ToxSci Advance Access originally published online on January 31, 2003
Toxicological Sciences 72, 3-18 (2003)
Copyright © 2003 by the Society of Toxicology
BIOTRANSFORMATION AND TOXICOKINETICS |
Physiological Modeling of Inhalation Kinetics of Octamethylcyclotetrasiloxane in Humans during Rest and Exercise
Micaela B. Reddy*,1,
Melvin E. Andersen*,
Paul E. Morrow
,
Ivan D. Dobrev*,
Sudarsanan Varaprath
,
Kathleen P. Plotzke and
Mark J. Utell
* Quantitative and Computational Toxicology Group, Center for Environmental Toxicology and Technology, Colorado State University, Fort Collins, Colorado 80523;
University of Rochester Medical Center, Departments of Medicine and Environmental Medicine, Pulmonary/Critical Care Division, Rochester, New York 14642; and
Toxicology, Health and Environmental Sciences, Dow Corning Corporation, Midland, Michigan 48686
Received July 16, 2002;
accepted November 13, 2002
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ABSTRACT
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In a recent pharmacokinetic study, six human volunteers were
exposed by inhalation to 10 ppm
14C-D
4 for 1 h during alternating
periods of rest and exercise. Octamethylcyclotetrasiloxane (D
4)
concentrations were determined in exhaled breath and blood.
Total metabolite concentrations were estimated in blood, while
the amounts of individual metabolites were measured in urine.
Here, we use these data to develop a physiologically based pharmacokinetic
(PBPK) model for D
4 in humans. Consistent with PBPK modeling
efforts for D
4 in the rat, a conventional inhalation PBPK model
assuming flow-limited tissue uptake failed to adequately describe
these data. A refined model with sequestered D
4 in blood, diffusion-limited
tissue uptake, and an explicit pathway for D
4 metabolism to
short-chain linear siloxanes successfully described all data.
Hepatic extraction in these volunteers, calculated from model
parameters, was 0.65 to 0.8, i.e., hepatic clearance was nearly
flow-limited. The decreased retention of inhaled D
4 seen in
humans during periods of exercise was explained by altered ventilation/perfusion
characteristics during exercise and a rapid approach to steady-state
conditions. The urinary time course excretion of metabolites
was consistent with a metabolic scheme in which sequential hydrolysis
of linear siloxanes followed oxidative demethylation and ring
opening. The unusual properties of D
4 (high lipophilicity coupled
with high hepatic and exhalation clearance) lead to rapid decreases
in free D
4 in blood. The success of D
4 PBPK models with a similar
physiological structure in both humans and rats increases confidence
in the utility of the model for predicting human tissue concentrations
of D
4 and metabolites during inhalation exposures.
Key Words: octamethylcylcotetrasiloxane; D4; inhalation pharmacokinetics; PBPK modeling; vapor retention; flow-limited metabolism; lipid sequestration.
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INTRODUCTION
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Octamethylcyclotetrasiloxane (D
4), a silicone fluid with a molecular
weight of 296, is an additive in personal care products, an
ingredient in high-performance cleaning products, and an intermediate
in the production of silicone polymers. Repeated inhalation
exposures of Fischer 344 (F344) rats to D
4 resulted in the induction
of CYP 2B family enzymes and epoxide hydrolase in the liver,
a pattern similar to the enzyme induction profile for phenobarbital.
Exposure to D
4 also produced hepatomegaly, transient hepatic
hyperplasia, and sustained hypertrophy in rats in a manner similar
to that resulting from phenobarbital exposure (McKim
et al.,
2001
). The general population may be exposed to low levels of
D
4 by the dermal and inhalation exposure routes, and workplace
exposures may occur by inhalation during the production of D
4 or silicone polymers.
Plotzke et al.(2000) studied the disposition of D4 in the rat following inhalation exposures. Groups of male and female F344 rats were exposed for 6 h to 7, 70, or 700 ppm 14C-D4 and tissues were collected at 10 different times during and after the exposures. In addition, other groups of rats were exposed to 7 and 700 ppm D4 for 15 days to determine the effect of multiple exposures on D4 pharmacokinetics. These data served as the basis for developing a physiologically based pharmacokinetic (PBPK) model for D4 in rats. Andersen et al.(2001) found that a conventional PBPK model structure including flow-limited uptake in the fat, liver, and rapidly and slowly perfused tissue compartments could not adequately describe the pharmacokinetics of D4 in rats. Specifically, this conventional model structure could not simultaneously describe the concentrations of D4 in the blood and exhaled air in the postexposure period with a single set of physiological parameters and partition coefficients. Some D4 appeared to be present in blood in a form that was not available for equilibration followed by exhalation in the alveolar region of the lung. A refined PBPK model was developed that included deep-tissue compartments in the liver and lung, a second fat compartment, and a storage compartment in blood from which D4 was not available for gas or tissue exchange. This storage compartment in blood is likely related to circulating lipids (Andersen et al., 2001); however, studies have not been done to track D4 in blood lipids over time after an inhalation exposure.
Because of the low order of D4 toxicity, two pharmacokinetic studies of D4 inhalation in humans have been performed in which volunteers were exposed to 10 ppm D4 during alternating periods of rest and exercise. In the more comprehensive of the two studies, 14C-D4 was administered and the concentration of parent compound in the blood and exhaled breath and the amount of metabolite in the blood and urine were determined (Utell, 2000). In this article we describe a PBPK model developed for D4 inhalation exposures in humans using these pharmacokinetic data. Adopting the strategy of Andersen et al.(2001), we first developed a simple PBPK model for human inhalation exposures to D4 and added additional components as necessary. The resulting refined human PBPK model that successfully described the data with the radiolabeled D4 was then validated by successfully predicting blood and exhaled breath levels for an earlier pharmacokinetic study of D4 in human volunteers conducted with unlabelled D4 (Utell et al., 1998). Our success in developing a consistent PBPK model with common physiological structure for both rats and humans indicates that this model should be useful for assessing tissue exposures from inhaled D4 in humans for a variety of exposure situations and supporting human risk assessments for this compound.
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MATERIALS AND METHODS
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Experimental data.
The pharmacokinetic study on the inhalation exposure of humans
to D
4 (Utell, 2000
) was completed at the University of Rochester
following the approval of the Human Subject Review Committee.
During a 1-h exposure to 10 ppm
14C-D
4 using a mouthpiece exposure
system described previously (Utell
et al., 1998
), six male volunteers
rested for 10 min, exercised for 10 min, rested for 20 min,
exercised for 10 min, and then rested for 10 min. For exercise,
the subjects biked at a resistance that tripled their resting
minute ventilation. For each subject, the respiration rate and
minute volume were determined during the exposure (Table 1
).
The D
4 concentration in the inhaled and exhaled air was monitored
regularly during the exposure, and the exhaled concentration
was monitored during a 20 to 30-min postexposure period. Samples
of expired breath were also obtained at 1, 3, 6, 24, 48, and
72 h after the exposure ended by the collection of end-expiratory
air in a 40-l Tedlar bag. Blood samples were drawn from the
forearms of each subject at 0, 30, 60, 120, 240, 420, and 1500
min after the exposure began. At the end of the 30-min postexposure
period, a spot urine sample was collected and each subject emptied
his bladder. For the remainder of the 24 h following the exposure,
subjects collected urine in three 8-h aliquots. After the first
24 h, spot urine samples were collected once a day for up to
seven days and adjusted for the total amount eliminated based
on the amount of creatinine in the urine samples.
Several analytical techniques were used to measure D
4 and metabolite
concentrations in various samples. During the exposure and 30-min
postexposure periods, the analysis of D
4 in the exhaled breath
was determined using a gas chromatograph (GC) with a flame ionization
detector (FID). Samples of exhaled breath taken after the 30-min
postexposure period were passed through an adsorbent for trapping
volatiles and then through a CO
2 absorbent to determine the
amount of
14C-CO
2 separately from the radioactivity associated
with volatile parent or metabolites. In rats, all radioactivity
captured in the volatile trap was parent compound (Plotzke
et al., 2000
), and the same was expected to be true for humans
(i.e., chemical trapped in the volatile trap can be assumed
to be parent D
4). Liquid scintillation counting (LSC) was used
to determine the amount of
14C-D
4 and
14C-CO
2 in samples of
exhaled breath collected more than 30 min after the exposure
ended. Whole blood and blood plasma samples were analyzed with
the LSC and gas chromatography/mass spectrometry (GC/MS, as
described by Varaprath
et al., 2000
) analytical techniques.
The amount of total metabolites in the blood can be calculated
by subtracting the amount of parent compound measured by GC/MS
from the amount of radioactivity measured by LSC (i.e., parent
compound and metabolite). Urine samples were analyzed using
LSC. Additionally, individual metabolites in urine were separated
using high-performance liquid chromatography (HPLC) and quantitatively
analyzed using LSC.
Model structure.
Initially, a fairly conventional PBPK model, as used by Ramsey and Andersen (1984) with styrene, was used to describe D4 disposition in humans with flow-limited uptake in the fat, liver, and rapidly and slowly perfused tissues, along with separate compartments for the venous and arterial blood (Fig. 1). In the simple model, all the D4 in the blood was available for equilibration with tissues and lung air. In the rat the rate of metabolism had been modeled by a Michaelis-Menten term in the liver and included provision for induction of metabolism at 700 ppm D4. Because the human subjects were exposed to only 10 ppm D4, metabolism was described with dose-independent liver clearance without provision for induction. The conventional model structure also included a one-compartment pharmacokinetic model for a combined metabolite pool in blood.
In the rat, PBPK modeling results indicated that some D
4 in
the blood was unavailable for exchange with exhaled air and
the amount of D
4 in this pool varied with time (Andersen
et al., 2001
). The successful model in the rat had deep tissue
compartments and a pool of D
4 in blood that was unavailable
for exhalation or tissue uptake. A second refined PBPK model
was developed with the human data to determine if such an elaboration
on the conventional model structure was also necessary to account
for human kinetics. The refined model (Fig. 2
) included a blood
pool of unavailable D
4. As with the rat model, this unavailable
pool of D
4 was assumed to be produced in the liver, transported
in the blood, and cleared by the fat tissue. This behavior is
representative of lipoprotein transport. A mass transfer resistance
was required to describe the uptake of D
4 by fat tissue in rats.
In the human model we included a mass transfer resistance to
uptake in the slowly perfused compartment and a deep storage
compartment in fat. The role of these compartments in describing
the experimental data is noted in the Results. Model equations
are provided in Appendix 1 and the code is available by e-mail
from the corresponding author.
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FIG. 2. Schematic diagram of (a) the refined PBPK model for D4 distribution in humans and (b) the submodel for the transport of unavailable D4 in blood lipids. The double line designates a variable from a component in another section of the model.
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Metabolism.
Time course data for the amount of individual metabolites in
the urine were available for the development of a more detailed
model of D
4 biotransformation pathways in humans. After determining
the kinetic parameters for net metabolic clearance of parent
D
4, the data for the amount of individual metabolites in the
urine were used to create a more complete description of the
formation and clearance of individual metabolites. The proposed
metabolic scheme and model structure (Figs. 3 and 4
) show the
expected interrelationships of the individual metabolites that
were included in the model for D
4 metabolism.
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FIG. 3. Proposed reaction mechanism for D4 metabolism in humans. *Designates compounds that were detected in urine samples.
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Parameterization.
A variety of physiological parameters were experimentally measured
or calculated for the individual subjects of the study (Table
1
). Effects of exercise were incorporated in the model by adjusting
the alveolar ventilation rate, QP, the cardiac output, QC, and
the blood flow rates to two tissue compartments (Table 2
; see
Appendix 2 for a listing of the abbreviations used in the models).
During exercise, the blood flow rate to the fat compartment
increased in a manner consistent with the study of Bulow and
Madsen (1978)
, and the blood flow rate to the slowly perfused
tissue compartment, which includes muscle tissue, increased
during exercise. The blood flow rates to the liver and rapidly
perfused tissue were the same during both the rest and exercise
periods.
To minimize the number of parameters to be estimated, values
of the liver:blood, fat:blood, and rapidly perfused tissue:blood
partition coefficients were calculated by dividing the experimental,
in vitro, rat-tissue values for the liver:air, fat:air, and
kidney:air partition coefficients, respectively, by the blood:air
partition coefficients (Andersen
et al., 2001
). Tissue partition
coefficients of rats and humans are expected to be similar because
tissue compositions are similar. Because
in vitro partitioning
data were not available for the slowly perfused tissue compartment,
the partition coefficient for D
4 between the slowly perfused
compartment and blood, PS, was set to 3. The value of PS cannot
be calculated from the
in vivo data because fits of the model
to these data (e.g., time course concentrations of D
4 in blood
plasma) were not sensitive to the value of PS. This parameter
did affect the estimates of the amount of chemical retained
during inhalation exposure. Although no experimental data were
available for the estimation of PS, the potential effect of
error in this parameter is small. The slowly perfused compartment
is large, but PS is small compared to the partition coefficients
of other compartments, and so it stores a relatively small amount
of chemical.
For the simple model, four parameters were estimated from the experimental data: (1) the blood:air partition coefficient (Pb), (2) the allometric scaling constant for metabolic clearance in the liver (KFC), (3) the renal clearance of metabolite into the urine (KEL), and (4) a scaling constant for the volume of distribution of the metabolite pool (VDISC). For the refined model, five additional parameters were estimated: (5) the first-order rate constant for the production of the mobile lipid pool in the liver (Kmlp), (6) the clearance of unavailable D4 in the mobile lipid pool to the fat (CLmlp), (7) a mass transfer coefficient for the slowly perfused compartment (PAS), (8) a first-order mass transfer coefficient for the movement of D4 from the fat compartment into a deep compartment (KFD), and (9) a first-order mass transfer coefficient for the movement of D4 from the deep compartment to the fat compartment (KDF). These parameters were estimated by comparing model output to the cumulative amount of chemical absorbed during the exposure, the concentration of D4 in the exhaled breath after the exposure, the concentration of D4 in the plasma, and the concentrations of total metabolites in the plasma and urine. Although the concentrations of D4 and metabolites were determined in both the whole blood and the blood plasma, parameter estimation was done using blood plasma concentrations. The concentrations of individual metabolites in the urine were also used to estimate parameters for the metabolism model.
Model equations were solved using two different software packages: Berkeley MadonnaTM and ACSLTM (Aegis Technologies). Optimum parameters were found using the multiple curve-fitting routine in Berkeley Madonna, which minimizes the root mean square deviation between the data points and the model output. When multiple data sets were used for parameter estimation (e.g., time course data for the amount of several different metabolites in urine), the residuals from each dataset were weighted by the inverse of the SD of the dataset since the datasets were assumed to have a constant coefficient of variance. For the refined model, after completing a global estimation of the best-fit parameters, we independently adjusted Kmlp and CLmlp to improve the fit for blood plasma concentrations taken at 1500 h and adjusted KDF to provide a better fit for exhaled breath concentrations for times longer than 1500 h. Because the concentrations in blood and exhaled breath at the longest time were more than four orders of magnitude smaller than those during exposure, the curve-fitting algorithm was relatively insensitive to these latter data points. When estimating multiple parameters by curve fitting, increasing the number of parameters to be fit increases the risk that the program will find a local minimum of residuals instead of the global minimum. To prevent identifying a combination of parameters resulting in a local optimum instead of a global optimum, the optimizer was run using several different starting values (i.e., initial guesses of parameter values). Additionally, by limiting the values of parameters to physically plausible values, unrealistic solutions were prevented and computational time was minimized (MGA Software, 1997).
Sensitivity analysis.
Identification of the key parameters affecting a pharmacokinetic measurement is important for calculating multiple parameters by curve-fitting with multiple datasets (Andersen et al., 2001). For example, a key parameter for determining the D4 concentration in exhaled air and blood plasma during the exposure and washout period is Pb. By fitting this parameter independently to data that are sensitive to the parameter (i.e., holding other parameters constant), its value can be constrained for the multiple curve-fitting algorithm, reducing the computational time required by the computer and the risk of calculating an unrealistic value of the parameter based on datasets lacking sensitivity to the parameter.
To determine sensitivity of the model output to the parameters estimated using the experimental data, log-normalized sensitivity parameters (LSPs), defined in Clewell et al.(1994) as
 | (1) |
were calculated. In Equation 1
, R is the model
output (i.e., for the calculations performed here, the concentrations
of D
4 in the venous blood plasma and exhaled breath) and x is
the parameter for which sensitivity is being determined. By
this definition, the percentage change in model output due to
a percentage change in a parameter is quantified, and thus the
LSP value represents the relative importance of a parameter
to model output. Values of LSP were calculated using the central
difference method. Because model output may be sensitive to
model parameters at different times, values of LSP were calculated
at four times: 30 min, 2 h, 12 h, and 48 h. Values of LSP greater
than one could result in error in the input causing amplified
error in the output, while very low values of LSP indicate that
model output are insensitive to a parameter (Clewell
et al.,
1994
).
Model validation.
A separate study in which 12 humans were exposed to 10 ppm D4 by inhalation during periods of rest and exercise (Utell et al., 1998) was used as a test set for limited model validation. In this study, the inspired D4 vapor concentration was determined using infrared spectrophotometry. Concentrations of D4 in the exhaled breath during the exposure and washout period were determined every 2 min by GC methods. Blood plasma D4 concentrations during, immediately after, and 1, 6, and 24 h after the exposure ended were determined using GC/MS analysis. Plasma sample concentrations 24 h after the exposure ended were below the limit of quantitation for this analytical method.
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RESULTS
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General Trends
Unlike many lipophilic chemicals with long half-lives for elimination
from the body, elimination of D
4 (logK
o/w = 5.1) from blood
was rapid. After humans were exposed to 10 ppm
14C-D
4 by inhalation,
D
4 blood concentrations decreased rapidly due to exhalation
and metabolism (Table 3
). In the 30-min period following the
exposure, about 13% of the absorbed dose of D
4 was eliminated
by exhalation. Metabolites were detected in the blood at the
earliest sampling time (30 min after the exposure began), and
the first urine sample taken 30 min after the exposure had ended
also had detectable levels of metabolites.
Model Structure
Consistent with the pharmacokinetics of D
4 in the rat, the refined
model more accurately described the disposition of D
4 in the
plasma and exhaled air (Fig. 5
). For example, both the simple
and refined model could match the concentration of D
4 in exhaled
air, but only the refined model could simultaneously match the
concentration of D
4 in blood plasma and exhaled air. Simulated
D
4 exhaled breath concentrations increased between 10 to 20
min and 40 to 50 min (i.e., during the exercise periods) due
to the physiological changes from exercise that were incorporated
in the model. This increase in exhaled D
4 concentrations is
consistent with the pharmacokinetic study results of Utell
et al.(1998)
, who noted decreased retention efficiency of D
4 during
the exercise periods.
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FIG. 5. Measured and calculated D4 concentrations in exhaled breath and blood plasma as a function of time for subjects (A) 1, (B) 2, (C) 3, (D) 4, (E) 5, and (F) 6 of the primary study. Theoretical curves were calculated with the simple (dashed curve) and refined (solid curve) models.
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Average values of D
4 concentrations in exhaled breath and plasma,
total metabolite concentration in the plasma, and cumulative
amount of metabolite in the urine for the six subjects exposed
to
14C-D
4 are shown in Figure 6
. The simulated curves were calculated
using the average values of the inhaled D
4 concentration and
physiological properties (Table 1
) and the average values of
calculated model parameters (Table 4
). Although model calculations
are presented for average parameter values, parameter values
for each individual subject are reported to illustrate the interindividual
variability in parameter values. As expected, the refined model
more accurately described the pharmacokinetic profiles. Although
the model prediction of the D
4 concentration in exhaled breath
is high during the first 500 min postexposure, in general the
refined model describes the concentration of D
4 in exhaled breath
and blood plasma, the concentration of total metabolite in blood
plasma, and the cumulative amount of metabolite in the urine.
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FIG. 6. Semilog plots of the average concentration of D4 in (A) exhaled breath and (B) blood plasma and plots of (C) the concentration of total metabolite in blood plasma and (D) the average cumulative amount of total metabolite in urine as a function of time. The error bars represent one SD for n = 5 or 6. The simulated curves were calculated using the refined model (solid curves) and simple model (dashed curves) with average best-fit parameters, physiological properties, and exposure conditions.
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TABLE 4 Parameters Calculated by Fitting the Model to the Data Obtained following Inhalation Exposures of Six Male Subjects to 14C-D4
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After the exposure ended, the D
4 concentration in exhaled breath,
Cex, decreased by more than four orders of magnitude. During
the exposure, the prime determinant of plasma concentration
was Pb (Table 5
). At the later times, the return of D
4 to plasma
from the lipophilic storage tissues in the body was also a prime
determinant of the concentration of D
4 in exhaled air. While
the overall time course for Cex, with the precipitous decline
over time, was accounted for by the simple model (Fig. 6
), the
curve decreased too rapidly and leveled off at a concentration
higher than the data. With this simple model, the characteristics
of the slowly perfused compartment, representing muscle and
skin, determined the curvature between 100 and 1500 min.
Describing the exhalation time course data more accurately required
the addition of diffusion limitations in storage for both the
slowly perfused and the fat compartments of the refined model.
Several characteristics of the refined model dominated the behavior
in different time periods. The characteristics of the slowly
perfused compartment were critical in fitting the transitional
period until about 1000 min and required incorporation of a
mass-transfer limitation on uptake and release of chemical from
this compartment. After about 2000 min, the more stable blood
level of D
4 was determined by return from the fat compartment.
If a flow-limited fat compartment without a deep compartment
were included, the model overestimated the exhaled concentrations
at longer times as shown by the dotted line. The presence of
a diffusion-limited fat compartment allowed adjustment of the
model fit for the final period of exhalation after 3000 min.
The exhalation behavior of D
4 is a sensitive monitor of the
characteristics of lipid storage compartments because of the
rapid clearance of D
4 by exhalation and metabolism after its
release from storage sites. Further refinements in the fit to
the exhaled breath curve were possible by subdividing the slowly
perfused compartment (e.g., as in Jonsson
et al., 2001
). We
did not believe that an increase in model complexity was warranted
by the limited data available from the single exhaled breath
data set.
Model Validation
The refined model was then applied to a second data set (Utell et al., 1998). Using average characteristics and exposure conditions of the eight male and four female subjects as input for the model (Table 1), concentrations of D4 in exhaled breath and blood plasma were simulated for male and female subjects using the average parameter values of the refined PBPK model (Table 4). The prediction (Fig. 7) agrees very well with these earlier results. However, since this dataset is similar to the data used for model construction, it might be better to regard this as test of reproducibility rather than a strict validation of the model. Although the model parameters were estimated using data from a study of six male subjects, the model was able to predict exposure outcomes for female subjects of the previous study.
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FIG. 7. Average measured and calculated D4 concentrations in exhaled breath and blood plasma as a function of time for (A) the men (n = 8) and (B) women (n = 4) from Utell et al.(1998). Simulated curves were calculated with the refined model. The error bars represent one SD.
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Metabolism Model
Consistent with metabolism studies performed in the rat (Varaprath
et al., 1999
), methylsilanetriol (monomer-triol) and dimethylsilanediol
(monomer-diol) were the major metabolites in humans (Fig. 8
).
Other metabolites in urine common to both rat and human metabolism
of D
4 were tetramethyldisiloxane-1,3-diol (dimer-diol), dimethyldisiloxane-1,3,3,3-tetrol
(dimer-tetrol), and hexamethyltrisiloxane-1,5-diol (trimer-diol;
Table 6
). Additionally, trimethyldisiloxane-1,3,3-triol (dimer-triol)
was a very minor metabolite in human urine. Although the exact
mechanism of D
4 metabolism is unknown, these metabolites can
be incorporated into a proposed scheme for metabolism (Fig.
3
) and assigned compartments in a metabolism model (Fig. 4
).
In all the proposed pathways, complete hydrolysis leads to 1
mol of monomer-triol and 3 mol of monomer-diol. However, intermediates
may also be filtered into urine. Large quantities of monomer-triol
were detected in the urine soon after the exposure ended, indicating
that the reaction of tetramer-triol to form monomer-triol and
trimer-diol is likely to be the major pathway for metabolism.
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FIG. 8. Average cumulative amounts in µmol of five metabolites in urine as a function of time. The error bars represent one SD. Unless otherwise indicated, n = 6. Points are connected; the line does not represent model simulation.
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One potential problem with the mechanism shown in Figure 3
is
that dimer-tetrol does not appear in the mechanism. The formation
of dimer-tetrol could be explained by another minor pathway.
During the initial step of the oxidation of D
4, if both methyl
groups on an Si were oxidized, silicic acid, i.e., Si(OH)
4,
could be formed. In the urine, which has a higher concentration
of metabolites than the blood, a condensation reaction between
silicic acid and monomer-diol could produce dimer-tetrol.
During the primary study, 14C-CO2 was detected in exhaled breath in concentrations that decreased exponentially and reached very low levels by 24 h after the exposure ended. It is likely that 14C-CO2 was produced from the oxidation of the methyl group from the intact D4 molecule (i.e., the first step in the metabolic pathway). Eight days after the exposure ended, about 26% of the D4 had been eliminated by metabolism. Because only one of the methyl groups on the D4 molecule is radiolabeled, about 3.25% (= 26%/8) of the radioactivity should be eliminated in the form of 14C-CO2, but only about 1.5% of the uptake of radioactivity was recovered as 14C-CO2. The exhaled breath was not analyzed for 14C-CO2 during the exposure and the 30-min postexposure period. Thus, more than half of the 14C-CO2 from the initial oxidation of D4 could have been eliminated without detection. Because less than 5% of the total radioactivity will be metabolized to 14C-CO2, this loss was not expected to significantly affect modeling results, and was not included in the model development.
The submodel for metabolism of D4 in humans (Fig. 4), developed to be consistent with the major pathway of the proposed reaction mechanism (Fig. 3), was then combined with the refined PBPK model. The equations are provided in Appendix 1. The metabolism submodel required values for seven additional parameters: the allometric scaling constants for the first-order metabolism rate constants of tetramer-triol, trimer-diol, and dimer-diol (i.e., K1C, K2C, and K3C, respectively) and the first-order rate constants for the elimination of monomer-triol, monomer-diol, dimer-diol, and trimer-diol into urine (i.e., KEL1, KEL2, KEL3, and KEL4, respectively). These seven parameters were determined by minimizing the difference between model output and six datasets (i.e., the cumulative amount of monomer-triol, monomer-diol, dimer-diol, and trimer-diol in urine, the cumulative amount of total metabolite in urine, and the concentration of total metabolites in plasma). Parameter estimation results are listed in Table 7.
This metabolism submodel adequately described time course concentrations
of three of the four individual metabolites in urine (i.e.,
monomer-diol, dimer-diol, and trimer-diol; Fig. 9
). However,
the model underpredicted the cumulative amount of monomer-triol
in the urine at later times by up to 56%. It appears that further
oxidative demethylation must occur after formation of the linear
siloxanes to account for the net amounts of monomer-triol found
in urine. The model structure was enlarged to include conversion
of monomer-diol to monomer-triol (i.e., the model shown in Figure
4
was modified to include an additional reaction with rate constant
K4). The expanded model was able to describe all the metabolite
data (Fig. 9
).
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FIG. 9. Measured and calculated cumulative amount in µmol of four individual metabolites in urine as a function of time for Subject 1. The simulated curves were calculated using the refined model modified to include metabolism. For the solid curves, K4 = 0, but the dashed curves were calculated including an additional demethylation step.
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DISCUSSION
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Discovering the Requirement for the Refined Model
For volatile organic compounds, the ratio of the chemical concentration
in arterial blood, Ca, to the concentration in end-alveolar
air, Calv, is expected to remain constant (i.e., Ca/Calv = Pb).
In the D
4 study, blood samples were obtained from the venous
blood, and a similar time-independent relationship is expected
after the exposure ends. The equation often used to calculate
Ca in PBPK models (e.g., the approach of Ramsey and Andersen,
1984
, for inhalation exposures to styrene) is
 | (2) |
where Cin is the concentration of chemical in the air entering
the lungs and Cv is the concentration of chemical in the venous
return. Equation 2
was developed by assuming that the absorbed
chemical rapidly equilibrates between lung blood and lung air.
Because Pb = Ca/Calv and after an exposure ends, Cin = 0, the
following relationship can be derived:
 | (3) |
After the exposure, the ratios Cv/Calv and also Cv/Cex should
have remained constant, but did not (Fig. 10
). The ratio Cv/Cex
increased substantially with time from about 5 soon after the
exposure ended to over 400 one day after the exposure ended.
This increase in Cv/Cex occurred over a time period where the
blood concentrations decreased by two orders of magnitude while
the exhaled air concentrations decreased by more than four orders
of magnitude.
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FIG. 10. Average values of Cv/Cex as a function of time. The error bars represent one SD for n = 6. The simulated curves were calculated using the refined model (solid curve) and simple model (dashed curve) with average best-fit parameters, physiological properties, and exposure conditions.
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The reason that blood concentrations did not fall as rapidly
as the exhaled air concentrations was the presence of a pool
of D
4 in blood that did not equilibrate with exhaled air, i.e.,
a pool of bound or sequestered D
4 that was unavailable for alveolar
equilibration. Free D
4 was rapidly exhaled or metabolized; the
bound D
4 was persistent in blood. The time evolution of the
amount in this nonexchangeable blood compartment determined
the values of Kmlp and CLmlp. According to model calculations,
when the exposure ended the fraction of D
4 in the blood that
was unavailable was 0.24, but by 1 h following the exposure
the fraction of unavailable D
4 had increased to 0.95. Consistent
with the results of Utell
et al.(1998)
, calculations with the
refined model show that the half-life for D
4 clearance from
the blood was shorter at early times than late times because
the fraction of available D
4 in the blood decreased with time.
When the exposure ended and the majority of D
4 in the blood
was free D
4, the half-life for clearance of D
4 from the blood
was about 1.4 h. However, later in the exposure when the majority
of the D
4 in the blood was unavailable, the half-life for clearance
was about 4.2 h. Due to the high sensitivity of blood concentrations
at long times to CLmlp (Table 5
), additional studies characterizing
the nature of the pools of unavailable D
4 in blood are important.
The model structure for D4 inhalation exposures in humans is perhaps more complex than warranted by the data because no tissue time-course concentration data were available. However, the model structure is also based on our experience in modeling D4 pharmacokinetics in the rat. The premise in developing the PBPK model with D4 in the rat was the assumption that the exhaled air D4 was in equilibrium with a pool of free D4 in blood. With this human model we retained the model structure required in the rat (i.e., the mobile-lipid pool concept with production from the liver, movement through the plasma, and clearance to the fat). Further research will be necessary to identify the plasma lipids that sequester D4.
Clearance of Circulating D4
Although D4 has a large fat:blood partition coefficient, it is not expected to undergo extensive bioaccumulation due to rapid clearance from the body by exhalation and metabolism. With xenobiotic compounds, elimination processes are frequently described by clearances (i.e., the volume of blood from which chemical is lost per time, with units of flow). With D4, we can calculate clearances by the two major pathways of elimination, exhalation and hepatic clearance. Based on the average values of KFC (Table 4) and liver blood flow (Table 2), the average liver clearance was 0.85 l/min compared to a liver blood flow of 1.29 l/min. At the extreme, with KFC = 0.2 l/min/kg0.7, hepatic clearance was 1.01 l/min (i.e., nearly 80% of hepatic blood flow). Under these conditions, hepatic clearance is essentially limited by blood flow to the liver.
Clearance by exhalation, CLex, can also be calculated from model parameters. In the postexposure period, CLex is calculated as
 | (4) |
Combining this relationship with
Equation 2
for Cin = 0 gives
 | (5) |
For
compounds like D
4 with small values of Pb, CLex is high. For
a Pb of 1.0 and resting QC and QP values of 5.03 and 7.83 l/min,
CLex was 3.06 l/min. Total clearance from hepatic metabolism
and exhalation was 3.91 (0.85 + 3.06) l/min (i.e., about 60%
of QC).
Metabolic clearance of D4 simply accounts for those reactions that metabolize D4 to downstream products. Because of the ability to speciate metabolites in urine over time, it was also possible to infer the metabolic pathway for the group of linear siloxanes produced from oxidation and ring cleavage. The sequential model with rapid production of the trimer-diol after oxidation followed by hydrolysis is sufficient to describe the results as long as a second oxidative pathway is provided for conversion of monomer-diol to monomer-triol. This latter step may be more favored than oxidation of other intermediates due to longer persistence of the monomer-diol than any of the other longer chain metabolites that serve as relatively shorter-lived intermediates. This model infers time course concentrations in the blood from the appearance of metabolites in urine. The relationships of blood and urinary concentrations depend on biotransformation and elimination rates.
In rodents, inhalation of D4 produces a dose-related hepatomegaly, transient hepatic hyperplasia, hypertrophy, and induction of cytochrome P450 enzymes in a manner similar to phenobarbital (McKim et al., 1998, 2001). This pattern of induction was also observed following oral exposure to D4 (Zhang et al., 2000). Although several hepatic enzymes are affected by D4 exposure, CYP2B1/2 enzymes are induced to the greatest extent. In addition, it appears that these enzymes are also capable of recognizing D4 as a substrate and therefore may play an important role in its elimination (Salyers et al., 1996). While there may eventually be value in a model for the metabolites to assess total exposures to siloxanes, development of a pharmacokinetic/pharmacodynamic model to study concentration response data for protein induction, enzyme activity, and liver weight changes demonstrated that the hepatic responses following D4 exposure are more likely to be related to parent D4 than to metabolites (Sarangapani et al., 2002). Additional evidence for the role of parent D4 is from structural reasons in relation to other xenobiotics that have phenobarbital-like induction in liver (Waxman, 1999). Unfortunately there is no specific information available on the toxicity of the individual metabolites for comparison with the studies of parent D4.
Blood:Air Partition Coefficient
The average value of Pb for humans estimated by fitting the model to the in vivo data was 0.96. The in vitro partition coefficient between rat blood and air was determined to be 4.3, while the Pb value required to describe the rat inhalation kinetics in vivo was also close to 1.0 (Andersen et al., 2001). Several investigators have noted that Pb values for volatile compounds are usually larger by about a factor of two for rat blood compared to human blood (Gargas et al., 1989). Thus, all available results are consistent with a Pb for D4 in humans near unity.
Recently, Luu and Hutter (2001) developed a PBPK model for D4 inhalation exposures in humans and rats that used a much different Pb, i.e., 20. The reasons for their use of a much larger Pb value were due to an oversight in the development of their rat model and the application of an unnatural constraint in the development of their human model (Andersen et al., 2002). They used total radioactivity in blood from the rat inhalation study without differentiating parent D4 from metabolites. Thus, their model fit the combined amount of D4 and metabolite in blood as if it were parent D4, even though by the end of the 6-h inhalation exposure in rats, the majority of radioactivity in blood was metabolite. Because of this oversight, a higher Pb value was required to maintain higher blood concentrations over time than due to D4 alone. In their human model, they applied the higher Pb to the human data set of Utell et al.(1998). They then used the total amount absorbed during exposure, about 11% of the total inhaled, not as an outcome to be matched by the model, but as a physical constraint. With this unnatural constraint for a PBPK model with a volatile compound, a much higher Pb is required to retain all inhaled compound. Our PBPK model for D4 was developed following the common approach for inhalation exposures to volatile compounds and describing D4 plasma concentrations without artificial constraints on uptake. Because our model described Ca using Equation 2, the proportion retained was an output of the model and not a constraint.
Retention Efficiency
Recently, Csanady and Filser (2001) modeled the effects of Pb, QC, and QP on chemical uptake during inhalation exposures with varying workloads, noting that increased physical activity can increase uptake. The effect of exercise on absorption during inhalation exposures can be studied using Equation 2. For a short time early in an exposure when the concentration in the venous return is low (i.e., Cv 
0), the proportion of absorbed chemical is as large as possible, and Equation 2 becomes
 | (6) |
For chemicals with a high Pb, Ca/Cin would be
approximately equal to QP/QC. The ratio QP/QC increases with
exercise. For example, the ratio was experimentally determined
to be about 0.8 at rest and about 2.0 at a workload of 50 W
by Astrand (1983)
. Thus, exercise would increase the amount
of chemical absorbed into the blood stream. However, for chemicals
like D
4 with a low Pb, Ca/Cin will not be greatly affected by
increasing QP/QC. A plot of Ca/Cin as a function of Pb, as predicted
by Equation 6
, shows that early in an exposure the effect of
exercise on the ratio of Ca/Cin is minor for chemicals with
Pb < 1 (Fig. 11A
). This result is consistent with Csanady
and Filser, who concluded that for chemicals with a Pb >
6, physical activity at work should be taken into account when
determining occupational limit concentrations in air.
Exercise can also affect the fraction absorbed, FA (i.e., the
fraction of chemical entering the lungs that absorbs into lung
blood), defined as
 | (7) |
To determine
Cex, Calv (i.e., Ca/Pb) must be adjusted for the concentration
of chemical in the dead space of the lungs as follows:
 | (8) |
where FDS is the fraction of dead space in the
lungs, which also decreases with exercise. In the study of Astrand
(1983)
, FDS was about 0.33 at rest and about 0.11 with a workload
of 50 W. Equation 9
, developed from Equations 6, 7, and 8
, shows
the effect of increasing QP/QC on FA:
 | (9) |
This equation predicts that FA will decrease during exercise
for chemicals with Pb < 3, but increase during exercise for
chemicals with Pb > 3 (Fig. 11B
). FA also decreases as the
length of the exposure increases because as tissue compartments
fill, Cv increases and the rate of absorption of chemical from
the lung air into the lung blood decreases. However, processes
that result in chemical clearing from the bloodstream (e.g.,
metabolism) increase the rate of absorption during an inhalation
exposure.
Utell et al.(1998) reported that during inhalation exposures to D4, FA decreased with increased alveolar ventilation during exercise. Because the D4 PBPK model included the major physiological effects of exercise, it quantitatively demonstrates how both exercise and time affect blood and exhaled D4 concentrations. A simulation of FA as a function of time by the refined PBPK model for Subject 1 (Fig. 12) illustrates the changes in retention with different workloads and with increasing time. For the simulation where Subject 1 is exposed to 10 ppm 14C-D4 at rest, early in the exposure FA was about 0.25, but as tissues fill up and the venous blood concentration rises, FA decreased. The simulated curve is more complex when the effects of exercise are included. In general, FA decreased with time, but FA also periodically increased and then decreased as physiological properties changed. Consistent with our calculated value of Pb = 0.96, the decrease of FA with exercise indicates that Pb is below 3.0 (Fig. 11).
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FIG. 12. Experimentally determined and simulated fraction absorbed (FA) as a function of time for Subject 1. The dashed curve was calculated assuming Subject 1 was at rest during the entire exposure while the solid curve was simulated including the physiological effects of periodic exercise in the PBPK model.
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Summary
The human inhalation PBPK model for D
4 presented here described
all available pharmacokinetic data for D
4 disposition in humans
following inhalation exposures. D
4 has the unusual combination
of low blood:air and high fat:blood partitioning, giving rise
to preferential storage in lipid compartments in the body, including
some sequestration in blood, and rapid elimination from all
tissues other than fat after cessation of exposure. This PBPK
model for D
4 provides a tool to quantify transport of highly
lipophilic chemicals throughout the blood and tissues and to
quantitatively characterize the retention, distribution, and
elimination of parent D
4 and its hydrolysis and oxidation products
from the body following inhalation exposures to humans. The
human D
4 model is similar to the rat model, with similar partition
coefficients and compartmental structures. The success in developing
consistent PBPK models for D
4 in two species indicates that
this human model should be useful for simulating tissue dosimetry
of D
4 in humans exposed by inhalation and to further support
the risk assessment of D
4.
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APPENDIX 1
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Simple Model
By modeling the lungs as a well-mixed compartment with an average,
one-directional airflow in the region of gas exchange (i.e.,
QP), and with rapid equilibration between lung air and blood
in the lung alveoli, the concentration in the blood exiting
the lungs, Ca, can be described as
 | (A-1) |
where CBLV is the free concentration of D
4 in the venous blood
compartment and Cin was 10 ppm D
4 during the exposure and zero
after the exposure ended. The concentration of D
4 in exhaled
breath, Cex, can be calculated using Equation 8
, with Calv =
Ca/Pb. Separate compartments were included for the venous and
arterial blood. The mass balance for the concentration of D
4 in the arterial blood compartment, CBLA, is
 | (A-2) |
where t is time and VBLA is the volume of the arterial blood
compartment. The rate of mass transfer of D
4 into the fat, rapidly
and slowly perfused tissues, and liver was limited by the blood
flow to the tissues, as shown in A-3 to A-6:
 | (A-3) |
 | (A-4) |
 | (A-5) |
 | (A-6) |
where CF, CR,
CS, and CL are the concentrations of D
4 in the fat, rapidly
and slowly perfused tissues, and liver, respectively. Because
D
4 is metabolized in the liver, A-6 includes the first-order
clearance constant KF. The blood flows from the organ compartments
combine in a mixed venous return compartment:
 | (A-7) |
where VBLV is the volume of the venous blood
compartment. A one-compartment model was used to describe the
disposition of the pooled metabolites with first-order renal
clearance as shown in A-8:
 | (A-8) |
where
CMET and VDIS are the blood plasma concentration and volume
of distribution of the combined metabolite pool, respectively.
The amount of total metabolite excreted into urine, AMEX, can
be calculated using the equation
 | (A-9) |
At the beginning of the exposure,
the concentration of D
4 in all compartments was assumed to be
zero (i.e., CA = 0, CBLA = 0, CF = 0, CR = 0, CS = 0, CL = 0,
and CBLV = 0 at t = 0), and the concentration of metabolite
in the blood plasma and the amount of metabolite in the urine
were assumed to be zero (i.e., CMET = 0 and AMEX = 0 at t =
0).
Refined Model
The refined model has a mobile lipid pool in blood with D4 that does not equilibrate with free D4 in blood. This lipid pool is generated in the liver and cleared by the fat. The mass balance on the liver, A-6, then becomes
 | (A-10) |
This sequestered D
4 in blood is cleared in the fat compartment,
where D
4 can also move into a deep fat compartment, and so Equation
A-3
becomes
 | (A-11) |
where
CAmlp is the concentration of unavailable D
4 (i.e., in the mobile
lipid pool) in the arterial blood and AFD is the amount of D
4 in the deep fat compartment, which is described as
 | (A-12) |
The mass balances for unavailable
D
4 in the arterial and venous blood are
 | (A-13) |
 | (A-14) |
where CVmlp is the concentration of unavailable D
4 (i.e., in
the mobile lipid pool) in the venous blood. The average concentration
of total D
4 (i.e., free and bound) in the mixed venous return,
CVMIX, can be calculated as
 | (A-15) |
At the beginning of the exposure, the concentration of unavailable
D
4 in both the arterial blood and venous blood is assumed to
be zero (i.e., CAmlp = 0 and CVmlp = 0 at t = 0).
In the refined model, the mass transfer in the slowly perfused compartment was limited by diffusion into the tissue. The mass balance on the slowly perfused compartment becomes
 | (A-16) |
In this case, the blood exiting
the slowly perfused tissue compartment has not equilibrated
with the compartment (i.e., the concentration in blood plasma
leaving the slowly perfused compartment, CVS, is not equal to
CS/PS), as illustrated by A-17:
 | (A-17) |
Finally, the mass balance equation for the venous return becomes
 | (A-18) |
For the refined
model, A-18 replaces A-7.
A model describing the plasma concentration of metabolites tetramer-triol, trimer-diol, dimer-diol, monomer-diol, and monomer-triol (i.e., CIVT, CIIID, CIID, CID, and CIT, respectively) was also developed. Instead of including a one-compartment model for a combined metabolite pool, a one-compartment model was included for each individual metabolite. The volume of distribution for each metabolite was assumed to be the same as it was for the combined metabolite pool. The rate of change of the metabolite concentrations are described as follows:
 | (A-19) |
 | (A-20) |
 | (A-21) |
 | (A-22) |
 | (A-23) |
where K1, K2, K3, and K4 are first-order reaction rate constants
for the metabolism of tetramer-triol, trimer-diol, dimer-diol,
and monomer-diol, respectively, as shown in Figures 3 and 4
.
The cumulative amount of monomer-triol, monomer-diol, dimer-diol,
and trimer-diol in the urine (i.e., AIT, AID, AIID, and AIIID,
respectively) can be calculated using the equations:
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ABSTRACT
INTRODUCTION
