Journal of Pharmacokinetics and Pharmacodynamics

, Volume 45, Issue 1, pp 107–125 | Cite as

Fractional calculus in pharmacokinetics

  • Pantelis Sopasakis
  • Haralambos Sarimveis
  • Panos Macheras
  • Aristides Dokoumetzidis
Original Paper


We are witnessing the birth of a new variety of pharmacokinetics where non-integer-order differential equations are employed to study the time course of drugs in the body: this is dubbed “fractional pharmacokinetics”. The presence of fractional kinetics has important clinical implications such as the lack of a half-life, observed, for example with the drug amiodarone and the associated irregular accumulation patterns following constant and multiple-dose administration. Building models that accurately reflect this behaviour is essential for the design of less toxic and more effective drug administration protocols and devices. This article introduces the readers to the theory of fractional pharmacokinetics and the research challenges that arise. After a short introduction to the concepts of fractional calculus, and the main applications that have appeared in literature up to date, we address two important aspects. First, numerical methods that allow us to simulate fractional order systems accurately and second, optimal control methodologies that can be used to design dosing regimens to individuals and populations.


Fractional pharmacokinetics Numerical methods Drug administration control Drug dosing 


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of Electrical Engineering (ESAT), STADIUS Center for Dynamical Systems, Signal Processing and Data AnalyticsKU LeuvenLeuvenBelgium
  2. 2.School of Chemical EngineeringNational Technical University of AthensAthensGreece
  3. 3.Department of PharmacyUniversity of AthensAthensGreece

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