title: Direct method of simulating concentration-time data for Michaelis-Menten elimination.
abstract: For pharmacokinetic models such as those indicated by the title, one obtains an implicit equation in concentration, which cannot be used to directly obtain a value of C corresponding to a given value of t. Usually numerical integration is employed to simulate concentration-time data. By introducing f = concentration (C)/initial concentration (C0), or f = C/steady-state concentration (Css), one can replace C by either fC0 or fCss then obtain time as an explicit solution, by letting f equal an arbitrary series of values such as 0.95, 0.9, . . . 0.05, 0.04, . . . , 0.01 when C0 is involved, or 0.05, 0.10, . . . , 0.95 when Css is involved. This procedure allows data to be simulated with just a pencil and paper, a hand-held calculator, or a microcomputer. The accuracy of the method depends only on the number of decimal places carried during the calculations. The method can provide a series of C, t values where delta C is constant, whereas with numerical integration one obtains a series of C, t values where delta is constant.
authors.affiliation: College of Pharmacy, Upjohn Center for Clinical Pharmacology, Medical School, University of Michigan, Ann Arbor 48109.
authors.forename: J G
authors.initials: JG
authors.lastname: Wagner
mesh_terms: D006801:Humans; D008838:Microcomputers; D008954:Models, Biological; D010599:Pharmacokinetics