New Mathematical Methods in Pharmacokinetic Modeling

Abstract

In recent years, several new methods for the mathematical modeling have gradually emerged in pharmacokinetics, and the development of pharmacokinetic models based on these methods has become one of the most rapidly growing and exciting application-oriented sub-disciplines of the mathematical modeling. The goals of our MiniReview are twofold: i) to briefly outline fundamental ideas of some new modeling methods that have not been widely utilized in pharmacokinetics as yet, i.e. the methods based on the following concepts: linear time-invariant dynamic system, artificialneural-network, fuzzy-logic, and fractal; ii) to arouse the interest of pharmacological, toxicological, and pharmaceutical scientists in the given methods, by sketching some application examples which indicate the good performance and perspective of these methods in solving pharmacokinetic problems.It often occurs in science that tools, knowledge, or techniques developed in one field enable advances in other fields. This applies also to methods for building mathematical models, i.e. tools that have been developed predominantly in the field of mathematics, computer science, and system engineering. In contrast to animal or disease models commonly used in pharmacology, mathematical models are mathematical structures which, on abstracting from reality, allow formulations in mathematical terms of essential assumptions believed to underlie particular actual-world problems. The mathematical modeling relies on: i) the sound understanding and appreciation of the problem under study; ii) the realistic mathematical representation of the important phenomena; iii) the finding of useful solutions; iv) the interpretation of the mathematical results, the model-based prediction or simulation, and so on. All that is required for the practical use of mathematical models is to understand these models properly and then to apply them to study phenomena of the interest in various fields of science, including pharmacokinetics. In the latter field, mathematical models have historically played a vital role, and methods for the development models such as deterministic linear compartment models, physiologically-based models, and population models have become quite common. Along with this, other modeling methods have gradually emerged in pharmacokinetics over recent years, and the Author for correspondence: Mária Ď urišová, Institute of Experimental Pharmacology, Slovak Academy of Sciences, Dubravska cesta 9, SK-841 04 Bratislava 4, Slovak Republic (fax π42 12 5477 5928, e-mail maria.durisova/savba.sk).development of pharmacokinetic models has become one of the most rapidly growing and exciting applicationoriented sub-disciplines of the mathematical modeling.The goals of this MiniReview are twofold: i) to briefly outline fundamental ideas of some mathematical methods that have not been widely utilized in pharmacokinetics so far, i.e. the methods based on the following concepts: linear time-invariant dynamic system, artificial-neural-network, fuzzy-logic, and fractal; ...

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