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

变异性和非线性是决定药物在复杂生物系统中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，如今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，这种情况已经改变。为了描述患者人群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用常微分方程定义的确定性背景下引入了不同水平的变异性，并为药理学的定量时代建立了背景，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。 面对这一现实，许多药理学的概念和方法开发的线性和确定性的原则，应重新审视和数学修订考虑到药物相关的非线性和可变性。随着确定的三个轴，药物药代动力学的非线性，药物摄入量和治疗结果的变异性，以及在变异性背景下改善药物评价问题，目前的研究计划将有助于加强这种定量趋势的药理学，其中数学是在中心位置，但也受益于新提出的问题。目前NSERC发现补助金的贡献将用于研究这一方向的各个方面。

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. Facing this reality, many pharmacological concepts and methods developed using linear and deterministic principles should be revisited and mathematically revised taking into account the drug related nonlinearity and variability. With the identified three axis, nonlinearity in drug pharmacokinetics, variability in drug intake and therapeutic outcomes, and improvement of drug evaluation issues in the context of variability, the current research program will help to intensify this quantitative trends of pharmacology where mathematics is in the central position but also benefits from new raised problematics. The contribution of the current NSERC discovery grant will be used to investigate various aspects in this direction.