* Department of Environmental Health Science, and
Department of Pharmaceutical and Biomedical Sciences, University of Georgia, Athens, Georgia 30602
Received April 25, 2003; accepted July 30, 2003
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ABSTRACT |
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Key Words: PBPK; TCE; cross-validation; lumping; liver.
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INTRODUCTION |
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TCE, in sufficiently high doses, has been shown to adversely affect a number of different organs (Barton and Clewell, 2000). High inhaled concentrations of TCE can cause arrhythmias by sensitizing the myocardium to catecholamines (White and Carlson, 1979
). The central nervous system (CNS) is a common target of the parent compound, although some metabolites (e.g., trichloroethanol [TCOH]) also exert CNS effects (Boyes et al., 2000
; Bruckner and Warren, 2001
). Adverse effects on target organs other than the CNS and heart are believed to be due primarily to metabolites of TCE. TCE-induced lung injury and cancer in mice are thought to result from high CYP2E1-mediated oxidation (Millen et al., 2003
) and impaired metabolism of chloral in Clara cells (Green, 2000
). Autoimmune or inflammatory responses of splenic cells have been associated with the presence of dichloroacetylated proteins in TCE-treated mice (Griffin et al., 2000
). The liver, the major site of biotransformation of TCE, is subject to tumorigenesis in B6C3F1 mice (Bull, 2000
). It is generally believed that TCEs glutathione conjugates are responsible for the majority of toxicity and carcinogenicity in the kidneys (Lash et al., 2000
), although Cummings et al.(2001)
have demonstrated that CYP2E1 also plays an important role in TCE bioactivation in rat kidney. From the foregoing, it is clear that knowledge of the systemic/tissue dosimetry of TCE can be very important in assessing this VOCs cancer and noncancer risks.
The metabolism and toxicokinetics of TCE have been extensively studied and modeled in mice and rats (Davidson and Beliles, 1991). TCE is readily absorbed into the blood from the lungs and gastrointestinal (GI) tract. This lipophilic chemical would be expected to be distributed to tissues largely according to their blood flow rate and fat content. As empirical data on the systemic disposition of TCE are quite limited for rodents and almost nonexistent for humans, physiologically based pharmacokinetic (PBPK) models have been developed to forecast the time-course of the parent compound and metabolites in the body (Clewell et al., 2000
; Fisher, 2000
). The most recent rodent PBPK models developed by Fisher and colleagues (Abbas and Fisher, 1997
; Greenberg et al., 1999
) contained six-compartment descriptions of parent compound distribution in B6C3F1 mice. The compartments included were lung, slowly perfused tissues, rapidly perfused tissues, fat, kidney, and liver. Levels of TCE and its major oxidative metabolites were monitored in blood, liver, kidney, lung, and fat following oral (Abbas and Fisher, 1997
) and inhalation (Greenberg et al., 1999
) exposure of mice. Comparisons of these experimental and model-predicted time-courses of the parent compound were limited to blood and fat. The PBPK model developed by Clewell et al.(2000)
also consisted of a six-compartment description of TCE distribution in the mouse, rat, and human. The six compartments included were the same as in the models developed by Fisher and colleagues with the exceptions that the lung was specified as tracheo-bronchial tissue, GI tissue was added, and kidney was not included. Model-predicted time-courses of TCE were compared to published experimental time-courses in rats, mice, and humans for blood only. Simmons et al.(2002)
recently developed a five-compartment PBPK model for TCE in vapor-exposed male Long-Evans rats. The compartments included were brain, fat, liver, and rapidly and slowly perfused tissues. Simmons et al. contrasted empirical and model-simulated blood, liver, brain, and fat TCE profiles, but had quite limited laboratory data for evaluation of their models predictions.
Dose-response analyses of the carcinogenic effects of TCE in laboratory animals have utilized alternative Fisher (2000) and Clewell et al.(2000)
PBPK model predictions of blood and liver TCA and DCA area under the curves (AUCs; Rhomberg, 2000
). Noncancer dose-response analyses have employed Clewell et al.(2000)
s PBPK model predictions of TCA blood AUC, total production of the thioacetylating intermediate from DCVC divided by the volume of the kidney and blood TCOH concentrations (Barton and Clewell, 2000
). Clewell et al. (2000)
acknowledge the lack of validation of their PBPK model predictions of DCVC concentrations in the kidney. In 2001, the EPA published a draft risk assessment for TCE that incorporated quantitative dose-response analyses based on PBPK model predicted dose metrics (U.S. EPA, 2001
). Overall, validation of the existing PBPK models for TCE and its metabolites have relied more heavily on blood concentration data than tissue dosimetry data. Validation of tissue concentration time course predictions are needed to increase our confidence in the use of target tissue dose metric predictions in risk assessment.
Model calibration is the process of fitting model parameters to experimental data, while model validation is the process of assessing model predictions compared to independent experimental data not used for model development. A trade-off arises between using all available data for parameter estimation, as this should result in the most accurate parameter estimates, and setting some data aside for use in model validation. To better negotiate this trade-off, a simple technique, leave-one-out cross-validation (Hawkins et al., 2003; Stone, 1974
) has been used in other applications. In its earliest applications, cross-validation entailed splitting all available data into two parts, using part of the data for calibration and part of the data for validation (Mosier, 1951
). This is analogous to the common practice in PBPK modeling to using part of the data for model development and part of the data for model validation. Cross-validation techniques became more sophisticated with leave-one-out cross-validation where repeated subsampling was employed (Lachenbruch and Mickey, 1968
). Leave-one-out cross-validation entails generating multiple subsamples of the original data for model calibration by leaving aside one test case in each subsample for validation purposes. Recently leave-one-out cross validation has been applied in Quantitative Structure Activity Relationship (QSAR) applications (Hawkins et al., 2003
). An objective of this work is to apply this technique in the PBPK context. Cross-validation methodology will enable us to better utilize the available data by allowing each data set to serve both for calibration and validation, resulting in a "weighted average" calibration and validation over the data used.
Simulations of the systemic disposition of TCE and its primary metabolites have been provided by lumped-compartment PBPK models based on limited tissue data. Dosimetry forecasts for a number of potential target organs have not been possible. Actual uptake and elimination characteristics of the major metabolizing (i.e., liver) and storage (fat) tissues may not be recognized without detailed time-courses and PBPK analysis for these organs. The main objective of this work is to expand previously developed PBPK models for TCE in the adult, male Sprague-Dawley (S-D) rat and B6C3F1 mouse and to validate these models with accurate, comprehensive blood and tissue TCE dosimetry sets for different routes of exposure. We used cross-validation, a novel application to PBPK modeling, to test the model predictions of liver TCE concentrations in the rat and mouse. Simulations of the expanded model were compared to those of a traditional model.
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MATERIALS AND METHODS |
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Chemicals.
TCE, 99 % pure, was purchased from Aldrich Chemical Co., Inc. (Milwaukee, WI). Chemical purity was verified by gas chromatographic (GC) analysis. Isooctane (99.98% pure) was obtained from Burdick-Jackson (Muskegon, MI). Alkamuls®, a polyethoxylated vegetable oil, was provided by Rhone-Poulenc (Cranbury, NJ). All other chemicals were purchased from Sigma-Aldrich Chemical Co. (St. Louis, MO).
Intraarterial (ia) experiment.
An indwelling arterial cannula was surgically implanted into rats 24 h prior to ia injection of TCE. A "cocktail" of ketamine HCl (100 mg/ml): acepromazine maleate (20 mg/ml):xylazine HCI (10 mg/ml) in a proportion of 3:2:1 (v/v/v), was injected in a volume 0.8 ml/kg body weight (bw) for surgical anesthesia. A 9-inch-long piece of PE-50 tubing was used to cannulate the left carotid artery. The cannula was tunneled sc, so that it exited at the nape of the neck. It was filled with heparinized saline (1000 U/ml) to maintain its patency. The exteriorized cannula was coiled and taped at the back of each rats neck to prevent manipulation, but allow complete freedom of movement. TCE was incorporated into a 5% Alkamuls® aqueous emulsion, and injected over a 30-s period via the carotid artery cannula. Each rat received its dose of 8 mg/kg of TCE in a volume of 0.3 ml/animal. Groups of six rats were dosed for each time-point. Serial sacrifices were conducted at intervals of 5 to 30 min for up to 3 h postinjection. Each animal was killed by cervical dislocation and blood taken by closed-chest cardiac puncture, in order to minimize TCE loss from specimens. The rats were then decapitated, rapidly exsanguinated, and 0.3- to 1.0-g portions of brain, liver, kidney, lung, heart, GI tract, skeletal muscle, spleen, and perirenal adipose tissue, taken within 3 min.
Oral dosing experiment.
Five percent Alkamuls® was used to incorporate TCE into an aqueous emulsion for po administration. A dose of 8 mg TCE/kg bw was given as a single bolus by gavage, using a curved, ball-tipped intubation needle. The total volume given was 0.7 to 1.0 ml per rat. Serial sacrifices of groups of six rats were performed at intervals of 5 to 20 min for as long as 180 min postdosing. Blood and tissue samples were quickly removed as described above.
Inhalation experiment.
Inhalation exposures of freely moving rats to 50 and 500 ppm TCE were conducted in a 1.0-m3 Rochester-type dynamic flow chamber. Groups of six rats were placed into wire-mesh cages and positioned in the chamber. Each animal was housed individually, so it could not limit its exposure by burying its nose in the fur of other rats. TCE vapor was generated in a flask that was heated at 90°C. The vapor was channeled to the chamber through a stainless steel tube, which was wrapped with a heating coil to prevent condensation. The vapor generating system was enclosed within a safety box. The box and chamber were maintained under a negative pressure of 20 to 50 mm Hg. Exhausts from the chamber and generation box were vented through HEPA and activated charcoal filters, so that the TCE was removed before release of effluent air to the buildings exterior. The chambers were operated at flow rates of 0.2 to 0.4 m3/min (one-quarter to one-half change of the chamber volume per min). Thereby, it was possible to rapidly establish a uniform TCE concentration throughout the chamber without producing drafts. The concentrations of TCE within the chamber were monitored continuously with a MIRAN Model 1B2 infrared gas analyzer (Foxboro Analytical, Foxboro, MA). The TCE concentration was maintained at 50 ± 2 or 500 ± 14 ppm (mean ± SD, n = 50).
Groups of rats were exposed to 50 and 500 ppm TCE for 2 h. Serial sacrifices of six rats per time-point were conducted at predetermined intervals, ranging from 5 to 20 min during the 2-h exposure period and for up to 5 h postexposure. Blood and tissue samples were taken as before.
Sample preparation and analysis.
At sacrifice, 1 to 2 ml of blood was withdrawn into a gas-tight syringe by cardiac puncture and immediately transferred to chilled, tightly capped glass vials containing 4 ml of isooctane. When TCE concentrations were high, dilutions of 1:10 or 1:100 were made. Tissue samples of up to 1.5 g were placed into 20-ml vials containing 5 ml of ice-cold isooctane: saline (4:1, v/v). The tissues were rapidly homogenized in the vials with a Tekmar Tissumizer® (Cincinnati, OH). The homogenates were vortexed for 20 s and then centrifuged in the cold at 2800 rpm for 5 min. A 5- to 20-µl aliquot of the overlying isooctane layer was transferred to a 10-ml headspace vial, which was capped with a Teflon®-coated cap and metal washer, and tightly crimped. This tissue extraction procedure has been described in detail by Chen et al.(1993).
Crimped sample vials containing an aliquot of isooctane were placed into a Perkin-Elmer HS-101 headspace analyzer maintained at 110°C. After an equilibration time of 30 min, a predetermined volume of vapor from each vial was automatically injected into a Perkin-Elmer Model 8500 GC fitted with a stainless steel column (6' x 1/8'') packed with 100/120 mesh Gas Chrom Q coated with 3% OV-17. The column was maintained at 65°C. The electron capture detector was operated at 360°, while the injection port was kept at 150°C. The carrier gas was 5% methane in argon, maintained at a flow rate of 60 ml/min. TCE eluted with a retention time of 1.2 to 1.4 min. TCE concentrations in samples were calculated from the slope of a standard plot of peak area versus TCE concentration. Concentrations were corrected for the percentage recovery from each tissue, as determined by Chen et al. (1993). Precise aliquots of TCE in isooctane, equivalent 1 to 15 ng, were transferred to headspace vials and analyzed as described above. Peak areas were plotted against TCE concentration to obtain standard plots each day.
PBPK model structure.
A PBPK model was developed that was similar to the six-compartment model structure developed for TCE in mice (Abbas and Fisher, 1997). A schematic of the model structure is shown in Figure 1
. Additional compartments were added for the spleen, heart, GI tract, and brain. Blood flows to the liver were explicitly modeled by separately modeling direct arterial blood flow to the liver and portal blood flow directly from the GI tract and spleen. All tissues were described by flow-limited conditions with the exception of fat. Diffusion-limited conditions were necessary to reproduce the slow release of TCE from the fat following ia (see Fig. 2B
) and po (see Fig. 3B
) exposures. Diffusion limitation was incorporated with standard diffusion equations (e.g., Medinsky and Valentine, 2001
).
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where Ql is the sum of the hepatic arterial blood flow rate and the venous blood flow rates from the spleen and GI, Vsl is the volume of the shallow liver compartment (mg), D is the diffusional clearance from the liver to the deep liver compartment (h-1) and Pdl:b (unitless) is the deep liver:blood partition coefficient. All other variables are consistent with normal PBPK model nomenclature. The rate of change of the concentration of TCE in the deep liver tissue (Vdl) can be described mathematically as
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For comparison to liver concentration time-courses, the concentration of TCE in total liver tissue was calculated as
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The PBPK model was developed using Advanced Continuous Simulation Language (ACSL) Version 11.8.4 (Aegis Technologies, Huntsville, AL).
Mouse simulations.
Liver concentrations in B63CF1 mice following PO gavage with 300, 600, 1200, or 2000 mg/kg were measured during the same experiments initially described in the Abbas and Fisher (1997) publication but first published by Bois (2000)
. These liver concentrations were simulated with the Abbas and Fisher (1997)
mouse TCE PBPK model. Initially, the model was used in its original form with no alterations. Subsequently, a deep liver compartment was added to the mouse model in the same manner as in the rat model.
Model parameterization.
PBPK model physiological and metabolic parameters are shown in Table 1. Tissue volumes for male S-D rats were taken from Schoeffner et al.(1999)
. S-D specific blood flows were taken from Delp et al.(1991)
with the exception of blood flow to the liver via the portal vein, which was taken from Brown et al.(1997)
. We used metabolic parameters (VmaxC = 11.0 mg/h/kg0.7 and Km = 0.25 mg/l) determined previously by gas uptake experiments in F344 rats (Andersen et al., 1987
). Alternate metabolism parameters (VmaxC = 7.34 mg/h/kg0.74 or 8.68 mg/h/kg0.74) have been determined by gas uptake experiments in Long-Evans rats (Simmons et al., 2002
). Preliminary model simulations of blood and tissue TCE concentrations following inhalation exposures to TCE indicated that a VmaxC value of 11.0 resulted in better predictions of blood and tissue (with the exception of the liver) concentrations of TCE when compared to 10, 9, 8, or 7.34 mg/h/kg0.7 (results not shown). Liver concentrations were considered an exception due to their obvious underprediction, which required model structure alterations and indicated more complex behavior. VmaxC and Km estimates, originally estimated from gas uptake using a flow-limited model, would not be expected to change if they were refit using a two-compartment liver description since the rate and amount of TCE metabolized in the liver was insensitive to the addition of the deep liver compartment (see Tables 6
and 7
later in this paper).
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Next, the k1 term was optimized to venous blood concentrations following po exposure to 8 mg/kg TCE. The starting value for k1 (5) was found by visually fitting the model to the data prior to running the optimization.
Liver deep compartment cross-validation and parameter estimation.
Leave-one-out cross-validation entails taking n subsamples of the original sample of n independent observations by omitting a single observation at a time. Each subsample consists of n - 1 observations formed by deleting a different observation from the sample. In this case, our experimental unit was considered to be each experiment, and for the cross-validation procedure we left out one data set at a time and used the remaining data sets for model calibration.
The proportion of the total liver volume that is deep liver (VDL) was set to 2% as set previously for the rat (Sarangapani et al., 2003). VDL was also set to 2% in the mouse (Brix et al., 2002
). Liver parameter estimation was performed following estimation of the diffusion-limited fat parameters and the first-order oral absorption rate, which were set at estimated values. The effect of the deep liver compartment on predictions in blood and other tissues was examined and found to be negligible, thus the fat and blood predictions were not altered by the addition of the deep-liver compartment. Three data sets were available, for estimating the rate of transfer to and from deep liver (D) and the deep liver:blood partition coefficient of TCE (Pdl:b) in the rat, namely po (8 mg/kg), ia (8 mg/kg), and inhalation (500 ppm). The 50-ppm liver concentrations were underpredicted by a factor of 10 and were not used for model parameterization to prevent spurious parameter estimates. Since the deep liver represents the lipid portion of the liver, the upper bound of Pdl:b was set to the species specific fat:blood partition coefficient. One data set was removed at a time (test case), leaving the remaining two data sets to be used to simultaneously estimate values for D and Pdl:b. This resulted in the three estimates of deep liver parameters shown in Table 3
. In turn, each pair of deep liver parameters was used to simulate TCE liver concentrations for visual comparison to the test case data set. The liver AUC for the test case was simulated and compared to the calculated value from the test case data set for a quantitative summary metric for cross-validation. This allowed for three separate validations of the rat liver predictions.
For cross-validation of the deep liver model in the mouse, a similar methodology was followed. Liver concentrations following four po doses (300, 600, 1200, and 2000 mg/kg) were available. One dose at a time was left out (test case), while the remaining three doses were used for model optimizations.
The leave-one-out subsample deep liver parameter estimates were also used to calculate jackknife parameter estimates and SEs. The jackknife is a nonparametric technique for estimating the SE of a statistic (Faller et al., 2001; Miller, 1974
; Quenouille, 1949
), which is similar to cross-validation because it is also based on leave-one-out subsamples. The jackknife parameter estimate was simply the average of the individual leave-one-out subsample estimates. The calculation of the jackknife SE is explained in the Appendix. For comparison sake, parameter estimates and SEs of D and Pdl:b, were estimated simultaneously from all data sets by maximum likelihood as implemented in ACSL Math.
Model discrimination.
Model discrimination between the final rat and mouse models and alternative nested models was performed by the log-likelihood ratio test (Andersen et al., 2001; Collins et al., 1999
; Keys et al., 1999
). Blood and fat predictions were compared between the rat final and flow-limited models. Liver predictions were compared between the rat and mouse final models and the well-stirred liver model. The log likelihood function was of the mathematical form described by Collins et al.(1999)
. For flow-limited simulations the PA term was set to 2000 l/h in the diffusion-limited model. At this value, the diffusional transfer to the fat tissue compartment from the fat blood compartment was so fast it was virtually instantaneous and no difference could be seen numerically from a "flow-limited" model (simulations not shown).
Kinetic analysis.
Liver concentration time-courses were analyzed by noncompartmental methods to obtain estimates of area under the curve up to the last measurement timepoint using the WinNonlin program (Pharsight Corp., Cary, NC). The log-linear trapezoidal method was used for po and inhalation data, while the linear trapezoidal method was used for ia data.
Testing effect of expanded compartments.
To test the effect of adding additional compartments on predictions in previous TCE models, the expanded rat PBPK model was reduced to a four-compartment model with gas exchange (liver, fat, rapidly and slowly perfused tissue) by removing the additional compartments. In the reduced model, the fat compartment was still modeled as diffusion-limited and the liver with a two-compartment (deep and shallow) description. Model simulations of liver and venous blood concentrations following 0.1, 1, 10, 100, or 1000 mg/kg po doses were made with the four-compartment and expanded 10-compartment models. Twenty-four-h AUCs for liver, venous blood, and fat concentrations were calculated and compared for both models.
Sensitivity analyses.
To test the effect of adding the deep liver compartment on predictions of TCE metabolism, the mouse PBPK model was run at a range of oral (0.11000 mg/kg) and 4-h inhalation (0.11000 ppm) doses. The model was run with and without (D was set to 0) a deep liver compartment, and the total amount of TCE metabolized in a 24-h period was recorded for each simulation.
Since TCE risk assessment has focused on dose metrics of TCE metabolites, a formal sensitivity analysis was performed to test the effect of new TCE PBPK model parameters on the rate of TCE metabolism (RAM). Sensitivity analysis was performed using ACSL Math Version 11.8.4 (Aegis Technology, Huntsville, AL). The method of central differences was selected for calculation with delta set to 0.01 or 1%. Sensitivity coefficients (SCs) were log-normalized and then multiplied by their respective parameter value. The resulting SC can be interpreted as the % change in RAM per % change in parameter value (i.e., a SC of 1.0 means that there is a 1% change in RAM for a 1% change in the parameter value). SCs were calculated for the rat and mouse TCE PBPK model simulations at 10, 100, or 500 mg/kg po dose and 2-h inhalation exposures to 10, 100, or 500 ppm and reported at 0.1, 1, 2, and 8 h postinitial exposure. For the rat PBPK model, sensitivity to both the additional deep liver and diffusion-limited fat parameters were calculated. For the mouse PBPK model, sensitivity to the deep liver parameters only was calculated. For both rat and mouse models. sensitivity to VmaxC and Km were calculated as positive controls or parameters to which sensitivity was expected.
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RESULTS |
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Mouse liver concentration predictions from models with and without the deep liver compartment are shown following po gavage to 300, 600, 1200, and 2000 mg/kg TCE (Fig. 5). The results were consistent with the rat model, namely that the model with the deep liver compartment better predicted the slower clearance of TCE from the liver than the model without the deep liver compartment. The mouse deep liver model gave statistically improved predictions of mouse liver concentrations compared to the homogeneous liver compartment model at 300 (df = 2, p < 0.01), 600 (df = 2, p < 0.005), 1200 (df = 2, p < 0.005), and 2000 (df = 2, p < 0.01) mg/kg.
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IA Simulations
Figure 2 shows blood and tissue TCE concentrations versus measured values for rats given 8 mg/kg ia. ia simulations of other tissues besides fat and liver closely matched measured values for most time-points. Peak concentrations, however, were generally predicted to be higher than measured values. This may be due to the underprediction of the uptake of TCE in the fat at early time-points. TCE is taken up into the fat more rapidly than the model predicts and is sequestered from the general circulation. Elimination phase concentrations were well predicted for blood, GI tract, and brain and slightly overpredicted for kidney, heart, lung, and spleen. The exception was muscle, for which concentrations were underpredicted at later time-points by the model. Muscle concentration time-courses were compared to model predictions of slowly perfused tissue concentrations. Predictions of GI tract, kidney, heart, lung, and spleen concentrations provided support for our observation that partition coefficients calculated from inhalation terminal phase concentration ratios were able to reasonably extrapolate to another route of exposure (ia) and to a lower exposure level (8 mg/kg vs. 500 ppm). As shown in Table 2
, partition coefficients for liver, muscle, fat, and brain calculated from dividing tissue concentration by blood concentrations following a 2-h 500 ppm exposure to TCE were comparable to partition coefficients obtained previously by in vitro methods.
Oral Simulations
Figure 3 shows blood and tissue TCE concentrations versus measured values in rats given an 8 mg/kg po dose. Oral simulations of tissue levels other than fat and liver reasonably matched measured values. Peak concentrations were accurately predicted in blood and brain and slightly overpredicted in kidney, heart, lung, and spleen. Terminal-phase TCE concentrations were well predicted in blood, kidney, heart, and lung and slightly underpredicted in the brain and spleen. Kidney, heart, lung, and spleen concentration predictions provided further confidence in estimated partition coefficients. Muscle concentrations at later time-points were also underpredicted by the oral simulation, as with the ia simulation. The shape of GI tract concentration simulations was qualitatively different from the shape of the measured values, which had a shallower slope and a secondary peak.
Inhalation Simulations
Figure 4 shows blood and tissue TCE concentrations versus measured values in rats inhaling 50 or 500 ppm for 2 h. Concentrations of TCE during exposures were generally well or slightly overpredicted. Exceptions include muscle levels that were again underestimated by inhalation simulations at both 50 and 500 ppm and brain concentrations that were slightly underestimated. Similar to the findings in the ia simulation, the uptake of TCE into the fat was underestimated at the 50-ppm concentration showing that uptake is more rapid than predicted by the current model. Predictions of TCE concentrations during the elimination phase were generally accurate or underpredicted. Predictions of GI tract, kidney, heart, lung, and spleen concentrations during and following 50-ppm exposures were further in support of estimated partition coefficients from terminal phase ratios following 500 ppm exposure.
Effect of Additional Compartments on Predictions
Little or no differences were seen in liver, venous blood, or fat concentrations dose metrics when comparing simulations by the reduced 4-compartment model to the full 10-compartment model. Table 5 shows predictions of liver, venous blood, and fat AUCs from the four- and 10-compartment models following a range of oral doses of TCE (0.1 mg/kg1 g/kg). All expanded model AUC values were within 10% of the reduced four-compartment model.
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The calculated sensitivty coefficients (SCs) for RAM to new model parameters are given in Table 7. The absolute value of the SCs for RAM to all three additional deep liver parameters (D, VLDC, Pdl:b) in the rat model are all below 0.1 in contrast to SCs to Vmaxc which had SCs ranging up to 1.02 in absolute value. Sensitivity coefficients of RAM to PA, an additional diffusion-limited fat parameter in the rat model are above 0.5 at 2 h post 10 and 100 mg/kg oral dosing and below 0.5 for all other reported oral time points and all inhalation timepoints. SCs were all below 0.1 for VBF. For the mouse model all SCs for deep liver parameters, D, VLDC, and Pdl:b, were below 0.01 (results not shown).
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DISCUSSION |
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The U.S. EPA draft risk assessment for TCE in 2001 utilized PBPK model predictions of mouse liver TCA AUC ([mg-h]/l), mouse liver DCA AUC([mg-h]/l), mouse lung chloral hydrate (CH) AUC ([mg-h]/l), mouse lung CH maximum concentration (mg/l), and rat kidney thiol (mg/l/day). To date, there has been no calibration or validation of PBPK model predictions of concentrations of TCE or its metabolites in the rat kidney. This work is the first attempt to do so and compares rat PBPK model predictions of TCE to measured concentrations following three routes of exposure. Results show good concordance between model predictions and measured values following oral and inhalation exposures while the model slightly overpredicts kidney concentrations following ia exposures. To our knowledge, this is the first PBPK model for TCE to include the heart and spleen, which will aid in predicting target tissue dosimetry for cardiac and immune-related adverse responses.
Rat and Mouse Liver Concentration Predictions
While there has been calibration/validation of TCA and DCA mouse liver concentrations following po exposures to 3002000 mg/kg TCE (Abbas and Fisher, 1997), and rat TCE liver concentrations during and following inhalation exposure to 2004000 ppm TCE (Simmons et al., 2002
), this work represents a lower dose validation of rat liver TCE predictions following po exposure to 8 mg/kg TCE and during and following inhalation exposure to 50 ppm TCE. The addition of a deep liver compartment enabled statistically better fits of rat liver TCE concentrations following po and ia administration and during and following inhalation exposure to 500 ppm TCE. The lack of ability of the PBPK TCE model to predict TCE liver concentrations during and following exposure to 50 ppm TCE indicates that the liver cannot be represented by a single uniform compartment or a two compartment shallow and deep liver description. The addition of a deep liver compartment also gave statistically better fits of mouse TCE liver concentrations following oral ingestion of 3002000 mg/kg, which indicates cross-species applicability of the deep liver TCE PBPK model. The estimates of the deep liver:blood partition coefficient were equal or similar to the fat:blood partition coefficients for each respective species (Pdl:b = 18.4 vs. Pf:b = 25.3 for the rat and Pdl:b estimated at the upper bound of 32.4 vs. Pf:b = 32.4 for the mouse). However, the rat deep liver transfer rate (D) (h-1) was an order of magnitude higher than the mouse.
The liver is not a homogenous tissue. The basic liver lobule is comprised of functionally dissimilar regions. Xenobiotic metabolism clearly differs from one region to another. CYP2E1 and CYP2B1/2, the two P450 isozymes largely responsible for TCE oxidation in rat liver, are expressed primarily in the centrilobular region (Lindros, 1997). PBPK models have been developed to address the complexity of the liver. Frederick et al.(1992)
incorporated a liver with periportal, midzonal, and centrilobular regions into their PBPK model for ethyl acrylate, in order to account for the VOCs rapid hepatic uptake and metabolism. Andersen et al.(1997)
developed a multicompartment geometric model of the liver consisting of two periportal zones surrounding three concentric centrilobular zones. Tirona and Pang (1996)
described an even more complex physiological model that consisted of three zonal units further subdivided into extracellular, cytosolic, and intracellular sequestration compartments. It is possible that TCE is sequestered into membrane lipids of the endoplasmic reticulum and other organelles, but little information is available on intracellular disposition of VOCs.
We suggest that the deep liver compartment represents a liver lipid pool. Once sequestered in liver lipid, TCE must pass through the shallow compartment, representing nonlipid tissue, before it can pass into the venous blood supply. The physiological basis for a deep liver compartment is not understood, though a number of factors might contribute to the phenomenon. Ready uptake of incoming TCE by periportal hepatocytes, coupled with preferential metabolism by centrilobular cells, may produce a dynamic TCE concentration gradient in each lobule. Intralobular differences in lipid metabolism and deposition may also be a factor in retention of TCE in the periphery of lobules. Dietary fatty acid uptake and incorporation into very low-density lipoproteins is relatively high in periportal hepatocytes. Cholesterol synthesis and ketogenesis are known to occur primarily in this region, though fatty acid synthesis is panlobular in male rat liver (Gebhardt, 1989). Preferential delivery and retention of small amounts of TCE in periportal regions may play a role in the slow hepatic clearance we observed with low TCE doses. Further study, however, will be necessary to demonstrate and to clarify the roles of such processes in intraorgan kinetics.
Liver concentration time courses in the rat and mouse were well represented by the addition of a second compartment to the liver, representing a liver lipid pool. Alternatively, there may be weak noncovalent binding of TCE in the liver that causes sequestration of TCE in the liver. In previous studies of liver concentrations during and following inhalation exposures to 2004000 ppm TCE, only one measurement post exposure was made (Simmons et al., 2002), which would not have been adequate to discriminate between alternative models of liver dosimetry.
The addition of a deep liver compartment had negligible effect on predictions of the total amount of TCE metabolized. This is likely due to the fact that metabolism of TCE in the liver is modeled as occurring in the shallow liver compartment only. The shallow liver compartment has the same liver:blood partition coefficient as on one-compartment liver description and thus liver venous blood concentrations of the one- and two- compartment liver models are very similar. Liver metabolism of TCE is a function of venous liver TCE concentrations. The implication of the lack of sensitivity of the total amount of TCE metabolized to the inclusion of a deep liver compartment is that previous PBPK modeling efforts that have focused on predictions of TCE metabolite dose metrics in the liver should not be affected by this alternative liver description. Metabolites of TCE are not lipophilic and thus their prediction would not be altered by using a deep-liver model description. However, for other lipophilic, well-metabolized compounds that are toxicologically active, this finding indicates that a well-stirred liver model may not be appropriate and a two-compartment liver description should be considered.
Cross-ValidationLiver Concentrations
Cross-validation allowed economical use of the available data for both model calibration and validation. This is a novel application in PBPK modeling and has potential for broader application to other PBPK models. As applied here cross-validation can be used when as few as two data sets exist for calibration and validation of a PBPK model. Formal optimization is also not strictly required, as visual exploration of the parameter space can also be performed on each subsample of data sets and the resulting parameters tested on the test case. More work is needed to develop the application of cross-validation to PBPK modeling, but this is a promising approach for model validation. When some model parameters are fit to data, it allows judicious use of available data sets for both estimation of model parameters and independent validation of model predictions.
Cross-validation of the rat TCE PBPK model indicated accurate prediction of liver AUCs following ia injection of 8 mg/kg and during and following inhalation exposure to 500 ppm. Cross-validation also demonstrated liver AUC values may be overpredicted following po exposures. Thus, the current model errs in the conservative direction. Liver concentrations were underpredicted during and following inhalation exposure to 50 ppm TCE. Caution should be employed before applying the current model to predictions of liver concentrations during and following inhalation exposures less than 500 ppm. Cross-validation also indicated successful predictions of mouse liver AUCs following po exposures to TCE doses < 600 mg/kg. Both predicted values were within 20% of calculated values. At po exposures of 1200 mg/kg and higher in the mouse liver concentrations appear to be underpredicted.
Jackknife parameter and SE estimation is a simpler and quicker alternative to more rigorous statistical approaches such as hierarchical modeling using maximum likelihood and Bayesian methods (e.g., Bois, 1999). Jackknife estimates of means for deep liver compartment parameters, D and Pdl:b are close to the maximum likelihood estimates (MLEs) yielded from ACSL Math. However, the maximum likelihood estimates of parameter SEs are 23 orders of magnitude smaller than jackknife SE estimates. This is partly due to the fact that each jackknife subsample contained different data sets obtained from different routes of exposure and/or doses. Thus, variability between subsample parameter estimates includes systematic model failures (e.g., performs better at low doses than high doses) as well as experimental error. Another factor in the large difference in SE estimates is that the experimental unit for ACSL Math MLE estimates is the individual observation and the SE estimate quantifies mostly intra-experimental variability. In contrast, the experimental unit for the jackknife estimate is the experiment and the SE quantifies interexperimental variability. Within experimental error is often of smaller magnitude than between experimental error. The maximum likelihood estimates generated by ACSL Math assume that errors are normally distributed. However, this does not account for systematic model failures or differences between inter- and intraexperimental variability. Thus, we used jackknife to overcome this deficiency. The statistical properties of the jackknife in this context are unknown. Furthermore, the small number of experiments (n = 3 or 4) likely make the jackknife SE estimates unstable. However, we feel the jackknife estimates of SE give a more realistic sense of the SE than the ACSL MATH estimates which seem overly precise (e.g., 1.6 x 10-4 ± 6.6 x 10-8 for a deep liver transfer rate). Caution should be taken before utilizing ACSL Math SE estimates in uncertainty analysis as they may underestimate uncertainty.
Diffusion-Limited Fat Description
Representation of adipose tissue as a flow-limited compartment resulted in a substantial underprediction of fat levels by our PBPK model. In contrast, the addition of diffusion-limitation statistically improved predictions of TCE fat concentrations following po or ia exposure to 8 mg/kg TCE. Describing fat distribution is important since TCE is a lipophilic compound and fat serves as a significant reservoir of TCE for slow-release subsequent to exposure. Fat distribution affects predictions of TCE dosimetry, as well as that of its toxic metabolites. The sensitivity analysis showed that levels of TCE in the venous blood of the liver were sensitive to the addition of diffusion-limitation to the fat at 2 h post PO gavage exposure. A 1% increase in the PA term resulted in a 0.7% increase in venous blood TCE levels 2 h following 10 or 100 mg/kg oral gavage. This is because an increase in the PA term causes an increase in the rate of release of TCE by the fat that causes a resulting initial increase in the amount of TCE in the venous blood of the liver. At latter time points (e.g., 8 h) the increased rate of release of TCE by the fat, results in a decrease in venous liver blood concentration as more TCE is released from fat earlier rather than later. The relative insensitivity of model predictions of the rate of TCE metabolism to the blood volume of fat indicates that a more precise determination of this parameter is not necessary. To date, PBPK TCE models have been calibrated/validated to fat concentrations of TCE following po exposure of mice to 3002000 mg/kg TCE (Abbas and Fisher, 1997), during and following inhalation exposure of mice to 100 and 600 ppm (Greenberg et al., 1999
) and during inhalation exposure of rats to 2004000 ppm (Simmons et al., 2002
). A diffusion-limited model and an axial-dispersion type model, which reflects the physiological heterogeneities of different fat depots in the body, have been used previously to simulate TCE fat concentrations (Albanese et al., 2002
), although no calibration of this model to fat concentration data has been performed. TCE is a small, uncharged, lipophilic molecule. Thus, it is generally believed to diffuse readily across vascular and hepatocellular membranes, as assumed with a flow-limited model. Diffusion-limitation has been used previously to describe lipophilic VOCs such as polychlorotrifluoroethylene (Vinegar et al., 1992
) and methylene chloride (Angelo et al., 1984
). Two fat compartments were employed by the prior research group. In view of interdepot differences in blood flow, adipocyte size, and metabolic activity (Crandall et al., 1997
; Slavin, 1985
), future models for lipophilic chemicals might include multiple fat compartments with their own physiological parameters.
The biological mechanism described here as diffusion-limitation may be rather heterogeneous fat characteristics such as a deep fat compartment. Previous concentration time courses of TCE in fat in rats did not include measurements post-exposure and are thus not sensitive to discriminating between flow and diffusion-limited models (Simmons et al., 2002). Previous concentration time courses of TCE in fat following oral exposure to mice of TCE to 3002000 mg/kg TCE paralleled TCE in the blood and were adequately described by a flow-limited model (Abbas and Fisher, 1997
). This indicates that perhaps the mechanism of slow release of TCE from the fat is limited to the rat or more likely to doses lower doses than 300 mg/kg in the mouse.
Overall, model predictions of TCE concentrations in blood and tissues show good concordance with measured values for all three routes of exposure. Predictions of TCE levels in blood, kidney, heart, lung, brain, and GI tract were quite accurate during uptake and elimination. Post exposure skeletal muscle levels, however, were routinely underpredicted. Most forecasts of liver and fat profiles were accurate, when provision was made for a two-compartment liver and diffusion-limitation in fat. The exception, liver concentrations following the 50-ppm inhalation exposure, may point to the need for a more complex liver model at low inhaled doses. At low doses where metabolism dominates as a route of excretion of TCE, uneven distribution of P450 activity in the liver may result in a wide range of liver TCE concentrations, which are not adequately represented by either a well-stirred liver compartment or a two-compartment description. Underprediction of TCE clearance from muscle may indicate that a well-stirred muscle compartment is inadequate for predicting muscle TCE concentrations, and a two-compartment model description (shallow and deep) may fair better if prediction of muscle concentrations is of concern.
Effect of Additional Compartments on Predictions
Comparisons of the expanded PBPK model with a reduced four-compartment model indicate minimal effect on simulation of liver, blood, and fat AUCs. This indicates that the effect on splitting out the additional compartments from the rapidly perfused compartment on PBPK predictions for original compartments (e.g., liver, fat, blood) is negligible. This is consistent with the theoretical results of Nestorov et al.(1998), who found that tissues with similar time constants could be lumped without loss of information. Nestorov et al. define a time constant as Vi*Pi/Qi where Vi, Pi, and Qi are tissue specific volumes, partition coefficients, and blood flows respectively. In the TCE rat model, calculated time constants for the split-out components of the rapidly perfused tissues range from 0.01 to 0.44 with an average value of 0.13, while values for liver, fat and muscle are 0.24, 23.49, and 2.32 respectively. The calculated time constant of the rapidly perfused compartment in the reduced four-compartment model is equal to 0.13, identical to the average of the split-out compartments. This theoretical result supports the simulation work yielding nearly identical results for the expanded and lumped models. While additional compartments do allow the benefit of prediction of additional target tissue concentrations, the TCE PBPK model does not appear to be sensitive to their inclusion. This lends confidence to simplifying lumping assumptions in prior TCE PBPK models that have been applied in the draft TCE risk assessment.
In summary, an expanded PBPK model for TCE in rats has been developed which predicts dosimetry of additional target tissues. The blood and tissue predictions have been validated across three routes of exposure. This is a more extensive tissue validation and at lower exposure doses than has been performed in previous TCE models. Inclusion of a deep liver compartment representing a lipophilic region of the liver containing TCE that is not readily available for metabolism or venous clearance, yielded improved predictions of liver dosimetry in the rat and mouse. The effect of the addition of the deep liver compartment on predictions of TCE metabolism was negligible indicating that previous models of TCE metabolites in the liver may not be sensitive to this model alteration. This modeling effort both increases the range of possible applications and increases confidence in application of TCE PBPK models in human health risk assessment.
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APPENDIX |
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The jackknife estimate of the SE of is J is
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ACKNOWLEDGMENTS |
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NOTES |
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REFERENCES |
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