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

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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.**