## Abstract

In this study, data for human dermal absorption of octamethylcyclotetrasiloxane, D4, and decamethylcyclopentasiloxane, D5, through axilla skin in vivo are interpreted using pharmacokinetic models of dermal absorption by adding the dermal exposure route to inhalation physiologically based pharmacokinetics models developed previously. The compartmental model describing dermal absorption of these compounds included volatilization of the applied chemical from the skin surface, diffusion of absorbed chemical back to the skin surface and evaporation of this chemical from the skin surface after the applied dose had cleared from the application site, uptake from the skin compartment into blood, and a storage compartment within the skin. Data from exposures in volunteers (i.e., D4 and D5 concentrations in exhaled air and plasma) were used to estimate model parameters. In volunteers exposed to either D4 or D5, the maximum concentration of chemical in exhaled air reached a maximum at or prior to 1 h following administration of the test chemical. Based on model calculations, the percent of applied dose of D4 that was absorbed into systemic circulation for men and women was 0.12 and 0.30%, respectively; for D5 about 0.05% of the applied dose was absorbed for both men and women. For both D4 and D5, model calculations indicate that more than 83% of the chemical that reached systemic circulation was eliminated by exhalation within 24 h. These whole-body pharmacokinetic models for dermal absorption of two semi-volatile compounds provide a valuable tool for understanding factors controlling their dermal absorption through axilla skin and for applying results from these studies in consumer product risk assessments.

Octamethylcyclotetrasiloxane, D4, and decamethylcyclopentasiloxane, D5, are silicone fluids found in a broad range of consumer and industrial products. Studies on both D4 (McKim et al., 2001) and D5 (Burns-Naas et al., 1998) have indicated a low order of toxicity in the Fischer 344 rat. The general population and workers involved in industrial applications of D4 and D5 may be exposed to low levels of these lipophilic, semi-volatile compounds by the dermal and inhalation exposure routes.

Recently, the dermal absorption of D4 and D5 was studied through human abdominal skin in vitro and in rats in vivo (Jovanovic et al., unpublished data). The rat in vivo study showed that >91% of applied neat D4 and >89% of applied neat D5 had volatilized from the skin application site by 24 h of application of the test chemical. Less than 1.0% of the applied dose for D4 and less than 0.1% for D5 penetrated the skin (i.e., passed from the skin into systemic compartments). Similarly, in vitro dermal studies indicated that >88% and >91% of D4 and D5, respectively, volatilized from skin before penetrating. An average of 0.5% of applied D4 and 0.04% of D5 penetrated human skin in vitro.

Assessing dermal absorption of volatile and semi-volatile chemicals can be difficult because evaporation can lead to loss of chemical. However, recent dermal absorption studies have exploited the nature of volatile chemicals. In vivo dermal absorption of several volatile chemicals, e.g., xylene (Thrall and Woodstock, 2003), methyl chloroform (Poet et al., 2000b), and trichloroethylene (Poet et al., 2000a), has been studied by exposing rats or humans to a chemical and quantifying the concentration of chemical in the exhaled air using mass dpectrometry/mass spectrometry real-time analysis. In these studies, the resulting data have been analyzed with physiologically based pharmacokinetics (PBPK) models to infer the amount of chemical absorbed through skin from the amount of chemical in exhaled air. Here, we adopt a similar technique to analyze the human, in vivo, dermal absorption data.

In this pharmacokinetic study, the dermal absorption of D4 and D5 was examined following application to axilla skin of human volunteers and the concentrations of D4 or D5 in the blood and exhaled air were determined in six volunteers for up to 24 h following the exposure. These dermal absorption studies of neat D4 and D5 are used to develop a mathematical model describing the uptake of these compounds from skin to aid in data interpretation and to add the dermal exposure route to the inhalation PBPK models to develop a multiroute model for use in human risk assessment.

A variety of mathematical models describing dermal absorption during various types of exposures are available (Roberts et al., 2001), and choosing an appropriate model structure can be difficult. Because skin is a membrane, membrane models of the skin appear more realistic (Scheuplein, 1978) but can be mathematically cumbersome. Compartment models have been developed as an alternative and permit easy combination with available PBPK models for whole-body distribution of chemicals (McCarley and Bunge, 2001). Here, we present a compartment model describing the dermal absorption of D4 and D5 that includes the storage capacity of the skin and evaporation either from the neat chemical on the skin or from chemical absorbed in skin that has diffused back to the skin surface. In vivo dermal absorption studies of D4 and D5 in the rat show that a model structure including evaporation of D4 or D5 is essential for describing the kinetics (Jovanovic et al., unpublished data). The dermal absorption data in human volunteers were used to estimate model parameters. For each compound, the dermal absorption model was combined with a human inhalation PBPK model that was developed using pharmacokinetic studies of human volunteers exposed to D4 or D5 by inhalation (Reddy et al., 2004; Reddy et al., 2003). The whole-body PBPK models that include the dermal exposure route were then used to estimate the amount of chemical that reached the blood during the dermal exposures of human volunteers to D4 or D5.

## MATERIALS AND METHODS

##### Human studies.

Studies of dermal absorption of D4 (Plotzke et al., 2000) and D5 (Plotzke et al., 2002) in human volunteers were conducted at the University of Rochester after approval from the Institutional Human Subjects Review Board. In these studies, 13C-labeled D4 and D5 were used so that siloxane absorbed during these experiments could be differentiated from that present in other sources (e.g., personal care products) and to increase the sensitivity of the analytical analysis. The D4 and D5 experiments both included three female and three male subjects. In the D5 study, subjects were asked not to shave their underarms for several days prior to the study. For the D4 study, it is not known if subjects were provided with that guideline. In two separate syringes, a total of 1.4 g 13C-D4 or 13C-D5 for men and 1.0 g for women was weighed. Subjects were positioned on their sides for the administration of the applied dose to their axillae. The contents of one syringe were administered to the indent of the axilla and allowed to absorb and evaporate for about 5 min. Then, the subject changed sides and the second half of the dose was administered to the other axilla. Because the test chemical was applied by different people during the two studies, the application area was different for D4 and D5. However, the area of the application site was measured and recorded during both studies (Table 1).

TABLE 1

Parameters Used for Model Simulations of D4 and D5 Human Dermal Exposuresa

 D4 D5 Women Men Women Men Age (years)b 30.3 ± 9.3 30.3 ± 11.8 36.7 ± 7.6 29.7 ± 3.5 Body weight (kg)c 60.0 c 70.0 c 59.6 ± 4.6 123 ± 26d Alveolar ventilation (l/min)e 6.0 7.5 6.0 7.5 Cardiac output (l/min)f 6.63 6.63 6.07 6.70 Total area of both axillae (cm2)b 30 ± 4 51 ± 21 61 ± 25 99 ± 30 Applied dose (g)b 0.96 ± 0.04 1.3 ± 0.05 0.94 ± 0.05 1.34 ± 0.05 Applied dose (mg/cm2) 32 25 15.4 13.5 For t < tclear: $k^$evap (mg/cm2/min)g 0.15 0.15 0.071 0.071 For t < tclear: $k^$1 (mg/cm2/min)h 6.1 5.1 3.0 2.6 For t > tclear: k−1 (min−1)i 120 200 0.011 0.0055 k−2 (min−1)i 0.00064 0.00030 0.0000054 0.0000057 kd (min−1)i 0.00085 0.0032 0.0084 0.00010 k−d (min−1)i 0.010 0.050 0.0040 0.0066
 D4 D5 Women Men Women Men Age (years)b 30.3 ± 9.3 30.3 ± 11.8 36.7 ± 7.6 29.7 ± 3.5 Body weight (kg)c 60.0 c 70.0 c 59.6 ± 4.6 123 ± 26d Alveolar ventilation (l/min)e 6.0 7.5 6.0 7.5 Cardiac output (l/min)f 6.63 6.63 6.07 6.70 Total area of both axillae (cm2)b 30 ± 4 51 ± 21 61 ± 25 99 ± 30 Applied dose (g)b 0.96 ± 0.04 1.3 ± 0.05 0.94 ± 0.05 1.34 ± 0.05 Applied dose (mg/cm2) 32 25 15.4 13.5 For t < tclear: $k^$evap (mg/cm2/min)g 0.15 0.15 0.071 0.071 For t < tclear: $k^$1 (mg/cm2/min)h 6.1 5.1 3.0 2.6 For t > tclear: k−1 (min−1)i 120 200 0.011 0.0055 k−2 (min−1)i 0.00064 0.00030 0.0000054 0.0000057 kd (min−1)i 0.00085 0.0032 0.0084 0.00010 k−d (min−1)i 0.010 0.050 0.0040 0.0066
a

Complete parameterization for the D4 and D5 inhalation PBPK models may be found in Reddy et al. (2003) and Reddy et al., (2004), respectively.

b

Reported values are the mean ± 1SD for three men or women.

c

Body weights were not reported in the D4 study, and so reference values were used.

d

This weight is higher than the “Reference Man” weight of 70 kg. The three male subjects weighed 99.8, 120, and 151 kg (i.e., 220, 264, and 332 lb). The compartment volumes in the D5 PBPK model were changed for the men to simulate obesity as described in the Materials and Methods section.

e

Reference values were used.

f

Calculated using the correlation (Brown et al., 1997): QC (l/min) = − 6.846 log (age, years) + 16.775.

g

This parameter was set to the experimentally measured rate of evaporation.

h

This parameter was set to the value required for the skin to clear of chemical in 5 min.

i

These parameters were calculated by fitting the model to the data.

For the D4 study, blood and exhaled air samples were obtained before the exposure and at 1, 2, 4, 6, and 24 h postexposure. For the exhaled air samples, subjects breathed 40 l of air, as determined using a dry test meter, into a specially adapted 40-l Tedlar bag using a Hans Rudolf nonrebreathing valve. For the D5 study, blood samples were drawn before the exposure and at 30 min and 1, 2, 4, and 6 h, and exhaled air samples were obtained before the exposure and at 15, 30, 45, 60, 75, 90, 105, 120, 240, 360, and 1440 min. For the air samples before the exposure, a 40-l Tedlar bag was used, but for all remaining samples a 5-l Tedlar bag was used. The concentration of 13C-D4 or 13C-D5 in plasma was determined by extracting the sample with tetrahydrofuran and then analyzing the sample using gas chromatography with mass spectrometry (GC/MS) as described by Varaprath et al. (2000). The concentration of 13C-D4 or 13C-D5 in exhaled air was determined by trapping the D4 or D5 on Tenax tubes, desorbing the chemical into pure hexane, and using GC/MS analysis.

##### Determination of evaporation rates.

Although evaporation characteristics of volatile silicones have been studied, the data could not be used for our purposes because the percent of applied dose that had evaporated was reported instead of the amount that had evaporated per area (Koini et al., 1999). A simple method was used to estimate the evaporation rate of neat D4 and D5. About 0.4 ml D4 or D5 was applied to an 8-cm diameter filter paper in a 9-cm diameter glass dish. This amount was chosen so that silicone fluid covered the entire filter paper at all times during the experiment. The dish was placed on a scale in a draft-free environment at 22°C. (The skin surface is typically about 32°C, but somewhat variable. We estimated the evaporation rate at room temperature, considering that a 10°C temperature difference would not be expected to alter the evaporation rate any more than twofold.) The weight of silicone fluid was recorded at time zero to determine the exact amount applied and 5 min later to determine the amount that had evaporated during that period. This timing is consistent with the human dermal absorption studies of D4 and D5 where the application site was only left undisturbed for about 5 min after the exposure because at that point the skin had dried. Although the rate of evaporation can decrease with time, over a period of 5 min for D4 and D5 the rate should remain constant (Koini et al., 1999). The mass balance equation describing the rate of change in the amount of chemical that has evaporated, Aevap, as a zero-order process is

(1)
where $k^$evap (mg/cm2/min) is a rate constant for evaporation, SA is the surface area exposed, and t is the time. Thus, the evaporation rates for D4 and D5 were approximated as
(2)
where ΔM is the decrease in mass observed over the time period Δt, with Δt = 5 min.

##### Compartment model for dermal absorption.

Here, we present a compartment model used to describe the dermal absorption of D4 and D5 (Fig. 1). During a dermal exposure to a neat, volatile chemical, the skin is exposed until the chemical has either evaporated or absorbed into skin (i.e., until the time required for the skin to clear of chemical, tclear). Before the skin clears of chemical, evaporation and dermal absorption of the neat chemical are both described as zero-order processes (i.e., with rates $k^$evap and $k^$1 [mg/cm2/min], respectively). Absorption into the skin is described as a zero-order process because the driving force for mass transfer (i.e., the concentration gradient) from a film of pure chemical on the skin is as high as it can be as long as the concentration of chemical in the skin remains well below saturation. After all the chemical has been cleared from the skin, chemical diffusion to and evaporation from the surface of the skin are controlled by a rate constant, k−1 (min−1). Intercompartmental rate constants are also used to control the transfer to and from a deep skin compartment and from the skin to the blood (i.e., kd, kd, and k−2 [min−1], respectively). Here, we assume that the concentration of absorbing chemical in the blood remains low relative to the amount of chemical in the skin at the exposed site; thus, the rate constant for return of chemical from the bloodstream is unnecessary.

FIG. 1.

Schematic diagram of the compartment (comp.) model for dermal absorption of D4 and D5 (A) before and (B) after all the chemical has evaporated or absorbed into the skin. The double line designates the compartment from the PBPK model to which the dermal absorption model is attached.

FIG. 1.

Schematic diagram of the compartment (comp.) model for dermal absorption of D4 and D5 (A) before and (B) after all the chemical has evaporated or absorbed into the skin. The double line designates the compartment from the PBPK model to which the dermal absorption model is attached.

Before all the D4 or D5 has cleared from the skin, the mass balance equation describing the amount of chemical on the application site, Aapp, is

(3)

By assuming that the chemical forms a uniform layer on the skin and that the skin is flat, the parameter tclear can be calculated as the time when Aapp decreases to zero. During this initial period, the amount of chemical in the skin, Askin, can be calculated using the equation

(4)
where Adeep is the amount of chemical in the deep skin compartment. Equation 4 is written assuming that D4 and D5 are not metabolized in the skin. After the application site is cleared of chemical, the driving force for mass transfer has reversed because the skin contains chemical but the air over the skin acts like an infinite sink. D4 and D5 can be eliminated from the skin by diffusion to and evaporation from the surface and by blood clearance. The mass balance equation describing Askin becomes
(5)

Using the following equation, Adeep can be calculated:

(6)

The rate at which chemical is absorbed systemically from the skin is calculated using the equation:

(7)
where Aabs is the amount absorbed systemically, i.e., the amount of applied compound that reaches the blood. At the beginning of the exposure, the amount of chemical on the skin is equal to the applied dose, the skin and deep skin compartments are free of chemical, and no penetration into cutaneous blood has occurred (i.e., at t = 0, Aapp = the amount of D4 or D5 applied to the axillae, Askin = 0, Adeep = 0, and Aabs = 0).

This model was used to analyze the data from the dermal absorption studies of D4 and D5 in humans (i.e., concentrations of absorbing chemical in the plasma and exhaled air following application of D4 or D5 to each axilla in turn). To accomplish this analysis, this dermal absorption model was combined with PBPK models describing D4 and D5 disposition in humans as shown in Figure 2. Because half of the dermal dose was applied to one axilla at time zero and the remaining half of the dose was applied to the other axilla 5 min later, two identical skin compartment models (i.e., one for each axilla) were included in the PBPK model. Additionally, it was assumed that while chemical was being applied to the second axilla, evaporation did not occur from the first axilla because the first arm was pressed under the body, which prevented the axilla from being open to the air. The skin compartment models act as input functions to the PBPK model, but the skin itself is included in the slowly perfused compartment. Chemical that penetrated the skin was assumed to enter the venous blood from the exposed site. The model equations were solved using Berkeley Madonna (Macey & Oster, Berkeley, CA).

FIG. 2.

Schematic diagram of (A) the generalized PBPK model structure and (B) the submodel for the transport of unavailable chemical in blood lipids used for both D4 (Reddy et al., 2003) and D5 (Reddy et al., 2004) pharmacokinetics in humans. The double lines designate variables from other components of the model.

FIG. 2.

Schematic diagram of (A) the generalized PBPK model structure and (B) the submodel for the transport of unavailable chemical in blood lipids used for both D4 (Reddy et al., 2003) and D5 (Reddy et al., 2004) pharmacokinetics in humans. The double lines designate variables from other components of the model.

The PBPK models for D4 (Reddy et al., 2003) and D5 (Reddy et al., 2004) are described in detail elsewhere but are discussed briefly here. The D4 PBPK model was developed using data from 14C-D4 inhalation exposures with human volunteers. In the PBPK model development, a deep compartment in the fat, a mass transfer resistance in the slowly perfused compartment, and a pool of unavailable D4 in the blood were required to adequately describe all the pharmacokinetic data. The D5 PBPK model, based on the D4 model but developed using data from a study of human volunteers exposed to D5 by inhalation, included deep compartments in the lungs and liver and a pool of unavailable D5 in the blood. For both D4 and D5, the unavailable form in the blood, presumably bound to lipoproteins, was produced in the liver, secreted to blood, and cleared into the fat.

##### Compartment model parameterization.

The compartment model for dermal absorption requires the estimation of six parameters (Table 1). The value of $k^$evap was determined experimentally and calculated using Equation 2. Because the skin looked dry 5 min after the application of D4 and D5, the rate constant $k^$1 was set so that the skin cleared of chemical in 5 min. Although the exact value of tclear is not precisely known for an accurate estimation of $k^$1, a rough estimate of this parameter is accurate enough for the model simulations because a large range of values for this parameter result in similar pharmacokinetic profiles (data not shown). This method of estimating $k^$1 results in the model simulating rapid absorption of chemical into the skin where it is available for systemic absorption; the rationale for choosing this model behavior will be addressed in detail in the Discussion section. The remaining four parameters were estimated by comparing experimentally determined and model-calculated concentrations of D4 and D5 in the exhaled air and plasma following the dermal exposure.

The dermal/inhalation model was fit to the average values of plasma concentrations and concentrations in exhaled air of men and women separately, resulting in separate sets of model parameters for men and women. Although both whole blood and plasma concentrations of D4 and D5 were determined, parameter estimation was done using plasma concentrations to be consistent with the earlier inhalation models that were also developed using plasma data. In the D5 dermal absorption study, the males had higher body weights than typical (Table 1), with a mean body weight of 123 kg. Therefore, for the analysis of the D5 male data, the volumes of tissue compartments were changed to simulate obese men (i.e., it was assumed that the liver, lung, and the rapidly perfused tissue compartment were the same size as for a 70-kg person, that the blood compartment remained at 0.059% of body weight, that the slowly perfused compartment [which includes muscle] was 20% bigger than that of a 70-kg person, and that the fat compartment was about 48% of body weight). Metabolic capability was assumed to be similar to that of a 70-kg person, instead of scaling the metabolic rate constant by body weight. For D5, the ratio of the concentration of D5 in the venous return to the concentration of D5 in exhaled air was used to estimate model parameters describing the pool of D5 sequestered in the blood.

Optimum parameters were estimated using the multiple curve-fitting routine in Berkeley Madonna as described by Reddy et al. (2003). Sensitivity analysis was used to verify that the model parameters could be determined based on the available data and that the model parameters were necessary to describe the pharmacokinetics from the dermal exposures. The model code is available from the corresponding author upon request.

## RESULTS

#### D4 and D5 Dermal Absorption in Human Volunteers

For both D4 and D5, chemical was detected in the bloodstream within an hour of the dermal exposure (Tables 2 and 3). For D4, the highest measured plasma and exhaled air concentrations for all subjects occurred at the earliest time that data were collected (i.e., 1 h following the exposure). Maximal blood concentrations must have occurred earlier than the 1-h sampling time. The concentrations of D4 in exhaled air and plasma were higher in women than in men. By 24 h, the amount of D4 in exhaled air had returned to background levels. For the D4 study, interindividual variability was significant, especially for the concentration of D4 in exhaled air. For example, the lowest and highest peak concentrations of D4 in exhaled air were 3.1 and 240 ng/l, respectively, while the lowest and highest peak concentrations of D4 in plasma were 0.85 and 7.02 μg/l, respectively (Table 2). However, true peak concentrations are unknown with D4 for most subjects since concentrations were already falling at the earliest sampling period. There might be less variability if true peak concentrations were available.

TABLE 2

Concentrations of D4 in Exhaled Air and Plasma in Humans Following a Dermal Exposurea

 Female subjects Male subjects Time (h) 1 2 3 Averageb 1 2 3 Averageb Concentration in exhaled air, ng/l 0 4.0c 0.2c 0.1c 1.4 ± 2.2c 0.1c 0.2c ND 0.165c 1 27 240 67 110 ± 110 15 73 3.1 30 ± 37 2 12 60 13 29 ± 28 5.6 12 1.5 6.2 ± 5.0 4 8.7 14 5.9 9.6 ± 4.3 1.9 4.6 0.90 2.5 ± 1.9 6 5.2 7.2 3.2 5.2 ± 2.0 1.1 3.3 0.80 1.7 ± 1.4 24 1.1 1.3 0.50 0.97 ± 0.42 0.33 0.90 0.20 0.48 ± 0.37 Concentration in plasma, μg/l 0 ND ND ND ND ND ND ND ND 1 6.5 7.02 3.94 5.8 ± 1.6 0.85 2.6 1.9 1.8 ± 0.9 2 4.77 4.84 2.19 3.9 ± 1.5 0.58 1.8 1.4 1.2 ± 0.6 4 2.72 2.34 1.24 2.1 ± 0.8 0.45 0.53 1.1 0.67 ± 0.34 6 2.13 1.26 0.49 1.3 ± 0.8 0.30 0.66 0.88 0.61 ± 0.29 24 NQ 0.31 0.12 —d ND 0.24 0.30 —d
 Female subjects Male subjects Time (h) 1 2 3 Averageb 1 2 3 Averageb Concentration in exhaled air, ng/l 0 4.0c 0.2c 0.1c 1.4 ± 2.2c 0.1c 0.2c ND 0.165c 1 27 240 67 110 ± 110 15 73 3.1 30 ± 37 2 12 60 13 29 ± 28 5.6 12 1.5 6.2 ± 5.0 4 8.7 14 5.9 9.6 ± 4.3 1.9 4.6 0.90 2.5 ± 1.9 6 5.2 7.2 3.2 5.2 ± 2.0 1.1 3.3 0.80 1.7 ± 1.4 24 1.1 1.3 0.50 0.97 ± 0.42 0.33 0.90 0.20 0.48 ± 0.37 Concentration in plasma, μg/l 0 ND ND ND ND ND ND ND ND 1 6.5 7.02 3.94 5.8 ± 1.6 0.85 2.6 1.9 1.8 ± 0.9 2 4.77 4.84 2.19 3.9 ± 1.5 0.58 1.8 1.4 1.2 ± 0.6 4 2.72 2.34 1.24 2.1 ± 0.8 0.45 0.53 1.1 0.67 ± 0.34 6 2.13 1.26 0.49 1.3 ± 0.8 0.30 0.66 0.88 0.61 ± 0.29 24 NQ 0.31 0.12 —d ND 0.24 0.30 —d
a

These data were reported by Plotzke et al. (2000). ND means that no D4 was detected and NQ indicates that the amount of D4 was not quantifiable.

b

Reported values are the mean ± 1SD for three men or women.

c

The air samples had a small, variable 13C-background level due to the reuse of a Rudolf valve, despite efforts to decontaminate the valve between uses.

d

For one subject, the amount of D4 was below the detection limit or the limit of quantification, and so the average value was not reported and this data point was not used for parameter estimation.

TABLE 3

Concentrations of D5 in Exhaled Air and Plasma in Humans Following a Dermal Exposurea

 Female subjects Male subjects Time (h) 1 2 3 Averageb 1 2 3 Averageb Concentration in exhaled air, ng/l 0 2.2c 3.0c 2.3c 2.5 ± 0.5c NQ NQ 1.9c 0.98 ± 0.82c 0.25 320 710 350 460 ± 220 700 150 1000 620 ± 430 0.5 260 700 91 350 ± 310 1700 140 1000 930 ± 770 0.75 420 370 260 350 ± 80 1600 680 210 830 ± 700 1 120 360 150 210 ± 130 2300 220 230 920 ± 1200 1.25 150 320 91 190 ± 120 520 280 180 330 ± 170 1.5 220 180 47 150 ± 90 740 360 270 460 ± 250 1.75 170 120 29 110 ± 70 670 300 98 350 ± 290 2 350 110 36 160 ± 160 620 250 58 310 ± 280 4 96 49 16 53 ± 40 120 24 22 55 ± 55 6 64 15 7.5 29 ± 31 26 17 7.4 17 ± 9 24 18 5.6 5.0 9.6 ± 4.5 3.9 13 6.3 7.6 ± 4.4 Concentration in plasma, μg/l 0 ND ND ND ND ND ND ND ND 0.5 0.53 1.4 0.65 0.87 ± 0.49 1.2 0.25 1.1 0.86 ± 0.53 1 0.95 2.0 0.77 1.2 ± 0.7 1.7 0.70 1.2 1.2 ± 0.5 2 0.92 1.8 0.50 1.1 ± 0.7 1.6 0.97 0.90 1.2 ± 0.4 4 0.90 1.5 0.34 0.91 ± 0.58 1.2 0.61 0.62 0.79 ± 0.31 6 0.75 0.82 0.21 0.52 ± 0.33 0.88 0.51 0.47 0.49 ± 0.23
 Female subjects Male subjects Time (h) 1 2 3 Averageb 1 2 3 Averageb Concentration in exhaled air, ng/l 0 2.2c 3.0c 2.3c 2.5 ± 0.5c NQ NQ 1.9c 0.98 ± 0.82c 0.25 320 710 350 460 ± 220 700 150 1000 620 ± 430 0.5 260 700 91 350 ± 310 1700 140 1000 930 ± 770 0.75 420 370 260 350 ± 80 1600 680 210 830 ± 700 1 120 360 150 210 ± 130 2300 220 230 920 ± 1200 1.25 150 320 91 190 ± 120 520 280 180 330 ± 170 1.5 220 180 47 150 ± 90 740 360 270 460 ± 250 1.75 170 120 29 110 ± 70 670 300 98 350 ± 290 2 350 110 36 160 ± 160 620 250 58 310 ± 280 4 96 49 16 53 ± 40 120 24 22 55 ± 55 6 64 15 7.5 29 ± 31 26 17 7.4 17 ± 9 24 18 5.6 5.0 9.6 ± 4.5 3.9 13 6.3 7.6 ± 4.4 Concentration in plasma, μg/l 0 ND ND ND ND ND ND ND ND 0.5 0.53 1.4 0.65 0.87 ± 0.49 1.2 0.25 1.1 0.86 ± 0.53 1 0.95 2.0 0.77 1.2 ± 0.7 1.7 0.70 1.2 1.2 ± 0.5 2 0.92 1.8 0.50 1.1 ± 0.7 1.6 0.97 0.90 1.2 ± 0.4 4 0.90 1.5 0.34 0.91 ± 0.58 1.2 0.61 0.62 0.79 ± 0.31 6 0.75 0.82 0.21 0.52 ± 0.33 0.88 0.51 0.47 0.49 ± 0.23
a

These data were reported by Plotzke et al. (2002). ND means that no D5 was detected and NQ indicates that the amount of D5 was not quantifiable.

b

Reported values are the mean ± 1SD for three men or women.

c

The air samples had a small, variable background level that may have been from contamination of the equipment.

With D5, the lowest and highest peak concentrations of D5 in exhaled air were 350 and 2300 ng/l, respectively (Table 3). The peak concentrations in exhaled air occurred at 1 h for one subject, at 45 min for two subjects, and at 15 min (i.e., the earliest time that air samples were obtained) for three subjects. The peak plasma concentrations occurred later (i.e., at 1 h for five subjects and at 2 h for the remaining subjects). The concentration of D5 in exhaled air was higher in men than in women for the first 2 h, but blood concentrations for men and women were similar at all times. By 24 h, the amount of D5 in exhaled air had not yet decreased to background levels.

#### Modeling Results for D4 and D5 Dermal Absorption in Human Volunteers

The experimentally determined rates of evaporation of D4 and D5 were estimated to be 0.15 ± 0.04 and 0.071 ± 0.027 mg/cm2/min, respectively (mean ± 1SD for n = 4). In their studies of the evaporation characteristics of volatile silicones, Koini et al. (1999) also found that D4 evaporated faster than D5. In their study, during the first 5 min more than seven times more D4 evaporated than D5. This discrepancy could be because the surface area covered by D4 on the filter paper was larger than that covered by D5 in the earlier study. From model calculations that incorporated the experimentally determined evaporation rates, only about 3 and 2.5% of the applied doses of D4 and D5, respectively, evaporated from the skin before it had cleared of chemical (i.e., in the first 5 min, after which it is assumed that all the chemical applied to the skin had evaporated or absorbed into the skin). Although the evaporation rate of D4 was about two times faster than the evaporation rate of D5 and similar doses were applied to the skin, the calculated percent of applied dose that evaporated within 5 min was similar for both chemicals because D5 was applied to a larger area than D4 (Table 1).

Data and model simulations for the concentration of D4 in plasma and exhaled air following the dermal exposure were compared for men and women (Fig. 3). Although this analysis suggests that most of the applied dose of D4 may have absorbed into the skin compartment, more than 99% of the D4 that entered the skin diffused back to the surface and evaporated before systemic absorption could occur. Model calculations indicated that for women 0.30% and for men 0.12% of the applied dose were systemically absorbed. The major route of D4 elimination following human inhalation exposures was exhalation (Reddy et al., 2003), and the same was true for dermal exposures. For example, model calculations showed that of the 2.9 mg that had systemically absorbed in women, 83% had been exhaled and 10% had been metabolized by 24 h (Table 4).

TABLE 4

Summary of PBPK Model Calculations for Human D4 and D5 Dermal Exposuresa

 D4 D5 Model calculation Women Men Women Men Maximum concentration in plasma (μg/l) 105 54 1.0 1.2 Time that maximum concentration occurred (min) 10 10 59 21 Percent of applied dose that was absorbed systemically 0.30 0.12 0.051 0.050 Amount systemically absorbed (mg) 2.9 1.6 0.48 0.67 Amount eliminated by exhalation in 24 h (mg) 2.4 1.4 0.44 0.62 Percent of systemically absorbed dose eliminated by exhalation in 24 h 83 88 92 93 Amount metabolized in 24 h (mg) 0.30 0.15 0.0076 0.0097 Percent of systemically absorbed dose metabolized in 24 h 10 9.4 1.6 1.4
 D4 D5 Model calculation Women Men Women Men Maximum concentration in plasma (μg/l) 105 54 1.0 1.2 Time that maximum concentration occurred (min) 10 10 59 21 Percent of applied dose that was absorbed systemically 0.30 0.12 0.051 0.050 Amount systemically absorbed (mg) 2.9 1.6 0.48 0.67 Amount eliminated by exhalation in 24 h (mg) 2.4 1.4 0.44 0.62 Percent of systemically absorbed dose eliminated by exhalation in 24 h 83 88 92 93 Amount metabolized in 24 h (mg) 0.30 0.15 0.0076 0.0097 Percent of systemically absorbed dose metabolized in 24 h 10 9.4 1.6 1.4
a

These results are all calculated using the PBPK model including the dermal exposure route. The maximum concentration in plasma and time to reach the maximum plasma concentration do not correspond to the data shown in Tables 2 and 3, but instead refer to the model-simulated values.

FIG. 3.

Semi-log plots of measured and simulated concentrations of D4 in exhaled air and plasma following a human dermal exposure for (A) men (•) and (B) women (▴). The error bars represent 1SD for n = 3. These data were reported by Plotzke et al. (2000).

FIG. 3.

Semi-log plots of measured and simulated concentrations of D4 in exhaled air and plasma following a human dermal exposure for (A) men (•) and (B) women (▴). The error bars represent 1SD for n = 3. These data were reported by Plotzke et al. (2000).

Data and model simulations for the D5 concentrations in plasma and exhaled air following the dermal exposure were also compared for men and women (Fig. 4). As with D4, this analysis suggests that most of the applied dose may have entered the stratum corneum during the 5-min drying time but more than 99% of the D5 that entered the skin evaporated back out before systemic absorption could occur. Model calculations indicated that 0.051 and 0.050% of the applied dose were absorbed systemically for women and men, respectively. Consistent with D5 inhalation exposures (Reddy et al., 2004), exhalation was the most important route of elimination for D5 (Table 4). In women, e.g., model calculations showed that of the 0.48 mg that was absorbed into systemic circulation, 92% had been exhaled and 1.6% had been metabolized by 24 h.

FIG. 4.

Semi-log plots of measured and simulated concentrations of D5 in exhaled air and plasma following a human dermal exposure for (A) men (•) and (B) women (▴). The error bars represent 1SD for n = 3. These data were reported by Plotzke et al. (2002).

FIG. 4.

Semi-log plots of measured and simulated concentrations of D5 in exhaled air and plasma following a human dermal exposure for (A) men (•) and (B) women (▴). The error bars represent 1SD for n = 3. These data were reported by Plotzke et al. (2002).

Model calculations indicate that more D4 than D5 was systemically absorbed during the dermal exposures (Table 4). However, plasma concentrations of D4 and D5 were similar and concentrations in exhaled air were higher for D5 than for D4 (Tables 2 and 3). Based solely on the experimental data, it could appear that more D5 was absorbed than D4. However, D5 penetrated the skin more slowly than D4. This difference is illustrated by the estimated rate constants for absorption into systemic circulation; e.g., k−2 was 3.0 × 10−4 min−1 for men exposed to D4 and 5.7 × 10−6 min−1 for men exposed to D5 (Table 1). For D5, peak concentrations could be readily identified from the time course data. For D4, however, dermal absorption was more rapid than it was for D5, and the peak concentrations in blood and exhaled air occurred prior to the first sampling period (e.g., in women exposed to D4, the model-calculated peak plasma concentration was 105 μg/l at 10 min after the exposure, but the experimentally determined maximum plasma concentration was 5.8 μg/l at the first sampling time of 1 h). For this reason, the in vivo experimental results are consistent with more D4 penetrating the skin than D5. Additionally, the percent of applied dose absorbed systemically was about 2.5 times higher in women than in men for D4, but for D5, the percent of applied dose absorbed systemically was similar in women and men. For the D5 study, subjects were asked not to shave their underarms for several days prior to the study, which may explain this difference between the two studies.

For both D4 and D5, the dermal absorption model more closely described blood concentrations than concentrations of chemical in exhaled air. The large variability of the measurements of D4 and D5 in exhaled air (Figs. 3 and 4) made it difficult to capture this behavior in the simulations. However, matching the time course concentrations of D4 and D5 in plasma is often the key requirement of a model needed for risk assessment purposes (i.e., the maximum concentration of a compound in the plasma or the area under the curve for plasma concentration time course data is often considered to be most related to pharmacodynamic effects), and the plasma concentrations of D4 and D5 are well described.

During parameter estimation for the D5 data set, it was determined that values for the parameters describing the generation and clearance of unavailable D5 in the blood (i.e., the rate constant for hepatic production of D5 in blood mobile lipid pool, Kmlp, and the clearance of unavailable D5 from mobile lipid pool to the fat, CLmlp) estimated using the data from the human inhalation exposure did not result in good fits for the dermal absorption data. During the human inhalation exposure, the values of these parameters were estimated as Kmlp = 0.076 ± 0.036 min−1 and CLmlp = 0.046 ± 0.027 l/min (mean ± 1SD for n = 5). The calculated value of the ratio of the concentration of chemical in the venous return to the concentration of chemical in exhaled air (i.e., Cv/Cex) is controlled by these parameters (Reddy et al., 2004), but this ratio could not be simulated for the dermal data without adjusting the values of Kmlp and CLmlp. By examining the ratio Cv/Cex, it was determined that Kmlp = 0.50 min−1 and CLmlp = 0.033 l/min were better parameter estimates for model application with the dermal absorption data set. This discrepancy may be due in part to data limitations in the inhalation model development; the D5 concentration in exhaled air was only available for up to 20 min after the exposure ended, and the ratio Cv/Cex could not be examined. Another possible explanation for the discrepancy could be physiological variability (e.g., the three male subjects exposed to D5 were obese with a mean body weight of 123 kg [Table 1], while the subjects in the D5 inhalation study used to develop the D5 inhalation PBPK model had a mean body weight of 88 kg).

## DISCUSSION

#### Skin Compartment Model Structure

In rats and humans, the physiological structure of skin is a multilayered membrane (Komarek et al., 2000; Scheuplein, 1977). For many chemicals, the outermost skin layer, the stratum corneum, is the rate-limiting barrier for mass transfer into and through skin. For highly lipophilic chemicals, the underlying viable epidermis can also act as a significant barrier (Cleek and Bunge, 1993; Reddy et al., 2000). The dermis, located beneath the epidermis, is a highly vascularized tissue that usually has sufficient blood flow to efficiently clear away all chemical passing through the epidermis. After a dermal exposure to a chemical ends and the skin is cleaned, the stratum corneum can act as a storage depot that slowly releases chemical into the viable epidermis and bloodstream. Physiologically relevant compartment models have been developed to match specific characteristics of membrane models (e.g., the flux and amount of chemical in the skin at steady state) (McCarley and Bunge, 2000) and are easy to incorporate into pharmacokinetic models. Because the data available for parameter estimation are for dermal absorption through the axilla, some of the assumptions made in the development of typical dermal absorption models (e.g., that mass transfer through sweat glands and hair follicles is unimportant) might not be applicable. For this reason, we represented the skin using a more empirical compartment model.

The in vivo dermal absorption data for D4 in the rat have been modeled previously by Sarangapani et al. (2003), who extended an inhalation PBPK model in the rat to the intravenous, oral, and dermal delivery routes. Sarangapani et al. (2003) modeled dermal absorption as a bolus dose to a topical compartment on top of the exposed skin. The model included the volatilization of D4 from the topical compartment. In the dermal absorption model presented here, a more detailed representation of skin was developed because the data set provided information regarding the characteristics of the skin depot.

The present model was developed for volatile chemicals that can evaporate from the skin surface. D4 and D5 evaporate relatively slowly; only about 3 and 2.5% of the applied doses of D4 and D5, respectively, evaporated from human skin in vivo before it had cleared of chemical (based on the rate of evaporation of D4 and D5 measured experimentally). The skin appeared dry 5 min after application of D4 or D5, suggesting that perhaps these lipophilic chemicals dissolve rapidly into at least the outermost layers of the skin compartment. However, during D4 and D5in vitro studies with human skin and in vivo studies with rat skin, the majority of applied chemical was recovered from the charcoal baskets covering the exposed sites. These chemicals must diffuse back to the skin surface and evaporate from the surface after absorption into the stratum corneum. This behavior is consistent with the observation that the amount of D4 absorbed into and through the viable skin layers in the rat in vivo decreased with time (Jovanovic et al., unpublished data). Diffusion back to the surface with evaporation of chemical from the skin is an essential addition to a dermal absorption model for these compounds.

The dermal absorption model developed here assumed that the observation that skin appeared dry 5 min after the application of D4 or D5 was primarily due to absorption into the stratum corneum (after which the driving force for mass transfer reverses, resulting in chemical evaporating out of skin). However, the assumption of rapid absorption conflicts with the theory that skin behaves like a membrane. If skin were behaving as a membrane, the lag time through the stratum corneum, tlag, could be roughly estimated using a correlation proposed by Reddy et al. (2000) (i.e., tlag(h) = 0.7 × 100.006 × MW). The value of tlag would be estimated to be about 10 h for D4 (MW = 297) and 29 h for D5 (MW = 371). For times less than tlag, it would be expected that chemical would not have had sufficient time to penetrate the membrane and enter systemic circulation. Based on the rapid appearance of D4 and D5 in the exhaled air following administration of the test compound, this assumption of rapid absorption into the skin compartment seems more reasonable than the alternative, i.e., that chemical remains on the skin surface. It remains to be determined whether this absorption behavior is due to charactetrisitcs of the application site (i.e., axilla skin) or the chemical properties of D4 and D5 (e.g., high hydrophobicity and low surface tension).

Several published skin compartment models do not allow for the reservoir capability of the stratum corneum (Reddy et al., 1998). For such models, as soon as the exposure ends the skin empties of chemical. Two aspects of the model presented here capture the ability of the skin to store chemical. First, instead of chemical partitioning from the skin into the blood, a rate constant controls the release of chemical into the blood, which allows the skin to act as the rate-limiting barrier to dermal penetration. Second, consistent with the model structure required to describe the dermal absorption of D4 in the rat (Sarangapani et al., 2003), a deep skin compartment, required to describe dermal absorption of D4 and D5 in humans, allows the simulation of the slow release of chemical stored in the skin into the cutaneous blood after the exposure ends.

The model presented here outlines factors that appear to be most important for dermal absorption of volatile chemicals. However, other factors not considered here might also be important, and possible alternative mechanisms could also be consistent with the data presented here. But the model proposed here can be used to design better experiments to elucidate the mechanisms underlying dermal absorption of volatile chemicals in future work. For example, these modeling results suggest that tape stripping data during the first 15 min following exposure to determine the distribution of chemical in the stratum corneum would provide useful information for understanding dermal absorption.

#### Model Limitations

The dermal absorption model presented here was developed using data for axilla skin exposed to neat D4 or D5. Because the skin in various regions of the body has different physiological properties (Scheuplein, 1977), the rate and extent of dermal absorption may be different for different regions of skin. During human, in vivo, dermal exposures to 14C-cortisol (Feldmann and Maibach, 1967), 14C-malathion, and 14C-parathion (Maibach et al., 1971), axilla skin absorbed between 3.6 and 7.4 times more chemical in 24 h than forearm skin. Thus, a model developed using axilla dermal absorption data may not predict dermal absorption accurately for exposures of other locations of skin. However, when using the skin model developed from axilla data for risk assessment purposes, the estimate of dermal absorption should be higher than expected for exposures of less permeable anatomic regions (e.g., the skin of the forearm and abdomen), resulting in a conservative estimate of risk.

Peak D4 plasma concentrations occurred before the first blood, and exhaled air samples were obtained at 1 h. Model estimates of the peak D4 blood concentration may be inaccurate because there were no data available in the critical time region. Nonetheless, our model was able to simulate the concentrations of D4 in the plasma and exhaled air in volunteers following a dermal exposure to D4.

#### Comparison of D4 and D5 Pharmacokinetics

In an in vitro study with abdominal skin, about 8.5 times more D4 than D5 had penetrated into the receptor fluid in 24 h. Similarly, in an in vivo rat study, 4.9 times more D4 than D5 was systemically absorbed (Jovanovic et al., unpublished data). During the human study with application to the axilla, in women systemic absorption was 6.0 times higher for D4 than for D5, and in men systemic absorption was 2.4 times higher for D4 than for D5, even though the same dose of D5 was applied to a larger exposure area. For both D4 and D5, exhalation is the primary route of elimination (Table 4), but more D5 is expected to be eliminated by exhalation than D4 because D5 has a lower blood:air partition coefficient than D4 (i.e., 0.4 compared to 1). In contrast, according to model calculations more D4 was metabolized than D5 (e.g., in women exposed to D4 and D5, 10 and 1.6% of the systemically absorbed dose was metabolized in 24 h, respectively, Table 4). Hepatic clearance of D4 in humans is sufficiently high that total metabolic clearance is limited by liver blood flow (Reddy et al., 2003), and D5 also appears to have high hepatic clearance (Reddy et al., 2004). However, metabolism was not a major pathway of elimination for either of these compounds following the dermal exposures because exhalation, both first-pass and continued exhalation, was so efficient that not very much of the dermally absorbed dose of D4 or D5 reached the liver for metabolism. Because PBPK models include physiologically meaningful blood flows, simulating the absorption of compound through the skin, into the venous blood, and through the lungs, before circulation through the rest of the body, the first-pass effect of the lungs for these dermal exposures could be accurately represented.

#### PBPK Model Structure

After an inhalation exposure has ended, the ratio of the concentration of chemical in the venous return to the concentration of chemical in exhaled air (i.e., Cv/Cex) is expected to remain constant over time for cases with simple partitioning between blood and air in the lungs (Reddy et al., 2003), and the same is expected to be true for dermal exposures. After humans were exposed to 10 ppm 14C-D4 by the inhalation exposure route, the ratio Cv/Cex increased from 4.8 soon after the exposure ended to 430 one day after the exposure ended. During the human dermal exposure to D4, the ratio Cv/Cex increased from 170 one hour after the exposure began (mean for six subjects, Table 2) to 560 one day after the exposure began (mean for four subjects with detectable plasma concentrations, Table 2). Similar behaviors have been noted in inhalation and dermal studies with rats (Andersen et al., 2001, Sarangapani et al., 2003). To describe this behavior, the conventional PBPK model structure (e.g., that developed by Ramsey and Andersen, 1984) was modified to include the production of a sequestered form of D4 that was produced in the liver, transported in the blood, and cleared into the fat, which resulted in model predictions that were consistent with the observation that the ratio Cv/Cex increased with time (Reddy et al., 2003).

The same increase in plasma concentrations relative to concentrations in exhaled air occurred in human volunteers with dermal exposures to D5 (Fig. 5). For D5, the ratio Cv/Cex increased from 2.5 thirty minutes after the exposure began to 37 six hours after the exposure began (mean of six subjects, Table 3). The spike in the model-simulated values of Cv/Cex at very short times occurs when the deep lung compartment in the D5 PBPK model fills up, causing less D5 to be exhaled. At later times, the rise in Cv/Cex over time can only be simulated in the model by including the time-varying production of the sequestered form of D5 in blood. Although the ratio Cv/Cex was lower for D5 than it was for D4 (e.g., 6 h after the dermal exposure began, Cv/Cex was about 380 for D4 compared to 37 for D5), it still increased with time. Thus, for D4 and D5 a PBPK model structure incorporating a pool of unavailable chemical in the blood, likely associated with blood lipoproteins, is required for describing pharmacokinetics during human inhalation and dermal exposures, although the quantitative contribution of the various processes varies between the two compounds.

FIG. 5.

Measured and simulated values of Cv/Cex as a function of time for men (•, dashed lines) and women (▴, solid lines) following a dermal exposure to D5. The error bars represent 1SD for n = 3.

FIG. 5.

Measured and simulated values of Cv/Cex as a function of time for men (•, dashed lines) and women (▴, solid lines) following a dermal exposure to D5. The error bars represent 1SD for n = 3.

## FUNDING

National Institute of Environmental Health Sciences, National Institutes of Health (T32 ES07321, F32 ES11425 to M.B.R.).

The authors thank Dr Justin Teeguarden and Dr Ray Yang for valuable discussions. The authors gratefully acknowledge Dr Jeanne Domoradzki for her valuable contributions. The authors certify that all research involving human subjects was done under full compliance with all government policies and the Helsinki Declaration.

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