title: Modeling of delays in PKPD: classical approaches and a tutorial for delay differential equations.
abstract: In pharmacokinetics/pharmacodynamics (PKPD) the measured response is often delayed relative to drug administration, individuals in a population have a certain lifespan until they maturate or the change of biomarkers does not immediately affects the primary endpoint. The classical approach in PKPD is to apply transit compartment models (TCM) based on ordinary differential equations to handle such delays. However, an alternative approach to deal with delays are delay differential equations (DDE). DDEs feature additional flexibility and properties, realize more complex dynamics and can complementary be used together with TCMs. We introduce several delay based PKPD models and investigate mathematical properties of general DDE based models, which serve as subunits in order to build larger PKPD models. Finally, we review current PKPD software with respect to the implementation of DDEs for PKPD analysis.
authors.affiliation: Department of Pharmaceutical Sciences, State University of New York at Buffalo, 403 Kapoor Hall, Buffalo, NY , 14214, USA, gilbertk@buffalo.edu.
authors.forename: Gilbert
authors.initials: G
authors.lastname: Koch
authors.forename: Wojciech
authors.initials: W
authors.lastname: Krzyzanski
authors.forename: Juan Jose
authors.initials: JJ
authors.lastname: Pérez-Ruixo
authors.forename: Johannes
authors.initials: J
authors.lastname: Schropp
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D006801:Humans; D007408:Intestinal Absorption; D008433:Mathematics; D015233:Models, Statistical; D008962:Models, Theoretical; D010599:Pharmacokinetics