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(up)PS(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.