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

Abstract

The many limitations in determining the pharmacokinetic parameters of firstorder invasion of, and elimination from, the onecompartment body model by the method of residuals or by “feathering” Ct 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 k_a>k_e or its converse, k_e>k_a,i.e., flip-flop, can permit a proper choice of the correct version. Estimation of k_e can be obtained by regression of (A₀/V)/C(oncentration) on AUC₁/ Cwhere A₀/Vis estimable from knowledge of C_max and t_max since $A_0 /V = C_{max} e^{k_e t_{max} }$.The ratio of the magnitude of the rate constant of invasion to that of elimination, m=k_a/k_e,is related to k_et_max by the expression k_et_max=ln m/ (m−1)for all possible values of m.A table for the determination of m from values of k_et_max is given. When bioavailability, γ=A₀/Dose,is known or complete, k_e and Vcan be determined from the respective ordinate and abscissa of the intersection of $A_0 /C_{max} e^{k_e t_{max} }$ and Cl(clearance)/k_e,both plotted against arbitrary k_e values. The two functions may not intersect at low values of mdue to errored C-t values but the k_e value when the two curves are closest (k_min)may approximate k_e.The intersections of $C_{max} e^{k_e t_{max} }$ and k_eAUCT (AUC_trap)plotted against variable k_e values (Method A) provide estimates of k_e from their abscissa values and A/Vfrom their ordinate values when γis unknown. Method B appears to give more reliable estimates of k_e at the k_min of the difference $e^{k_e t_{max} } /k_e - AUCT/C_{max}$ plotted against k_e.Since k_min of this plot is 1/t_max when m=1,the identity of the mas unity underlying the C-t data is indicated when either k_mint_max is approximately unity or k_min ispractically synonymous with 1/t_max.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.