二室开放身体模型中半衰期（t1/2）与平均驻留时间（MRT）之间的关系。

Sobol Eyal, Bialer Meir

Department of Pharmaceutics, School of Pharmacy, Faculty of Medicine, The Hebrew University of Jerusalem, Jerusalem, Israel.

Biopharm Drug Dispos. 2004 May;25(4):157-62. doi: 10.1002/bdd.396.

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(-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.

原理

在静脉注射给药后的单室模型中，药物的平均驻留时间（MRT）总是大于其半衰期（t(1/2)）。然而，静脉注射给药后，药物血浆浓度（C）与时间（t）的关系最好用双室模型或双指数方程来描述：C = Ae^(-αt) + Be^(-βt)，其中A和B是浓度单位系数，α和β是指数系数。双室模型中t(1/2)与MRT之间的关系尚未得到探讨，目前尚不清楚在该模型中MRT是否也总是大于t(1/2)。

方法

在本文中，已经推导了新的方程，用于描述静脉推注、静脉输注（零级输入）和口服给药（一级输入）后双室模型中终末t(1/2)（或t(1/2β)）与MRT之间的关系。

结果

已经推导了一个临界值（CV），其等于(1 - ln2)与(1 - β/α)的商（CV = (1 - ln2)/(1 - β/α) = 0.307/(1 - β/α)），并与双室方程第一个指数项相关的药物消除分数（f(1)）或AUC（AUC - C与t曲线下面积）进行了比较。静脉推注后，CV的范围在最小值0.307(1 - ln2)到无穷大之间。只要f(1) < CV，MRT > t(1/2)，反之亦然，当f(1) = CV时，则MRT = t(1/2)。静脉输注和口服给药后，CV方程的分母不变，但其分子分别增加到(0.307 + βT/2)（T为输注持续时间）和(0.307 + β/ka)（ka为吸收速率常数）。给出了各种药物的例子。

结论

对于静脉推注后呈现双室处置动力学的每种药物，可以得出以下结论：（a）当f(1) < 0.307时，f(1) < CV，因此，MRT > t(1/2)。（b）当β/α > ln2时，CV > 1 > f(1)，因此，MRT > t(1/2)。（c）当ln2 > β/α > (ln4 - 1)时，1 > CV > 0.5，因此，为使t(1/2) > MRT，f(1)必须大于其互补分数f(2)（f(1) > f(2)）。（d）当β/α < (ln4 - 1)时，即使f(2) > f(1)，只要f(1) > CV，就有可能t(1/2) > MRT。（e）随着β接近α，CV接近其最大值（无穷大），因此，MRT > t(1/2)的可能性增加。（f）与α相比，β变得越小，β/α接近零，分母接近1，因此，CV达到其最小值，t(1/2) > MRT的可能性增加。（g）零级和一级输入后，与静脉推注相比，MRT增加，CV也增加，因此，MRT > t(1/2)的可能性增加。