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

Purpose The goal of this study was to develop a new method, based on robust pharmacokinetic (PK) parameters, for determining tmax (time of peak plasma concentration) and the magnitude of difference between the absorption (ka) and elimination (k) rate constants in the one compartment body model with first order input and output. Methods 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 tmax was derived and its limits were determined. Results The functions F(X) and G(X) depend only on the ratio between k and ka. 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/ka. A table with 1% increments of the relevant b‐value for every a‐value was derived. The appropriate tmax 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. Conclusions A new method that allows the calculation of tmax and the k/ka ratio and derivation of a simple criterion of the equality between k and ka 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. Copyright © 1999 John Wiley & Sons, Ltd.