Kinetic Considerations Relating to the Accrual and Elimination of Drug Metabolites

Abstract

Consideration of the therapeutic effect or toxic action of a drug must also include consideration of the potential effect of its metabolites. Therefore regard should be given not only to the qualitative aspects of drug metabolism, but also to the kinetics of metabolite formation and metabolite elimination.The following considerations relate to the application of kinetic equations to the processes of elimination of a drug and its metabolites and their use for the evaluation of rate constants for these processes from urinary excretion data.Drugs are eliminated from the body by excretion and by transformation to metabolites. These processes occur simultaneously but the extent of each varies from one drug to another. The metabolites of the drug are then also eliminated by excretion and further metabolism. The amount of drug in the body at any time depends both on its rate of absorption and its rate of elimination. Similarly the amount of a metabolite in the body will depend on its rate of formation and its rate of elimination and will increase until these rates are equal; this growth in the amount of metabolite has been referred to by Cummings & Martin (1963) as metabolite accrual. It is well recognized that when a drug is rapidly metabolized to a metabolite which is slowly eliminated, the amount of metabolite in the body may eventually exceed the amount of drug. Little consideration has been given, however, to the amount of metabolite in the body when the metabolite is rapidly eliminated, and it has sometimes been incorrectly assumed that the rate of elimination of a metabolite can then be equated to its rate of formation. Drug excretion, drug metabolism and metabolite elimination can be treated as a number of consecutive and parallel processes for which it is frequently possible to obtain overall rate constants and in certain instances specific rate constants. The magnitude and duration of metabolite accrual is governed by the value of these rate constants.Kinetic equations for the elimination of a model drug and its metabolitesThe elimination of a drug by excretion and metabolism and the subsequent elimination of the metabolites, is considered in respect of a model drug. In the first instance this drug is postulated to be instantaneously absorbed and equilibrated in the body water, so that the amount of drug in the body at zero time is equated to the amount administered. The

Drug Urinary Excretion Data—some Aspects Concerning the Interpretation

“…It has been shown (Cummings, Martin & Park, 1967) (8) and a plot of (Muw -Mu) against time therefore relates not only to that fraction of the drug in the body which is ultimately eliminated as metabolite, but includes also the amount of the metabolite in the body.…”

“…Two methods, the " Rate v Amount " method (Martin, 1967) and the " Terminal-ratio" method (Cummings, Martin & Park, 1967) have recently been proposed for the determination of the excretion rate constant of a metabolite from urinary excretion data. Their application has been exemplified by Cummings, King & Martin (1967).…”

“…The log " Sigma-minus " plot for a metabolite can give rise to a terminal linear section and its slope will depend on whether the excretion rate constant of the metabolite (ku) is greater or smaller than the elimination rate constant of the drug (K), according to one or other of the following equations (Cummings, Martin & Park, 1967 A knowledge of D uor and Mucc is required not only for the construction of the respective "Sigma-minus" plots, but also for the assessment of the extent of drug absorption and for the calculation of the specific rate constants which govern drug excretion and metabolite formation. The rate constants governing metabolite formation also constitute the only valid basis for the comparison of the rate of metabolism of drugs.…”

“…(ii) The "Rate" method A log "Rate" plot relating to the excretion of a metabolite in the urine can also give rise to a terminal linear section and its slope will depend on which of the rate constants, ku or K, is the greater (Cummings, Martin & Park, 1967 (12)) can be calculated from the slope of the plot of log Amu against time.…”

Pharmacokinetic model for the successive demethylation and biliary secretion of methyl orange in the rat

“…K is already known from the plot described by equation 14 and the problem is to obtain an estimate of kc + k. As t becomes large the curve will tend to become linear and the slope of the linear portion will depend on the relative values of K and k2+ k4 (Cummings, Martin & Park, 1967 …”