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ToxSci Advance Access originally published online on April 1, 2008
Toxicological Sciences 2008 104(1):210-217; doi:10.1093/toxsci/kfn070
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© The Author 2008. Published by Oxford University Press on behalf of the Society of Toxicology. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

Effect of PBPK Model Structure on Interpretation of In Vivo Human Aqueous Dermal Exposure Trials

Anayi M. Norman*, John C. Kissel*,1, Jeffry H. Shirai*, Joseph A. Smith*, Kelly L. Stumbaugh* and Annette L. Bunge{dagger}

* University of Washington, Seattle, Washington 98105 {dagger} Colorado School of Mines, Golden, Colorado 80401

1 To whom correspondence should be addressed at Environmental & Occupational Health Sciences, University of Washington, 4225 Roosevelt Way NE, Suite 100, Seattle, WA 98105-6099. Fax: (206) 543-8123. E-mail: jkissel{at}u.washington.edu.

Received October 17, 2007; accepted March 14, 2008


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 FUNDING
 REFERENCES
 
Multiple research teams have reported data from in vivo human trials in which breath was monitored during and after whole-body or partial immersion in aqueous solutions of volatile organic compounds. Estimation of total dermal absorption from exhaled breath measurements requires modeling, a task to which physiologically based pharmacokinetic (PBPK) models have often been applied. In the context of PBPK models, the exposed skin compartment can be modeled in many different ways. To demonstrate potential effects of alternative skin models on overall PBPK model performance, alternative models of skin have been incorporated in a PBPK model used to predict chloroform in breath during and after immersion in aqueous solution. The models investigated include treatment of skin as both a homogeneous phase and as a membrane in which concentration varies with depth. Model predictions are compared with in vivo human experimental results reported in the prior literature. In the example chosen, the common practice of modeling skin as a homogenous phase leads to prediction of more rapid initial uptake and lower cumulative uptake than does modeling skin as a membrane. Numerical estimates of the permeability coefficient are shown to be dependent upon skin model form and temperature of the aqueous solution.

Key Words: absorption; biomonitoring; breath; model; skin; VOCs.


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 FUNDING
 REFERENCES
 
Results have been reported from multiple human in vivo trials conducted to assess dermal absorption of volatile organic compounds (VOCs) from aqueous solution (Gordon et al., 1998Go; Poet et al., 2000aGo, bGo; Thrall and Woodstock, 2003Go; Thrall et al., 2002Go; Xu and Weisel, 2005Go). Because these experiments utilized VOC concentration in exhaled breath as the indicator of exposure, interpretation requires modeling of the relationship between total VOC absorbed and VOC exhaled. Physiologically based pharmacokinetic (PBPK) models can be and have been applied to this task. Dermal absorption is typically characterized by a compound- and external medium-specific permeability coefficient (Kp). By using Kp as a fitting parameter to match PBPK model predictions to breath data, results from the in vivo experiments noted above can be employed to estimate Kp. Values of Kp calculated in this manner can be compared with values obtained using the modified Potts-Guy equation recommended by the U.S. Environmental Protection Agency (EPA) in current guidance (U.S. EPA, 2004Go). The modified Potts-Guy equation is based on results obtained in vitro. If interpreted appropriately, in vivo experiments therefore represent a potential check on EPA's estimation method.

Published PBPK models have not routinely included skin as most were developed for investigation of oral or other non-dermal dosing scenarios. However, PBPK models can easily be modified by adding skin compartments. McCarley and Bunge (2001)Go have reviewed various versions of one- and two-compartment skin models. They distinguish three types of one-compartment model that employ properties of actual skin layers (stratum corneum, viable epidermis, dermis) with respect to transport resistance and storage to represent overall skin function either by assuming particular layers are controlling or negligible or by some sort of averaging of their properties. Two-compartment skin models are typically utilized when neither the stratum corneum nor viable epidermis can be neglected because both contribute to transport resistance or storage. Regardless of the number of compartments in these simple adaptations, internal concentration in each compartment is considered uniform at all locations. The term continuously stirred tank reactor (CSTR) is generally used in chemical engineering to describe a modeled volume in which this condition applies. Although modeling of skin as one or two CSTRs is common, experiments have shown that skin behaves like a membrane (Scheuplein, 1972Go), that is, concentration of penetrating chemical varies with position. However, because mathematical models treating the skin as a membrane require somewhat more cumbersome mathematics and computing resources, they are less utilized despite their greater plausibility.

For purposes of comparison, three variations of a PBPK model are applied here. In each case, the core of the model is the same, with only treatment of skin altered. The first version, referred to below as the CSTR model, describes skin as a single compartment that is homogeneous with respect to concentration. This approach is common in the prior literature, and merely involves creating a skin compartment analogous to other physiological compartments, which are traditionally modeled as CSTRs. Treatment of skin as a membrane in which a one-dimensional concentration gradient forms is more sophisticated and more consistent with what is known about the physiology of the skin. Because the membrane model used here employs a finite-difference scheme to simulate skin as a membrane, it is referred to as the finite-difference (FD) model. Alternatively, by modifying the CSTR rate constants to match predictions of a membrane model for specific conditions, an approximate membrane model can be created that is computationally simpler than a true membrane model. McCarley and Bunge (1998)Go have developed several models of this type. The simplified time lag (STL) model is the simplest that contains most of the essential features and is used here to demonstrate the performance of an intermediate skin model form.

In all three models used here, the skin compartment is assumed to have the physiological properties of the stratum corneum only. This is a reasonable assumption for absorption of chloroform (CHCl3), which is used as a test compound. CHCl3 was chosen to take advantage of prior efforts of Gordon et al. (1998)Go and Corley et al. (1990Go, 2000Go). Gordon et al. (1998)Go performed experiments in which subjects were immersed in water containing CHCl3 in hydrotherapy tubs while breathing purified air to eliminate inhalation exposure. Exhaled breath concentration of CHCl3 was monitored during the roughly 0.5-h exposure period and postexposure. Water concentration (c. 90 ppb) and temperature (nominally 30°C, 35°C, and 40°C), and immersion time varied slightly across subjects. A total of 10 (five male, five female) volunteers participated, but not all subjects produced data at each of the target temperatures. Corley et al. (2000)Go analyzed these experiments after adapting their prior CHCl3 PBPK model (Corley et al., 1990Go) by adding a (CSTR) skin compartment.

The objective of this paper is to demonstrate potential differences in overall PBPK model performance when using the CSTR, approximate membrane (STL), and true membrane (FD) models of skin. If model predictions vary across the model types, values of any parameters, such as Kp that are estimated by fitting may also be model-dependent. Unless model-induced effects are either known to be negligible or understood and controlled, comparisons of apparent results across laboratories, species or techniques (e.g., in vivo/in vitro) may lead to incorrect conclusions regarding differences or lack thereof in values of parameters used to describe dermal phenomena.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 FUNDING
 REFERENCES
 
All three model versions, CSTR, STL, and FD, were created using Matlab 7.2 (The Mathworks, Natick, MA). All models were composed of differential equations representing the compartments shown schematically in Figure 1. The general approach used here is similar to that reported by Corley et al. (2000)Go. Base equations describing the systemic distribution and elimination of a chemical are presented in Table 1. Those equations are consistent with the approach taken by Corley et al. as is the assumption that alveolar respiration accounts for 70 percent of total respiration (Ramsey and Andersen, 1984Go). Notable conceptual differences include (1) implementation of versions (discussed below) that do not model skin as a CSTR, (2) characterization of skin using properties of the stratum corneum rather than the whole skin, (3) inclusion of the kidney within richly perfused tissue rather than as a discreet compartment, and (4) restriction of CHCl3 metabolism to the liver only. Corley et al. modeled the kidney discreetly to gain insight into potential toxicological effects that are not a topic of this paper. The contribution of the kidney to total metabolism was negligible and is therefore ignored here. In addition to these conceptual changes, numerical values of some input parameters and the manner in which cardiac output, ventilation rates, and blood flow to tissues were estimated for exposures at different temperatures differ from Corley et al. (2000)Go. Corley et al. estimated metabolic parameters by extrapolation from rodent experiments. More recent human data reported by Lipscomb et al. (2003Go, 2004Go) are used here. Parameters for the models are shown in Tables 2 and 3. The skin/water partition coefficient was estimated using a formula relating the stratum corneum/water partition coefficient (Kscw) to Kow (Bunge et al., 1995Go):


Figure 1
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  		FIG. 1. Schematic of the PBPK framework used here. (In the FD model, the skin compartment is further segmented into 20 layers.)

 

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  		TABLE 1 Equations Governing Compartments Other than Exposed Skin

 

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  		TABLE 2 Temperature-Independent Model Parameter Values

 

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  		TABLE 3 Temperature-Dependent Model Parameter Values

 

Formula (1)

The skin/blood partition coefficient was calculated by dividing the skin/water partition coefficient by the blood/water partition coefficient. The blood/water partition coefficient was estimated as the product of the blood/air partition coefficient (average of values reported by Steward et al., 1973Go and Gargas et al., 1989Go) and the Henry's law constant for CHCl3 at body temperature. Cardiac output and blood flow to the skin were estimated using data from sources shown in Table 3. The density of all tissues was assumed to be 1 kg/l. Values of the permeability coefficient from water, Kp, were estimated individually for each model and bath water temperature by Markov chain Monte Carlo (MCMC) fitting to observed breath data from Gordon et al.‘s trials using subject no. 7. Those calculations were conducted in WinBUGS 1.4.2 with BlackBox 1.5.

Movement of a chemical compound among water, skin, and blood compartments for the CSTR and STL model versions is depicted in Figure 2. The rate at which the chemical moves among the compartments is controlled by the rate constants (k1, k–1, k2, and k–2) and the concentration of the chemical in each compartment. Equations for the CSTR and STL model rate constants are shown in Table 4. The STL model mimics the membrane model for certain conditions (McCarley and Bunge, 1998Go, 2001Go). Equations for the exposed skin compartment for the CSTR and STL models are shown in Table 5. The membrane model utilizes a second-order FD scheme (Table 6). In the postexposure period, the external phase is air rather than water. Postexposure evaporation from the exposed skin is allowed by the models presented here. For a volatile compound such as CHCl3, skin-side mass transfer resistance would be expected to control evaporation, and the exposure model equations will still apply if Cw = 0.


Figure 2
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  		FIG. 2. Schematic diagram of the movement of a chemical compound among water, skin, and blood for a single skin compartment PBPK model (adapted from Reddy et al., 1998Go).

 

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  		TABLE 4 Rate Constants for the CSTR and STL Models (Reddy et al., 1998Go)

 

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  		TABLE 5 Equations for Exposed Skin Compartment in the CSTR and STL Models

 

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  		TABLE 6 Finite-Difference Scheme for Membrane (FD) Model

 

   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 FUNDING
 REFERENCES
 
Concentration profiles of CHCl3 in exhaled breath generated by the three models are displayed in Figure 3 as are breath data from Gordon et al. (subject no. 7, 39°C). In each case values of Kp were obtained by MCMC estimation using breath data from the approximately 30-min exposure period. The CSTR model predicts a peak CHCl3 breath concentration of less than 7 ppb at the end of the exposure period. Both the STL and FD models predict higher peak breath concentrations. In the case of the FD model, the peak occurs shortly after the end of the 29-min exposure period (i.e., at about 31 min) due to continuing exhalation of previously absorbed CHCl3. The CSTR model predicts immediate appearance of CHCl3 in the exhaled breath upon initiation of exposure and immediate decline upon cessation. The STL and FD models predict more gradual appearance of CHCl3 in the exhaled breath with the FD breath profile exhibiting a distinct initial lag period (i.e., delayed initial appearance of CHCl3 in the breath). Both membrane models also predict more gradual decline of CHCl3 in breath after exposure ends.


Figure 3
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  		FIG. 3. Breath concentration profiles for the CSTR (dotted line), approximate membrane/STL (dot-dashed line), and membrane/FD (solid line) models using water permeability coefficients obtained by MCMC fit to 29-min exposure phase data from Gordon et al.‘s (1998)Go subject no. 7 (39°C trial).

 
The membrane models also predict differing disposition of CHCl3 (Figs. 4 and 5) than the CSTR model. In the CSTR output the cumulative mass of CHCl3 transferred from the water into the skin is essentially the same as the mass transferred from the skin to blood, that is, storage of CHCl3 in the skin is negligible (Fig. 4a). In contrast, the STL (Fig. 4b) and FD (Fig. 4c) models predict that skin-to-blood transfer lags water-to-skin transfer, leading to substantial accumulation of CHCl3 in the skin at 30 min. The cumulative mass of CHCl3 predicted to be transferred from water into skin by the membrane models is roughly double that predicted by the CSTR model during the exposure period, but the corresponding transfer from skin to blood in the first 30 min is roughly the same across the three models. Each of the models also predicts that roughly half of the CHCl3 transferred from skin to blood would be accounted for by storage in compartments other than skin at the end of the exposure period. The remaining mass of CHCl3 passing through the skin is approximately equally divided between metabolism and exhalation. Internal checks confirm that all three models conserve mass within a reasonable margin of error.


Figure 4
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  		FIG. 4. (a, b, and c) Mass balance on skin for the CSTR, approximate membrane (STL), and membrane (FD) models during the 29-min exposure to 39°C water. The solid, dotted, and dashed lines represent the net mass (mg) of CHCl3 transferred from water to exposed stratum corneum, mass (mg) of CHCl3 stored in the stratum corneum, and mass (mg) of CHCl3 transferred from stratum corneum to blood, respectively.

 

Figure 5
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  		FIG. 5. (a, b, and c) Disposition of absorbed mass as predicted by the CSTR, approximate membrane (STL), and membrane (FD) models during the 29-min exposure to 39°C water. The dashed, solid, dot-dashed, and dotted lines represent the net mass (mg) of CHCl3 transferred from exposed stratum corneum to the bloodstream, mass (mg) of CHCl3 stored in compartments other than exposed stratum corneum, mass (mg) of CHCl3 exhaled, and mass (mg) of CHCl3 metabolized, respectively.

 

   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
FUNDING
 REFERENCES
 
Because a CSTR model overestimates initial breath concentration, fitting of such a model to breath data will lead to underestimation of subsequent breath concentration. This effect is apparent in Figure 3. Some prior investigators have "manually" induced a lag in a CSTR skin model by starting simulations at t > 0. Although this tactic may produce an apparent improvement in fit initially, it has the effect of requiring that the actual exposure period be artificially shortened. Because the STL (approximate membrane) model is a modified CSTR, it also predicts instantaneous appearance of VOC in breath. However, the effect is dampened and more gradual. The true membrane (FD) model predicts a lag more consistent with the data shown in Figure 3. However, the FD model is computationally more expensive than the other two models. A potential advantage of the STL approach is that it requires only slightly more computing time than the CSTR model, but produces a result very similar to the FD model. In applications in which the model must be run repeatedly, such as MCMC fitting or other stochastic simulations, approximate membrane solutions may be very useful.

Overall absorbed doses predicted by the membrane models were larger than those predicted by the CSTR model. If chronic exposures are of primary interest, CSTR approaches may underestimate dose. Conversely if acute effects are of primary interest, CSTR approaches may overstate short-term dose. In effect, CSTR models dump penetrants into the blood stream very quickly. This phenomenon may be important in scenarios in which the doses being evaluated are near those that produce acute effects.

Permeability coefficients estimated using the various models are presented in Table 7. The three approaches used here are contrasted for each of the Gordon et al. exposure temperatures. Dependence of the estimated Kp on both model type and temperature is evident. For the 39°C case, estimates derived from membrane approaches were about 25% larger than the value produced for the CSTR model. For the lower temperatures, Kp estimates from the membrane approaches were 1.5–5 times the CSTR estimates. The 28°C values are of particular interest because the data on which the Potts-Guy model is based were obtained in vitro at or near 30°C. In this case, values of Kp obtained from fitting the STL and FD models at the lowest experimental temperature are both closer to the Potts-Guy estimate than the value obtained from fitting the CSTR model. This is a logical outcome because the Potts-Guy estimates are based on membrane interpretation of in vitro data. Failure to match a Kp derived from (similar temperature) human in vivo data to the Potts-Guy estimate should therefore not be assumed to be evidence of in vivo/in vitro differences as it could also be explained by dissimilarity of modeling approaches.


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  		TABLE 7 Estimates of Kp (cm/h)

 
Substantially elevated Kp estimates at the higher temperatures are reported here, a finding consistent with the prior interpretation of Corley et al. (2000)Go. This result is attributable to higher observed breath concentrations at higher water temperatures and is relatively insensitive to assumptions regarding blood flow rates. Increasing total cardiac output and relative blood flow to the skin with increasing temperature, as assumed here, have countervailing effects on the magnitude of Kp required to match the breath data in all three models. A finding of substantially elevated Kp suggests that the ratio of dermal to ingestion exposure to CHCl3 (and by extension to other VOCs in water) may be much greater than estimated in EPA guidance (U.S. EPA, 2004Go), in which dermal exposure calculated using the modified Potts-Guy regression is contrasted with exposure associated with consumption of 2 l of drinking water.

In summary, the predictions of PBPK models that incorporate a skin compartment are generally sensitive to the form of the skin model used and the temperature of the external medium. If values of the permeability coefficient, Kp, are back-fit from experimental data, these effects should be considered.


   FUNDING
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 FUNDING
REFERENCES
 
U.S. Environmental Protection Agency (cooperative agreement R-82963201); and Centers for Disease Control and Prevention/National Institute for Occupational Safety and Health (training grant T42/CCT010418-11) to A.M.N. and J.A.S. and (T42/OH008433) to K.L.S.


   ACKNOWLEDGMENTS
 
Material presented here has not been reviewed by EPA and no Agency endorsement should be inferred. We thank S. Gordon for sharing data.


   REFERENCES
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 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 FUNDING
 REFERENCES
 
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