Rethinking and Formulating Integrative Methodologies for a Better Understanding of Quantitative Drug-Related Issues

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The research program proposed here addresses highly topical issues that became very important with the increasing role that mathematics play in the drug research area. It focuses on the development of advanced and novel mathematical approaches that account for the variability and nonlinearity emanating from the patient’s drug intake, drug disposition in the body and its action on it, with the aim to update the most widely used (pharmaco) metrics, previously formulated in a deterministic and static way, and to improve the overall mechanistic understanding of this complex interlationship. This reformulation takes different aspects : 1) with the integration of available pharmacokinetic (PK) and pharmacodynamic (PD) metrics together, usually considered separately in the drug assessment, to obtain more information-loaded metrics, then 2) the addition of the variability of drug input into these new integrative PKPD metrics, 3) retrace the patient’s drug history from limited drug information, by considering realistic clinical situations that cannot be easily tested in practice, 4) formulate, for the first time, analytically or in approximative closed forms, the kinetics of more complex pharmacokinetic models with absorption and/or elimination of mixed nature. All these mathematical aspects are crucial to make the drug process more efficient and effective, adding rigour and rationality to the emerging area of pharmacometrics. Mathematical sciences can benefit, in turn, from the emergence of new pharmacological problems that are challenging in their quantitative nature and lead to new mathematical topics, such as those described in the current proposal, beyond the traditional area of establishment of biomathematical models for the description of biological phenomena. Going through this path, it will be possible to enrich the current modeling vision and potentially open a new area in applied mathematics. In fact, these mainstream pharmacomentric problems lie within the scope of public interest and are of high socioeconomic impact. Solving these mathematical problems presents conceptual and technical opportunities and challenges that will value the role of mathematicians for generations to come.