The Importance of Anatomical Realism for Validation of Physiological Models of Disposition of Inhaled Toxicants

TOXICOLOGY AND APPLIED PHARMACOLOGY ARTICLE NO.

147, 448 – 458 (1997)

TO978289

The Importance of Anatomical Realism for Validation of Physiological Models of Disposition of Inhaled Toxicants Michael C. Kohn Laboratory of Computational Biology and Risk Analysis, National Institute of Environmental Health Sciences, PO Box 12233, Mail Drop A3-06, Research Triangle Park, North Carolina 27709 Received April 25, 1997; accepted August 22, 1997

The Importance of Anatomical Realism for Validation of Physiological Models of Disposition of Inhaled Toxicants. Kohn, M. C. (1997). Toxicol. Appl. Pharmacol. 147, 448 – 458. The goodness of fit of three PBPK models to data for inhalation uptake of 1,3-butadiene by mice from closed chambers were compared. These models included a classical flow-limited model with blood consolidated into arterial and venous compartments, a flowlimited model with implicit blood and alveolar compartments, and a model with an actual alveolar compartment and blood distributed among compartments for arterial, venous, and capillary spaces. Using physiological and biochemical parameters from the literature, all three models reproduced observed steady-state blood butadiene concentrations. However, the first two models predicted more rapid uptake of butadiene than was observed. Assumptions such as ignoring extrahepatic metabolism or reducing the ventilation rate by 75% were required to enable these models to fit the butadiene uptake data. The behavior of the third model resembled that of the other two models when the single-pass extraction ratio of butadiene for all tissues was close to 1, but the model did reproduce observed butadiene uptake when an extraction ratio of 0.5 was used. The difference in predictions of the three models was traced to smaller computed blood:tissue gradients and tissue butadiene concentrations, hence reduced rates of metabolic clearance, when the blood is distributed. These results suggest that the common assumption of flow limitation in the disposition of an inhaled gas may not always be appropriate. Because structurally different models can reproduce the same uptake data and all these models cannot be correct, the assumptions on which these models were based must be investigated experimentally to ensure that they are physiologically realistic.

The mathematical equations in a physiologically based pharmacokinetic (PBPK) model are isomorphic with the structure of the biological system being simulated and, given sufficient data, can predict expected behavior from first principles (Andersen et al., 1995). This high degree of correspondence can provide insight into physiological function and mechanisms of response (D’Souza and Boxenbaum, 1988). It has been suggested (Kohn, 1995) that demonstrating the correspondence between the model’s equations and the properties of 0041-008X/97

the actual biological system should be a major component of the process of validating a model (i.e., demonstrating that a model accurately predicts the system’s actual behavior). Because of the complexity of animal physiology and biochemistry, simplified mathematical representations are required to make simulation of the responses of test animals to toxicants tractable. Such representations differ in the degree to which the structure of the biological system is abstracted, but rarely are the consequences of such simplifications explored. Modeling requires drawing inferences from a large body of data and resolving quantitative inconsistencies among these data. Although this exercise can often be justified on the basis of subject knowledge and experience, the uncertainties associated with the introduced approximations preclude demonstrating that the model is correct or even mathematically unique (Oreskes et al., 1994). For example, fortuitous cancellation of errors may permit several models to reproduce the observed behavior of a real biological system (Oreskes et al., 1994). Models with different levels of detail in their representation of biological structure may yield sufficiently different predictions to permit experimental testing of the models’ validity. Predictions should be tested against data that were not used to construct the model or estimate its parameter values. When physiological modeling was first described by Teorell (1937a,b), computers were unavailable and highly simplified models had to be employed. These models were typically mammillary compartmental models (D’Souza and Boxenbaum, 1988) in which all tissues equilibrated with a single blood compartment. Bischoff and Brown (1966) described how anatomical realism could be introduced into PBPK models and outlined possible simplifications. Lutz et al. (1980) detailed the mathematical representation of transport in such a model. They stated that if the permeability of the cell membrane with respect to a chemical is sufficiently high, the intracellular and interstitial pools of the chemical should be nearly at equilibrium and could be represented by a single compartment. If the permeability is much greater than the tissue perfusion rate, the uptake of the chemical from the tissue capillary space into the tissue space is limited by the rate of blood flow to the tissue. This approximation has become standard in PBPK modeling (Leung, 1991), but the conditions under which the assumption of flow limitation is valid have not been explored sys-

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ANATOMICAL REALISM AND VALIDATION OF MODELS

FIG. 1. Generalized tissue compartmental model. Ai is the amount of chemical in compartment i; Qt is blood flow rate through the tissue; p is the permeability of the tissue (equal to the product of the specific permeability and the surface area accessible to the permeant); P is the tissue:blood partition coefficient.

tematically. This report examines possible consequences of assuming flow limitation. Of particular interest is whether the amount of detail affects the ability of the model to reproduce observed behavior under the assumption of flow limitation. MODEL ASSEMBLY Figure 1 shows a generic tissue submodel including spaces for the tissue and associated capillary blood. A portion of a chemical in the capillary blood is transported into the tissue, and the remainder is swept out of the tissue into the venous effluent at a rate proportional to the tissue blood flow rate (Qt). The contribution of transport to the rate of change of the amount of chemical in the blood (dAb/dt; t 5 time) is the tissue permeability (p) times the concentration of the chemical in the blood (Ab/Vb; Vb 5 volume of tissue capillary blood). The single-pass extraction ratio, e, is the rate of uptake by the tissue divided by the sum of rates of transport from capillary blood to tissue and venous spaces and into capillary blood from the tissue. This sum equals the rate of delivery to the capillary space from arterial blood at steady state. On the first pass of blood through the tissue following administration of the compound there is no chemical in the tissue (At 5 0) and the extraction ratio is

e5

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PBPK model (Fig. 2) in which blood is consolidated into compartments for arterial and venous spaces. This model also includes compartments for lung, liver, kidney, fat, aggregated rapidly perfused tissues (termed ‘‘viscera’’), and aggregated slowly perfused tissues (termed ‘‘muscle’’). Venous blood was treated as flowing into the lung and exiting that tissue as arterial blood. Butadiene in the chamber air was treated as partitioning into the arterial blood. Transport of butadiene between compartments was treated as flow limited, i.e., the unidirectional flux between two compartments is the product of the concentration in the originating compartment times the blood flow rate to that compartment. The second model (Andersen et al., 1987) investigated is a variant of the widely used Ramsey and Andersen (1984) model. It interposes a gas exchange compartment between the venous blood and the lung tissue (Fig. 3). This compartment is associated with the lung capillary blood, which equilibrates with gas in the inhaled air and passes through the lung tissue compartment before joining the arterial blood. This model does not include differential equations for butadiene in the alveoli and the arterial, venous, and lung blood; i.e., no butadiene is stored in these spaces and their volume is implicitly zero. Although these compartments do not participate in mass balance, they are associated with calculated butadiene concentrations. Flow-limited transport of butadiene among these compartments and tissue spaces depends upon these concentrations. A third model (Fig. 4) distributes the blood among arterial, venous, and tissue capillary spaces with nonzero volume, and it includes an alveolar space with nonzero volume. The GI tract was separated from the viscera compartment to permit more realistic representation of hepatic perfusion. For example, 20% of liver perfusion is via the hepatic artery and 80% is via the portal vein, which drains the GI tract capillaries. In the other two models hepatic portal vein flow passes through the liver only.

p A b /V b p A b /V b 5 . p A b /V b 2 p A t /~V t z P! 1 Q t A b /V b p A b /V b 1 Q t A b/V b

The above equation is similar to the equation derived by Gillette (1987) and Wilkinson (1987) for clearance of drugs from the blood. The quantity p is the product of the specific permeability (cm/hr) and the tissue surface area (cm2) accessible to the permeant chemical. Solving for the uptake permeability gives

p5

e Q. 12e t

Accounting for the differences in solubility of the chemical in the tissue and blood, the permeability for export is Qt p e 3 5 . P 12e P The work reported here investigated how large the extraction ratio must be for the permeability to be high enough to satisfy the criterion of Lutz et al. (1980) for flow limitation (p @ Qt). To determine the effects of different mathematical representations on flowlimited distribution, three models of inhalation uptake by mice of 1,3-butadiene from closed chambers were constructed.1 The first model is a classical

1

These models are presented as examples of gas inhalation models and should not be considered definitive models of butadiene uptake.

FIG. 2. Structure of the consolidated blood PBPK model. Blood is divided between arterial and venous compartments in the volumetric ratio of 1:3 (Menzel et al., 1987).

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MICHAEL C. KOHN The mouse tissue:blood partition coefficients used in all three models were from Medinsky et al. (1994) except for muscle, which value the authors said may be unreliable because all the fat may not have been removed from the muscle in their dissections. Their value for rat muscle was used instead. The blood:air partition coefficient of Medinsky et al. (1994) could not reproduce the equilibrium air concentration in closed chambers containing mice treated with dithiocarb to inhibit P450 activity (Kreiling et al., 1986). The average of values for this partition coefficient reported by Medinsky et al. (1994) and Johanson and Filser (1993) did reproduce the equilibrium air concentration and was used instead. The kidney partition coefficient was taken from Johanson and Filser (1993), and their value for the spleen was used for the viscera compartment. The viscera partition coefficient was used for the GI tract when it was separated from the viscera compartment in the distributed blood model. The partition coefficients used in these simulations were 1.95 (blood:air), 1.10 (lung:blood), 1.01 (liver:blood), 0.687 (kidney:blood), 14.3 (fat:blood), 0.649 (viscera:blood), and 1.10 (muscle:blood). Metabolic kinetic constants for P450-catalyzed oxidation of butadiene were obtained from the apparent Km values (2 mM, liver; 5.01 mM, lung) and specific activities measured by Csana´dy et al. (1992) in mouse microsomes. Maximal velocities of 4.66 (liver) and 1.33 (lung) mmol/L/hr were calculated using 30 mg microsomal protein/g liver tissue (Alberts et al., 1983) and 9 mg microsomal protein/g lung tissue (Smith and Bend, 1980). The kidney microsomal activity of Sharer et al. (1992) was converted to maximal velocity (12.9 mmol/L/hr) using 9 mg microsomal protein/g kidney tissue (Coughtrie et al., 1987). The lung Km value was used for the kidney for lack of a measured kidney value. These tissue metabolic activ-

FIG. 3. Structure of the Ramsey–Andersen (1984) PBPK model as modified by Andersen et al. (1987). Compartments for blood and alveolar spaces are denoted by dashed borders to indicate that these spaces have zero volume in this model. The concentrations of chemical in arterial, venous, and lung capillary blood compartments are assumed to be in equilibrium with tissues, and the alveolar concentration is assumed to be in equilibrium with lung blood.

The compartment volumes and blood flow rates used in the three models are given in Table 1. Tissue volumes and perfusion rates in the model are consensus values taken from the literature. The volume of each tissue is identical in all three models. When a compartment in one model is divided into several compartments in another model, the sum of the corresponding spaces is identical to the volume of the undivided compartment in the first model. Capillary blood spaces were taken from Altman and Dittmer (1971). Blood outside of capillary spaces was distributed between arteries and veins in a 1:3 ratio (Menzel et al., 1987). The compartment volumes sum to only 94.7% of the body weight because bone (5.3% of body weight; ILSI, 1994) is omitted. As the Andersen et al. (1987) model does not include differential equations for blood concentrations, the sum of compartment volumes is reduced by the volume of the blood (5% of body weight). An average value of cardiac output (15.3 L/hr/kg0.7) was calculated from literature sources and used for all three models. Blood flow rates sum to 100% of cardiac output for all models. When the GI tract was separated from the viscera in the distributed blood model, the sum of the blood flow rates to these two compartments was identical to the viscera flow rate in the other two models. Similarly, the sum of the portal flow from the GI tract and the hepatic artery flow in the distributed blood model is identical to the total flow to the liver in the other three models. An average value of alveolar ventilation (20.2 L/hr/kg0.7; 70% of minute volume per Arms and Travis, 1988) was also computed from literature sources and used for all three models. Bond et al. (1986) demonstrated that the ventilation rate was unchanged by the presence of butadiene at various concentrations in the inhaled air.

FIG. 4. Structure of the PBPK model with blood distributed among capillary beds of the individual tissues. The GI tract was separated from the rapidly perfused tissues compartment to represent hepatic perfusion in a more anatomically realistic manner. The alveolar space has a nonzero volume.

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ANATOMICAL REALISM AND VALIDATION OF MODELS ities sum to 480 mmol/hr/kg body weight, comparable to the value of 400 mmol/hr/kg estimated by Laib et al. (1990) using a two-compartment model for butadiene uptake. Medinsky et al. (1994) observed that butadiene in the chamber air was adsorbed onto the chamber walls and onto the fur of dead animals placed in the dessicator used in their experiments. Such adsorption was included in the present model. A first-order rate constant of 0.02 hr21, similar to the value estimated by Medinsky et al. (1994), was used in all three PBPK models described here. These models were used to simulate the experiments of Kreiling et al. (1986) in which eight mice averaging 28 g in body weight were placed in 6.4-L desiccators containing air with various initial concentrations of butadiene. The chamber air was sampled at a series of time points during the exposure, and the residual concentration of butadiene was measured. The three models were encoded in SCoP (Kootsey et al., 1986; Kohn et al., 1994; Simulation Control Program available from Simulation Resources, Inc., Berrien Springs, MI). Five to 12.5 hr of exposure was simulated, and the models’ predictions were compared on the basis of how well they reproduced the measured uptake.

RESULTS

The consolidated blood and Andersen et al. (1987) PBPK models both fit (coefficients of variation were about 1%) the equilibration of dithiocarb-treated animals (to inhibit cytochrome P450) with chamber air initially containing 100 ppm butadiene (Fig. 5). The extraction ratio is a parameter in the

FIG. 5. Fit of the three PBPK models to uptake of 1,3-butadiene from closed chambers by eight mice previously treated with the P450 inhibitor dithiocarb. An extraction ratio of 0.5 was used for the distributed blood model; higher values predict a slightly faster approach to equilibrium between the chamber air and the mice.

distributed blood model. As butadiene is likely to enter the tissue by molecular diffusion rather than by a carrier-mediated process, the specific permeability should be the same for all

TABLE 1 Parameter Values in the Physiological Models Consolidated blood model

Andersen et al. (1987) model

Distributed blood model

Tissue compartment volumes (% body weight) Arterial blood Venous blood Lung Alveoli GI tract Liver Kidney Fat Viscera Muscle

1.25 3.75 0.6

5.5 1.67 6 11.43 64.5

0.6

5.5 1.67 6 11.43 64.5 Capillary bed volumes (% tissue volume)

Lung blood GI tract blood Liver blood Kidney blood Fat blood Viscera blood Muscle blood

0.661 1.983 0.6 5 7.5 5.5 1.67 6 3.93 64.5 11 2.9 11 10.2 3 7.1 1.3

Blood flow rates (% cardiac output) GI tract Liver Kidney Fat Viscera Muscle

22.5 16.3 5 22.4 33.8

22.5 16.3 5 22.4 33.8

18.1 4.4 (hepatic artery only) 16.3 5 22.4 33.8

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MICHAEL C. KOHN

FIG. 6. Effect of extraction ratio on the uptake of 1,3-butadiene by eight mice from closed chambers predicted by the distributed blood model. Even at high extraction ratios this model does not predict as rapid uptake as do flow-limited models. Similar results were obtained for other chamber concentrations.

tissue compartments, resulting in similar extraction ratios. Therefore, the same value was used for all tissues in the distributed blood model. Values of e between 0.5 and 0.99 fit the data for butadiene uptake by metabolically inhibited animals with coefficients of variation of 1–2%. The dependence on the extraction ratio of the fit of the distributed blood model to uptake from chambers initially containing 100 ppm butadiene by mice not inhibited with dithiocarb (Kreiling et al., 1986) was investigated to select an appropriate value of the extraction ratio. No other data were used and no other parameters were adjusted. Figure 6 shows the effect of varying e on uptake from chambers containing an initial butadiene concentration of 100 ppm and compares the predicted uptake of this model to that of Andersen et al. (1987). Similar behavior was observed with the consolidated blood model. An extraction ratio of 0.5 gave the best fit (Fig. 6). However, even a value of e 5 0.99 did not predict as rapid uptake as did the flow-limited models. Calculations were performed to confirm that subdividing compartments in the consolidated blood model into separate spaces in the distributed blood model did not affect the total amount of butadiene in the corresponding spaces. For example, all three models predict about 2, 23, and 200 mM butadiene in

the viscera compartment after 1 hr exposure of mice in a chamber initially containing 100, 1000, and 5000 ppm butadiene, respectively. The computed concentrations in the GI tract in the distributed blood model was identical to that in the viscera, indicating that for nonmetabolizing tissues the concentration achieved depends mostly on the tissue:blood partition coefficient. As long as the total tissue volume and blood flow rate are unchanged, subdividing compartments has a negligible effect. Himmelstein et al. (1994) measured butadiene concentrations in the blood of restrained mice exposed nose only. The models were modified to exclude adsorption of butadiene on chamber surfaces and fur and the air concentration of butadiene was held constant at the values used by Himmelstein et al. (1994). The response of the mice was simulated for 6 hr to ensure achievement of a steady state. The computed blood concentrations are compared with the observed values in Table 2. All three models reproduce the data within 20% error, but the distributed blood model fits better than the other two at the highest dose. As steady-state levels are largely determined by the partition coefficients, such a result is not unexpected and demonstrates the importance of using temporal data to validate models. Figures 7 and 8 show the fit of the consolidated blood and Andersen et al. (1987) PBPK models, respectively, to the butadiene uptake data. These models exhibit nearly identical behavior and predict too rapid uptake from the chambers, especially at initial chamber concentrations below 1000 ppm. The distributed blood model with e 5 0.5 fits the uptake data well (Fig. 9) even though only the lowest exposure data were used to estimate the extraction ratio. The source of the difference in predictions can be seen in Table 3, which gives the computed concentrations of butadiene in fat and the metabolizing tissues after a 1-hr exposure of mice in a chamber initially containing 100, 1000, or 5000 ppm butadiene. Distributing the blood among the various capillary spaces introduced a stepped decrease in butadiene concentration in the compartments through which the chemical must pass, significantly reducing calculated tissue concentrations. This was true even for the fat, which serves as a passive storage compartment. The inclusion of intermediary blood compartments predicted smaller gradients between blood and metabolizing compart-

TABLE 2 Steady-State Venous Blood Concentrations (mM) Following Nose-Only Exposure to 1,3-Butadiene for 6 Hr Air butadiene (ppm)

Consolidated blood model

Andersen et al. (1987) model

Distributed blood model

Himmelstein et al. (1994)

62.5 625 1250

2.18 28.8 75.1

2.14 28.7 74.9

2.69 28.6 64.0

2.4 6 0.2 37 6 3 58 6 3

ANATOMICAL REALISM AND VALIDATION OF MODELS

FIG. 7. Fit of the consolidated blood PBPK model to data for uptake of 1,3-butadiene from closed chambers containing eight mice (Kreiling et al., 1986). Coefficients of variation were 13.9% (5000 ppm), 13.3% (2000 ppm), 23.4% (1000 ppm), 32.8% (500 ppm), 33.3% (250 ppm), and 32.3% (100 ppm).

ments (Table 3) and lower rates of transport (Table 4) at most exposures. Hence, a smaller tissue concentration is required to achieve a rate of metabolic clearance that matches the rate of uptake into the tissue (Table 4). The lower concentration in the adipose tissue follows by simple equilibration of butadiene among the compartments. At an initial chamber concentration of 5000 ppm butadiene, however, metabolism is saturated and all three models predict the same blood:tissue gradients (Table 3) and metabolic rates (Table 4). Simulations by deLannoy and Pang (1987) clarify the role of diffusional clearances in extraction of material from hepatic sinusoids. At low diffusional clearances relative to the hepatic

FIG. 8. Fit of the Andersen et al. (1987) PBPK model to data for uptake of 1,3-butadiene from closed chambers containing eight mice (Kreiling et al., 1986). Coefficients of variation were 14.0% (5000 ppm), 13.3% (2000 ppm), 23.2% (1000 ppm), 32.6% (500 ppm), 33.0% (250 ppm), and 32.1% (100 ppm).

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FIG. 9. Fit of the distributed blood PBPK model for uptake of 1,3butadiene from closed chambers containing eight mice (Kreiling et al., 1986). Coefficients of variation were 11.8% (5000 ppm), 5.7% (2000 ppm), 5.4% (1000 ppm), 8.2% (500 ppm), 3.7% (250 ppm), and 6.1% (100 ppm).

blood flow rate, they calculated a considerable gradient between sinusoidal blood and liver tissue, but this gradient was computed to vanish at high diffusional clearance relative to the hepatic blood flow rate. This equilibration between blood and tissue was confirmed in the present simulations with the distributed blood model. With an initial chamber concentration of 1000 ppm and an extraction ratio of 0.5, a 16 mM butadiene gradient was computed between liver blood and liver tissue after a 1-hr exposure (Table 3). At a value of e 5 0.99 this computed gradient vanished, leaving a 21 mM gradient between arterial blood and liver tissue comparable to the 22 mM value obtained with the Andersen et al. (1987) model (Table 3). Parameter sensitivity coefficients were computed by the finite differences method using the SCoP software in order to identify those quantities which have the strongest effects on the computed residual chamber concentration of butadiene after a 1-hr exposure. Sensitivities are given in Table 5 for initial chamber concentrations of 100, 1000, and 5000 ppm butadiene. The cardiac output and ventilation rates were among the most important parameters. At higher doses, the distributed blood model was twice as sensitive to the these rates as were the flow-limited models. The fractional extraction by tissues in the distributed blood model was also an important parameter. Among all the partition coefficients, alteration in Pblood:air was computed to have the largest effect on butadiene uptake. For an initial chamber butadiene concentration of 5000 ppm the sensitivities of the residual chamber air concentration to the fat: blood and muscle:blood partition coefficients were appreciable, owing to the relatively large amount of butadiene stored in those tissues. However, the values of these coefficients were only about 20% of the Pblood:air sensitivity coefficient. Sensitivities to the maximal activities of the metabolizing enzymes increased with increasing dose and were much less important than distribution parameters at the lowest dose.

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MICHAEL C. KOHN

TABLE 3 Computed 1,3-Butadiene Concentrations (mM) Following 1 Hr Exposurea

Chamber

Consolidated blood model

Andersen et al. (1987) model

Distributed blood model

1.88 23.4 165

1.80 29.3 324 2.46 34.3 306 1.68 26.8 295

1.89 23.5 165 1.27 17.6 157 2.47 34.4 306 2.65 37.7 337 2.41 34.2 306 1.65 26.7 296

0.195 12.6 283

0.191 12.5 284

0.353 10.1 190 40.8 544 4156

0.346 10.0 191 40.0 543 4167

2.61 27.2 167 2.13 22.6 158 3.20 35.3 291 3.44 38.6 320 3.20 35.3 292 2.63 29.5 280 1.67 19.4 267 0.129 3.39 244 1.78 21.0 263 0.252 4.67 161 38.3 416 3077

Alveolar

Lung blood

Lung

Arterial

Venous

Liver blood

Liver

Kidney blood

Kidney

Fat

a

Initial chamber concentrations: 100 ppm (roman), 1000 ppm (italic), 5000 ppm (bold).

DISCUSSION

The three PBPK models described here use the same literature values for their physiological and biochemical parameters but differ in the extent of their anatomical detail. The lessdetailed (consolidated blood and Andersen et al., 1987) models were based on the assumption of flow-limited delivery of butadiene to tissues and were unable to reproduce the observed uptake of butadiene from closed chambers. The more detailed (distributed blood) model was able to reproduce observed uptake of the gas if the assumption of flow limitation was removed. It is conceivable that delivery of material to tissues could be reduced below that predicted by flow limitation if butadiene is sequestered in red blood cells. To test this hypothesis, butadiene in the blood compartments was treated as equilibrating between plasma and red blood cells. Using a literature value of 0.45 for the hematocrit (Davies and Morris, 1993), the fractional extraction that would reproduce the uptake of butadiene from the chamber was estimated with the SCoPfit program (part of the SCoP package), using a maximum likelihood criterion. The optimal value was 0.05, suggesting that sequestration in red blood cells does not limit the extraction of butadiene from the blood. PBPK models are often constructed under the assumption that all of the metabolism of a xenobiotic chemical occurs in the liver (Droz, 1986; Leung, 1991) and that the kinetic con-

TABLE 4 Computed Fluxes (mmol/Hr) Following 1 Hr Exposure to 1,3-Butadienea

Alveolar extraction

Lung uptake

Sensitivity to the activity in the lung was relatively significant only at the lowest dose, especially for the distributed blood model. All three models exhibited similar sensitivities to the kinetic constants at 100 ppm initial butadiene concentration. At the highest dose, sensitivities to the enzyme capacities were similar for all three models, but at 1000 ppm the flow-limited models were much more sensitive to uncertainties in these parameters than was the distributed blood model. Sensitivities to the Km values were always smaller than for the maximal activities and were comparable in magnitude to those for the Vmax sensitivities only at an initial chamber concentration of 100 ppm. This behavior is consistent with the property that enzymatic flux does not increase significantly as the substrate concentration approaches saturating values.

Lung metabolism

Liver uptake

Liver metabolism

Kidney uptake

Kidney metabolism

a

Consolidated blood model

Andersen et al. (1987) model

Distributed blood model

8.22 77.1 106 0.471 1.50 1.71 0.473 1.53 1.76 5.01 49.3 56.6 5.11 49.5 57.0 3.17 32.2 46.9 3.18 32.2 47.0

8.22 77.2 107 0.616 1.55 1.71 0.618 1.58 1.76 5.00 49.3 56.6 5.01 49.5 57.0 3.11 32.1 46.9 3.11 32.2 47.0

6.40 60.0 118 0.726 1.56 1.71 0.728 1.58 1.76 3.47 36.1 56.5 3.47 36.1 56.9 2.31 23.3 46.7 2.31 23.3 46.8

Initial chamber concentrations: 100 ppm (roman), 1000 ppm (italic), 5000 ppm (bold).

ANATOMICAL REALISM AND VALIDATION OF MODELS

TABLE 5 Parameter Sensitivity Coefficients of Residual Chamber 1,3-Butadiene Following 1 Hr Exposurea

Parameter Cardiac output

Ventilation rate

Pblood:air

Consolidated blood model

Andersen et al. (1987) model

20.169 20.377 20.413 20.116 20.362 20.253 20.214 21.10 24.13

20.176 20.370 20.411 20.115 20.359 20.246 20.214 21.09 24.04

20.011 21.39 21.91 20.00976 20.0466 20.0596 20.0172 20.849 21.58

20.0111 21.39 21.93 20.00845 20.0434 20.0578 20.0173 20.853 21.59

Extraction ratio

Liver Vmax

Lung Vmax

Kidney Vmax

Distributed blood model 20.123 21.02 20.737 20.104 20.796 20.521 20.157 21.41 23.51 20.123 21.01 20.732 20.00332 20.282 21.83 20.0151 20.0357 20.0576 20.00628 20.217 21.51

a

Initial chamber concentrations: 100 ppm (roman), 1000 ppm (italic), 5000 ppm (bold).

stants can be estimated by fitting the gas uptake data (e.g., Andersen et al., 1984; Fisher et al., 1991). Johanson and Filser (1993), Evelo et al. (1993), and Medinsky et al. (1994) have described PBPK models of the Andersen et al. (1987) type for butadiene disposition. Metabolic kinetic constants in these models were adjusted to obtain the best fit to the uptake data. The results of the present study indicate that this modeling strategy can lead to erroneous estimates of distribution of enzymatic activity and concentrations of the toxicant achieved in the target tissues. To investigate the relationship between the models presented here and previous modeling work, the lung and kidney P450 activities were set to zero in the present model of the Andersen et al. (1987) type. The modified model matched the observed uptake of butadiene from the chamber for initial chamber butadiene concentrations of 100 –1000 ppm but underpredicted uptake for initial concentrations of 2000 and 5000 ppm. This behavior, due to flow-limited delivery of butadiene to the liver at low doses and saturation of the hepatic metabolizing enzyme at high doses, was obtained by Johanson and Filser (1993) also. Increasing the metabolic capacity in the liver compartment in excess of its measured value (see above) permits fitting the high-dose data while maintaining a good fit at low doses where clearance is limited by delivery to the liver. Johanson and Filser (1992) observed that clearances of inhaled gases from closed chambers are, on average, 60% of the

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rates calculated from an inhalation model of the Ramsey– Andersen type. Such a model assumes that inhaled air instantaneously equilibrates with the blood and that net uptake is directly proportional to the chemical concentration in the ambient air. These assumptions are supported by simulations with the distributed blood model in which the concentration of butadiene in the air was held constant. The concentration of butadiene in the lung capillary blood was computed to achieve 90% of its steady-state value within 10 –20 min of the start of exposure. The computed butadiene absorption rate was roughly linear in exposure concentration for exposures up to 1000 ppm, but deviated from linearity at higher doses where the computed metabolic rate was a substantial fraction of the tissue capacity. Extraction of butadiene from the air was not constant, however. The calculated fraction of butadiene in the inspired air that is absorbed into the blood steadily declined with increasing exposure concentration—from 19% at 1 ppm to 4% at 5000 ppm. The discrepancy between observed and calculated clearances may be due to reduced ventilation because of chemicalinduced irritation or anesthesia or to adsorption of the chemical in the airway on inhalation and desorption on exhalation (Johanson and Filser, 1992). In either case, the amount of inhaled chemical reaching the alveolar space might be reduced relative to the amount predicted by the measured ventilation rate, but different chemicals would be expected to affect delivery of the chemical to different extents. As Bond et al. (1986) found butadiene not to affect the ventilation rate, only the hypothesis of temporary adsorption of inhaled material in the airway is consistent with the observations for this gas. Johanson and Filser (1993) employed a 40% reduction in the measured ventilation rate in their PBPK model of butadiene disposition. A 75% reduction in the ventilation rate in the consolidated blood and Andersen et al. (1987) models described here was required to abolish the overprediction of uptake by these models. The difference in the reduction in ventilation rate required by the Johanson and Filser and current models is due to the omission or inclusion of extrahepatic metabolism, corresponding to whole-body metabolic clearance rates of 320 and 480 mmol/hr/kg body wt, respectively. In the PBPK models described here, the sum of the in vitro Vmax values for the metabolizing enzymes agrees with the maximal in vivo whole-body clearance rate. Thus, modeling can be used to demonstrate that in vitro data are consistent with in vivo observations. The hepatic specific activity for butadiene oxidation found by Sharer et al. (1992) is equivalent to 634 mmol/hr/kg body wt, almost 60% higher than the whole-body elimination rate. This lack of correspondence suggests that the conditions of the assay or the calculations performed in arriving at the enzymatic activity conflict with in vivo conditions. Because the butadiene uptake computed by these models is sensitive to the enzyme tissue capacities, careful measurement of these activities under conditions representative of in vivo conditions is essential for understanding their role in butadiene uptake.

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The simulations reported here suggest that very high extraction ratios are required to satisfy the assumption of rapid equilibration between blood and tissue. Measurement of the single-pass extraction ratio for a chemical in isolated organs perfused with blood containing an inhibitor of the chemical’s metabolism can test the assumption of flow limitation. The simulations also demonstrate that very large reductions in measured ventilation rates are required for flow-limited models to match gas uptake data when extrahepatic metabolism is included. The extent of alveolar extraction and holdup of material by the airway mucosa could be measured using the isolated perfused ventilated lung (Skelly and Shertzer, 1983) to test the hypothesis of reduced delivery of a gas to the alveolar compartment. Because structurally different models can produce comparable fits to uptake data and all of these models cannot be correct, such data are insufficient for validation of a proposed model. The models do predict different tissue concentrations of butadiene at given exposures. Comparison of the predictions to such data would be more likely to discriminate among competing candidate models. The differences in kinetics arising from different distributions of material in anatomical spaces indicates that measurements of tissue concentration time courses would be most useful in selecting the correct model. Introduction of assumptions at variance with measured physiological behavior and the consequent necessary adjustment of parameter values may actually hinder identification of the correct model. Anatomically realistic representations of competing hypotheses that do not ignore or alter observed properties of the system under study would help discriminate among competing models. As indicated by the sensitivity analysis, verification of the correctness of the mathematical representations of inhalation, distribution, and the tissue activities of the metabolizing enzymes would be most effective in reducing the uncertainties concerning the adequacy of these PBPK models. APPENDIX Equations for the Consolidated Blood Compartments Model TotalVentilation 5 Ventilation 3 BodyWeight0.7 3 animals TotalBloodFlow 5 CardiacOutput 3 BodyWeight0.7 3 animals Air9 5 2TotalVentilation 3 Air/AirVolume 1 TotalVentilation 3 Arterial/ (ArterialVolume 3 AirPartition) 2 kadsorb 3 Air Arterial9 5 TotalVentilation 3 Air/AirVolume 2 TotalVentilation 3 Arterial/ (ArterialVolume 3 AirPartition) 2 FatFlow 3 Arterial/ArterialVolume 2 LiverFlow 3 Arterial/ArterialVolume 2 KidneyFlow 3 Arterial/ArterialVolume 2 VisceraFlow 3 Arterial/ArterialVolume 2 MuscleFlow 3 Arterial/ArterialVolume 1 TotalBloodFlow 3 Lung/(LungVolume 3 LungPartition) Venous9 5 LiverFlow 3 Liver/(LiverPartition 3 LiverVolume) 1 Kidney Flow 3 Kidney/(KidneyPartition 3 KidneyVolume) 1 VisceraFlow 3 Viscera/(VisceraPartition 3 VisceraVolume) 1 FatFlow 3 Fat/(FatPartition 3 FatVolume) 1 MuscleFlow 3 Muscle/(MusclePartition 3 Muscle Volume) 2 TotalBloodFlow 3 Venous/VenousVolume Lung9 5 TotalBlood Flow 3 Venous/Venous Volume 2 Total BloodFlow 3 Lung/(LungVolume 3 Lung Partition) 2 V lung max z Lung/ (Klung 1 Lung) m

Liver95 Liver Flow 3 Arterial/ArterialVolume 2 LiverFlow 3 Liver/ liver (LiverPartition 3 LiverVolume) 2 V liver 1 Liver) max z Liver/(K m Kidney9 5 KidneyFlow 3 Arterial/ArterialVolume 2 Kidney Flow 3 kidney Kidney/(KidneyPartition 3 KidneyVolume) 2 V kidney 1 max z Kidney/(K m Kidney) Fat9 5 FatFlow 3 Arterial/Arterial Volume 2 FatFlow 3 Fat/(Fat Partition 3 FatVolume) Viscera9 5 VisceraFlow 3 Arterial/Arterial Volume 2 VisceraFlow 3 Viscera/ (VisceraPartition 3 VisceraVolume) Muscle9 5 MuscleFlow 3 Arterial/ArterialVolume 2 MuscleFlow 3 Muscle/(MusclePartition 3 MuscleVolume) Equations for the Andersen et al. (1987) Model TotalVentilation 5 Ventilation 3 BodyWeight0.7 3 animals TotalBloodFlow 5 CardiacOutput 3 BodyWeight0.7 3 animals ArterialConc 5 Lung/(LungVolume 3 LungPartition) VenousConc 5 (LiverFlow 3 Liver/(LiverPartition 3 LiverVolume) 1 (KidneyFlow 3 Kidney/(Kidney Partition 3 Kidney Volume) 1 FatFlow 3 Fat/(FatPartition 3 FatVolume) 1 VisceraFlow 3 Viscera/(VisceraPartition 3 VisceraVolume) 1 MuscleFlow 3 Muscle/(MusclePartition 3 MuscleVolume))/TotalBloodFlow LungBloodConc 5 (TotalBloodFlow 3 VenousConc 1 TotalVentilation 3 Air/AirVolume)/(TotalBloodFlow 1 TotalVentilation/AirPartition) AlveolarConc 5 LungBloodConc/AirPartition Air9 5 2TotalVentilation 3 Air/AirVolume 1 TotalVentilation 3 AlveolarConc 2 kadsorb 3 Air Lung9 5 TotalBloodFlow 3 LungBloodConc 2 TotalBloodFlow 3 Arterial lung Conc 2 V lung 1 Lung9) max z Lung/(K m Liver9 5 LiverFlow 3 ArterialConc 2 Liver Flow 3 Liver/(LiverPartition 3 liver LiverVolume) 2 V liver 1 Liver) max z Liver/(K m Kidney9 5 KidneyFlow 3 ArterialConc 2 KidneyFlow 3 Kidney/(KidneyPartition 3 Kidney Volume) 2 V kidney z Kidney/(K kidney 1 KidneyFat9) max m 5 FatFlow 3 ArterialConc 2 FatFlow 3 Fat/(Fat Partition 3 FatVolume) Viscera9 5 VisceraFlow 3 ArterialConc 2 VisceraFlow 3 Viscera/(VisceraPartition 3 VisceraVolume) Muscle9 5 MuscleFlow 3 ArterialConc 2 MuscleFlow 3 Muscle/(MusclePartition 3 MuscleVolume) Equations for the Distributed Blood Model TotalVentilation 5 Ventilation 3 BodyWeight0.7 3 animals TotalBloodFlow 5 CardiacOutput 3 BodyWeight0.7 3 animals Perm 5 ExtractionRatio/(1 2 ExtractionRatio) Air9 5 2TotalVentilation 3 Air/AirVolume 1 TotalVentilation 3 Alveolar/ AlveolarVolume 2 kadsorb 3 Air Alveolar9 5 TotalVentilation 3 Air/AirVolume 2 TotalVentilation 3 Alveolar/AlveolarVolume 2 TotalVentilation 3 Alveolar/AlveolarVolume 1 TotalVentilation 3 LungBlood/(LungBloodVolume 3 AirPartition) LungBlood9 5 TotalVentilation 3 Alveolar/AlveolarVolume 2 TotalVentilation 3 LungBlood/(LungBloodVolume 3 AirPartition) 1 TotalBloodFlow 3 Venous/VenousVolume 2 TotalBloodFlow 3 LungBlood/LungBloodVolume 1 TotalBloodFlow 3 Perm 3 Lung/(LungPartition 3 LungVolume) 2 TotalBloodFlow 3 Perm 3 LungBlood/LungBloodVolume Arterial9 5 TotalBloodFlow 3 LungBlood/LungBloodVolume 2 LiverFlow 3 Arterial/ArterialVolume 2 KidneyFlow 3 Arterial/ArterialVolume 2 FatFlow 3 Arterial/ArterialVolume 2 VisceraFlow 3 Arterial/ArterialVolume 2 MuscleFlow 3 Arterial/ArterialVolume 2 GItractFlow 3 Arterial/ArterialVolume Venous9 5 2TotalBloodFlow 3 Venous/VenousVolume 1 (LiverFlow 1 GItractFlow) 3 LiverBlood/LiverBloodVolume 1 KidneyFlow 3 KidneyBlood/KidneyBloodVolume 1 FatFlow 3 FatBlood/FatBloodVolume 1 VisceraFlow 3 VisceraBlood/VisceraBloodVolume 1 MuscleFlow 3 MuscleBlood/ MuscleBloodVolume LiverBlood9 5 LiverFlow 3 Arterial/ArterialVolume 1 GItractFlow 3 GItractBlood/ GItractBloodVolume 2 (LiverFlow 1 GItractFlow) 3 LiverBlood/LiverBlood-

ANATOMICAL REALISM AND VALIDATION OF MODELS Volume 2 (LiverFlow 1 GItractFlow) 3 Perm 3 LiverBlood/LiverBloodVolume 1 (LiverFlow 1 GItractFlow) 3 Perm 3 Liver/(LiverPartition 3 LiverVolume) KidneyBlood9 5 KidneyFlow 3 Arterial/ArterialVolume 2 KidneyFlow 3 KidneyBlood/KidneyBloodVolume 2 KidneyFlow 3 Perm 3 KidneyBlood/KidneyBloodVolume 1 KidneyFlow 3 Perm 3 Kidney/(KidneyPartition 3 Kidney Volume) FatBlood9 5 FatFlow 3 Arterial/ArterialVolume 2 FatFlow 3 FatBlood/FatBloodVolume 2 FatFlow 3 Perm 3 FatBlood/FatBloodVolume 1 FatFlow 3 Perm 3 Fat/(FatPartition 3 FatVolume) VisceraBlood9 5 VisceraFlow 3 Arterial/ArterialVolume 2 VisceraFlow 3 VisceraBlood VisceraBloodVolume 2 VisceraFlow 3 Perm 3 VisceraBlood/VisceraBloodVolume 1 VisceraFlow 3 Perm 3 Viscera/(VisceraPartition 3 Viscera Volume) MuscleBlood9 5 MuscleFlow 3 Arterial/ArterialVolume 2 MuscleFlow 3 MuscleBlood/MuscleBloodVolume 2 MuscleFlow 3 Perm 3 MuscleBlood/MuscleBloodVolume 1 MuscleFlow 3 Perm 3 Muscle/(MusclePartition 3 Muscle Volume) GItractBlood9 5 GItractFlow 3 Arterial/ArterialVolume 2 GItractFlow 3 GItract Blood/GItractBloodVolume 2 GItractFlow 3 Perm 3 GItractBlood/GItract BloodVolume 1 GItractFlow 3 Perm 3 GItract/(VisceraPartition 3 GItractVolume) Lung9 5 TotalBloodFlow 3 Perm 3 LungBlood/LungBloodVolume 2 TotalBloodFlow 3 Perm 3 Lung/(LungPartition 3 LungVolume) 2 V lung max z Lung/ (K lung m 1 Lung) Liver9 5 (LiverFlow 1 GItractFlow) 3 Perm 3 LiverBlood/LiverBloodVolume 2 (LiverFlow 1 GItractFlow) 3 Perm 3 Liver/(LiverPartition 3 LiverVolume) 2 liver V liver max z Liver/(K m 1 Liver) Kidney9 5 KidneyFlow 3 Perm 3 KidneyBlood/KidneyBloodVolume 2 KidneyFlow 3 Perm 3 Kidney/(KidneyPartition 3 KidneyVolume) 2 V kidney max z Kidney/ (K kidney 1 Kidney) m Fat9 5 FatFlow 3 Perm 3 FatBlood/FatBloodVolume 2 FatFlow 3 Perm 3 Fat/(FatPartition 3 FatVolume Viscera9 5 VisceraFlow 3 Perm 3 VisceraBlood/VisceraBloodVolume 2 VisceraFlow 3 Perm 3 Viscera/(VisceraPartition 3 VisceraVolume) Muscle9 5 MuscleFlow 3 Perm 3 MuscleBlood/MuscleBloodVolume 2 MuscleFlow 3 Perm 3 Muscle/(MusclePartition 3 MuscleVolume) GItract9 5 GItractFlow 3 Perm 3 GItractBlood/GItractBloodVolume 2 GItractFlow 3 Perm 3 GItract/(VisceraPartition 3 GItractVolume)

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