Toward improved predictions of pharmacokinetics of transported drugs in hepatic impairment: Insights from the extended clearance model

Abstract

Hepatic impairment (HI) moderately (<5‐fold) affects the systemic exposure (i.e., area under the plasma concentration–time curve [AUC]) of drugs that are substrates of the hepatic sinusoidal organic anion transporting polypeptide (OATP) transporters and are excreted unchanged in the bile and/or urine. However, the effect of HI on their AUC is much greater (>10‐fold) for drugs that are also substrates of cytochrome P450 (CYP) 3A enzymes. Using the extended clearance model, through simulations, we identified the ratio of sinusoidal efflux clearance (CL) over the sum of metabolic and biliary CLs as important in predicting the impact of HI on the AUC of dual OATP/CYP3A substrates. Because HI may reduce hepatic CYP3A‐mediated CL to a greater extent than biliary efflux CL, the greater the contribution of the former versus the latter, the greater the impact of HI on drug AUC ratio (AUCR_HI). Using physiologically‐based pharmacokinetic modeling and simulation, we predicted relatively well the AUCR_HI of OATP substrates that are not significantly metabolized (pitavastatin, rosuvastatin, valsartan, and gadoxetic acid). However, there was a trend toward underprediction of the AUCR_HI of the dual OATP/CYP3A4 substrates fimasartan and atorvastatin. These predictions improved when the sinusoidal efflux CL of these two drugs was increased in healthy volunteers (i.e., before incorporating the effect of HI), and by modifying the directionality of its modulation by HI (i.e., increase or decrease). To accurately predict the effect of HI on AUC of hepatobiliary cleared drugs it is important to accurately predict all hepatobiliary pathways, including sinusoidal efflux CL.

Study Highlights.

• WHAT IS THE CURRENT KNOWLEDGE ON THE TOPIC?

Hepatic impairment (HI) affects the systemic exposure of drugs that are OATP/CYP3A4 substrates (area under the plasma concentration–time curve [AUC] increasing >10‐fold) to a greater extent than those drugs that are substrates of OATP/biliary efflux transporters (AUC increasing <5‐fold).

• WHAT QUESTION DID THIS STUDY ADDRESS?

Why does HI affect the systemic exposure of dual OATP/CYP3A4 substrates greater than those that are transported by OATP/biliary efflux transporters? Can this difference be predicted by physiologically‐based pharmacokinetic modeling and simulation?

• WHAT DOES THIS STUDY ADD TO OUR KNOWLEDGE?

Using the extended clearance (CL) model, we highlighted factors that drive the increase in HI in the blood AUC of OATP/CYP3A4 versus OATP/biliary efflux transporter substrates. We showed that accurate estimation of all hepatobiliary CLs, including the often‐overlooked sinusoidal efflux CL, and their modulation in HI, are critical factors to improve predictions of pharmacokinetic changes of drugs in HI.

• HOW MIGHT THIS CHANGE DRUG DISCOVERY, DEVELOPMENT, AND/OR THERAPEUTICS?

By better understanding what drives pharmacokinetic changes of OATP/CYP3A substrate drugs in HI, we can better predict the effect of HI on their systemic exposure.

INTRODUCTION

Hepatic impairment (HI) affects the pharmacokinetics (PKs) of drugs through physiological changes, such as modulation of drug metabolizing enzyme and transporter (DMET) abundance, reduction of liver functional volume, reduction in drug‐binding protein concentration and hematocrit, and modulation of mesenteric and hepatic (arterial and portal) blood flows. ¹ , ² , ³ , ⁴ , ⁵ These changes often result in increased systemic exposure (i.e., the area under the plasma concentration–time curve [AUC]) of drugs, which can impact their safety profile. Therefore, regulatory agencies recommend that the PKs of drugs that are hepatically cleared should be assessed in people with HI to inform dose‐adjustment in these subjects. ⁶ , ⁷

Physiologically‐based PK modeling and simulation (PBPK M&S) is a promising approach to assess the impact of HI on drug PKs, ⁴ , ⁸ , ⁹ , ¹⁰ and can either replace or supplement PK studies in HI or inform PK study design in HI to avoid adverse drug reactions. However, before using such PBPK models with confidence, their prediction performance in HI needs to be assessed. Whereas PBPK M&S studies assessing the effect of HI on drugs that are metabolized by cytochromes P450 (CYP) are available, ¹⁰ , ¹¹ there are limited data on the predictive performance of such models for drugs that are substrates of hepatic drug transporters, such as the sinusoidal organic anion transporting polypeptides (OATPs) and the ABC efflux transporters, such as P‐glycoprotein (P‐gp), Breast Cancer Resistance Protein (BCRP), or multidrug resistance proteins 2, 3, or 4 (MRP2/3/4). ¹² These transporters, as well as hepatic metabolism, can affect the systemic exposure and response of many drugs, including cholesterol‐lowering (e.g., HMG‐CoA reductase inhibitors), antihypertensive (e.g., angiotensin II receptor blockers), antiviral (e.g., NS3/4A protease inhibitors), and antidiabetic (e.g., meglitinides) drugs. ¹³ , ¹⁴ , ¹⁵

Interestingly, the AUC of drugs that are OATP substrates and significantly metabolized, in particular by cytochrome P450 (CYP) 3A enzymes, can increase significantly (as much as 32‐fold) in patients with HI (Table 1). This increase in AUC increases with the degree of HI, classified as the Child‐Pugh (CP) score CP‐A (mild), CP‐B (moderate), or CP‐C (severe; Table 1). In contrast, the AUC of OATP and biliary efflux transporter (BET) substrates, that are not significantly metabolized and mostly excreted unchanged in the urine and/or bile, such as pitavastatin, rosuvastatin, valsartan, pravastatin, and gadoxetic acid, are less affected by HI (<5‐fold; Table 1). The reason for this difference needs to be elucidated to successfully predict, through PBPK M&S, the impact of HI on the AUC of drugs that are OATP/BET or OATP/CYP3A substrates. To note, in this paper, we refer to OATP/BET substrates as OATP substrates whose hepatic elimination is primarily mediated by biliary excretion of the unchanged drug and OATP/CYP3A4 (we recognize that these drugs may also be metabolized by CYP3A5, but for simplicity we refer to only CYP3A4) substrates as OATP substrates whose hepatic elimination is mediated by CYP3A4‐mediated metabolism (even though they may also be partially eliminated by BET).

TABLE 1.

Effect of different degrees of HI on the plasma AUC of OATP substrate drugs as well as their major route of elimination.

Drug	AUCRHI (CP‐A)	AUCRHI (CP‐B)	AUCRHI (CP‐C)	Uptake transport (liver)	Efflux transport (liver)	Metabolism	Major elimination route
Asunaprevir	0.79	9.83	32.1	OATP1B1, OATP2B1	P‐gp	CYP3A	Metabolism + biliary excretion
Glecaprevir	1.15	1.89	15.8	OATP1B1/3	BCRP, P‐gp	CYP3A	Biliary excretion
Grazoprevir	1.66	4.82	11.7	OATP1B1	BCRP, P‐gp	CYP3A	Biliary excretion
Paritaprevir	0.72	2.05	9.84	OATP1B1/3	BCRP, P‐gp	CYP3A	Metabolism
Atorvastatin	4.4	9.8	–	OATP1B1/3, OATP2B1, NTCP	BCRP, P‐gp, MRP2 c , MRP3, MRP4 c	CYP3A, minor: UGT	Metabolism
Elagolix	0.98	3.04	6.83	OATP1B1	P‐gp	CYP3A4 (major), CYP2D6, CYP2C8, UGT (minor)	Metabolism
Voxilaprevir	–	4.49	6.25	OATP1B1/3	BCRP, P‐gp	CYP3A4 (major), CYP2C8, CYP1A2	Biliary excretion
Fimasartan	1.11	5.17	–	OATP1B1, OATP2B1	BCRP	CYP3A4 (major), UGT1A3, UGT1A1, UGT	Biliary excretion
Repaglinide	–	4.3 a	4.3 a	OATP1B1, OATP1B3 c	P‐gp c	CYP2C8, CYP3A, minor: UGT	Metabolism
Pitavastatin	1.28	3.54	–	OATP1B1/3, OATP2B1, NTCP	BCRP, P‐gp, MRP3 c , MRP4 c	Minimal d : UGT2B7, CYP2C9	Biliary excretion
Valsartan	2.21	2.14	–	OATP1B1/3, OATP2B1 c	MRP2, P‐gp c	Minimal d : CYP2C9	Biliary excretion
Gadoxetic acid (i.v.)	1.58	1.31	1.62	OATP1B1/3, NTCP	MRP2	Minimal d	Biliary + renal excretion
Pravastatin	1.34 b	1.34 b	1.34 b	OATP1B1/3, OATP2B1, NTCP	MRP2, MRP3 c , MRP4 c , BCRP c	Minimal d : CYP3A, UGT	Biliary excretion
Rosuvastatin	1.05	1.21	–	OATP1B1/3, NTCP, OATP2B1	BCRP, MRP2, P‐gp, MRP3 c	Minimal d : CYP2C9, CYP2C19, CYP3A, UGT	Biliary (major) + renal excretion

Note: Data were retrieved from the University of Washington Drug Interaction Database (DIDB) (http://www.druginteractionsolutions.org; last accessed August 2023). See Appendix S1 for a full list of references for each drug. Hepatic impairment studies were conducted in populations consisting of mainly (>80%) White subjects, except for pitavastatin and fimasartan, which were conducted primarily in Asian subjects. SLCO1B1 genotype information was not provided.

Abbreviations: AUCR_HI, ratio of drug area under the concentration–time curve in HI vs. healthy; CP, Child‐Pugh; HI, hepatic impairment; NA, not available.

^a Mixed CP‐B and CP‐C populations.

^b CP score not reported.

^c Conflicting data for the involvement of the indicated pathway (e.g., different in vitro systems provide different conclusions); further investigation is needed to confirm contribution.

^d Minimal metabolism was concluded by the absence of significant clinical drug–drug interaction (AUC ratio < 20%) with known inhibitors of the involved pathways.

The aims of this study were three‐fold: (1) to understand the key factors that can affect the increase in HI of AUC of the dual OATP/BET or OATP/CYP3A4 substrates using the extended clearance model; (2) to assess the performance of PBPK models (using Simcyp, Certara, NJ) to predict the changes in AUC of OATP/BET substrates (pitavastatin, rosuvastatin, valsartan, and gadoxetic acid) or OATP/CYP3A4 substrates (atorvastatin and fimasartan) for various degrees of HI (CP‐A to C); and (3) to use the insights gained from 1 above to improve PBPK model predictions of the effect of HI on the systemic exposure of OATP/CYP3A4 substrates using atorvastatin and fimasartan as test drugs.

METHODS

Systemic exposure of hepatically transported drugs after intravenous administration

The extended clearance (CL) model stipulates that all hepatobiliary CLs (uptake, efflux, and metabolism), in addition to hepatic blood flow (Q _H ), and the unbound fraction in blood (f _u,b) determine hepatic drug CL (CL_H). ¹⁶ , ¹⁷ , ¹⁸ , ¹⁹ Here, we have deliberately chosen to quantify the change in unbound blood AUC (AUC_u) in HI, rather than total blood or plasma AUC, as it is the unbound blood concentration that drives drug efficacy and toxicity.

When a transported drug is predominately eliminated hepatically (i.e., negligible renal or intestinal excretion), its AUC_u following i.v. dosing is defined as follows (derived from ref. 19):

$$\frac{\mathrm{A}{\mathrm{UC}}_{\mathrm{u}}}{\text{Dose}\left(\mathrm{IV}\right)}=\frac{{\mathrm{fu}}_{\mathrm{b}}}{Q_H}+\frac{1}{{\mathrm{CL}}_{\text{in}}^{\mathrm{s}}}\bullet \left(1+\frac{{\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}}{{{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}}\right)$$ (1)

where ${\mathrm{CL}}_{\text{in}}^{\mathrm{s}}$ is the intrinsic sinusoidal influx CL, ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ is the intrinsic sinusoidal efflux CL, ${\mathrm{CL}}_{\mathrm{met}}$ is the intrinsic metabolic CL, and ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}$ is the intrinsic canalicular efflux CL. Here, the ${\mathrm{CL}}_{\text{in}}^{\mathrm{s}}$, ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$, and ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}$ include both active transport and passive diffusion.

When ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}\ll {{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}$, AUC_u is a function of f _u,b, Q _H , and ${\mathrm{CL}}_{\text{in}}^{\mathrm{s}}$ only, as follows:

$$\frac{\mathrm{A}{\mathrm{UC}}_{\mathrm{u}}}{\text{Dose}\left(\mathrm{IV}\right)}=\frac{{\mathrm{fu}}_{\mathrm{b}}\bullet {\mathrm{CL}}_{\text{in}}^{\mathrm{s}}+{\mathrm{Q}}_{\mathrm{H}}}{Q_H\bullet {\mathrm{CL}}_{\text{in}}^{\mathrm{s}}}$$ (2)

In this case, the hepatic uptake is the rate‐determining step (RDS) of the drug hepatic CL (scenario referred here as RDS_CL,H = uptake).

Systemic exposure of transported drugs after oral administration

For oral administration, according to the extended clearance model, the AUC_u of a drug predominately eliminated hepatically is described as follows (derived from ref. 19):

$$\frac{\mathrm{A}{\mathrm{UC}}_{\mathrm{u}}}{\text{Dose}\left(\mathrm{PO}\right)}=f_a\bullet F_G\bullet \frac{1}{{\mathrm{CL}}_{\text{in}}^{\mathrm{s}}}\bullet \left(1+\frac{{\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}}{{{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}}\right)$$ (3)

Therefore, the blood AUC_u of drugs administered p.o. is affected by changes in f _a ,·F _G , and in ${\mathrm{CL}}_{\text{in}}^{\mathrm{s}}$, as well as changes in the ratio ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}/\left({{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}\right)$. Note, for oral administration, Q _H is not a determinant of drug blood AUC_u.

When ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}\ll {{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}$ (i.e., RDS_CL,H = uptake):

$$\frac{\mathrm{A}{\mathrm{UC}}_{\mathrm{u}}}{\text{Dose}\left(\mathrm{PO}\right)}=\frac{f_a\bullet F_G}{{\mathrm{CL}}_{\text{in}}^{\mathrm{s}}}$$ (4)

F _G can be estimated from the villi blood flow (Q _villi), gut metabolism, and drug permeability in the gastrointestinal tract, as described before ²⁰ :

$$F_G=\frac{Q_{\text{villi}}}{Q_{\text{villi}}+{\mathrm{fu}}_{\mathrm{G}}\bullet {\mathrm{CL}}_{\mathrm{met},\mathrm{G}}\bullet \left(1+\raisebox{1ex}{$Q_{\text{villi}}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{CL}}_{\text{perm}}$}\right.\right)}$$ (5)

fu_G is the unbound drug fraction in the enterocytes, CL_met,G is the intrinsic metabolic CL in the gut, and CL_perm is the drug intestinal permeability.

Simulation of the effect of CP‐C on the exposure of transported virtual compounds administered i.v.

First, we illustrate the importance of the ratio ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}/\left({{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}\right)$ (which determines the RDS of CL_H) on the effect of HI on the AUC_u of i.v. administered drugs. The i.v. administration was chosen to focus on hepatic (vs. gut) drug CL. We created virtual compounds with fixed hepatic intrinsic CLs (CL_int,H) of 100, 1000, and 10,000 mL/min, corresponding to low hepatic extraction (E _H  = 6%), intermediate E _H (37%), and high E _H (86%), where CL_int,H is a function of all hepatobiliary intrinsic CLs:

$${\mathrm{CL}}_{\mathrm{int},\mathrm{H}}=\frac{{\mathrm{CL}}_{\text{in}}^{\mathrm{s}}\bullet \left({{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}\right)}{{\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}+{{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}}$$ (6)

Different E _H were examined because Equation 1 suggests that hepatic blood flow is a determinant of the blood AUC of i.v.‐administered drugs.

For each level of E _H (see Figure 1 for details), two scenarios of the rate‐determining step of CL_H were investigated: RDS_CL,H = uptake (i.e., ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}\ll {{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}$), and RDS_CL,H = all (i.e., condition ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}\ll {{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}$ does not apply and CL_H is determined by all hepatobiliary CLs). The ratios ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}/\left({{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}\right)$ and ${\mathrm{CL}}_{\text{in}}^{\mathrm{s}}/{\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ were kept the same for compounds A, C, and E, for which RDS_CL,H = uptake (0.02 and 102, respectively), and for compounds B, D, and F, for which RDS_CL,H = all (9 and 2, respectively); those ratios were chosen arbitrarily to satisfy the different RDS_CL,H scenarios for given CL_int,h values.

FIGURE 1.

After i.v. administration, both the rate‐determining step of hepatic clearance and the hepatic extraction ratio affect the magnitude of the effect of hepatic impairment on the blood unbound AUC of the transported drugs. All clearance units are in mL/min. AUCR_HI,u, ratio of area under the blood unbound concentration–time profile in hepatic impaired subjects vs. healthy volunteers; CL_int,H, intrinsic hepatic clearance; ${\mathrm{CL}}_{\mathrm{met}}$, intrinsic metabolic clearance; ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}$, intrinsic canalicular efflux clearance; ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$, intrinsic sinusoidal efflux clearance; ${\mathrm{CL}}_{\text{in}}^{\mathrm{s}}$, intrinsic sinusoidal influx clearance; RDS_CL,H, rate‐determining step of hepatic clearance (CL_H).

For these virtual compounds, we assumed that: (1) renal elimination was negligible; (2) ${\mathrm{CL}}_{\text{in}}^{\mathrm{s}}$ was mediated via OATP1B1 (CL_int,OATP1B1 = 95% of ${\mathrm{CL}}_{\text{in}}^{\mathrm{s}}$) and passive diffusion (CL_int,pd = 5% of ${\mathrm{CL}}_{\text{in}}^{\mathrm{s}}$); (3) ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ was mediated by passive diffusion only (no active transport, i.e., ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}={\mathrm{CL}}_{\mathrm{int},\mathrm{pd}}$); (4) ${{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}$ was mediated by CYP3A4 metabolism (CL_int,CYP3A4 = 90% of ${{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}$), CYP2C9 metabolism (CL_int,CYP2C9 = 5% of ${{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}$), and P‐gp canalicular efflux (CL_int,P‐gp = 5% of ${{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}$); (5) f _u,b was equal to 1 and unaffected in HI. A summary of physiological parameters and incorporated changes in HI is described in Table S1. Briefly, relevant PK parameters were modulated in CP‐C as follows (from the most affected to the least affected): CL_int,CYP3A4 (−85%), CL_int,OATP1B1 (−77%), CL_int,P‐gp (−75%), CL_int,CYP2C9 (−73%), CL_int,pd (−56%), and Q _H (−6%). Note that for DMETs, the changes described above reflect the modulation of DMET abundance (if any) at the cellular level (i.e., DMET abundance in pmol per million cells or per mg of microsomal protein) and functional liver weight in HI, whereas for passive diffusion, the change reported is explained by the reduction of the functional liver weight. Note, we assumed that the enzyme/transporter activity per pmol of enzyme/transporter did not change between healthy volunteers and those with HI. The changes described above are based on the Simcyp version 21 healthy volunteers (HVs) and CP‐C population representatives, that is, the individual that represents the features of the majority part of a given population. ²¹

The drugs' AUC_u in the CP‐C population was calculated using Equation 1 and changes in Q _H , passive diffusion, and DMET abundance described above and in Table S1. AUCR_HI,u was calculated as the ratio of AUC_u in patients with HI versus HVs. We chose to simulate AUCR_HI,u in the CP‐C population as it is associated with the greatest effect in HI.

Simulation of the effect of CP‐C on the exposure of Compound X, a model OATP/CYP3A4 drug administered p.o.

In the second set of simulations, we predicted the AUCR_HI,u after p.o. administration of a model OATP/CYP3A4 drug, named “Compound X" (modeled on atorvastatin; Table 2). CL_int,H was calculated (Equation 6) assuming that the hepatic uptake was mediated 95% by OATP1B1 and 5% by passive diffusion, sinusoidal efflux was mediated only by passive diffusion, metabolism was 100% via CYP3A4, and canalicular efflux CL was 100% via P‐gp, with negligible renal excretion. CL_met,g was estimated from the hepatic CL_met using the ratio of the abundance of CYP3A4 in the gut and the liver in the HVs (“Sim‐Healthy Volunteers”) population of Simcyp version 21 (Table S1). The f _a ·F _G was estimated from Equation 5, where f _a  = 1 (mediated only by passive diffusion), f _u,G = 1 and CL_perm = 1.16 mL/min/kg (calculated from the effective intestinal permeability in atorvastatin library compound of Simcyp version 21 [Table S6], as previously described ²⁰ ).

TABLE 2.

Simulated effect of hepatic impairment on the unbound blood exposure (AUCR_HI,u) of Compound X.

Parameter	Initial value (HVs)	Simulated value in CP‐C	Simulated change in CP‐C
${\mathrm{CL}}_{\text{in}}^{\mathrm{s}}$	405	96	−76%
${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$	25	11	−56%
CLmet	58	8.5	−85%
${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}$	4.3	1.1	−75%
CLint,h	290	45	−85%
${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}/\left({{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}\right)$	0.40 a	1.1	+188%
$1+{\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}/\left({{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}\right)$	1.40	2.1	+43%
${\mathrm{CL}}_{\mathrm{met}}/\left({{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}\right)$	0.93	0.89	−5%
${\mathrm{CL}}_{\mathrm{met},\mathrm{g}}$	0.42	0.20	−52%
fa· Fg	0.69	0.84	+21%
AUCRHI,u (CP‐C)	–	7.84	–

Note: Initial values of ${\mathrm{CL}}_{\text{in}}^{\mathrm{s}}$, ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$, ${\mathrm{CL}}_{\mathrm{met}}$, and ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}$ were obtained from atorvastatin in vitro in vivo extrapolation of hepatic CL. ³⁴ , ³⁵ The units of all CLs in this table are in mL/min/kg body weight.

Abbreviations: AUCR_HI,u, ratio of unbound blood AUC in HI versus healthy; ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}$, intrinsic canalicular efflux clearance; CL_int,h, intrinsic hepatic clearance; ${\mathrm{CL}}_{\mathrm{met}}$, intrinsic hepatic metabolic clearance; ${\mathrm{CL}}_{\mathrm{met},\mathrm{g}}$, intrinsic gut metabolic clearance; ${\mathrm{CL}}_{\text{in}}^{\mathrm{s}}$, intrinsic hepatic influx clearance; CP‐C, Child‐Pugh C; F _g , fraction escaping gut metabolism; HVs, healthy volunteers.

^a ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}/\left({{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}\right)=0.40$ suggests that the hepatic clearance is rate‐determined by all hepatic clearances rather than uptake only. ³⁵

To predict AUCR_HI,u of Compound X in CP‐C, we incorporated changes in hepatic passive diffusion, OATP1B1, and P‐gp transport, hepatic CYP3A4 metabolism described above and in Table S1. Gut CYP3A4‐mediated CL_int (−52%) and Q_villi (+100%) in CP‐C were also modulated (Table S1). We assumed that CL_perm was not affected in HI.

Sensitivity analyses of the ratio ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}/\left({{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}\right)$ on the AUCR_{HI ,u} of compound X

To analyze the effect of varying the ratio ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}/\left({{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}\right)$ (and consequently, the different RDS_CL,H scenarios) on the simulated AUCR_HI,u in CP‐C of Compound X, we performed sensitivity analyses of AUCR_HI,u by scaling either ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ or ${\mathrm{CL}}_{\mathrm{met}}$ (and therefore ${\mathrm{CL}}_{\mathrm{met},\mathrm{G}}$; derived from ${\mathrm{CL}}_{\mathrm{met},\mathrm{H}}$) in HVs (i.e., before incorporating the effect of CP‐C) by a factor of 0.001 to 1000 while keeping the other hepatobiliary CLs the same as in the initial model (Table 2). No sensitivity analysis for ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}$ was performed as this was a minor (<10%) elimination pathway of Compound X (Table 2). The effects of CP‐C on all physiological parameters (f _u,b, DMET abundance, and blood flows) were kept the same as described above.

Our research group previously reported a 38% increase in the abundance of MRP3 in cirrhosis. ² Therefore, assuming that Compound X's sinusoidal efflux is 90% mediated by MRP3 and 10% passive diffusion (vs. by passive diffusion only in earlier simulations), we performed similar sensitivity analyses, as described above, but using this reported increase in MRP3 abundance in cirrhosis.

Prediction of the effect of HI on the systemic PKs of OATP/BET and OATP/CYP3A4 substrates using PBPK M&S

The effect of CP‐A, CP‐B, and CP‐C on the plasma AUC of four OATP/BET substrates (pitavastatin, rosuvastatin, valsartan, and gadoxetic acid) and two dual OATP/CYP3A4 substrates (atorvastatin and fimasartan) was simulated in Simcyp version 21. These drugs were chosen because they are all OATP substrates and either had available PBPK models on Simcyp version 21 (valsartan and atorvastatin) or had i.v. PK data that could be used to develop new PBPK models (pitavastatin, rosuvastatin, gadoxetic acid. and fimasartan; see Appendix S1). For all these compounds, a full PBPK distribution model with the permeability‐limited liver model was used. All models were validated by comparing the simulated and observed PK profiles from three to six studies, including the HV controls of the HI studies, where available (Figures S1–S6). This validation was not comprehensive as it did not include drug–drug interaction studies, tissue imaging studies, genotype differences, or metabolites/excreta data. These studies used for model validations were distinct from those used for model development and optimization.

We then simulated the drugs' AUCR_HI (i.e., the plasma AUCR in HI vs. HVs) in CP‐A, CP‐B, and, for gadoxetic acid, CP‐C (data in CP‐C were not available for other drugs), and compared them with reported data ²² , ²³ , ²⁴ , ²⁵ , ²⁶ , ²⁷ (see Table S8 for trial design and demographic information). Note, we simulated the effect of HI on plasma AUC rather than AUC_u because the measured concentrations in HI trials used for validation were total and not unbound plasma (or, in the case of gadoxetic acid, serum) concentrations. Two types of simulations of the effect of HI were conducted: first, using Simcyp cirrhosis populations (“Sim‐cirrhosis CP‐A,” “Sim‐cirrhosis CP‐B,” and “Sim‐cirrhosis CP‐C”) without incorporating changes in transporter abundance at the cellular level (i.e., abundance in pmol/million hepatocytes) but including the change in the functional liver volume (tissue volume fold‐scalar in the Tissue Composition Tab, reported in Table 3); second, with transporter abundance changes at the cellular level (this was done by applying transporter abundance changes reported in Table 3 [based on Simcyp version 21 cirrhosis population files]). Physiological changes, other than transporter abundance and tissue volume scalar, were kept the same as those in the population library in Simcyp simulator version 21. Population‐specific physiological parameters are summarized elsewhere. ¹¹ Root mean square error and mean error were used to compare performances in terms of precision and bias, respectively.

TABLE 3.

Changes in hepatic transporter abundance and functional volume incorporated in PBPK model predictions of the effect of hepatic impairment on the systemic exposure of transported drugs.

	Ratio CP‐A vs. HVs	Ratio CP‐B vs. HVs	Ratio CP‐C vs. HVs
Hepatic transporter abundance (pmol/million hepatocytes)
NTCP	1	1	1
OATP1B1	1	0.81	0.52
OATP1B3	0.81	0.45	0.28
OATP2B1	1	1	1
MRP3	1	1	1
P‐gp	0.57	0.57	0.57
MRP2	0.69	0.73	0.73
BCRP	1	1	1
Hepatocellularity (million hepatocytes/g of liver)	1	1	1
Liver volume (L)	0.86	0.71	0.59
Liver density (g/L)	1	1	1

Note: Data based on “Sim‐Healthy Volunteers” (HVs), “Sim‐Cirrhosis CP‐A,” “Sim‐Cirrhosis CP‐B,” and “Sim‐Cirrhosis CP‐C” populations in Simcyp version 21.

Abbreviations: CP, Child‐Pugh; PBPK, physiologically‐based pharmacokinetic.

Sensitivity analyses of ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ values of atorvastatin and fimasartan on AUCR_HI in moderate HI (CP‐B)

To optimize predictions of AUCR_HI in CP‐B for atorvastatin and fimasartan, we increased the ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ in both compound files (initially assumed to be equal to passive diffusion for atorvastatin and negligible for fimasartan) up to 10,000‐fold and observed the resulting effect on AUCR_HI. Negligible ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ was assumed in the initial fimasartan model to estimate ${\mathrm{CL}}_{\text{in}}^{\mathrm{s}}$ from i.v. clinical data (assuming RDS_CL,H = uptake) because data on passive diffusion and hepatobiliary CLs of the drug are not available. For these simulations, the transporter abundance changes at the cellular level were included (Table 3). Additionally, we performed the same sensitivity analyses but arbitrarily assumed that 90% of the sinusoidal efflux was mediated by MRP3 (vs. passive diffusion only) and incorporated our previous data on MRP3 modulation by cirrhosis (+38%; described above).

RESULTS

The RDS_{CL ,H} and the hepatic extraction of a drug determine the magnitude of AUCR_{HI ,u} after i.v. administration

Simulations of different scenarios of RDS_CL,H and E _H for i.v. administration show that AUCR_HI,u is greater when RDS_{CL , H} = all than when RDS_{CL , H} = uptake (e.g., B vs. A, D vs. C, and F vs. E in Figure 1). This is because for the former (RDS_CL,_H = all), the AUC_u in HI is determined by changes in ${\mathrm{CL}}_{\text{in}}^{\mathrm{s}}$, ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}/\left({{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}\right)$, and Q _H (note that here, for simplicity, f _u,b was assumed to equal 1; Equation 1). In contrast, when RDS_CL,H = uptake (i.e., ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}\ll {{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}$ as in A, C, and E), the modulation of the ratio ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}/\left({{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}\right)$ in HI (e.g., reduced CYP3A4 or biliary CL) should not affect the AUC_u of the drug (Equation 2). ¹⁷

In addition, irrespective of the RDS_CL,H, as E _H increases toward 100% (i.e., as E _H approaches hepatic blood flow), AUCR_HI,u diminishes. Indeed, HI has little effect on Q _H (Table S1). Therefore, for i.v. administration, the AUCR_HI,u is higher for low E _H drugs (where CL_H is highly dependent on CL_int,H) than for high E _H drugs (where CL_H is highly dependent on Q _H ).

The ratio ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}/\left({{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}\right)$ and f_a· F _G are major determinants of AUCR_{HI ,u} of orally administered drugs

In the case of p.o. administration, when RDS_CL,H = all, AUCR_HI,u is affected by changes in ${\mathrm{CL}}_{\text{in}}^{\mathrm{s}}$, the ratio ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}/\left({{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}\right)$, and f _a ·F _G (Equation 3).

The simulated AUCR_HI,u of Compound X in CP‐C is 7.84 (Table 2). Through sensitivity analyses, we determined whether changes in ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ or ${\mathrm{CL}}_{\mathrm{met}}$ could affect Compound X's AUCR_HI,u (Figure 2). Note that Figure 2a,c show simulations where sinusoidal efflux is assumed to be mediated by passive diffusion (which decreases in HI due to change in liver functional volume), whereas Figure 2b,d show simulations where sinusoidal efflux is assumed to be mediated by MRP3 (fraction transported f _t  = 90%) and where MRP3 abundance in HI increases by 38%. ²

FIGURE 2.

Both the sinusoidal efflux CL and hepatic plus intestinal metabolic CL affect the magnitude of the AUCR_HI,u of orally administered transported drugs. For panels (a, c), drug sinusoidal efflux was assumed to be passive (and decreasing in HI as a result of loss of functional liver volume; see Table 3), whereas for panels (b, d), 90% of the drug was assumed to be transported across the sinusoidal membrane by MRP3, and the abundance of MRP3 in CP‐C was assumed to increase by 38%, based on our proteomic data. ² The effect of CP‐C on each component of Equation 3 are also shown, that is, gut availability (dotted blue lines), intrinsic hepatic influx (dashed green lines) and sinusoidal efflux relative to hepatic elimination (metabolism and canalicular efflux; dash‐dotted purple lines). AUCR_HI,u (shown as a continuous red lines) is the product of the ratio of each of these three components in CP‐C vs. HVs (i.e., the continuous red lines are the products of the other three lines). AUC_u, area under the blood unbound concentration–time profile; AUCR_HI,u, ratio of blood unbound AUC in hepatic impairment vs. healthy volunteers; ${\mathrm{CL}}_{\mathrm{met}}$, intrinsic metabolic clearance; ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}$, intrinsic canalicular efflux clearance; ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$, intrinsic sinusoidal efflux clearance; ${\mathrm{CL}}_{\text{in}}^{\mathrm{s}}$, intrinsic sinusoidal influx clearance; CP, Child‐Pugh; f _a , fraction of the administered drug absorbed in enterocytes; F _G , fraction of the drug escaping gut metabolism; HV, healthy volunteers.

We found that AUCR_HI,u was sensitive to variation in ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ (Figure 2a,b), and could be as large as 45 for Compound X (Figure 2b). This is because, as ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ increases (in the HV model, using the diamond as a reference point), drug CL_H become more dependent on hepatic elimination (i.e., ${{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}$) than on hepatic uptake (${\mathrm{CL}}_{\text{in}}^{\mathrm{s}}$); when CYP3A4‐mediated ${\mathrm{CL}}_{\mathrm{met}}$ is the main contributor to hepatic elimination, this results in a large AUCR_HI,u because this parameter is more affected by HI than ${\mathrm{CL}}_{\text{in}}^{\mathrm{s}}$. In contrast, as ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ decreases, AUCR_HI,u decreases because CL_H becomes rate‐determined by uptake only, and any modulation of ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$, ${\mathrm{CL}}_{\mathrm{met}}$, and/or ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}$ by HI does not affect drug AUC_u.

The relationship between ${\mathrm{CL}}_{\mathrm{met}}$ and AUCR_HI,u is less straightforward (Figure 2c,d). Indeed, the extent of metabolism (i.e., ${\mathrm{CL}}_{\mathrm{met}}$ value) affects not only the RDS_CL,H, but also gut availability (i.e., f _a ∙F _G ). In Figure 2c, decreasing ${\mathrm{CL}}_{\mathrm{met}}$ (using the diamond as a reference point) results first in a slight increase in the predicted AUCR_HI,u because hepatic elimination decreases. However, as ${\mathrm{CL}}_{\mathrm{met}}$ continues to decrease, hepatic elimination becomes driven by canalicular efflux rather than metabolism (note that in the initial model, hepatic elimination was 93% driven by metabolism; Table 2). Because the abundance of canalicular efflux transporters is less affected by HI than the abundance of CYP3A4 (Table S1; ¹ , ² ), AUCR_HI,u is lower when hepatic elimination is mediated by canalicular efflux rather than metabolism. These opposite effects are reflected by the dash‐dotted purple line in Figure 2c,d, showing a bump around the initial prediction. In addition, as the extent of metabolism (in both the liver and the gut; gut metabolism was estimated based on hepatic metabolism and the relative CYP3A4 abundance in gut vs. liver) decreases, more drug escapes intestinal metabolism (i.e., f _a ∙F _G increases, getting closer to 1, and therefore less affected by HI; see dotted blue line in Figure 2c,d). Increasing ${\mathrm{CL}}_{\mathrm{met}}$ had the opposite effect: as ${\mathrm{CL}}_{\mathrm{met}}$ increases, the RDS_CL,H becomes uptake (dash‐dotted purple line in Figure 2c,d), but intestinal availability (f _a ·F _G ) becomes more vulnerable to the decrease in intestinal CYP3A4 abundance in HI (dotted blue line in Figure 2c,d).

We found that the predicted AUCR_HI,u were higher when we assumed that ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ was mediated by active transport (MRP3, f _t  = 90%), which might increase in HI ² (see discussion for conflicting data) than when we assumed that ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ was mediated by passive diffusion, which decreases in HI as a result of the loss of functional liver volume (Figure 2b vs. Figure 2a and Figure 2d vs. Figure 2c).

Note that we simulated here the effect of HI on the blood unbound AUC, because unbound concentrations (rather than total) drive efficacy and toxicity. In other words, we did not incorporate the effect of HI on drug binding to plasma proteins (i.e., f _u,b). Should we have considered the total (bound + unbound) blood AUC, the effect of HI would have been smaller, because f _u,b generally increases in HI due to a decrease in the abundance of drug binding plasma proteins. ⁵ , ²⁸

The AUCR_HI of OATP/BET substrates were relatively well predicted by PBPK M&S

Using PBPK M&S, we predicted the AUCR_HI of OATP/BET substrates pitavastatin, rosuvastatin, valsartan, and gadoxetic acid within two‐fold of the observed data (Figure 3; Figures S7 and S8). Predictions were modestly improved (reduced root mean square error and mean error) when accounting for hepatic transporter abundance changes in addition to changes in functional liver volume in HI (Figure 3b) versus accounting only for changes in functional liver volume (Figure 3a).

FIGURE 3.

PBPK modeling achieves relatively good predictions of the AUCR_HI for poorly metabolized OATP substrates (pitavastatin, rosuvastatin, valsartan, and gadoxetic acid). Simulations using PBPK modeling were done in Simcyp version 21, without (a) and with (b) incorporation of changes in transporter abundance at the cellular level. In both cases, the PBPK models included loss of functional liver volume (Table 3). Apart from gadoxetic acid administered i.v., all drugs were administered orally. The continuous lines represent the lines of unity, the dotted lines represent the bioequivalence prediction range (i.e., AUCR_HI P/O ranging 0.8–1.25) and the dashed lines represent the two‐fold prediction range (i.e., AUCR_HI P/O ranging 0.5–2). AUCR_HI, ratio of area under the plasma concentration–time profile (AUC) in hepatic impairment subjects versus healthy volunteers; CP‐A, Child‐Pugh A; CP‐B, Child‐Pugh B; CP‐C, Child‐Pugh C; ME, mean error; PBPK, physiologically‐based pharmacokinetic; RMSE, root mean square error.

The AUCR_HI of the OATP/CYP3A4 substrates atorvastatin and fimasartan were relatively well‐predicted by PBPK M&S, but these predictions improved when CL_{int ,s,ef} was increased

AUCR_HI for dual OATP/CYP3A4 substrates atorvastatin (in both CP‐A and CP‐B) and fimasartan (in CP‐B) were predicted within two‐fold of the observed values, but, except for fimasartan in CP‐A, fell below the 0.8 to 1.25‐fold bioequivalence range (Figure 4a,b; Figures S7 and S8). Therefore, based on the outcome of the sensitivity analyses discussed above, we hypothesized that an increase in the ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ values of the two drugs would move the predicted AUCR_HI into the bioequivalence range. Indeed, the AUCR_HI of the two drugs fell within the bioequivalence range when we assumed that ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ was increased (rather than decreased) in HI (Figure 4c,d).

FIGURE 4.

Prediction of atorvastatin (a, c) and fimasartan (b, d) AUCR_HI using PBPK modeling improved by increasing the extent of sinusoidal efflux (${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$) and by affecting the directionality of the change in ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ in HI. (a, b) Simulations were conducted with Simcyp version 21 using one of two scenarios in HI: using the default reduction in functional liver volume without (blue bars) and with incorporation of changes in hepatic transporter abundance at the cellular level (red bars; Table 2). (c, d) Predictions of AUCR_HI in CP‐B were improved by increasing the

$${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$$

of the drug (i.e., before incorporating the effect of HI). Empty and full symbols respectively show simulations where sinusoidal efflux was assumed to be mediated predominately (90%) by MRP3 (and MRP3 abundance was increased in HI ² ) or only by passive diffusion (decreased in HI due to loss of functional liver volume; see text for details). Initial ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ values and resulting simulated AUCR_HI are highlighted in the yellow box. The dashed lines represent the observed mean value (refs. 26, 27) and dotted lines and shaded gray area represent the twofold and 1.25‐fold (i.e., bioequivalence) prediction ranges, respectively. AUCR_HI, ratio of area under the plasma concentration–time profile (AUC) in hepatic impairment subjects versus healthy volunteers; CP, Child‐Pugh.

DISCUSSION

The systemic exposure of drugs that are OATP substrates increases significantly in HI. Whereas the AUCR_HI in CP‐A to CP‐C is modest (<5‐fold) for substrates of OATPs that are predominately excreted unchanged in the bile, it can be large (>10) for drugs that are metabolized by CYP3A4 enzymes (Table 1). Our simulations of AUCR_HI,u, using the extended clearance model, for virtual OATP/CYP3A4 model drug compounds administered i.v. and p.o. provide an explanation for this differential effect of hepatic impairment on OATP substrates:

• For most (if not all) OATP substrate drugs, it is likely that RDS_CL,H = all rather than RDS_CL,H = uptake; therefore the magnitude of AUCR_HI,u is sensitive to the ratio ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}/\left({{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}\right)$. RDS_CL,H = uptake is often assumed for low permeability compounds (i.e., ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}\ll {{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}$; in which case, sinusoidal efflux is assumed to be mediated by passive diffusion). However, we recently showed, using positron emission tomography imaging, that this is not true for the classical low permeability OATP‐substrate, rosuvastatin. ²⁹ When RDS_CL,H = all, AUCR_HI,u is larger than when RDS_CL,H = uptake, because the modulation of all hepatobiliary CLs in HI is responsible for the reduced hepatic CL of drugs in HI (Figure 1). In this case, the greater the ratio ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}/\left({{\mathrm{CL}}_{\mathrm{met}}+\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{c}}\right)$, the greater the AUCR_HI,u, until a plateau is reached for very large ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ (Figure 2a,b).

• When RDS_CL,H = all and hepatic elimination is driven primarily by CYP3A4 metabolism, AUCR_HI,u can be large because of the larger decrease in hepatic CYP3A4 abundance in HI (Figure S9). This likely explains the larger AUCR_HI values (>10) reported for dual OATP/CYP3A4 vs. OATP/BET substrates (Table 1). This effect is amplified with oral administration when the drug is also highly extracted by intestinal CYP3A4 metabolism. In that event, F _G (in HVs) will be low and therefore AUCR_HI,u will likely be sensitive to any decrease in gut CYP3A4 abundance caused by HI (Figure 2c,d). Note that we focused here on CYP3A metabolism, but this may apply to substrates of other enzymes that are relevant for both liver and gut metabolism (such as uridine 5′‐diphospho‐glucuronosyltransferases; see Table 1).

• When RDS_CL,H = all and hepatic elimination is mainly driven by biliary excretion of the unchanged drug, AUCR_HI,u is limited by the lower impact of HI on the abundance of biliary efflux transporters (vs. impact on hepatic enzymes, such as CYP3A4; Figure S9). This likely explains the smaller AUCR_HI values (<5) reported for OATP substrates (Table 1).

• When RDS_CL,H = all, the directionality (i.e., increase/decrease) of the modulation of ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ in HI significantly affects the AUCR_HI,u. Indeed, an increase in ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ in HI (as a result of increased abundance of sinusoidal efflux transporters ² ) further magnifies the effect of reducing hepatic elimination on drug CL (i.e., increases AUCR_HI,u; Figure 2b–d). Oppositely, a decrease in ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ in HI (e.g., if it is mediated only by passive diffusion; Figure 2a–c) increases drug CL and its dependency on ${\mathrm{CL}}_{\text{in}}^{\mathrm{s}}$ and therefore reduces AUCR_HI,u. This is of particular interest as there are conflicting data from different groups regarding the directionality of the modulation of the abundance of sinusoidal efflux transporters (MRP3 and MRP4) in HI: in‐house data from our group suggest that MRP3 abundance increases in HI, whereas others using a different peptide for quantification have shown a downregulation of the transporter in HI ² , ³ , ³⁰ ; similarly MRP4 abundance was shown to be increased by some ³ whereas reduced by others. ³⁰

These insights from the extended clearance model were leveraged to improve PBPK M&S predictions of AUCR_HI for the two dual OATP/CYP3A4 substrates, atorvastatin and fimasartan. Indeed, whereas the AUCR_HI of OATP/BET substrates pitavastatin, rosuvastatin, valsartan, and gadoxetic acid was relatively well‐predicted by PBPK M&S (Simcyp version 21; Figure 3), there was a trend towards underprediction for the two dual OATP/CYP3A4 substrates (Figure 4a,b). An important challenge of PBPK model development for hepatic transporter substrates is the inability to definitively estimate all hepatobiliary CLs, including ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ (unless imaging data are available). Therefore, for atorvastatin, we assumed that its hepatic sinusoidal efflux was mediated only by passive diffusion (see atorvastatin model development in Appendix S1). For fimasartan, because only limited data were available, we estimated CL_int,uptake from the intravenous drug CL, assuming that RDS_CL,H = uptake (see fimasartan model development in Appendix S1). Therefore, ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ was assumed to be negligible. Because these assumptions might not hold true (in particular, for atorvastatin, there is a report of active transport by MRP3 ³¹ ), we investigated the impact of changing the ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ values on the AUCR_HI for these two drugs. Increasing ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ of atorvastatin and fimasartan moved the AUCR_HI into or closer to the bioequivalence range (Figure 4c,d). In addition, the predictions were further improved when ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ was assumed to be mediated primarily (90%) by MRP3 (and its abundance was increased in HI ² ). Whether MRP3 or MRP4 contributes to the sinusoidal efflux of the two drugs, and, if so, the fraction‐transported (f _t ) of this contribution, is unclear and needs further investigation.

There are a few limitations to this work. First, PBPK model development and verification can be challenging for transporter substrates as it is often difficult to determine and verify the absolute values of the hepatobiliary CLs estimates, and the relative contribution of different transporters (influx and efflux) and drug metabolizing enzymes. Only for rosuvastatin and gadoxetic acid were clinical imaging data available that were used to back‐calculate the in vitro hepatic influx and efflux CLs estimates (Appendix S1). Although PBPK model fits in HV were deemed satisfying for our application, we acknowledge that PBPK models could be further improved (e.g., pitavastatin). This will likely involve a better characterization of the hepatobiliary CLs of drugs. Whereas the bottom‐up in vitro in vivo extrapolation approaches were used to estimate the relative contribution of transporters to hepatic uptake and efflux (e.g., rosuvastatin or pitavastatin), data were not always available to do so (e.g., gadoxetic acid and fimasartan). Therefore, caution should be used when interpreting data from the PBPK models regarding the assumptions made (e.g., assuming RDS_CL,H = uptake, or that a CL pathways is mediated 100% by a given transporter; see Appendix S1). The simulations presented are only for illustration of given principles and the models presented need further validation (including perturbation of metabolism/transport pathways by validated in vivo inhibitors/inducers). Second, besides the blood AUC of drugs, it is important to consider the impact of HI on drug concentrations at the site of efficacy and toxicity. For example, irrespective of the RDS, the hepatic AUC is dependent on the metabolic and canalicular efflux CLs, but not on ${\mathrm{CL}}_{\text{in}}^{\mathrm{s}}$ or ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$, unless there is significant extrahepatic elimination, as previously noted. ¹⁷ Third, this work used the extended clearance model (derived from the well‐stirred model) to simulate the effect of HI on the AUC of transported drugs, and the authors acknowledge the limitations of using the well‐stirred model for high extraction compounds. Extreme scenarios where CL_met and/or ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$ are very large might be better described by other models. However, it is unlikely that the overall conclusions of this paper would be affected by the use of a different model. Fourth, in this study, we assumed that changes in transporter‐mediated and metabolic clearances were driven by changes in DMET abundance. Such changes can also be the result of changes in the DMET affinity for drugs.

In conclusion, simulations of AUCR_HI,u for different scenarios using the extended clearance model have provided a better understanding of factors that drive AUCR_HI,u for dual OATP/CYP3A4 substrates, for which large AUCR_HI have been reported. In addition, principles derived from this work can be applied to substrates of other DMETs when abundance data (e.g., obtained by proteomics ³² ) are available to inform predictions. This work emphasizes the need to obtain accurate estimates of all hepatobiliary CLs of drugs, including ${\mathrm{CL}}_{\mathrm{ef}}^{\mathrm{s}}$, to accurately predict the effect of HI (and the effect of other intrinsic and extrinsic factors) on drug blood AUC. Assuming RDS_CL,H = uptake based on permeability data alone is likely not justified (see considerations on rosuvastatin above). In this regard, imaging data (when available) and in vitro–in vivo extrapolation methods (in particular, proteomics‐informed) ³³ can be used to obtain such estimates.

AUTHOR CONTRIBUTIONS

All authors wrote the manuscript. F.S., M.K.L., and J.D.U. designed the research. F.S. performed the research. F.S., M.K.L., and J.D.U. analyzed the data.

FUNDING INFORMATION

This research was supported by the University of Washington Research Affiliate Program on Transporters (UWRAPT), funded by Gilead Sciences, Amgen, Takeda, and Janssen Pharmaceuticals.

CONFLICT OF INTEREST STATEMENT

X.L., Y.L., P.C., O.E., and R.E. are/were employees of their respective companies and received stocks or stock options from their companies. All other authors declared no competing interests for this work.

Supporting information

Appendix S1

Storelli F, Ladumor MK, Liang X, et al. Toward improved predictions of pharmacokinetics of transported drugs in hepatic impairment: Insights from the extended clearance model. CPT Pharmacometrics Syst Pharmacol. 2024;13:118‐131. doi: 10.1002/psp4.13062