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A physiologically based model of hepatic ICG clearance: Interplay between sinusoidal uptake and biliary excretion
European Journal of Pharmaceutical Sciences 44 (2011) 359–365
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European Journal of Pharmaceutical Sciences journal homepage: www.elsevier.com/locate/ejps
A physiologically based model of hepatic ICG clearance: Interplay between sinusoidal uptake and biliary excretion Michael Weiss a,⇑, Tom C. Krejcie b, Michael J. Avram b a b
Section of Pharmacokinetics, Department of Pharmacology, Martin Luther University Halle-Wittenberg, Halle, Germany 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 2011 Received in revised form 28 June 2011 Accepted 20 August 2011 Available online 26 August 2011 Keywords: ICG Hepatic uptake Biliary excretion Pharmacokinetic model Isoflurane Dog
a b s t r a c t Although indocyanine green (ICG) has long been used for the assessment of liver function, the respective roles 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 ICG disposition 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 with 3.5% isoflurane were subjected to population analysis. The results suggest that ICG elimination in dogs is uptake limited since it depends on hepatocellular uptake capacity and on biliary excretion but not on hepatic blood flow. Isoflurane caused a 63% reduction in cardiac output and a 33% decrease in the ICG biliary excretion rate constant (resulting in a 26% reduction in elimination clearance) while leaving unchanged the sinusoidal uptake rate. The terminal slope of the concentration–time curve, K, correlated significantly with elimination clearance. The model could be useful for assessing the functions of sinusoidal and canalicular ICG transporters. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Indocyanine green (ICG) is an organic anion dye that is eliminated exclusively by the liver. It is widely used to assess hepatic function, 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 is known 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 transport is 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 review, see Kusuhara and Sugiyama, 2010). However, under in vivo conditions where only plasma ICG concentrations are measured, the roles of these processes are poorly understood. It appears that hepatocellular uptake and not hepatic blood flow may be rate limiting in dogs (Ketterer et al., 1960), but there is little quantitative information on the relative contribution of each process to ICG elimination. Thus, the goal of the present study was to determine whether modeling of ICG disposition curve could reveal the interplay between sinusoidal uptake and biliary excretion in determining hepatic ICG clearance (i.e., when the time profile of biliary ⇑ Corresponding author. Tel.: +49 345 5571657; fax: +49 345 5571835. E-mail address: [email protected] (M. Weiss). 0928-0987/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ejps.2011.08.018
excretion is not available). To this end, we applied a novel pharmacokinetic model to ICG plasma concentration–time data obtained using frequent arterial sampling in awake and isoflurane anesthetized dogs (Avram et al., 2000). Estimation of hepatocellular uptake clearance and biliary excretion rate constant of ICG was based on a circulatory model. Lumping the systemic organs into two subsystems, hepatosplanchnic and non-splanchnic circulation, the approach is similar to that used to describe [13N]ammonia kinetics (Weiss et al., 2002) and is an extension of the circulatory model of ICG disposition (Weiss et al., 2006, 2007). Thus, in contrast to previous approaches based on compartmental modeling (for a review, see Ott, 1998), we have adopted a minimal physiological model of ICG whole body pharmacokinetics that includes a space-distributed liver model (Weiss and Roberts, 1996). This model has been used to analyze data obtained in the isolated perfused rat liver (Weiss et al., 2000; Hung et al., 2002). The difficulty with a more complex model lies in the large number of model parameters relative to the available data. Prior information obtained on the system without liver (Weiss et al., 2006) was incorporated in parameter estimation using a population approach (D’Argenio et al., 2009) to facilitate parameter identifiability. The fact that isoflurane anesthesia decreased cardiac output to about 37% of that in the awake state (Avram et al., 2000) allowed an examination of the effect of liver blood flow. The advantages of physiologically-based pharmacokinetic (PBPK) modeling have been reviewed recently (Rowland et al.,
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2011). Although PBPK models are normally based on a compartmental structure (differential equations), in the present approach the subsystems of the body were modeled by transit time density (TTD) functions for at least two reasons. First, since ICG distributes within the vascular system, we are also aiming to describe the initial phase (the first minutes) of the disposition curve to estimate cardiac output as a main determinant of the mixing process (Weiss, 2009). This would be not possible using a conventional compartmental model for the lung. The initial peak of the arterial concentration time curve mainly represents the TTD through the lung. That the latter can be described by the inverse Gaussian density has been shown in tracer kinetics (Sheppard et al., 1968). The usefulness of the inverse Gaussian TTD in pharmacokinetics can be explained by the facts that it represents the first passage time distribution of a random walk process with drift (Seshadri, 1999) and that it is the solution to the convection–dispersion organ model (Roberts et al., 2000). Second, in a PBPK model based on differential equations it would not be possible to integrate a space-distributed liver model. Furthermore, while due to their structural complexity, PBPK models are typically used for simulation, this study is an attempt to develop a minimal PBPK model for ICG that can be identified using plasma concentration data. This method may lead to a better understanding of the processes determining ICG clearance in vivo, e.g., for characterizing the function of transporters involved in sinusoidal uptake and biliary excretion of ICG in normal and disease states. The model was also used to examine the role of the terminal slope of the ICG concentration– time curve (blood disappearance rate, K), that is routinely used as 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 disposition in 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 stated, at time t = 0 min, 5 mg of ICG in 1 ml of ICG diluent was flushed into the right atrium within 4 s using 10 ml of a 0.9% saline
Div
solution. Arterial blood samples were collected via an indwelling iliac artery catheter every 1.8 s for the first 28.8 s and every 3.6 s for the next 32.4 s using a roller pump and fraction collector. Subsequently, 18 3-ml arterial blood samples were drawn manually at 12 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 measured by high-performance liquid chromatography and plasma concentrations were converted to blood concentrations by multiplying them by one minus the hematocrit. For further details on study design, protocol, and measurements, please see Avram et al. (2000). 2.2. Model To develop a circulatory model of ICG disposition that can be identified solely on the basis of arterial blood concentration–time data, its structural complexity must be reduced to a minimum. The most rigorous structural simplification is given in terms of the pulmonary and systemic circulation, both of which are characterized by transit time density (TTD) functions of ICG molecules (Weiss et al., 2006). The pulmonary (p), or central, circulation is located between the points of injection and arterial sampling. Here the systemic circulation is split into two subsystems arranged in parallel, the hepatosplanchnic circulation and rest of the systemic circulation (rs) (i.e., extrasplanchnic vascular beds) (Fig. 1). The hepatosplanchnic circulation consists of two organs in series, the gut and the liver. When the TTD of the subsystems are non-exponential (no well mixed compartments), the equation for the arterial blood ICG concentration, C(t), after bolus venous injection (dose, Div) in a recirculatory system is only available in the Laplace domain. Denoting the Laplace transform of a function f(t) by ^f ðsÞ ¼ L½f ðtÞ, the model consists of the pulmonary and systemic subsystem with TTDs, ^f p ðsÞ and ^f s ðsÞ. Since the TTDs of two subsystems connected in series is the product, ^f ðsÞ ¼ ^f 1 ðsÞ^f 2 ðsÞ, and the input to the pulmonary circulation is given by ^ ^f s ðsÞ þ Div =Q , i.e., the output of the systemic circulation ^ pul;in ¼ CðsÞ C plus contribution of bolus dose (Q denotes cardiac output). From ^ pul;in ðsÞ^f p ðsÞ, we finally obtain: ^ ^ pul;out ¼ C CðsÞ ¼C
^f ðsÞ p ^ ¼ D iv CðsÞ Q 1 ^f s ðsÞ^f p ðsÞ
ð1Þ
fˆp ( s)
ke
Liver
Q
Gut
qQ
kout Vb,hep
C(t)
Pulmonary Circulation
kin
Rest Systemic Circulation
fˆrs ( s )
(1-q)Q
Fig. 1. Circulatory model of hepatic ICG elimination kinetics consisting of heterogeneous subsystems, the pulmonary and systemic circulation, in which the latter is split into two parallel subsystems, the hepatosplanchnic bed (gut and liver in series) and the rest of the systemic circulation, with blood flows qQ and (1 q)Q, respectively (Q is cardiac output). All subsystems are characterized by transit time density functions in the Laplace domain. The pulmonary circulation and the rest of the systemic circulation as well as the gut are characterized by inverse Gaussian transit time density functions denoted by ^f i ðsÞ. In the distributed model of hepatic ICG elimination, Vb,hep is the extracellular liver volume, kin is the sinusoidal uptake rate constant (which is determined by the uptake clearance and extracellular liver volume, kin = CLuptake/Vb,hep), kout is the rate constant of back-transport, and ke the canalicular excretion rate constant.
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Splitting the systemic circulation into subsystems as shown in Fig. 1, we have:
and that the measurement error had a standard deviation that was a linear function of the measured quantity:
^f ðsÞ ¼ q^f ðsÞ^f ðsÞ þ ð1 qÞ^f ðsÞ s gut rs hep
VARi ¼ ½r0 þ r1 Cðt i Þ2
ð2Þ
where q = Qhep/Q is the fractional liver blood flow and ^f hep ðsÞ, ^f gut ðsÞ and ^f rs ðsÞ denote the TTD of the liver, the gut, and the rest of the systemic (rs) circulation. We use the inverse Gaussian density (Sheppard et al., 1968) as empirical TTD for all subsystems except the liver:
fi ðtÞ ¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi MTT i 2p RD2i t
"
exp 3
ðt MTT i Þ2
#
2 RD2i MTT i t
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 transform of the inverse Gaussian TTD is given by (Seshadri, 1999)
8 " !#1=2 9 < 1 = V =Q 1 i i ^f ðsÞ ¼ exp sþ i 2 2 2 :RDi ; 2ðV i =Q i ÞRDi RDi =2
ð4Þ
Thus, Eq. (4) is used for ^f p ðsÞ, ^f gut ðsÞ, and ^f rs ðsÞ, with parameters (Q, Vp, RD2p ), (qQ, Vgut, RD2gut ) and ((1 q)Q, Vrs, RD2rs ), respectively. The transit time density function of ICG molecules across the liver, ^f ðsÞ, is described in terms of the extracellular transit time density hep of non-permeating reference (sucrose), ^f b;hep ðsÞ, as (Weiss et al., 2000):
kin ðke þ sÞ ^f ðsÞ ¼ ^f hep b;hep s þ kout þ ke þ s
ð7Þ
‘‘Goodness of fit’’ was assessed using the Akaike Information Criterion (AIC) and by plotting the predicted versus the measured response. Furthermore, MLEM provided the approximate coefficients of variation of individual parameter estimates. To reduce the number of adjustable parameters, the vascular volumes Vb,hep and Vgut were modeled as fractions of circulating blood volume, Vb,hep = 0.08Vb and Vgut = 0.16Vb, (Horvath et al., 1957) where Vb = Vp + Vrs + Vb,hep + Vgut. For the vascular dispersions across the liver and gut, values of RD2b;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 hepatic circuit (Weiss et al., 2006) were used as priors to set the ranges for of Q, Vp, Vrs, RD2p , and RD2rs . Note that the results of the MLEM fit depend on this prior probability distribution rather than the starting values. Parameter estimates are presented as population mean and inter-subject variability (percent standard error). The paired t-test was applied to the individual subject parameters (conditional means) in order to evaluate the effect of isoflurane compared with awake. If the p value was <0.05, the difference was considered to be significant. 2.4. Sensitivity analysis
ð5Þ
where kin = CLuptake/Vb,hep is the uptake rate constant in the liver, CLuptake is the sinusoidal uptake clearance, Vb,hep is the extracellular liver volume, ke is the canalicular excretion rate constant, and kout is the rate constant of back-transport (Fig. 1). The TTD ^f b;hep (s) is also described by an inverse Gaussian TTD [Eq. (4)], with parameters Qhep (i.e., qQ), Vb,hep, and RD2b;hep . Note that, for the sake of simplification, the dual blood supply to the liver (hepatic artery and portal vein) was neglected and all organs of the hepatosplanchnic circulation other than the liver are lumped into the subsystem ‘‘gut’’. Note also that the hepatic clearance, CLhep, is obtained from Eq. (5) as CLhep ¼ Q hep ½1 ^f hep ðsÞ for s ! 0 (where Qhep = qQ): ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi13 2 0v u u2CLuptake RD2b;hep ke þ Q hep kout þ Q hep ke 1 A5 CLhep ¼ Q hep 4 2 exp @t Q hep RD4b;hep ðke þ kout Þ RDb;hep
ð6Þ
A useful measure of the ability to estimate a parameter p from the data C(t) is the sensitivity function:
Sp ðtÞ ¼
" # ^ p @CðtÞ p 1 @ CðsÞ ¼ L CðtÞ @p CðtÞ @p
ð8Þ
which determines the relative change in C(t) caused by a small relative change in the model parameter p. Since Sp is non-dimensional, it allows a comparison of results obtained for different parameters. Thus, Sp(t) represents the relative importance of parameter p to model output. If the sensitivity functions of two parameters are proportional, this indicates that the parameters are correlated and hardly identifiable in practice. The sensitivity functions [Eq. (7) substituting Eq. (1)] were calculated using MAPLE 8 (Maplesoft, Waterloo, Ontario, Canada) after implementing a numerical method of inverse Laplace transformation (Schalla and Weiss, 1999). 2.5. Slope of the ICG disposition curve
2.3. Parameter estimation Data fitting (population analysis) was carried out with maximum likelihood (ML) estimation via the EM algorithm using the software ADAPT 5 (D’Argenio et al., 2009), where the program (MLEM) is implemented. To deal with the mismatch between model complexity and available data, prior information was incorporated (see below). The program provides estimates of the population mean and intersubject variability as well as of the individual subject parameters (conditional means). Since the equation for the ICG concentration–time curve resulting from the model is only available in the Laplace domain [Eq. (1)], a numerical inverse Laplace transformation has to be performed to obtain the concen^ tration–time curve in the time domain, CðtÞ ¼ L1 ½CðsÞ. We implemented Talbot’s algorithm into ADAPT 5 (Schalla and Weiss, 1999). It was assumed that the model parameters were log-normally distributed among subjects (to constrain parameters to be positive)
Given that the terminal slope of the disposition curve (K) (also called plasma disappearance rate) is measured routinely, how K changes with time and how it is affected by hepatic uptake clearance and biliary excretion is of interest. In accordance with the procedure in the clinical ICG elimination tests, the elimination rate constant K (terminal slope of the disposition curve) of each dog was estimated by fitting a monoexponential function to the data between 10 and 20 min after injection. 3. Results The population parameters estimated in the awake state and under isoflurane anesthesia are presented in Table 1. Fig. 2 (top and bottom right) shows the correlation of the individual predicted versus measured concentration values. The individual fits (based on conditional estimates) are characterized by an R2 of
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Table 1 Parameters for the model of ICG kinetics with typical values and interindividual variability as relative standard error (%) in brackets, estimated in dogs in the awake state and under isoflurane anesthesia (n = 4). Parameters
Awake
Isoflurane
4590 (12) 784 (12) 0.056 (39)
1680 (6)** 671 (17) 0.068 (14)
RD2rs
1130 (25) 3.04 (47)
1520 (28) 4.13 (47)
Liver CLuptake (ml/min) ke (min1) kout (min1) q CLhep (ml/min)a
599 (13) 0.823 (8) 0.762 (4) 0.327 (2) 269 (32)
554 (19) 0.551 (3)*** 0.650 (2) 0.413 (15) 199 (30)**
Circulation Q (ml/min) Vp (ml) RD2p Vrs (ml)
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 constant of back-transport; q, fractional liver blood flow; CLhep, hepatic clearance. ** p < 0.01. *** p < 0.001.
0.94 ± 0.04 and 0.97 ± 0.04 (mean ± S.D.) in the awake and isoflurane states, respectively. The fits are illustrated in Fig. 2 (top and bottom left) for the dog with the lowest R2 value in the
101.0 9
awake state. Generally, good fits were obtained, but, as in previous applications of the recirculation model (Weiss et al., 2006), deviations in the vicinity of the recirculation peak were observed in some cases. The sensitivity functions for CLuptake, ke, q, and RD2rs are depicted in Fig. 3. The information on the relative dispersion of the rest of the systemic circulation (RD2rs ) is concentrated in the first two minutes. The sensitivities of this and all other non-hepatic parameters are nearly identical to those of the minimal circulatory 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) were 0.105 ± 0.028 and 0.084 ± 0.026, in the awake state and under isoflurane anesthesia, respectively (p < 0.05). The measured K correlates with clearance CLhep (Fig. 4). Figs. 5 and 6 show how sinusoidal uptake clearance (CLuptake) and canalicular excretion (ke) determine ICG clearance. There was a 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) did not affect CLuptake. That the reduction in ke is a direct effect of isoflurane and not secondary to the change in hepatic blood flow is indicated in Fig. 6. The interplay between sinusoidal uptake and canalicular excretion in determining hepatic ICG clearance is simulated in Fig. 7 using Eq. (6) and the population mean parameters of the awake dogs.
Awake
8 7 6 5
8 7 6 5
4
4
3
3
2
2
10-0..0 9
100
8 7 6 5
8 7 6 5 4
3
3
10-1.0 0
5
10 1.09 8 7 6 5
10
15
20
Isoflurane
4 3
Predicted C ICG (t) (µg/ml)
4
2
ICG concentration (µg/ml)
Awake
101
2
2
101
3
4
5
6 7 8
100
6 7 8
100
2
3
4
2
3
4
5
6 7 8
101
Isoflurane
8 7 6 5 4 3
2
2
10 0.09
100
8 7 6 5
8 7 6 5
4
4
3
3
2
2
10 -1.0
0
5
10
Time (min)
15
20
2
3
4
5
Observed C
5
6 7 8
101
ICG (t) (µg/ml)
Fig. 2. Examples of individual fits (based on conditional estimates) of the circulatory model to ICG disposition data in an awake dog (top left) and in the same dog while anesthetized with isoflurane (bottom left), together with goodness-of-fit plots showing the individual predicted vs. observed arterial blood ICG concentrations in the awake (top right) and isoflurane anesthetized state (bottom right).
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300
R2= 0.98, P < 0.05 CL hep (ml/min)
Awake 250
R2= 0.98, P < 0.01
Isoflurane 200
150 400
500
600
700
CL uptake (ml/min) Fig. 5. Correlation between individual estimates of CLhep and CLuptake in the awake state (s) and under isoflurane anesthesia (d). Note that the decrease in cardiac output (hepatic blood flow) under isoflurane anesthesia did not affect CLuptake.
Awake
Fig. 3. Normalized sensitivity of the ICG disposition curve C(t) with respect to relative dispersion in the rest of the systemic circulation (RD2rs ), fractional liver blood flow (q), canalicular excretion rate constant (ke) and sinusoidal uptake clearance (CLuptake).
k e (1/min)
0.8
0.14
0.7
R2= 0.71, P < 0.01 0.12
0.6
K (1/min)
Isoflurane 0.10 0.5 400
0.08
600
800
1000
1200
1400
1600
1800
Q hep (ml/min) Fig. 6. Biliary excretion rate constants (ke) estimated in the awake state (s) and under isoflurane anesthesia (d) as a function of hepatic blood flow (Qhep).
0.06
0.04 140
160
180
200
220
240
260
280
300
320
CL hep (ml/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–time curve) was estimated by a monoexponential fit of the data between 10 and 20 min after injection.
4. Discussion The present study was conducted in dogs, in which hepatic extraction of ICG is low and clearance is nearly independent of hepatic blood flow (Ketterer et al., 1960). Our results suggest that the hepatic clearance of ICG is determined by both hepatocellular uptake (i.e., sinusoidal membrane transport) and canalicular excretion (Figs. 5–7). According to available literature, both processes are transporter mediated (Kusuhara and Sugiyama, 2010; de Graaf et al., 2011). The values of CLuptake, 559 and 554 ml/min, estimated in the awake and anesthetized state, respectively, are consistent with that observed in the isolated perfused rat liver (Lund et al., 1999), since the uptake rate constant in the rat liver (3.2 min1)
is virtually identical to those obtained here as kin = CLuptake/Vb,hep (with Vb,hep = 170 ml, kin = 3.28 and 3.26 min1, while awake and anesthetized, respectively). In each group, the interindividual variability in ICG clearance could be attributed to the variability in CLuptake (Fig. 5). Hepatic uptake clearance of ICG was much lower than hepatic blood flow and independent of it. Simulation of our liver 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 transporter), uptake may become the rate-determining process in the hepatic elimination of ICG. Such knowledge of the respective roles of hepatic uptake and hepatocellular elimination in defining ICG clearance is important since disease states or interaction with other drugs can affect both processes differently. Assuming that the interpretation of ke is correct (see below), the reduction in biliary ICG excretion observed under isoflurane anesthesia (Fig. 6) would be a novel result. In the literature such information is available only in rats, in which isoflurane reduced bile salt secretion (Bridges et al., 1989) but did not influence the biliary secretion of the organic anion dibromosulphthalein (DBSP) (Watkins,1989). To avoid misunderstanding, it should be noted that the rate constant ke stands for biliary excretion of ICG across the canalicular
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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)].
membrane rather than the much slower recovery rate of ICG measured in collected bile, where ICG appears after a delay of about 20 min (Sergi et al., 2008). Since ICG is not metabolized, ke represents only biliary excretion. The ability to discriminate between hepatic uptake and biliary elimination may be intuitively unexpected but is suggested by both the finding that isoflurane only affected biliary excretion and the sensitivity analysis, i.e., the finding that the transient sensitivities regarding changes in CLuptake and ke were not parallel (Fig. 3). Note that such a discrimination appears possible only for a vascular marker like ICG because otherwise tissue distribution will obscure the effect of hepatic distribution. While a compartmental model for which instantaneous intravascular mixing was assumed failed to fit our data (for obvious reasons), such a model can be useful when biliary excretion data are available and blood sampling starts after the early distribution phase (Sathirakul et al., 1993; Kusuhara and Sugiyama, 2010). However, the present distributed liver model, like any model, is a simplification and does not explicitly include intracellular diffusion and binding of ICG, a fact that should be considered in a physiological interpretation of the parameter ke, which may be model dependent. While our interpretation of ke appears reasonable on the basis of the given data and prior knowledge, the estimate could be biased due to the effect of cytosolic distribution kinetics. Thus ke could partly account for quasi-irreversible cytosolic binding rather than biliary excretion. The finding that the disappearance rate constant K (terminal slope 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 the higher hepatic extraction of ICG. This, however, is not surprising in view of the fact that ICG does not exhibit one-compartment disposition kinetics, i.e., mono-exponential decline (Fig. 2, left). One limitation of this study is that, in contrast to the previous circulatory model (Weiss et al., 2006), the extended model with the liver as a separate subsystem (Fig. 1) was too complex for the available data, necessitating the use of prior information. This prior knowledge about the pharmacokinetic system and associated model parameters was incorporated in the form of prior parameter distributions using a population modeling approach. Note that the latter has proven successful when parameters are poorly estimated using individual fits (Krudys et al., 2006). Because the present
approach is based on prior information, it comprises elements of so-called forward modeling, i.e., it resembles methods used in physiologically based pharmacokinetic modeling. As a consequence of the low sensitivity of fractional liver blood flow (q) (Fig. 3), it remains an open question whether a change of this parameter in altered physiological states can be detected in dogs with our approach. While the present model may have low sensitivity for the fractional liver blood flow in the dog because their ICG elimination clearance is flow-independent, the situation is likely to be different in humans in whom the hepatic extraction of ICG is high and the elimination clearance is flow-dependent. However, rather than define a unique set of model parameters, the aim of this study was to understand the respective roles of sinusoidal and canalicular transport in determining ICG clearance. The main indication that the present model and the estimated liver parameters are relevant is provided by Figs. 5 and 6. If hepatic uptake is rate-limiting (Fig. 5), one should indeed expect that biliary excretion will be independent of hepatic blood flow (Fig. 6). Furthermore, 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 hepatic clearance (CLhep) are consistent with those estimated in the same dogs using thermodilution technique and a recirculatory compartmental model, respectively (Avram et al., 2000). Furthermore, the parameter estimates for the circulatory system, Q, Vp, Vrs and RD2rs , are not much different from those obtained with the minimal circulatory model in awake dogs (Weiss et al., 2006). It should be also noted that the occurrence of the secondary peak (Fig. 2), is not primarily related to the hepatosplanchnic circulation but a general property of recirculatory models; thus, the recirculation peak could be described by using different models of the systemic circulation (Henthorn et al., 1992; Oliver et al., 2001; Weiss et al., 2006, 2007). Furthermore, this secondary peak observed earlier 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; Weiss et 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) (scaled to liver volume) (see above). Thus, despite the limitations expressed above, the present results provide further insight into the mechanisms determining hepatic ICG pharmacokinetics in the dog. The minimal circulatory model of hepatic ICG kinetics in dogs represents a first step towards a physiologically-based approach that allows more information to be extracted from ICG disposition data than could be obtained from commonly used K or CL estimates. The model can be adapted for use in humans, in whom sinusoidal and canalicular ICG transporters may undergo different regulation in disease states (Kortgen et al., 2009). A similar model (without hepatosplanchnic bed) has been recently used to analyze ICG kinetics in patients (Weiss et al., 2011). It remains to be tested whether ICG concentration could be measured by non-invasive pulse dye densitometry (Niemann et al., 2002) in order to avoid frequent 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 physiologic markers. Anesthesiology 92, 1757–1768. Avram, M.J., Krejcie, T.C., Henthorn, T.K., Niemann, C.U., 2004. Beta-adrenergic blockade affects initial drug distribution due to decreased cardiac output and altered blood flow distribution. J. Pharmacol. Exp. Ther. 311, 617–624.
M. Weiss et al. / European Journal of Pharmaceutical Sciences 44 (2011) 359–365 Berezhkovskiy, L.M., 2009. Prediction of the possibility of the secondary peaks of iv bolus drug plasma concentration time curve by the model that directly takes into 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 and isoflurane 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. Biomedical Simulations 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 and indocyanine green. J. Hepatol. 54, 738–745. Goresky, C.A., 1963. A linear method for determining liver sinusoidal and extravascular 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 indocyanine green. 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. Liver Transpl. 12, 605–613. Horvath, S.M., Kelly, T., Folk Jr, G.E., Hutt, B.K., 1957. Measurement of blood volumes in 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 by fibrosis 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 biliary excretion of indocyanine green and its use in estimation of hepatic blood flow 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. Prospective assessment of hepatic function and mechanisms of dysfunction in the critically ill. Shock 32, 358–365. Krudys, K.M., Kahn, S.E., Vicini, P., 2006. Population approaches to estimate minimal model indexes of insulin sensitivity and glucose effectiveness using full and reduced sampling schedules. Am. J. Physiol. Endocrinol. Metab. 291, E716– E723. Kusuhara, H., Sugiyama, Y., 2010. Pharmacokinetic modeling of the hepatobiliary transport mediated by cooperation of uptake and efflux transporters. Drug Metab. Rev. 42, 539–550. Lund, M., Kang, L., Tygstrup, N., Wolkoff, A.W., Ott, P., 1999. Effects of LPS on transport 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 the splanchnic circulation with indocyanine green pharmacokinetics in liver transplant patients. Liver Transpl. 8, 476–481. Oliver, R.E., Jones, A.F., Rowland, M., 2001. A whole-body physiologically based pharmacokinetic model incorporating dispersion concepts: short and long time characteristics. J. Pharmacokinet. Pharmacodyn. 28, 27–55.
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Ott, P., 1998. Hepatic elimination of indocyanine green with special reference to distribution 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–dispersion model and transit density functions in the analysis of organ distribution kinetics. J. Pharm. Sci. 89, 1579–1586. Rowland, M., Peck, C., Tucker, G., 2011. Physiologically-based pharmacokinetics in drug development and regulatory science. Annu. Rev. Pharmacol. Toxicol. 51, 45–73. Sakka, S.G., van Hout, N., 2006. Relation between indocyanine green (ICG) plasma disappearance rate and ICG blood clearance in critically ill patients. Intensive Care 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 Eisai hyperbilirubinemic mutant rats. J. Pharmacol. Exp. Ther. 265, 1301–1312. Schalla, M., Weiss, M., 1999. Pharmacokinetic curve fitting using numerical inverse Laplace transformation. Eur. J. Pharm. Sci. 7, 305–309. Sergi, C., Gross, W., Mory, M., Schaefer, M., Gebhard, M.M., 2008. Biliary-type cytokeratin pattern in a canine isolated perfused liver transplantation model. J. Surg. Res. 146, 164–171. Seshadri, V., 1999. The Inverse Gaussian Distribution: Statistical Theory and Applications. Springer, New York. Sheppard, C.W., Uffer, M.B., Merker, P.C., Halikas, G., 1968. Circulation and recirculation 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 the hepatobiliary clearance of cholephilic xenobiotics. J. Pharmacol. Exp. Ther. 250, 421–427. Weiss, M., 2009. Cardiac output and systemic transit time dispersion as determinants 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 transit time dispersion of drugs in organs: application of a stochastic model to the rat hindlimb. J. Pharmacokinet. Biopharm. 24, 173–196. Weiss, M., Krejcie, T.C., Avram, M.J., 2006. Transit time dispersion in the pulmonary and 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 of thiopental distribution kinetics based on a multiple indicator approach. Drug Metab. Dispos. 35, 1525–1532. Weiss, M., Kuhlmann, O., Hung, D.Y., Roberts, M.S., 2000. Cytoplasmic binding and disposition 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 and interstitial distribution kinetics of rocuronium: a population analysis in patients. 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 recirculatory model. Eur. J. Nucl. Med. Mol. Imaging 29, 1648–1656.
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European Journal of Pharmaceutical Sciences journal homepage: www.elsevier.com/locate/ejps
A physiologically based model of hepatic ICG clearance: Interplay between sinusoidal uptake and biliary excretion Michael Weiss a,⇑, Tom C. Krejcie b, Michael J. Avram b a b
Section of Pharmacokinetics, Department of Pharmacology, Martin Luther University Halle-Wittenberg, Halle, Germany 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 2011 Received in revised form 28 June 2011 Accepted 20 August 2011 Available online 26 August 2011 Keywords: ICG Hepatic uptake Biliary excretion Pharmacokinetic model Isoflurane Dog
a b s t r a c t Although indocyanine green (ICG) has long been used for the assessment of liver function, the respective roles 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 ICG disposition 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 with 3.5% isoflurane were subjected to population analysis. The results suggest that ICG elimination in dogs is uptake limited since it depends on hepatocellular uptake capacity and on biliary excretion but not on hepatic blood flow. Isoflurane caused a 63% reduction in cardiac output and a 33% decrease in the ICG biliary excretion rate constant (resulting in a 26% reduction in elimination clearance) while leaving unchanged the sinusoidal uptake rate. The terminal slope of the concentration–time curve, K, correlated significantly with elimination clearance. The model could be useful for assessing the functions of sinusoidal and canalicular ICG transporters. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Indocyanine green (ICG) is an organic anion dye that is eliminated exclusively by the liver. It is widely used to assess hepatic function, 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 is known 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 transport is 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 review, see Kusuhara and Sugiyama, 2010). However, under in vivo conditions where only plasma ICG concentrations are measured, the roles of these processes are poorly understood. It appears that hepatocellular uptake and not hepatic blood flow may be rate limiting in dogs (Ketterer et al., 1960), but there is little quantitative information on the relative contribution of each process to ICG elimination. Thus, the goal of the present study was to determine whether modeling of ICG disposition curve could reveal the interplay between sinusoidal uptake and biliary excretion in determining hepatic ICG clearance (i.e., when the time profile of biliary ⇑ Corresponding author. Tel.: +49 345 5571657; fax: +49 345 5571835. E-mail address: [email protected] (M. Weiss). 0928-0987/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ejps.2011.08.018
excretion is not available). To this end, we applied a novel pharmacokinetic model to ICG plasma concentration–time data obtained using frequent arterial sampling in awake and isoflurane anesthetized dogs (Avram et al., 2000). Estimation of hepatocellular uptake clearance and biliary excretion rate constant of ICG was based on a circulatory model. Lumping the systemic organs into two subsystems, hepatosplanchnic and non-splanchnic circulation, the approach is similar to that used to describe [13N]ammonia kinetics (Weiss et al., 2002) and is an extension of the circulatory model of ICG disposition (Weiss et al., 2006, 2007). Thus, in contrast to previous approaches based on compartmental modeling (for a review, see Ott, 1998), we have adopted a minimal physiological model of ICG whole body pharmacokinetics that includes a space-distributed liver model (Weiss and Roberts, 1996). This model has been used to analyze data obtained in the isolated perfused rat liver (Weiss et al., 2000; Hung et al., 2002). The difficulty with a more complex model lies in the large number of model parameters relative to the available data. Prior information obtained on the system without liver (Weiss et al., 2006) was incorporated in parameter estimation using a population approach (D’Argenio et al., 2009) to facilitate parameter identifiability. The fact that isoflurane anesthesia decreased cardiac output to about 37% of that in the awake state (Avram et al., 2000) allowed an examination of the effect of liver blood flow. The advantages of physiologically-based pharmacokinetic (PBPK) modeling have been reviewed recently (Rowland et al.,
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2011). Although PBPK models are normally based on a compartmental structure (differential equations), in the present approach the subsystems of the body were modeled by transit time density (TTD) functions for at least two reasons. First, since ICG distributes within the vascular system, we are also aiming to describe the initial phase (the first minutes) of the disposition curve to estimate cardiac output as a main determinant of the mixing process (Weiss, 2009). This would be not possible using a conventional compartmental model for the lung. The initial peak of the arterial concentration time curve mainly represents the TTD through the lung. That the latter can be described by the inverse Gaussian density has been shown in tracer kinetics (Sheppard et al., 1968). The usefulness of the inverse Gaussian TTD in pharmacokinetics can be explained by the facts that it represents the first passage time distribution of a random walk process with drift (Seshadri, 1999) and that it is the solution to the convection–dispersion organ model (Roberts et al., 2000). Second, in a PBPK model based on differential equations it would not be possible to integrate a space-distributed liver model. Furthermore, while due to their structural complexity, PBPK models are typically used for simulation, this study is an attempt to develop a minimal PBPK model for ICG that can be identified using plasma concentration data. This method may lead to a better understanding of the processes determining ICG clearance in vivo, e.g., for characterizing the function of transporters involved in sinusoidal uptake and biliary excretion of ICG in normal and disease states. The model was also used to examine the role of the terminal slope of the ICG concentration– time curve (blood disappearance rate, K), that is routinely used as 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 disposition in 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 stated, at time t = 0 min, 5 mg of ICG in 1 ml of ICG diluent was flushed into the right atrium within 4 s using 10 ml of a 0.9% saline
Div
solution. Arterial blood samples were collected via an indwelling iliac artery catheter every 1.8 s for the first 28.8 s and every 3.6 s for the next 32.4 s using a roller pump and fraction collector. Subsequently, 18 3-ml arterial blood samples were drawn manually at 12 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 measured by high-performance liquid chromatography and plasma concentrations were converted to blood concentrations by multiplying them by one minus the hematocrit. For further details on study design, protocol, and measurements, please see Avram et al. (2000). 2.2. Model To develop a circulatory model of ICG disposition that can be identified solely on the basis of arterial blood concentration–time data, its structural complexity must be reduced to a minimum. The most rigorous structural simplification is given in terms of the pulmonary and systemic circulation, both of which are characterized by transit time density (TTD) functions of ICG molecules (Weiss et al., 2006). The pulmonary (p), or central, circulation is located between the points of injection and arterial sampling. Here the systemic circulation is split into two subsystems arranged in parallel, the hepatosplanchnic circulation and rest of the systemic circulation (rs) (i.e., extrasplanchnic vascular beds) (Fig. 1). The hepatosplanchnic circulation consists of two organs in series, the gut and the liver. When the TTD of the subsystems are non-exponential (no well mixed compartments), the equation for the arterial blood ICG concentration, C(t), after bolus venous injection (dose, Div) in a recirculatory system is only available in the Laplace domain. Denoting the Laplace transform of a function f(t) by ^f ðsÞ ¼ L½f ðtÞ, the model consists of the pulmonary and systemic subsystem with TTDs, ^f p ðsÞ and ^f s ðsÞ. Since the TTDs of two subsystems connected in series is the product, ^f ðsÞ ¼ ^f 1 ðsÞ^f 2 ðsÞ, and the input to the pulmonary circulation is given by ^ ^f s ðsÞ þ Div =Q , i.e., the output of the systemic circulation ^ pul;in ¼ CðsÞ C plus contribution of bolus dose (Q denotes cardiac output). From ^ pul;in ðsÞ^f p ðsÞ, we finally obtain: ^ ^ pul;out ¼ C CðsÞ ¼C
^f ðsÞ p ^ ¼ D iv CðsÞ Q 1 ^f s ðsÞ^f p ðsÞ
ð1Þ
fˆp ( s)
ke
Liver
Q
Gut
kout Vb,hep
C(t)
Pulmonary Circulation
kin
Rest Systemic Circulation
fˆrs ( s )
(1-q)Q
Fig. 1. Circulatory model of hepatic ICG elimination kinetics consisting of heterogeneous subsystems, the pulmonary and systemic circulation, in which the latter is split into two parallel subsystems, the hepatosplanchnic bed (gut and liver in series) and the rest of the systemic circulation, with blood flows qQ and (1 q)Q, respectively (Q is cardiac output). All subsystems are characterized by transit time density functions in the Laplace domain. The pulmonary circulation and the rest of the systemic circulation as well as the gut are characterized by inverse Gaussian transit time density functions denoted by ^f i ðsÞ. In the distributed model of hepatic ICG elimination, Vb,hep is the extracellular liver volume, kin is the sinusoidal uptake rate constant (which is determined by the uptake clearance and extracellular liver volume, kin = CLuptake/Vb,hep), kout is the rate constant of back-transport, and ke the canalicular excretion rate constant.
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Splitting the systemic circulation into subsystems as shown in Fig. 1, we have:
and that the measurement error had a standard deviation that was a linear function of the measured quantity:
^f ðsÞ ¼ q^f ðsÞ^f ðsÞ þ ð1 qÞ^f ðsÞ s gut rs hep
VARi ¼ ½r0 þ r1 Cðt i Þ2
ð2Þ
where q = Qhep/Q is the fractional liver blood flow and ^f hep ðsÞ, ^f gut ðsÞ and ^f rs ðsÞ denote the TTD of the liver, the gut, and the rest of the systemic (rs) circulation. We use the inverse Gaussian density (Sheppard et al., 1968) as empirical TTD for all subsystems except the liver:
fi ðtÞ ¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi MTT i 2p RD2i t
"
exp 3
ðt MTT i Þ2
#
2 RD2i MTT i t
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 transform of the inverse Gaussian TTD is given by (Seshadri, 1999)
8 " !#1=2 9 < 1 = V =Q 1 i i ^f ðsÞ ¼ exp sþ i 2 2 2 :RDi ; 2ðV i =Q i ÞRDi RDi =2
ð4Þ
Thus, Eq. (4) is used for ^f p ðsÞ, ^f gut ðsÞ, and ^f rs ðsÞ, with parameters (Q, Vp, RD2p ), (qQ, Vgut, RD2gut ) and ((1 q)Q, Vrs, RD2rs ), respectively. The transit time density function of ICG molecules across the liver, ^f ðsÞ, is described in terms of the extracellular transit time density hep of non-permeating reference (sucrose), ^f b;hep ðsÞ, as (Weiss et al., 2000):
kin ðke þ sÞ ^f ðsÞ ¼ ^f hep b;hep s þ kout þ ke þ s
ð7Þ
‘‘Goodness of fit’’ was assessed using the Akaike Information Criterion (AIC) and by plotting the predicted versus the measured response. Furthermore, MLEM provided the approximate coefficients of variation of individual parameter estimates. To reduce the number of adjustable parameters, the vascular volumes Vb,hep and Vgut were modeled as fractions of circulating blood volume, Vb,hep = 0.08Vb and Vgut = 0.16Vb, (Horvath et al., 1957) where Vb = Vp + Vrs + Vb,hep + Vgut. For the vascular dispersions across the liver and gut, values of RD2b;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 hepatic circuit (Weiss et al., 2006) were used as priors to set the ranges for of Q, Vp, Vrs, RD2p , and RD2rs . Note that the results of the MLEM fit depend on this prior probability distribution rather than the starting values. Parameter estimates are presented as population mean and inter-subject variability (percent standard error). The paired t-test was applied to the individual subject parameters (conditional means) in order to evaluate the effect of isoflurane compared with awake. If the p value was <0.05, the difference was considered to be significant. 2.4. Sensitivity analysis
ð5Þ
where kin = CLuptake/Vb,hep is the uptake rate constant in the liver, CLuptake is the sinusoidal uptake clearance, Vb,hep is the extracellular liver volume, ke is the canalicular excretion rate constant, and kout is the rate constant of back-transport (Fig. 1). The TTD ^f b;hep (s) is also described by an inverse Gaussian TTD [Eq. (4)], with parameters Qhep (i.e., qQ), Vb,hep, and RD2b;hep . Note that, for the sake of simplification, the dual blood supply to the liver (hepatic artery and portal vein) was neglected and all organs of the hepatosplanchnic circulation other than the liver are lumped into the subsystem ‘‘gut’’. Note also that the hepatic clearance, CLhep, is obtained from Eq. (5) as CLhep ¼ Q hep ½1 ^f hep ðsÞ for s ! 0 (where Qhep = qQ): ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi13 2 0v u u2CLuptake RD2b;hep ke þ Q hep kout þ Q hep ke 1 A5 CLhep ¼ Q hep 4 2 exp @t Q hep RD4b;hep ðke þ kout Þ RDb;hep
ð6Þ
A useful measure of the ability to estimate a parameter p from the data C(t) is the sensitivity function:
Sp ðtÞ ¼
" # ^ p @CðtÞ p 1 @ CðsÞ ¼ L CðtÞ @p CðtÞ @p
ð8Þ
which determines the relative change in C(t) caused by a small relative change in the model parameter p. Since Sp is non-dimensional, it allows a comparison of results obtained for different parameters. Thus, Sp(t) represents the relative importance of parameter p to model output. If the sensitivity functions of two parameters are proportional, this indicates that the parameters are correlated and hardly identifiable in practice. The sensitivity functions [Eq. (7) substituting Eq. (1)] were calculated using MAPLE 8 (Maplesoft, Waterloo, Ontario, Canada) after implementing a numerical method of inverse Laplace transformation (Schalla and Weiss, 1999). 2.5. Slope of the ICG disposition curve
2.3. Parameter estimation Data fitting (population analysis) was carried out with maximum likelihood (ML) estimation via the EM algorithm using the software ADAPT 5 (D’Argenio et al., 2009), where the program (MLEM) is implemented. To deal with the mismatch between model complexity and available data, prior information was incorporated (see below). The program provides estimates of the population mean and intersubject variability as well as of the individual subject parameters (conditional means). Since the equation for the ICG concentration–time curve resulting from the model is only available in the Laplace domain [Eq. (1)], a numerical inverse Laplace transformation has to be performed to obtain the concen^ tration–time curve in the time domain, CðtÞ ¼ L1 ½CðsÞ. We implemented Talbot’s algorithm into ADAPT 5 (Schalla and Weiss, 1999). It was assumed that the model parameters were log-normally distributed among subjects (to constrain parameters to be positive)
Given that the terminal slope of the disposition curve (K) (also called plasma disappearance rate) is measured routinely, how K changes with time and how it is affected by hepatic uptake clearance and biliary excretion is of interest. In accordance with the procedure in the clinical ICG elimination tests, the elimination rate constant K (terminal slope of the disposition curve) of each dog was estimated by fitting a monoexponential function to the data between 10 and 20 min after injection. 3. Results The population parameters estimated in the awake state and under isoflurane anesthesia are presented in Table 1. Fig. 2 (top and bottom right) shows the correlation of the individual predicted versus measured concentration values. The individual fits (based on conditional estimates) are characterized by an R2 of
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Table 1 Parameters for the model of ICG kinetics with typical values and interindividual variability as relative standard error (%) in brackets, estimated in dogs in the awake state and under isoflurane anesthesia (n = 4). Parameters
Awake
Isoflurane
4590 (12) 784 (12) 0.056 (39)
1680 (6)** 671 (17) 0.068 (14)
RD2rs
1130 (25) 3.04 (47)
1520 (28) 4.13 (47)
Liver CLuptake (ml/min) ke (min1) kout (min1) q CLhep (ml/min)a
599 (13) 0.823 (8) 0.762 (4) 0.327 (2) 269 (32)
554 (19) 0.551 (3)*** 0.650 (2) 0.413 (15) 199 (30)**
Circulation Q (ml/min) Vp (ml) RD2p Vrs (ml)
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 constant of back-transport; q, fractional liver blood flow; CLhep, hepatic clearance. ** p < 0.01. *** p < 0.001.
0.94 ± 0.04 and 0.97 ± 0.04 (mean ± S.D.) in the awake and isoflurane states, respectively. The fits are illustrated in Fig. 2 (top and bottom left) for the dog with the lowest R2 value in the
101.0 9
awake state. Generally, good fits were obtained, but, as in previous applications of the recirculation model (Weiss et al., 2006), deviations in the vicinity of the recirculation peak were observed in some cases. The sensitivity functions for CLuptake, ke, q, and RD2rs are depicted in Fig. 3. The information on the relative dispersion of the rest of the systemic circulation (RD2rs ) is concentrated in the first two minutes. The sensitivities of this and all other non-hepatic parameters are nearly identical to those of the minimal circulatory 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) were 0.105 ± 0.028 and 0.084 ± 0.026, in the awake state and under isoflurane anesthesia, respectively (p < 0.05). The measured K correlates with clearance CLhep (Fig. 4). Figs. 5 and 6 show how sinusoidal uptake clearance (CLuptake) and canalicular excretion (ke) determine ICG clearance. There was a 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) did not affect CLuptake. That the reduction in ke is a direct effect of isoflurane and not secondary to the change in hepatic blood flow is indicated in Fig. 6. The interplay between sinusoidal uptake and canalicular excretion in determining hepatic ICG clearance is simulated in Fig. 7 using Eq. (6) and the population mean parameters of the awake dogs.
Awake
8 7 6 5
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Fig. 2. Examples of individual fits (based on conditional estimates) of the circulatory model to ICG disposition data in an awake dog (top left) and in the same dog while anesthetized with isoflurane (bottom left), together with goodness-of-fit plots showing the individual predicted vs. observed arterial blood ICG concentrations in the awake (top right) and isoflurane anesthetized state (bottom right).
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300
R2= 0.98, P < 0.05 CL hep (ml/min)
Awake 250
R2= 0.98, P < 0.01
Isoflurane 200
150 400
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CL uptake (ml/min) Fig. 5. Correlation between individual estimates of CLhep and CLuptake in the awake state (s) and under isoflurane anesthesia (d). Note that the decrease in cardiac output (hepatic blood flow) under isoflurane anesthesia did not affect CLuptake.
Awake
Fig. 3. Normalized sensitivity of the ICG disposition curve C(t) with respect to relative dispersion in the rest of the systemic circulation (RD2rs ), fractional liver blood flow (q), canalicular excretion rate constant (ke) and sinusoidal uptake clearance (CLuptake).
k e (1/min)
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Q hep (ml/min) Fig. 6. Biliary excretion rate constants (ke) estimated in the awake state (s) and under isoflurane anesthesia (d) as a function of hepatic blood flow (Qhep).
0.06
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CL hep (ml/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–time curve) was estimated by a monoexponential fit of the data between 10 and 20 min after injection.
4. Discussion The present study was conducted in dogs, in which hepatic extraction of ICG is low and clearance is nearly independent of hepatic blood flow (Ketterer et al., 1960). Our results suggest that the hepatic clearance of ICG is determined by both hepatocellular uptake (i.e., sinusoidal membrane transport) and canalicular excretion (Figs. 5–7). According to available literature, both processes are transporter mediated (Kusuhara and Sugiyama, 2010; de Graaf et al., 2011). The values of CLuptake, 559 and 554 ml/min, estimated in the awake and anesthetized state, respectively, are consistent with that observed in the isolated perfused rat liver (Lund et al., 1999), since the uptake rate constant in the rat liver (3.2 min1)
is virtually identical to those obtained here as kin = CLuptake/Vb,hep (with Vb,hep = 170 ml, kin = 3.28 and 3.26 min1, while awake and anesthetized, respectively). In each group, the interindividual variability in ICG clearance could be attributed to the variability in CLuptake (Fig. 5). Hepatic uptake clearance of ICG was much lower than hepatic blood flow and independent of it. Simulation of our liver 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 transporter), uptake may become the rate-determining process in the hepatic elimination of ICG. Such knowledge of the respective roles of hepatic uptake and hepatocellular elimination in defining ICG clearance is important since disease states or interaction with other drugs can affect both processes differently. Assuming that the interpretation of ke is correct (see below), the reduction in biliary ICG excretion observed under isoflurane anesthesia (Fig. 6) would be a novel result. In the literature such information is available only in rats, in which isoflurane reduced bile salt secretion (Bridges et al., 1989) but did not influence the biliary secretion of the organic anion dibromosulphthalein (DBSP) (Watkins,1989). To avoid misunderstanding, it should be noted that the rate constant ke stands for biliary excretion of ICG across the canalicular
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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)].
membrane rather than the much slower recovery rate of ICG measured in collected bile, where ICG appears after a delay of about 20 min (Sergi et al., 2008). Since ICG is not metabolized, ke represents only biliary excretion. The ability to discriminate between hepatic uptake and biliary elimination may be intuitively unexpected but is suggested by both the finding that isoflurane only affected biliary excretion and the sensitivity analysis, i.e., the finding that the transient sensitivities regarding changes in CLuptake and ke were not parallel (Fig. 3). Note that such a discrimination appears possible only for a vascular marker like ICG because otherwise tissue distribution will obscure the effect of hepatic distribution. While a compartmental model for which instantaneous intravascular mixing was assumed failed to fit our data (for obvious reasons), such a model can be useful when biliary excretion data are available and blood sampling starts after the early distribution phase (Sathirakul et al., 1993; Kusuhara and Sugiyama, 2010). However, the present distributed liver model, like any model, is a simplification and does not explicitly include intracellular diffusion and binding of ICG, a fact that should be considered in a physiological interpretation of the parameter ke, which may be model dependent. While our interpretation of ke appears reasonable on the basis of the given data and prior knowledge, the estimate could be biased due to the effect of cytosolic distribution kinetics. Thus ke could partly account for quasi-irreversible cytosolic binding rather than biliary excretion. The finding that the disappearance rate constant K (terminal slope 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 the higher hepatic extraction of ICG. This, however, is not surprising in view of the fact that ICG does not exhibit one-compartment disposition kinetics, i.e., mono-exponential decline (Fig. 2, left). One limitation of this study is that, in contrast to the previous circulatory model (Weiss et al., 2006), the extended model with the liver as a separate subsystem (Fig. 1) was too complex for the available data, necessitating the use of prior information. This prior knowledge about the pharmacokinetic system and associated model parameters was incorporated in the form of prior parameter distributions using a population modeling approach. Note that the latter has proven successful when parameters are poorly estimated using individual fits (Krudys et al., 2006). Because the present
approach is based on prior information, it comprises elements of so-called forward modeling, i.e., it resembles methods used in physiologically based pharmacokinetic modeling. As a consequence of the low sensitivity of fractional liver blood flow (q) (Fig. 3), it remains an open question whether a change of this parameter in altered physiological states can be detected in dogs with our approach. While the present model may have low sensitivity for the fractional liver blood flow in the dog because their ICG elimination clearance is flow-independent, the situation is likely to be different in humans in whom the hepatic extraction of ICG is high and the elimination clearance is flow-dependent. However, rather than define a unique set of model parameters, the aim of this study was to understand the respective roles of sinusoidal and canalicular transport in determining ICG clearance. The main indication that the present model and the estimated liver parameters are relevant is provided by Figs. 5 and 6. If hepatic uptake is rate-limiting (Fig. 5), one should indeed expect that biliary excretion will be independent of hepatic blood flow (Fig. 6). Furthermore, 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 hepatic clearance (CLhep) are consistent with those estimated in the same dogs using thermodilution technique and a recirculatory compartmental model, respectively (Avram et al., 2000). Furthermore, the parameter estimates for the circulatory system, Q, Vp, Vrs and RD2rs , are not much different from those obtained with the minimal circulatory model in awake dogs (Weiss et al., 2006). It should be also noted that the occurrence of the secondary peak (Fig. 2), is not primarily related to the hepatosplanchnic circulation but a general property of recirculatory models; thus, the recirculation peak could be described by using different models of the systemic circulation (Henthorn et al., 1992; Oliver et al., 2001; Weiss et al., 2006, 2007). Furthermore, this secondary peak observed earlier 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; Weiss et 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) (scaled to liver volume) (see above). Thus, despite the limitations expressed above, the present results provide further insight into the mechanisms determining hepatic ICG pharmacokinetics in the dog. The minimal circulatory model of hepatic ICG kinetics in dogs represents a first step towards a physiologically-based approach that allows more information to be extracted from ICG disposition data than could be obtained from commonly used K or CL estimates. The model can be adapted for use in humans, in whom sinusoidal and canalicular ICG transporters may undergo different regulation in disease states (Kortgen et al., 2009). A similar model (without hepatosplanchnic bed) has been recently used to analyze ICG kinetics in patients (Weiss et al., 2011). It remains to be tested whether ICG concentration could be measured by non-invasive pulse dye densitometry (Niemann et al., 2002) in order to avoid frequent 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 physiologic markers. Anesthesiology 92, 1757–1768. Avram, M.J., Krejcie, T.C., Henthorn, T.K., Niemann, C.U., 2004. Beta-adrenergic blockade affects initial drug distribution due to decreased cardiac output and altered blood flow distribution. J. Pharmacol. Exp. Ther. 311, 617–624.
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