Direct method of simulating concentration-time data for Michaelis-Menten elimination

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.