Tothfalusi Laszlo, Endrenyi Laszlo
Semmelweis Medical University, Department of Pharmacodynamics, Budapest Hungary, H-1445 P.O.B. 370.
J Pharmacokinet Pharmacodyn. 2003 Oct;30(5):363-85. doi: 10.1023/b:jopa.0000008159.97748.09.
Following the oral administration of drugs, the plasma concentration generally reaches, in principle, a single, well-defined peak (Cmax) at the time of Tmax. A complication for the direct estimation of Cmax and Tmax is that measurements of concentrations are recorded only at discrete time points. Theoretical equations characterizing the population distribution of Cmax and Tmax are derived in relationship to the pharmacokinetic model, its parameters, their variabilities, and experimental errors. These equations can be solved by numerical integration. The resulting means, variances and other summary statistics of Cmax and Tmax are evaluated under various conditions involving single and multiple drug administrations. Results gained by the proposed numerical method agree closely with results gained by Monte-Carlo simulations. It is argued that the numerical method could be useful to study the statistical properties of the investigated measures and could, in some cases, provide a viable alternative to simulations. It is demonstrated that Cmax is estimated directly with positive bias, especially following repeated drug administrations. As a consequence, the recorded peak-trough fluctuation (PTF), measured in the steady state, can be excessively large (even by orders of magnitude) particularly when drug accumulation is high. These results have practical implications for the development of drugs and drug formulations.
口服给药后，血浆浓度原则上通常会在达峰时间（Tmax）达到一个单一、明确的峰值（Cmax）。直接估算Cmax和Tmax的一个复杂情况是，浓度测量仅在离散时间点进行记录。根据药代动力学模型、其参数、参数变异性以及实验误差，推导了表征Cmax和Tmax总体分布的理论方程。这些方程可通过数值积分求解。在涉及单次和多次给药的各种条件下，对所得的Cmax和Tmax的均值、方差及其他汇总统计量进行评估。所提出的数值方法得到的结果与蒙特卡洛模拟得到的结果非常吻合。有人认为，该数值方法对于研究所调查测量的统计特性可能有用，并且在某些情况下，可以为模拟提供可行的替代方法。结果表明，Cmax的直接估计存在正偏差，尤其是在重复给药后。因此，在稳态下测量的记录峰谷波动（PTF）可能会过大（甚至相差几个数量级），特别是当药物蓄积较高时。这些结果对药物和药物制剂的开发具有实际意义。
