Lag Time Before Essentially Constant Urinary Excretion Rate is Attained

Abstract

If a substance is continuously infused intravenously at a constant rate, the plasma concentration will increase until it reaches an asymptotic concentration. If the urinary excretion rate of the substance is directly proportional to its plasma concentration, the urinary excretion rate will become essentially constant as the asymptotic plasma concentration is approached. Analogously, if a metabolite is formed at a constant rate, due to saturation of an enzyme system metabolizing the drug, the plasma concentration of the metabolite would be expected to approac hsome asymptotic concentration. If the urinary excretion rate of the metabolite is directly proportional to its plasma concentration, the urinary excretion rate of the metabolite would become essentially constant as the asymptotic plasma concentration is approached. Equations were derived to estimate the lag time between initiation of the maintained constant input rate to the plasma compartment and the time when, for all practical purposes, the asymptotic plasma concentration and the constant urinary excretion rate may be considered to have been reached for both the one- and two-compartment open models. The theoretical expectation is that, if the cumulative excretion curve is nearly linear, then there must be an appreciable negative intercept when the line is extrapolated back to zero time. It is theoretically impossible for a cumulative urinary excretion curve to be linear and the line extrapolate through the origin corresponding to zero excretion at zero time.