Generalizations in linear pharmacokinetics using properties of certain classes of residence time distributions. I. Log-convex drug disposition curves.

Introducing the phenomenological concept of a time-varying fractional rate of elimination kD(t) and applying the theory of lifetime distributions, implications of the log-convexity of drug disposition curves are examined and some important applications are described. Linear pharmacokinetic systems exhibiting a log-convex impulse response and satisfying the basic conditions underlying the noncompartmental approach have the following properties: (1) The time-varying volume of distribution V(t) increases, and consequently the fractional rate of elimination kD(t) = CL/V(t) decreases monotonically. (2) The concentration-time curve and the time course of total amount of drug in the body, respectively, have an exponential tail [where V(t) approaches the equilibrium value VZ]. The relative dispersion of residence times (CV2D = VDRT/MDRT2) and the ratio Vss/VZ (Vss is the volume of distribution at steady state) act as measures of departure from pure monoexponential decay (one-compartment behaviour). The role of the latter parameters as shape parameters of the curve that characterize the distributional properties of drugs is discussed. Upper and lower bounds of the time course of drug amount in the body are derived using the parameters MDRT and CV2D or lambda Z (terminal exponential coefficient), respectively. This approach is also employed to construct upper bounds on the fractional error in AUC determination by numerical integration that is due to curve truncation. The significance of the fractional elimination rate concept as a unifying approach in interspecies pharmacokinetic scaling is pointed out. Some applications of the results are demonstrated, using digoxin data from the literature.