The transient dermal dose problem
H.F. Frasch*, A.M. Barbero
National Institue for Occupational Safety and Health, Morgantown, United States
Background
Many experimental measurements of steady-state dermal absorption rates of chemical compounds have been reported, and considerable progress has been made in the prediction of these rates. Most real-world dermal exposures, however, are not steady-state. Unfortunately, much less work has been devoted toward experimental and theoretical understanding of the transient dermal dose situation.
Here we consider the following scenario: an amount of chemical is applied to the skin and removed a “short time” later, before significant depletion of the chemical has occurred. This scenario might be mimicked in the workplace, for example, where a worker splashes some chemical on his skin and effectively washes it some time later. Experiments were performed using in-vitro diffusion cells to measure the transient dose dermal absorption of diethyl phthalate. Theoretical predictions are compared with the experimental results as a demonstration of concept.
Methods
Theory
We seek a solution to the diffusion equation for the boundary conditions outlined above. A chemical of concentration C is applied at time t = 0 to a homogeneous membrane of thickness h, and removed at time t = t1. It can be shown that the cumulative amount of chemical per unit area that penetrates the membrane over time (m(t)) is given by:
(1)
where
L-1 indicates the inverse Laplace transform of a function of the complex variable s, Kmv is the membrane-vehicle partition coefficient, D is diffusivity, and
. An analytical solution of this equation is unknown to us; however the time domain solution can readily be obtained via numerical methods (we use Scientist, MicroMath Scientific Software, Salt Lake City, UT).
If it is desired only to obtain the TOTAL amount of chemical that penetrates the membrane after a “long” time, this amount can be determined using the final value theorem of Laplace transform theory:
(2)
M(s) is the expression within the large parentheses in eq. (1). In other words, the total amount of chemical that penetrates the membrane, per unit area, is given simply as the product of the permeability coefficient, the concentration of the chemical, and the amount of time the chemical is in contact with the membrane.
Experiments
Abdominal skin from male hairless guinea pigs (HGP) was used. Skin was dermatomed (315 mm) and discs were placed in static diffusion cells (37 oC). Receptor fluid consisted of HEPES-buffered Hanks Balanced Salt Solution. Donor solution consisted of saturated diethyl phthalate (DEP) in buffer.
Steady-state permeability and lag time
Saturated DEP was added to the donor compartments. Samples were removed from the receptor compartments at times up to 5 hr for subsequent analysis. Donor solution was also sampled, and was changed every hour to maintain infinite dose conditions. Total mass accumulation over time was calculated. The permeability coefficient
(kp) and lag time (t) were determined from the mass accumulation curves.
Transient dose experiments
Saturated DEP was added to the donor compartments and removed after 1 hr. Donor compartments were rinsed 4x using fresh buffer to remove DEP from the skin surface. Receptor compartments were sampled up to 4 hr, and donor solution was also sampled. Mass accumulation curves were calculated.
DEP analysis
DEP concentrations were quantified using automated solid-phase microextraction (85 mm polyacrylate fiber) and gas chromatography with flame ionization detection
(Frasch and Barbero, 2005).
Data Analysis
Results of the transient dose experiments were compared with the prediction of eq. (1). Nonlinear regression of the data yielded estimates for the unknown parameters in eq. (1) to arrive at a “best fit” of the model with the data.
In addition, several existing skin-membrane theories were used to model the transient dose experiments. For these models, it is assumed that the only directly measured quantity is the permeability coefficient, kp. All unknown parameters are model-based estimates or estimates from the literature, and were used in eq. (1) to predict mass accumulation. C and t1 are known quantities.
Steady state model.
It is assumed that steady state diffusion occurs instantaneously. The only variable required is kp.
Homogeneous membrane model.
It is assumed that the stratum corneum (SC) is a homogeneous membrane. In addition to kp, required are h, D, and Kmv. It is assumed h = 0.002 cm. Kmv is calculated according to Vecchia and Bunge
(3)
where Kow is the octanol-water partition coefficient of DEP (= 240).
D is then calculated from the relationship
(4)
Lipid pathway model (Frasch and Barbero, 2003)
It is assumed that diffusion through the stratum corneum occurs exclusively along the lipid bilayers. In addition to kp, also required are h*, D* and Klv. Here, h* and D* are the thickness and diffusivity of a homogeneous membrane having the same permeability per unit area and lag time as the SC lipid pathway. Klv is the lipid-vehicle partition coefficient, related to Kmv by
(5)
where φlip is the lipid volume fraction of stratum corneum (» 0.1). Based on reasonable SC geometry, h* » 40 h = 0.06 cm. D* is then calculated from the relationship:
(6)
where A*/A0 is the fractional area of lipid on the membrane surface (»1/400).
Random walk model (Frasch 2002)
It is assumed that corneocytes are permeable and that chemicals partition between lipids and corneocytes, so that diffusion may occur transcellularly. Effective diffusivity and effective SC thickness are calculated as described (Frasch 2002). Kmv is then calculated from eq. (4) using these values.
Both Kp and t known
Additionally, we calculated mass accumulation (eq. (1)) based on experimental knowledge not only of kp but also of lag time t. Here, h is (arbitrarily) chosen as h = 0.002 cm and D is calculated from the equation for lag time of a homogeneous membrane:
(7)
Kmv is then calculated from eq. (4)
Results
The measured kp was 0.065 cm/hr, and t was 0.40 hr (mean from n = 4 skin discs).
Figure 1 displays measured DEP accumulation from the transient dose experiments (circles; mean ± SEM, n = 8), along with a best-fit approximation of eq. (1) with the data (solid line). This demonstrates that eq. (1) is a good model for these experimental conditions.
Figure 2 shows comparisons among the experimental data (circles) and the predictions of the 4 skin-membrane models. Note that the predictions of the homogeneous membrane model and the lipid pathway model are indistinguishable. Also shown in Fig. 2 (dotted lines) is the prediction of eq. (1) when both permeability coefficient and lag time are known independently from experiments.
Discussion and Conclusions
These data demonstrate that a simple mathematical expression (eq. (1)) can be used to model the transient dose experimental protocol described here. The regression of eq. (1) with the experimental data (Fig. 1) is excellent.
The application of existing skin-membrane models using only known kp values, however, does not appear to replicate the dynamic features of the experimental data (Fig. 2). The steady-state model, of course, cannot replicate transient phenomena. It, like the others, does a good job of predicting the steady-state or total mass accumulation after a long time. Equation (2) shows that this steady-state value is totally dependent upon the permeability coefficient for similar experimental conditions. Because kp is a measured input in these calculations, all membrane models achieve the same steady-state value. This steady-state value is a bit less than the amount reached at 4 hr of the transient dose experiments, perhaps owing to incomplete washing of the skin membranes following the transient dose.
The non-static membrane models fail to closely replicate the dynamic features of the experimental data. The homogeneous membrane and lipid pathway models underestimate the time delay, while the random walk model overestimates it (Fig. 2). However, if additional information (ie, lag time) is known from independent experiments, then the dynamic features of the experimental data can be replicated quite well. Permeability and lag time can be used to predict the time-dependent mass accumulation following a transient exposure, for this particular compound under these particular conditions (Fig. 2, dotted line).
If the only concern is to estimate the total amount of permeant that penetrates the skin after a long time, then this value can be predicted from the permeability coefficient using eq. (2). This equation has been suggested by others (eg, McDougal, 1998) to predict total absorption from a dermal exposure, but perhaps without the theoretical underpinnings developed here. In fact, it is believed that eq. (2) is a broad estimate, not valid for short exposures or chemicals with long lag times. However, the current analysis suggests that eq. (2) is more generally valid for this type transient dose exposure.
The current analysis does not consider dose depletion during the time of exposure. Also, the specified boundary condition after exposure (zero concentration at surface) strictly applies only to volatile compounds. Different specifications (zero flux at surface) apply for non volatile compounds. Nevertheless, the model does appear to account for a more realistic occupational exposure scenario than experiments that consider only the steady state response to an infinite dose.
Acknowledgement
The authors thank Dr. Annette L. Bunge for helpful comments.
References
Frasch HF, 2002. A random walk model of skin permeation. Risk Analysis 22: 265-276.
Frasch HF and AM Barbero, 2003. Steady-state flux and lag time in the stratum corneum lipid pathway: results from finite element models. Journal of Pharmacuetical Sciences 92: 2196-2207.
Frasch HF and AM Barbero, 2005. Application of solid-phase microextraction to in vitro skin permeation experiments: example using diethyl phthalate. Toxicology in Vitro 19: 253-259.
McDougal JN 1998. Prediction—physiological models. In MS Roberts and KA Walters, eds. Dermal Absorption and Toxicity Assessment. New York, Marcel Dekker, pp 189-202.
Vecchia BE and AL Bunge 2003. Partitioning of chemicals into skin: results and predictions. In RH Guy and J Hadgraft, eds. Transdermal Drug Delivery (2nd edition). New York, Marcel Dekker, pp 143-198.
Content last modified: 2 June 2005
