Assessing Liver-to-Plasma Partition Coefficients and In Silico Calculation Methods: When Does the Hepatic Model Matter in PBPK?

Abstract

The primary models used in pharmacokinetics (PK) to assess hepatic clearance (CLh ) are the well-stirred (WSM), parallel tube (PTM), and dispersion model (DM) that differ in their internal flow patterns and assumed unbound liver concentrations. Physiologically-Based Pharmacokinetic (PBPK) models require a hepatic intrinsic clearance (CLint ) and tissue-to-plasma partition coefficient (Kp ). Given measured systemic and liver concentration-time profiles, these hepatic models perform similarly but yield model-specific CLint and Kp estimates. This work provides mathematical relationships for the three basic hepatic models and assesses their corresponding PBPK-relevant Kp values with literature-reported single-dose blood and liver concentration-time data of 14 compounds. Model fittings were performed with an open-loop approach where the CLh and extraction ratio (ER) were first estimated from fitting the blood data yielding CLint values for the three hepatic models. The pre-fitted blood data served as forcing input functions to obtain PBPK-operative Kp estimates that were compared with those obtained by the tissue/plasma area ratio (AR), Chen & Gross (C&G) and published in silico methods. The CLint and Kp values for the hepatic models increased with the ER and both showed a rank order being WSM > DM > PTM. Drugs with low ER showed no differences as expected. With model-specific CLint and Kp values, all hepatic models predict the same steady-state Kp (Kp ss ) that is comparable to those from the AR and C&G methods and reported by direct measurement. All in silico methods performed poorly for most compounds. Hepatic model selection requires cautious application and interpretation in PBPK modeling. Significance Statement The three hepatic models generate different single-dose (non-steady-state) values of CLint and Kp in PBPK models especially for drugs with high ER; however, all Kp ss values expected from constant rate infusion studies were the same. These findings are relevant when using these models for IVIVE where a model-dependent CLint is used to correct measured tissue concentrations for depletion by metabolism. This model-dependency may also have an impact when assessing the PK/pharmacodynamic relationships when effects relate to assumed hepatic concentrations.