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

Purpose: The tissue-to-plasma partition coefficient (K_p) 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 K_p,ss, while the tissue-plasma concentration ratio (C_T/C_p) in the terminal phase after intravenous doses is often utilized. The Chen and Gross (C&G) method converts a terminal slope C_T/C_p to K_p,ss based on assumptions of perfusion-limited distribution in tissue-plasma equilibration. However, considering blood flow (Q_T) and apparent tissue permeability (f_upPS_in) in the rate of tissue distribution, this report extends the C&G method by utilizing a fractional distribution parameter (f_d).

Methods: Relevant PBPK equations for non-eliminating and eliminating organs along with lung and liver were derived for the conversion of C_T/C_p values to K_p,ss. The relationships were demonstrated in rats with measured C_T/C_p and K_p,ss values and the model-dependent f_d for 8 compounds with a range of permeability coefficients. Several methods of assessing K_p were compared.

Results: Utilizing f_d in an extended C&G method, our estimations of K_p,ss from C_T/C_p were improved, particularly for lower permeability compounds. However, four in silico methods for estimating K_p performed poorly across tissues in comparison with measured K_p values. Mathematical relationships between K_p and K_p,ss that are generally applicable for eliminating organs with tissue permeability limitations necessitates inclusion of an extraction ratio (ER) and f_d.

Conclusion: Since many different types/sources of K_p are present in the literature and used in PBPK models, these perspectives and equations should provide better insights in measuring and interpreting K_p values in PBPK.