The transient dermal exposure: Theory and experimental examples using skin and silicone membranes

PHARMACOKINETICS, PHARMACODYNAMICS ANDDRUG METABOLISM

The Transient Dermal Exposure: Theory and ExperimentalExamples Using Skin and Silicone Membranes

H. FREDERICK FRASCH, ANA M. BARBERO

Health Effects Laboratory, National Institute for Occupational Safety and Health, Morgantown, West Virginia 26505

Received 20 December 2006; revised 15 March 2007; accepted 7 April 2007

Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jps.21035

Corresponde285-5755; Fax:

Journal of Pharm

� 2008 Wiley-Liss

1578 JOURN

ABSTRACT: A diffusion model is presented to account for the disposition of chemicalsapplied to skin as transient exposures. Two conditions are considered that apply to theskin surface following the exposure period, which are applicable to chemicals exhibitingtwo extremes of chemical volatility. For one case, representing highly volatile com-pounds, the solution is generalized to apply to multiple transient exposures. For bothcases, algebraic expressions are derived to calculate the total amount of chemical thatpenetrates the skin. The theory is applied to experimental measurements of the in vitropenetration of diethyl phthalate applied to hairless guinea pig (HGP) skin and siliconerubber membranes (SRMs) as transient exposures. The transient exposure theoryably models the experimental data, with coefficients of determination greater than0.97 (HGP) and greater than 0.99 (SRM). The ability of parameters derived fromconcurrent infinite dose experiments to predict the time course of absorption fromtransient exposures is explored. Discrepancies were found between measured cumula-tive penetration of chemical from transient exposure experiments and penetrationpredicted from parameters derived from infinite dose experiments, particularly forHGP. Possible reasons are explored. The current model may provide a realistic frame-work for estimating absorption from occupational, environmental and pharmaceuticaldermal exposures. � 2007 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm

Sci 97:1578–1592, 2008

Keywords: skin; permeability; diffu

INTRODUCTION

Many exposures of chemicals to skin do not reacha steady state rate of absorption. In industrialand environmental exposures, individuals may be

nce to: H. Frederick Frasch (Telephone: 304-304-285-6041; E-mail: [email protected])

aceutical Sciences, Vol. 97, 1578–1592 (2008)

, Inc. and the American Pharmacists Association

AL OF PHARMACEUTICAL SCIENCES, VOL. 97, NO. 4, APR

transiently exposed following dermal contactuntil the chemical is washed off or evaporates.In cosmetic applications, exposures to perfume orfragrance materials and vehicles may be shortlived, and in pharmaceutical applications, nonsteady state conditions are important considera-tions in, for example, absorption from dermalpatches.

In contrast to these realistic exposures, mostskin permeation studies have been performed

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TRANSIENT DERMAL EXPOSURE 1579

by measuring the steady state rate of dermalabsorption from large doses. From these measure-ments the skin permeability coefficient (kp) isderived, which is the skin’s conductance to achemical from a particular vehicle. The amount ofchemical penetrating the skin can be estimatedfrom these measurements, but the calculation isvalid only for the steady state and does not takeinto consideration the transient absorption thatoccurs during the initial stages of exposure, nordoes it include absorption that persists afterremoval of the chemical. Transient conditionsneed to be considered for a full and accurateaccounting of dermal disposition from skinexposures.

Some previous studies have not employed largedoses but instead have examined the finite doseregime,1–7 where a small amount of chemical isapplied to the skin and its disposition is followedas the dose depletes from the skin surface throughabsorption and possibly evaporation. In thepresent study, we investigate a related butdifferent exposure scenario. In the transientexposure considered here, a donor chemical isapplied to the skin and removed at a later time,possibly prior to establishment of steady state andbefore significant depletion of the chemical hasoccurred. This scenario differs from the finite doseexposure in that total absorption depends, amongother variables, on the time of exposure of the skinto the chemical. Both exposure regimes arerelevant to ‘‘real world’’ exposures. The transientexposure scenario might occur in the workplace,for example, when a worker splashes somechemical on his skin and effectively washes itsome time later. A full accounting of the disposi-tion of applied chemical in such an exposurerequires consideration of the fate of chemical thatresides in the skin after the chemical is removed.

In these studies, theory is first developed tosolve for the diffusion of chemical from transientexposures. Analytical solutions, applicable to aneffective homogeneous membrane, are obtained inthe Laplace domain for concentration and fluxdistributions and mass accumulation at the lowermembrane surface. Two cases are presented thatrepresent two extremes of volatility of the appliedchemical, and for one case the solution is general-ized for multiple transient exposures. The theorypredicts that parameters that can be derivedfrom infinite dose permeation experiments (per-meability and lag time), should enable theprediction of the time course of mass accumula-tion for the transient exposures. Diffusion cell

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experiments are described that explore thevalidity of the developed theory. Numericalinversion of the Laplace domain solutions permitscomparison of the theoretical models with experi-mental results. Skin from hairless guinea pigswas used, and silicone rubber membranes (SRMs)were also studied to examine the legitimacy ofthe homogeneous membrane approximation. Bymanipulating the post exposure boundary condi-tions, we were able to mimic the effects of bothextremes of chemical volatility with one modelcompound. Infinite dose experiments were runconcurrently with the transient exposure experi-ments, permitting a comparison among all threeexposures of derived penetration parameterspermeability and lag time.

To our knowledge these Laplace domain solu-tions have not hitherto been published, althoughtime domain solutions can be arrived at usingwell-known solutions for the time during whichthe skin is exposed to chemical,8 combined withheat conduction solutions presented by Carslawand Jaeger9 that can be adapted for use followingthe exposure period. The latter are complicatedand not directly usable in their published form.The solutions require evaluation of an infinitenumber of terms of a non trivial definite integral,where each term itself contains an infinitenumber of terms, and also require the solutionof a transcendental equation for each term. Ofcourse, for practical purposes the series can betruncated to a manageable number of terms, butfor small values of time a larger number of termsare required. The overall simpler approach ofnumerical inversion of the Laplace solutions, andthe ability to solve the equations for both large andsmall values of time to within a defined error,make this approach superior in our estimation.

THEORETICAL FRAMEWORK

The skin is modeled as an effective homogeneousmembrane (Fig. 1). This means that the macrodiffusion properties of a heterogeneous structuresuch as skin can be described in terms of effectivetransport properties for an equivalent homoge-neous membrane.10–12 Different exposure condi-tions are considered, but for all cases themembrane is initially free of chemical and atthe lower surface (x¼h), zero concentration (sinkcondition) is maintained for all time. At the uppersurface (x¼ 0) the skin is exposed to a chemical ofconcentration C1 for a finite time T1, after which

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Figure 1. Schematic of effective homogeneous mem-brane diffusion model. A: Input concentration of tran-sient exposure. A chemical of concentration C1 isapplied to the surface of the membrane at time t¼ 0and removed at time t¼T1. Dashed line following T1

indicates that boundary concentration is not necessarilydefined for that time. B: Initial and boundary conditionsfor transient exposure model. Themembrane is initiallyfree of permeant (C(x, 0)¼0), and sink conditions exist atthe lower boundary for all time (C(h, t)¼ 0). For Case 1,surface concentration is specified following the expo-sure time (sink condition; C(0, t)¼0 for t>T1). For Case2, flux is specified after the exposure (zero flux;@C=@xjx¼0 ¼ 0 for t > T1).

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the chemical is completely removed. Two bound-ary conditions are considered for the time follow-ing the exposure. These represent conditions thatapply to exposures to chemicals that exhibit twoextremes of volatility. In Case 1, zero concentra-tion is imposed on the skin surface for time greaterthan T1. This sink condition applies to highlyvolatile chemicals that evaporate rapidly fromthe skin surface and dissipate in ambient air. Italso represents the case where the chemical isremoved from the skin from a continuous rinse orsolvent immersion for a timemuch longer than thelag time of the membrane. In Case 2, zero flux isimposed on the skin surface for time greater thanT1. This boundary condition applies to non-volatile chemicals that partition preferentiallyin skin as opposed to the surrounding air.Intermediate volatilities require specification ofthe volatile flux at the skin surface and will beconsidered in a subsequent study.

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Analytical solutions for concentration and fluxdistributions and mass accumulation at themembrane surfaces are obtained in the Laplacedomain. For Case 1, the solution is generalized formultiple or repeated transient dermal exposuresof varying concentrations and durations. Forall transient dose cases, the total amounts ofchemical that penetrate the skin are given byalgebraic equations. For Case 1, the equation isquite simple and does not depend on membranelag time.

We seek solutions for concentrationC of the one-dimensional diffusion equation:

@C

@t¼ D

@2C

@x2(1)

whereD is (constant) effective diffusivity, t is timeand x is position. The flux or rate at which thediffusing substance emerges from unit area isgiven by:

f ðx; tÞ ¼ �D@C

@x(2)

This expression evaluated at the lower surfacex¼h, then integrated with respect to t, gives thetotal mass accumulation per unit area that haspassed through the membrane in time t:

mðtÞ ¼Zt

0

f ðh; tÞdt (3)

In diffusion cell experiments, this is the totalmass accumulation measured in receptor fluid.

Transient Dose Exposure Conditions

A chemical of concentration C1 is applied at timet¼ 0 to the upper surface of a membrane andremoved at t¼T1. Two boundary conditions afterthe exposure time are explored here.

Case 1: Zero Concentration (Sink Condition)at Upper Surface

After the initial exposure, the concentration atthe surface of the skin is maintained at zero.This boundary condition corresponds to aninfinite, well-stirred reservoir on the skin surfaceand represents the idealized case of a highlyvolatile compound. As chemical diffuses upwardto the skin surface from deeper skin regions, itimmediately evaporates from the surface anddiffuses freely into surrounding air and is carried

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TRANSIENT DERMAL EXPOSURE 1581

away by ambient air currents. For this condition,the Laplace domain solution of Eq. (1) is:

CðxÞ ¼ KmvC1ð1� e�sT1Þ sinh½lðh� xÞ�s sinhðlhÞ (4)

A circumflex indicates a Laplace domain func-tion of the complex variable s, and l ¼

ffiffiffiffiffiffiffiffiffis=D

p. Kmv

is the membrane-vehicle partition coefficient.Flux is given by:

FðxÞ ¼ �DdC

dx

¼ KmvC1Dlð1� e�sT1Þ cosh½lðh� xÞ�s sinhðlhÞ (5)

and the mass accumulation per unit area belowthe skin is:

M ¼ FðhÞs

¼ KmvC1Dlð1� e�sT1Þs2 sinhðlhÞ (6)

The total mass accumulation, that is massaccumulation as time approaches infinity, can bedetermined from the Final Value Theorem ofLaplace transform theory:

m1 ¼ A limt!1

mðtÞ ¼ A lims!0

sM ¼ AKmvD

hC1T1

¼ kpAC1T1 (7)

where A is the area of skin exposed to chemicaland kp¼Kmv D/h is the permeability coefficient,with Kmv the membrane-vehicle partition co-efficient.

For the general case of multiple (n) intermittentexposures of concentrations Ci and durations Ti,delayed by times Tdi, the applied surface concen-tration can be represented as

Cs ¼ Cð0; tÞ

¼Xni¼1

Ci½uðt� TdiÞ � uðt� ðTdi þ TiÞÞ� (8)

where

uðt� DÞ ¼ 1 t > D

0 t < D

�

is defined as the shifted unit step function.(In the limiting case of n¼ 1, this reduces to thesingle transient exposure considered above ifTd1¼ 0.) For this multiple exposure, the concen-

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tration, flux and mass accumulation are:

CðxÞ ¼ sinh½lðh� xÞ�s sinhðlhÞ Kmv

Xni¼1

Cie�sTdi ð1� e�sTiÞ

(9)

FðxÞ ¼ Dl cosh lðh� xÞ½ �s sinhðlhÞ Kmv

Xni¼1

Cie�sTdi ð1� e�sTiÞ

(10)

M ¼ Dl

s2 sinhðlhÞKmv

Xni¼1

Cie�sTdi ð1� e�sTiÞ (11)

The total mass accumulation is:

m1 ¼ kpXni¼1

AiCiTi (12)

Case 2: Zero Flux at Upper Surface

After the exposure period, the upper skin surfacepresents an impermeable barrier to diffusion. Thisrepresents the case of a non volatile compound, forwhich the skin is the preferred environment forthe chemical as opposed to the surrounding air.The solutions for t�T1 are the same as for Case 1.For t>T1:

CðxÞ ¼ R0 sinhðl½h� x�Þ � Rhl coshðlxÞl coshðlhÞ

þ CpðxÞ (13)

where

R0 ¼ �C1

sh

� 2C1

p

X1n¼1

knnðDk2n þ sÞ expð�DT1k

2nÞ (14)

Rh ¼ � 2C1

p

X1n¼1

sinðknhÞnðDk2n þ sÞ expð�DT1k

2nÞ (15)

Cp xð Þ ¼ C1

s� C1x

sh

� 2C1

p

X1n¼1

sin knxð Þn Dk2n þ s� � exp �DT1k

2n

� �(16)

with kn¼np/h.

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Flux is given by

FðxÞ ¼ �DdC

dx

¼ DR0l coshðl½h� x�Þ þ Rhl

2 sinhðlxÞl coshðlhÞ

� �

�DdCp

dx(17)

where

dCp

dx¼ �C1

sh

� 2C1

p

X1n¼1

kn cosðknxÞnðDk2n þ sÞ expð�DT1k

2nÞ (18)

Additional (t>T1) mass accumulation is givenby:

M ¼ FðhÞs

(19)

The total mass accumulation as time appro-aches infinity is most easily calculated as the sumof the amount in the membrane at time t¼T1:

mm ¼ AhC1

21� 8

�2

X1n¼0

1

ð2nþ 1Þ2expð�Dð2nþ 1Þ2�2T1=h

2Þ" #

ð20Þ

plus the amount that has passed through themembrane at time t¼T1:

mT1¼ AhC1

� DT1

h2� 1

6� 2

p2

X1n¼1

ð�1Þn

n2exp �Dn2p2T1=h

2� �" #

(21)

Both quantities are given by Crank.8 The sum,rewritten in terms of permeability coefficient andlag time, yields:

m1 ¼ kpAC1 T1 þ 2t � 12t

p2

X1n¼1

1

n2exp �n2p2T1

6t

� �" #

(22)

Where t¼h2/(6D) is the membrane lag time.For relatively long exposure times compared to

lag time, the terms in the exponential seriesbecome insignificant. For example, for T1� t, theerror is <10% if the infinite series is ignored. In

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this case, Eq. (22) can be approximated as:

m1 � kpAC1ðT1 þ 2tÞ (23)

For very long exposure times (T1� 2t), itfollows that

m1 � kpAC1T1 (24)

which is the same as Eq. (7). That is, at this limitthe total mass accumulation in Case 2 is similar tothat in Case 1. An equivalent condition existswhen lag time is very small. As t! 0, total massaccumulation in Case 2 is also similar to that inCase 1 and is given by Eq. (24).

Time Domain Solutions

Time domain solutions of the Laplace domainequations for concentration and flux distributionand mass accumulation over time are obtained bynumerical inversion using Scientist (MicroMathScientific Software, Salt Lake City, UT). Thissoftware implements both Weeks’ and Piessens’methods of numerical inversion.

EXPERIMENTAL METHODS

In vitro diffusion cell experiments were under-taken to investigate the applicability of thetransient exposure theory outlined above. Diethylphthalate (DEP) was used as a low volatilitymodel compound (CAS: 84-66-2; MW¼ 222.2; logKow¼ 2.47; vapor pressure¼ 2.1� 10�3 mmHg at258C).13 DEP is widely used as a stabilizing agentin perfumes and other cosmetic formulations.14

For these experiments, both hairless guineapig skin and homogeneous SRMs were used. Side-by-side diffusion cells allowed us to approximateboth of the idealized post exposure boundaryconditions (Cases 1 and 2), in addition to theinfinite dose condition, using one compound.

Hairless Guinea Pig Skin Experiments

Male hairless guinea pigs (HGPs), �500 g, of thestrain Crl:IAF(HA)-hrBR were obtained fromCharles River Laboratories (Wilmington, MA)

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TRANSIENT DERMAL EXPOSURE 1583

and their use was approved by our Animal Careand Use Committee. HGPs were euthanizedwith CO2 and back skin was harvested and usedthe same day. Skin was dermatomed (PadgettModel B, Integra LifeSciences, Plainsboro, NJ) ata setting of 315 mm thickness. Skin discs wereobtained using a 3/4

00 circular stainless steel punch,weighed and mounted onto diffusion cells. Ablocked experimental design was implementedin which each HGP contributed skin discs to eachof three experimental protocols.

From each of 8 HGPs, 6 skin punches weremounted on horizontal (side-by-side) diffusioncells (Perme-Gear, Bethlehem, PA) and thereceptor compartments were filled with warmed,degassed buffer. Buffer consisted of HEPES-buffered Hank’s balanced salt solution. 5.96 gHEPES free acid was stirred into 1000 mL ofHank’s. Then 0.32 g of NaHCO3 and 0.05 ggentamycin sulfate were added. The pH wasbrought to 7.40 at 378Cby dropwise addition of 6NNaOH.

Receptor and donor volumes were 5 ml and thediameter of exposed skin was 9 mm. Receptor anddonor compartments (when filled) were stirred at�1000 rpm. The water-jacketed cells were kept at378C via a recirculating water bath.

Donor solution consisted of saturated DEP inbuffer. An excess of DEP was added to buffer andvortexed�24 h at room temperature. Themixturewas centrifuged (3000 rpm for 30 min) and thesupernatant was used as donor.

Two of the six skin disks were assigned to one ofthree exposure protocols, corresponding to the twocases described in the Theoretical Frameworksection plus an infinite dose exposure. For allthree exposure protocols, 5 ml of saturated DEPwere added to each of the six donor compartmentsat time zero.

Infinite Dose Experiments

The skin disks were exposed to donor solution forthe duration of the experiment (4 h).

Transient Exposure Experiments

Case 1: Transient Exposure, Zero Concentrationafter Exposure. At the conclusion of the exposureperiod (T1¼ 40 min), donor solution was pipettedfrom the donor compartments. The donor com-partments were rapidly rinsed 3–4 times withfresh buffer, and finally 5 ml of fresh buffer wereplaced in the well-stirred donor cells for theremainder of the experiment. The intention here

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was to keep the concentration at the skin surfacevery small, which wouldmimic the case of a highlyvolatile compound that evaporates quickly fromthe skin surface following the exposure period.

Case 2: Transient Exposure, Zero Flux afterExposure. At the conclusion of the exposure period(40 min, same as Case 1), donor solution waspipetted from the cells. The donor compartmentswere rapidly rinsed 3–4 times with fresh buffer,then the skin surfaces were gently patted with acotton swab. Donor cells remained empty for theremainder of the experiment. Because of the lowvapor pressure of DEP, flux out of the skin surfacefollowing the exposure period is expected to beminimal.

Sampling Protocol

For all experiments, 1.5 ml samples weredrawn from receptor compartments at times 0,20, 40, 60, 90, 120, 180, and 240 min and placed in2 mL autosampler vials, then capped for subse-quent analysis. Removed receptor fluid wasreplaced with fresh buffer. Samples of donorcompartment solution were also taken and diluted1:100 in buffer for analysis of donor concentra-tions. From each of the eight HGPs, the meanof the two skin punches for each of the threeexposure conditions was taken at each time point.

Silicone Rubber Membrane Experiments

Experiments were repeated using SRMs. SRMdiscs were cut from a single sheet (Pharmelast, SFMedical, Hudson, MA; nominal thickness, 0.020in.; measured thickness of hydrated membranes,0.410 mm). The discs were rinsed of coatingpowder and soaked overnight in distilled water,then mounted on diffusion cells as before.Exposure conditions and methods were the sameas for the HGP skin experiments, except that T1

was 24 min in an attempt to maintain a similarratio of exposure time to membrane lag time, ascompared with HGP skin and determined frompreliminary experiments. Also the temperature ofthe recirculating bath was set at 238C instead of378C in order to reduce the large permeation ratethrough SRMs compared with HGP skin. Totalexperiment duration was 2 h, and sample timeswere 0, 12, 24, 36, 48, 72, 96, and 120 min. Tominimize donor depletion, donor solution wasreplaced at 36 and 72 min for the infinite dose

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exposures. Six SRMs for each exposure groupwere used.

DEP Quantification

DEP concentrations were quantified using auto-mated solid phase microextraction (SPME) andgas chromatography (GC) as described pre-viously.15 Briefly, 85 mm polyacrylate SPMEfibers were used (Supelco, Bellefonte, PA), and anew, conditioned fiber was used for each experi-ment. Extraction procedures were automatedwith a Combi Pal autosampler (CTC Analytics,Zwingen, Switzerland). The fiberwas immersed inwarmed (408C), agitated sample for 45 min, thendesorbed in the injector of a Varian CP-3800 GC(Varian, Inc., Walnut Creek, CA) with flameionization detector. GC conditions were asdescribed.15 The current analyses incorporatedknown standards which were included at thestart of each run and after every 8–12 samples.A gradual decrease in the SPME fiber responsethat was observed over the course of an experi-mental run that included over 50 samples wascompensated for by linear regression of the GCresponse to these known standards. A calibrationwas performed prior to each experiment withconcentrations from 0.1 to 10 mg/mL, a range thatencompassed all sample concentrations exceptthose at time zero.

From the measured concentrations, the cumu-lative amount of DEP penetrating eachmembranewas calculated, accounting for the amount of DEPremoved with each sample.

DEP Saturation

The average saturation concentration of DEP inbuffer was found to be 895 mg/mL. Thus �4500 mgof well mixed DEP were available for penetrationfrom the 5 ml donor compartments. Infinite doseconditions were approximated for HGP experi-ments (total accumulation <200 mg) and SRMexperiments (total accumulation �1000 mg butdonor solution was changed at 36 and 72 min).Maximum receptor compartment concentrationsof DEP were <20 mg/ml for HGP experiments and<60 mg/ml for SRM experiments, suggesting thatsink conditions were well-approximated in thereceptor compartments.

Data Analysis

Nonlinear regression was used to compare themass accumulation data from HGP skin and

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SRMs with predictions of the diffusion equationfor the particular exposure conditions. Thisanalysis provides estimates for parameter valuesthat give the best fit of the diffusion equationsolutions to the experimental data.

Infinite Dose Experiments

For the exposure conditions representing infinitedose experiments, the time domain solution is wellknown and given by Crank:8

mðtÞ ¼ kpC1t� kpC1t

� 12kpC1t

p2

X1n¼1

ð�1Þn

n2exp

�n2p2t

6t

� �(25)

There are two unknown parameters thatdetermine the solution of this equation: perme-ability coefficient kp and lag time t. Nonlinearregressions of the mass accumulation datawith Eq. (25) were performed using SigmaPlot9.0 (Systat, Inc., San Jose, CA). The equationwas truncated to seven terms in the series. Use ofEq. (25) is mathematically equivalent to calculat-ing kp from the slope of the steady-stateDEP accumulation curve and t as the interceptof this asymptote with the time axis. However,use of Eq. (25) is quantitatively precise andeliminates subjectivity of the analyst in thesedeterminations.

Transient Exposure Experiments

Nonlinear regressions of the transient exposuremass accumulation data for Case 1 and Case2 were performed using the software packageScientist 2.0 (MicroMath Scienfic Software).Regression of Case 1 data with Eq. (6), and ofCase 2 data with Eq. (19) (which uses Eqs. (14, 15,17, and 18)), yielded estimates of kp and t.

Statistical Analyses

Statistical analyses were performed using Sigma-Stat 3.11 (Systat, Inc.). Differences in theestimated quantities kp and t among treatmentgroups (infinite dose; transient exposure Case 1;transient exposure Case 2) were detected usingOne Way Analysis of Variance (ANOVA). If adifference (p< 0.05) was detected, all pairwisemultiple comparisons were performed using theHolm-Sidak test. One Way ANOVA was alsoperformed on HGP skin disc weights.

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TRANSIENT DERMAL EXPOSURE 1585

Estimates of total mass accumulation fromexperimental estimates of kp and t were madeusing Eq. (7) (Case 1) or Eq. (21) (Case 2) withmeasured values of C1. Comparisons were madebetween the estimates derived from transientdose experiments with estimates based on theparameters derived from infinite dose experi-ments, using paired t-tests.

RESULTS

Figure 2 displays modeled flux and mass accu-mulation data for both Case 1 and Case 2transient exposures. Membrane properties andinput concentration are the same for all simula-tions, and flux and mass accumulation are shownfor different exposures ranging from 0.25t to 4t.Case 2 results differ from Case 1 in that there isa longer relaxation time for flux followingthe exposure time. For a given exposure time,

Figure 2. Transient exposure model resultsaccumulation (m(t)) are shown for Case 1 (Aexposures. Results from various exposure timwith increasing exposure times correspondincurves. Membrane properties and input concenquantities are arbitrary units. Time is norma

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there is greater overall mass accumulation forCase 2 exposures compared with Case 1, but thedifference diminishes as exposure time increases.These features are consequences of the differentpost exposure boundary conditions as discussedsubsequently (Discussion).

Figure 3 compares total mass accumulationsfrom Case 1 and Case 2 post exposure boundaryconditions. Displayed is the ratio of Case 2 toCase 1 total mass accumulation; that is, the ratioof Eq. (22) to Eq. (7), as a function of exposure timerelative to lag time (T1/t). Greater mass accumu-lations are predicted for Case 2 exposurescompared with Case 1, as seen also in Figure 2,but for large T1/t, the ratio of mass accumulationsapproaches 1. For T1> 2t, for example, there isless than a twofold difference in the predictedmass accumulations from the two equations.

Modeled data from a multiple transient Case 1exposure are displayed in Figure 4. Input con-centration, flux and mass accumulation areshown for exposures of different magnitudes

. Flux at lower surface ( f(h, t)) and massand B) and Case 2 (C and D) transientes are shown: 0.25t; 0.5t; 1t, 2t, and 4t,g to increasing total mass accumulationtrations are same for all simulations. Alllized by membrane lag time t.

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Figure 4. Multiple Case 1 transient exposure modelresults. Input surface concentration (Cs, A) and modelresults for flux at lower surface ( f(h, t), B) and massaccumulation (m(t), C) are displayed. All quantitiesarbitrary units.

Figure 3. Ratio of total mass accumulations fromzero flux (Case 2) and zero concentration (Case 1) postexposure boundary conditions. Curve displays ratio ofEq. (22) to Eq. (7), as a function of exposure time/lagtime (T1/t).

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1586 FRASCH AND BARBERO

and durations. Note that it is not required to reacha steady-state level of flux prior to changes in theinput concentration.

Turning to the experimental data, there wereno detectable differences in HGP skin discweights among the three experimental groups.MeansSD (mg; n¼ 16 per group) were: 10524 (infinite dose); 105 16 (Case 1); 106 23(Case 2). Assuming a density of 1000 mg/cm3,these 3/4

00 diameter disc weights correspond todermatomed skin thicknesses (mm) of 370 84,369 55, and 374 80 respectively.

Figure 5 displays DEP cumulative penetrationdata from the hairless guinea pig skin experi-ments. Panel A shows infinite dose experiments;Figure 5B shows Case 1 transient dose experi-ments, and Figure 5C displays Case 2 transientdose data. Experimental data are shown as meansand standard deviations (SDs) from n¼ 8 HGPs.The solid lines are best-fit regressions of the datathrough the mean experimental values, and theestimates for kp and t determined from theseregressions are given in the figures. The dashedlines in Figure 5B and C represent the predictedmass accumulation for these transient exposureexperiments based on the values of kp and t

determined from the infinite dose experiments.Figure 6 displays the corresponding DEP

penetration data for experiments using SRMs.These data represent experiments from n¼ 6SRMs for each exposure condition.

Figure 7 displays the early time cumulativepenetration data for the different exposure con-ditions from HGP (Fig. 7A) and SRM (Fig. 7B)experiments. Up until exposure time T1 (40 minfor HGP; 24 min for SRM), the membranes areexposed to the same infinite dose conditions.Therefore there should be no differences up untilthis time in the mass accumulations among thethree exposure groups. Figure 7 shows that thisis the case, and therefore the different regres-sions that were found for different post exposureboundary conditions were not influenced by somespurious variation among the different groups.For clarity, data points have been slightly offset onthe time axis. The solid lines correspond to theinfinite dose regressions.

Permeability and lag time data are given inTable 1. These data are the means and SDscalculated from all HGPs or SRMs individually.Therefore mean values may differ from thequantities given in Figures 5 and 6, which re-present values that were derived from all experi-ments pooled. ANOVA revealed no statistically

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Figure 6. DEP penetration through silicone rubbermembranes. Mass accumulation through the mem-branes from infinite dose (A) and Case 1 (B) and Case2 (C) transient exposures (exposure time¼ 24 min) aredisplayed. Data represent meansSD for n¼ 6 SRMs.Solid lines are best fit regression curves for the givenexposure conditions as described in text, with resultingparameter values for permeability (kp) and lag time (t).r2 is the coefficient of determination. Dashed lines in (B)and (C) represent predicted mass accumulations basedon the values of kp and t determined from the infinitedose experiments.

Figure 5. DEP penetration through hairless guineapig skin. Mass accumulation through the skin frominfinite dose (A) and Case 1 (B) and Case 2 (C) transientexposures (exposure time¼ 40 min) are displayed. Datarepresent meansSD for n¼ 8 HGPs. Solid lines arebest fit regression curves for the given exposure condi-tions as described in text, with resulting parametervalues for permeability (kp) and lag time (t). r2 is thecoefficient of determination. Dashed lines in (B) and (C)represent predicted mass accumulations based on thevalues of kp and t determined from the infinite doseexperiments.

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TRANSIENT DERMAL EXPOSURE 1587

Figure 7. Early DEP penetration data from hairlessguinea pig skin (A) and silicone rubber membrane (B)experiments. MeansSD’s are shown for the durationsof the exposure times. The data demonstrate that nodifferences exist among the groups during the time inwhich all were subjected to the same exposures. Forclarity, data points have been slightly offset on thetime axis. The solid lines correspond to infinite doseregressions performed over the entire time course ofexposures.

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significant differences in kpmeasured in SRM; in tmeasured in SRM; or in t measured in HGP skin.A difference was detected in kp measured in HGPskin. Pairwise comparisons found a significantdifference between kp measured from infinite dose

Table 1. Estimates of Permeability Coefficient (kp) and La

Hairless Guinea Pig Skin (n

kp (cm/h) t

Infinite dose 0.059 0.006 0.50Transient, Case 1 0.047 0.009y 0.40Transient, Case 2 0.041 0.009y 0.35

Values are means standard deviations for the indicated numbySignificantly different (p< 0.05) from infinite dose value.

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experiments compared with kp measured fromeither Case 1 or Case 2 transient dose exposures,but no difference between kp measured from Case1 compared with Case 2 exposures.

Table 2 presents estimates of total massaccumulation from the transient exposures. Theseestimates were obtained from Eq. (7) (Case 1) orEq. (21) (Case 2) using parameter values sum-marized in Table 1. There were significantdifferences between calculations based on thetransient dose exposures compared with esti-mates based on infinite dose experimental para-meters, for all cases except Case 1 studies inSRMs. In all cases, the use of infinite doseexperimental parameters overestimated the totalmass accumulation that was measured from thetransient exposures. This holds true not only forthe mean values reported here, but also for alleight individual Case 2 HGP experiments and allsix Case 2 SRM experiments, as well as seven ofeight Case 1HGP but only three of six Case 1 SRMexperiments.

DISCUSSION

Estimation of the disposition of chemicals appliedto skin as transient exposures is a complexproblem. Despite the importance of this topic inoccupational, environmental, pharmaceutical,and cosmetic applications, little work has beenperformed in this area that can be quantifiedwithin a reasonable analytical framework. In thisstudy, straightforward solutions to the problemhave been made by adopting simplifying assump-tions about the skin and physical characteristicsof the applied chemical and its interaction withskin. In particular, skin is considered to be aneffective homogeneous membrane; the appliedchemical is assumed either to be very volatile ornot at all volatile; and there is no interaction of theapplied chemical with skin. With these assump-tions, Laplace domain solutions to the diffusion

g Time(t) of DEP from Different Exposures

¼ 8) Silicone Rubber Membranes (n¼ 6)

(hr) kp (cm/h) t (h)

0.17 0.628 0.037 0.34 0.08 0.10 0.595 0.110 0.39 0.04 0.13 0.513 0.143 0.32 0.06

er (n).

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Table 2. Total Mass Penetration of DEP from Transient Exposures Compared with Predicted Values Derived fromInfinite Dose Experiments

Hairless Guinea Pig Skin (n¼ 8) Silicone Rubber Membranes (n¼ 6)

Transient DosePrediction

Infinite DosePrediction

Transient DosePrediciton

Infinite DosePrediction

Transient, Case 1 26.5 4.4y 33.6 5.0 244 51 256 15Transient, Case 2 46.5 12.5y 79.6 17.6 460 108y 648 80

Amounts (mg/cm2) calculated by Eq. (7) (Case 1) or Eq. (22) truncated to five terms (Case 2), using values summarized in Table 1.Exposure times were 40 min (HGP) or 24 min (SRM).

Values are means standard deviations for the indicated number (n).ySignificantly different (p<0.05) from prediction based on infinite dose experiments.

TRANSIENT DERMAL EXPOSURE 1589

equation for the transient dose condition havebeen found. The applicability of these solutionshas been explored through in vitro experimentsin which skin or SRMs were briefly exposed to amodel chemical. The use of side-by-side diffusioncells and a low volatile test compound, whilecontrolling the conditions at the donor side ofthe skin during the post exposure period,allowed us to approximate both extremes of postexposure boundary conditions using one chemical,diethyl phthalate. This process in turn permitsquantitative comparisons among the diffusionparameter estimates that are obtained from thedifferent experimental conditions.

The experimental data shown here in Figures 5and 6 demonstrate the robustness of the develop-ed theory. In general, the experiments are welldescribed by the solutions to the diffusionequation for the given exposure conditions. Agood measure of this is the coefficient of determi-nation, r2, which indicates the closeness of fitbetween the data and the model equation(1.0 being a perfect fit). While the infinite doseexperiments produced excellent r2 (>0.999), verygood correlations also resulted from the pooledtransient dose experiments describe here, withr2> 0.97 for HGP skin and r2> 0.99 for SRM.

However, if the homogeneous membraneapproximation is valid and experimental bound-ary conditions are as described, then parameterestimates for all exposure conditions should beidentical. For example, permeability and lag timesestimated from the infinite doseHGP experimentsshould be able to predict the time course of massaccumulation for either of the transient doseregimes. This is important because it would be ofgreat benefit if transient exposures could bepredicted from the more common and simpler toperform experiments using an infinite dose.In Figures 5 and 6, the dashed lines in (B) and

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(C) indicate the predicted mass accumulationsbased on the measured kp and t from the infinitedose experiments. The data indicate significanttrends in that the parameters derived frominfinite dose experiments predict greater levelsof mass accumulation than those measured fromthe transient exposure experiments, particularlyfor the Case 2 studies (C). Statistical analysisverifies that the estimate of kp from infinite doseHGP experiments is significantly greater than theestimates obtained from either transient expo-sure. Consequently, the use of kp and t derivedfrom infinite dose studies overestimates totalmass accumulation from either Case 1 or Case 2transient exposures, as demonstrated from thedata in Table 2.

By repeating the experiments with SRMs, wewere able to investigate skin membrane hetero-geneity as a possible explanation for the dispa-rities between the measured transient exposuremass accumulations and the predictions frominfinite dose experiments. Silicone rubber formsa simple homogeneous membrane, thereforeestimates of kp and t from any of the threeexposures should not differ. The data (Tab. 1;Fig. 6) indicate that, although there are nosignificant differences detected with the numberof experiments performed here, there are definitetrends similar to those observed with the HGPstudies. The infinite dose experiments tend toover predict mass accumulation, particularly inCase 2 studies where a significant difference wasdetected (Tab. 2).

There are several possible explanations forthese observations. One possibility relates tonon homogeneous diffusion properties of skin.Watkinson et al.16 explored depth dependentdiffusion coefficients but found little effect onmodeled steady-state concentration profiles. Anis-simov and Roberts17 modeled SC diffusion

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and partition coefficient heterogeneity and foundthat it could explain reported discrepanciesbetween penetration and desorption experiments.The split-thickness HGP skin samples usedhere contained both stratum corneum andviable epidermis. These layers have differentpermeability properties and it is likely that thesedifferences have much larger effect than depthdependent diffusion within the stratum corneumitself. Support for some mechanism related toskin heterogeneity is given here by a comparisonbetween HGP skin transient dose experimentswith SRM transient dose experiments. Thelater exhibit a much smaller difference in massaccumulation from that predicted by the infinitedose experiments. These data are more inaccordance with the homogeneous membranetheory than the HGP data.

Another contributing factor could be the finitetime required for washing of the membranes. Thistime was purposely kept as brief as possible.Nevertheless, some diffusion surely occurredbetween the membrane (skin or SR) and thebuffer during the time the membrane was incontact with the washing solution. This wouldlessen the amount of compound in the membraneat the end of the exposure period comparedwith what was assumed by the ideal boundaryconditions. Because the wash time is short, areasonable worst case estimate of the amount lostduring washing can be made by assumingdiffusion out of a semi-infinite membrane into asink, as follows:18

Mwash ¼ 2AkpC1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi6twasht

p

r(26)

With a liberal wash time (twash) estimate of1 min, �8.5 mg of DEP could have been lost duringwash from the HGP skin, and �75 mg from theSRMs. The overall result could be a significantdecrease in the measured mass accumulationfollowing the exposure period, as was observed.

Although we deliberately selected a compound(DEP) with low volatility for these studies,another factor contributing to the observed resultscould have been evaporation of the compound.Some evaporative flux through the membranesurface could account for the discrepanciesobserved for Case 2 data in both HGP and SRMexperiments.

A final factor that we have considered is thepossible binding of DEP to skin elements.Irreversible or slowly reversible binding of DEP

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to skin would lead to mass accumulation curvesthat exhibit features displayed in Figure 5. Thatis, binding of DEP would lessen the amount ofDEP that desorbed from the membrane followingthe exposure period.

Any or all of these factors could have con-tributed to the observed phenomenon. Interest-ingly, however, the model presented here exhibitsa superior ability to predict the transient exposuredata from parameters derived from infinite doseexperiments than the more complex multilayermodel described by Kruse et al.19 was able topredict finite dose mass accumulation frominfinite dose data. Reasons for this are not known.Kruse et al. claim their finite dose model predic-tions are adequate when restricted to limitedexposure times, and it is not clear from theirdescription how they handle post exposureboundary conditions. We studied only one com-pound here while Kruse et al. presented data onfive compounds exhibiting a range of lipophili-cities. It remains to be seen if the present modelcan be validated with additional compounds andexposure times.

From the standpoint of dermal risk assessment,themain quantity of interest is the total amount ofpermeant that penetrates the skin in response toan exposure. It is important to keep in mind thatthis total includes the amount that accumulatesup until the end of the chemical exposure, plus theamount that accumulates after the exposureperiod, that is, after the chemical is removedfrom the skin surface, from the skin depot. Eqs.(7), (12), (22), and (23) are algebraic expressionsthat may prove useful for exposure assessment.Eq. (7) is what one would obtain if one naivelyapplied the steady state absorption rate (flux) tothe entire exposure period, without considerationof initial transient absorption prior to establish-ment of steady state or absorption that continuesfollowing the exposure period. In fact, a rearran-gement of Eq. (7) has been proposed as a means ofestimating the exposure time required for skinabsorption to reach a specified level.20 The currentanalysis places Eq. (7) on firm theoretical groundand clarifies the limitation that it should only beused for highly volatile compounds, or forcompounds that are continually washed awayfrom the skin surface, or for non volatiles whenexposure time ismuch greater thanmembrane lagtime. For exposures from non volatiles when T1

is not �t, Eq. (22) is the appropriate expression.Eq. (22) places an upper limit on the amount ofchemical that penetrates the skin from transient

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TRANSIENT DERMAL EXPOSURE 1591

exposures, as it assumes that all chemical withinthe skin at the end of the exposure period willeventually penetrate. This upper bound couldserve as a conservative estimate for risk assess-ment. Unfortunately, there is not much reliablelag time data in the literature that would allowbroad use of this equation at this time. Formoderately long exposure times, for exampleT1� t, Eq. (23) can be used as a simpler form ofEq. (22).

Comparison of Eq. (22) with Eq. (7) showsthat predicted total mass accumulation fromCase 2 transient exposures exceeds that ofCase 1 exposures, all other conditions being equal(Fig. 3). This can be understood on the basis of thepost exposure boundary conditions. For the twocases, the total mass accumulation is the same upuntil the end of exposure time (T1). Afterward, forCase 2 all the permeant in the membrane atthe end of the exposure period must penetrate thelower membrane surface (x¼h). For Case 1, someof the permenat in the membrane at the end ofthe exposure period penetrates the lower surface,but some diffuses outward through the uppersurface (x¼ 0) as well, depending on the localconcentration gradient within the membrane.Therefore, total accumulation in Case 2 exceedsthat of Case 1. Also, the time required to reachsteady state after T1 is longer for Case 2 (Fig. 2)because of the overall greater distance withinthe membrane that the bulk of permeant musttraverse, and because diffusion time is propor-tional to the square of the molecules’ meandisplacement.

In conclusion, the model proposed hereaccounts for more realistic exposure scenariosthan the more common theory that considersonly the steady state response to an infinitedose. This theory provides a framework forestimating occupational, cosmetic and pharma-ceutical dermal exposures that are transient orintermittent in nature. When used in conjunctionwith the related finite dose theory, a wide varietyof realistic dermal exposure scenarios can beanalyzed.

ACKNOWLEDGMENTS

The authors are grateful to Prof. Annette L.Bunge of the Colorado School of Mines for helpfuldiscussions.

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