* McLaughlin Research Institute, Great Falls, Montana 59405; and
Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433-7400
Received December 14, 2001; accepted July 30, 2002
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ABSTRACT |
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Key Words: TCA; isolated perfused rat liver; kinetics; modeling; transport parameters; protein binding.
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INTRODUCTION |
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The IPRL system is a useful tool for investigating metabolism and kinetics of chemicals in the liver. A biologically based kinetic (BBK) model of the IPRL that includes metabolism, membrane transport, and protein binding of chemicals has been developed for water-soluble compounds (Frazier 1998). A schematic diagram of the BBK model for the IPRL system is shown in Figure 1
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MATERIALS AND METHODS |
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Animals.
Male Fischer 344 rats weighing between 220 and 290 g were used for liver isolations. Rats had free access to food and water purified by reversed osmosis. Animal use described in this study was conducted in accordance with the principles stated in the Guide for the Care and Use of Laboratory Animals (National Research Council, 1996) and the Animal Welfare Act of 1966, as amended.
Liver isolation and perfusion.
Liver surgery was performed as described previously (Toxopeus and Frazier, 1998). The liver perfusion cabinet was the same as described by Wyman et al. (1995)
. Sterile Krebs-Ringer buffer (200 ml) supplemented with 4% (w/v) low endotoxin BSA and 11.5 mM glucose was used to perfuse the liver during experiments. The flow rate of the perfusate was 40 ml/min and the perfusate temperature was maintained at 37°C. To sustain bile production, taurocholate was infused into the perfusion medium at a rate of 33.5 µmol/h. The medium was oxygenated by passing it through a gas exchange apparatus and equilibrated with 95% O2/5% CO2. Medium pH was maintained between 7.37 and 7.42. Temperature, pH, and the percentage oxygen saturation of the perfusion medium and hydrostatic pressure on the liver were constantly monitored. Body weight of donor rats, liver weight, and liver water content are summarized in Table 1
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Liver water content.
An aliquot of approximately 1 g liver was collected from the liver at the end of the experiment, weighed (wet weight, W), dried for 4 days at 120°C in a vacuum oven and weighed again (dry weight, D). The percentage water content was calculated as:
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All abbreviations used in Equations 110 are listed in Table 2
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![]() | (2) |
Bile flow.
Bile was collected in preweighed microcentrifuge tubes over intervals of 15 or 30 min. Bile flow was expressed as µl/(min x g) liver, assuming that the density of bile is 1.0 g/ml.
Kinetic studies.
In order for the liver to recover from surgery, kinetic studies were started 1 h after connecting the excised liver into the perfusion system. Time is measured relative to the time that the chemical is dosed into the reservoir (t = 0). Exposures were started by adding 5, 50, or 200 µmol of TCA dissolved in approximately 1 ml nanopure H2O to the reservoir that contained 200 ml perfusion medium. These dosages resulted in initial concentrations of 25, 250, or 1000 µM, respectively. To determine the time course of chemical concentration in the perfusion medium, samples (1 ml) were taken from the reservoir at 2, 5, 10, 20, 30, 60, 90, and 120 min after TCA addition. In washout experiments, not only were samples taken at the standard times, but additional samples were collected immediately after the perfusion medium was switched to TCA-free medium at t = 30 min and at 45, 75, and 105 min. Bile was collected over intervals of 30 min in the standard experiments. In the washout experiments bile was collected at 15-min intervals. All samples were kept on ice until analyzed. At the end of the 120-min experiment, the liver was perfused with 10 ml ice cold chemical-free perfusion medium to flush the sinusoids free of TCA. The liver was homogenized in 0.9% NaCl (1 g liver to 3 ml saline). TCA concentrations in the liver are reported as average liver concentration (CL-AVG (µmol/kg)) and as the theoretical concentration in intracellular water:
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Binding Studies in Vitro
The binding of TCA to protein (BSA) in perfusion medium and liver homogenates was investigated. The procedures used were similar to those reported in (Templin et al. 1995).
Perfusion medium.
Perfusion medium used in binding studies was sterile Krebs-Ringer buffer supplemented with 4% (w/v) low endotoxin BSA and 11.5 mM glucose, identical to that used for liver perfusion studies.
Liver homogenate.
Rats were anesthetized with diethyl ether and the portal vein was cannulated using an 18-gauge 2-inch catheter. The liver was flushed with 2 ml prewarmed heparin/saline solution (500 U heparin/ml in 0.9% NaCl). Following severance of the inferior vena cava, the liver was perfused with ice cold Krebs-Ringer medium supplemented with 11.5 mM glucose and saturated with 95% O2/5% CO2, pH 7.40, at a flow rate of 25 ml/min. The liver was excised, minced, and homogenized (1 g of minced liver to 3 ml ice-cold buffer) using a Potter-Elvehjem tissue grinding chamber (Thomas; No. A 62247) and motor driven teflon pestle (AHT Co.; Model S 756). The liver was kept on ice throughout all procedures. Homogenates were stored at 80°C and used in binding studies within two weeks after preparation.
Binding studies.
An aliquot (400 µl) of perfusion medium or liver homogenate containing radiolabeled TCA, ranging in concentration from 3 µM to 20 mM, was incubated for 60 min at 37°C on an incubator shaker. A sample (40 µl) of this mixture was transferred to a scintillation vial, mixed with 5.5 ml Pico Fluor-40 and the radioactivity determined by liquid scintillation counting (Packard Tri-Carb 2200CA). Radioactivity measurements were converted to TCA equivalents using the specific activity and the concentration obtained represented the total TCA concentration. The remaining mixture was centrifuged at 2000 x g for 5 min (perfusion medium) or 30 min (homogenate) at 4°C in Centrifree micropartitioning tubes (Amicon, Inc., MA) to obtain protein-free filtrate. A sample (40 µl) of the filtrate was transferred to a scintillation vial, mixed with 5.5 ml Pico Fluor-40 and assayed for radioactivity. The TCA equivalent concentration in the ultrafiltrate represents the free TCA concentration. The concentration of bound TCA was determined by the difference between the total and the free TCA concentrations.
Binding curve analysis.
Standard binding curves and Schatchard analysis were used to evaluate TCA binding parameters. The binding of TCA in the perfusion medium was analyzed assuming a combination of linear binding and a saturable binding site. The following equation was used to fit the experimental data for binding in the perfusion medium (Taira and Terada, 1985):
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BP (dimensionless) is the coefficient for linear binding of TCA in the perfusion medium, and BMAXP (µM) and KDP (µM) are the maximum binding capacity and the dissociation constant for saturable binding, respectively, in the perfusion medium. The parameters were determined by fitting the experimental binding data to Equation 4 using SigmaPlot version 5.00 (Jandel Scientific, San Rafael, CA). A similar analysis was conducted for TCA binding in the liver homogenate (liver binding parameters are designated by replacing P in Equation 4
with L).
Experimental determination of TCA binding in the IPRL experiments.
Aliquots of 600 µl of perfusion medium (collected at t = 5 and t = 120 min) or 400 µl of liver homogenate (prepared at the end of the experiment, t = 120 min) were processed as described above for TCA binding in perfusion medium. Since TCA used in the perfusion studies was not radioactive, TCA concentrations were determined in the whole homogenate and the filtrate as described in the analytical methods section below. In order to obtain enough filtrate from liver homogenate samples for analysis, four aliquots of homogenate were centrifuged under identical conditions and the filtrates obtained pooled. The concentration of TCA in the liver homogenate filtrate (CL-FILTRATE) was used to estimate the free TCA concentration in liver intracellular water space:
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The factor of 3.79 is included to correct for dilution of the liver while preparing the homogenate and 0.58 is the ratio of the intracellular water volume of the liver to the weight of the liver.
Analytical methods.
TCA in perfusion medium, bile, liver homogenate, and ultrafiltrates from IPRL experiments was derivatized to methyl esters by dimethyl sulfate under acidic conditions and quantified by GC using electron capture detection (Ketcha et al., 1996). To prevent conversion of TCA to DCA, 100 µl of sample was mixed with 100 µl of 20% lead acetate and stored at 20°C. For derivatization, the samples (200 µl) were mixed with 100 µl H2O and 100 µl 2,2-dichloropropionic acid (10 µg/ml), an internal standard. After cooling on ice, 500 µl concentrated sulfuric acid and 100 µl dimethyl sulfate were added. The reaction mixture was shaken for 30 min at 60°C, cooled to room temperature, and 1 ml hexane was added. Samples were extracted on an incubator shaker for 1 h at 3040°C and centrifuged (10 min, 2000 x g) to separate the aqueous phase from the hexane phase. The hexane layer was analyzed for TCA on a Hewlett Packard 5890 GC (Avondale, PA) equipped with a Hewlett Packard 7673A liquid autosampler and a 30 m x 0.53 mm Supelco Wax column (Bellefonte, PA). Derivatization products were detected by electron capture and concentrations corrected for extraction efficiency using the internal standard.
Model Implementation
The BBK model was coded using Advanced Computing Simulation Language (ACSL level 11, MGA Associates, Concord, MA), a numerical integration package. For details on the model structure see Frazier (1998). The physiological parameters used in the BBK model are shown in Table 3
. To utilize the BBK model to analyze the experimental data for TCA kinetics in the IPRL, the three important factors that control chemical kinetics (metabolism, protein binding, and membrane transport) were addressed as follows. Metabolism plays a negligible role in TCA kinetics (Larson and Bull, 1992
; Toxopeus and Frazier, 1998
). Therefore, the VMAX for TCA metabolism was set to zero in the generic BBK model. Parameters for protein binding were determined experimentally for TCA in both perfusion medium and liver homogenate as described above and subsequently incorporated into the BBK model. The BMAXP and KDP were not allowed to vary in any parameter fitting activities. To our knowledge no parameters for TCA membrane transport have been reported in the literature. Therefore, values for membrane transport of TCA, both at the sinusoidal and canalicular membranes, were derived from fitting TCA kinetics in the IPRL using the BBK model.
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CLI-FREE (µM) is the concentration of free TCA in liver intracellular space; PLI-P (l/[h x kg]) is the linear transport rate constant; and TLI-P (l/h) is the apparent transport rate coefficient from the liver intracellular space into the perfusion medium and is assumed to be independent of CLI-FREE. It is further assumed that the linear transport rate constant, i.e., the diffusion permeability, is equal in both directions:
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Even though the apparent transport rate coefficient, TP-LI in Equation 6, may be concentration dependent, it can be considered concentration independent for a particular experiment if the concentration driving the transport is relatively constant during the experiment. For the TCA studies described here, the free concentration in the perfusion medium is relatively constant over the majority of the experiment. Therefore, the experimental data obtained at the three TCA concentrations were individually fitted to obtain the apparent transport rate coefficients at the sinusoidal membrane, TP-LI and TLI-P, for each experiment. The values obtained for TP-LI at the various doses were plotted against the free TCA concentration in the perfusion medium. These data were fitted using Equation 6
for the membrane transport rates and the average values for PD, UTMAX:P-LI, and KT:P-LI were estimated.
If it is assumed at the mechanistic level that the linear (diffusional) component of sinusoidal transport, PD, is similar between livers, then any variability in the apparent transport rate constant is due to the saturable transport component. In particular, the variability of the apparent transport rate constant in each experiment is most likely due to variability in UTMAX:P-IL. Therefore, the second step in evaluating the sinusoidal transport parameters is to estimate the value of UTMAX:P-LI for each individual experiment. This is accomplished by refitting each experimental data set with PD and KT:P-LI fixed to the average values estimated in the first fitting exercise and varying UTMAX:P-LI. The set of individual values for UTMAX:P-LI obtained from each experiment represent an estimate of the population distribution for this parameter.
Fitting transport parameters for the canalicular membrane.
Since the concentration of TCA in bile was calculated to be similar to that of the free TCA in the liver intracellular water space (Toxopeus and Frazier, 1998), experimental data were fitted assuming that the transport of TCA through the canalicular membrane was linear. In this case the rate of transport was given by:
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Sensitivity analysis.
The relative sensitivity of the state variables to variations in the model parameters was investigated. The relative sensitivity is defined as
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RESULTS |
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The excretion of TCA in bile is linear in time and started almost immediately after TCA was added to the system (Fig. 6). The simulated curves closely match the experimental data. The scaled graphs reveal that the relative amount of TCA excreted in bile increased with TCA dose. This increase in biliary excretion rate parallels the increase in free TCA in liver intracellular space. The total amount of TCA excreted during the experiments was approximately 0.05, 0.10, and 0.20% at the 5 µmol, 50 µmol, and 200 µmol doses, respectively. The transport rate coefficient for biliary elimination of TCA corrected for liver weight, TLI-B/WL, from all experiments is estimated to be 0.017 ± 0.006 l/(h x kg); see Table 4
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TCA Kinetics in Washout Experiments
The IPRL model for TCA kinetics was validated by investigating the simulation of TCA kinetics in the washout experiments where livers were exposed to 1000 µM TCA for 30 min and then perfused with TCA-free medium for an additional 90 min. In Figure 8 the lower and upper limits were simulated for each state variable in the washout experiments. The lower limit simulation was obtained using the mean minus one SD for UTMAX:P-LI and TLI-B (Table 4
) in the simulation. The upper limit simulation used the mean plus one SD. For UTMAX:P-LI the values used were 4.0 and 7.4 µmol/(h x kg), and for TLI-B the values were 0.011 and 0.023 l/(h x kg). The values for the other model parameters were the same as those used for fitting the kinetic parameters. The experimental data for three separate washout experiments were also plotted in Figure 8
as the means ± one SD (n = 3). Both the total and free concentration of TCA in perfusion medium fell within the limits of the simulated curves (Figs. 8A and 8B
). The inserted graph shows in detail the TCA concentration in perfusion medium after switching to clean medium. The model predicts an increase in TCA concentration in perfusion medium as TCA leaks out of the liver. This prediction is confirmed by the experimental data. Figures 8C and 8D
show the simulated curves for CL-AVG and CLI-FREE respectively. The model predicted a rapid decrease in the TCA concentration in the liver after switching the IPRL system to TCA-free perfusion medium. The inserted graphs show that the experimental data for TCA concentration in the liver at the end of the experiment confirmed the decrease in concentration as predicted by the simulations. The experimental data for cumulative TCA excretion in bile fell within the upper and lower simulated limits (Fig. 8E
). Note, as a result of the rapid washout of TCA from the liver, biliary excretion of TCA immediately ceases after switching to TCA-free perfusion medium at t = 30 min.
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The sensitivity of CP-FREE, CLI-FREE, and cumulative TCA excretion in the bile to changes in KDP was about 1.0 at 25 µM TCA and about 0.5 at 1000 µM TCA. The lower sensitivity of these state variables to changes in KDP at 1000 µM TCA can be explained by looking at the equation for liver transport (Equation 6). KDP and CP-FREE are additive factors in the denominator and as a result the relative contribution of KDP to the denominator is less at higher CP-FREE.
In the standard uptake experiments, the only state variable affected by a change in the linear binding constant for TCA in liver, BL, is CL-AVG with a sensitivity of about 0.15. However, varying BL in the simulation of the washout experiment does affect the final concentration of TCA in the perfusion medium after the switch to clean perfusion medium. This is because BL has a significant influence on how much TCA is loaded into the liver during the 30 min uptake phase of the washout experiment.
Effect of sinusoidal transport parameters on state variables.
The total TCA concentration in perfusion medium was relatively insensitive to changes in the transport parameters PD, KT:P-LI, and PLI-B. The sensitivity of the average liver TCA concentration and the cumulative biliary excretion to a change in PD is about 0.7 for 25 µM TCA and 0.4 for 1000 µM. This indicates that increasing the linear transport rate constant across the sinusoidal membrane decreases the liver intracellular free TCA concentration by allowing more TCA to leak out down the concentration gradient across the sinusoidal membrane. The reduction in intracellular TCA concentration then reduces biliary excretion. This effect is more important at low concentrations where the concentration gradient is greater than at high concentrations.
Average liver TCA concentration and cumulative TCA excretion in bile have similar sensitivities to changes in UTMAX:P-LI, the sensitivity being about 0.73 for 25 µM TCA and 0.43 for 1000 µM. In addition, liver kinetics at 25 µM are more affected by a change in KT:P-LI than at 1000 µM, relative sensitivities being about 0.6 and 0.18 respectively. The reason for this differential sensitivity is the same as for the sensitivity to the binding constant KPD. KT:P-LI and CP-REE are additive factors in the denominator for saturable transport. This makes the relative contribution of KT:P-LI to mediated transport less at higher CP-FREE.
Effects of biliary transport parameters on state variables.
TCA concentration in perfusion medium and liver are relatively insensitive to changes in PIL-B. However, the cumulative excretion of TCA in the bile is highly sensitive to changes in PIL-B; S 1 for both 25 µM and 1000 µM TCA.
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DISCUSSION |
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Consistency of model predictions with experimental data does not prove that a particular model is "correct." However, in this case the BBK model for TCA kinetics in the IPRL is capable of accounting for several subtle features of TCA kinetics suggesting that the assumptions made in constructing the model may be valid. One feature is the slight nonlinearities that are observed with increasing dose. These effects, i.e., the increase in the proportion of free TCA in the perfusion medium at the highest dose and the increase in the proportion of cumulative biliary excretion at the highest dose, can be explained adequately by the nonlinear binding of TCA to albumin in the perfusion medium. CP-FREE increases from 4% of total TCA concentration in the perfusion medium at the 25 µM TCA dose to 15% at 1000 µM TCA, about a four-fold increase in the percentage free. Concurrently, the cumulative TCA excretion in bile increases by a similar factor, increasing from 0.05% of total dose at the 25 µM TCA dose to 0.2% of total dose at the 1000 µM TCA dose. It is clear from these studies that TCA binding to albumin is a major factor controlling TCA kinetics in the IPRL system. This conclusion is also supported by the sensitivity analysis where the average TCA liver concentration and cumulative biliary excretion are highly sensitive to changes in protein binding parameters.
Another interesting issue is the elevated concentration of free TCA in the liver intracellular space relative to the free concentration of TCA in the perfusion medium. This effect has been observed in vivo in rats (Yu et al., 2000). The hypothesis proposed to explain this observation is that there is an asymmetry in the transport of TCA across the plasma membrane of the hepatocytes. In the BBK model, this hypothesis is described by assuming that diffusion of TCA occurs in both directions with the same linear rate constant, i.e., diffusional permeability (PD), and that there is also a saturable transport mechanism that can transport TCA into the cell but not in the reverse direction (see Equations 6 and 7
). As a consequence of this hypothesis, the transport rate coefficient in the forward direction into the cell, TP-LI, is greater than the transport rate coefficient in the reverse direction, TIL-P, at equal concentrations of free TCA. Thus, for a quasi-steady state to be established between the perfusion medium and the hepatic intracellular water space, which occurs within the first 30 min of exposure to TCA, the forward and reverse transport rates must be approximately equal. These rates can only be equal if the intracellular free concentration of TCA is significantly greater than the free TCA concentration in the perfusion medium. This conclusion is consistent with the experimental data.
The estimation of the maximum transport rate constant for mediated uptake of TCA across the sinusoidal membrane, UTMAX:P-LI, from the experimental data indicated a significant variation of this parameter between livers. It was suggested that this variability may be related to the variability in the expression of a mediated transport system in the sinusoidal membrane between livers. Although there are several assumptions that are made to arrive at this conclusion (see section on fitting transport parameters for sinusoidal membrane), the concept that the internal dose to the liver may be controlled by a genetic factor regulating membrane transport is intriguing. The sensitivity analysis of the BBK model indicates that the free intracellular concentration of TCA is sensitive to the value of UTMAX:P-LI. Thus, variations in this parameter between individuals would significantly impact on the integrated dose in the hepatic intracellular water space.
In the BBK model, it is assumed that biliary excretion of TCA is linear. If this is correct, then the transport rate coefficient for TCA transport into bile, PLI-B, should be independent of the free intracellular concentration of TCA. There is a tendency for PLI-B to increase with increasing TCA concentrations as shown in Table 4, however this increase is not statistically significant. There are no signs of saturation of the rate of TCA transport into bile in these studies. In addition, the concentration of TCA in bile is similar to the concentration of free TCA in the liver water intracellular space, CLI-FREE (Toxopeus and Frazier, 1998
). Together, these data suggest that TCA may move across the canalicular membrane along with intracellular water as bile is formed and is not excreted into bile via mediated transport processes.
The TCA washout experiment was conducted to validate the BBK model for TCA kinetics in the IPRL. The TCA concentration selected for the validation study, 1000 µM, was chosen to maximize the accumulation of TCA in the liver during the 30-min loading phase to ensure that the leakage of TCA into the perfusion medium could be detected. Although the concentration of TCA used in the validation study corresponded to the highest TCA concentration used in the uptake studies to develop the BBK model, the experimental data were collected in independent experiments using different liver perfusions. The washout data fell within the range of values predicted by the model for all the state variables and are consistent with the model assumptions. The washout of TCA from the liver, as indicated by the increase in TCA concentration in the perfusion medium after switching to TCA free medium, is mainly controlled by the linear transport rate constant at the sinusoidal membrane, PD. The observed kinetic fit substantiates the estimate for PD as obtained from the standard kinetic studies. The cumulative excretion of TCA, which is dependent on several model parameters, behaved as predicted and falls within the upper and lower limit simulated (Figure 8E). Although the predictions of the BBK model for TCA are consistent with the washout experiments, the observations are based on relatively high concentrations of TCA. The possibility always exists that high affinitylow capacity nonlinear processes (either protein binding, membrane transport or even metabolism) could be present and would have an impact on chemical kinetics at concentrations below the lowest concentration studied experimentally.
The sensitivity analysis showed that kinetic behavior of TCA in the IPRL system is most sensitive to changes in the albumin binding parameters, BMAXP and KDP, mediated through their effect on CP-FREE. Preliminary binding studies using rat serum albumin indicated that TCA binds to a lower extent to rat serum albumin as compared to BSA (results not shown). Therefore, similar serum concentrations of TCA in the rat in vivo as compared to perfusion medium in the IPRL system will imply greater concentrations of TCA in the liver intracellular water space in vivo than in the liver in the IPRL system. This observation will have implications for interspecies extrapolation, particularly to human beings. The sensitivity of CP-FREE, CLI-FREE, and cumulative TCA excretion in bile to changes in parameters for protein binding in perfusion medium emphasizes the importance of having accurate values for binding parameters for the species of interest.
Parameters for transport of TCA over the sinusoidal membrane and the canalicular membrane have not been published before to our knowledge. The values reported in this paper for TCA transport will be applied to the liver compartment in future fitting of the in vivo rat kinetic data of TCA as reported by Yu et al. (2000).
The generic BBK model for the IPRL used in these studies of TCA kinetics requires further validation using a range of water-soluble chemicals. One feature not investigated in this study is the role of metabolism in chemical kinetics. Additional studies with chemicals that undergo hepatic metabolism will expand the usefulness of this BBK model. Future kinetic studies using the IPRL system and analyzing data using the BBK model will add to our understanding of the role of the liver in systemic kinetics of chemicals.
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ACKNOWLEDGMENTS |
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NOTES |
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