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

在复杂的生物系统中，变异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，已被证明是在靶向现象的观察范围之外产生有偏见的预测的原因之一。二十多年前，随着群体药代动力学/药效动力学建模方法(非线性混合效应模型)的引入，这种情况得到了改变。为了描述药物在患者群体中的血药浓度和治疗效果的演变，这种新的方法成功地在以前用常微分方程式定义的确定性环境中引入了不同程度的可变性，并为药理学的量化时代奠定了基础，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，许多利用线性和确定性原理开发的药理学概念和方法应该重新审视和数学修改，同时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，药物摄取和治疗结果的可变性，以及在可变性的背景下药物评价问题的改进，当前的研究计划将有助于加强药理学的这种量化趋势，其中数学处于中心地位，但也受益于新提出的问题学。目前NSERC发现基金的贡献将用于调查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.**