Physiological Modeling Reveals Novel Pharmacokinetic Behavior for Inhaled Octamethylcyclotetrasiloxane in Rats

Melvin E. Andersen*, Ramesh Sarangapani{dagger},1, Richard H. Reitz{ddagger}, Robert H. Gallavan§, Ivan D. Dobrev* and Kathleen P. Plotzke§

* Department of Environmental Health, CETT/Foothills Campus, Colorado State University, Fort Collins, Colorado 80523; {dagger} ICF Consulting, K. S. Crump Group, PO Box 14348, Research Triangle Park, North Carolina 27709; {ddagger} RHR Toxicology Consulting Services, Midland, Michigan 48640; and § Toxicology, Health and Environmental Sciences, Dow Corning Corporation, Midland, Michigan 48686

Received June 27, 2000; accepted November 30, 2000


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Octamethylcyclotetrasiloxane (D4) is an ingredient in selected consumer and precision cleaning products. Workplace inhalation exposures may occur in some D4 production operations. In this study, we analyzed tissue, plasma, and excreta time-course data following D4 inhalation in Fischer 344 rats (K. Plotzke et al., 2000, Drug Metab. Dispos. 28, 192–204) to assess the degree to which the disposition of D4 is similar to or different from that of volatile hydrocarbons that lack silicone substitution. We first applied a basic physiologically based pharmacokinetic (PBPK) model (J. C. Ramsey and M. E. Andersen, 1984, Toxicol. Appl. Pharmacol. 73, 159–175) to characterize the biological determinants of D4 kinetics. Parameter estimation techniques indicated an unusual set of characteristics, i.e., a low blood:air (Pb:a {cong} 0.9) and a high fat:blood partition coefficient (Pf:b {cong} 550). These parameters were then determined experimentally by equilibrating tissue or liquid samples with saturated atmospheres of D4. Consistent with the estimates from the time-course data, blood:air partition coefficients were small, ranging from 1.9 to 6.9 in six samples. Perirenal fat:air partition coefficients were large, from 1400 to 2500. The average Pf:b was determined to be 485. This combination of partitioning characteristics leads to rapid exhalation of free D4 at the cessation of the inhalation exposure followed by a much slower redistribution of D4 from fat and tissue storage compartments. The basic PK model failed to describe D4 tissue kinetics in the postexposure period and had to be expanded by adding deep-tissue compartments in liver and lung, a mobile chylomicron-like lipid transport pool in blood, and a second fat compartment. Model parameters for the refined model were optimized using single-exposure data in male and female rats exposed at three concentrations: 7, 70, and 700 ppm. With inclusion of induction of D4 metabolism at 700 ppm (3-fold in males, 1-fold in females), the parameter set from the single exposures successfully predicted PK results from 14-day multiple exposures at 7 and 700 ppm. A common parameter set worked for both genders. Despite its very high lipophilicity, D4 does not show prolonged retention because of high hepatic and exhalation clearance. The high lipid solubility, low blood:air partition coefficient, and plasma lipid storage with D4 led to novel distributional characteristics not previously noted for inhaled organic hydrocarbons. These novel characteristics were only made apparent by analysis of the time-course data with PBPK modeling techniques.

Key Words: siloxane; pharmacokinetics; rat; inhalation; PBPK modeling..


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Cyclic methyl siloxanes have a repeating [-O-Si(CH3)2-]n structure. The tetramer, octamethylcyclotetrasiloxane (D4), is used in selected consumer products. D4 (CAS number 556-67-2) is a colorless, odorless liquid with a boiling point of 175°C and vapor pressure of 0.681 torr at 20°C. Thus, there is a potential for daily low-level exposure to D4 by both dermal and inhalation routes in the workplace and to consumers. These organosilicone compounds are regarded to have very low biological activity. However, because of the widespread use of D4 and the potential for human exposure, a comprehensive program has been initiated to expand the safety profile of D4.

McKim et al. (1998, 1999) reported liver and thyroid enlargement, increases in cell division and hepatocyte size, and induction of hepatic enzymes following repeated inhalation exposure to high concentrations of D4 in Fischer 344 rats. The profile of metabolic enzymes induced by D4 has also been observed after dosing with the rat liver and thyroid tumor promoter phenobarbital (PB). Among the induced proteins are cytochrome P450s 2B1/2 in both female and male F344 rats. Transient hepatic and thyroid hyperplasia and increases in liver size are also observed after administration of PB (Dragan et al., 1994Go, 1996Go; Kolaja et al., 1996Go). The mode of action for these short-term hepatic effects of D4 is not known. However, based on analogy with PB, they are likely to be the result of changes in gene expression and proliferative actions on hepatocytes resulting from interaction of D4 or some metabolite(s) with the putative PB receptor. Dose–response analysis of these hepatic changes will require knowledge of the time course of D4 in liver for various exposure conditions. At present, it has not been possible to definitively conclude that D4, rather than a metabolite, is responsible for these effects. However, the differences in structure between parent D4 and the monomeric and dimeric linear metabolites would seem to favor D4 as the active inducing compound. In addition, Sarangapani et al. (2001) have successfully described the induction of hepatic CYP 2B1/2 with a pharmacodynamic model that includes interaction of D4 with a putative receptor.

Recently, Plotzke et al. (2000) measured the retention, distribution, metabolism, and excretion of D4 in male and female Fischer 344 rats following single or multiple (15 consecutive days) 6-h/day exposures to 7, 70, and 700 ppm of radiolabeled D4. The radioactivity from 14C-labeled D4 was widely distributed throughout the rat tissues following inhalation. The radioactivity time courses in the tissues of male and female rats were similar and the disposition of radioactivity in the multiple-exposure experiments was similar to that seen in the single-exposure studies.

Only limited efforts have been made to model the disposition of D4. As part of ongoing research to understand the disposition of inhaled D4, Utell et al. (1998) measured respiratory uptake of D4 in 12 healthy volunteers. Using a steady-state analysis, Utell et al. (1998) derived an analytical expression to compute deposition efficiency of D4 in the lung as a function of minute ventilation. Their steady-state model assumed that diffusional resistance in the gas exchange region limited uptake of D4 by the lung and completely ignored any role for metabolism as a factor in determining uptake of the parent D4. Metabolism of inhaled vapors is known to be the major determinant of the proportion of inhaled vapor that is retained in the body at steady-state exposure conditions (Andersen, 1981Go).

In this paper we develop a physiologically based pharmacokinetic (PBPK) inhalation model to quantitatively characterize the retention, distribution, and elimination of parent D4 and its hydrolysis and oxidation products from the body following controlled inhalation exposures in the rat. Concentration of D4 in plasma, liver, lung, fat, exhaled breath, and urinary metabolite excretion data from the single-exposure and multiple-exposure experiments (Plotzke et al., 2000Go) formed the basis for model calibration and validation. This PBPK model is intended to provide the basis for estimating tissue dosimetry of D4 and to support risk assessment extrapolations across dose, dose route, and species for D4 and possibly for other volatile cyclic methyl siloxanes.


    MATERIALS AND METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Experimental data.
Single-exposure and multiple-exposure studies were performed with male and female F344 rats exposed by inhalation to 7, 70, and 700 ppm of D4 (Plotzke et al., 2000Go). In single-exposure studies, these animals were exposed to 14C-D4 vapor for 6 h in a cylindrical flow-past nose-only inhalation chamber following a conditioning period of 4 days. In multiple-exposure studies, after receiving the same conditioning, animals received a 6-h exposure of unlabeled D4 for 14 consecutive days followed by a 6-h exposure of 14C-D4 vapor on the 15th day. Immediately after the last exposure, rats were placed in glass metabolism cages for collection of excreta (urine and feces) and expired air. Excreta were collected at 6, 12, and 24 h and subsequently at 24-h intervals up to 168 h postexposure. Expired volatiles were collected at 1, 2, 4, 6, 9, 12, and 24 h and at 24-h intervals up to 168 h postexposure. In addition to these two end points, blood, perirenal fat, lung tissue, and liver tissue samples were processed for radioactivity measurements and chemical analysis of parent D4 at similar time points.

Radioactivity was widely distributed throughout the rat tissues following inhalation, with the highest concentrations in the lung, liver, and fat. The peak concentration of D4 in most of the solid tissues and in plasma occurred within 1 h postexposure. The radioactivity time course in these tissues showed multiphasic behavior, characterized by a relatively rapid initial decline up to 24 h postexposure followed by a much slower terminal phase. Radioactivity persisted longer in the fat, with peak concentrations occurring only after several hours (3–24 h) postexposure. Unlike the other tissues, the decline in fat D4 concentration was monoexponential. Plotzke et al. (2000) also observed that the excretion of radioactivity following exposure to radiolabeled D4 was mainly via exhaled breath and urine, and to a much lesser extent in the feces. Whereas the radioactivity in the expired volatiles was almost all parent D4, the radioactivity detected in the urine was entirely due to metabolized D4. The radioactivity time courses in the tissues of male and female rats were similar and the disposition of radioactivity in the multiple-exposure experiments was similar to that seen in the single-exposure studies. No attempt was made to remove the urine from contact with the chamber air during collection of excreta. This is unlikely to lead to any serious errors, as the concentration of volatile parent in urine was very low and the time course of appearance of volatiles in the air was consistent with exhalation, without the pulsatile behavior that would be expected by episodic urination.

Basic PK model structure.
A basic PBPK model structure used in the first part of this analysis was an inhalation model initially developed to study the disposition of inhaled styrene (Ramsey and Andersen, 1984Go) and inhaled methyl chloroform (Reitz et al., 1988Go). It has been applied successfully to a diverse variety of compounds since 1984 with very good success. D4, like styrene, is a volatile compound that is biotransformed through a pathway that starts with a single dominant oxidation step: epoxidation for styrene and oxidative demethylation for D4. The initial model structure applied to analyze the disposition of D4 in rats consisted of five compartments: fat, liver, blood, a group of rapidly perfused tissues, and a group of slowly perfused tissues (Fig. 1Go). The individual tissue compartments are connected by the systemic circulation. The model has distinct venous and arterial blood compartments and the tissues are described as homogenous well-mixed tissue compartments. In this model, all D4 in the blood equilibrates with D4 in the alveolar air. In the model development, plasma and blood concentrations are assumed to be equal, as reported by Plotzke et al. (2000).



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FIG. 1. Schematic of the basic PBPK model developed to study D4 kinetics. The basic model consists of a lung compartment for gas exchange, slowly perfused tissue (muscle/skin), rapidly perfused tissue (viscera), adipose tissue compartment (fat), and liver compartment for metabolism.

 
The arterial blood flows out of the lung compartment at a rate equal to the cardiac output and supplies D4 to the tissue compartments. Parent D4 is stored in the fat and other tissue compartments depending on their physiological parameters, i.e., tissue volumes, regional blood perfusion rates, and tissue:blood partition coefficient. The venous blood exiting each compartment is equilibrated with the mixed mean tissue concentration of D4 in the respective compartments. The venous effluents of the various compartments combine to yield a flow-averaged venous concentration of D4. The mixed venous blood returns to the lung at a flow rate equal to the cardiac output. Metabolism of D4 occurs in the liver by a single metabolic pathway following saturable (Michaelis-Menten) kinetics. In vitro measurements of enzyme activity in the liver of control rats and rats repeatedly exposed to D4 vapor indicate that enzymes involved in the metabolism of D4 are induced upon multiple exposures (McKim, 1998Go; McKim et al., 1998Go), with maximal induction occurring after 3 or 4 days of exposure. Enzyme induction in the liver is accounted for empirically in the model for the 700-ppm exposure group.

To simulate metabolite clearance data observed experimentally, a simplified description of total metabolite kinetics was appended to the model for D4. Metabolism of D4 results in at least seven different metabolic products with linear arrangements of the siloxane units (Varaprath et al., 1999Go). In general, the metabolism of D4 appears to follow a sequence in which an initial methyl oxidation produces an intermediate that is subject to hydrolysis and ring opening. This process would yield a linear trimer and a monomeric siloxane unit. Subsequent hydrolysis of the trimer would produce dimers and monomers. Our PK model was not designed to track the concentration of individual metabolites of D4, as insufficient information was available for this purpose from the inhalation studies. Instead, the model described clearance of the two metabolites produced from the oxidation/hydrolysis ring breaking using first-order elimination rate constants for each of the two metabolites from the plasma to the urine. The concentration of the metabolites in plasma was calculated by dividing the total amount of metabolite in the body by a constant volume of distribution. The schematic for the metabolite pool in this model was similar to that used in the refined model in Figure 2Go.



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FIG. 2. Schematic of the refined PBPK model to study D4 kinetics in rats. In addition to the compartments in the basic structure, the refined model has multiple fat compartments and deep compartments to sequester D4 in the lung, liver, and blood.

 
Refined PK model.
Predicted kinetic behaviors from the basic PK model were in poor correspondence with the data for postexposure tissue and plasma concentrations. Because D4 is highly lipophilic, a sizable fraction of inhaled D4 is sequestered in various fat stores in the body. To account for the unusual physiochemical properties of this chemical, the basic model was altered using an iterative, hypothesis-driven model refinement process (Fig. 2Go). To model sequestered D4, a - compartment, which represents the tissue lipid, was added to the liver and the lung-tissue compartments. The shallow tissue compartment contains free D4 in equilibrium with the blood perfusing the tissues. The net transport of D4 between the deep compartment and the shallow tissue compartments is equal to the product of a diffusional transfer coefficient and the concentration gradient of free D4 between the two compartments. Equations for these transport processes are found in the Appendix.

Blood concentrations of D4 in the postexposure period fall off much less rapidly than is predicted by the basic model in which all circulating D4 is available for exhalation and metabolism. Several alternate model structures were evaluated that included a persistent nonexchangeable pool of D4 in blood. One strategy had a deep lipid compartment in blood similar to the compartments included in liver and lung. This pool of D4 would be derived from the pool of free D4 in blood. A second strategy followed earlier work with lipophilic compounds in which a blood-lipid pool was modeled to include lipid secretion from the sequestered liver compartment, accumulation in a blood-lipid pool, and removal of the blood lipid by fat (Fig. 2Go). This transported-lipid compartment in blood can be regarded as similar to the transport of chylomicrons from the liver to peripheral tissue. The concentration of D4 in this mobile blood-lipid pool is determined by a production rate of carrier lipid from the liver to the blood and a removal rate of D4 from blood into fat. For this model, the mass of D4 produced in the liver and transported to the blood was derived from the shallow liver compartment.

A sizable fraction of the inhaled D4 is retained in the fat stores in the body and is not readily accessible for exchange into blood and exhalation from the lung. Typically, the various fat depots in the body, such as the perirenal, epididymal, and omental fat, as well as the adipose component of tissues, are grouped and represented as a single fat compartment in PK models (Kety, 1951Go; Ramsey and Andersen, 1984Go). This lumping process is valid when the characteristic time constant for chemical disposition in the various regions is comparable. In the refined model, the various fat stores were further subdivided. The size of adipose tissue of a 0.2-kg rat is approximately 4% of body weight (Brown et al., 1997Go). In the refined model, fat depots in the body have been apportioned into two compartments: one small fat compartment (~ 0.5% of body weight) that represents a sequestered fat depot in the body such as the perirenal fat and another diffuse fat compartment (~ 3.5% body weight) that constitutes the remaining mass of adipose tissue in the body. This distribution was partially derived from curve fitting, as will be described later.

Thus, the refined PK model (Fig. 2Go) has multiple fat compartments, sequestered lipid compartments in lung and liver, and a mobile blood-lipid pool derived from the liver. As noted later, the model with sequestered lipid in blood derived from the free D4 in blood performs poorly in fitting single-exposure and multiple-exposure data. Mass balance equations that describe the rate of change of parent D4 in the various compartments and the total excreted metabolite in the urine appear in the Appendix. The resulting series of differential equations were solved by numerical integration using the Gear Algorithm for stiff systems in ACSL® (Advanced Continuous Simulation Language, Pharsight, Palo Alto, CA). The model was coded so as to simulate both single- and multiple-exposure experiments and output the D4 concentration time course in the lung, liver, fat, blood, urine, and expired air.

Parameterization.
Physiological parameters such as tissue volumes and blood perfusion rates for the various organs were obtained from the literature (Brown et al., 1997Go). These model parameters are provided in Table 1Go. All other parameters in the model, such as partition coefficients and metabolic and absorption rates, had to be estimated from the experimental data. The challenge was to derive a set of parameter values that would simultaneously fit a relatively large set of data on parent D4 concentration in tissue, plasma, fat, urine, and exhaled air collected in male and female rats following both single and multiple exposures for three different exposure concentrations. The basic model has 10 adjustable parameters, including the blood:air partition coefficient, the various tissue:blood partition coefficients (i.e., lung, liver, fat), the Michaelis-Menten kinetic parameters for metabolism, first-order excretion rate of D4 metabolites into urine, uptake clearance to the fat (Appendix), the maximum fractional increase in metabolic capacity with induction, and the volume of distribution of the metabolites. In addition to these parameters, the refined model has partition coefficients for the deep, sequestered lipid compartments in the liver and lung, transfer rates for D4 into blood from liver, and blood perfusion rate to the multiple sequestered tissue compartments, resulting in 18 adjustable parameters.


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TABLE 1 Physiological Parameters for Tissue Weight and Regional Perfusion Used in the Rat Model
 
Trial-and-error methodology for parameter estimation is inefficient, especially when the number of model parameters to be estimated is large. The approach used to overcome this simultaneous parameterization problem was a sequential estimate-and-fit method using the method of maximum log-likelihood function (LLF) as implemented in the ACSL® software (Collins et al., 1999Go; Keys et al., 1999Go). The optimal parameter set for a given model structure is one that maximizes the LLF.

In order to apply a sequential estimate-and-fit approach, the various data sets available for fitting the model were ordered in a nested series, where all of the parameters estimated with a previous data set in the series can be held fixed while fitting the next data set. The first step in applying this methodology was to identify the key parameter(s) that has the maximal influence on a particular pharmacokinetic measurement. For instance, the dominant parameters that influence the D4 concentration in the fat compartments are the fat:blood partition coefficient and the blood perfusion rates to these compartments. The optimization algorithm varied these parameters until the model-derived fat D4 concentration optimally fit the experimental data. The performance of the fit was evaluated using both visual inspection and statistical evaluation. With a statistical evaluation, a contour plot was generated using the LLF as the objective function (Fig. 3Go). The contour plot helped identify the parameter values that give the maximum LLF and the parameter range within which this maximum was embedded. Once the optimization was completed for a given set of parameter(s), the next set of parameters influencing another pharmacokinetic dose measure was varied to fit the model to the new data, while all the previously estimated parameters were held fixed. This process was continued in a systematic manner until all the model parameters were estimated. These parameter estimates, obtained by optimizing the individual PK data set sequentially, were used as the seed value for a global optimization where all parameters are estimated simultaneously using the complete PK data set.



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FIG. 3. Contour plot of the log-likelihood function following optimization of the refined model to fit the fat D4 pharmacokinetic data using the fat:blood partition coefficient and the blood perfusion rate to the fat compartment, showing dependence of LLF on parameters 1 and 2.

 
Model optimization.
Parameter estimations were completed using single-exposure PK data from all three dose levels in both the male and female F344 rats. For the basic model, the following sequence was adopted to arrive at an initial estimate for all the model parameters: (1) the blood:air partition coefficient, the liver:blood partition coefficient, and the kinetic constants in the liver were optimized using the liver D4 time-course data; (2) the fat:blood partition coefficient and the uptake clearance rate to the fat compartment were optimized using fat D4 PK data; (3) the lung:blood partition coefficient was optimized using the lung tissue D4 PK data; (4) the first-order excretion rates of D4 metabolites into urine and the volume of distribution were optimized using excreta PK data; and (5) the maximum fractional increase in metabolic capacity was optimized using liver tissue D4 PK data following multiple-day exposure to 700 ppm D4. As induction has been shown to occur only after repeated exposure to high doses of D4 (McKim, 1998Go; McKim et al., 1998Go), the INDmax parameter, i.e., the maximal fold-induction over the basal Vmax for metabolism, was set to zero while simulating single exposures and low-dose multiple exposures. Furthermore, this parameter was optimized separately for male and female rats, as induction has been shown to be gender specific. A different sequence was followed to ensure that the optimization procedure converged on the same final values for the various parameters.

The initial value for blood:air partition coefficient was estimated from the time course in plasma. For the refined model, the following sequence was then adopted to arrive at an initial estimate for all the model parameters: (1) the blood:air partition coefficient, the liver and deep-liver:blood partition coefficients, the transfer rate between the shallow- and deep-liver compartments, and the kinetic constants for metabolism in the liver were estimated using the liver D4 PK data; (2) the tissue:blood partition coefficient and the apparent blood perfusion rate to the fat compartment were estimated using the fat D4 data; (3) the diffuse-fat:blood partition coefficient and the apparent blood perfusion rate to the diffuse fat compartment were estimated from the exhaled air D4 PK data; (4) lung:blood partition coefficients and the transfer rate between the shallow-lung and deep-lung compartments were estimated using the lung-tissue D4 data; (5) transfer rates into and out of blood via the lipid pool were estimated from plasma D4 data; and (6) the first-order excretion rates of D4 metabolites into urine and the volume of distribution were estimated from the data on rate of excretion into the urine.

The optimized values, obtained by sequential fitting of the model to the individual PK data sets, were used as the initial values in a global optimization process. For the global optimization, all model parameters were simultaneously estimated using the Nelder-Mead algorithm on the complete PK data set. The heteroscedasticity parameter (Bard, 1974Go; Collins et al., 1999Go; Steiner et al., 1990Go) was two for all the optimization runs in order to minimize the relative error between the predicted and observed D4 concentrations. Table 2Go lists all the optimized parameters in the basic and the refined models.


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TABLE 2 Initial Estimate and the Optimized Values for Parameters Used in the Basic and Refined Model
 
Partition coefficients.
Although the original goals of the PBPK modeling with D4 were to assess the partitioning and metabolic parameters based on the time course of D4 following inhalation, the novelty of the kinetic behavior observed and the inferences regarding unusual partition characteristics derived from the PBPK modeling effort required independent verification of these conclusions. Partition coefficients were estimated by equilibrating rat blood, corn oil, water, or saline homogenates of perirenal fat, liver, kidney, and lung from several rats with a saturated atmosphere of D4 at 37°C (Table 3Go).


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TABLE 3 Sample-to-Air Partition Coefficients for D4 at 37°C
 
To accomplish equilibration, a series of scintillation vials was placed in a large-mouthed plastic canister (about 500 ml volume) with a screw-top seal. The vials were filled with the four fluids, except for one vial, which contained several milliliters of D4 (98% purity, obtained from Aldrich Chemical Co., St. Louis, MO). The large-mouthed canister had a sampling port bored into the cap. The canister was sealed and placed in a water bath and gently agitated for 24 or 48 h. Two sampling times were used to ensure that the samples were equilibrated. The atmosphere was sampled through the port on the top of the canister. After air sampling, the canister was carefully opened and aliquots of the samples were transferred to a conical separatory funnel containing either tetrahydrofuran (THF) or hexane.

Following volume adjustment, the mixture of THF and test sample was briefly centrifuged, and samples of the supernatant were removed and analyzed for D4. When using hexane, samples of the hexane layer were removed and water was removed by adding magnesium sulfate. Analysis for D4 was carried out using an HP 6890 gas chromatograph (GC) equipped with a capillary column (HP-5, 3-m/0.32 mm with 0.25-µM film thickness) and flame ionization detection (FID). FID gases were hydrogen and synthetic air. Nitrogen, at a flow rate of 1.5 ml/min, was used as the carrier gas. The GC oven was held at 40°C for 1 min and heated at 10°C/min to a final temperature of 180°C. The injector port and detector temperatures were 150 and 250°C, respectively. One-microliter aliquots of samples were injected in splitless mode. Under these conditions, D4 retention time was 8.51 min. Data analysis was performed using HP Chemstation software. Prior to experimentation, calibration curves were constructed by dilutions of THF in air.


    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
The basic model was optimized as noted previously, and the values obtained for the optimized parameter estimates are listed in Table 2Go. Figure 4Go compares the basic model performance with experimentally measured data in the exhaled air, fat, urine, liver, lung, and plasma, respectively. These plots compare model output in male and female rats with PK measurements at three different exposure concentrations (700, 70, 7 ppm) for the single exposure. Model predictions were then compared to PK measurements at two different dose levels (700, 7 ppm) for the multiple exposures for both genders (Fig. 5Go). The parameterization analysis used all the single-exposure results to estimate model parameters. The multiple-exposure kinetics in Figure 5Go were predicted using these parameters. The multiple-exposure prediction served as a test of the model with another data set.




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FIG. 4. AC. Plots comparing basic model simulations to experimentally observed D4 concentration in (A) exhaled air, (B) fat, and (C) excreted urine in female and male rats following a single 6-h exposure to D4 at three different dose levels (7, 70, and 700 ppm). Error bars represent standard error of the mean. DF. Plots comparing basic model simulations to experimentally observed D4 concentration in (D) liver tissue, (E) lung tissue, and (F) plasma in female and male rats following a single 6-h exposure to D4 at a dose level of 700 ppm. Error bars represent standard error of the mean.

 



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FIG. 5. AB. Plots comparing basic model simulations to experimentally observed D4 concentration in (A) exhaled air and (B) fat in female and male rats following a 6-h/day, 14-day exposure to D4 at two different dose levels (7 and 700 ppm). Error bars represent standard error of the mean. CE. Plots comparing basic model simulations to experimentally observed D4 concentration in (C) liver tissue, (D) lung tissue, and (E) plasma in female and male rats following a 6-h/day, 14-day exposure to D4 at 700 ppm. Error bars represent standard error of the mean.

 
This basic model provides reasonable fits to D4 concentration in the fat and liver tissue following both single and multiple exposure. However, the model performed poorly in predicting D4 concentrations in plasma (Fig. 4FGo), lung tissue (Fig. 4EGo), expired air (Fig. 4AGo), and the excreted D4 metabolites in the urine. The model underestimated plasma concentrations by several orders of magnitude in the postexposure period for both single and for the repeat exposures. The exhalation rate of D4 was also poorly represented by the basic model. With the single exposure, the predicted rate of D4 exhalation showed systematic errors at each of the three concentrations (Fig. 4AGo). Similar discrepancies were also present when the basic model was used to predict the multiple-exposure, exhaled-air D4 curves (Fig. 5AGo).

The model prediction of plasma D4 immediately after exposure drops sharply due to the low blood:air partition coefficient and the high fat:blood partition coefficient. The former leads to rapid exhalation clearance of D4 at the cessation of exposure, and the latter leads to very slow redistribution after the cessation of the exposure. The persistence of D4 in blood after cessation of exposure at concentration orders of magnitude above those predicted by the basic model indicates that the D4 in the blood was not free and available for exhalation. The tissue:blood partition coefficients required to fit liver and lung concentrations, assuming well-mixed tissues, were also very large. With these values (see Table 2Go), the initial concentrations in the organs were significantly overestimated and the lung concentrations were never adequately described, even in the postexposure period.

Concentrations of D4 in the plasma, lung, and liver were polyexponential, characterized by a rapid initial decline followed by a slower terminal phase. Such a concentration time-course data for a compound with a low blood:air partition coefficient indicated that a sizable fraction of D4 in these tissues at later times is in a sequestered state, inaccessible for direct exchange with free D4 in blood. This reasoning led us first to construct a second-generation model with deep-tissue compartments in the lung and liver. The deep-liver and deep-lung compartments in the refined model were used to account for the tissue-lipid fraction that effectively sequesters lipophilic compounds in a manner similar to that used for methylene chloride (Angelo and Pritchard, 1984Go). A similar compartment was included in the blood where free D4 in plasma diffused into a deep lipid pool in the blood. This model improved the description of the time course of D4 in liver, lung, and blood for the single exposures. However, any description with a deep sequestered compartment in blood that communicated with the free D4 blood compartment overpredicted the multiple-day plasma data (Fig. 6Go). Thus, the refined model structure also contained a sequestered lipid pool in the blood that was formed by transport of lipid from a shallow-liver compartment to blood and from blood to the diffuse-fat compartment. The transported-lipid compartment in blood in the refined model conceptually accounts for liver-peripheral tissue transport of chylomicrons enriched in D4. A similar, although more biologically detailed, model construct was developed to describe the disposition of nonvolatile chlorinated biphenyls and dioxins (Roth et al., 1993Go, 1994Go).



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FIG. 6. Model behavior when the blood contains a sequestered liver compartment filled by diffusion from the pool of free plasma D4. Parameters that fit the single-day time-course data in male rats at 700 ppm predict accumulation following multiple exposures to 700 ppm D4 in male rats, in contrast to the observations.

 
In addition to the blood-lipid pool, the enhanced model subdivided the fat into two discrete subcompartments. The concentration time course for D4 in the exhaled air was multiphasic, with rapid exhalation of free D4 immediately following cessation of exposure and a more gradual decline in expired D4 concentration a few hours postexposure. This behavior occurs because a sizable fraction of the inhaled D4 is retained in the various fat stores in the body and is slowly exchanged into blood at different rates, depending on the clearance characteristics for the individual fat stores in the body. The basic model structure with a single fat compartment performed poorly while predicting D4 concentration in exhaled air. To account for D4 kinetics in exhaled air, the fat stores in the body were subdivided in the refined model. The adipose tissue was modeled as two fat compartments, each with a distinct time constant. This model improved the description of the time course of D4 in exhaled air for the single exposures (Fig. 7Go).



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FIG. 7. Model fit to exhaled air PK data following single 6-h exposure to 700 ppm. D4 in male rats. Model simulations using one and two fat compartments. Error bars represent standard error of the mean.

 
Figure 8Go compares curves obtained with the refined model to experimentally measured PK data in the exhaled air, fat, urine, liver, lung, and plasma following single exposures. In all cases, the refined model performed better than the basic model. To partially validate the model parameterization procedure, the optimized values derived using the single-exposure PK data were used to predict blood, tissue, excreta, and exhaled air D4 concentration following multiple exposures (Fig. 9Go). The refined model accurately predicts the multiphasic decline in D4 concentration in the exhaled air and the gradual accumulation and decline in the fat D4 concentration following multiple-day, 6-h exposures to D4. It also predicts a gradual increase in the average value of the cyclicly varying lung-tissue D4 concentration during the 15-day exposure and rapid decline in the tissue D4 concentration postexposure. A similar trend was predicted for the liver tissue D4 concentration. However, the model fit the postexposure concentration data in the liver only after accounting for a 3-fold induction of metabolism in male rats and 1-fold increase in female rats (Fig. 10Go). Inclusion of induction improved the fit to both the liver and the plasma D4 time-course data in the multiple exposures in males. The improvement of the plasma curve occurred because the input into the plasma compartment is from the liver. Although the refined model has some discrepancies with the multiple-day plasma D4 concentration, the overall consistency of the refined model and the time-course data increases confidence in both the model structure and parameterization. In addition to making comparison using visual inspection, the ability of the each alternate structure to fit the experimental data was compared quantitatively using a log-likelihood ratio test.




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FIG. 8. AC. Plots comparing refined model simulations to experimentally observed D4 concentration in (A) exhaled air, (B) fat, and (C) excreted urine in female and male rats following a single 6-h exposure to D4 at three different dose levels (7, 70, and 700 ppm). Error bars represent standard error of the mean.

DF. Plots comparing refined model simulations to experimentally observed D4 concentration in (D) liver, (E) lung, and (F) plasma in female and male rats following a single 6-h exposure to D4 at a dose level of 700 ppm. Error bars represent standard error of the mean.

 



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FIG. 9. AB. Plots comparing refined model simulations to experimentally observed D4 concentration in (A) exhaled air, and (B) fat in female and male rats following 6-h/day, 14-day exposure to D4 at two different dose levels (7 and 700 ppm). Error bars represent standard error of the mean.

CE. Plots comparing refined model simulations to experimentally observed D4 concentration in (C) liver tissue, (D) lung tissue, and (E) plasma in female and male rats following a 6-h/day, 14-day exposure to D4 at 700 ppm. Error bars represent standard error of the mean.

 


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FIG. 10. Improvements in the model fit to liver tissue D4 pharmacokinetic data after inclusion of enzyme induction in male rats following multiple-day exposures to 700 ppm D4. Error bars represent standard error of the mean.

 
Model Discrimination
The process of maximizing the log-likelihood function not only helps in parameter estimation, but is also a statistically rigorous tool for model discrimination. Two models that have the same functional form, wherein one model is a reduction or subset of the other, are called "nested" models. The likelihood ratio test is applied to statistically compare nested models. In general, Model One is preferred to Model Two if the maximum likelihood attainable with Model One is greater than Model Two. The likelihood ratio test states that two models are equivalent if twice the difference between their maximum log likelihood is lesser than or equal to the chi-square distribution (Bard, 1974Go; Collins et al., 1999Go; Steiner et al., 1990Go)

where {lambda} is the maximum likelihood ratio and {chi}2f,{alpha} is a chi-square distribution with f degrees of freedom and a significance level of {alpha} (or a confidence level of 1-{alpha}). The degrees of freedom (f) are the difference in the number of adjustable parameters between the two models. This null hypothesis is rejected when the product of –2 and the log of the maximum likelihood ratio is greater than {chi}2f,{alpha}.

With addition of a new fat compartment to the refined model, three additional degrees of freedom are introduced into the model (fat compartment volume, fat:blood partition coefficient, and blood perfusion rate). In the refined model, the total body fat volume was fixed at 4% of the body weight and only the diffuse-fat:blood partition coefficient and blood perfusion rate were varied to fit the exhaled air PK data. The difference in degrees of freedom between the models is two. The optimized LLF using the one and two fat compartment models were 190.2 and 414.0, respectively. The chi-square distribution value for two degrees of freedom at a confidence level of 0.99 is 9.2 (Steiner et al., 1990Go). Since –2*(190.2–414) = 447.6 is greater than 9.2, the null hypothesis is rejected and the model performance is shown to improve statistically with the addition of a second fat compartment. Splitting the adipose tissue into more fat compartments did not result in marked improvements to the model fit. Hence, the final refined model used two fat compartments.

Although the refined model gives a better visual fit and improved LLF compared to the basic model for all the PK data, the results with the two model structures also need to be compared statistically. To complete the statistical evaluation, all the parameters that were optimized in the basic model were reoptimized in the refined model along with the new parameters unique to the latter. The overall LLF for the basic and the refined model are –215.7 and 398.6, respectively (Table 4Go). The difference in the number of adjustable parameters between the two models is 10. The chi-square distribution value for 10 degrees of freedom and at a confidence level of 0.99 is 23.21 (Steiner et al., 1990Go). Since

the refined model can be said to give a statistically better fit than does the basic model.


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TABLE 4 Comparing the Optimized LLF of the Basic and Refined Models Exhaled airLLF for basic modelLLF for refined model
 
Partition Coefficients
The partition coefficients for D4 in corn oil, blood, and several tissues were determined to assess whether the inferences drawn from parameter estimation, based on kinetic data, compared well with direct measurement (Table 3Go). The blood partition coefficient derived from extensive equilibration with a saturated atmosphere of D4 (1.9 to 6.9) was somewhat higher than that estimated from the parameter estimation routine (0.9). The fat:blood partition coefficient estimated as the average of the various determinations of fat:air and blood:air partition coefficients was 485. This value should be compared with the estimate obtained from the fitting procedure of 550. We regard this as good agreement, as the curve fitting determines the partition coefficient of a lumped fat compartment rather than the perirenal fat compartment alone. With the methods used here, we were unable to estimate the water:air partition coefficient due to the very low solubility of D4 in the water and the presence of column artifacts when trying to measure very low levels of D4 in the sample.


    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Organosiloxane Physical Characteristics
D4 has unusual tissue solubility characteristics. With volatile hydrocarbons, blood:air and tissue:air partition coefficients tend to increase in a roughly parallel manner. For styrene, the blood:air partition coefficient (Pb:a) is about 40 and fat:blood partition coefficient (Pf:b) is close to 86 (Gargas et al., 1989Go). Substitution of oxygen into the hydrocarbon tends to increase Pb:a and decrease Pf:b. Despite the presence of oxygen in the D4 ring, the blood:air partition coefficient is very low and the fat:blood partition coefficient is very high. For most inhaled substances, high blood:air partitioning with high lipophilicity leads to more prolonged elimination by exhalation from blood after cessation of exposure. With D4 the elimination of free compound from blood by exhalation is very rapid and the residual contribution to blood concentrations is expected to arise from slow redistribution from lipid storage compartments. Plotzke et al. (2000) report that the radioactivity time course of D4 in plasma and other solid tissue was multiphasic, characterized by a rapid initial decline up to 24 h postexposure followed by a much slower terminal phase. This behavior is qualitatively consistent with such a redistribution.

The partition coefficients measured in vitro by equilibration of a saturated D4 atmosphere with blood and fat were consistent with the estimates derived from fitting the time-course curves, although the in vivo and in vitro estimates of the blood:air partition coefficient differed by about a factor of 5. This discrepancy will need further evaluation by assessing the behavior of other siloxanes. However, it is of some interest that, in the experience of one of the authors (MEA), a similar discrepancy occurred with another compound, hexane. Hexane inhalation kinetics were studied by Baker and Rickert (1981). In their studies with inhalation exposures spanning concentrations from 200 to 10000 ppm, the estimated blood:air partition coefficient was about 0.8. This partition coefficient was estimated in a series of PBPK modeling studies; some of which were reported in a U.S. technical report (Andersen and Clewell, 1983Go). The partition coefficient estimated by vial equilibration methods (Gargas et al., 1989Go) was higher (2.29 ± 0.11).

Discrepancies between D4 and Results with Other Volatiles
It is of some interest to compare the behavior of D4 with other inhaled volatile compounds to see if the unusual partitioning characteristics with D4 produce different kinetic behaviors. The basic PK model used here had already successfully described the tissue kinetics after inhalation exposures for many different volatile compounds. However, this model failed to predict plasma and tissue levels of D4, requiring alteration in the model structure. Our approach with D4 was to focus on the exhaled air time course as a reliable measure of the free form of exchangeable D4 in blood. Thus, when initially examining the rat inhalation studies, efforts were made to fit the plasma concentrations at the end of exposure to estimate the blood:air partition coefficient. We concluded that the persistence of D4 in blood was related to a pool that could not be available for exhalation. Thus, the basic model failed with the estimation of blood D4, while performing much better with the estimation of the exhalation rate of D4. More than any other factor, the availability of the exhaled breath data provided confidence in modifying the conventional basic model structure to include different lipid storage compartments in the refined PK D4 model.

Recognizing the Unusual Behavior
Interestingly, neither the analysis of the human time course of D4 during and after a 1-h inhalation exposure (Utell et al., 1998Go) nor the qualitative analysis of the rat time-course curves (Plotzke et al., 2000Go) by themselves indicated any discrepancy from results with other inhaled volatiles. The exhalation curves and the blood kinetic curves in each case looked coherent, decreasing polyexponentially. A physiological modeling approach, however, provided an expectation of the shape and time course of tissue concentrations based on physical, chemical, and physiological processes. Through the lens of a model-based analysis, the coherent curves noted by observation were actually displaced in concentrations by orders of magnitude. It remains to be seen if this lipid sequestration behavior is quantitatively important with other lipophilic volatile compounds. This behavior was only apparent with D4 because of the low blood: air partition coefficient. The more lipophilic organic hydrocarbons have a much higher Pb:a and correspondingly smaller exhalation clearance.

The Lipid Storage Compartments
The major changes in the refined model were the addition of several storage compartments for D4 that were not well mixed with respect to blood concentrations. These compartments were 1) the deep lipid compartments in the liver and lung; 2) the diffusion-limited fat tissue compartments; and 3) the mobile lipid pool in blood. Further studies will be helpful in examining the physiological basis of these deep compartments. This modeling work indicates that the blood-lipid compartment is unlikely to be a simple lipid portion of blood with a diffusional limitation in filling from the free blood compartment. A model with transport of lipid from liver to other tissue was more successful and was at least partially validated by the prediction of the multiday exposure time-course behavior in plasma. The compartmentalization of D4 in blood in the postexposure period could be evaluated by fractionation of blood lipids and analysis of the pools with which the D4 is associated. We rationalize the present model as consistent with storage of D4 in a lipid particle with a charged aqueous surface structure, i.e., in chylomicronlike structures. The hydrophilic surface layer could impede diffusion to the blood and permit carriage of the D4 in the particle to fat stores in the body without appreciable molecular diffusion through the hydrophilic surface into the blood.

Lastly, the deep-tissue compartments were modeled with volumes equal to expected percentages of lipid in the individual tissues. This lipid is obviously not a well-defined depot. Rather, it is diffusely distributed within the organ. The validity of modeling the distribution in relation to fat content might be evaluated by studying animals with different fat lipid contents.

Persistence of Lipophilic Compounds
Clearly, some nonvolatile lipophilic compounds have the potential to accumulate and persist in the body for long periods of time. The multiple-day studies with D4 do not show significant accumulation. The attributes that lead to accumulation are lipophilicity, poor metabolism, and the absence of clearance pathways from the body other than metabolism. With D4 there are two significant clearance pathways: metabolism and exhalation. In the rat, intrinsic metabolic clearance from the liver, given by the ratio of Vmax to Km, is sufficiently large that hepatic clearance approaches liver blood flow at low inhaled concentrations. In addition, pulmonary clearance of a volatile compounds is approximated by cardiac output times the ratio of 1/(1+Pb:a). For D4, with Pb:a {cong} 0.9, pulmonary clearance is over 50% of cardiac output. Thus, these two clearance pathways serve to rapidly deplete free concentrations and create concentration gradients that move D4 from the lipid compartments into the circulation, where it can be metabolized or exhaled. Induction of metabolism with flow-limited hepatic clearance will not enhance clearance at low concentrations; however, it will extend the concentration range over which flow-limited metabolic clearance contributes (Andersen, 1981Go). Thus, the induction of metabolism can only be evaluated at the higher inhaled concentration—700 ppm. Clearance at 7 and 70 ppm would be insensitive to enhanced Vmax, as the clearance at these concentrations is limited by hepatic blood flow.

Dose Measures
This study focused solely on kinetics without a direct measure of response upon which to base analysis of dose measures related to D4. The goal with most PK models is estimation of the free concentration of compounds, whether environmental compounds or drugs, in target tissues. For compartments that are assumed to be well mixed with blood, the dose to the tissue of free compound is accurately represented by the blood time course of free compound. With D4, however, the free compound in blood is not easily calculated from direct measurement of total D4, especially in the postexposure period. The PK model will be useful for tracking both total and free D4. Either free, sequestered, or some combination of these D4 pools may be the measure of dose to liver tissue for the observed biochemical and physiological responses. Modeling efforts that relate free or total liver D4 to the effects on liver will be important as the next step in determining which of these measures of dose is more closely related to the biological effects of D4. The initial expectation is that the responses should relate to free D4.

Comparison with Other Modeling Efforts
Utell et al. (1998) provided a model to account for reductions in retention of inhaled D4 as ventilation rates increased. Their model assumed that the reduced uptake with increasing ventilation was solely related to an inherent diffusion limitation in transfer of D4 from alveolar spaces to arterial blood in the alveolus without any contribution from metabolism. Our present model is more consistent with previous descriptions with other volatiles for the expected relationship between net uptake and metabolism (Andersen, 1981Go). However, the present model also assumes that alveolar D4 equilibrates with arterial blood according to the blood:air partition coefficient of D4, i.e., there is no diffusional limitation to uptake. Evaluation of the time course of uptake into human blood in the volunteer study showed rapid equilibration during the exposure, suggesting that there is actually little diffusional resistance to equilibration. With other metabolized volatile compounds, the uptake from inhaled air after reaching tissue steady state is primarily due to metabolism (Andersen, 1981Go). The extraction from the airstream, equivalent to the retention efficiency described by Utell et al. (1998), is readily expressed in the present model in terms of ventilation (Qp) and hepatic clearance (Clh) (see Andersen, 1981).


As demonstrated by this relationship, the extraction of compound from the airstream will diminish as the ventilation rate increases. The extent of diminution with changes in ventilation rates depends on the relative values of liver clearance and ventilation. The results of Utell et al. (1998) in humans are also consistent with this relationship, even though their empirical model had no explicit term for metabolism.

In summary, compared to other volatile lipophilic compounds, D4 has unusual distributional properties that became apparent only when the time-course data for blood and tissues were examined with a quantitative PBPK model. Its low blood:air partitioning and high fat:blood partitioning led to its incorporation into lipid storage compartments that were not equilibrated with free circulating D4. Despite the unusual transport and storage behavior in lipid compartments, high pulmonary and hepatic clearance, coupled with induction of metabolizing enzymes at high exposure concentrations, rapidly remove free D4 from the body and ensure that there is no accumulation on multiple exposures. D4 may serve as a useful model compound to assess fat compartment characteristics in test animal species. Inferences regarding tissue and blood solubilities derived from fitting the time-course data for D4 agreed well with experimental determinations of these parameters.


    APPENDIX
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
In the refined model, inhaled D4 in alveolar air equilibrates rapidly with arterial blood. Mass conservation in the lung stipulates that the loss of D4 from the inhaled air is balanced by the amount gained in the arterial blood and the lung tissue. Furthermore, the transport of D4 from a deep-lung tissue compartment provides for an additional elimination pathway (Fig. 2Go). The transport of D4 between the shallow and deep-lung tissue compartments is modeled by a diffusional clearance process. The diffusional flux of D4 between the shallow and deep layers is proportional to the concentration gradient of free D4 between the two compartments. The rate of change of mass of D4 (mg/h) in the shallow-lung tissue is then given by

where Clu is concentration of free D4 in the lung tissue (mg/l), Vlu is the volume of lung tissue (L), Cin is the inhaled D4 concentration (mg/l), Qp and Qc are the alveolar ventilation and cardiac output, respectively, in l/h, and Plu:b, Pb:a, Pdlu:b are the tissue:blood, blood:air, and deep-lung tissue:blood partition coefficients, respectively, and Dlu is the diffusional clearance from the lung to the deep-lung compartment (l/h). In this formulation, free D4 in the arterial blood equilibrates very rapidly with D4 in the alveolar air and free D4 in the lung tissue. Hence, the ratio of D4 concentration in arterial blood to that in alveolar air and the shallow lung tissue is a constant specified by the blood:air and tissue:blood partition coefficients, respectively.

The rate of change of D4 in the liver is a balance between amount gained due to blood perfusion and the cumulative amount lost due to metabolism, transfer to deep-liver tissue and elimination of mass into the mobile lipid pool in blood. The rate of change of parent D4 in the liver is formulated as

where Vli is the volume of the liver tissue, Ca is the concentration of parent D4 in the arterial blood, K1 is the first-order elimination of D4 from the liver to the blood via the chylomicronlike pool, Vmax,t (mg/h) and Km (mg/l) are the kinetic parameters for D4 metabolism in the liver, Cli/Pli:b and Cdli/Pdli:b are the free D4 concentration in liver and deep liver, respectively, and Dli is the diffusional clearance from the liver to the deep-liver compartment. Enzyme induction in the liver for male rats at 700 ppm is accounted for using an empirical relation

where V0max (mg/h) is the normal enzyme activity, INDmax is the maximum fractional increase in the metabolic capacity due to induction, and T0.5 is the half-life for induction.

The rate of change of amount of D4 in the slowly and richly perfused tissues is equal to the difference in flux into the tissue due to arterial blood flow and efflux due to free concentration in the venous blood:

where Vt is the volume of the tissue compartment, Qt is the perfusion rate to the tissue, and Ct/Pt:b is the free concentration in the tissue. As transport of D4 into very poorly perfused tissues such as the adipose tissue can be diffusion limited, they are modeled as two compartments: a fat-tissue compartment and a parallel blood compartment (Fig. 11Go).



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FIG. 11. Axial and radial transport processes governing the mass balance in the fat compartment.

 
Assuming well-mixed conditions in the blood, the net flux between the blood and fat is flux = K(Cv - Cf/Pf:b), where Ca (mg/L) is the arterial concentration, Cv (mg/L) is the venous concentration, and Cf/Pf:b (mg/L) is the D4 concentration in the fat-blood interface, and K is the diffusional transfer coefficient (l/h). For overall mass balance to hold, the rate of gain of D4 in the fat compartment should equal the rate of loss of D4 in the blood compartment, which in turn should equal the net flux of D4 from the blood into the fat compartment. Hence,

Rearranging the terms, the rate of change of amount of D4 in the fat can be expressed as

where Q*f if the apparent perfusion rate to the fat compartment. The terms for uptake clearance for the two fat compartments, Q*f, in Table 2Go represent this mixture of flow and diffusional uptake into the fat tissue from the fat blood.


    ACKNOWLEDGMENTS
 
We thank Dow Corning Corporation for support for this work and Ms. Suzanne Cecil for providing expert technical assistance in the preparation of this manuscript. We also appreciate the thoughtful review of early drafts of this manuscript by Dr. Justin Teeguarden, The K. S. Crump Group, Inc., and Ms. Amy Collins, Chemical Industry Institute of Toxicology, for assistance with statistical model evaluation. This work was supported in part by the Silicones Environmental, Health and Safety Council of North America.


    NOTES
 
1 To whom correspondence should be addressed. Fax: (919) 547-1710. E-mail: rsarangapani{at}icfconsulting.com. Back


    REFERENCES
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 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
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