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Challenging the Relevance of Unbound Tissue-to-Blood Partition Coefficient (Kpuu) on Prediction of Drug-Drug Interactions



To examine the theoretical/practical utility of the liver-to-blood partition coefficient (Kpuu) for predicting drug-drug interactions (DDIs), and compare the Kpuu-approach to the extended clearance concept AUCR-approach.


The Kpuu relationship was derived from first principles. Theoretical simulations investigated the impact of changes in a single hepatic-disposition process on unbound systemic (AUCB,u) and hepatic exposure (AUCH,u) versus Kpuu. Practical aspects regarding Kpuu utilization were examined by predicting the magnitude of DDI between ketoconazole and midazolam employing published ketoconazole Kpuu values.


The Kpuu hepatic-disposition relationship is based on the well-stirred model. Simulations emphasize that changes in influx/efflux intrinsic clearances result in Kpuu changes, however AUCH,u remains unchanged. Although incorporation of Kpuu is believed to improve DDI-predictions, utilizing published ketoconazole Kpuu values resulted in prediction errors for a midazolam DDI.


There is limited benefit in using Kpuu for DDI-predictions as the AUCR-based approach can reasonably predict DDIs without measurement of intracellular drug concentrations, a difficult task hindered by experimental variability. Further, Kpuu changes can mislead as they may not correlate with changes in AUCB,u or AUCH,u. The well-stirred model basis of Kpuu when applied to hepatic-disposition implies that nuances of intracellular drug distribution are not considered by the Kpuu model.

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Fig. 1
Fig. 2
Fig. 3


A H :

Amount of drug in the liver


Area under the concentration time curves expressed as the ratio of interaction to control

AUC B,u :

Area under the concentration time curve of unbound drug in the blood following an oral dose

AUC H,u :

Area under the concentration time curve of unbound drug in the liver following an oral dose

C B :

Total concentration of drug in the blood

C B,u :

Unbound drug concentration in blood

C H :

Total concentration of drug in the liver

C H,bil :

Total concentration of drug in the liver driving biliary excretion

C H,eff :

Total concentration of drug in the liver driving basolateral efflux

C H,met :

Total concentration of drug in the liver driving metabolism

CL H,int :

Hepatic intrinsic clearance (sum of metabolic intrinsic clearance and intrinsic biliary secretion)

CL H,int,bil :

Hepatic intrinsic biliary secretion

CL H,int,met :

Hepatic intrinsic metabolic clearance

C H,u :

Unbound drug concentration in the liver


Cytochrome P450


Drug-drug interaction

F abs :

Fraction absorbed

F G :

Fraction escaping intestinal elimination

f u,B :

Fraction of unbound drug in blood

f u,H :

Fraction of unbound drug in liver

f u,inc :

Fraction of unbound drug in an in vitro incubation

f u,plasma :

Fraction of unbound drug in plasma

I max,u :

Maximal unbound plasma concentration of inhibitor drug

K i :

Unbound inhibition constant of inhibitor drug

Kp uu :

Unbound liver-to-blood partition coefficient


Physiologically-based pharmacokinetic



PS eff,int :

Basolateral efflux (both active and passive) intrinsic clearance

PS inf,int :

Basolateral influx (both active and passive) intrinsic clearance


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Acknowledgements and DISCLOUSURES

This work was supported in part by a Mary Ann Koda-Kimble Seed Award for Innovation. Ms. Sodhi was supported in part by an American Foundation for Pharmaceutical Education Predoctoral Fellowship, NIGMS grant R25 GM56847 and a Louis Zeh Fellowship. Dr. Benet is a member of the UCSF Liver Center supported by NIH grant P30 DK026743. All authors contributed to the writing, derivations, simulations and analysis of this manuscript. The authors declare no conflict of interest.

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Correspondence to Leslie Z. Benet.

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Sodhi, J.K., Liu, S. & Benet, L.Z. Challenging the Relevance of Unbound Tissue-to-Blood Partition Coefficient (Kpuu) on Prediction of Drug-Drug Interactions. Pharm Res 37, 73 (2020).

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Key Words

  • Kp uu
  • liver-to-blood partitioning
  • drug-drug interactions
  • well-stirred model