Physiologically Based Pharmacokinetic Model Parameter Estimation and Sensitivity and Variability Analyses for Acrylonitrile Disposition in Humans

Lisa M. Sweeney*,1, Michael L. Gargas*, Dale E. Strother{dagger} and Gregory L. Kedderis{ddagger}

* The Sapphire Group, 4027 Colonel Glenn Highway, Fourth Floor, Dayton, Ohio 45431; {dagger} BP, Arlington, Virginia 22209; {ddagger} 1803 Jones Ferry Road, Chapel Hill, North Carolina 27516

Received June 21, 2002; accepted October 2, 2002


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX 1
 APPENDIX 2
 REFERENCES
 
A physiologically based pharmacokinetic (PBPK) model of acrylonitrile (ACN) and cyanoethylene oxide (CEO) disposition in humans was developed and is based on human in vitro data and scaling from a rat model (G. L. Kedderis et al ., 1996, Toxicol. Appl. Pharmacol .140, 422–435) for application to risk assessment. All of the major biotransformation and reactivity pathways, including metabolism of ACN to glutathione conjugates and CEO, reaction rates of ACN and CEO with glutathione and tissues, and the metabolism of CEO by hydrolysis and glutathione conjugation, were described in the human PBPK model. Model simulations indicated that predicted blood and brain ACN and CEO concentrations were similar in rats and humans exposed to ACN by inhalation. In contrast, rats consuming ACN in drinking water had higher predicted blood concentrations of ACN than humans exposed to the same concentration in water. Sensitivity and variability analyses were conducted on the model. While many parameters contributed to the estimated variability of the model predictions, the reaction rate of CEO with glutathione, hydrolysis rate for CEO, and blood:brain partition coefficient of CEO were the parameters predicted to make the greatest contributions to variability of blood and brain CEO concentrations in humans. The main contributor to predicted variance in human blood ACN concentrations in people exposed through drinking water was the Vmax for conversion of ACN to CEO. In contrast, the main contributors for variance in people exposed by inhalation were expected to be the rate of blood flow to the liver and alveolar ventilation rate, with the brain:blood partition coefficient also contributing to variability in predicted concentrations of ACN in the brain. Expected variability in blood CEO concentrations (peak or average) in humans exposed by inhalation or drinking water was modest, with a 95th-percentile individual expected to have blood concentrations 1.8-times higher than an average individual.

Key Words: acrylonitrile; cyanoethylene oxide; physiologically based pharmacokinetic modeling; interspecies extrapolation; sensitivity analysis; variability analysis.


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX 1
 APPENDIX 2
 REFERENCES
 
Acrylonitrile (ACN) is a chemical used primarily for production of acrylic fibers (ATSDR, 1990Go). The tumorigenicity of ACN has been tested in 10 studies in rats (summarized in Kirman et al., 2000Go) that indicate the brain is the primary target organ. Epidemiology studies have not provided persuasive evidence of a relationship between human central nervous system tumors and ACN exposure (Collins and Strother, 1999Go). Postulated modes of action consider the epoxide metabolite cyanoethylene oxide (CEO) to be more directly related to tumor causation in rats than the parent compound (Kirman et al., 2000Go).

The aim of this work was to develop a physiologically based pharmacokinetic (PBPK) model to compare dosimetry of ACN and CEO in rats and humans for application in risk assessment. Sensitivity and variability analyses of the model were performed to identify key parameters and sources of interindividual variability. Because no in vivo pharmacokinetic data were available for human model validation, human in vitro data were scaled using a "parallelogram approach" (Reitz et al., 1989Go). Rat in vivo metabolic parameters were determined by model optimization (Gargas et al., 1995Go; Kedderis et al., 1996Go) and in vitro studies (Kedderis et al., 1993Go; Kedderis and Batra, 1993Go). A correction factor for in vitro to in vivo scaling in the rat was calculated and applied to scaling the human in vitro data. A sensitivity analysis of the human model indicated parameter values that are key in determining the predicted dose metrics of interest for the ACN-CEO model and permitted a more focused critique of these parameter values and hence the reliability of the model predictions. Model sensitivity combined with known parameter variability permitted a preliminary evaluation of how much interindividual variability in relevant dose metrics would be expected. Based on a normal distribution of parameter values, it was calculated that the 95th-percentile individual would have a blood CEO concentration roughly twice the value of an average individual, a moderate degree of interindividual variability.


    MATERIALS AND METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX 1
 APPENDIX 2
 REFERENCES
 
Model structure.
The model structure, depicted in Figure 1Go, is based on the structure previously used for the PBPK model of ACN and CEO in rats (Kedderis et al., 1996Go). The model consists of several tissue compartments, modeled as being well-mixed, linked through blood flow. The blood exiting the tissue is assumed to be in equilibrium with tissue. Exposure to ACN can occur by inhalation or by drinking water consumption. In the liver, ACN is metabolized by two pathways, glutathione (GSH) conjugation or epoxidation to CEO. The disposition of CEO is also described using several well-mixed tissue compartments. In humans, CEO is metabolized by GSH conjugation or hydrolysis. ACN and CEO may both also react with hemoglobin and sulfhydryls in the blood. A mathematical description of the model is provided in Appendix 1.



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FIG. 1. Model structure for the PBPK model for acrylonitrile and cyanoethylene oxide.

 
Selection of parameter values.
For discrete tissues (liver, brain, stomach, and fat), the volumes used are presented in Brown et al.(1997)Go, with the exception of arterial and venous blood volumes, which are taken from ICRP (1975)Go. If all the organ weights in Brown et al.(1997)Go are added (including unperfused tissues, such as bone), they account for only 87.77% of the body weight. The remaining 12.23% was divided between the richly and poorly perfused tissues based on their relative contributions to body weight.

The alveolar ventilation rate, cardiac output, and percent blood flow to liver, brain, and fat are taken directly from human values recommended by Brown et al.(1997)Go. The alveolar ventilation rate and cardiac output are consistent with the ~ 1:1 ventilation/perfusion ratio expected in a healthy individual (West and Wagner, 1991Go). The percent blood flow to the stomach is the percentage measured for the rat by Delp et al.(1991)Go. Similar to the tissue weights, the percent flows to tissues presented in Brown et al.(1997)Go do not add up to 100; rather, they add up to only 91.5. The remaining 8.5% was divided between the richly and poorly perfused tissues based on their relative contributions to the percent of cardiac output.

Partition coefficients for ACN and CEO in rat tissue were reported (Teo et al., 1994Go). The human blood:air partition coefficient for ACN was determined in freshly drawn heparinized blood samples (n = 5) containing diethyl maleate using vial equilibration techniques (Teo et al., 1994Go). Tissue:blood partition coefficients for the human model were calculated as rat tissue:air partition coefficient (determined by Teo et al., 1994Go) divided by the measured human blood:air partition coefficient. The rate of reaction of ACN with human blood sulfhydryls was determined from the time course of ACN disappearance using gas chromatography. A literature review was conducted to identify GSH concentrations in human tissues. Reported values (Table 1Go) are based on tissues retrieved from healthy individuals via biopsy from three separate studies, with the exception of brain, for which data from one in vivo study (by nuclear magnetic resonance measurements) and one study using surgically removed tissues (lobectomy) were used.


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TABLE 1 Model Parameter Values
 
Scaling methods.
The VmaxC for ACN oxidation was calculated by taking the optimized rat VmaxC (Kedderis et al., 1996Go) and adjusting it for the differences in the human and rat in vitro rates of oxidation by microsomal protein, differing microsomal protein content of rat versus human livers, 40 mg/g tissue for rats (Ploemen et al., 1997Go) and 56.9 mg/g in human liver (Lipscomb et al., in press a) and adjusting for the differences in relative liver sizes. The human liver microsomal protein content reported by Lipscomb et al. (in press a) is based on a sample of 20 adults, consisting of two black males, eight Caucasian males, one Hispanic male, seven Caucasian females, and two Hispanic females (Lipscomb et al., in press b).

Hydrolysis of CEO was scaled from human in vitro microsomal rates by assuming that the in vivo:in vitro ratio for P450 mediated metabolism was the same as the in vivo:in vitro ratio for hydrolysis, since these reactions both occur in the endoplasmic reticulum. Kms for all reactions were assumed to be equal to the average of the human in vitro values.

GSH conjugation rates for ACN and CEO were also scaled from the in vivo rates for the rat, adjusted for differences in metabolism rates in vitro, liver size and protein content, and differing tissue concentrations of the cofactor GSH. Details of the scaling procedures are provided in Appendix 2.

Simulation.
Simulations were conducted using ACSL Sim 11.8 (AEgis Technologies, Austin, TX).

Internal dosimetry comparison.
Peak and AUC of blood and brain ACN and CEO were considered to be dose metrics potentially relevant to the carcinogenicity of ACN in rats (Kirman et al., 2000Go). These dose metrics were compared in rats and humans for different exposure scenarios. The first scenario was an 8-h inhalation exposure to 2 ppm, the current threshold limit value for ACN (ACGIH, 2001Go). The second scenario was one week of continuous inhalation exposure to 868 µg/m3 ACN (0.4 ppm). The third exposure scenario was one week of periodic exposure to 0.12 mg/l ACN in drinking water. The periodic exposure consists of multiple po doses (described as a bolus input to the stomach) throughout the day on a schedule that approximately mimics drinking water patterns of rats and humans (Kirman et al., 2000Go; Reitz et al., 1997Go). The exposure levels in the second and third scenarios (continuous inhalation and intermittent drinking water consumption) were selected based on conditions estimated to produce a lifetime excess cancer risk of 1 x 10–6 in rats, using a threshold assumption (Kirman et al., 2000Go).

Sensitivity analysis.
Sensitivity analysis was performed to identify which parameters must be known with the greatest precision in order to most accurately calculate human risk. Each parameter value was increased by 1% and dose metrics of interest computed. The percent increase in the prediction of interest divided by 1% (the parameter increase) was defined as the normalized sensitivity coefficient (normalized SC). The two continuous exposure scenarios described above were used as the baseline for the sensitivity analysis. The dose metrics to be examined for this exposure were peak blood and brain concentrations of ACN and CEO and the area under the blood concentration versus time curves for ACN and CEO. The precise values of the exposure concentrations were not expected to be important, as they were low enough that all blood and tissue concentrations of ACN and CEO had a linear relationship with exposure concentration. In the inhalation scenario, only the sensitivity of the blood and brain ACN and CEO AUC predictions were determined, because with continuous exposure the steady-state blood or tissue concentration was essentially equal to the peak concentration.

To identify parameters of importance in population variation in the dose metrics, a variability analysis was conducted. The variability analysis accounts for both the model sensitivity (i.e., does the model prediction change when a parameter value changes) and the known or estimated variability in the input parameter (i.e., what is the range of reasonable input values for this parameter). The approximate CV for the model output (CVm) is predicted using a propagation of error formula (Vardeman, 1994Go, cited in Licata et al., 2001Go, with formulas substituted to be in terms of normalized SC) shown below.


Where i indicates the ith parameter, normalized SCi is the normalized sensitivity coefficient relative to changes in parameter i, and CVi is the coefficient of variation in parameter i.

CVi values were calculated from experimental data or estimates taken from the published literature for all model parameters. CVm was calculated for the same dose metrics for which the sensitivity analyses were conducted. The fractional contribution of each parameter to the predicted variance was calculated, and those with the greatest contribution to the total model variance were identified.


    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX 1
 APPENDIX 2
 REFERENCES
 
Model Structure and Parameter Values
The model structure depicted in Figure 1Go is the same as that used previously for the PBPK model of ACN and CEO disposition in rats (Kedderis et al., 1996Go) with the addition of CEO hydrolysis, which does not occur at an appreciable rate in rat tissues (Kedderis and Batra, 1993Go). Parameter values for the human ACN-CEO model are summarized in Table 1Go. Physiological parameters and partition coefficients are generally similar to those in the previous rat model. A notable exception is that the human blood:air partition coefficient is 154, compared to 512 in rats. The calculated VmaxC value for ACN epoxidation in humans is approximately three-fold greater than the rat VmaxC, and the human Km for this reaction is roughly two-fold smaller than the rat Km. Conjugation rates of ACN with GSH are also greater in humans than in rats, but CEO conjugation in humans is slower.

Internal Dosimetry
The results are presented in Table 2Go. Blood and brain concentrations of ACN and CEO are generally predicted to be similar in rats and humans. An exception is that under the periodic drinking water scenario, peak concentrations of ACN in the blood and brain of rats are expected to be higher. It should be noted that the comparisons are based on equal concentrations in drinking water. Volume of drinking water consumed is scaled based on BW0.7, so the daily dose in mg/kg/day is higher in rats than in humans.


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TABLE 2 Predicted Tissue Dosimetry  Final blood and brain concentrationsSpecies0.0000.0000.000000.0000
 
Sensitivity and Variability Analyses, Intermittent Drinking Water Exposure Scenario
Parameter coefficients of variation.
Parameter coefficients of variation were calculated from experimental data or taken from estimates in the published literature and summarized in Tables 3–6GoGoGoGo and briefly discussed below.


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TABLE 3 Coefficients of Variation for Model Parameters: Physiological Parameters
 

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TABLE 4 Coefficients of Variation for Model Parameters: Tissue Glutathione Concentrations
 

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TABLE 5 Coefficients of Variation for Model Parameters: Metabolism and Binding Parameters and Oral Uptake Rate First order reaction rate for conjugation of CEO0.000Composite of Kedderis et al., 1993Goin vitro rate (CV = 0.293); Lipscomb et al.,
 

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TABLE 6 Coefficients of Variation for Model Parameters: Partition Coefficients
 
The CVs for tissue volumes and blood flows are all estimates taken from Allen et al.(1996)Go. Allen et al. based their estimates in part on the ILSI (1994) report (later published as Brown et al., 1997Go). The CVs for human tissue GSH are based on the same studies from which the average values are calculated.

Some rate terms (VmaxCs for ACN oxidation and CEO hydrolysis and first order rates for ACN and CEO conjugation with glutathione) are composites of variability in the various factors used in scaling (e.g., microsomal protein content of the liver). "Composite" CVs for rate terms were calculated as the square root of the sum of the squares of the CVs of the parameters that went into scaling the term. For cytochrome P450 and epoxide hydrolase-mediated reactions, variability in microsomal protein content of human liver was taken from Lipscomb et al. (in press a). In the absence of any information on variability of cytosolic protein content, this same value was used for first order reactions with GSH. The variability of human Vmax and Km in subcellular fractions was calculated from studies of Kedderis and coworkers.

The CV of binding rates to hemoglobin and reaction with blood RSH was estimated as 0.3, based on Allen et al.(1996)Go. The CV for the oral uptake rate, 0.2, was also taken from Allen et al.(1996)Go.

CEO-related dose metrics.
Normalized sensitivity coefficients (normalized SC) were calculated for 46 model parameters for four CEO-related dose metrics—AUC for CEO in the blood and brain and peak concentration of CEO in the blood and brain. Normalized SC ranged from –0.75 to 1.00. For 23 parameters, |normalized SC| was < 0.1 for each of the four dose metrics, i.e., the model predictions were essentially insensitive to changes in these parameters. For the sake of brevity, only those parameters with |normalized SC| > 0.20 for at least one dose metric are shown in Figure 2Go.



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FIG. 2. Sensitivity analysis of CEO-related dose metrics, for exposure to 0.12 mg ACN/l drinking water. Parameter abbreviations as in Table 1Go. Only parameters with |sensitivity coefficient| > 0.2 for at least one dose metric shown.

 
The expected variability of the model predictions derives from both model sensitivity and parameter variability. Parameters accounting for 98% of the variance were determined for these four dose metrics, and are summarized in Figure 3Go. Model CVs for blood CEO AUC and peak concentration are 0.51 and 0.48 respectively, while brain CEO AUC and peak CVs are 0.68 and 0.59, due to the uncertainty regarding the brain:blood partition coefficient for CEO. Brain concentrations of CEO have approximately a linear dependence (normalized SC of about 1), so the relatively large uncertainty in the brain:air partition coefficient (CV = 0.4) drives up the model CV for brain concentrations of CEO, as compared to the variability of blood CEO.



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FIG. 3. Contributors to predicted variability of CEO-related dose metrics for exposure to 0.12 mg ACN/l drinking water. (A) Blood AUC, (B) brain AUC, (C) peak concentration in blood, (D) peak concentration in brain.

 
ACN-related dose metrics.
Normalized sensitivity coefficients (normalized SC) were calculated for 46 model parameters for four ACN-related dose metrics—AUC for ACN in the blood and brain and peak concentration of ACN in the blood and brain. Normalized SC ranged from –0.83 to 1.00. For 25 parameters, |normalized SC| was < 0.1 for each of the four dose metrics, i.e., the model predictions were essentially insensitive to changes in these parameters. For the sake of brevity, only those parameters whose |normalized SC| was > 0.20 for at least one dose metric are shown in Figure 4Go.



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FIG. 4. Sensitivity analysis of ACN-related dose metrics, for exposure to 0.12 mg ACN/l drinking water. Parameter abbreviations as in Table 1Go. Only parameters with |sensitivity coefficient| > 0.2 for at least one dose metric shown.

 
The expected variability of the model predictions derives from both model sensitivity and parameter variability. Parameters accounting for 98% of the variance were determined for these four dose metrics, and are summarized in Figure 5Go. Model CVs for blood ACN AUC and peak concentration are 0.47 and 0.50 respectively, while brain ACN AUC and peak CVs are 0.49 and 0.51.



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FIG. 5. Contributors to predicted variability of ACN-related dose metrics for exposure to 0.12 mg ACN/l drinking water. (A) Blood AUC, (B) brain AUC, (C) peak concentration in blood, (D) peak concentration in brain.

 
Sensitivity and Variability Analyses, Constant Inhalation Exposure Scenario
CEO-related dose metrics.
Normalized sensitivity coefficients (normalized SC) were calculated for 45 model parameters for two CEO-related dose metrics—AUC for CEO in the blood and brain. Normalized SC ranged from –0.74 to 1.00. For 24 parameters, |normalized SC| was < 0.1 for both dose metrics, i.e., the model predictions were essentially insensitive to changes in these parameters. For the sake of brevity, only those parameters whose |normalized SC| was > 0.20 for at least one dose metric are shown in Figure 6Go.



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FIG. 6. Sensitivity analysis of CEO-related dose metrics, for exposure to 0.4 ppm ACN by continuous inhalation. Parameter abbreviations as in Table 1Go. Only parameters with |sensitivity coefficient| > 0.2 for at least one dose metric shown.

 
The expected variability of the model predictions derives from both model sensitivity and parameter variability. Parameters accounting for 98% of the variance were determined, and are summarized in Figure 7Go. Model CVs for blood CEO AUC and brain CEO AUC are 0.56 and 0.72. The CV for brain AUC is greater due in large part to the uncertainty regarding the brain:blood partition coefficient for CEO.



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FIG. 7. Contributors to predicted variability of CEO-related dose metrics for exposure to 0.4 ppm ACN by continuous inhalation. (A) blood AUC, (B) brain AUC.

 
ACN-related dose metrics.
Normalized sensitivity coefficients (normalized SC) were calculated for 45 model parameters for two ACN-related dose metrics—AUC for ACN in the blood and brain. Normalized SC ranged from –0.80 to 1.00. For 37 parameters, |normalized SC| was < 0.1 for both dose metrics, i.e., the model predictions were essentially insensitive to changes in these parameters. For the sake of brevity, only those parameters whose |normalized SC| was >0.20 for at least one dose metric are shown in Figure 8Go.



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FIG. 8. Sensitivity analysis of ACN-related dose metrics, for exposure to 0.4 ppm ACN by continuous inhalation. Parameter abbreviations as in Table 1Go. Only parameters with |sensitivity coefficient| > 0.2 for at least one dose metric shown.

 
Parameters accounting for 98% of the predicted variance are summarized in Figure 9Go. Model CVs for blood ACN AUC and brain ACN AUC are 0.30 and 0.29.



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FIG. 9. Contributors to predicted variability of ACN-related dose metrics for exposure to 0.4 ppm ACN by continuous inhalation. (A) Blood AUC, (B) brain AUC.

 
Main contributors to ACN and CEO variability.
While the model predictions of brain and blood CEO are sensitive to a number of parameters, a limited number have a significant impact. Uncertainty in parameter values has impact in two ways. First, the uncertainty about the average value affects the point estimate. Second, uncertainty about the variability affects how much the calculated doses vary from the mean for individuals who are not "average." Parameters affecting the variability, those with relatively large contribution to estimated variance (accounting for 64–85% of the expected variability) are the Vmax and Km for the hydrolysis of CEO and the first order reaction rate of CEO with GSH (for all CEO-related dose metrics of interest), and brain:blood partition coefficient of CEO (for dose metrics related to concentrations in the brain).

Blood and brain ACN concentrations are predicted to be less variable than the CEO concentrations (model CVs of 0.29–0.51 for ACN-related endpoints). Unlike CEO, where contributors to variability were similar for inhalation and drinking water routes, contributors to predicted variability of ACN concentrations are route-specific. For the drinking water exposure scenario, variability in Vmax for biotransformation of ACN to CEO accounts for more than half the expected variability. Additional contributors to variability are the Km for ACN metabolism to CEO and (for peak concentrations) the blood flow to the liver. Predicted variability in blood and brain ACN AUC for inhalation exposure is controlled mostly by the fraction of cardiac output flowing to the liver and alveolar ventilation rate. The brain:blood partition coefficient also contributes significantly to predicted variability in the brain ACN AUC.


    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX 1
 APPENDIX 2
 REFERENCES
 
The results of the sensitivity analysis indicate that model predictions of blood and brain CEO are strongly affected by the choice of values of some of the metabolic constants. These metabolic constants are, in turn, dependent on both in vitro rates of reaction and the amount of subcellular protein in the liver. Additional parameters of importance in predicting brain CEO concentrations include the brain:blood partition coefficient for CEO. The variability analyses indicate that human blood and brain CEO predictions are likely to be somewhat variable (CVs of 0.48–0.72). A limitation of the variability analysis is that some of the model input parameters may more appropriately be characterized as lognormally distributed, rather than distributed normally. A Monte Carlo analysis, with appropriate parameter distributions, may be informative for estimating population variability.

Since the parameters contributing most to variability in predicted blood CEO concentrations are parameters describing the metabolism of CEO, confidence in these values is critical to confidence in use of the human model in risk assessment. The Km for CEO hydrolysis is based on six samples, with values ranging from 0.6 to 3.2 mM (Kedderis and Batra, 1993Go). If Km could be measured in a greater number of samples, the extreme values may be found to be outliers, and the CV for this parameter (currently 0.454) might be reduced. The first order reaction rate between CEO and GSH and the Vmax for hydrolysis of CEO are both "composite" parameters, in that they are calculated, by scaling, from other parameters. The largest contributor to variability of both of these parameters is the protein content of the subcellular fractions. The information on the variability of microsomal protein content (Lipscomb et al., in press a,b) is based on a sample size of 20. Additional analyses would not be expected to substantially increase the calculated SD. There was minimal information available on the actual cytosolic protein content of human liver and its variability, so the variability of microsomal protein content was used as surrogates. Thus the actual amount and the interindividual variability of cytosolic protein content of human liver are probably the areas in which further research may impact human PBPK model predictions of CEO dosimetry. In general, the biochemical parameters are more variable and/or known with less certainty than most of the physiological parameters. This uncertainty extends not only to the metabolic parameters, but to the GSH measurements. Reliable data (e.g., using fresh tissue with a reasonable number of individual samples) are not readily available for many important tissues.

Toxicity related to ACN exposure may also potentially be considered to be related to the ACN concentrations, rather than metabolite concentrations. Important parameters for predictions of ACN-related dose metrics vary based on the route of exposure. For humans exposed by inhalation, internal dosimetry is controlled primarily by physiological factors (flow to liver) and physicochemical factors (tissue solubility). For an oral exposure, metabolic parameters (Vmax and Km for ACN epoxidation to CEO) are more important.

Assessments of the risk to human health from ACN exposure are likely to be based on toxicity studies in laboratory animals, extrapolated to estimated human risks. Postulated modes of action for ACN generally consider the epoxide metabolite CEO to be a greater concern than ACN itself. Based on this hypothesis, risk evaluations should be based on concentrations of CEO in blood or target tissue. According to the PBPK model, blood and brain concentrations of CEO in rats and humans are generally expected to be similar for a given exposure scenario. Because of the lack of human data for model validation, the sensitivity of the model to measured and estimated parameter values was evaluated. Because parameter values are known to be variable among individuals, a variability analysis for the model predictions was also conducted. While the model structure has many parameters (> 40), the outputs of interest were sensitive (|normalized SC| > 0.2) to fewer than half of these parameters (Figs. 2, 4, 6, and 8GoGoGoGo). When variability or uncertainty was taken into account, the number of parameters of concern in the risk assessment was reduced even further, with seven or fewer parameters accounting for > 85% of the variability (Figs. 3, 5, 7, and 9GoGoGoGo).

This analysis indicates that human variability in blood predictions is modest—a model CV of 0.48 to 0.56 for peak or average blood concentrations of CEO for ACN exposure in drinking water or by inhalation. Based on a normal distribution, this suggests that the 95th percentile individual (1.6 SDs above the mean) would have blood CEO concentrations approximately 1.8 times the concentration in the average individual. For the 99th-percentile individual (2.3 SDs above the mean) the ratio would be 2.2. This is low, relative to the default pharmacokinetic uncertainty factor for intraspecies human variability of 3.2 (Renwick and Lazarus, 1998Go). Overall, the PBPK modeling analysis suggests no heightened sensitivity of humans in general to toxic effects of ACN based on pharmacokinetic differences.


    APPENDIX 1
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX 1
 APPENDIX 2
 REFERENCES
 
Model equations presented below are consistent with the abbreviations defined in Table 1Go.

Alveolar ventilation

QP = QPC x BW0.74 (l/h)

Cardiac output.

QC = QCC x BW0.74 (l/h)

Tissue blood flow

Qj = QjC x QC (l/h) where j = L (liver), F (fat), S (slowly perfused tissue), ST (stomach), BR (brain), R (richly perfused tissues)

Tissue volumes

Vj = VjC x BW (l) where j = same tissues as for blood flows

Venous blood volume

VVB = BVC x BW x VVBC (l) where BVC = fraction of body weight as blood and VVBC is the fraction of blood that is venous blood

Arterial blood volume

VAB = BVC x BW x (1 – VVBC) (l)

Maximal oxidative metabolism of ACN

VMAX = VMAXC x BW0.7 (mg/h)

Rate of oxidative metabolism of ACN

RAM1 = (VMAX x CVL)/(KM + CVL) (mg/h)

Maximal enzymatic hydrolysis of CEO

VMAX2 = VMAXC2 x BW0.7 (mg/h)

Rate of hydrolysis of CEO

RAM2 = (VMAX2 x CVL)/(KM2 + CVL) (mg/h)

Reaction rate for GSH conjugation with ACN in liver

Kf = KfC/BW0.3 (h–1)

Rate of GSH conjugation with ACN in the liver

RAMGL1 = Kf x CVL x VL (mg/h)

Reaction rate for GSH conjugation with CEO in liver

Kf2 = KfC2/BW0.3 (h–1)

Rate of GSH conjugation with CEO in liver

RAMGL2 = Kf2 x CVL2 x VL (mg/h)

Tissue:blood partition coefficients for ACN

Pj = PjA/PB, where j = same tissues as listed for blood flows

Tissue:blood partition coefficients for CEO

Pj2 = PjA2/PB2, where j = same tissues as listed for blood flows

CI = inhaled concentration of ACN

CI = CONC x molecular weight/24450 or 0 (mg/l)

CAL = Concentration of ACN in arterial lung blood (mg/l)

CAL= (QC x CV + QP x CI)/(QC + (QP/PB)) (mg/l)

Concentration of ACN in systemic arterial blood after binding

dAAB/dt = (QC x CAL) – (QC x CA) – (KB x CA x VAB) – (KFB x CA x VAB) (mg/h) where KB = binding rate to hemoglobin and KFB = binding rate to blood sulfhydryls

CA = AAB/VAB (mg/l)

Aj = Amount of ACN in tissue "j" with nonenzymatic GSH conjugation but no oxidative metabolism (slowly perfused, rapidly perfused, and brain tissue)

d Aj/dt = Qj x (CA – CVj) – KSO x Cj x GSHj x Vj (mg/h) where KSO is the second-order spontaneous GSH conjugation rate with ACN

CVj = Aj/(Vj x Pj) (mg/l)

Cj = Aj/Vj (mg/l)

Amount of ACN in gut (AG) and amount absorbed from the stomach (AAG)

Daily dose = 0.102 x BW0.7 x concentration in drinking water (mg/day)

Total dose = Fraction of daily dose ingested x daily dose (mg)

AG = Total dose – AAG (mg)

d AAG/dt = KA x AG (mg/h)

Stomach mass balance for ACN

d AST/dt = QST x (CA – CVST) + KA x AG – KSO x CST x GSHST x VST (mg/h)

CVST = AST/(VST x PST) (mg/l)

CST = AST/VST (mg/l)

Liver mass balance, and venous blood and tissue concentrations for ACN

d AL/dt = QL x CA + QST x CVST – (QL + QST) x CVL) – RAM1 – RAMGL1 (mg/h)

CVL = AL/(VL x PL) (mg/l)

CL = AL/VL (mg/l)

Fat mass balance and venous blood and tissue concentrations for ACN

d AF/dt = QF x (CA – CVF) (mg/h)

CVF = AF/(VF x PF) (mg/l)

CF = AF/VF (mg/l)

Mixed venous blood concentration of ACN before binding

CVb = (QF x CVF + (QL + QST) x CVL + QS x CVS + QR x CVR + QBR x CVBR)/QC (mg/l)

Mixed venous blood concentration of ACN after binding

dAVB/dt = (QC x CVB) – (QC x CV) – (KB x CV x VVB) – (KFB x CV x VVB) (mg/h) where KB = binding rate to hemoglobin and KFB = binding rate to blood sulfhydryls

CV = AVB/VVB (mg/l)

Concentration of CEO in arterial lung blood (mg/l)

CAL2= QC x CV2/(QC + (QP/PB2)) (mg/l)

Concentration of CEO in systemic arterial blood after binding

dAAB2/dt = (QC x CAL2) – (QC x CA2) – (KB2 x CA2 x VAB) – (KFB2 x CA2 x VAB) (mg/h) where KB2 = binding rate to hemoglobin and KFB2 = binding rate to blood sulfhydryls

CA2 = AAB2/VAB (mg/l)

Liver mass balance, and venous blood and tissue concentrations for ACN

d AL2/dt = QL x CA2 + QST x CVST2 – (QL +QST) x CVL2) +RAM1 x MW2/MW1 – RAM2 – RAMGL2 (mg/h)

CVL2 = AL2/(VL x PL2) (mg/l)

CL2 = AL2/VL (mg/l)

Fat mass balance and venous blood and tissue concentrations for CEO

d AF2/dt = QF x (CA2 – CVF2)

CVF2 = AF2/(VF x PF2) (mg/l)

CF2 = AF2/VF (mg/l)

Aj2 = Amount of CEO in tissue "j" with GSH conjugation but no enzymatic hydrolysis (all tissues except liver and fat)

d Aj2/dt = Qj x (CA2 – CVj2) – 0.1 x Kf2 x (GSHj/GSHL) x CVj2 x Vj (mg/h)

CVj2 = Aj2/(Vj x Pj2) (mg/l)

Cj2 = Aj2/Vj (mg/l)

Mixed venous blood concentration of CEO before binding

CVb2 = (QF x CVF2 + (QL + QST) x CVL2 + QS x CVS2 + QR x CVR2 + QBR x CVBR2)/QC (mg/l)

Mixed venous blood concentration of CEO after binding

dAVB2/dt = (QC x CVb2) – (QC x CV2) – (KB2 x CV2 x VVB) – (KFB2 x CV2 x VVB) (mg/h) where KB2 = binding rate to hemoglobin and KFB2 = binding rate to blood sulfhydryls

CV2 = AVB2/VVB (mg/l)


    APPENDIX 2
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX 1
 APPENDIX 2
 REFERENCES
 
Scaling from microsomal fractions to whole-organ metabolism for ACN epoxidation is as follows:

Vmaxin vivo = Vmaxin vitro x [microsomal protein/g liver] x VL x CFin vivo/in vitro

CFin vivo/in vitro can be calculated for rat (where Vmaxin vivo was found by optimization), and it is assumed that this correction factor is constant across species (Corley et al., 1990Go; Reitz et al., 1989Go, 1996aGo, bGo; Thrall et al., 2000Go).

Since Vmaxin vivo = VmaxCin vivo x BW0.7, and VL = VLC x BW


and


Substituting,


4

The GSH conjugation rates derived for the rat (Kedderis et al., 1996Go) were scaled to the human by multiplying by the ratio of combined microsomal and cytosol enzymatic conjugation in humans in vitro by the combined rate in rats in vitro, as reported in Table 4Go of Kedderis et al.(1995)Go. As the rat GSH conjugation rates were based on the tissue content of GSH, they were adjusted to reflect the differences in rat versus human tissue GSH content. The values in Table 4Go of Kedderis et al.(1995)Go were also adjusted, using average rates rather than the highest human rates, and more recent values for microsomal (Lipscomb et al. [in press a], for human, Ploemen et al. [1997]Go, for rat) and cytosolic protein content (Boogaard et al., 2000Go).


Since Kf = KfC x BW-03


For tissues, an adjustment factor of 0.1 for conjugation with GSH in tissues other than liver was empirically derived for the rat (Gargas et al., 1995Go), and represents an adjustment for the relative amounts of glutathione-S-transferase activity in the different tissues.



    ACKNOWLEDGMENTS
 
We thank Sara D. Held for measuring the human blood:air partition coefficient for ACN. This research was supported by the Acrylonitrile Group.


    NOTES
 
1 To whom correspondence should be addressed. E-mail: lms29{at}alumni.cwru.edu. Back


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 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX 1
 APPENDIX 2
 REFERENCES
 
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