem, Israel.
authors.forename: Eyal
authors.initials: E
authors.lastname: Sobol
authors.forename: Meir
authors.initials: M
authors.lastname: Bialer
mesh_terms: D006207:Half-Life; D008962:Models, Theoretical; D010599:Pharmacokinetics