Simplified methods for the evaluation of the parameters of the time course of plasma concentration in the one-compartment body model with first-order invasion and first-order drug elimination including methods for ascertaining when such rate constants are equal.

The many limitations in determining the pharmacokinetic parameters of first-order invasion of, and elimination from, the one-compartment body model by the method of residuals or by "feathering" C-t data can be minimized by applying the simplified methods outlined herein. Comparisons of the apparent volumes of distribution, V, calculated on the premises that the Bateman Function represents ka > ke or its converse, ke > ka, i.e., flip-flop, can permit a proper choice of the correct version. Estimation of ke can be obtained by regression of (A0/V)/C(oncentration) on AUCt/C where A0/V is estimable from knowledge of Cmax and tmax since A0/V = Cmax eketmax. The ratio of the magnitude of the rate constant of invasion to that of elimination, m = ka/ke, is related to ketmax by the expression ketmax = ln m/(m - 1) for all possible values of m. A table for the determination of m from values of ketmax is given. When bioavailability, gamma = Ao/Dose, is known or complete, ke and V can be determined from the respective ordinate and abscissa of the intersection of A0/Cmax eketmax and Cl(clearance)/ke, both plotted against arbitrary ke values. The two functions may not intersect at low values of m due to errored C-t values but the ke value when the two curves are closest (kmin) may approximate ke. The intersections of Cmax eketmax and keAUCT (AUCtrap) plotted against variable ke values (Method A) provide estimates of ke from their abscissa values and A/V from their ordinate values when gamma is unknown. Method B appears to give more reliable estimates of ke at the kmin of the difference eketmax/ke - AUCT/Cmax, plotted against ke. Since kmin of this plot is l/tmax when m = 1, the identity of the m as unity underlying the C-t data is indicated when either kmintmax is approximately unity or kmin is practically synonymous with l/tmax. This was clearly shown when 12 constructed m = 1, C-t cases with 10% random error were evaluated by Method B. Better estimates were effected by all procedures when the raw C-t data were smoothed.