Keller F, Czock D, Zellner D, Giehl M
Medical Department, University Hospital, Ulm, Germany.
Int J Clin Pharmacol Ther. 1998 Mar;36(3):168-75.
A pharmacodynamic parameter relating time-dependent changes of the effect with time-dependent changes of concentrations has yet to be developed. In pharmacokinetics, half-lives (T1/2kin) are used to describe the relation between concentration (C) and time (t). In pharmacodynamics, often the sigmoid Emax model and the Hill equation are used (E = Emax CH/(EC50H + CH)) to describe the relation between effect (E) and concentration (C). To describe the correlation between effect (E) and time (t), a pharmacodynamic half-life (T1/2dyn) could be estimated if the use of the term half-life is not restricted only to log-linear first order processes. To bisect the drug effect a variable time (t1-2 = t2-t1) will be required for this nonlinear process. The bisection of the effect (E2 = 1/2 E1) is associated with a decrease in concentrations (C2 = C1 exp(-0.693 t1-2/T1/2kin)). A mathematical relationship can be derived between pharmacodynamic half-life (T1/2dyn = t1-2) and pharmacokinetic half-life (T1/2dyn = T1/2kin (ln (1 + ln(a)/ln(2))/H ) with (a = (EC50H + C1H)/(EC50H + C2H)). For concentrations in the range of the EC50 value with the Hill coefficient (H = 1), the pharmacodynamic half-life will be 1.6-2.0 times the kinetic half-life (T1/2dyn < or = 2.0 T1/2kin). For high concentrations (C1 > EC50), the dynamic half-life will grow much longer than the kinetic half-life, consequently the effect of a drug will not increase but it will last longer. The pharmacodynamic half-life turns out to be a specific estimate for the effect time relation, being a concentration-dependent function of the kinetic half-life.
一个将效应随时间的变化与浓度随时间的变化联系起来的药效学参数尚未被开发出来。在药代动力学中，半衰期（T1/2kin）用于描述浓度（C）与时间（t）之间的关系。在药效学中，常使用S形Emax模型和希尔方程（E = Emax CH/(EC50H + CH)）来描述效应（E）与浓度（C）之间的关系。为了描述效应（E）与时间（t）之间的相关性，如果半衰期这一术语不限于对数线性一级过程，那么可以估计出药效学半衰期（T1/2dyn）。对于这个非线性过程，需要一个可变时间（t1-2 = t2 - t1）来平分药物效应。效应的平分（E2 = 1/2 E1）与浓度的降低（C2 = C1 exp(-0.693 t1-2/T1/2kin)）相关。可以推导出药效学半衰期（T1/2dyn = t1-2）与药代动力学半衰期（T1/2dyn = T1/2kin (ln (1 + ln(a)/ln(2))/H )之间的数学关系，其中（a = (EC50H + C1H)/(EC50H + C2H)）。对于希尔系数（H = 1）且浓度在EC50值范围内，药效学半衰期将是动力学半衰期的1.6 - 2.0倍（T1/2dyn ≤ 2.0 T1/2kin）。对于高浓度（C1 > EC50），动态半衰期将比动力学半衰期长得多，因此药物的效应不会增加但会持续更长时间。药效学半衰期结果是效应 - 时间关系的一个特定估计值，是动力学半衰期的浓度依赖性函数。
