Consideration of Fractional Distribution Parameter fd in the Chen and Gross Method for Tissue-to-Plasma Partition Coefficients: Comparison of Several Methods.

Abstract

The tissue-to-plasma partition coefficient (Kp) describes the extent of tissue distribution in physiologically-based pharmacokinetic (PBPK) models. Constant-rate infusion studies are common for experimental determination of the steady-state Kp,ss, while the tissue-plasma concentration ratio (CT/Cp) in the terminal phase after intravenous doses is often utilized. The Chen and Gross (C&G) method converts a terminal slope CT/Cp to Kp,ss based on assumptions of perfusion-limited distribution in tissue-plasma equilibration. However, considering blood flow (QT) and apparent tissue permeability (fupPSin) in the rate of tissue distribution, this report extends the C&G method by utilizing a fractional distribution parameter (fd). Relevant PBPK equations for non-eliminating and eliminating organs along with lung and liver were derived for the conversion of CT/Cp values to Kp,ss. The relationships were demonstrated in rats with measured CT/Cp and Kp,ss values and the model-dependent fd for 8 compounds with a range of permeability coefficients. Several methods of assessing Kp were compared. Utilizing fd in an extended C&G method, our estimations of Kp,ss from CT/Cp were improved, particularly for lower permeability compounds. However, four in silico methods for estimating Kp performed poorly across tissues in comparison with measured Kp values. Mathematical relationships between Kp and Kp,ss that are generally applicable for eliminating organs with tissue permeability limitations necessitates inclusion of an extraction ratio (ER) and fd. Since many different types/sources of Kp are present in the literature and used in PBPK models, these perspectives and equations should provide better insights in measuring and interpreting Kp values in PBPK.