New and Simple Method to Predict Dosage of Drugs Obeying Simple Michaelis-Menten Elimination Kinetics and to Distinguish Such Kinetics from Simple First Order and from Parallel Michaelis-Menten and First Order Kinetics

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Abstract
It has been found empirically that either average or minimum steady-state plasma concentrations (Css) of drugs obeying Michaelis-Menten elimination kinetics give essentially linear plots on semilogarithmic graph paper when Css is plotted versus the maintenance dose (D) or dose rate (R). The equations of such straight lines may be converted to the following nonlinear equation: Css = abD which fits the Css,D data essentially as well as D = Vm Css/(Km + Css). The parameter b is analogous to unity plus the interest fraction in logarithmic growth or compound interest calculations, and each drug appears to have a characteristic value of this parameter, with extremely small intersubject variation. From the above equation the following equation, Dn + 1 = Dn + ln(Cn + 1/Cn)ln b can be derived, which forms the basis for predicting the needed dosage, Dn + 1, to obtain a desired steady-state concentration, Cn + 1, using one initial steady state concentration, Cn, obtained with dose, Dn, and using a population value of b for the drug. It appears that it is the value of the "initial capital" (i.e., a in relation to the initial dose) rather than the "interest fraction" (i.e., b - 1) that causes most of the intersubject variation in Css of a given drug. Several drugs illustrate the usefulness of the method. A semilogarithmic plot also appears to be an excellent method to distinguish simple Michaelis-Menten kinetics from parallel Michaelis-Menten and first order elimination kinetics and from simple first order kinetics with steady-state data in the range 0.3-3 Km.