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

这里提出的研究计划解决了高度热门的问题，成为非常重要的数学在药物研究领域发挥越来越大的作用。它侧重于先进和新颖的数学方法的发展，这些方法解释了患者药物摄入量，药物在体内的分布及其作用的可变性和非线性，目的是更新最广泛使用的（药理学）指标，以前以确定性和静态的方式制定，并提高对这种复杂的相互作用的整体机制的理解。这一重新表述涉及不同的方面：1）将通常在药物评估中单独考虑的可用药代动力学（PK）和药效学（PD）度量整合在一起，以获得更多的信息加载度量，然后2）将药物输入的可变性添加到这些新的整合PKPD度量中，3）从有限的药物信息追溯患者的药物历史，通过考虑在实践中不容易测试的实际临床情况，4）首次以分析或近似封闭形式制定具有混合性质的吸收和/或消除的更复杂药代动力学模型的动力学。所有这些数学方面是至关重要的，使药物过程更有效，更有效，增加了严谨性和合理性的新兴领域的药物计量学。反过来，数学科学可以受益于新的药理学问题的出现，这些问题在其定量性质上具有挑战性，并导致新的数学主题，例如当前提案中描述的那些，超越了建立描述生物现象的生物数学模型的传统领域。通过这条道路，将有可能丰富当前的建模视野，并可能在应用数学中开辟一个新的领域。事实上，这些主流的药物中心性问题属于公共利益的范围，具有很高的社会经济影响。解决这些数学问题提出了概念和技术的机会和挑战，将价值的作用，数学家的后代。

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.