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 (C_ss), one can replace C by either fC₀ or fC_ss 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 C_ss 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 ΔC is constant, whereas with numerical integration one obtains a series of C, t values where Δt is constant.