Nonlinear turnover models for systems with physiological limits.
Physiological limits have so far not played a central role in mechanism-based pharmacodynamic modeling, except in models of feedback, where physiological limits act intrinsically on deviations from a pre-set physiological ground state (e.g., the baseline value or a set-point value). However, recently these concepts were introduced in turnover models acting on the production or loss of response, respectively, even for simple (nontolerant) systems. In the latter case, the physiological limit kicks in when the state variable (response) approaches either a lower or an upper limit, not before. In this paper we propose a new approach with either one (lower or upper) limit or two (simultaneously acting lower and upper) limits (dual limits). We present an analytical mathematical treatment as well as a numerical treatment via model simulations. This approach allows for a baseline value to be only weakly dependent on the lower/upper physiological limit. It also allows dual limits, one below and one above, which is attractive because it may be applicable to commonly studied physiological and biochemical systems such as turnover of water or fat.
Peletier
Lambertus A
LA
Mathematical Institute, Leiden University, PB 9512, 2300 RA Leiden, The Netherlands. peletier@math.leidenuniv.nl
Gabrielsson
Johan
J
D000273:Adipose Tissue / Q000187:drug effects / Q000254:growth & development; D000465:Algorithms; D000818:Animals; D063387:Cannabinoid Receptor Antagonists; D003198:Computer Simulation; D004305:Dose-Response Relationship, Drug; D007700:Kinetics; D051379:Mice; D008954:Models, Biological; D017711:Nonlinear Dynamics; D000069437:Pharmacological Phenomena; D010829:Physiological Phenomena / Q000187:drug effects; D010880:Piperidines / Q000494:pharmacology; D011720:Pyrazoles / Q000494:pharmacology; D000077285:Rimonabant
D063387:Cannabinoid Receptor Antagonists; D010880:Piperidines; D011720:Pyrazoles; D000077285:Rimonabant