European Journal of Pharmaceutical Sciences 44 (2011) 359–365

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European Journal of Pharmaceutical Sciences

journal homepage: www.elsevier .com/ locate/e jps

A physiologically based model of hepatic ICG clearance: Interplay betweensinusoidal uptake and biliary excretion

Michael Weiss a,⇑, Tom C. Krejcie b, Michael J. Avram b

a Section of Pharmacokinetics, Department of Pharmacology, Martin Luther University Halle-Wittenberg, Halle, Germanyb Department of Anesthesiology and the Mary Beth Donnelley Clinical Pharmacology Core Facility, Feinberg School of Medicine, Northwestern University, Chicago, IL, USA

a r t i c l e i n f o

Article history:Received 20 January 2011Received in revised form 28 June 2011Accepted 20 August 2011Available online 26 August 2011

Keywords:ICGHepatic uptakeBiliary excretionPharmacokinetic modelIsofluraneDog

0928-0987/$ - see front matter � 2011 Elsevier B.V. Adoi:10.1016/j.ejps.2011.08.018

⇑ Corresponding author. Tel.: +49 345 5571657; faxE-mail address: michael.weiss@medizin.uni-halle.d

a b s t r a c t

Although indocyanine green (ICG) has long been used for the assessment of liver function, the respectiveroles of sinusoidal uptake and canalicular excretion in determining hepatic ICG clearance remain unclear.Here this issue was addressed by incorporating a liver model into a minimal physiological model of ICGdisposition that accounts of the early distribution phase after bolus injection. Arterial ICG concentration–time data from awake dogs under control conditions and from the same dogs while anesthetized with3.5% isoflurane were subjected to population analysis. The results suggest that ICG elimination in dogsis uptake limited since it depends on hepatocellular uptake capacity and on biliary excretion but noton hepatic blood flow. Isoflurane caused a 63% reduction in cardiac output and a 33% decrease in theICG biliary excretion rate constant (resulting in a 26% reduction in elimination clearance) while leavingunchanged the sinusoidal uptake rate. The terminal slope of the concentration–time curve, K, correlatedsignificantly with elimination clearance. The model could be useful for assessing the functions of sinusoi-dal and canalicular ICG transporters.

� 2011 Elsevier B.V. All rights reserved.

1. Introduction excretion is not available). To this end, we applied a novel pharma-

Indocyanine green (ICG) is an organic anion dye that is elimi-nated exclusively by the liver. It is widely used to assess hepaticfunction, e.g., in hepatic injury and septic states (Kortgen et al.,2009), and to determine donor liver function after transplantation(Niemann et al., 2002; Hori et al., 2006). From studies in rats, it isknown that hepatic ICG clearance is determined by two processes,sinusoidal uptake and canalicular excretion (Sathirakul et al.,1993). There is evidence that in human liver sinusoidal transportis mainly mediated by the organic anion transporting polypeptide(OATP), whereas the multi-drug resistance associated protein(MRP2) and the multi-drug resistance P-glycoprotein (MDR3)may be involved in canalicular efflux of organic anions (for a re-view, see Kusuhara and Sugiyama, 2010). However, under in vivoconditions where only plasma ICG concentrations are measured,the roles of these processes are poorly understood. It appears thathepatocellular uptake and not hepatic blood flow may be rate lim-iting in dogs (Ketterer et al., 1960), but there is little quantitativeinformation on the relative contribution of each process to ICGelimination. Thus, the goal of the present study was to determinewhether modeling of ICG disposition curve could reveal the inter-play between sinusoidal uptake and biliary excretion in determin-ing hepatic ICG clearance (i.e., when the time profile of biliary

ll rights reserved.

: +49 345 5571835.e (M. Weiss).

cokinetic model to ICG plasma concentration–time data obtainedusing frequent arterial sampling in awake and isoflurane anesthe-tized dogs (Avram et al., 2000).

Estimation of hepatocellular uptake clearance and biliary excre-tion rate constant of ICG was based on a circulatory model. Lump-ing the systemic organs into two subsystems, hepatosplanchnicand non-splanchnic circulation, the approach is similar to thatused to describe [13N]ammonia kinetics (Weiss et al., 2002) andis an extension of the circulatory model of ICG disposition (Weisset al., 2006, 2007). Thus, in contrast to previous approaches basedon compartmental modeling (for a review, see Ott, 1998), we haveadopted a minimal physiological model of ICG whole body phar-macokinetics that includes a space-distributed liver model (Weissand Roberts, 1996). This model has been used to analyze data ob-tained in the isolated perfused rat liver (Weiss et al., 2000; Hunget al., 2002). The difficulty with a more complex model lies inthe large number of model parameters relative to the availabledata. Prior information obtained on the system without liver(Weiss et al., 2006) was incorporated in parameter estimationusing a population approach (D’Argenio et al., 2009) to facilitateparameter identifiability. The fact that isoflurane anesthesiadecreased cardiac output to about 37% of that in the awake state(Avram et al., 2000) allowed an examination of the effect of liverblood flow.

The advantages of physiologically-based pharmacokinetic(PBPK) modeling have been reviewed recently (Rowland et al.,

360 M. Weiss et al. / European Journal of Pharmaceutical Sciences 44 (2011) 359–365

2011). Although PBPK models are normally based on a compart-mental structure (differential equations), in the present approachthe subsystems of the body were modeled by transit time density(TTD) functions for at least two reasons. First, since ICG distributeswithin the vascular system, we are also aiming to describe the ini-tial phase (the first minutes) of the disposition curve to estimatecardiac output as a main determinant of the mixing process (Weiss,2009). This would be not possible using a conventional compart-mental model for the lung. The initial peak of the arterial concen-tration time curve mainly represents the TTD through the lung.That the latter can be described by the inverse Gaussian densityhas been shown in tracer kinetics (Sheppard et al., 1968). Theusefulness of the inverse Gaussian TTD in pharmacokinetics canbe explained by the facts that it represents the first passage timedistribution of a random walk process with drift (Seshadri, 1999)and that it is the solution to the convection–dispersion organmodel (Roberts et al., 2000). Second, in a PBPK model based ondifferential equations it would not be possible to integrate aspace-distributed liver model. Furthermore, while due to theirstructural complexity, PBPK models are typically used for simula-tion, this study is an attempt to develop a minimal PBPK modelfor ICG that can be identified using plasma concentration data. Thismethod may lead to a better understanding of the processes deter-mining ICG clearance in vivo, e.g., for characterizing the function oftransporters involved in sinusoidal uptake and biliary excretion ofICG in normal and disease states. The model was also used toexamine the role of the terminal slope of the ICG concentration–time curve (blood disappearance rate, K), that is routinely usedas a marker of liver function, as a surrogate for hepatic clearance.

2. Methods

2.1. Data

The data were obtained from a previous study of ICG dispositionin dogs (Avram et al., 2000). Four dogs (body weight 28.4 ± 5.9 kg)were studied while awake and again while anesthetized with 3.5%isoflurane (2.3 minimum alveolar concentration, MAC). Briefly sta-ted, at time t = 0 min, 5 mg of ICG in 1 ml of ICG diluent wasflushed into the right atrium within 4 s using 10 ml of a 0.9% saline

kin

ke

koutVb,hep

Div

Fig. 1. Circulatory model of hepatic ICG elimination kinetics consisting of heterogeneoustwo parallel subsystems, the hepatosplanchnic bed (gut and liver in series) and the rest ofoutput). All subsystems are characterized by transit time density functions in the Laplaceas the gut are characterized by inverse Gaussian transit time density functions denoted bliver volume, kin is the sinusoidal uptake rate constant (which is determined by the uconstant of back-transport, and ke the canalicular excretion rate constant.

solution. Arterial blood samples were collected via an indwellingiliac artery catheter every 1.8 s for the first 28.8 s and every 3.6 sfor the next 32.4 s using a roller pump and fraction collector. Sub-sequently, 18 3-ml arterial blood samples were drawn manually at12 s intervals to 2 min, at 30 s intervals to 4 min, at 5 and 6 min,and every 2 min to 20 min. Plasma ICG concentrations were mea-sured by high-performance liquid chromatography and plasmaconcentrations were converted to blood concentrations by multi-plying them by one minus the hematocrit. For further details onstudy design, protocol, and measurements, please see Avramet al. (2000).

2.2. Model

To develop a circulatory model of ICG disposition that can beidentified solely on the basis of arterial blood concentration–timedata, its structural complexity must be reduced to a minimum.The most rigorous structural simplification is given in terms ofthe pulmonary and systemic circulation, both of which are charac-terized by transit time density (TTD) functions of ICG molecules(Weiss et al., 2006). The pulmonary (p), or central, circulation is lo-cated between the points of injection and arterial sampling. Herethe systemic circulation is split into two subsystems arranged inparallel, the hepatosplanchnic circulation and rest of the systemiccirculation (rs) (i.e., extrasplanchnic vascular beds) (Fig. 1). Thehepatosplanchnic circulation consists of two organs in series, thegut and the liver. When the TTD of the subsystems are non-expo-nential (no well mixed compartments), the equation for the arte-rial blood ICG concentration, C(t), after bolus venous injection(dose, Div) in a recirculatory system is only available in the Laplacedomain. Denoting the Laplace transform of a function f(t) byf ðsÞ ¼ L½f ðtÞ�, the model consists of the pulmonary and systemicsubsystem with TTDs, f pðsÞ and f sðsÞ. Since the TTDs of twosubsystems connected in series is the product, f ðsÞ ¼ f 1ðsÞf 2ðsÞ,and the input to the pulmonary circulation is given byCpul;in ¼ CðsÞf sðsÞ þ Div=Q , i.e., the output of the systemic circulationplus contribution of bolus dose (Q denotes cardiac output). FromCðsÞ ¼ Cpul;out ¼ Cpul;inðsÞf pðsÞ, we finally obtain:

CðsÞ ¼ Div

Qf pðsÞ

1� f sðsÞf pðsÞð1Þ

Pulmonary Circulation

Rest Systemic Circulation

Liver Gut

)(ˆ sf p

)(ˆ sfrs

Q

qQ

(1-q)Q

C(t)

subsystems, the pulmonary and systemic circulation, in which the latter is split intothe systemic circulation, with blood flows qQ and (1 � q)Q, respectively (Q is cardiacdomain. The pulmonary circulation and the rest of the systemic circulation as well

y f iðsÞ. In the distributed model of hepatic ICG elimination, Vb,hep is the extracellularptake clearance and extracellular liver volume, kin = CLuptake/Vb,hep), kout is the rate

M. Weiss et al. / European Journal of Pharmaceutical Sciences 44 (2011) 359–365 361

Splitting the systemic circulation into subsystems as shown inFig. 1, we have:

f sðsÞ ¼ qf hepðsÞf gutðsÞ þ ð1� qÞf rsðsÞ ð2Þ

where q = Qhep/Q is the fractional liver blood flow and f hepðsÞ, f gutðsÞand f rsðsÞ denote the TTD of the liver, the gut, and the rest of thesystemic (rs) circulation. We use the inverse Gaussian density(Sheppard et al., 1968) as empirical TTD for all subsystems exceptthe liver:

fiðtÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

MTTi

2p RD2i t3

sexp � ðt �MTTiÞ2

2 RD2i MTTit

" #ð3Þ

where the mean transit time is given by, MTTi = Vi/Qi (Vi and Qi

denote the vascular volume and blood flow), and RD2i denotes the

relative dispersion of each subsystem and the index i stands for p(pulmonary), rs (rest of the systemic), and gut. The Laplace trans-form of the inverse Gaussian TTD is given by (Seshadri, 1999)

f iðsÞ ¼ exp1

RD2i

� Vi=Q i

RD2i =2

sþ 12ðVi=QiÞRD2

i

!" #1=28<:

9=; ð4Þ

Thus, Eq. (4) is used for f pðsÞ, f gutðsÞ, and f rsðsÞ, with parameters(Q, Vp, RD2

p), (qQ, Vgut, RD2gut) and ((1 � q)Q, Vrs, RD2

rs), respectively.The transit time density function of ICG molecules across the liver,f hepðsÞ, is described in terms of the extracellular transit time densityof non-permeating reference (sucrose), f b;hepðsÞ, as (Weiss et al.,2000):

f hepðsÞ ¼ f b;hep sþ kinðke þ sÞkout þ ke þ s

� �ð5Þ

where kin = CLuptake/Vb,hep is the uptake rate constant in the liver,CLuptake is the sinusoidal uptake clearance, Vb,hep is the extracellularliver volume, ke is the canalicular excretion rate constant, and kout isthe rate constant of back-transport (Fig. 1). The TTD f b;hep (s) is alsodescribed by an inverse Gaussian TTD [Eq. (4)], with parametersQhep (i.e., qQ), Vb,hep, and RD2

b;hep. Note that, for the sake of simplifica-tion, the dual blood supply to the liver (hepatic artery and portalvein) was neglected and all organs of the hepatosplanchnic circula-tion other than the liver are lumped into the subsystem ‘‘gut’’. Notealso that the hepatic clearance, CLhep, is obtained from Eq. (5) asCLhep ¼ Qhep½1� f hepðsÞ� for s! 0 (where Qhep = qQ):

CLhep ¼Qhep1

RD2b;hep

�exp

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2CLuptakeRD2

b;hepkeþQhepkout þQhepke

QhepRD4b;hepðkeþkoutÞ

vuut0@

1A

24

35ð6Þ

2.3. Parameter estimation

Data fitting (population analysis) was carried out with maxi-mum likelihood (ML) estimation via the EM algorithm using thesoftware ADAPT 5 (D’Argenio et al., 2009), where the program(MLEM) is implemented. To deal with the mismatch betweenmodel complexity and available data, prior information wasincorporated (see below). The program provides estimates of thepopulation mean and intersubject variability as well as of the indi-vidual subject parameters (conditional means). Since the equationfor the ICG concentration–time curve resulting from the model isonly available in the Laplace domain [Eq. (1)], a numerical inverseLaplace transformation has to be performed to obtain the concen-tration–time curve in the time domain, CðtÞ ¼ L�1½CðsÞ�. We imple-mented Talbot’s algorithm into ADAPT 5 (Schalla and Weiss, 1999).It was assumed that the model parameters were log-normally dis-tributed among subjects (to constrain parameters to be positive)

and that the measurement error had a standard deviation thatwas a linear function of the measured quantity:

VARi ¼ r0 þ r1CðtiÞ½ �2 ð7Þ

‘‘Goodness of fit’’ was assessed using the Akaike InformationCriterion (AIC) and by plotting the predicted versus the measuredresponse. Furthermore, MLEM provided the approximate coeffi-cients of variation of individual parameter estimates.

To reduce the number of adjustable parameters, the vascularvolumes Vb,hep and Vgut were modeled as fractions of circulatingblood volume, Vb,hep = 0.08Vb and Vgut = 0.16Vb, (Horvath et al.,1957) where Vb = Vp + Vrs + Vb,hep + Vgut. For the vascular dispersionsacross the liver and gut, values of RD2

b;hep = 0.3 and RD2gut = 0.7 were

assumed. While RD2b;hep was calculated from isolated dog liver data

(Goresky, 1963), RD2gut was estimated by trial and error. To facilitate

estimation of the remaining 9 adjustable parameters (Q, Vp, RD2p,

Vrs, RD2rs, q, CLuptake, ke, kout), the population estimates obtained in

previous experiments for the same system without a hepaticcircuit (Weiss et al., 2006) were used as priors to set the rangesfor of Q, Vp, Vrs, RD2

p , and RD2rs. Note that the results of the MLEM

fit depend on this prior probability distribution rather than thestarting values. Parameter estimates are presented as populationmean and inter-subject variability (percent standard error). Thepaired t-test was applied to the individual subject parameters(conditional means) in order to evaluate the effect of isofluranecompared with awake. If the p value was <0.05, the differencewas considered to be significant.

2.4. Sensitivity analysis

A useful measure of the ability to estimate a parameter p fromthe data C(t) is the sensitivity function:

SpðtÞ ¼p

CðtÞ@CðtÞ@p

¼ pCðtÞ L

�1 @CðsÞ@p

" #ð8Þ

which determines the relative change in C(t) caused by a small rel-ative change in the model parameter p. Since Sp is non-dimen-sional, it allows a comparison of results obtained for differentparameters. Thus, Sp(t) represents the relative importance ofparameter p to model output. If the sensitivity functions of twoparameters are proportional, this indicates that the parametersare correlated and hardly identifiable in practice. The sensitivityfunctions [Eq. (7) substituting Eq. (1)] were calculated using MA-PLE 8 (Maplesoft, Waterloo, Ontario, Canada) after implementinga numerical method of inverse Laplace transformation (Schallaand Weiss, 1999).

2.5. Slope of the ICG disposition curve

Given that the terminal slope of the disposition curve (K) (alsocalled plasma disappearance rate) is measured routinely, how Kchanges with time and how it is affected by hepatic uptake clear-ance and biliary excretion is of interest. In accordance with theprocedure in the clinical ICG elimination tests, the elimination rateconstant K (terminal slope of the disposition curve) of each dogwas estimated by fitting a monoexponential function to the databetween 10 and 20 min after injection.

3. Results

The population parameters estimated in the awake state andunder isoflurane anesthesia are presented in Table 1. Fig. 2 (topand bottom right) shows the correlation of the individual predictedversus measured concentration values. The individual fits (basedon conditional estimates) are characterized by an R2 of

Table 1Parameters for the model of ICG kinetics with typical values and interindividualvariability as relative standard error (%) in brackets, estimated in dogs in the awakestate and under isoflurane anesthesia (n = 4).

Parameters Awake Isoflurane

CirculationQ (ml/min) 4590 (12) 1680 (6)**

Vp (ml) 784 (12) 671 (17)

RD2p

0.056 (39) 0.068 (14)

Vrs (ml) 1130 (25) 1520 (28)

RD2rs

3.04 (47) 4.13 (47)

LiverCLuptake (ml/min) 599 (13) 554 (19)ke (min�1) 0.823 (8) 0.551 (3)***

kout (min�1) 0.762 (4) 0.650 (2)q 0.327 (2) 0.413 (15)CLhep (ml/min)a 269 (32) 199 (30)**

a Derived parameter [Eq. (6)]. Q, cardiac output; Vp and RD2p , volume and relative

dispersion of the pulmonary (p) circulation, respectively; Vrs and RD2rs , volume and

relative dispersion of the rest of the systemic (rs) circulation, respectively; CLuptake,sinusoidal uptake clearance; ke, canalicular excretion rate constant; kout, rate con-stant of back-transport; q, fractional liver blood flow; CLhep, hepatic clearance.** p < 0.01.*** p < 0.001.

362 M. Weiss et al. / European Journal of Pharmaceutical Sciences 44 (2011) 359–365

0.94 ± 0.04 and 0.97 ± 0.04 (mean ± S.D.) in the awake andisoflurane states, respectively. The fits are illustrated in Fig. 2(top and bottom left) for the dog with the lowest R2 value in the

0 5 10 15 2010-1.0

100.0

101.0

2

3

4

56789

2

3

4

56789

Time (min)

ICG

con

cent

ratio

n(µ

g/m

l)

Awake

Isoflurane

0 5 10 15 20

2

3

456789

2

3

456789

10-1.0

10-0..0

101.0

Fig. 2. Examples of individual fits (based on conditional estimates) of the circulatory manesthetized with isoflurane (bottom left), together with goodness-of-fit plots showing t(top right) and isoflurane anesthetized state (bottom right).

awake state. Generally, good fits were obtained, but, as in previousapplications of the recirculation model (Weiss et al., 2006), devia-tions in the vicinity of the recirculation peak were observed insome cases. The sensitivity functions for CLuptake, ke, q, and RD2

rs

are depicted in Fig. 3. The information on the relative dispersionof the rest of the systemic circulation (RD2

rs) is concentrated inthe first two minutes. The sensitivities of this and all other non-he-patic parameters are nearly identical to those of the minimal circu-latory model (Weiss et al., 2006).

Isoflurane anesthesia significantly reduced cardiac output (Q),hepatic clearance (CLhep), and biliary excretion rate constant (ke).The estimates of the slope of the ICG disposition curve (K) were0.105 ± 0.028 and 0.084 ± 0.026, in the awake state and under iso-flurane anesthesia, respectively (p < 0.05). The measured K corre-lates with clearance CLhep (Fig. 4).

Figs. 5 and 6 show how sinusoidal uptake clearance (CLuptake)and canalicular excretion (ke) determine ICG clearance. There wasa strong correlation between the individual estimates of CLhep

and CLuptake in the awake and anesthetized state, respectively(Fig. 5). The change in cardiac output (hepatic blood flow) didnot affect CLuptake. That the reduction in ke is a direct effect ofisoflurane and not secondary to the change in hepatic blood flowis indicated in Fig. 6. The interplay between sinusoidal uptakeand canalicular excretion in determining hepatic ICG clearance issimulated in Fig. 7 using Eq. (6) and the population mean parame-ters of the awake dogs.

100 1012 3 4 5 6 7 8 2 3 4 5 6 7 8

100

101

2

3

45678

2

3

45678

100 1012 3 4 5 6 7 8 2 3 4 5 6 7 8

100

101

2

3

45678

2

3

45678

Awake

Observed C ICG (t) (µg/ml)

Pred

icte

d C

ICG

(t)

(µg/

ml)

Isoflurane

odel to ICG disposition data in an awake dog (top left) and in the same dog whilehe individual predicted vs. observed arterial blood ICG concentrations in the awake

Fig. 3. Normalized sensitivity of the ICG disposition curve C(t) with respect torelative dispersion in the rest of the systemic circulation (RD2

rs), fractional liverblood flow (q), canalicular excretion rate constant (ke) and sinusoidal uptakeclearance (CLuptake).

140 160 180 200 220 240 260 280 300 3200.04

0.06

0.08

0.10

0.12

0.14

R2= 0.71, P < 0.01

CL hep (ml/min)

K(1

/min

)

Fig. 4. Correlation between the individual estimates of CLhep and K in awake dogs.The disappearance rate constant K (terminal slope of the ICG concentration–timecurve) was estimated by a monoexponential fit of the data between 10 and 20 minafter injection.

CL uptake (ml/min)

CL

hep

(ml/m

in)

007006005004150

200

250

300

007006005004150

200

250

300

R2= 0.98, P < 0.05

R2= 0.98, P < 0.01

Awake

Isoflurane

Fig. 5. Correlation between individual estimates of CLhep and CLuptake in the awakestate (s) and under isoflurane anesthesia (d). Note that the decrease in cardiacoutput (hepatic blood flow) under isoflurane anesthesia did not affect CLuptake.

400 600 800 1000 1200 1400 1600 18000.5

0.6

0.7

0.8

Qhep (ml/min)

k e(1

/min

)Awake

Isoflurane

Fig. 6. Biliary excretion rate constants (ke) estimated in the awake state (s) andunder isoflurane anesthesia (d) as a function of hepatic blood flow (Qhep).

M. Weiss et al. / European Journal of Pharmaceutical Sciences 44 (2011) 359–365 363

4. Discussion

The present study was conducted in dogs, in which hepaticextraction of ICG is low and clearance is nearly independent of he-patic blood flow (Ketterer et al., 1960). Our results suggest that thehepatic clearance of ICG is determined by both hepatocellular up-take (i.e., sinusoidal membrane transport) and canalicular excre-tion (Figs. 5–7). According to available literature, both processesare transporter mediated (Kusuhara and Sugiyama, 2010; de Graafet al., 2011). The values of CLuptake, 559 and 554 ml/min, estimatedin the awake and anesthetized state, respectively, are consistentwith that observed in the isolated perfused rat liver (Lund et al.,1999), since the uptake rate constant in the rat liver (3.2 min�1)

is virtually identical to those obtained here as kin = CLuptake/Vb,hep

(with Vb,hep = 170 ml, kin = 3.28 and 3.26 min�1, while awake andanesthetized, respectively). In each group, the interindividual var-iability in ICG clearance could be attributed to the variability inCLuptake (Fig. 5). Hepatic uptake clearance of ICG was much lowerthan hepatic blood flow and independent of it. Simulation of our li-ver model shows CLhep as a function of both CLuptake and ke (Fig. 7);changes in hepatic uptake markedly influence ICG clearance. Thus,if CLuptake decreases (e.g., due to the inhibition of the uptake trans-porter), uptake may become the rate-determining process in thehepatic elimination of ICG. Such knowledge of the respective rolesof hepatic uptake and hepatocellular elimination in defining ICGclearance is important since disease states or interaction withother drugs can affect both processes differently. Assuming thatthe interpretation of ke is correct (see below), the reduction in bil-iary ICG excretion observed under isoflurane anesthesia (Fig. 6)would be a novel result. In the literature such information is avail-able only in rats, in which isoflurane reduced bile salt secretion(Bridges et al., 1989) but did not influence the biliary secretion ofthe organic anion dibromosulphthalein (DBSP) (Watkins,1989).

To avoid misunderstanding, it should be noted that the rateconstant ke stands for biliary excretion of ICG across the canalicular

Fig. 7. Hepatocellular uptake clearance (CLuptake) and canalicular excretion rate (ke)as determinants of hepatic ICG clearance (CLhep) in awake dogs. The estimates(population means) of these three parameters are indicated (d and arrows).[Simulated using Eq. (6)].

364 M. Weiss et al. / European Journal of Pharmaceutical Sciences 44 (2011) 359–365

membrane rather than the much slower recovery rate of ICG mea-sured in collected bile, where ICG appears after a delay of about20 min (Sergi et al., 2008). Since ICG is not metabolized, ke repre-sents only biliary excretion. The ability to discriminate betweenhepatic uptake and biliary elimination may be intuitively unex-pected but is suggested by both the finding that isoflurane only af-fected biliary excretion and the sensitivity analysis, i.e., the findingthat the transient sensitivities regarding changes in CLuptake and ke

were not parallel (Fig. 3). Note that such a discrimination appearspossible only for a vascular marker like ICG because otherwise tis-sue distribution will obscure the effect of hepatic distribution.While a compartmental model for which instantaneous intravas-cular mixing was assumed failed to fit our data (for obvious rea-sons), such a model can be useful when biliary excretion data areavailable and blood sampling starts after the early distributionphase (Sathirakul et al., 1993; Kusuhara and Sugiyama, 2010).However, the present distributed liver model, like any model, is asimplification and does not explicitly include intracellular diffu-sion and binding of ICG, a fact that should be considered in a phys-iological interpretation of the parameter ke, which may be modeldependent. While our interpretation of ke appears reasonable onthe basis of the given data and prior knowledge, the estimate couldbe biased due to the effect of cytosolic distribution kinetics. Thus ke

could partly account for quasi-irreversible cytosolic binding ratherthan biliary excretion.

The finding that the disappearance rate constant K (terminalslope of the ICG concentration–time curve) is determined by CLhep

(Fig. 4) is consistent with results in humans (Sakka and van Hout,2006), in whom no better correlation was observed despite thehigher hepatic extraction of ICG. This, however, is not surprisingin view of the fact that ICG does not exhibit one-compartment dis-position kinetics, i.e., mono-exponential decline (Fig. 2, left).

One limitation of this study is that, in contrast to the previouscirculatory model (Weiss et al., 2006), the extended model withthe liver as a separate subsystem (Fig. 1) was too complex forthe available data, necessitating the use of prior information. Thisprior knowledge about the pharmacokinetic system and associatedmodel parameters was incorporated in the form of prior parameterdistributions using a population modeling approach. Note that thelatter has proven successful when parameters are poorly estimatedusing individual fits (Krudys et al., 2006). Because the present

approach is based on prior information, it comprises elements ofso-called forward modeling, i.e., it resembles methods used inphysiologically based pharmacokinetic modeling. As a conse-quence of the low sensitivity of fractional liver blood flow (q)(Fig. 3), it remains an open question whether a change of thisparameter in altered physiological states can be detected in dogswith our approach. While the present model may have low sensi-tivity for the fractional liver blood flow in the dog because their ICGelimination clearance is flow-independent, the situation is likely tobe different in humans in whom the hepatic extraction of ICG ishigh and the elimination clearance is flow-dependent. However,rather than define a unique set of model parameters, the aim ofthis study was to understand the respective roles of sinusoidaland canalicular transport in determining ICG clearance. The mainindication that the present model and the estimated liver parame-ters are relevant is provided by Figs. 5 and 6. If hepatic uptake israte-limiting (Fig. 5), one should indeed expect that biliary excre-tion will be independent of hepatic blood flow (Fig. 6). Further-more, previous evidence that isoflurane inhibits biliary excretion(Bridges et al., 1989) is found reflected in Fig. 6.

As expected, the estimated values of cardiac output (Q) and he-patic clearance (CLhep) are consistent with those estimated in thesame dogs using thermodilution technique and a recirculatorycompartmental model, respectively (Avram et al., 2000). Further-more, the parameter estimates for the circulatory system, Q, Vp,Vrs and RD2

rs, are not much different from those obtained with theminimal circulatory model in awake dogs (Weiss et al., 2006). Itshould be also noted that the occurrence of the secondary peak(Fig. 2), is not primarily related to the hepatosplanchnic circulationbut a general property of recirculatory models; thus, the recircula-tion peak could be described by using different models of the sys-temic circulation (Henthorn et al., 1992; Oliver et al., 2001; Weisset al., 2006, 2007). Furthermore, this secondary peak observed ear-lier than 2 min after bolus injection in dogs (e.g., Henthorn et al.,1992; Avram et al., 2000) and in humans (Avram et al., 2004; Weisset al., 2011) is different from that described by Berezhkovskiy(2009). Finally, our estimate of hepatic uptake clearance (CLuptake)is similar to that reported for the rat liver (Lund et al., 1999) (scaledto liver volume) (see above). Thus, despite the limitations ex-pressed above, the present results provide further insight intothe mechanisms determining hepatic ICG pharmacokinetics inthe dog.

The minimal circulatory model of hepatic ICG kinetics in dogsrepresents a first step towards a physiologically-based approachthat allows more information to be extracted from ICG dispositiondata than could be obtained from commonly used K or CL esti-mates. The model can be adapted for use in humans, in whom sinu-soidal and canalicular ICG transporters may undergo differentregulation in disease states (Kortgen et al., 2009). A similar model(without hepatosplanchnic bed) has been recently used to analyzeICG kinetics in patients (Weiss et al., 2011). It remains to be testedwhether ICG concentration could be measured by non-invasivepulse dye densitometry (Niemann et al., 2002) in order to avoidfrequent early blood sampling.

Acknowledgement

We thank Dhanesh K. Gupta, M.D. for helpful discussions.

References

Avram, M.J., Krejcie, T.C., Niemann, C.U., Enders-Klein, C., Shanks, C.A., Henthorn,T.K., 2000. Isoflurane alters the recirculatory pharmacokinetics of physiologicmarkers. Anesthesiology 92, 1757–1768.

Avram, M.J., Krejcie, T.C., Henthorn, T.K., Niemann, C.U., 2004. Beta-adrenergicblockade affects initial drug distribution due to decreased cardiac output andaltered blood flow distribution. J. Pharmacol. Exp. Ther. 311, 617–624.

M. Weiss et al. / European Journal of Pharmaceutical Sciences 44 (2011) 359–365 365

Berezhkovskiy, L.M., 2009. Prediction of the possibility of the secondary peaks of ivbolus drug plasma concentration time curve by the model that directly takesinto account the transit time through the organ. J. Pharm. Sci. 98, 4376–4390.

Bridges, R., Kirk, D., Strunin, L., Shaffer, E., 1989. Acute effects of halothane andisoflurane on bile secretion in the rat. Br. J. Anaesth. 63 (Suppl.), 631.

D’Argenio, D.Z., Schumitzky, A., Wang, X., 2009. ADAPT 5 User’s Guide:Pharmacokinetic//Pharmacodynamic Systems Analysis Software. BiomedicalSimulations Resource, Los Angeles.

de Graaf, W., Häusler, S., Heger, M., van Ginhoven, T.M., van Cappellen, G., Bennink,R.J., Kullak-Ublick, G.A., Hesselmann, R., van Gulik, T.M., Stieger, B., 2011.Transporters involved in the hepatic uptake of (99m)Tc-mebrofenin andindocyanine green. J. Hepatol. 54, 738–745.

Goresky, C.A., 1963. A linear method for determining liver sinusoidal andextravascular volumes. Am. J. Physiol. 204, 626–640.

Henthorn, T.K., Avram, M.J., Krejcie, T.C., Shanks, C.A., Asada, A., Kaczynski, D.A.,1992. Minimal compartmental model of circulatory mixing of indocyaninegreen. Am. J. Physiol. Heart Circ. Physiol. 262, H903–H910.

Hori, T., Iida, T.-, Yagi, S., Taniguchi, K., Yamamoto, C., Mizuno, S., Yamagiwa, K., Isaji,S., Uemoto, S., 2006. KICG value, a reliable real-time estimator of graft function,accurately predicts outcomes in adult living-donor liver transplantation. LiverTranspl. 12, 605–613.

Horvath, S.M., Kelly, T., Folk Jr, G.E., Hutt, B.K., 1957. Measurement of blood volumesin the splanchnic bed of the dog. Am. J. Physiol. 189, 573–575.

Hung, D.Y., Chang, P., Cheung, K., McWhinney, B., Masci, P.P., Weiss, M., Roberts,M.S., 2002. Cationic drug pharmacokinetics in diseased livers determined byfibrosis index, hepatic protein content, microsomal activity, and nature of drug.J. Pharmacol. Exp. Ther. 301, 1079–1087.

Ketterer, S.G., Wiegand, B.D., Rapaport, E., 1960. Hepatic uptake and biliaryexcretion of indocyanine green and its use in estimation of hepatic bloodflow in dogs. Am. J. Physiol. 199, 481–484.

Kortgen, A., Paxian, M., Werth, M., Recknagel, P., Rauchfuss, F., Lupp, A., Krenn, C.G.,Müller, D., Claus, R.A., Reinhart, K., Settmacher, U., Bauer, M., 2009. Prospectiveassessment of hepatic function and mechanisms of dysfunction in the criticallyill. Shock 32, 358–365.

Krudys, K.M., Kahn, S.E., Vicini, P., 2006. Population approaches to estimate minimalmodel indexes of insulin sensitivity and glucose effectiveness using full andreduced sampling schedules. Am. J. Physiol. Endocrinol. Metab. 291, E716–E723.

Kusuhara, H., Sugiyama, Y., 2010. Pharmacokinetic modeling of the hepatobiliarytransport mediated by cooperation of uptake and efflux transporters. DrugMetab. Rev. 42, 539–550.

Lund, M., Kang, L., Tygstrup, N., Wolkoff, A.W., Ott, P., 1999. Effects of LPS ontransport of indocyanine green and alanine uptake in perfused rat liver. Am. J.Physiol. Gastrointest. Liver Physiol. 277, G91–G100.

Niemann, C.U., Yost, C.S., Mandell, S., Henthorn, T.K., 2002. Evaluation of thesplanchnic circulation with indocyanine green pharmacokinetics in livertransplant patients. Liver Transpl. 8, 476–481.

Oliver, R.E., Jones, A.F., Rowland, M., 2001. A whole-body physiologically basedpharmacokinetic model incorporating dispersion concepts: short and long timecharacteristics. J. Pharmacokinet. Pharmacodyn. 28, 27–55.

Ott, P., 1998. Hepatic elimination of indocyanine green with special reference todistribution kinetics and the influence of plasma protein binding. Pharmacol.Toxicol. 83 (Suppl. 2), 1–48.

Roberts, M.S., Anissimov, Y.A., Weiss, M., 2000. Using the convection–dispersionmodel and transit density functions in the analysis of organ distributionkinetics. J. Pharm. Sci. 89, 1579–1586.

Rowland, M., Peck, C., Tucker, G., 2011. Physiologically-based pharmacokinetics indrug development and regulatory science. Annu. Rev. Pharmacol. Toxicol. 51,45–73.

Sakka, S.G., van Hout, N., 2006. Relation between indocyanine green (ICG) plasmadisappearance rate and ICG blood clearance in critically ill patients. IntensiveCare Med. 32, 766–769.

Sathirakul, K., Suzuki, H., Yasuda, K., Hanano, M., Tagaya, O., Horie, T., Sugiyama, Y.,1993. Kinetic analysis of hepatobiliary transport of organic anions in Eisaihyperbilirubinemic mutant rats. J. Pharmacol. Exp. Ther. 265, 1301–1312.

Schalla, M., Weiss, M., 1999. Pharmacokinetic curve fitting using numerical inverseLaplace transformation. Eur. J. Pharm. Sci. 7, 305–309.

Sergi, C., Gross, W., Mory, M., Schaefer, M., Gebhard, M.M., 2008. Biliary-typecytokeratin pattern in a canine isolated perfused liver transplantation model. J.Surg. Res. 146, 164–171.

Seshadri, V., 1999. The Inverse Gaussian Distribution: Statistical Theory andApplications. Springer, New York.

Sheppard, C.W., Uffer, M.B., Merker, P.C., Halikas, G., 1968. Circulation andrecirculation of injected dye in the anesthetized dog. J. Appl. Physiol. 25, 610–618.

Watkins 3rd, J.B., 1989. Exposure of rats to inhalational anesthetics alters thehepatobiliary clearance of cholephilic xenobiotics. J. Pharmacol. Exp. Ther. 250,421–427.

Weiss, M., 2009. Cardiac output and systemic transit time dispersion asdeterminants of circulatory mixing time: a simulation study. J. Appl. Physiol.107, 445–449.

Weiss, M., Roberts, M.S., 1996. Tissue distribution kinetics as determinant of transittime dispersion of drugs in organs: application of a stochastic model to the rathindlimb. J. Pharmacokinet. Biopharm. 24, 173–196.

Weiss, M., Krejcie, T.C., Avram, M.J., 2006. Transit time dispersion in the pulmonaryand systemic circulation: effects of cardiac output and solute diffusivity. Am. J.Physiol. Heart Circ. Physiol. 291, H861–H870.

Weiss, M., Krejcie, T.C., Avram, M.J., 2007. A minimal physiological model ofthiopental distribution kinetics based on a multiple indicator approach. DrugMetab. Dispos. 35, 1525–1532.

Weiss, M., Kuhlmann, O., Hung, D.Y., Roberts, M.S., 2000. Cytoplasmic binding anddisposition kinetics of diclofenac in the isolated perfused rat liver. Br. J.Pharmacol. 130, 1331–1338.

Weiss, M., Reekers, M., Vuyk, J., Boer, F., 2011. Circulatory model of vascular andinterstitial distribution kinetics of rocuronium: a population analysis inpatients. J. Pharmacokinet. Pharmacodyn. 38, 165–178.

Weiss, M., Roelsgaard, K., Bender, D., Keiding, S., 2002. Determinants of[13N]ammonia kinetics in hepatic PET experiments: a minimal recirculatorymodel. Eur. J. Nucl. Med. Mol. Imaging 29, 1648–1656.