Evidence of the need for modified well-stirred model in vitro to in vivo extrapolation

ElsevierVolume 177, 1 October 2022, 106268European Journal of Pharmaceutical SciencesHighlights•

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.

Abstract

In 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.

Keywords

Well-stirred model

Modified well-stirred model

Hepatic clearance

In vitro to in vivo extrapolation

Multinomial logistic regression

AbbreviationsAGP

alpha-1-acid glycoprotein

Cin

drug concentration entering liver

Cout

drug concentration exiting liver

ECCS

e extended clearance classification system

ERH

hepatic extraction ratio

ESF

empirical scaling factor

fub

fraction of unbound in blood

fup

fraction of unbound in plasma

fuinc

fraction of unbound in incubation

HBA

hydrogen-bond acceptor

IPRL

isolated perfused rat liver

IVIVE

in vitro to in vivo extrapolation

logP

partition coefficient

MWSM

modified well-stirred model

OATP

organic anion–transporting polypeptide

PBSF

physiologically based scaling factor

pKa

acid dissociation constant

PLR

plasma-to-whole-liver ratio

RMSE

root mean squared error

υ

rate change in amount of drug

Vss

volumes of distribution at steady-state

© 2022 The Authors. Published by Elsevier B.V.

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