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, 1.- Pharmaceutical Research, Vol. 12. No. 7, 1995 Report A New Method for Estimating Dermal Absorption from Chemical Exposure. 3. Compared with Steady-State Methods for Prediction and Data Analysis Annette L. Bunge,'*jRobert L. Cleek,' and Brent E.Vecchia' Received July 20,1994; accepted February 8, 1995 hrrparr. This paper compares unsteady-state and steady-state meth- ods for estimatingdermal absorption or analyzing dermal absorption data. The unsteady-state method accounts for the larger absorption rates during short exposure times as well as the hydrophilic barrier which the viable epidermis presents to lipophilic chemicals. Mcih- ods. Example calculations for dermal absorption from aqueous solutions are presented for five environmentally relevant chemicals with molecular weights between 50 and 410 and log,,,KK, between 0.91 and 6.8 chloromethane, chloroform, chlordane, 2,3,7,8-TCDD, and dibenz(a,h)anthracene. Also,the new method is used to evalu- ate experimental procedures and data analyses of in vivo and in vitro permeation measurements. Results. In the five example cases, we show that the steady-state approach significantly underestimated the dermal absorption. Also, calculating permeability values from cumulative absorption data measured for exposure periods less than 18 times the stratum corneum lag time wiU overestimate the actual permeability. Conclusions. In general, steady-state predictions of dermal absorption will underestimate dermal absorption predictions which consider unsteady-state conditions. Permeability values cal- culated from data sets which include unsteady-state data will be incorrect. Strategiesfor analyzing in vitro W s i o n cell experiments and codinning steady state are described. ~~~~ ~ KEY WORDS dermal absorption; exposure assessment; percuta- neous absorption; stratum corneum; permeability; octanol-water partitioning. the skin layers was zero, and the chemical concentration in the body system remains at zero during the entire exposure event. By plotting normalized Mi,against dimensionless texprwe can compare chemical exposures with different concentrations, exposure areas (A), or physicochemicalproper- ties (SC-vehicle partitioning K,,, SC diffusivity D,, and SC thickness LJ on an equal basis. The parameter B measures the SC permeability relative to the EPI permeability and correlates with the lipophilic character as indicated by the octanol-water partition coefficient, KO,. As illustrated by the solid curves in Figure 1, the cumulative mass absorbed does not increase linearly in time, and the rate of mass absorption is not always constant, or steady. Specifically, during the early period of exposure, the absorption rate is proportional to l / c , meaning that at the onset of an exposure (i.e., at t, = 0) the absorption rate is infinitely rapid. The absorption rate decreases from this extremely large value to eventually reach the steady-state value. Once steady state is established, the normalized cumulative mass absorbed becomes linear in time. Even when steady state has been reached, the cumulative mass absorbed includes the mass absorbed during the unsteady-state period. Permeability is an important quantity for characterizing the barrier properties of a membrane. Strictly, the permeability of a chemical through a membrane is only meaningful when measured at steady state. For skin including both the SC and EPI, the steady-state permeability of a chemical from a given vehicle v, P,, depends on the steady-state per- meabilities for the SC (Pcv)and EPI (P,,): which are defined as: -Pcv = KCVDC LC INTRODUCTION Estimates of systemic chemical exposure from dermal absorption should be based on the total mass absorbed including chemical that has entered but not yet left the stktum corneum (SC). Cleek and Bunge (1) describe a mathematical model for dermal absorption including unsteady-state effects and the hydrophilicbarrier which the viable epidermis (EPI) presents to lipophdic compounds. Figure 1, taken from Cleek and Bunge (l),shows the normalized mass of chemical absorbed into the SC, (M,/(AL,K&:)) as a function of the dimensionless exposure time (7 = t,,,D&) for the SC-EPI composite membrane, assuming the vehicle concentration remains constant at Cg, the initial chemical concentration in ' Chemical Engineeringand Petroleum Refining.Department, Colo- rado School of Mines, Golden, Colorado 80401. Cox Laboratory for Biomedical Engineering, Rice University, 'Houston, Texas 77251. TO whom correspondence should be addressed. (3) In Figure 1, the SC only B = P,JP,,, permeability and consequently according to: .P, is related to P, = -l P+cvB (4) Many in vitro and in vivo experiments on human and animal skins have been conducted to determine skin permeability of various chemicals. In some experiments, the amount of chemical absorbed was measured. In others, the amount of chemical or radioactivity which has crossed the skin barrier to appear in a receiving chamber, blood, or excreted materials (i.e., urine or feces) was determined. Since only the steady-state permeability has meaning, an important concern is whether in vivo or in vitro data were collected and analyzed to insure that a steady-statepermeability value was obtained. ~ The mathematical expression plotted as the solid curves in Figure 1 is complex and impractical (1). However, Cleek I i 0 7 2 C 8 7 4 1 1 7 . S C V O 0 1995 Rcnum pllbluhrno Corporation 972 Estimating Dermal Absorption from Chemical Exposure. 3. 973 2.53 uO > 1 Table 1. Summary of the B-Method Equations for Calculating the \ - Cumulative Mass Absorbed c? $,- bi ai 4 For Lr4nt*, G- .- 3 -.35-: 2 P 0 05 I I .5 2 Fort,. > t*, +10gloP,w(c&) = -2.8-0.006(MW) 0.7410g,oK, B = PCW (2.6 c&) W Dimensionless Exposure Time, L', Figure 1. Normalized cumulative mass entering the stratum corneum when the vh@eepidermis is present plotted as a function of dimensionless txp and B (a: B 8 0.01; b: B = 0.1; c: B = 1; d: B = 2; e: B = 10; f: B 3 100). Solid curves represent the unsteady-state case: dashed lines, the steady-state Eqn.(8). and Bunge (1)have developed two simple algebraic expressions which closely approximate the curves in Figure 1. They also proposed an approach for estimating a priori the physicochemical parameters describing both the SC and EPI. The complete set of expressions, which we call the B-method, can be used to predict dermal absorption for a given exposure scenario. In addition, the B-method provides a simplified framework for comparing steady and unsteadystate analyses of experimental data and for evaluating the validity of resulting permeability values. THEORY For B 6 0.6, t* = -0.4 DC For B > 0.6, where b and c are defined as: b = 2 -(1 + B)* - c 71 c = 1 + 3B + 3BZ 3(1 + B) log,& = 0.74IOg&,, For aqueous vehicles, Kc, = kW. For nonaqueous vehicles, K, = %wKw L-C? CY The B-Method The B-method approximately represents the solid curves in Figure 1 with algebraicexpressionswhich are summarized in lhble 1 (1,2).During the early absorption period &e., t, c t*), the cumulative mass absorbed into the SC increases as a function of Vi&, whereas after teXp> t*, the cumulative mass absorbed is linear in teXp.The transition time t* represents the exposure time required to reach steady state. Notably, t* is related but not equivalent to the lag time ( t d . Since the rate of absorption asymptotically approaches the steady-state rate, different values for t* are given depending on how closely one requires that the absorptionrate approximatethe steady-staterate. As a general rule, for chemicals with moderate to low lipophilicity, t* is approximately 2.4 t,w Experimentalvalues for either DJL, or K,, should not be mixed with estimates made from Eqns. ("9)or VlO)for the other parameter. These equations are internally consis- tent in that the product of the parameters in Eqns. ("9)and (T10) consistently estimates the steady-state SC permeability as predicted by Eqn. (T3). The B-method estimate of the steady-state SC-EPI composite permeability, P,, by Eqn. (4) includes contributions fromboth the SC and EPI and also indicateswhen one or the other completely controls absorption. As seen in Figure 1, the SC controls absorption when B s 0.01,the EPI controls when B z= 100,and both the SC and EPI contribute to the barrier resistance when 0.01 < B c 100.Likewise, when B d 0.01, Eqn. (4)predicts that P, = P, and when B P 100, Eqn. (4)predicts that P, = P,,. When B is between 0.01 and 100,Eqn. (4)predicts that the presence of the EPI alters the permeability of the SC-EPI composite even when the SC permeability is still smaller than the EPI permeability. That is, P, is less than P,, even when B (i.e., PcJPe,) is as small as 0.01. Steady-State Method Some researchers (references 3-5, to name only a few) have suggested calculating dermal absorption assuming steady state applies for all exposure times. That is, In Eqn. (5). the permeability of the SC-EPI composite P, is either measured or estimated using a correlation such as Eqn. (T3) when the vehicle is water. Since Eqn. ("3)repre- sents the steady-state permeability of the SC and not the SC-EPI composite, it will predict permeabilities for highly j lipophilic compounds which are higher than possible even if the SC is absent only the EPI remains. In this situation, Flynn (6) suggested comparing P, calculated from a corre- lation such as Eqn. m)with an estimate of Pew,usually taken to be between 0.1 and 1.0 c& (0.28 X - 2.8 x c d s ) (e.g., pp 4-21 and 5-12 in reference 7). Then, Flynn proposed: 40 30' Pw = Pm when Pcw< Pew P, = Pew when Pcw3 Pew I Calculationsmade using the Flynn procedure, Eqns. (6)and (7), assume that only one of the skin layers, either the SC or the EPI, entirely controls permeation. In fact, for many lipophilic compounds, Pewis not much smaller than P,, meaning that both contribute significantly to the barrier re- sistance. In such situations, the skin barrier actually will be more resistant than indicated by assuming that P, equals only Pew. In contrast, Eqn. (4) more accurately represents con~butionsfrom both the EpI and sc with exactly the Same information as required by Eqns. (6)and (7): P, and Pew(or B = P,,JPe,). Consequently, we modify the steady-state expression, Eqn. (s), to include this improved representation for the combined SC-EPI permeability, Eqn. (4): -ME- A -- PCvCg +1 B txp (8) The normalized cumulative mass absorbed, ME/(AL,K,, Cg), as calculated from Eqn. (8) is shown in Figure 1 as the dashed lines. APPLICATIONSAND DISCUSSION Methods for estimating dermal absorption can be used in two distinctly merenwtays: (1) to predict absorption from either measured or estimated values of K,, and DJL,, or (2) to analyze in vivo or in vitro experimental data to obtain values for &, and DJL, separately or their product KcVDJLcwhich equals P,,. First, we will consider differences in predictions the and steady-state methods. In light of these results, we will then examine common experimental approaches and data analyses for determining permeability. PreitictingDermalEXpanue The comparison of unsteady and steady-state predictions in Figure 1 shows that the steady-state approach does not include the quicker absorption which occurs during the early exposure period while the SC reservoir is being fiued. As a consequence, steady-state predictions of the cumulative mass absorbed are always less than would actually occur. Figure 2 illustrates the predicted cumulative mass absorbed from aqueous solutions for dibenz(a,h)anthracene. Bble 2 reports predictions for dibenz(a,h)anthracene and four other chemicals of environmental interest with widely varying MW and Kow: chloromethane,,chloroform, chlordane, and 2,3,7,8-TCDD. Bble 2 also summarizes published and calculated parameters used in these predictions, including the approximate time to reach steady state (t*) and B. texp. hr Figure2. Cumulative mass of dibenz(a,h)anthracene absorbed into the SC as a function o f t , predicted by the B and steady-state expressions. These Cahlations assumed that the chemical exposure to aqueous solutions, that there was no depletionof chemical during the exposure, that skin permeation was rate controlling, and that the SC thickness was 0.001 cm. The dermal absorption predictions in Figure 2 and Table 2 are reported in three differentways: (1) the mass absorbed normalized by the vehicle concentration, (2) the mass absorbed from a saturated aqueous solution, (3) and the volume of water of the same concentration that one must ingest to equal the estimated dermal exposure. The left hand axis in Figure 2 reports dermal absorption normalized by the aqueous concentration, Cc. The actual mass absorbed per area can be determined by multiplying plotted values by the known or estimated Cc. The largest amount of absorption would occur at the largest possible concentration, that is at the saturation limit in water, Cgt. Furthermore, dermal absorption rates from any other saturated vehicle, the saturated vapor, or the neat chemical should all be the same as or less than from saturated water, provided that the vehicle or the chemical itself do not damage or alter the skin (IS)and water is essentially insoluble in the neat chemical. (If the neat chemical has some water solubility, then absorption from a saturated *,aqueous solution will be less than from the neat chemical.) For lipophilic chemicals, the mass absorbed from water at reported in Figure 2 as the leftmost of the two right hand axes, very nearly represents the m a h u m possible absorption of each chemical even from a neat solution. The assumptions that water is insoluble in the neat chemical,and that the neat chemical does not alter the skin will probably not be strictly valid for chloroform or chloromethane, which are not highly lipophilic and which may extract some of the lipid components from the SC. However, for these compounds, the exposure scenarioof greatest concern is contact with aqueous solutions during showering, bathing or swimming and not with the neat chemical. The rightmost of the right hand axes in Figure 2 reports the predicted dermal absorption in terms of the Ingested Water Equivnlent Volume (IWEV). This is the volume of water one would have to drink to absorb a mass equivalent to immersing the entire body (18,000 cm2) in an aqueous solution at the same concentration. Assuming 100% of the ingested chemical is absorbed and no chemical depletion in &timating Dermal Absorption from Chemical Exposure. 3. Tabk 2. Example Estimates of Dermal Absorption from Aqueous Solutions Chloromethane Chloroform \ chlordane 2.3,7,8-TCDD -AMCiZ, ' cm -la cm2 *IWEV, L 0.91 (7) 50.5 4800 (11) 0.010 0.0037 0.37 0.0037 4.71 7.89 x 10-7 12.7 30.4 1 *a 0.00527 *b 0.0037 *C M* a 25.3 b 17.8 CM a 0.0949 b 0.0667 CM 1.90 (8) 119.4 7900 (12) 0.033 0.0078 0.24 0.0075 25.5 3.05 x 10-7 32.8 78.8 1 a 0.0159 b 0.0078 c na a 26 b 61.6 c na 6.25 (9) 409.8 0.056 (13) 1.81 0.232 0.13 0.083 4.22 x 10' 5.51 x 10-9 1,815 7,330 (5.1 days) 12 a 12.2 b 2.78 c na a 0.686 b 0.1% c na 6.80 (7) . ' 322 7.91 X 10-6(14) 13.77 2.00 0.145 0.135 1.08 x Id 1.85 X 540 2,470 (1.7 days) 12 ' a 57.4 b 24 c 12 a 0.000454 b 0.00019 c 0.000095 a 0.286 b 0.140 c na a 220 b 50.5 CM a 1030 b432 , c 216 * a: B-Method; b: Steady-state;,,P c: Steady-state, P, = 1.0 cmih; na: not applicable. * Ingested Water Equivalent Volume, Eq. (9). 975 dibcnz(a,h)anthracene 6.50 (10) 278.4 2.49 x 10-3 (io) 14.03 2.19 0.156 0.146 6.46 x 10' 3.39 x 10-8 295 1,350 (22.5 h) 12 a 46.5 b 26.3 c 12 a 0.116 b 0.0654 c 0.0299 a 837 b 473 c 216 the aqueous solution contacting the skin, a material balance mass absorbed over only one hour. In contrast, exposures to shows that the ingested volume equivalent, Vi,,,, is related to chemicals such as TCDD, chlordane, and dibenz(a,h)- dermal absorption according to: anthracene are likely to be longer, so exposure periods up to 12 hours have been considered. Vh* = ( 2 ) A Chloromethane, the least lipophilic compound shown (9) here (log,&, = 0.91), is predicted to reach steady-state absorption after about 30 minutes. In contrast, the most li- where for Figure 2 and Table 2 (WAC;) is calculated from pophilic compound,TCDD (log,&ow = 6.8), does not reach Eqns. (Tl) and (T2)and A was taken as 18,000 cm'. For steady state until almost 2 days of exposure. Chlordane, with smaller areas of exposure, VinOwill be proportionally its large MW, is not predicted to reach steady state for more smaller. For example, an exposure of 10% of the body will than 5 days. The large difference in the time to reach steady correspond to 0.1 of the ,V from a whole body exposure. state for chloromethane and chlordane arises because chlor- Presented in this way, the relative importance of the dermal dane (MW = 409.8) diffuses much more slowly than does and ingestion exposure routes are easily recognized. Specif- the smaller chloromethane (MW = 50.5). The deleterious ically, when dermal and ingestion exposures are both possi- effect which an increased MW has on permeability is evident ble, but ,V is larger than 2 L (the estimated daily volume from the relatively small increase (only about&fold) in P, for drinking water (la)), dermal absorption usually will rep of chlordane over chloromethane despite a more than Id resent the primary exposure risk. increase in K., In Figure 2 and 'hble 2, we compare calculationsby the We can draw some general conclusions, based on the 3 and steady-state methods. For both methods PCwwas es- results presented in Figure 2 and 'hble 2. First, the ingested timated using Eq. (T3). The steady-state calculations, la- water equivalent volumes are largest for the most lipophilic beled as p,,, were made using Eqn. (8) and assuming that B chemicals. For chemicals with large &, water solubilities was always zero (i.e., Pw = Pew). For two of the five chem- are so small that one would need to drink huge volumes to icals (TCDD and dibenz(a,h)anthracene),the calculated PCw experience the same exposure level possible from dermal exceeded 1.0 cmlhr, which Flynn (6) estimated as the limit- absorption. However, it is important to remember that the ing permeability value of the SC-EPI composite. For these dennal absorption estimates assume constant vehicle con- chemicals, we also report the steady-state prediction based centration during the exposure: Cow does not change. For on Flynn's recommendation, Eqn. (7), which is labeled as chemicals with extremely low C r , this means that the skin 1.0 cm/hr. must be able to contact large volumes of water. This might For chloromethaneand chloroform, the most important occur in a swimming, bathing or showering scenario. How- exposure situations are bathing, showering or swimming in ever, for smaller volume exposures such as occasional chlorine treated drinking water. Consequently, we report the splashing, the volume of contact may be too small to main- 676 Bunge, Clcek, and Vecchia tain CG a s constant. Nevertheless, we can anticipate that mass in the receiving chamber. However it is still useful, the dermal exposure route may at least equal the ingestion since it gives a means to examine if steady state has been route for highly lipophilic chemicals. reached. For example, in situations when the SC controls However, at the maximum exposure level, CG = Crt, absorption, we can quantitatively evaluate whether an i,l the predicted cumulative mass absorbed for the larger KO, vitro experiment measuring the cumulative mass appearing chemicals (e.g., chlordane, dibenz(a,h)-anthracene and in the receiving chamber has been conducted long enough to TCDD), even after 24 hours, is much smaller than for the be at steady state. The procedure is illustrated in Figure 3 more moderate KO, compounds (chloromethane and chlo- and summarized in Table 3. The simulated data points in roform) after an exposure of only 1 hour. Consequently, a Figure 3 were generated by numerically imposing errors on large steady-state SC permeability from water does not im- calculated mass absorption values using random numbers ply a large dermal absorption rate. In fact, the maximum from a uniformly distributed population with a mean of zero steady-state mass flux from water (and any other vehicle, and a standard deviation of 10% of the calculated mass ab- vapor, or neat chemical, provided the skin is not altered and sorbed. The solid curve represents the true cumulativemass water is insoluble in the neat chemical) is PwCFt.In the case which would appear in the receiving chamber as a function of chlordane, dibenz(a,h)anthracene, and especially TCDD, of time (1). all of the increases in P, from a large KO, are more than The permeability can be deduced from the slope of the offset by decreases in Crt. For example, Czt for chloroform line fitting the simulated cumulative mass absorption data is 9 orders of magnitude larger than Crt for TCDD! normalized by C;. Since the SC controls absorption in this Finally, the steady-state approach for estimating dermal example, the time-intercept of that line should represent the absorption always underpredicts the expected levels of ab- lag time for the SC,tlag.c,which is theoretically equivalent to sorption. The difference in the B and steady-state methods L$/(6Dc).Based on Eqn. (TS), any data points taken at times was greatest for the highest molecular weight compound. As less than t* = 2.4 tlagecshould not be used to calculate the we show later, the steady-state calculation will approach the line representing the steady-state appearance of mass. An B-method result for exposure times approaching about 18 iterative process may be required as shown in Figure 3. The tlpg,cwhere tla9,, is the lag time across the SC. Since tlae,c data are regressed to determine an apparent tlas,c.This first increases with MW, at a specified teXpthe largest MW chem- regression may include data points which were at times less ical will be most poorly represented by the steady-state than 2.4 t,ae,c.These unsteady-state data points are then dis- method. However, even for chloromethane (MW = 50), the carded and a new linear regression is made. This process IS steady-stateprediction for a one hour exposure is about two- continued until no data taken at times less than 2.4 tlaS,,are thirds of the amount expected when the early rapid absorp- included in the linear regression. The slope of the resulting tion is included. For the highly lipophilic chemicals with P, line is then equal to P,. For the case illustrated in Figure 3, greater than 1.0 cm/hr (Le., TCDD and dibenz(a,h)- the random variation in the simulated data causes P,, esti- anthracene), the steady-state calculation using the SC per- meability (P,,) rather than the SC-EPI composite permeabil- ity (p, = 1.0 c&) more closely predicts the actual mass absorbed. However, if the exposure continues long enough, the PCwsteady-state prediction will eventually exceed the actual mass absorbed because the added resistance from the EPI has not been considered. We have now compared the predictive applicationof the B and steady-state methods. An equally important applica- tion of these two methods is analysis of experimenpl data to calculate skin permeabilities, which we discuss next. Analyzing in Vitro Diffusion Cell Experiments I Skin permeability is frequently measured in vitro in a W s i o n cell where skin is mounted between two solution chambers and solute transfer is followed by monitoring concentration in the receiving chamber. Typically, the cumulative mass of solute appearing in the receiving chamber is plotted as a function of time since the exposure began. Pro- vided that the vehicle concentration remains essentially constant and that sink conditionsare maintained in the receiving chamber, the cumulative mass of solute appearing in the receiving chamber eventually becomes linear in time, indicatingthat steady state has been established. The permeability can then be calculated from the slope of the steady-state line (i.e., the slope = P,C;). The B-method describes the mass absorbed, and is, efore, not appropriate for describing the appearance of Estimating Dermal Absorption from Chemical Exposure. 3. 977 Table 3. Data from Steady-State Permeability Analysis in Figure 3 Regression line no. 1 2 3 Data t- t* I = 2.4 t- used (m) (rnin) '>20min I 21.4 >70min 24.4 >!lo min 35.9 51.4 58.6 86.1 ~~ ,K = 10 M W = 112.9 .,, L, = 0.001cm D, = 3.33 X IO-'cm/hr t, -- I 30.0min t* = .72.0 min B = 0.00748 PCw = 0.00183 cmlhr Pw = 0.00182cmflV 1 standard deviation corresponds to 10% error of the true value PW (chr) 0.00159 0.00166 0.00186 (10) when the lag time through the EPI (t-,,J is at least 10times larger than t,,,= (which will always be the case unless the SC is damaged or the SC diffusivity is significantly enhanced otherwise). For lipophilic chemicals where B is larger than 0.6, Eqn. (10) and (T6) combine to give the time to approximately reach steady state: where t,, is the lag time across the SC-EPI composite barrier, and b and c are defined by Eqns. (T7)and (T8) in Table l. Because lag times (either tlagecor t,) increase with increasing MW, the time to reach steady state also increases with increasing MW. According to calculations made by Potts and Guy (18), it will take nonanol28 times longer than methanol to reach steady state. Potts and Guy (18) also examined the effect of MW on apparent permeability measurements. Analyzing in Vivo Absorption Experiments To derive permeability values from in vivo experiments which follow blood, urine or feces concentrations as a function of tsxp,one must include systemic pharmacokinetics in the analysis (e.g., reference 19).This requirement introduces additional experimentation and also uncertainties in the resulting percutaneous absorption parameters. Consequently, in vivo experiments which measure absorption directly have many advantages. As already mentioned, for steady-statepermeability values, experimental conditions must be at steady state, and therefore changes in the vehicle concentration must be small. (Steady-state P, can be deduced from experiments with varying vehicle concentration, provided that rate of concentration change is known and is small relative to the rate of dermal absorption.) The common in vivo experiment which deposits chemical dissolved in a volatile vehicle on the skin surface is therefore inappropriate for determining P,; since C, changes rapidly and dramatically while the vehicle evaporates. Furthermore, the form of the deposited chemical after the vehicle evaporates (e.g., crystalline or amorphous solid or liquid), can profoundly but unaccountably affect absorption. Only a few in vivo experiments have directly measured absorption while keeping C, essentially constant. A set of such experiments was recently reported for absorption of l4C-labe1ed tetrachloroethylene into hairless guinea pigs (20,21). The animals were immersed up to the neck in beakers of aqueous solutionfor IO min and the amount of chemical remaining in the exposure solution was determined,by liquid scintillation. Five replicate experiments were con-" ducted. In each experiment, the first measurement was made at an exposure time of 10 min, and all reported values were normalizedwith respect to this first measurement. The initial concentrations, if known, were not reported. The 10 min concentrations were calculated from the net disintegrations per minute. Chemical loss from the exposure solution, modified for evaporation (which, as measured in separate control experiments, proved to be minor), was attributed to dermal absorption. Excretion efficiencies, measured by monitoring appearance of radioactivity in urine and fecal samples for 2 to 4 weeks followingexposure, proved to be similar for dermal and subcutaneous delivery, supporting this assumption within the accuracy of the data. Figure 4 shows the averaged cumulative mass absorbed (adjusted for differences in vehicle volumes and exposure areas) and one standard deviation for each time point plotted relative to the first measurement at 10 rnin (texp- 10 min = 0). The cumulative mass absorbed is plotted relative to the mass absorbed at 10 min, normalized by the mass remaining in the vehicle at 10 min (Le., [M,, (at texp)- M,(at texp= 10 min)]/[VCg - M, (at tcxp= 10 min)]). Accordingly, a linear regression of steady-state data from Figure 4 is of the form: [Mi, (at bxp)- Mi,(at brp= 10 min)l -- 1Mi,(at bxp= 10 min) vc; S (texp - 10 min) + I (12) ,0 2 5 4 I A o o o d - eE ' IC I I , I Ij,, 0 10 20 30 40 50 I 60 ieXp- 10, min Figure 4. Cumulative mass of tetrachloroethylene dermally absorbed in hairless guinea pigs normalized with respect to the mass available for absorption 10 min after the exposure began. . ,-C 978 Bunge, Cleek, and Vecchia After substituting the steady-state Eqn. (T2) for Mi, (at texp), For tetrachloroethylene, Bogen et al. (20,21) reported the slope (S) and intercept (I) are defined as: Po = 0.37 (20.13) c d h r , calculated by averaging slopes from linear regressions of each of the five experiments (in- Mi, (at texp-= 10 min) (13) cluding all data points but not forcing I = 0) and assuming that Mi, (at texp = 10 min) and B were both small (Le., = zero). Bogen el al. estimated this 95% confidence interval P,,(10 min) + L, K,, Mi, (at texp= 10 min) Mi, (at texp = 10 min) from the standard deviation of the permeability values for the five animals. To calculate P,, from S, we must know Mi, (at texp= 10 rnin). If, as Bogen et al. assumed, t* 10 min, then Mi, (at teXp= 10 min) is calculated from Eqn. (T2), leading to the conclusions that I = 0 in Eqn. (14), and that S in Eqn. (13) (14) depends on the unknown value of (K,,L,) in addition to P,,. where A is the average area of exposure, and v is the aver- Unfortunately, insufficient information is provided by Bogen age volume of solution in the beaker. Because Bogen et measured absorption relative to the absorption which oc- c m e d in the first 10 min, the mass absorbed in the first 10 min must be known or estimated to calculate the permeabil- ity from the slope. If steady state is achieved within the first 10 min of exposure, then M, (at tcxp = 10 min) is repre- sented by Eqn. (n)and the intercept, I, should be approx- imately zero. ~i~~~~4 shows different linear regressions (the dashed lines labeled as a, b and c), each implying different assumptions. The data point at texp - 10 f i n = 0 was not included in the line a regression of the average cumulative mass absorbed values (S = 0.16 2 0.06 hr-' and I = 0.046 + 0.0431-0.059), thereby making the assumption that all et 01- to estimate (K,,L,) Separately from P,,. If we arbitrarily assume that the chemical capacity of the SC is small (i*e*K* cwLc 01, then the mass absorbed relative to the mass in the beaker, Mi, (at teXp = 10 min)/ (vc;) 1-97cm), AaPncdwp,,( l o = 0.36 cmmi/nhlrh. rA)Nssu(mthiengavthearatgMe, (at wteaxsp = 10 min) 0, we calculated that P, = 0.37 (20.13) c d r , exactly as estimated by Bogen et al. (20,21). Since log,,K,, = 3.40 for tetrachloroethylene, assuming B = 0 is reason- able, but it is unlikely that the capacity of the SC is insignif- icant (i-e., K,,L, + 0). Consequently, Mi, (at texp= 10min)/ (vet) will be larger than estimated above, leading to smaller values for p=w. ____ Esf ir term lowe *(Le., 10 min < t* d 15min). The regressed S and I values are reported as the mean the 95% confidence interval. Unless noted otherwise, we report 95% confidence limits (lower 2.5% and upper 97.5%) determined by superimposing the normal distributionfunctions of S and I from regressions of ship into Eqns. (13) and (14), P, and (K,,L,) can be deduced from S and I determined by linear regression of steady-state absorption values. ciAccording to Eqn. (Tl), any data points in Figure 4 at exposure times less than t* should be a function of average cumulative mass absorbed data points while forcing providing evidence that Eqn. (Tl) correctly represents unI = 0. In this approach, the absorption rate is assumed to steady-state absorption. error is random, we expect I for type b regression lines from We stochastically generated the mean and distribution funcreplicate experiments to vary randomly around zero. The tions for P,, and (K,,L,) separately for each animal using posed the distribution functions for P, and (K,,L,) to de- Estimating Dermal Absorption from Chemical Exposure. 3. termine the mean values and the 95% confidence limits (i.e., lower 2.5% and upper 97.5%). Using PCw= 0.22 c d r and (Kc,Lc) = 0.90 cm, we estimate that Mi, (at texp= 10 min)/(VCE) 0.10, which is more than 6 of the total amount absorbed in the entire 70 min exposure (Le., Mi, (at tcxp = 70min)/(VCE) = 0.30). The 0.37 (k0.13) cm/hr value calculated by Bogen et al. (20,21) is almost two times larger and significantly different than the Pcwvalue of 0.22 (kO.15) cm/hr, calculated here using data from tcxp2 30 min and correcting for absorption during the first 10 min of exposure. As y e prove shortly, calculating permeability coefficients from 'direct measurements of absorption which include unsteady-state data always overestimates the true permeability. Using the same experimental procedures as for tetrachloroethylene, Bogen et d.(20,21) measured absorption of chloroform and trichloroethylene into guinea pigs. We have examined these data also and determined that, for these compounds (MW =' 119.4 and 131.4 respectively for chloroform and trichloroethylene compared to 165.8 for tetrachlo- roethylene), t* for the guineapig is approximatelyequal to or less than the time of their first data point at 10 min. Assuming t* for tetrachloroethylene is 20 to 30 min and adjustingfor MW using Eqns. (TS) and (T9), we estimate that t* is between 10 and 16 min for chloroform and between 12 and 18 rnin for trichloroethylene which are reasonably consistent with our data analysis. Although Eqn. (T9) is for human rather than guinea pig SC, significant differences in the MW dependence are not expected. A review of the literature indicates that time course data, like those in the guinea pig experimentsjust described, are quite unusual. More commonly, researchers report a single value of the cumulative mass absorbed in a given period of time. Since this cumulative mass measurement would in- epp,clude absorption during the unsteady-state period, the ap- parent permeability, calculated from: will always be larger than the true permeability P,. This is illustrated in Figure 5 which plots the cumulative mass absorbed into the skin from an aqueous solution, normalized by the concentration CE and area of exposure A, as a function of time for a hypothetical chemical with properties listed in Table 3. The slopes of the dashed lines in Figure 5 corre- spond to P"Zpvalues that would be obtained from the cumu- lative mass absorption measured for two experiments conducted at different t,,, (20 and 80 rnin). The true permeability in this case is represented by the slope of the linear portion of the solid curve. The correct P, of 0.00182 cmlhr, is significantly less than Pkppof 0.0062 cmlhr based on the cumulative mass absorbed in 20 min, or 0.0032 cmhr for 80 min. This example may explain some of the reported differences between in vitro and in vivo experiments. Steady state is more easily confirmed in in vitro experiments, and therefore, permeability values from in vitro experiments are more likely to be steady-state values. Frequently, permeability coefficientscalculated from in vivo experiments are larger than the true steady-state value because they are based on data -*.'A3i 0 2 5 5 0 7 5 100 125 150 teXp, min .il Figure 5. Illustrating the relationship between the actual steadystate permeability and the apparent permeability as estimated from the cumulative mass absorbed (KOw= 10, MW = 112.9, ,P = 0.00183 cdh). which include absorption during the unsteady-state period'.' A better approach for determining steady-statepermeabfity coefficients from in vivo data is to use the rate of mass absorption once steady state has been achieved. That is, To use Eqn. (16) properly, steady state must be demonstrated which would require absorption data for no fewer than three exposure times. Even then, with data scatter, confirmation of steady state will be difficult. If the exposure time is long enough (Le., tcxp> t'), then the combination of the more rapid absorption during the unsteady-state period will be comparably small and the apparent permeability coefficient calculated from Eqn. (15) would be reasonably correct. How large does t' need to be? This is easily estimated by calculatingthe exposure time t' at which MEIA from Eqn. (8) equals a specified fraction (F) of MJA from Eqn. (T2): t# = (1 + 3B)F _Lf 3(1 - F) D, -- 2(1 + 3B)F (1 - F) tlag'c (17) Equation (17) is based on the SC lag time (Le., = Lfl (6D,). When B is small, the steady-state estimate of the cumulative mass absorbed will predict less than 90% of the actual mass absorbed (Le., F < 0.9) for exposure times less than 18 tlagYcF.or larger values of B, predictions of the cumulative mass absorbed from the steady-state equations will underestimate the actual absorption even for texp> 18 tL"B.c. Estimates of the apparent permeability calculated according to Eqn. (15) will overestimate the actual steady-stateP, by a factor of 1/F. Consequently, steady-state permeabilities cal- culated from cumulative mass absorption data will be within 10% of the actual permeability only if the experiment is conducted for teXp> 18 flag.=. The shorter the exposure time, the more P p pwill overestimate the actual P,. The relationship between Ptppcalculated from Eqn. (15) and the actual steady-state P, can be estimated by substituting Eqns. (Tl) and (T2)for MiJA into Eqn. (IS) to yield: . 986 Bunge, Cleek, and Vecchia for texpd t* pcv where cppPcvis the lag time across Only the sc.Strictly, these The dashed curves referenced to the right hand axis of Fig- ure 6 represent as a function of texdtlag,,for various are approximations, since Eqns. (T1) and (T2) are ap- values of B. proximate representations of the curves in Figure 1 (albeit As for the Epp/Pcvurves, discontinuities appear from excellent representationsespecially for texp=S t* and B < 1 using the approximate representations of the unsteady-state (1)). Eqn. (19) is especidy interesting since it shows that absorption equations, (Tl) and (T2). The discontinuities fall ~ P dPoes not equal P, even though steady state has been at different values for teXpltlagb,,ecause t* is larger when B is reached @e., texp> t*). This is because Eqn. (15) does not 100 than when B is 0.01. For times less than t*, P$pP,, is adjust for the more rapid rate of absorption during the independent of B because chemical absorption is completely shorter exposure times. Eqn. (15) incorrectly assumes that controlled by the SC alone and any influencefrom the EPI is the absorption rate has been constant during the entire ex- not felt. When texpis larger than t*, the B equal 0.01 and 100 posure. curves separate. For highly lipophilic chemicals, the SC per- Figure 6 shows P?,pp/P,, Eqns. (18) and (19), as a func- meability, P,, will be larger than the true permeability for the cpption of tex$la$,c for various values of B. Discontinuitiesarise SC-EPI composite, P,. In this case eventually will be, at t* as the calculation switches from Eqn. (18) to (19), al- though these are barely visible. As expected, EPpis always smaller than P,, and their ratio will become less than one. For more hydrophilic compounds, P, is approximately P,, cpplarger than P, and only approaches P, after long exposure and consequently, ePp/P,, will approach one at long expo- times. For t, of about can be larger than P, by sure times. Most importantly, Figure 6 shows that when texp one or more orders of magnitude, depending on B. For is less than about 2 flag,,,PB,PpPc,can be 2 or greater. highly lipophilic (large B) chemicals, the EPI chokes the Results in Figures 5 and 6 may explain reported discrep- chemical's penetration and the permeability across the SC- ancies between in vitro diffusion cell permeability coeffi- EPI composite barrier (P,) is much smaller than P,,. In ad- cients and in vivo permeability coefficients calculated from dition, the SC capacity for chemical as reflected in K,, is the cumulative mass absorbed. In fact, the skin permeabili- large for highly lipophilic chemicals, so that the effect of the ties in the in vivo and in vitro experiments could have been cppPv.unsteady-state absorption period is more important when B the same, but the apparent in vivo permeability was larger is large. Finally, MW also affects Recall that t,ae,c than its actual value because it was calculated from Eqn. depends on D,, and hence, the absorbing chemical's MW but (15) without a constant concentration exposure for at least cppnot its.,K This means that the exposure time needed for to closely represent P, will be particularly long for a 18 flag,,. eppchemical with higher MW regardless of its lipophilic charac- ter (18). CONCLUSIONS To compare to the steady-state permeability of only A predictive approach, which we call the B-method, has the SC,as might be measured in an in vitro SC-only diffusion been developedfor estimatingthe cumulativemass absorbed cell experiment or calculated from Eqn. (T3), we substitute during a dermal exposure including the faster rates during Eqn. (4) into Eqns. (18) and (19) to obtain: short exposures and the EPI resistance presented to li- pophilic chemicals. Previous papers have developed the nec- essary equations and recommended procedures for estimat- ing all of the required physicochemical data. In this paper, we have examined the B-method compared to steady-state methods for predicting absorption and for analyzing in vitro and in vivo data. Example calculations are presented for dermal absorp- tion from aqueous solutions for five chemicals with a wide range of M W (50.5 to 409.8) and,log,,K,, (0.91 to 6.80). These estimates are compared Fo predictions from the steady-state permeability approach, which underpredicts ab- sorption in all the cases presented. If water is nearly insol- uble in the neat chemical, then the maximum absorption rates occur at Crt. For this group, the highly lipophilic 0 5 IO 15 20 chemicals at C F absorb more slowly than less lipophilic chemicals because the increase in their permeabilities is more than offset by decreases in their C?'. However, these low CFtdecrease the risk from ingestion compared to dermal absorption. Estimating Dermal Absorption from Chemical Exposure. 3. Strictly, permeability coefficients are only meaningful when derived from steady-state data. Permeability coefficients calculated from data which include unsteady-state effects will not be correct. Based on the B-method, we have developed a procedure for confirming that in vifro permeability coefficients are calculated fiom data which are at steady state. A similar procedure is not possible for in vivo experiments. However, we do illustrate the effect of calculating apparent permeability coefficients from cumulative mass absorption data which include absorption during the unsteady-state period. The differ;encebetween the apparent and true permeability coefficient depends on the exposure time relative to the chemical's lag time. We show that tcxp must be at least 18 tu,, for the apparent permeability coefficient to be within 10% of the true permeability coefficient. Correct steady-state permeability coefficients may be determined from absorption rate data which are taken after steady state is achieved. ,r NOMENC~TURE A = surface area of chemical exposure. b = parameter in t* calculation, Eqns. (T6) and ("7). B = parameter for the SC-EPI composite measuring the relative size of the SC permeability to the EPI permeability. c = parameter in t* calculation, Eqns. (T6), (T7)and (T8). 12: = concentration of the absorbing chemical in the ve- hicle. Assumed to remain constant during the exposure period, texp. CFt = saturation concentration of the absorbing chemical in the vehicle. CO, = concentration of the absorbing chemical in water. Assumed to remain constant during the exposure period, texp. ' Ct: = saturation concentration of the absorbing chemical in water. D, = effectivedfiusivity of the absorbingchemical in the sc. De = effective dsusivity of the absorbingchemical in the EPI. EPI = viable epidermis. F = fraction of the MiJA calculated from Eqn. (T2). Used in Eqn. (17). 1 = intercept of linear regressions of steady-state der- mal absorption data. Defined in Eqns. (12) and (14). K,, = equilibrium partition coefficient between the SC and vehicle for the absorbing chemical. K,, = equilibrium partition coefficient between the SC and water for the absorbing chemical. K,, = equilibrium partition. coefficient between the EPI and the vehicle for the absorbing chemical. KO, = octanol-water partition coefficient. K,, = equilibrium partition coefficient between water and the vehicle for the absorbing chemical. L, .= effective thickness of the SC. Le = effective thickness of the EPI. M,, = cumulative mass absorbed into the SC during an exposure period, try*. M;; = cumulative mass absorbed into the SC dunn exposure period, tcxp,calculated from the stead state Eqns. (5) and (8). , MW = molecular weight of the absorbing P,, = steady-statepermeability of the SC vehicle. P,, = steady-state permeability of the SC from wa P,, = steady-state permeability of the EPI from a fied vehicle. P, = steady-state permeability of the SC-EPI membrane from a specified vehicle. EPP = apparent permeability estimated fiom the tive mass absorbed as given in Eqn. (Is). P, = steady-state permeability of the SC-EPI com membrane from water. S = slope of linear regressions of steady-state absorption data. Defined in Eqns. (12)'and SC = stratumcorneum. t* = time to approximately reach steady state. Estima- tions are given in Eqns. ("5) through (T8) and (11). t" = time required for the steady-state calculation, Eqn. (S), to predict a specified frisction F of the amount which has actually absorbed as estimated by Eqn. (T2). Estimation is given in Eqn. (17). texp = time period of exposure event. Lg,, = lag time across the SC, equals DJ(6L3. t,, = lag time across the skin including both the SC and EPI, Eqn. (10). V = volume of solution in the exposure solution. Ving = ingested volume of water required to give an ab- sorption equivalent to the dermal exposure. ACKNOWLEDGMENTS This work was supported in part by the United States Environmental Protection Agency under Assistance Agreement Nos. CR817451 and CR822757. We thank R. Hertz- berg, D.E. Burmaster, R.H. Guy, R.O. Potts,J. Parks, K. McCarley and K. Hoang for their helpful comments. REFEENCES 1. Cleek, R.L. and A.L. Bunge. A new method for estimating dermal absorption from chemical exposure. 1. General a p proach. Pharm. Res. 10, 497-506 (1993). 2. Bunge, A.L. and R.L. Cleek. A new method for estimating dermal absorption from chemical exposure. 2. Effect of molecular weight and octanol-water partitioning. Phorm. Res. 12.8794 (1995). 3. Yu,C.D., J.L. Fox, N.F.H. Ho, and W.I. Higuchi. Physical model evaluation of topical prodrug delivery-Simultaneous transport and bioconversion of vidarabine-S'-valerateI: Physical model development.J . Pharm. Sci. 68, 1341-1346 (1979). 4. 'hi,J.S., D. Danielson, and J.W. Woltersom. Effects of polyoxypropylene 15 stearyl ether and propylene glycol on percu- taneous penetration rate of diflorasone&acetate. 1.Pharm. Sci. 68, 275-280 (1979). 5. Woodford, R. and B.W. Barry. Optimization and bioavailability of topical steroids: Thermodynamic control. 1.Invest. Derrn. 79, 388-391 (1982). 6 . Flynn, G . Physicochemical determinantsof skin absorption. In Principles of Route-to-Route Extrapolation for Risk Assess- . ," :,.:,, ' & - '. * --.-..- . Bunge, Cleek, and Vecchia P.Y. Lu. The fate uatic model eco- rmination model for dermal exposure assessment. In Drinking Water Contaminafion and Health: Integration of Exposure Assessment, Toxicology, and Risk Assessment (R. Wang, Ed.) Marcell Dekker, New York, 347-314 (1994). 16. ICRP (Intl. Commission on Radiological Protection). Report of the Task Group on Reference Man, ICRP No. 23, Perrnagon Press, New York, NY (1975). 17. Vecchia, B. Personal communication, Colorado School of Mines, Golden, CO (1994). 18. Potts, R.O.and R.H. Guy. Drug transport across the skin and the attainment of steady-state flux. Proc. Intl. Symp. Control. Rel. Bioact. Mater. 21 (1994). 19. Silcox, G.D., G.E. Parry, A.L. Bunge, L.K. Pershing, and D.W. Pershing. Percutaneous absorption of benzoic acid across human skin 11: Prediction of an in vivo skin flap system using in vitro parameters. Pharm. Res. 7 , 352-358 (1990). 20. Bogen, K.T., B.W. Colston, Jr., L.K. Machicao. Dermal absorption of dilute aqueous chloroform, trichloroethylene, and tetrachloroethylene in hairless guinea pigs. Fund. Appl. ToxiC O ~18., 30-39 (1992). 21. Bogen, K.T., B.W. Colston, Jr., L.K. Machicao. Percutaneous absorption of dilute aqueous chlorinated organic solvents in hairless guinea pigs. In Drinking Water Contamination and Health: Integration of Exposure Assessment, Toxicology, and Risk Assessment (R. Wang, Ed.) Marcell Dekker, New York, 323-346 (1994). 22. Crystal Ball, Version 3.0, Decisioneering. Inc., Denver, Colorado (1993). Evalual Topical in Derr Anita H. 1 R. Richart Pamela Bc F. Ivy Cai Received Se Purpose. Op ically active (1) relative t toxicity. Me1 in the lipopl evaluated fo of "PA-indu though mort fied, none pc 1. Concluswi responsiblf hyperprolife low systemic icity, this la treatment of KEY WORI perkeratiniz INTRODU Retino to be activ ornithine c desirable e