Well-stirred model and modified well-stirred model should coexist to fully illustrate the well-stirred concept.
•Drug physicochemistry and pharmacokinetic could affect the driving concentration and thus play a pivotal role in determining a suitable hepatic model in IVIVE.
•A new empirical method was established for the practical use of MWSM in IVIVE.
AbstractIn vitro to in vivo extrapolation (IVIVE), an approach for hepatic clearance (CLH) prediction used worldwide, remains controversial due to systematic underprediction. Among the various probable factors, the original assumption of the hepatic mathematical model (i.e., the well-stirred model, WSM) may become problematic, leading to the underestimation of drug CLH. Having a similar prerequisite that the well-stirred conditions are homogenous with perfectly mixed reactants, but using a different driving concentration, the modified well-stirred model (MWSM) stands apart from the WSM. However, we believe that both models should coexist so that the entire well-stirred scenario can be completely illustrated. Consequently, we collected published data from the literature and employed a logistic regression method to differentiate the optimal timing of use between WSM and MWSM in drug CLH prediction. Generally, variances adopted in the regression, including partition coefficient (logP), fraction unbound (fu), volumes of distribution at steady-state (Vss), and mean residence time (MRT), corresponded to our assumption when protein-facilitated uptake was considered. Furthermore, a new empirical approach was introduced to allow practical use of the MWSM. The results showed that this model could provide a more precise prediction compared to previous empirical approaches. Therefore, these preliminary results not only delineated a more detailed structure and mechanism of MWSM but also highlighted its necessity and potential.
KeywordsWell-stirred model
Modified well-stirred model
Hepatic clearance
In vitro to in vivo extrapolation
Multinomial logistic regression
AbbreviationsAGPalpha-1-acid glycoprotein
Cindrug concentration entering liver
Coutdrug concentration exiting liver
ECCSe extended clearance classification system
ERHhepatic extraction ratio
ESFempirical scaling factor
fubfraction of unbound in blood
fupfraction of unbound in plasma
fuincfraction of unbound in incubation
HBAhydrogen-bond acceptor
IPRLisolated perfused rat liver
IVIVEin vitro to in vivo extrapolation
logPpartition coefficient
MWSMmodified well-stirred model
OATPorganic anion–transporting polypeptide
PBSFphysiologically based scaling factor
pKaacid dissociation constant
PLRplasma-to-whole-liver ratio
RMSEroot mean squared error
υrate change in amount of drug
Vssvolumes of distribution at steady-state
© 2022 The Authors. Published by Elsevier B.V.
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