A Semiphysiological Population Model for Prediction of thePharmacokinetics of Drugs under Liver and Renal

Disease Conditions

Ashley Strougo, Ashraf Yassen, Walter Krauwinkel, Meindert Danhof, and Jan Freijer

Global Clinical Pharmacology and Exploratory Development, Astellas Pharma Europe, Leiderdorp, The Netherlands (A.S., A.Y.,W.K., J.F.); and Division of Pharmacology, Leiden/Amsterdam Center for Drug Research, Leiden University, Leiden,

The Netherlands (A.S., M.D.)

Received December 15, 2010; accepted April 12, 2011

ABSTRACT:

The application of model-based drug development in special pop-ulations becomes increasingly important for clinical trial optimiza-tion, mostly by providing a rationale for dose selection and therebyaiding risk-benefit assessment. In this article, a semiphysiologicalapproach is presented, enabling the extrapolation of the pharma-cokinetics from healthy subjects to patients with different diseaseconditions. This semiphysiological approach was applied to solif-enacin, using clinical data on total and free plasma and urineconcentrations in healthy subjects. The analysis was performedusing nonlinear mixed-effects modeling and relied on the use of ageneral partitioning framework to account for binding to plasmaproteins and to nonplasma tissues together with principles fromphysiology that apply to the main pharmacokinetic process, i.e.,bioavailability, distribution, and elimination. Application of thesephysiology principles allowed quantification of the impact of key

physiological parameters (i.e., body composition, glomerular func-tion, liver enzyme capacity, and liver blood flow) on the pharma-cokinetics of solifenacin. The prediction of the time course of thedrug concentration in liver- and renal-impaired patients only re-quired adjustment of the physiological parameters that are knownto change upon liver and renal dysfunction without modifying thepharmacokinetic model structure and/or its respective parameterestimates. Visual predictive checks showed that the approachapplied was able to adequately predict the pharmacokinetics ofsolifenacin in liver- and renal-impaired patients. In addition, betterinsight into the pharmacokinetic properties of solifenacin was ob-tained. In conclusion, the proposed semiphysiological approach isattractive for prediction of altered pharmacokinetics of com-pounds influenced by liver and renal disease conditions.

Introduction

Disease conditions can involve important alterations in drug dis-position, metabolism, and/or absorption compared with the healthycondition. In liver and renal impairment, the main alterations arecaused by changes in organ blood flow and plasma protein bindingthat affect the intrinsic capacity of the organ to metabolize/excretedrugs. Such physiological changes may affect the pharmacokinetics ofdrugs; therefore, in cases where the drug is likely to be administeredunder these pathological conditions, the pharmacokinetics should beassessed in clinical studies to provide alternative dosing recommen-dations. Model-based analysis and simulation is invaluable in optimi-zation of these clinical studies mostly by providing a rationale fordose selection, thereby avoiding side effects due to unexpectedly high

exposure of the drug. In this manner, this approach aids in risk-benefitassessments of dose selection.

The impact of altered liver function on the pharmacokinetics of adrug often depends on the stage of the disease, which occurs throughdifferent pathological mechanisms. Some of the known physiologicalchanges that can affect pharmacokinetics are shunting of blood pastthe liver, impaired hepatocellular function, impaired biliary excretion,and decreased plasma protein binding (Schuppan and Afdhal, 2008).The impact of enzyme activities, plasma protein concentration, andhepatic blood flow (portal plus arterial) on the clearance (CL) ofdifferent compounds has been characterized previously according tothe Child-Pugh score classification and use of well stirred models(Edginton and Willmann, 2008; Johnson et al., 2010).

A reduction in liver function can also be caused by a reduction inrenal function. To this end, the pharmacokinetics of drugs that aremainly metabolized by the liver can be markedly affected by renalimpairment. Chronic renal disease not only influences glomerularfiltration rate (GFR), tubular secretion, and protein binding but alsohas an impact on intestinal and hepatic uptake transporters (Nolin etal., 2008). In brief, a reduction in renal clearance leads to accumula-tion of uremic toxins and chronic inflammation, which then perturbs

This work was performed within the framework of the Dutch Top InstitutePharma project D2-104.

The authors have no conflicts of interest that are directly relevant to thecontents of this study.

Article, publication date, and citation information can be found athttp://dmd.aspetjournals.org.

http://dx.doi.org/10.1124/dmd.110.037838.

ABBREVIATIONS: CL, clearance; GFR, glomerular filtration rate; WB-PBPK, whole-body physiologically based pharmacokinetic model; YM905,(�)-(1S,3�R)-quinuclidin-3�-yl 1-phenyl-1,2,3,4-tetrahydroisoquinoline-2-carboxylate monosuccinate; AGP, �1-acid glycoprotein; NSB, nonspe-cific binding; CV, coefficient of variation.

1521-009X/11/3907-1278–1287$25.00DRUG METABOLISM AND DISPOSITION Vol. 39, No. 7Copyright © 2011 by The American Society for Pharmacology and Experimental Therapeutics 37838/3696946DMD 39:1278–1287, 2011

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metabolic and transport processes in the liver and intestine(Dreisbach, 2009). In end-stage renal disease, dialysis removes uremicfactors (Dreisbach, 2009), and consequently patients with severe renalimpairment, who are not yet undergoing dialysis, in theory have thegreatest risk of higher drug exposure.

Model-based pharmacokinetic analysis can be used to gain moreinsights in how (patho-)physiological changes can affect the pharma-cokinetics of a compound. To date, whole-body physiologically basedpharmacokinetic (WB-PBPK) models have been proposed in twopreviously published reports for prediction of the pharmacokinetics inpatients with liver impairment (Edginton and Willmann, 2008; John-son et al., 2010). WB-PBPK requires a large number of physiologicalinput parameters and a good understanding of all active processesaffecting the pharmacokinetic properties of a drug. Thus, the lack ofsufficient in vitro and in vivo data may hamper the use of thisapproach. In this investigation, we propose an approach that takes intoaccount key principles from physiology in combination with thepower of nonlinear mixed-effects modeling for estimation of popula-tion and random-effects parameters.

This semiphysiological population approach is proposed to predict thepharmacokinetics from healthy subjects to patients with two differentdisease conditions, i.e., renal and liver impairment. This approach com-bines an empirical compartmental model structure, a partitioning frame-work to describe protein binding in plasma, and the principles of thephysiology that apply to volume of distribution (VSS) and CL to deter-mine the impact of key physiological parameters [i.e., free fraction inplasma (fu), total body water composition, liver weight, liver blood flow(QH) and GFR] on the pharmacokinetic profiles.

The clinical utility of the proposed approach is illustrated withsolifenacin [(�)-(1S,3�R)-quinuclidin-3�-yl 1-phenyl-1,2,3,4-tetrahy-droisoquinoline-2-carboxylate monosuccinate, YM905, Vesicare],which is a once-daily orally administered selective muscarinic (M1

and M3) receptor antagonist for the treatment of overactive bladder(Simpson and Wagstaff, 2005; Payne, 2006). Solifenacin is primarilymetabolized by the cytochrome P450 3A4 isozyme, leading to roughly7% of the dose being excreted unchanged in the urine (Michel et al.,2004; Doroshyenko and Fuhr, 2009). Furthermore, solifenacin exhib-its a dose-proportional pharmacokinetics and extensively binds to�1-acid glycoprotein (AGP) and to a lesser extent to albumin, whichmakes it a suitable model compound to investigate the utility of theproposed semiphysiological approach.

Materials and Methods

Clinical Studies. An overview of the clinical studies used for modeldevelopment and comparison with model predictions is shown in Table 1. Intotal, the data of 59 subjects of three phase I clinical studies after administra-tion of 5 and 10 mg of solifenacin were used for model development includingdata of young healthy male adults, young healthy female adults, elderlyfemales, and elderly males. The data from 26 patients with liver and renalimpairment were exclusively used to verify the model predictions. In total, dataof approximately 8 patients with liver impairment and 6 patients with renalimpairment were available for each group. Patients with liver impairmentincluded in study 2 were classified as type B in the Child-Pugh category, andrenal impairment in patients was classified as mild (GFR �50 and �80ml/min), moderate (GFR �30 and �50 ml/min), or severe (GFR �30 ml/min).For the patient classification, GFR was calculated according to the Cockcroft-Gault equation (Cockcroft and Gault, 1976). In all studies, solifenacin con-centrations were analyzed using liquid chromatography-mass spectrometrywith a limit of quantification of 1.38 nmol/l for total solifenacin and 0.55nmol/l for free solifenacin. A comprehensive description of these studies andresults have been reported elsewhere (Krauwinkel et al., 2005; Kuipers et al.,2006; Smulders et al., 2007).

Structural Model. The structural model to describe the pharmacokineticsof solifenacin is shown in Fig. 1. In brief, the biphasic pharmacokinetics of

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total and free solifenacin in plasma was described by a two-compartmentmodel with first-order absorption. The urine concentrations were described bylinking the urinary excretion to the central compartment. To account for theeffect of protein binding on the central volume of distribution (V1), the centralcompartment of this system was assumed to have different components that arein instantaneous equilibrium: solifenacin-AGP, solifenacin-albumin, solifena-cin-free, and solifenacin-nonspecific binding (NSB) (Fig. 1). NSB was as-sumed to be outside of the plasma so that variations in the concentration ofplasma proteins would have an effect on the total solifenacin plasma concen-trations. The higher the concentration of plasma proteins, the less solifenacindistributes from plasma to the NSB and consequently the higher are the totalsolifenacin concentrations observed in plasma.

By applying the “law of mass action” to the plasma distribution component,the fu could be defined as in eq. 1:

fu �1

1 �CAGP

kAGP�

CAlb

kAlb

(1)

in which CAGP is the AGP plasma concentration, CAlb is the albumin plasmaconcentration, kAGP is the partition coefficient for AGP, and kAlb is thepartition coefficient for albumin.

To describe V1 eq. 2 was derived:

V1 � Vplasma � �1 � � � fu� (2)

where � represents a compilation of the concentration in the NSB dividedby the partition coefficient for NSB, and Vplasma is the volume of plasmacalculated as 5% of the lean body mass (Boer, 1984; Janmahasatian et al.,2005).

In addition, the effect of fu on VSS was included in the model by taking into accountits physiological determinants (eq. 3) (Gibaldi and McNamara, 1978; Mehvar, 2005):

Vss � Vplasma � Vwater � � fu

ftissue� (3)

in which ftissue is the free fraction in tissue and Vwater is the aqueous volumeoutside of the plasma into which the drug distributes (Rowland and Tozer,1995). Hence, Vwater was assumed to be total body water composition minusplasma water volume, which is approximately 90% of Vplasma. Total bodywater composition was calculated according to Watson et al. (1980).

The simultaneous analysis of the solifenacin plasma and urine concentra-tions enables the characterization of both renal clearance (CLR) and hepaticclearance (CLH) as illustrated in eq. 4:

CL � CLR � CLH (4)

Renal clearance has been characterized as a fraction of the clearance due tothe glomerular filtration (CLGFR) as displayed in eq. 5:

CLR � � � CLGFR

CLGFR � GFR � fu(5)

where � is a fraction of CLGFR. If � �1, tubular active secretion is mainlyinvolved in renal clearance, if � �1 reabsorption is mainly involved in renalclearance, and if � � 1, GFR is sufficient to explain all renal clearance. GFRwas calculated according to the modification of diet in renal disease equation(Levey et al., 1999) and corrected for body surface area (Haycock et al., 1978).

To characterize the CLH, the well stirred model concept was included in themodel according to eq. 6 (Yang et al., 2007):

TABLE 2

Overview of the demographic covariates, physiological parameters, and estimated and derived model parameters

Model Input Model Output

Demographic Covariates Physiological Parameters Estimated Parameters Derived Parameter (Primary) Derived Parameter (Secondary)

CAlb, CAGP kAlb, kAGP fu CLR, CLH, F, VSS, V1, QWeight QH CLinvivo CLint CLH, FGender, age, and weight Liver weightRace, gender, age, and creatinine GFR � CLR

Gender, weight, and height Vplasma � V1

Gender, weight, and height Vplasma ftissue VSS

Gender, age, weight, and height Vwater

Absorption compartmentcompartment

ka

AGP-Solifenacin QNSB-SolifenacinAlbumin-Solifenacin

Solifenacinfree

Central compartment (V1) Peripheral compartment (V2)

CLR CLH

Urine compartment

FIG. 1. Schematic representation of the semiphysiologicalmodel developed for solifenacin. The arrows within the centralcompartment represent instantaneous equilibrium, and arrowsbetween compartments represent kinetic processes. Total andfree solifenacin plasma concentrations as well as plasma proteinconcentrations were measured in the compartments indicated bythe bold lines and gray color. The urine concentration wasmeasured in the compartment named “urine compartment.”

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CLH �QH � fu � CLint

QH � fu �CLint

Cblood/Cplasma

(6)

where QH was calculated according to Wynne et al. (1989), Cblood/Cplasma is thetotal blood plasma concentration ratio, which was fixed at 0.89 as establishedin vitro (T. Minematsu and T. Hashimoto, unpublished results), and CLint isintrinsic clearance, which was calculated as in eq. 7:

CLint � CLinvivo � liver weight � MPPGL (7)

where CLin vivo is the in vivo clearance, liver weight was calculated accordingto Chouker et al. (2004), and MPPGL is the milligrams of microsomal proteinper gram of liver, adult levels of which were reported to be 35 mg/g (Johnsonet al., 2006).

Intercompartmental clearance (Q) of solifenacin was assumed to be depen-dent on fu (eq. 8):

Q � Q* � fu (8)

in which Q* was a model constant.Maximal oral bioavailability (Fmax) was physiologically characterized in

this model as described in eq. 9:

Fmax �QH

QH � CLint �fu

Cblood/Cplasma

(9)

Table 2 shows an overview of the demographic covariates necessary tocalculate the physiological parameters and consequently to derive modelparameters.

Random Effects. Random interindividual variability for each pharmacoki-netic parameter was perceived as a log-normal distribution (eq. 10):

Pi � Ptypical � exp��i� (10)

where Pi represents the parameter value for the ith individual, Ptypical is theparameter for a typical group value and � is the interindividual random effectwith �i � N(0, �2).

The residual errors were separately defined for total and free solifenacinconcentrations in plasma and solifenacin concentrations in urine:

Cobs,ij � Cpred,ij � �1 � �ij� (11)

where Cobs, ij and Cpred, ij are, respectively, the observed concentration and thepredicted concentration in individual i at time j and �ij is the residual error with�i � N(0, 2).

Model Performance. Throughout model development, NONMEM subrou-tine ADVAN6 and first-order conditional estimation with interaction was used.Samples below the limit of quantification were considered as missing values.Model performance was evaluated by both visual inspection and the likelihoodratio test. Physiological considerations and the conventional critical values forthe likelihood ratio test (p � 0.001) were used for model development.Precision of parameter estimates was evaluated as the coefficient of variation(CV) calculated by the ratio of the estimated S.E. and its respective parameterestimate multiplied by 100.

Model Evaluation. Internal model validation was performed by means of avisual predictive check, which evaluates whether the identified model is ableto predict the observed total plasma concentrations, urine excretion rates, andfu (Post et al., 2008). Plasma concentration-time, urine excretion rate-time, andfu plasma protein curves were simulated for 1000 hypothetical subjects. In allsimulations, the correlation matrix for estimates was considered to accountfor parameter uncertainty.

For the simulation of plasma concentration and urine excretion rate curves,the physiological parameters (i.e., Vplasma, Vwater, QH, liver weight, and GFR)were calculated by sampling the required demographic covariates and theplasma protein concentrations (i.e., AGP plasma concentration and albuminplasma concentration) from the data set used for model development. Forsimulations of the fu AGP curve, the albumin plasma concentration was fixedto the average value observed in the data set and the AGP plasma concentrationwas allowed to vary within the observed range. The opposite was applied forthe simulations of the fu albumin curve.

Graphical representation of total plasma and urine data shows 90% pre-dicted population variability explained by the differences in the physiologicalparameters alone and combined with the estimated interindividual variability.For graphical representation of urine data, the urine excretion rate was calcu-lated by dividing the simulated amount of total solifenacin excreted in the urineduring a certain time interval by the time interval. The graphical display of fushows the 95% confidence interval of the population median. The observed fuwas calculated by dividing free solifenacin by total solifenacin plasma con-centrations per time point.

Extrapolations. The model developed for the healthy subjects was subse-quently used to extrapolate the pharmacokinetics in plasma and urine topatients with liver and renal impairment. For the extrapolations, the data inpatients was compared with the model predictions, which were exclusivelybased on the alterations of the physiological parameters. To evaluate to what

TABLE 3

Overview of the expected changes in the physiological parameters in liver- andrenal-impaired patients as a fraction of the values in healthy subjects

PhysiologicalParameter

Liver-Impaired (Edginton andWillmann, 2008) Renal-Impaired

CAGP 0.56 1.4 (severe) (Vasson et al., 1993)CAlb 0.68 1QH 0.85 1CLint 0.40 0.6a (severe) (Nolin et al., 2008)GFR 0.70 Uniform distribution according to

classification as specified in theprotocol (see clinical studies)

a Assuming that hepatic transporters are involved in the metabolism of the compound.

TABLE 4

Summary statistics of the physiological parameters in various pathological conditions

Data are median (range).

Physiological Parameter Control(n � 61)

Liver-Impaired(n � 8)

Renal-Impaired

Milda

(n � 6)Moderatea

(n � 6)Severea

(n � 6)

CAGP (mg/dl) 79.5 (54–138) 43.5 (30–70) 81 (74–126) 87.5 (67–132) 111 (83–166)CAlb (g/dl) 4.17 (3.6–4.95) 4.14 (2.53–4.23) 4.20 (3.7–4.3) 4.00 (3.8–4.6) 3.85 (2.9–4.3)Vplasma (liters) (Boer, 1984;

Janmahasatian et al., 2005)3.43 (2.21–4.4) 3.51 (2.18–3.74) 3.4 (2.81–3.67) 3.52 (3.02–4.12) 3.27 (3.01–3.98)

Vwater (liters) (Watson et al., 1980) 41.1 (28.4–52.4) 41.3 (28.1–45) 39 (32.6–42.4) 43.2 (36–51.1) 39.4 (36.5–48)Liver weight (g) (Chouker et al.,

2004)2070 (1690–2550) 1990 (1830–2420) 1800 (1550–2060) 2240 (1770–2520) 2100 (1880–2240)

GFR (ml/min/1.73 m2) (Leveyet al., 1999)

87.8 (66.1–124) 78.8 (64.9–85) 57.4 (37.1–79.5) 28.7 (21.8–54.8) 19.5 (11.4–28.6)

a GFR classification based on the Cockcroft-Gault equation: mild (GFR �50 and �80 ml/min), moderate (GFR �30 and �50 ml/min), or severe (GFR �30 ml/min).

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extent the identified model is able to predict the plasma and urine data in thesepathological conditions, a visual predictive check of the full pharmacokineticprofiles was performed. A posterior predictive check of VSS, CL, and renalclearance was performed to characterize the possibility that the pharmacoki-netic parameter predictions are in accordance with the limited amount ofpatients recruited for the clinical studies.

The visual predictive check was performed similarly to the model evalua-tion. The physiological alterations were considered by using literature reportedvalues (Table 3) and by using the observed physiological parameters (Table 4).Alterations in QH and intrinsic clearance were in both cases assumed to be asreported in the literature. Graphical representation of plasma and urine datashows 90% predicted population variability explained by alterations in thephysiological parameters combined with the estimated random interindividualvariability in healthy subjects.

For the posterior predictive check, only the observed alterations in the physi-ological parameters (Table 4) were used to predict VSS, CL, and renal clearance.In total, 1000 data sets for each pathological condition were simulated, containingthe same number of patients/samples as observed in the original data set. The 1000simulated data sets each provided a value for the median and hence an estimate ofthe posterior predictive distribution. The simulated median and its 95% confidence

interval were compared with the median of the observed pharmacokinetic param-eters originating from a post hoc analysis. If the medians of the post hoc valueswere within the 95% confidence interval of the posterior predictive distribution,then the prediction was deemed plausible.

For the renal-impaired patients, the fraction 0.6 used in the extrapolations toreflect the change in intrinsic clearance is the average change in hepaticclearance between healthy subjects and severe renal-impaired patients forcyclophosphamide (0.69), felbamate (0.65), reboxetine (0.44), and telithromy-cin (0.68) reported by Nolin et al. (2008). Compounds for which dialysis-dependent patients were included were not considered. In this publication,severe renal-impaired patients were often considered as the patients with aGFR within the range of 10 and 40 ml/min/1.73 m2.

Software. Nonlinear mixed-effects modeling was implemented usingNONMEM version 7 (GloboMax, Ellicott City, MD). Data managementand simulations were performed using R version 2.10.1 (R Foundation forStatistical Computing, Vienna, Austria).

Results

Data. Table 4 compares the physiological parameters of the controlgroup of studies 1 and 2 (Table 1) with the physiological parametersof the liver-impaired patients and mild, moderate, and severe renal-impaired patients. The median AGP plasma concentration in theliver-impaired patients was 1.6 times lower and in the severe renal-impaired patients was 1.4 times higher than that in the control group.Mild and moderate renal-impaired patients did not show markeddifferences in AGP plasma concentration. The albumin plasma con-centration was not markedly changed in liver- and mild renal-im-paired patients and was reduced in moderate and severe renal-im-paired patients. GFR was shown to decrease by a factor of 0.89 in theliver-impaired patients compared with that in the control groups.

In renal-impaired patients, GFR calculated using the modificationof diet in renal disease equation resulted in lower GFR values thanthose using the Cockcroft-Gault equation, which were the base for theclassification of the patients as mild, moderate, or severe renal-impaired. For all other physiological parameters, no clear differenceswere observed between the control groups and the liver and (mild,moderate, and severe) renal-impaired patients.

Structural Model. The semiphysiological model to describe theeffect of protein binding and key physiological parameters on thepharmacokinetics of solifenacin is illustrated in Fig. 1. During modeldevelopment, eq. 9 was used to calculate the bioavailability, whichwas found to be comparable to the bioavailability obtained in aclinical study (Kuipers et al., 2004). Similarity of the results allowedinclusion of Fmax as F in the model.

Table 5 displays the pharmacokinetic parameters that were esti-mated and derived by the final model in healthy subjects. All struc-tural parameters were estimated with good precision (CV �20%). The

FIG. 2. Relationship between fu (fplasma) andAGP (A), and fu and albumin (B). E, observeddata used for model development (controlgroup study 1 and 2 and study 3); ‚, observeddata used for extrapolation (liver- and renal-impaired groups in study 1 and 2); line, popu-lation prediction (median); shaded area, 95%confidence interval of the predicted median.

TABLE 5

Population parameter estimates including CV percentage and median of thederived structural parameters including range, if applicable

Values are CV (%) or median (range: minimum–maximum).

Value

Structural estimated parameterska (/h) 0.304 (12)CLin vivo (l � h1 � g liver protein1) 0.00451 (6.4)� 5.56 (8.1)Q* (l/h) 1120 (20)� 5810 (11)ftissue 0.00142 (4.6)kAGP (nmol/l) 659(18)kAlb (nmol/l) 293000 (22)

Structural derived parametersF 0.93 (0.891–0.954)V1 (liters) 331 (165–982)V2 (liters) 161 (89.2–264)VSS (liters) 484 (303–1150)CL (l/h) 6.15 (2.41–18.7)CLH (l/h) 5.62 (2.11–16.3)CLR (l/h) 0.587 (0.247–2.36)Q (l/h) 23.1 (15.6–29.7)fu 0.0205 (0.0139–0.0264)

Random interindividual variability�2 V1 0.114 (20)�2 CLH 0.163 (18)�2 CLR 0.212 (19)

Residual error2 total 0.0181 (12)2 free 0.186 (83)2 urine 0.176 (30)

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value of fu was 0.0205 (range, 0.0139–0.0264), VSS was 484 (range,303–1150 liters), CL was 6.15 (range, 2.41–18.7 l/h), and renalclearance was 0.587 (range, 0.247–2.36). Interindividual variabilitywas estimated for V1 and hepatic and renal clearance. The correlationbetween interindividual variability of V1 and hepatic and renal clear-ance was accounted for using an omega matrix. No relevant shrinkagein the omega distribution was observed (1.1% for V1, 0.3% forhepatic clearance, and 9.6% for renal clearance).

Model Validation. The adequacy of the approach to describe theeffect of changes in protein plasma concentration on the free fractionof solifenacin is shown in Fig. 2. The AGP plasma concentration wasdemonstrated to have a strong effect on fu, whereas the effect ofalbumin was shown to be negligible. This observation is in agreementwith the roughly 1000 times lower partition coefficient observed forAGP (Table 5), which overcomes the greater molar plasma concen-tration of albumin. As a consequence, the variation in AGP ends upplaying a main role in the plasma binding of solifenacin.

An adequate description of the plasma and urine data by the modelis illustrated by the internal visual predictive check (Fig. 3). Slightmodel overprediction of the plasma concentrations is observed onlyfor the control group of study 2 (Fig. 3A). The internal visual predic-tive check also illustrates that part of the interindividual variabilitycan be explained by considering only the variability in the physiolog-ical parameters, i.e., without random effects (inner shaded area). Forthe urine data, the variability in the physiological parameters (innershaded area) can explain most of the interindividual variability observed.

Extrapolations. Figures 4 and 5 illustrate the results of the visualpredictive check performed to evaluate the predictive power of thesemiphysiological approach for liver- and renal-impaired patients,respectively. In the liver-impaired patients, the approach slightlyoverpredicts the terminal half-life of the observed total plasma con-centrations, whereas in renal-impaired patients, the observed totalplasma concentrations are underpredicted, especially in the patients

classified as having severe impairment and to a lesser extent in thepatients classified as having moderate impairment (Fig. 6, A–C).Predictions substantially improved when the potential involvement ofhepatic uptake transporters was taken into account by increasing theintrinsic clearance by a factor of 0.6 in patients with a GFR lower than40 ml/min/1.73 m2 (Fig. 6, D–F). The population prediction and theinterindividual variability did not markedly change when the modelpredictions were based on either the observed or literature-reportedalterations (Table 3) of the physiological parameters (Figs. 4 and 5).

Table 6 illustrates the posterior predictive check results for VSS, CL,and renal clearance for liver-impaired patients and mild, moderate,and severe renal-impaired patients. The medians of the post hocestimates were inside the 95% confidence interval of the posteriorpredictive distribution. For severe renal-impaired patients, the poste-rior predictive check results confirmed the improvements in the pre-dictions observed after consideration of the potential involvement ofhepatic uptake transporters.

Discussion

The application of model-based drug development in special pop-ulations becomes increasingly important for clinical trial optimization,mostly by providing a rationale for dose selection and thereby aidingthe risk-benefit assessment. At present, WB-PBPK models have beenused for prediction of the pharmacokinetics in patients with liverimpairment (Edginton and Willmann, 2008; Johnson et al., 2010).However, attempts to use this approach sometimes fail because WB-PBPK models require extensive knowledge of all active processesaffecting the pharmacokinetics of the drug. As an alternative, asemiphysiological approach is proposed for pharmacokinetic extrap-olations. This concept takes into account key principles from physi-ology in combination with the nonlinear mixed-effects modelingapproach for estimation of population and random-effect parameters.In this article, the semiphysiological concept is presented, enabling

FIG. 3. Internal visual predictive check of thetotal solifenacin plasma concentrations (A andB) and urine (C and D) excretion rate aftersingle (A and C) and multiple (B and D) doseadministration of 5 and 10 mg once daily ofsolifenacin. E, observed data of study 1 and 3;‚, observed data study 2; line, population pre-diction (median); inner shaded area, 90% pre-dicted population variability explained by thedifferences in the physiological parameters;outer shaded area, 90% predicted populationvariability including differences in the physio-logical parameters and random effects.

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prediction of the pharmacokinetics from healthy subjects to patientsunder two different disease conditions, i.e., liver and renal impairment.

The uniqueness of this approach relies on the use of a generalpartitioning framework to account for binding to plasma proteins andto nonplasma tissues together with principles from physiology thatapply to the main pharmacokinetic process (i.e., bioavailability, dis-tribution, and elimination). In combination with compartmental mod-

eling, the proposed semiphysiological approach can be used to inves-tigate the impact of (patho-)physiological alterations on the timecourse of drug concentration. An important feature of the proposedsemiphysiological approach is that the model captures physiologicalparameters that are believed to change under pathophysiological con-ditions. To this end, extrapolation of the pharmacokinetics fromhealthy volunteers to liver- and renal-impaired patients relies on the

FIG. 4. Plasma (A and B) and urine (C and D)extrapolation results to patients with liver im-pairment. A and C, extrapolations based onexpected changes in the physiological parame-ters (Table 3); B and D, extrapolations based onobserved physiological parameters (Table 4).‚, observed data study 2; line, population pre-diction (median); shaded area, 90% includingdifferences in the physiological parameters andrandom effects.

FIG. 5. Plasma (A and B) and urine (C and D)extrapolation results for patients with renal im-pairment. A and C, extrapolations based onexpected changes in the physiological parame-ters; B and D, extrapolations based on observedphysiological parameters. E, observed datamild impaired group; ‚, observed data moder-ate group; �, observed data severe group; line,population prediction (median); shaded area,90% including differences in the physiologicalparameters and random effects.

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key principle that only the physiological parameters change withoutthe need for adjustment of the model structure and/or pharmacokineticparameter estimates.

In this investigation, solifenacin served as a model compound toshow the validity of the concept. Rich clinical pharmacokinetic datafor total solifenacin were available from healthy subjects and patientswith impaired liver and/or renal function. In addition, free solifenacinin plasma and solifenacin in urine were included in the analysis.Because solifenacin extensively binds to AGP, which is known towidely vary under impaired liver and renal conditions, it was antici-pated that protein binding would be a physiological parameter of keyrelevance. Accordingly, solifenacin was considered a suitable modelcompound to investigate the utility of the proposed semiphysiologicalapproach.

First, the semiphysiological approach was applied to character-ize the pharmacokinetics of solifenacin in healthy subjects (Fig. 1).Characterization of the binding of solifenacin to plasma proteins in

the model was a key step for the inclusion of the physiologicalprinciples, which allowed investigation of the impact of key phys-iological parameters on the time course of solifenacin concentra-tion. These key physiological parameters represented body com-position, glomerular function, liver enzyme capacity, and liverblood flow. In addition, inclusion of the physiological principlesimproved the understanding of the pharmacokinetic properties ofsolifenacin by interpretation of model estimates. For example, theagreement between the model estimated bioavailability and thebioavailability obtained in a clinical study (Kuipers et al., 2004)indicates that bioavailability of solifenacin is mainly affected bythe first-pass metabolism in the liver. In addition, the 10-folddifference between the measured CLin vitro (results not published)and the estimated CLin vivo (0.00451 l � h1 � g liver protein1;Table 5) indicated the involvement of influx hepatic drug trans-porters promoting the in vivo hepatic clearance of solifenacin (Wuand Benet, 2005). This 10-fold difference is well above the average

TABLE 6

Posterior predictive check for VSS, CL, and renal clearance in various pathological conditions

For every pharmacokinetic parameter, the first row depicts the median of the observed values (post hoc analysis) and the second row depicts the simulated median and the 95% confidenceinterval of the posterior distribution (n � 1000). In the control group only data from study 1 and 2 were used.

Pharmacokinetic Parameter Control Liver-ImpairedRenal-Impaired

Milda Moderatea Severea

VSS (liters) 604 771 447 582 474537 (451–664) 768 (532–1030) 499 (395–633) 614 (479–774) 479 (356–626)

CL (l/h) 7.76 6.24 4.17 3.72 3.006.75 (5.31–8.60) 4.48 (3.15–6.34) 5.50 (4.06–7.66) 6.74 (4.86–9.32) 5.24 (3.86–7.38)

4.97 (3.43–7.01)b 4.66 (3.05–7.20)b 3.29 (2.25–4.87)b

CLR (l/h) 0.988 0.798 0.319 0.375 0.1510.701 (0.513–0.990) 0.817 (0.525–1.26) 0.428 (0.265–0.653) 0.251 (0.152–0.432) 0.133 (0.0774–0.218)

a GFR classification based on the Cockcroft-Gault equation.b Predictions assuming differences in CLint for GFR �40 ml/min/1.73 m2.

FIG. 6. Plasma extrapolation results for patients with renal impairment subclassified as mild, moderate, and severe. All extrapolations were based on observed physiologicalparameters. A, B, and C, extrapolations with unchanged intrinsic clearance; D, E, and F, extrapolation where the intrinsic clearance was assumed to change by 0.6 in patientswith a GFR lower than 40 ml/min/1.73 m2. E, observed data mild impaired group; ‚, observed data moderate group; �, observed data severe group; line, populationprediction (median); shaded area, 90% including differences in the physiological parameters and random effects.

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5-fold difference that Hallifax et al. (2010) demonstrated as notsufficient to support the role of hepatic transporters.

For the extrapolation of the pharmacokinetics of solifenacin topatients with hepatic and renal impairment, only the physiologicalparameters were adapted according to expected alterations as reportedin the literature (Table 3) or to the alterations observed in the patientsincluded in the clinical trials (Table 4). Of interest, the observedchanges in physiological parameters are in good agreement with thevalues derived from the literature. Hence, the expected alterations asreported in the literature are deemed suitable for predictions of thepharmacokinetics under these disease conditions, except for the albu-min plasma concentration in liver-impaired patients whose reporteddifferences of 0.68 (Table 3) were not supported by the observed data,which showed no differences (Table 4). Because solifenacin mainlybinds to AGP, it is expected that the difference in albumin concen-tration has only a minimal impact on the model performance. This isconfirmed by the fact that the predictions using literature-reportedchanges in the physiological parameters are comparable to the pre-dictions using the observed parameters (Fig. 4). Therefore, the slightoverprediction of the terminal half-life of liver-impaired patients iscaused by the relatively low number of patients included in this studyand the cross-study differences in solifenacin concentrations alsoobserved for the control group (Fig. 3).

For predictions of the pharmacokinetic time course in renal-im-paired patients, alterations in CL were initially assumed to be limitedto increased AGP concentration and decreased GFR. Evaluation of thepredictions, as depicted in Table 6 and Fig. 5, indicates that imposingonly these assumptions results in underprediction of CL. Consideringa decrease in the hepatic intrinsic clearance for renal-impaired patientswith a GFR lower than 40 ml/min/1.73 m2 resulted in a betterprediction of CL (Fig. 6; Table 6). This alteration in hepatic clearancerepresents literature evidence that hepatic transporters are likely to bealtered under renal-impaired conditions (Nolin et al., 2008). Thequantification of the potential changes in the activity of the hepaticuptake transporter appears to be independent of the type of thetransporter involved and is in agreement with the hepatic clearancereductions reported by Dreisbach and Lertora (2003). The accuracy ofthese extrapolations also supports the role of hepatic transporters.

Additional evidence that hepatic transporters play a more promi-nent role than renal transport mechanisms is provided by the fact thatthe semiphysiological model adequately predicted the urine extractionratio in liver- and renal-impaired patients (Table 6; Fig. 5). In thisrespect, any potential reduction in the transporters involved in theactive tubular secretion as reported by Dreisbach et al. (2009) was notaccounted for by the model. However, we believe that further expan-sion of the semiphysiological model accounting for tubular secretionwill not result in a further improvement of the predictions as only asmall percentage of total solifenacin is renally excreted.

Overall, application of the semiphysiological model to predict thetime course of solifenacin concentration in renal- and liver-impairedpatients shows that distribution of solifenacin is mainly driven bydifferences in fu and intrinsic clearance and less by other key physi-ological variables that may change under disease conditions. Forexample, underestimation of body composition by the anthropometricequations (Himmelfarb et al., 2002; Proulx et al., 2005) did notinfluence the accuracy of the pharmacokinetic predictions (Table 6) inliver- and renal-impaired patients. For other populations, like obesepatients, body composition may play a more prominent role thanprotein binding in the determination of the time course of drugconcentration.

In conclusion, the proposed semiphysiological approach combinesphysiological principles with the nonlinear mixed-effects modeling,

allowing estimation of population and random-effects parameters.This allowed better understanding of the pharmacokinetic propertiesof solifenacin. Moreover, the semiphysiological approach enablesprediction of the time course of solifenacin concentration in liver- andrenal-impaired patients by using a priori knowledge of changes inphysiological parameters. To this end, the semiphysiological approachis instrumental for prediction of altered pharmacokinetics of com-pounds influenced by disease conditions.

Acknowledgments

We gratefully acknowledge Carla Santillan for her assistance in acquiringthe data required for model development and extrapolation.

Authorship Contributions

Participated in research design: Strougo, Krauwinkel, Danhof, and Freijer.Performed data analysis: Strougo.Wrote or contributed to the writing of the manuscript: Strougo, Yassen, and

Freijer.

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Address correspondence to: Dr. Ashley Strougo, Global Clinical Pharmacologyand Exploratory Development, Astellas Pharma Global Development Europe, Elisabeth-hof, 1 2353 EW Leiderdorp, The Netherlands. E-mail: ashley.strougo@eu.astellas.com

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