Development and adaptation of mathematical methodologies for drug evaluation and use

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Model-based drug research and development is now promulgated by regular authorities as an important approach that substantially contributes to drug management and decision-making. The same vision has been embraced by academia through launching of several fundamental research activities and specialized curricula. We observe that drug-related research has been progressively evolving towards an exact science discipline that can benefit from great mathematical inspiration and interest. The objective of the present research program is to build a solid theoretical framework for drug development and evaluation by introducing appropriate mathematical methodologies. This direction in our research simply echoes the increasing need for more accurate metrics for therapeutic evaluation and prediction. It is undeniable that the deterministic mathematical representation based on differential equations has brought great insights to the biopharmaceutical field and traced the path towards its quantitative era. However, the increasingly reported variability, supported by newly acquired data through advanced measurement techniques, along with the progress in drug-related knowledge, challenges this deterministic vision for many aspects of the field. Since this variability is not generally included into traditional metrics, and because of the increasingly reported evidence for its impact, proposition of theoretically-based pharmacological metrics becomes an unavoidable step in order to provide a fair evaluation of drug performance and reduce consequences of inappropriate drug use. The probabilistic features, which undoubtedly are intrinsic part of this variability, should be allocated a sufficient weight for this new investigation. Using various mathematical approaches, we will work at different levels that contribute to therapeutic variability, going from the drug intake, to drug absorption and disposition within the body and then to drug action.