ToxSci Advance Access originally published online on October 12, 2005
Toxicological Sciences 2006 89(1):188-204; doi:10.1093/toxsci/kfj014
© The Author 2005. Published by Oxford University Press on behalf of the Society of Toxicology. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org
A Physiologically Based Pharmacokinetic Model of Organophosphate Dermal Absorption
D. van der Merwe,
J. D. Brooks,
R. Gehring,
R. E. Baynes,
N. A. Monteiro-Riviere and
J. E. Riviere1
Center for Chemical Toxicology Research and Pharmacokinetics, College of Veterinary Medicine, NC State University, Raleigh, North Carolina, 27606
1 To whom correspondence should be addressed at Center for Chemical Toxicology Research and Pharmacokinetics, and Biomathematics Program, NC State University, 4700 Hillsborough Street, Raleigh, NC, 27606. Fax: (919) 513 6358. E-mail: Jim_Riviere{at}ncsu.edu.
Received August 10, 2005;
accepted September 29, 2005
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ABSTRACT
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The rate and extent of dermal absorption are important in the
analysis of risk from dermal exposure to toxic chemicals and
for the development of topically applied drugs, barriers, insect
repellents, and cosmetics.
In vitro flow-through cells offer
a convenient method for the study of dermal absorption that
is relevant to the initial processes of dermal absorption. This
study describes a physiologically based pharmacokinetic (PBPK)
model developed to simulate the absorption of organophosphate
pesticides, such as parathion, fenthion, and methyl parathion
through porcine skin with flow-through cells. Parameters related
to the structure of the stratum corneum and solvent evaporation
rates were independently estimated. Three parameters were optimized
based on experimental dermal absorption data, including solvent
evaporation rate, diffusivity, and a mass transfer factor. Diffusion
cell studies were conducted to validate the model under a variety
of conditions, including different dose ranges (6.3–106.9
µg/cm
2 for parathion; 0.8–23.6 µg/cm
2 for
fenthion; 1.6–39.3 µg/cm
2 for methyl parathion),
different solvents (ethanol, 2-propanol and acetone), different
solvent volumes (5–120 µl for ethanol; 20–80
µl for 2-propanol and acetone), occlusion versus open
to atmosphere dosing, and corneocyte removal by tape-stripping.
The study demonstrated the utility of PBPK models for studying
dermal absorption, which can be useful as explanatory and predictive
tools that may be used for
in silico hypotheses generation and
limited hypotheses testing. The similarity between the overall
shapes of the experimental and model-predicted flux/time curves
and the successful simulation of altered system conditions for
this series of small, lipophilic compounds indicated that the
absorption processes that were described in the model successfully
simulated important aspects of dermal absorption in flow-through
cells. These data have direct relevance to topical organophosphate
pesticide risk assessments.
Key Words: dermal absorption; PBPK model; parathion; fenthion; methyl parathion.
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INTRODUCTION
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Knowledge of the rate and extent of dermal absorption is important
in the analysis of risk from dermal exposure to toxic chemicals
and for the development of topically applied drugs, barriers,
insect repellents, and cosmetics. Dermal absorption parameters
can be estimated from
in vitro and
in vivo experimental data
(Riviere, 2005
), but the substantial investment of resources
required and the need for reducing the numbers of animals used
in research limits the use of the
in vivo approach. Estimates
of absorption parameters under defined experimental conditions
also do not necessarily reflect the values of such parameters
under different exposure conditions. The limitations of the
experimental approach to absorption parameter estimation have
generated much interest in the development of mathematical or
so-called
in silico models of skin permeability.
Published models of dermal absorption may be divided into two types: quantitative structure–activity relationship (QSAR) models and mathematical models that simulate the effects of partition and transport processes involved in absorption (Fitzpatrick et al., 2004). Quantitative structure–activity relationship techniques are widely used to predict the behavior of molecules. When applied to dermal absorption, they are usually based on statistical correlations of physical-chemical properties of permeants, solvents, and chemical mixtures with steady-state permeability constants (Geinoz et al., 2004; Ghafourian et al., 2004; Potts and Guy, 1995; Riviere and Brooks, 2005; Sartorelli et al., 1998, 1999). The combination of quantitative structure–activity relationship and steady-state permeability is widely used as an indicator of absorption potential, but its accuracy is hampered by the scarcity of high quality, comparable absorption data (Fitzpatrick et al., 2004). Steady-state permeability also does not predict absorption over time frames outside the steady-state portion of the absorption/time curve. A large number of mathematical models that simulate the effects of chemical partitioning into skin and the transport across skin over time have been developed (McCarley and Bunge, 2001; Roberts et al., 2001; Williams et al., 1990). These models vary in their degree of correlation with skin physiology and anatomy. At one end of the spectrum are models that are similar to traditional compartmental pharmacokinetic models. They are mathematical constructs that describe the aggregate result of all the processes involved in determining the flux/time curve of dermal absorption. The compartments used are not physiologically or anatomically relevant. Such models are not suited to hypothesis generation and testing involving specific anatomical or physiological changes. On the other hand, physiologically based pharmacokinetic (PBPK) models of dermal absorption are constructed from mathematical descriptions of body compartments, tissues, and processes of partitioning, movement, and metabolism that influence the dermal distribution, absorption, and elimination of drugs. Model compartments and processes can be linked to skin physiology and anatomy, which makes such models suitable for hypotheses generation and testing involving anatomical, physiological, and environmental change. Furthermore, PBPK model parameters can be scaled to reflect species, breed, life-stage, or pathological differences and changes. The advantages of PBPK models are, however, difficult to realize because the necessary anatomical and physiological parameters are often not available, and the processes are not well understood. This can result in oversimplification of the physiological processes involved, which limits the advantage of PBPK models over traditional compartmental models. The inclusion of uncertain parameters may also restrict degrees of freedom to the extent that model-based predictions are irrelevant.
The stratum corneum is the most significant barrier to dermal absorption (Bouwstra et al., 2003; Monteiro-Riviere, 1986). Flow-through diffusion cells offer a convenient method for the study of dermal absorption that is relevant to the initial processes of dermal absorption, including solvent and chemical mixture effects on the skin surface, as well as partitioning into and transport through the stratum corneum. Parameters such as temperature, absorption surface area, skin thickness, and receptor fluid flow rate can be controlled. Results obtained from flow-through cells are generally relevant to in vivo dermal absorption (Bronaugh et al., 1982; Howes et al., 1996). However, the effects of metabolism in the viable epidermis and dermis, differences between the composition of blood and receptor fluid, and the resistance to permeant transfer in these layers may cause the results from flow-through cells to deviate from those obtained with perfused skin or in vivo systems. Therefore such effects should be considered when results are used to predict in vivo absorption parameters.
Small lipophilic compounds tend to partition into the stratum corneum lipid matrix after contact with the stratum corneum surface (Raykar et al., 1988). The stratum corneum lipid matrix is also the principal route of absorption for such compounds (Albery and Hadgraft, 1979). It is possible to describe the micro-structure of the stratum corneum lipid pathway in terms of the average corneocyte dimensions and their relative positioning to characterize the pathway length, lateral bilayer diffusional resistance, and volume (Frasch and Barbero, 2003; Johnson et al., 1997). This offers an opportunity to move away from the use of simple, uniform compartments to represent the stratum corneum, to the use of anatomically more correct descriptions of the absorption pathway. Solvent evaporation, which has an effect on the permeant concentration gradient across the skin, and permeant partitioning into the stratum corneum can be estimated independently.
The availability of detailed data on skin structure, dermal absorption in flow-through cells and chemical-specific parameters reduce the limitations of PBPK models of dermal absorption. This study describes a PBPK model developed to simulate the absorption of organophosphate pesticides, such as parathion, through normal porcine skin in flow-through diffusion cells. Pigs are important food animals in many cultures around the world. Dermal absorption models of porcine skin could be used in the estimation of chemical residues in food after accidental or therapeutic topical exposure of pigs to pesticides and other potentially hazardous chemicals. It could also be of value in the development of topical medications. Because of its physiological and structural similarity to human skin, porcine skin is widely accepted as an appropriate surrogate model for human skin (Chilcott et al., 2005; Monteiro-Riviere, 2001; Schmook et al., 2001; Singh et al., 2002). The model was primarily developed and validated for parathion absorption, but it was also applied to the dermal absorption of two other organophosphate compounds: fenthion and methyl parathion. Secondary aims of the study were to demonstrate the utility of the model for hypotheses generation and as an in silico experimental system; to identify critical model parameters; to determine the effects of critical model parameters on the shape of the absorption/time curve; to model the effects of solvent evaporation on dermal absorption; and to model the effects of the removal of stratum corneum layers on dermal absorption.
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MATERIALS AND METHODS
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Software.
PBPK models were constructed using acslXstreme continuous simulation
software (Aegis Technologies (Huntsville, AL).
Chemicals.
Methyl parathion-ring-UL-14C (specific activity = 13.8 mCi/mmol, purity = 99.5%) and parathion-ring-UL-14C (specific activity = 9.2 mCi/mmol, purity = 97.1%) and propylene glycol (PG) (purity = 99%) were obtained from Sigma Chemical Co. (St. Louis, MO). Fenthion-ring-UL-14C (specific activity = 55mCi/mmol, purity = 98.5%) was obtained from American Radiolabeled Chemicals, Inc. (St. Louis, MO). Absolute (200 proof) ethanol was obtained from Aaper Alcohol and Chemical Co. (Shelbyville, KY). Double-distilled water was obtained from our in-house still. Bovine serum albumin (Fract V; cold alcohol precipitated), NaCl (Certified A.C.S.), KCl (Certified A.C.S.), CaCl (Certified A.C.S.; anhydrous), KH2PO4 (Certified A.C.S.), MgSO4-7H2O (Certified A.C.S.), NaHCO3 (Certified A.C.S.), acetone (GC grade; Certified A.C.S.), 2-propanol (Certified A.C.S.), and dextrose (Certified A.C.S.; anhydrous) were obtained from Fisher Scientific (Pittsburgh, PA). Amikacin (250 µg/ml) was obtained from Abbott Labs (Chicago, IL). Heparin (1,000 units/ml) was obtained from Elkins-Sinn (Cherry Hill, NJ). Penicillin G sodium (250,000 units/ml) was obtained from Pfizer Inc. (New York, NY). The receptor solution was prepared according to published methods (Riviere et al., 1986) and consisted of 13.78 g NaCl, 5.50 g NaHCO3, 0.58 g MgSO4-7H2O, 0.32 g KH2PO4, 0.56 g CaCl, 0.71 g KCl, 2.40 g dextrose, 90.0 g bovine serum albumin, 0.1 ml penicillin G sodium, 10 ml heparin, and 0.25 ml amikacin made up to 2 l with water.
Stratum corneum/solvent partitioning.
Parathion, fenthion, and methyl parathion partitioning coefficients between isolated porcine stratum corneum and ethanol at equilibrium were obtained from the literature (van der Merwe and Riviere, 2005).
Flow-through diffusion cell system.
Porcine skin disks were prepared from the back skin of female weanling Yorkshire pigs dermatomed to 0.5 mm, and were used as barrier membranes in a flow-through diffusion cell system according to the methodology of Bronaugh and Stewart (1985), as adapted by Chang and Riviere (1991). An 8 h experimental period was used. Perfusate was collected at 15-min intervals for the first 2 h, and at 1-h intervals thereafter. Radioactivity in the perfusate was determined by liquid scintillation counts (Packard Model 2500TR liquid scintillation counter, Packard Chemical Co.). For occlusion experiments (see Fig. 6), diffusion cells were occluded with Parafilm M (SPI Supplies, West Chester, PA) directly after the dose was deposited to the skin surface. Perfect occlusion was not achieved, but ethanol evaporation was reduced.
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FIG. 6. Observed flux/time curves of 20.9 µg/cm2 (SE = 0.03) parathion dosed in 20 µl and 40 µl ethanol under occluded (OCC) and non-occluded (NOC) conditions.
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The permeant concentrations used were selected based on the
amount of radiolabel needed for efficient detection by scintillation
counting. Concentrations were then multiplied to investigate
the range of inference of the model and the validity of assumptions
related to the use of Fick's first law.
Solvent evaporation.
Solvent evaporation was estimated gravimetrically, with a calibrated Mettler AE 200 scale (Mettler Toledo, Columbus, OH) at 32°C and 30% relative humidity, by estimating weight loss of solvent in flow-through cells in a temperature- and humidity-controlled chamber. Evaporation rates were estimated from the slope of the linear regression of the linear portion of the weight/time curve.
Physical dimension estimates.
The physical dimensions of major stratum corneum structures were estimated from transmission electron micoscopy (TEM) micrographs and phase contrast microscopy of dermatomed back skin from female weanling Yorkshire pigs. Skin sections (three sections per pig from three pigs) were fixed in Trump's fixative, processed, and then embedded in Spurr's resin. Thin sections (800–1000 Å) were examined with a Philips EM208S electron microscope. Three pictures per sample were examined. Corneocyte layers were counted, corneocyte overlaps were estimated, and corneocyte thickness and inter-corneocyte gap widths were estimated. Corneocyte diameters were estimated with an Olympus CK40 inverted phase contrast microscope (Opelco, Sterling, VA).
Stratum corneum removal by tape stripping.
The clipped back skin of a female weanling Yorkshire pig was divided into three areas. Adhesive tape (Crystal Clear HP260, Henkel Consumer Adhesives Inc., Avon, OH) was briefly attached to the skin and then pulled away. One area was not tape stripped, one area was tape stripped five times, and one area was tape stripped 80 times. The skin was dermatomed to a depth of 0.5 mm after tape stripping for use as barrier membranes in flow-through cells.
The research adhered to the Guide for the Care and Use of Laboratory Animals (National Institutes of Health publication #85–23, revised 1985).
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THE MODEL
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Model Organization
The model was built from a set of differential and algebraic
equations using a block diagram format, which enabled conceptual
divisions within the model to be visually represented (
Fig. 1).
The blocks also correlated with compartments, which enabled
the simulation of solute spatial distribution over time. The
first block consisted of a dermal exposure simulator and a tortuosity
calculator. It simulated a single dose in the dosing chamber
of the flow-through cell, which is altered by solvent evaporation,
solute evaporation, and solute diffusion into the skin. The
tortuosity calculation was added to the first block for convenience,
but the calculation is independent of time and is therefore
independent of the flux/time curve. The second block simulated
permeant partitioning into the stratum corneum, diffusion through
the stratum corneum lipids, and partitioning into the extracellular
fluid of the viable epidermis. The third block simulated the
viable epidermis and the dermis to the dermatomed depth. The
viable skin volume was the combined volume of the viable epidermis
and the dermis. The fourth block represented the receptor fluid
flowing through the receptor fluid chamber of the flow-through
cell.
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FIG. 1. Model block diagram showing conceptual model compartments, rate constants for permeant transfer between compartments and receptor fluid flow.
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Assumptions
It would be incorrect to assume that the model fully captures
all the processes involved in dermal absorption. This is especially
true of processes occurring in the deeper layers of the skin,
where oversimplification is implicit in the assumptions that
the viable skin is an insignificant barrier and that metabolism
is negligible. The major metabolites of parathion,
p-nitrophenol,
and paraoxon, found in proportion to the parent compound in
a perfused porcine skin flap model were 14.6% and 3.4%, respectively,
and 78.5% of the parent compound remained intact (Chang
et al.,
1994
). Because the bulk of the parathion remained intact in
a perfused porcine skin model, it was assumed that, although
the extent of absorption could be altered to some degree by
metabolism, the overall shape of the flux/time curve derived
from radiolabeled parathion absorption would be similar in the
absence of metabolism. The shape of the flux/time curve is determined
for the most part by the initial processes of dermal absorption,
including solvent evaporation effects on solute concentration
on the skin surface, partitioning into the stratum corneum,
and rate of movement across the stratum corneum, because the
stratum corneum is the primary barrier membrane. The model is
therefore most relevant to the initial processes of dermal absorption,
and its use as an
in silico experimental system should be limited
to those processes.
It was assumed that solutes partitioned exclusively into the lipid phase of the stratum corneum and that absorption occurred exclusively through the lipid phase. The stratum corneum was assumed to be uniform in character from its surface to its base, which avoided the need for second-order partial differential equations.
The viable skin was assumed to be a well-mixed environment and an insignificant barrier to diffusion. Minimum solvent volume was 0.1 µl. It was assumed that system conditions remained constant throughout the experimental period. The number of corneocyte layers was assumed to be equal to the average number of layers observed in back skin processed for TEM, except where changed to test hypotheses. Solvent and permeant loss to the experimental apparatus was assumed to be negligible. Because of the low volatility of organophosphate pesticides, permeant evaporation was assumed to be negligible.
Tortuosity Calculation
The effective tortuosity (
) of the stratum corneum was calculated according to the method of Johnson et al. (1997):
 | (1) |
where
is the effective tortuosity
(ratio of diffusivity in stratum corneum with impermeable corneocytes
to diffusivity in stratum corneum without impediments),
kd is
corneocyte diameter (equivalent to "d" of Johnson
et al., 1997
),
kt is corneocyte thickness (equivalent to "t" of Johnson
et al., 1997
),
N is the number of corneocyte layers,
ah is the
stratum corneum thickness (equivalent to "h" of Johnson
et al.,
1997
),
g is the vertical gap between corneocytes,
s is the lateral
gap between corneocytes, and
is the ratio between the long
overlap and short overlap of successive corneocytes (
Fig. 2).
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FIG. 2. Schematic representation of the stratum corneum depicting the parameters used to calculate effective tortuosity and minimum pathway length.
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The minimum pathway length (minpath) was predicted from
 | (2) |
where
d2 is the short leg of corneocyte overlap.
The minimum pathway length is equivalent to the geometric pathway
length (
hg) proposed by Talreja
et al. (2001)
, which is given
by
 | (3) |
where
ah is the actual stratum
corneum thickness predicted from
 | (4) |
The
effective skin thickness (
h) was predicted from
 | (5) |
where dermisdepth is the thickness of the dermatomed
skin in centimeters.
Permeant Flux Prediction
The fractional rate of permeant entry into the stratum corneum (Jf1) was predicted from:
 | (6) |
where
P is the solvent/stratum corneum partitioning coefficient,
D is
permeant diffusivity in the stratum corneum lipid, and area
is the surface area of the skin disk.
The fractional rate of permeant returning to the skin surface (Jf2) was predicted from
 | (7) |
The solute concentration on the skin surface (Cs) was predicted from
 | (8) |
where Asurface is the amount
of permeant on the skin surface and solventvol is the solvent
volume on the skin surface. The solvent volume was predicted
from the initial solvent volume, altered by the rate of evaporation
to a minimum of 0.1 µl.
The rate of change of permeant on the skin surface (achangesurface) was predicted from:
 | (9) |
where Csc is the
solute concentration in the stratum corneum and doseevap is
the rate of solute evaporation into the atmosphere.
The stratum corneum lipid volume (SClipidvol) was predicted from
 | (10) |
The fractional rate of the permeant in the stratum corneum moving into the viable skin (Jf3) was predicted from
 | (11) |
where Scepipart is the water/stratum corneum
partition coefficient.
The fractional rate of the permeant in the viable skin moving into the stratum corneum was predicted from
 | (12) |
The rate of change of permeant in the stratum corneum (achangesc) was predicted from:
 | (13) |
where Cvs is
the permeant concentration in the viable skin and Csc is the
permeant concentration in the stratum corneum.
The rate of change of permeant in the viable skin and receptor fluid (achangevs) was predicted from
where
Rm is the rate of metabolism and
Qb is the receptor fluid flow
rate.
The lag time of permeant flux (lag) was predicted from
 | (14) |
It should be noted that this is the theoretical
minimum lag time based on the minimum pathway length and the
rate of permeant movement in the stratum corneum as predicted
from diffusivity. It is unlikely that this lag time will be
experimentally observable. The apparent lag time observed during
experiments is the result of the absorption of detectable quantities
of permeant, which results in the apparent lag time being longer
than the theoretical minimum lag time.
The percent flux (% dose/h) of permeant exiting from the stratum corneum (starting at time 0 + lag) was predicted from
 | (15) |
where indose is the marker dose applied to the
skin surface at time 0 and achangevslag is the rate of change
in the permeant amount in the viable skin and receptor fluid,
incorporating the time lag owing to permeant diffusion through
the stratum corneum.
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RESULTS
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Solvent Evaporation
Evaporation rates from a flow-through cell at 32°C and 30%
relative humidity were 3.79 µl/min (
R2 = 0.9985) for acetone,
1.93 µl/minute (
R2 = 0.9960) for ethanol, and 0.54 µl/min
(
R2 = 0.9835) for 2-propanol (
Fig. 3).
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FIG. 3. Evaporation rates of acetone (A), ethanol (B) and 2-propanol (C) from flow-through cells at 32°C and 30% relative humidity. Linear trend lines, trend line equations, R2 – values of the trend line/data correlations and evaporation rates in terms of volume/time are displayed.
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The apparent lag time observed for parathion in seven different
volumes of ethanol (
Fig. 5) was correlated (
R2 = 0.9082) with
the time to solvent depletion, predicted based on the estimated
evaporation rate for ethanol, using an exponential function
(
Fig. 4). Apparent lag time could be predicted from
y = 17.716e
0.0437x,
where
y is the predicted apparent lag time and
x is the predicted
time to solvent depletion. The error in the predicted apparent
lag time, as a fraction of the apparent lag time, was more significant
at lower solvent volumes (
Table 1).
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FIG. 5. The effects of different non-occluded solvent volumes on observed flux/time curves: 20.2 µg/cm2 (SE = 0.35) parathion dosed in 5 µl, 10 µl, 20 µl, 30 µl, 50 µl, 80 µl, and 120 µl ethanol (A); 25.1 µg/cm2 (SE = 0.15) parathion dosed in 20 µl, 40 µl and 80 µl 2-propanol (B) and 24.7 µg/cm2 (SE = 0.01) parathion dosed in 20 µl, 40 µl, and 80 µl acetone (C).
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FIG. 4. The predicted time to solvent depletion based on an estimated evaporation rate of 1.93 µl/min; compared to the observed lag time of parathion absorption from 5, 10, 20, 30, 50, 80, and 120 µl ethanol.
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TABLE 1 Estimated Time to Depletion (TD) of Different Volumes of Ethanol Compared to the Observed Apparent Lag Times (OL) of Parathion Absorption and the Predicted Apparent Lag Times (PL) Based on the Exponential Function: PL = 17.716e0.0437*TD
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Physical Dimension Estimates
Porcine back skin corneocyte diameter was 32.09 micron (standard
error: 1.02), corneocyte thickness was 0.19 micron (standard
error: 0.006), and number of corneocyte layers was 21.9 (standard
error: 1.04; maximum: 28; minimum 14). Vertical and lateral
gaps between corneocytes were 0.019 micron (standard error:
0.0006).
Flow-Through Experiments and Simulations
The flux/time curves of parathion dosed in various volumes of ethanol, 2-propanol, and acetone are summarized in Figure 5. Different volumes could be differentiated based on apparent lag time, with increased volumes associated with increased apparent lag times, except for acetone. Acetone evaporated too rapidly for different lag times to be differentiated at the 15-min observation intervals used during the first 2 h of the experiments.
The effects of occluding the top of the flow-through cells on the flux/time curves of parathion dosed in 20 and 40 µl of ethanol are summarized in Figure 6. Occlusion increased the apparent lag time of absorption from 45 min to 75 min (20 µl ethanol) and from 90 min to 240 min (40 µl ethanol). Peak flux was significantly increased by occlusion (p = 0.03).
Observed flux/time curves of parathion dosed in 20 µl and 40 µl ethanol at water bath temperatures of 25°C and 37°C and simulated flux/time curves of parathion at 25°C and 37°C are summarized in Figure 7. The apparent lag time was increased at the lower water bath temperature. To achieve optimal simulation of 20 µl ethanol volume at 25°C, diffusivity was 0.0005, evaporation rate was 0.25 µl/min, and the mass transfer factor was 15. For 20 µl ethanol volume at 37°C, diffusivity was 0.0002, evaporation rate was 0.35 µl/min, and the mass transfer factor was 20. For 40 µl ethanol volume at 25°C, diffusivity was 0.0008, evaporation rate was 0.18 µl/min, and the mass transfer factor was 21. For 40 µl ethanol volume at 37°C, diffusivity was 0.0006, evaporation rate was 0.4 µl/min, and the mass transfer factor was 12.
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FIG. 7. Observed flux/time curves of 20.5 µg/cm2 (SE = 0.31) parathion dosed in 20 µl (A) and 40 µl (B) ethanol at a water bath temperature of 25°C, 20.4 µg/cm2 (SE = 0.18) parathion dosed in 20 µl (A) and 40 µl (B) ethanol at a water bath temperature of 37°C and simulated flux/time curves of parathion at 25°C and 37°C.
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The influence of the range of observed numbers of corneocyte
layers was simulated and is summarized in
Figure 8. All model
parameters were kept constant, except for the number of corneocyte
layers, which were varied from 14 to 28. To approximate the
observed data, diffusivity was 0.0004, evaporation rate was
0.4 µl/min, and the mass transfer factor was 5. The simulation
(
Fig. 8A) predicted that the number of corneocyte layers had
a substantial influence on absorption. This hypothesis was supported
by the observed effect of removal of corneocyte layers through
tape stripping (
Fig. 8B).
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FIG. 8. Simulated flux/time curves of parathion with 14, 21.9, and 28 corneocyte layers (N) in the stratum corneum (A) and observed flux/time curves of 19.4 µg/cm2 (SE = 0.00) parathion dosed in 20 µl ethanol on control skin, skin that was tape-stripped 5 times and skin that was tape-stripped 80 times (B).
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The flux/time curves of six different masses of parathion (6.3
µg/cm
2, 11.1 µg/cm
2, 22.5 µg/cm
2, 43.3 µg/cm
2,
106.9 µg/cm
2, and 209.1 µg/cm
2) dosed in 20 µl
ethanol are summarized in terms of percent dose/h in
Figure 9.
The fractions/time of parathion absorbed decreased with increased
concentrations, whereas the absolute mass/time of parathion
absorbed increased with increased concentrations. The fraction
of the dose remaining in the skin at the conclusion of the experiments
and the disintegrations per minute counted in the skin are summarized
in
Figure 10. The dose fractions remaining in the skin ranged
from 71.9% to 88.7% and were not correlated with the doses used
(
R2 = 0.5236). Simulated and observed flux/time curves of 22.5
µg/cm
2 and 209.1 µg/cm
2 parathion dosed in 20 µl
ethanol expressed in terms of percent dose/h are summarized
in
Figure 11. The diffusivity, mass transfer factor, and solvent
evaporation rate values used to achieve optimal simulations
are summarized in
Tables 2 and
3. The fractions of the dose
absorbed after 8 h decreased with increased concentrations.
The relationship between the concentrations used and the fractions
absorbed could be described with a power function (
R2 = 0.9941):
y = 6.3945
x–0.4628, where
y is the dose in µg/cm
2 and
x is the fraction absorbed (
Fig. 12).
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FIG. 9. Observed flux/time curves of parathion (A), fenthion (B) and methyl parathion (C) dosed in 20 µl ethanol. The doses used were: 6.3 µg/cm2 (n = 5), 11.1 µg/cm2 (n = 4), 22.5 µg/cm2 (n = 6), 43.3 µg/cm2 (n = 3), 106.9 µg/cm2 (n = 4) and 209.1 µg/cm2 (n = 4) for parathion; 0.8 µg/cm2 (n = 4), 1.5 µg/cm2 (n = 3), 3.0 µg/cm2 (n = 4), 5.8 µg/cm2 (n = 5), 11.7 µg/cm2 (n = 5) and 23.6 µg/cm2 (n = 4) for fenthion; and 2.8 µg/cm2 (n = 5), 5.1 µg/cm2 (n = 2), 10.2 µg/cm2 (n = 4), 19.0 µg/cm2 (n = 5) and 39.3 µg/cm2 (n = 4) for methyl parathion.
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FIG. 10. The fraction of parathion (A), fenthion (B) and methyl parathion (C) doses remaining in the skin and the disintegrations per minute (DPM) counted in the skin at the conclusion of 8-h experiments. Doses were: 6.3 µg/cm2, 11.1 µg/cm2, 22.5 µg/cm2, 43.3 µg/cm2, 106.9 µg/cm2 and 209.1 µg/cm2 for parathion; 0.8 µg/cm2, 1.5 µg/cm2, 3.0 µg/cm2, 5.8 µg/cm2, 11.7 µg/cm2 and 23.6 µg/cm2 for fenthion; 1.6 µg/cm2, 2.8 µg/cm2, 5.1 µg/cm2, 10.2 µg/cm2, 19.0 µg/cm2 and 39.3 µg/cm2 for methyl parathion.
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FIG. 11. Simulated (SIM) and observed (OBS) flux/time curves: parathion (A) dosed at 22.5 µg/cm2 (n = 5) and 209.1 µg/cm2 (n = 4) in 20 µl ethanol; fenthion (B) dosed at 3.0 µg/cm2 (n = 4) and 23.6 µg/cm2 (n = 4) in 20 µl ethanol and methyl parathion (C) dosed at 5.1 µg/cm2 (n = 5) and 39.3 µg/cm2 (n = 4) in 20 µl ethanol.
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TABLE 2 Independently Estimated and Optimized Parameters Used to Simulate Observed Flux/Time Curves of 22.5 µg/cm2 Parathion Dosed in 20 µl Ethanol
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TABLE 3 Independently Estimated and Optimized Parameters Used to Simulate Observed Flux/Time Curves of 209.1 µg/cm2 Parathion Dosed in 20 µl Ethanol
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FIG. 12. Scatter plots of the dose (µg/cm2) and the percent of the dose absorbed after 8 h for parathion (A), fenthion (B), and methyl parathion (C) including power function trendlines, power function equations and their associated R2-values.
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The flux/time curves of six different masses of fenthion (0.8
µg/cm
2, 1.5 µg/cm
2, 3.0 µg/cm
2, 5.8 µg/cm
2,
11.7 µg/cm
2, and 23.6 µg/cm
2) dosed in 20 µl
ethanol are summarized in terms of percent dose/h in
Figure 9.
The fractions/time of fenthion absorbed decreased with increased
concentrations, whereas the absolute mass/time of fenthion absorbed
increased with increased concentrations. The fraction of the
dose remaining in the skin at the conclusion of the experiments
and the disintegrations per minute counted in the skin are summarized
in
Figure 10. The dose fractions remaining in the skin ranged
from 62.2% to 83.7% and were not correlated with the doses used
(
R2 = 0.5007). Simulated and observed flux/time curves of 3.0
µg/cm
2 and 23.6 µg/cm
2 fenthion dosed in 20 µl
ethanol expressed in terms of percent dose/h are summarized
in
Figure 11. The diffusivity, mass transfer factor, and solvent
evaporation rate values used to achieve optimal simulations
are summarized in
Tables 4 and
5. The fractions of the dose
absorbed after 8 h decreased with increased concentrations.
The relationship between the concentrations used and the fractions
absorbed could be described with a power function (
R2 = 0.8739):
y = 1.6268
x–0.3739, where
y is the dose in µg/cm
2 and
x is the fraction absorbed (
Fig. 12).
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TABLE 4 Independently Estimated and Optimized Parameters Used to Simulate Observed Flux/Time Curves of 3.0 µg/cm2 Fenthion Dosed in 20 µl Ethanol
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TABLE 5 Independently Estimated and Optimized Parameters Used to Simulate Observed Flux/Time Curves of 23.6 µg/cm2 Fenthion Dosed in 20 µl Ethanol
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The flux/time curves of six different masses of methyl parathion
(1.6 µg/cm
2, 2.8 µg/cm
2, 5.1 µg/cm
2, 10.2
µg/cm
2, 19.0 µg/cm
2, and 39.3 µg/cm
2) dosed
in 20 µl ethanol are summarized in terms of percent dose/h
in
Figure 9. The fractions/time of methyl parathion absorbed
decreased with increased concentrations, whereas the absolute
mass/time of fenthion absorbed increased with increased concentrations.
The fraction of the dose remaining in the skin at the conclusion
of the experiments and the disintegrations per minute counted
in the skin are summarized in
Figure 10. The dose fractions
remaining in the skin ranged from 59.2% to 91.6% and were not
correlated with the doses used (
R2 = 0.527). Simulated and observed
flux/time curves of 5.1 µg/cm
2 and 39.3 µg/cm
2 fenthion
dosed in 20 µl ethanol expressed in terms of percent dose/h
are summarized in
Figure 11. The diffusivity, mass transfer
factor, and solvent evaporation rate values used to achieve
optimal simulations are summarized in
Tables 6 and
7. The fractions
of the dose absorbed after 8 h decreased with increased concentrations.
The relationship between the concentrations used and the fractions
absorbed could be described with a power function (
R2 = 0.9164):
y = 11.017
x–0.4784, where
y is the dose in µg/cm
2 and
x is the fraction absorbed (
Fig. 12).
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TABLE 6 Independently Estimated and Optimized Parameters Used to Simulate Observed Flux/Time Curves of 5.1 µg/cm2 Methyl Parathion Dosed in 20 µl Ethanol
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TABLE 7 Independently Estimated and Optimized Parameters Used to Simulate Observed Flux/Time Curves of 39.3 µg/cm2 Methyl Parathion Dosed in 20 µl Ethanol
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A sensitivity analysis of the parameters used to optimize the
simulation of 22.5 µg/cm
2 parathion absorption from 20
µl ethanol, including diffusivity, mass transfer factor,
and solvent evaporation rate, is represented in
Figure 13. As
expected, all parameters showed low sensitivity before the apparent
lag time. Diffusivity and solvent evaporation rate sensitivity
were high at the time period directly following the apparent
lag time, but it was low at later times. This indicated that
these parameters had a high influence during the period from
apparent lag time to peak flux, and that these parameters did
not have a large influence on the extent of total absorption
over the experimental period. Mass transfer factor sensitivity
also increased after the apparent lag time, but it remained
high, indicating that it had a significant influence on the
total absorption over the experimental period. Sensitivity analyses
using higher volumes of ethanol revealed the same pattern, but
the higher volumes delayed the onset of high sensitivity for
all parameters.
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FIG. 13. Sensitivity analysis of parameters used to optimize the simulation of 22.5 µg/cm2 parathion absorption from 20 µl ethanol, including diffusivity, mass transfer factor, and solvent evaporation rate.
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Sensitivity analysis of the parameters used to describe the
stratum corneum and to determine effective tortuosity associated
with 22.5 µg/cm
2 parathion absorption from 20 µl
ethanol is represented in
Figure 14. Corneocyte diameter had
a significant influence during the period immediately following
the apparent lag time. The number of corneocyte layers and the
width of the vertical gap between corneocytes was significant
from the apparent lag time to the end of the experimental period.
The sensitivity associated with the number of corneocyte layers
also had a peak during the period immediately following the
apparent lag time, which is likely to be associated with its
influence on the length of the lipid matrix pathway.
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FIG. 14. Sensitivity analysis of parameters used to describe the stratum corneum and determine effective tortuosity associated with 22.5 µg/cm2 parathion absorption from 20 µl ethanol – including vertical gap between corneocytes (g), lateral gap between corneocytes (s), corneocyte thickness (kt), corneocyte diameter (kd), long leg of corneocyte overlap (d1), short leg of corneocyte overlap (d2) and number of corneocyte layers (N).
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DISCUSSION
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Mathematical models of biological structures and processes are
becoming common tools in the analysis of complex problems related
to risk assessment, where one of the goals is the reduction
of variance associated with predictions and another is the explanation
of observations (Spear, 2002
). For a mechanistic model to be
plausible, the model must be phenomologically consistent with
observed data. It emphasizes
a priori model structure and hypotheses
relating to current understanding of processes and variables
and its causal relationship to observations (Spear, 2002
). PBPK
models, such as the model presented here, are mechanistic in
nature and useful for qualitative, explanatory analysis.
We could adopt one of two approaches to decisions on the inclusion or exclusion of physiological and anatomical detail. A "lumping" approach involves using the smallest amount of biological description required to demonstrate observed data. A "splitting" approach involves the inclusion of as much system biology as can be conceptualized and supported with data (Clark et al., 2004). We used the latter approach because, in complex models, the influence of model parameters and variables is not always intuitively apparent and the importance of parameters may be changeable depending on system conditions. Many of this model's parameters were independently estimated, which made it possible to be detailed without loss of degrees of freedom. Also, the retention of code that accounts for processes that have little influence under the system conditions primarily modeled, such as metabolism, may be of value when hypothetical questions regarding the probable influence of alternative system conditions are raised. The availability of adequate computing power permits simulations to be run on highly complex models without any significant time penalty. This diminishes the historical practical advantage of collapsing model sections that have little impact on the model output into single parameters. The possibility of losing degrees of freedom when including more parameters in more complex models should, however, be emphasized. Including more unknown parameters decreases confidence in the validity of simulations. By estimating parameters independently, the dependent parameters in the current model were reduced to three, each of which had a uniquely identifiable effect on the flux/time curve (Table 8).
Under equivalent system conditions, dermal absorption with different
solvents, solvent volumes, and solutes could be simulated by
calibrating solvent evaporation rate, solute diffusivity, and
mass transfer factor. The values of these parameters were dependent
on the simulated system conditions and the assumptions used.
They were therefore conditional in nature and relevant when
interpreted comparatively. The simulated apparent lag time was
determined by solvent evaporation rate, which, because of permeant
super saturation on the skin surface, causes a rapid increase
in the transdermal concentration gradient at low solvent volumes.
This model-derived hypothesis was supported by observed correlations
between solvent volume and apparent lag time (
Fig. 5), the increased
apparent lag time associated with occlusion (
Fig. 6), and the
increased apparent lag time at lower water bath temperatures
(
Fig. 7). The evaporation rates required by the model were,
however, significantly slower than the evaporation rates observed
in a temperature- and humidity-controlled chamber (
Fig. 2).
This slowing of evaporation may be due to the relatively high
rate of atmosphere turnover in the temperature- and humidity-controlled
chamber, a higher temperature in the chamber than at the skin
surface in the flow-through cell because of inefficient heat
transfer between the water bath and the skin surface. An uneven
skin surface may reduce surface area as the solvent reaches
low volumes. The remnants of hair and the hygroscopic nature
of solvents such as ethanol can absorb atmospheric water and
possibly extract water from the skin surface, and the presence
of solutes could also alter solvent evaporation rates. Differences
between the surface texture, hair density, and atmospheric conditions
could explain the variation in apparent ethanol evaporation
rates at a water bath temperature of 37°C (varied from 0.3
µl/cm
2/min to 0.4 µl/cm
2/min) needed for optimal
simulations.
The apparent lag times observed for single studies should be interpreted with caution because of the possible effects of environmental conditions and interindividual skin variability on apparent lag time. It should be noted that the apparent lag time is influenced both by the time it takes for the permeant to diffuse through the skin and by the sensitivity of the method used for permeant detection. These factors, and the limitations on the apparent lag time accuracy due to sampling intervals, made the use of predicted apparent lag times based on estimated time to solvent depletion impractical at the relatively low solvent volumes used in the simulations. Predicting the apparent lag time for higher solvent volumes was, however, more successful (Table 1; Fig. 3). More data for higher solvent volumes would be needed to firmly establish a quantitative relationship between apparent lag time and solvent volume, but the existence of a relationship between apparent lag time and the time to solvent depletion due to evaporation was supported in these studies.
The hypothesis that super saturation due to solvent evaporation increases absorption rates is also supported by studies comparing dermal absorption from ethanol with a relatively non-volatile solvent, such as propylene glycol. Permeability from propylene glycol, which never reaches super saturation conditions during the experimental period, is markedly lower than permeability from ethanol, which reaches super saturation conditions early in the experimental period (van der Merwe and Riviere, 2005).
The time from apparent lag to peak flux could be simulated by optimizing diffusivity, and this correlation was used to determine diffusivity when simulating observed data. The diffusivity used in the model refers to the rate of solute movement in the stratum corneum lipids and should not be confused with the apparent diffusivity used in traditional models, which is based on the observed lag time and membrane thickness. Simulating conditions in which the skin surface is open to the atmosphere is relevant to the most common conditions of exposure to environmental toxins, but changing the solvent evaporation rate can simulate different degrees of occlusion or total occlusion.
The mass of solute transferred across the stratum corneum over time, as reflected by the area under the curve, was related to the mass transfer factor. This factor was needed because solute partitioning determined from in vitro partitioning between isolated stratum corneum and solvent (van der Merwe and Riviere, 2005) did not fully account for the apparent solute penetration into the stratum corneum and partitioning from the stratum corneum to viable skin under the simulated conditions. This may be due to solvent-solute co-absorption, different physical conditions between the partitioning experiments and the flow-through diffusion experiments, such as temperature and exposure to the atmosphere versus total occlusion and immersion in the solvent, and to differences between isolated stratum corneum and the stratum corneum of intact, fresh skin. The lipophilicity of the viable skin is different from that of water, and the mass transfer factor adjusted the stratum corneum/water partition coefficient used to describe stratum corneum/viable skin partitioning in the model. Assuming the minimum solvent volume on the skin surface to be 0.1 µl was also a possible source for error in permeant partitioning based on independently estimated partitioning values. The value of the mass transfer factor therefore adjusts for a number of possible sources of error, and more work, such as detailed partitioning studies in intact skin, is needed to differentiate between different contributors to the mass transfer factor. Because the mass transfer factor was a significant contributor to the total extent of absorption over the experimental period, the model should be used with caution for predictions of the total extent of absorption in the absence of experimental data. However, the model can be a useful tool for predicting dermal absorption under different exposure scenarios comparatively, and for developing hypotheses on the effects of specific structural changes on dermal absorption.
Our assumption of constant barrier membrane properties throughout the experimental period was not consistently supported by the observed data. Longer exposure of the skin to ethanol when using higher volumes resulted in higher peak flux (Fig. 5). Increased peak flux was also observed when flow-through cells were occluded (Fig. 6). This may be attributed to disruption of the lipid matrix over time due to the penetration of ethanol into the stratum corneum (Kim and Chien, 1996; Kim et al., 1996), which could enhance solute partitioning into the stratum corneum, increase the rate of solute movement in the lipid matrix, and open additional lipid channels to solute transfer.
The number of corneocyte layers had a marked influence on the effective tortuosity, which is correlated with the effectiveness of the stratum corneum as a barrier (Fig. 8). Sensitivity analysis of the number of corneocyte layers (Fig. 14) revealed that this parameter had a highly significant influence on the total absorption over the experimental period and that there was a peak in its influence in the period immediately following the apparent lag time. The peak in sensitivity was probably due to its effect on the length of the lipid matrix pathway through the stratum corneum and its consequent influence on the time of diffusion through the stratum corneum. The sustained significance of the number of corneocyte layers was probably related to its influence on the stratum corneum lipid volume and, therefore, on permeant concentration in the stratum corneum. Variability of the number of corneocyte layers in the stratum corneum is a potential source of inter-experimental variability and predictive uncertainty. This potential is illustrated by the inter-experimental variability observed between the absorption of similar concentrations of parathion in different experiments using skin from different pigs (Figs. 8, 9, and 11). It also has implications for dermal absorption through skin from different body sites with different stratum corneum thickness and skin with altered corneocyte layers, such as damaged or diseased skin. Finally, it has a significant effect on interspecies comparisons based on skin thickness alone. The model-derived hypothesis of the importance of the effect of the number of corneocyte layers was supported by observed differences in dermal absorption between tape-stripped and control skin. The assumption that the number of corneocyte layers was equal to the average number of layers observed in back skin may have been an underestimation because of the possibility of losing corneocyte layers during skin preparation.
The simulation of methyl parathion absorption underpredicted the flux during the latter part of the simulation. The effect was more pronounced in the simulation of the lower concentration (Fig. 11). The same phenomenon was observed for the simulation of the lower concentration of parathion. A possible explanation could be that a significant portion of the permeant is bound to structures in the stratum corneum and is therefore unavailable for diffusion. The results of such an effect would be more pronounced at lower concentrations. This is, however, a speculative explanation, and further studies are needed to establish the cause of this effect.
It is often assumed that dermal absorption is a first order process of mass diffusion as predicted by Fick's first law, at least for low solute concentrations at steady state. Our observations across a wide range of parathion and fenthion doses, however, did not show absorption to be a first order process (Fig. 9). The relationship between dose concentration and absorption of parathion, fenthion, and methyl parathion could be described using power functions (Fig. 12). It is a well-established and long-standing assumption that Fick's law offers a reasonable approximation of the processes of dermal absorption (Blank, 1964; Scheuplein and Blank, 1971; Treherne, 1956; Wahlberg, 1968). It is also the basis for the assumption that permeability can be characterized by a permeability constant (Kp), which is defined as Kp = Jss/
C, where Jss is the steady-state flux and C is the concentration gradient across the skin. An assumption of Fickian diffusion is inherent in predictions of dermal absorption by QSAR models based on correlations between molecular descriptors and observed Kp values (Geinoz et al., 2004; Ghafourian et al., 2004; Potts and Guy, 1995; Sartorelli et al., 1998, 1999). For example, Kp is used by regulatory agencies to characterize the dermal absorption of compounds for comparative and risk assessment purposes using standardized methods. However, lack of confidence in the validity of Kp values determined outside the dose range of typical exposures and the concentrations used in chemical products compelled regulatory agencies to recommend that Kp values should be determined using typical product formulations or expected exposure concentrations (EPA, 1992; OECD, 2000). It is clear that an assumption of the validity of Fick's law, at least as an adequate approximation, plays a central role in current understanding of dermal absorption and that there is a need to identify the conditions under which it is applicable.
Fick's law can be explained in molecular terms by the molecular-kinetic mechanism of Brownian motion in fluid systems (Einstein, 1905; Von Smoluchowski, 1906), but the assumptions required include the presence of a dilute, homogeneous suspension; rigid, elastically colliding particles; no solvent–solute interaction; and a system that tends toward equilibrium. These assumptions are not compatible with biological barriers, including the stratum corneum (Agutter et al., 2000). It is also evident from the results of published studies that Fick's law does not invariably offer a good approximation of dermal absorption (Billich et al., 2005; Blank, 1964). Examples of studies in which an assumption of Fickian diffusion appears to be reasonable across some spectrum of concentrations can be found (Payan et al., 2003; Wahlberg, 1968), but it should be emphasized that a continuation of Fickian diffusion across wider spectra of concentrations cannot be assumed from such studies. Permeability constants can also be misleading when the permeability associated with neat compounds is used to infer the permeability of compounds in solvents (Korinth, et al. 2005) or mixtures (Riviere and Brooks, 2005). Although our model made use of the same expressions that are used in describing Fickian diffusion (Equation 6), accurate simulation of observed data required non-constant diffusivity and mass transfer. Because the absorbed fraction of the solute was not correlated with the fraction partitioned into the skin across a range of doses, diffusivity and mass transfer would be constant if Fickian diffusion occurred in the stratum corneum. However, for the compounds tested, diffusivity and mass transfer appeared to be altered depending on the concentration and solvent used, resulting in non-Fickian absorption patterns.
Diffusivity is related to the kinetic energy of the diffusing molecules and is temperature dependent, although the extent of the effect at the moderate temperature differences in these experiments (Fig. 7) is expected to be relatively small. Higher temperature may also affect the fluidity of stratum corneum lipids, which could increase diffusivity. However, phase changes indicating altered lipid crystal structure in the stratum corneum are typically detected at significantly higher temperatures than those used in these experiments (Bouwstra et al., 2003). Slightly increased diffusivity was therefore expected to be associated with higher water bath temperatures, but diffusivity appeared to be increased at lower water bath temperatures (Tables 9–12 ). This was likely due to the effects of longer contact between ethanol and skin on diffusivity overriding the temperature effect on diffusivity. This hypothesis is supported by the fact that the diffusivity was highest when the contact between ethanol and skin was longest (40 µl ethanol at 25°C). The mass transfer factor was also increased at longer ethanol-to-skin contact times, which may indicate disruptive effects leading to altered permeant partitioning and effective tortuosity. Altered diffusivity due to solvents, such as ethanol, may be explained by the disruptive effects that solvents may have on stratum corneum lipid bilayers (Kim and Chien, 1996; Kim et al., 1996
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ABSTRACT
INTRODUCTION