Use of mean residence time to determine the magnitude of difference between rate constants and to calculate tmax in the Bateman equation.

Abstract

The goal of this study was to develop a new method, based on robust pharmacokinetic (PK) parameters, for determining t(max) (time of peak plasma concentration) and the magnitude of difference between the absorption (k(a)) and elimination (k) rate constants in the one compartment body model with first order input and output. The function F(X) that describes the ratio of the AUC (area under the curve) from MRT (mean residence time) to infinity and the AUC from zero to MRT as a function of ratio between the first-order absorption and elimination constants (X) was derived and its limits were determined. Similarly, the function G(X) that describes the ratio between MRT and t(max) was derived and its limits were determined. The functions F(X) and G(X) depend only on the ratio between k and k(a). Thus, the different values of the functions F(X) (a-values) and G(X) (b-values) were calculated as a function of the ratio k/k(a). A table with 1% increments of the relevant b-value for every a-value was derived. The appropriate t(max) was thus calculated from the quotient MRT and the relevant b-value. A useful application of the new method to a drug product with prolonged absorption and long half life was presented. A new method that allows the calculation of t(max) and the k/k(a) ratio and derivation of a simple criterion of the equality between k and k(a) has been developed. This method is applicable to the one compartment open body model with first order absorption and elimination and is not based on single point parameters but on robust pharmacokinetic parameters such as AUC and MRT.