Time-dependent kinetics. V: Time course of drug levels during enzyme induction (one-compartment model)

Equations were derived to describe the time course of drug levels during auto- and heteroinduction under a variety of input conditions. These equations were based on a pharmacokinetic theory of induction which assumes that metabolic clearance increases exponentially to a maximum value and that the rate of this increase is governed by the degradation rate constant of the induced enzyme (k'). Closed form solutions could be obtained only for intravenous single-dose (case I) and multiple-dose (case IV) administration. For each of the other cases, constant-rate intravenous infusion (case III), oral single-dose administration (case II), and multiple-dose administration (case V), an exact solution (not closed form) and an approximation (closed form) were derived. Two sets of equations were derived for each of the five cases to take into consideration the possibility of a latency term (lambda). Plots of drug amount X (or concentration C) vs. time (t) were constructed. In case I, a log X vs. t plot was convex, the slope increasing with time. In case II, X increased, reached a peak, and decayed as in case I. In case III (lambda greater than 5 ln 2V/Q) C reached a preinduction steady state before decreasing to a lower (induced) steady state. The behavior of C vs. t for cases IV and V was similar to that for case III. Determination of parameters was attempted in case III. Nonlinear least-square fitting of generated data with 3-9% error yielded reasonable estimates of k'.