Revisiting pharmacological concepts and quantitative techniques where nonlinearity and variability are critical

在复杂的生物系统中，可变性和非线性是决定药物命运的两个主要因素。由于缺乏测量和计算技术，临床药理学社区长期以来一直局限于线性确定性或简单的汇总统计方法。然而，目前的药物发现为这两个因素在药物动力学和动力学中的决定性作用提供了强有力的证据。在开发药物数学模型时忽略可变性和非线性，已被证明是产生偏离目标现象观察范围的有偏差预测的原因之一。二十多年前，随着群体药代动力学/药效学建模方法（非线性混合效应模型）的引入，这种情况得到了改变。为了描述患者群体中药物血浆浓度和治疗效果的演变，这种新方法成功地在以前由常微分方程定义的确定性环境中引入了不同水平的可变性，并为药理学的定量时代奠定了基础，在这个时代，数学正在获得更多的基础，数学家成为主要参与者之一。

Variability and nonlinearity are the two main factors that determine the drug fate in a complex biological system. Because of the paucity of measuring and computing techniques, the community of clinical pharmacology has long been restricted to linear deterministic or simple summary statistical methodologies. However, nowadays drug discovery provides strong evidence for the decisive roles of these two factors in drug kinetics and dynamics. Ignoring variability and nonlinearity when developing drug mathematical models, has been proved to be one reason producing biased predictions out of observed ranges of targeted phenomena. This situation has been changed with the introduction of the population pharmacokinetics/pharmacodynamics modeling approach (Nonlinear Mixed Effect Models) more than two decades ago. With the intention to describe the evolution of drug plasma concentrations and therapeutic effects in a patient population, this new approach successfully introduced different levels of variability within the previously deterministic context defined with ordinary differential equations, and set up the context for the quantitative era of pharmacology, where mathematics are gaining more ground and mathematicians becoming one of the principal actors.