* ICF Consulting, P.O. Box 14348, Research Triangle Park, North Carolina 27709;
Environ Corporation, 933 Mesa Lane, Collegeville, Pennsylvania 19426;
Department of Environmental Health, CETT/Foothills Campus, Colorado State University, Ft. Collins, Colorado 80523;
RHR Toxicology Consulting Services, Midland, Michigan 48640; and
¶ Toxicology, Health and Environmental Sciences, Dow Corning Corporation, Mail CO3101, Midland, Michigan 48686
Received July 25, 2002; accepted October 18, 2002
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ABSTRACT |
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Key Words: inhalation, oral; dermal; iv; multiroute; pharmacokinetics; PBPK model; siloxane.
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INTRODUCTION |
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A multiroute PBPK model for D4, once extended to humans, would be used to support estimation and extrapolation of tissue dosimetry, specifically, the amount of biologically active ("free") D4 in humans exposed via multiple routes across dose, dose route, and species. A successful multiroute PBPK model would identify and address route-specific differences in disposition, metabolism, and bioavailability of D4, and could be used for exposure assessment or to reconstruct human exposure from measurements of tissue concentrations in humans. Since chemical toxicity is a consequence of the delivery of active forms of toxic compounds to target tissues, where specific chemical interactions initiate organ-level responses, PBPK models that permit estimation of pertinent tissue-dose metrics are a useful tool to implement mode-of-action driven risk assessments.
In this paper, an extension to the existing inhalation model (Andersen et al., 2001) is developed to quantitatively characterize the retention, distribution, and elimination of D4 and its hydrolysis and oxidation products following dermal, oral, and intravenous (iv) exposures in the rat. Concentrations of D4 in plasma, exhaled breath, and urinary metabolite excretion data, measured following dermal, oral, or iv dosing, formed the basis for the model extension and validation. A major focus of this work was to identify and accommodate route-specific pharmacokinetic behaviors, and as such, the results of previously published simulations of inhalation exposures are not repeated here (Andersen et al., 2001
) This PBPK model is intended to provide the basis for estimating tissue dosimetry of D4 and for supporting extrapolations of tissue dose across dose, dose route, and species for D4, and possibly other volatile cyclic methyl siloxanes.
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MATERIALS AND METHODS |
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Experimental data from intravenous administration.
D4 pharmacokinetic behavior following a single iv dose has been evaluated in male and female rats (Kirkpatrick, 1995). Ten male and ten female Sprague-Dawley (CD) rats (195225 g, Harlan Olac Ltd, Bicester, Oxon, U.K.) per dose group were acclimated for 5 days and administered 7 mg/kg D4 intravenously. D4 was administered as an emulsion, 1:1:7 ethanol, Emulphor EL620 (Rhone Poulenc, NJ) and saline (0.9% w/v Baxter Healthcare, Ltd, Thetford, Norfolk, U.K.). Blood samples were taken at 11 time points between 0 and 48 h following dosing. An additional group of 5 female and 5 male rats were administered 7 mg D4/kg and moved to glass metabolism cages for separate collection of urine, feces, and expired air, to demonstrate a good recovery of radioactivity (98 and 93% of administered dose for males and females, respectively). Radioactivity in blood, urine, and expired air (as 14CO2 from combusted charcoal trap contents) were quantified by liquid scintillation counting in terms of D4 equivalents.
Experimental data from oral exposures.
Three groups of rats (female Fischer 344, 149177 g, Charles River Laboratories, Raleigh, NC) received oral doses of 300 mg D4/kg (25 mCi 14C-D4), either in a neat form or in simethicone (Dow Corning® 79254 LVA) or in corn oil (Mazola) (Plotzke, 1998). One group of 50 rats per formulation (5 animals per time point, 10 time points) was used for determination of plasma D4. Following dosing, the blood group animals were placed in stainless steel metabolism cages. Five animals per time point were anesthetized and blood was collected at 15 and 60 min, 6, 12, 24, 48, 72, 96, 120, and 144 h. D4 content in blood samples was determined by GC/MS (Varaprath et al., 1998
, 2000
).
One group of 5 rats was used for mass balance and determination of D4 and metabolites in excreta (urine, feces) and expired air. The excreta group also served as the 168-h time point for blood collection. Excreta groups were acclimated in all glass metabolism cages for at least 2 days prior to administration of test material. Immediately following the administration of 14C-D4 by oral gavage, the animals in the excreta group were housed individually in glass metabolism cages suitable for the separate collection of excreta (urine, feces) and of expired air (14CO2 and other volatiles). Urine, feces, and expired CO2 were collected at 6, 12, 24, 48, 72, 96, 120, 144, and 168 h. Expired volatiles were collected at 1, 2, 4, 6, 24, 48, 72, 96, 120, 144, and 168 h postexposure. Urine and feces were collected over dry ice, expired 14CO2 was trapped in a single 4-N potassium hydroxide (KOH) trap, and expired volatiles were collected via charcoal tubes. Total radioactivity (14C-D4/metabolites) in excreta, expired CO2 and volatiles (as toluene extracts of the charcoal traps or directly as aliquots from the KOH trap), and blood was determined by liquid scintillation counting. Mass balance calculations demonstrated good recovery of radioactivity following administration of D4 in corn oil (93.2%), simethicone (92.74%), and as neat D4 (82.9%).
Experimental data from dermal exposures.
Female Fischer 344/CrlBR rats (Charles River Breeding Laboratories) were exposed by the dermal route to 25, 12, or 5 mg of neat 14C-D4 applied over a skin surface area of approximately 2.5 cm2 for a 24-h duration (Jovanovic et al., 2000). In this dermal exposure experiment, the skin was semioccluded with a charcoal basket to capture volatilized D4. The charcoal basket was removed after 24 h and the dosed skin area was washed. Each exposure group contained 2 control and 24 treated animals. Blood kinetics data were collected via jugular cannula in 8 rats, and excreta (urine, feces) and exhaled volatiles and 14CO2 were collected (as described previously) in 16 rats placed in glass metabolism cages after the start of dosing. Urine, feces, and expired CO2 were collected at 6, 12, 24, 48, 72, 96, 120, 144, and 168 h. Expired volatiles were collected at 1, 2, 4, 6, 24, 48, 72, 96, 120, 144, and 168 h postexposure. Plasma D4 concentration was assessed at 0.5, 1, 2, 4, 6, 10, 24, and 168 h postexposure. The plasma D4 concentrations were very low in the high-dose group and were below detection limit in the two lowest dose groups. Radioactivity was determined by liquid scintillation counting as described previously. Total parent D4 in exhaled air was determined by GC/MS (Varaprath et al., 1998
, 2000
) following toluene extraction of the charcoal traps. Mass balance calculations demonstrated good recovery of radioactivity following dermal administration of D4. At 168 h postexposure, total dose recovery at all three dose levels was higher than 91%.
PBPK model structure.
A PBPK model developed to study the disposition of inhaled D4 has been applied successfully to estimate a diverse set of tissue level dose metrics in rats, following a variety of exposure scenarios to D4 (Andersen et al., 2001). The initial multiroute model structure (Fig. 1
), applied to analyze the disposition of D4 in rats following dermal, oral, and iv exposure, is simply an extension of a D4 inhalation model (Andersen et al., 2001
) to other exposure routes. This initial model consists of multiple compartments representing fat, liver, lung, blood, GI tract, rapidly perfused tissues, skin, and other slowly perfused tissues (Fig. 1
). These individual tissues are described as homogenous, well-mixed compartments and are connected by the systemic circulation. Following inhalation exposure to D4, the arterial blood that flows out of the lung compartment, at a rate equal to the cardiac output, supplies D4 to these tissue compartments. Parent D4 is stored in fat and other tissue compartments, depending on their physiological parameters; i.e., tissue volumes, regional blood perfusion rates, and tissue:blood partition coefficients. 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.
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Since 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 initial model had deep compartments to represent the tissue-lipid pool in the lung, liver, and blood. The shallow tissue compartment containing free D4 is in equilibrium with the blood perfusing the tissues. The net transport of D4 between the deep and the shallow tissue compartments in the liver and lung was estimated as the product of a diffusional transfer coefficient and the concentration gradient of free D4 between the two compartments. 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 using two fat compartments in the initial model: 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. D4 in the deep blood compartment was formulated as a balance between a first-order transfer from the deep liver compartment and slow clearance into the fat compartment.
Following standard approaches to model exposure routes, the iv exposure was introduced in the initial model structure as a bolus dose into the venous blood compartment. The oral dose was introduced as a bolus dose to the GI tract compartment. D4 was cleared from the GI tract compartment by a first-order uptake term into the shallow liver tissue and by another first-order clearance term into the feces. Dermal exposure was modeled as a bolus dose to a (virtual) topical compartment placed on top of the dosed skin compartment. D4 was transported from the topical compartment, either by volatilization (into a charcoal basket compartment) or permeation into the dosed skin area, both represented by first-order clearance terms. The blood perfusing the dosed skin compartment was assumed to be in equilibrium with tissue D4 and contributed directly to the mixed venous circulation (Fig. 1).
The governing mass balance equations that describe the rate of change of parent D4 in the various compartments, and the total excreted metabolite in the urine appearing in the initial multiroute model, are similar to those presented elsewhere (Andersen et al., 2001) and are not repeated here. The resulting series of differential equations were solved by numerical integration using the Gear algorithm for stiff systems in ACSL® (Advanced Continuous-Simulation Language, AEgis Technologies, Huntsville, AL).
Model parameterization.
Physiological parameters such as tissue volumes and blood perfusion rates for the various organs were obtained from the literature (Brown et al., 1997). All other parameters used in the inhalation PBPK model, such as partition coefficients and hepatic metabolism parameters and diffusional transfer rates between deep and shallow pools, were retained unchanged in the multiroute model. Simulations of inhalation exposure pharamacokinetics, which are not repeated here, are not different in this version of the model from those previously published (Andersen et al., 2001
). The remaining route-specific model parameters such as first-order absorption rate into the liver from the gut, first-order elimination rate from the gut into the feces, rate of volatilization from the topical compartment, and the penetration rate into the skin for the topical dose had to be estimated from the experimental data. A small subset of the available PK data was used for model calibration and the remaining was used in validating the model. The estimated model parameters are provided in Table 1
.
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PK data following dermal exposure were available at three different dose levels. D4 concentration time course data in charcoal basket (data not shown) and D4 in exhaled air from the high dose group (25 mg) were used to parameterize the model for the dermal exposure, and the remaining two lower dose groups were used to validate the model for this exposure route. The rate of volatilization was estimated by fitting the model to the D4 concentration time course in the charcoal basket, and the rate of penetration into the skin was estimated by fitting the model to the D4 concentration time course in exhaled air.
For the oral gavage dose, absorption and transfer rate constants were estimated for each carrier fluid: corn oil, simethicone, and neat. For each of the carrier fluids, the elimination rate from the gut was estimated by matching model-derived feces D4 concentrations to experimental measured values. Similarly, the absorption rate from the gut into the liver was estimated by visually fitting the model predictions for D4 excretion rate in urine to measured data. The uptake rate constant was highest with corn oil as the carrier and lowest for simethicone, with neat falling in the middle. This behavior is consistent with the observation that uptake of lipophilic compounds by the GI tract and transport via the lymphatics are influenced by dietary fat concentrations (Roth et al., 1993b). D4 concentrations in plasma and data on exhaled D4 were used to validate the model following oral exposure.
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RESULTS |
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The oral route was revised to be consistent with slow uptake (conceptualized as lymphatic system transport) and delivery of a nonexchangeable form of D4 into the blood. D4 was first delivered as a bolus input into the GI tract compartment, with a first-order uptake into a deep blood compartment, after a short time delay in the refined multiroute model (Fig. 8). D4 bound in this deep storage pool was assumed to diffuse reversibly to the exchangeable blood pool. Consistent with the liver and lung tissue, the net transport of D4 between the deep and the shallow blood compartments was proportional to a diffusional transfer coefficient and the concentration gradient of free D4 between the two compartments. D4 bound to the blood lipoproteins may be selectively sequestered in the fat depots and in the liver and modeled as first-order clearance from the deep blood compartment. Consistent with the earlier inhalation model, transfer of hepatic D4 into the blood lipoproteins was modeled as a first-order uptake term into deep blood. The iv exposure route was revised and D4 was introduced as a bolus dose into the deep blood, rather than exchangeable blood compartment (Fig. 8
). The governing mass balance equations for the various compartments in the refined multiroute model are derived in the Appendix and model parameters are presented in Table 1
.
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A comparison of relative fractional clearance of D4 by exhalation and excretion following inhalation, dermal, oral, or iv exposures shows that greater than 90% of absorbed dose is cleared by gas exchange in the lung for inhalation/dermal routes and the remaining (less than 10%) is excreted in urine. Only a very small fraction of the absorbed dose (less than 0.3%) is retained in the body, postexposure from inhalation/dermal routes (Fig. 9). However, for the oral/iv routes, the relative significance of exhalation and excretion is approximately equal (
49%) and a much larger fraction (
2%) is retained in the fat depots postexposure (Fig. 9
).
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DISCUSSION |
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Route-specific D4 disposition.
The processes that govern delivery of D4 to the blood compartment are similar between the inhalation and dermal routes of exposure. Air phase delivery of D4 to the blood from the pulmonary region and dermal delivery of D4 following topical exposure occur by partitioning and passive diffusion controlled by the free D4 concentration gradient. The form of D4 delivered to the blood is not expected to differ for these two routes. D4 is delivered to the blood as free D4, in what can be described as a molecular infusion-like process. Thus, the tissue distribution, metabolism, and clearance of D4 would be similar for these routes of exposure, and the parameterization for distribution and clearance determined by fitting multiple inhalation data sets (Andersen et al., 2001) provides accurate simulations of pharmacokinetics following dermal exposure, given a standard model of dermal absorption of D4.
D4 delivered by oral or iv routes appears to enter the blood compartment in a form different from that for the inhalation and dermal routes, which are diffusion-controlled processes. D4 most likely enters the blood as lipid-like particles when administered as an emulsion by the iv route. For the oral route, significant amounts of D4 may be delivered via the lymphatics within the lipid core of chylomicrons and other lipoproteins (Roth et al., 1993b). Refining the oral route submodel to approximate some pharmacokinetic characteristics of delivery of D4 through the lymphatics to the deep blood compartment led to improved fits to the observed plasma D4, exhaled D4, and urinary metabolite elimination rate. Similarly, modifying the iv submodel to deliver D4, not as free D4 into the blood but directly into the blood lipoprotein pool (deep blood), restricted clearance of D4 from the blood and significantly improved simulations of plasma and exhaled D4 as well as metabolic clearance (urinary metabolites). The route-specific differences in pharmacokinetics and the biologically motivated refinements necessary to represent them imply that the disposition and clearance of D4 is strongly controlled by its distribution in the blood lipoproteins (deep blood). Inhalation and dermal are the major routes of exposure for D4 in humans. Given the route-specific nature of D4 pharmacokinetics, PK data collected using iv or oral routes of exposure are not going to be useful in understanding the bioavailabilty or tissue kinetics of D4 for the inhalation or dermal routes. A lack of understanding of these route-specific differences in D4 pharmacokinetics and the consequent misrepresentation of these processes in a PBPK model (Luu and Hutter, 2001
) can result in misleading and erroneous conclusions (Andersen et al., 2002). Adequately characterizing these route-specific differences and incorporating them into PBPK models will be critical for conducting model-based interspecies and dose-route extrapolation for D4.
Deep compartments.
Preferential storage in lipid-rich tissues such as fat and, if hepatic metabolism is limited, the liver, is a common characteristic of lipophilic chemicals. These tissues act as depots with slow time constants for equilibration with blood, and lead to identifiable pharmacokinetics. D4 is a highly lipophilic compound with an uncharacteristically low blood:air partition coefficient. These attributes lead to blood and tissue pharmacokinetics that are unusually sensitive to fat and other tissue storage (Andersen et al., 2001). Successful modeling of D4 concentrations or its metabolites in the lung, liver, fat, and blood tissue, as well as exhaled D4 concentrations, required the inclusion of standard and "slow" tissue and blood depots. The latter were referred to as "deep" compartments, reflecting slower kinetics of equilibrium with blood. The physiological correlates of these deep compartments are not known with certainty. Slow and fast depots of endogenous lipophilic compounds such as cholesterol have been described for most tissues (Oh et al., 1976
). It is possible that these slow depots are common to all tissues, but tissue size, and in the case of D4, the tissues for which concentration data are available, limit the sensitivity of the model to the presence of these compartments.
Liver and adipose tissue exchange cholesterol, here a proxy for lipophilic chemicals, into two kinetically independent pools. Elimination kinetics identifies a slow and fast depot in both tissues (Oh et al., 1976), consistent with a membrane-free pool and an intracellular pool. The origin of the intracellular pool may differ from tissue to tissue, representing the lipid environment of the endoplasmic reticulum and/or the membranes of the various organelles or some cell type-specific lipid pool. Given the two pools in the liver, it appears unnecessary to invoke the possibility of an inducible binding protein, as was identified for TCDD (Leung et al., 1990
; Poland et al., 1989
; van Birgelen and van den Berg, 2000
). However, specific physiological and biochemical structures exist that may also represent specific deep compartments for the lung and blood compartments.
The physical chemical properties of hydrophobic compounds such as hormones, fat-soluble vitamins, and xenobiotics like D4 severely limit their solubility in blood. Transport of D4 through the blood seems to be controlled by the movement of fat-soluble carriers that provide a hydrophobic microenvironment (Roth et al., 1993a). Serum proteins such as albumin can bind lipophilic compounds, but the affinity and capacity of these proteins for lipophilic compounds is greatly exceeded by the plasma lipoprotein pool (Koller-Lucae et al., 1997
; Vost and Maclean 1984
). Ocatadecane, hexadecane, DDT, and BP are carried in the blood primarily in the lipoprotein pool (Vost and Maclean, 1984
). While it appears that the solutes carried within the core triglyceride pool are available for metabolism and uptake by tissues, hydrocarbons administered intravenously in chylomicrons, for instance, have been shown to be "transferable" to the liver (Vost and Maclean, 1984
). It is possible that a fraction of this pool is less available and represents the deep blood compartment required to describe all routes of administration. This distribution to lipoproteins would be consistent with blood half-lives, which differ significantly between the various components of the lipoprotein pool. High-density lipoproteins (HDL) have a half-life on the order of several days, while very low density lipoproteins (LDL) have a half-life of several hours (Wasan and Morton, 1996
). Lipophilic compounds such as D4 may also be distributed to, and carried in, erythrocyte membranes (Koller-Lucae et al., 1997
), which may also be described with the addition of a deep blood compartment description. The model structure, which describes transport of D4 from the lipoprotein pool to the liver and sequestration in a blood lipid pool is consistent with these observations. In contrast, we assume that "free" D4 in the blood is freely available to exchange with tissues and air, behavior that is consistent with the available pharmacokinetic data. The hypotheses regarding the availability of lipoprotein-bound D4 may be tested and verified by determining the distribution of free and lipoprotein-bound D4 in venous blood following exposure by these various routes.
The observed sequestration of D4 into the lungs of rats treated by the inhalation route exceeds that which can be described based on the lipid content of the lung (Andersen et al., 2001), which is relatively low compared to organs such as the liver (Anderson et al., 1993
). A "deep lung" compartment, which has a large time constant for D4, was used to model the observed accumulation and loss of D4 from the lung compartment in the previously published PBPK model (Andersen et al., 2001
). Excellent simulations were obtained when the deep compartment was approximately 2% of lung volume, which is consistent with the fraction of the lung represented by Clara cells (Jones, 1992; Martin, 1993; Mercer et al., 1994
). The Clara cell is the site of accumulation of the methylsulfonyl derivatives of PCBs and of parent PCBs (Anderson et al., 1993
; Lund et al., 1988
; Stripp et al., 1996
). The accumulation of the metabolites of PCBs has been causally linked to the presence of Clara cell secretory protein (CCSP). This structure is a transport protein for lipophilic substances in plasma and bronchioalveolar fluid (Burmeister et al., 2001
), and is preferentially expressed in Clara cells, relative to Type II pulmonary epithelial cells (Lag et al., 2000
). Endogenous ligands for CCSP include other lipophilic compounds such as retinoic acids and the steroid hormone progesterone (Lopez de Haro et al., 1988
). The capacity of CCSP to bind lipophilic molecules makes it a candidate for binding other lipophilic molecules such as D4.
The number and size of Clara cells in the rat lung have been determined by quantitative morphometric analysis, and these studies report a total of 17.3 x 106 Clara cells in the rat lung (Mercer et al., 1994). Martin and coworkers (Martin et al., 1993
) reported a Clara cell fraction (fraction of total lung cells) of 2.8% for F344 rats. A smaller fraction of 0.8% was reported in an earlier study in Sprague-Dawley rats (Jones et al., 1982
). Based on terminal bronchiolar surface area, epithelial cell thickness, the fractional density of Clara cells, and whole lung volume (Mercer et al., 1994
), we estimated that Clara cells occupy
1% of the total lung volume in the rat. This volume fraction compares favorably to the volume of the deep compartment in the lung. The binding of D4 to CCSP would be consistent with the finding that a small volume compartment in the lung, of approximately the size of the Clara cell volume, retains D4.
The biological identity of all of the pharmacokinetically identifiable deep compartments described in the model are not yet known with certainty, but given the influence they have on the simulation of D4 kinetics, it is of interest to conduct experiments designed to test specific hypotheses regarding their identity. Characterizing the distribution of D4, specifically the amount of free D4, and the D4 associated with the lipid core of the various lipoproteins in portal and venous blood, as well as that found in the lymph system following oral exposure, would establish the extent to which uptake in the lymphatics occurs. Extending these analyses to other routes of administration would establish any dose-route dependencies of blood distribution, and the relative importance of blood lipoproteins for transport and storage in the blood for each route of administration. Such experiments might bring new insights into the processes that influence uptake, distribution, and clearance of other lipophilic compounds.
Summary
As part of ongoing research in understanding the pharmacokinetics of D4, a physiologically based pharmacokinetic (PBPK) model has been constructed to describe the tissue dosimetry, plasma concentration, and clearance in the rat following inhalation, dermal, oral, and iv exposure. The failure of a previous PBPK model for D4 to accurately describe its kinetics is credited with bringing to light route-specific differences in pharmacokinetics that otherwise may have been overlooked. This ability to evaluate expectations by simulation is strength of PBPK model-based approaches to analyzing the pharmacokinetics of novel compounds. The multiroute D4 model provides reasonably good fits to the dose route-specific pharmacokinetic behaviors of D4. The inhalation model that incorporates a simple description for dermal uptake provided excellent fits to the observed concentration time course of D4 metabolites in urine and D4 exhalation rates following dermal exposures. However, the pharmacokinetics of D4 following oral and iv exposure were sensitive to the mode of entry into the blood compartment. A refined model, describing delivery of D4 from the GI tract to the deep blood compartment as D4 within the triglyceride core in chylomicrons via the lymphatic system, and transport of D4 from the deep blood compartment to the two fat compartments provided the best fits to observed plasma D4, exhaled D4, and D4 metabolites excreted in the urine following oral exposure. Pharmacokinetics following iv administration was best described by delivery of D4 directly into the deep blood compartment, reflecting a kinetically identifiable characteristic of the administration of D4 as an emulsion for the intravenous route of exposure. This implies that the physical forms of D4 delivered by the inhalation and dermal routes are similar to each other and different from the form delivered by the iv or oral routes.
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APPENDIX |
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The rate of change of D4 in the liver is a balance between amounts gained from blood perfusion and transfer from the blood lipoprotein pool 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 shallow and deep liver compartments are:
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The rate of change in 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. The governing equation is given by:
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Chemical mass balance equations in the fat compartments and skin compartment dosed with D4 are similar to those in the richly perfused and poorly perfused tissues, except for an additional transfer term. For the fat compartments, this is a first-order transfer rate from the blood lipoprotein to the fat. For the skin compartment, it is a first-order transfer rate from the topical dose into the skin. The governing equations in the fat and skin compartments are respectively:
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The mass balance in the venous blood compartment is determined by the flow averaged D4 concentration exiting all the tissue compartments and the transfer to the blood lipoprotein pool (deep blood compartment). The governing equation is given by:
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D4 in the nonexchangeable/deep blood compartment is assumed to be in equilibrium with free D4 in the exchangeable blood compartment. D4 bound to the blood lipoproteins is assumed to be selectively sequestered in the fat depots and in the liver. These processes are modeled as first-order clearance terms from the deep blood compartment. Consistent with the earlier inhalation model (Andersen et al., 2001), transfer of hepatic D4 into the blood lipoproteins is modeled as a first-order uptake term into deep blood. Furthermore, D4 administered as an iv bolus or D4 absorbed from the GI tract following an oral gavage dose is transported to the deep blood compartment in the refined multiroute PBPK model (Fig. 8
), instead of being transported to the shallow blood compartment or the liver, respectively, as is implemented in the initial model. The rate of change of D4 in the nonexchangeable/deep blood compartment is then given by:
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ACKNOWLEDGMENTS |
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NOTES |
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2 To whom correspondence should be addressed. Fax: (989) 496-5595. E-mail: kathy.plotzke{at}dowcorning.com.
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