title: Impact of saturable distribution in compartmental PK models: dynamics and practical use.
abstract: We explore the impact of saturable distribution over the central and the peripheral compartment in pharmacokinetic models, whilst assuming that back flow into the central compartiment is linear. Using simulations and analytical methods we demonstrate characteristic tell-tale differences in plasma concentration profiles of saturable versus linear distribution models, which can serve as a guide to their practical applicability. For two extreme cases, relating to (i) the size of the peripheral compartment with respect to the central compartment and (ii) the magnitude of the back flow as related to direct elimination from the central compartment, we derive explicit approximations which make it possible to give quantitative estimates of parameters. In three appendices we give detailed explanations of how these estimates are derived. They demonstrate how singular perturbation methods can be successfully employed to gain insight in the dynamics of multi-compartment pharmacokinetic models. These appendices are also intended to serve as an introductory tutorial to these ideas.
authors.affiliation: Mathematical Institute, Leiden University, PB 9512, 2300 RA, Leiden, The Netherlands. peletier@math.leidenuniv.nl.
authors.forename: Lambertus A
authors.initials: LA
authors.lastname: Peletier
authors.affiliation: Janssen Research & Development, Janssen Prevention Center, Archimedesweg 6, 2333 CN, Leiden, The Netherlands.
authors.forename: Willem
authors.initials: W
authors.lastname: de Winter
mesh_terms: D003198:Computer Simulation; D004305:Dose-Response Relationship, Drug; D006801:Humans; D016014:Linear Models; D008954:Models, Biological; D017711:Nonlinear Dynamics; D004364:Pharmaceutical Preparations / Q000097:blood*; D010599:Pharmacokinetics; D013997:Time Factors
chemical_list: D004364:Pharmaceutical Preparations
keywords: Distribution; Pharmacokinetics; Saturation