150 JOURNAL OF COSMETIC SCIENCE 9 8 7 .._,6 2 1 0 I 'I- 1.00 0.83 0.50 Solution Composition of SDS, =s Figure 2. The effect of increasing the SDS concentration in the contacting solution on the concentration of SDS in the epidermis after a five-hour exposure (C.,,•i,). For each composition (% = 1, 0.83, and 0.50), the concentrations of SDS in the contacting solution are 25 mM (empty bats), 50 mM (solid bars), and 100 mM (striped bars). The error bars reflect a 95% confidence interval based on six samples at each SDS concentration. The increase in Cski, , with increasing total SDS concentration observed in Figure 2 for tx• -- 1, 0.83, and 0.50 clearly indicates that the micelies present in these solutions do contribute to SDS penetration into the epidermis, with their contribution decreasing as tx s decreases. Specifically, by comparing the observed increase in Cski, , as the SDS con- centration in the contacting solution is increased from 25 mM to 100 mM (AC,•i, ,) for each tx s value examined, it is clear that the pure SDS micelies (ix s = 1) contribute more to C•i, , (AC•i, , • 0.08) than the mixed micelies corresponding to tx s = 0.83 (AC•in = 0.03) and to tx s = 0.50 (Ac,kin = 0.02). This is clear evidence that changing tXs, and hence tXm, can affect the ability of the miceliar SDS to penetrate into the epidermis, because for each tx s value examined, the SDS concentration in the contacting solution increases by the same amount (from 25 to 100 raM), but the effect on AC•i, , is found to decrease as tx s is decreased. Although this simple analysis, based on the experimental results presented in Figure 2, clearly demonstrates that adding C]2E 6 to the SDS solution reduces the ability of the miceliar SDS to penetrate into the epidermis, as proposed in mechanism (ii), a more quantitative analysis, presented below, is required to determine the contributions of mechanisms (i) and (ii) to SDS skin penetration. It should be kept in mind that the ability to reduce the penetration of the miceliar SDS into the skin by mechanisms (i), (ii), or both should have a pronounced effect on reducing the skin irritation induced by SDS. We have recently demonstrated that the contribution of the miceliar SDS to C•i, , is comparable to the contribution of the monomeric SDS at low SDS concentrations (28). However, because the concentration of SDS micelies increases as the total SDS concen- tration increases beyond the CMC, while the concentration of SDS monomers remains constant, we concluded (28) that it is the penetration of the miceliar SDS that leads to

PENETRATION OF MIXED MICELLES INTO THE EPIDERMIS 151 the dose-dependent skin irritation response observed by many researchers (2,3,8,13,16,18). Indeed, we found that the SDS miceliar contribution overwhelms the SDS monomeric contribution at the higher SDS concentrations (28). Accordingly, re- ducing, or preventing, the contribution of the miceliar surfactant to C,/•i , by mixing surfactants should lead to a reduction in the skin irritation potential of the surfactant mixture, in addition to any beneficial effect due to a reduction in the surfactant mono- met concentration. REGRESSION ANALYSIS OF THE CONTRIBUTIONS OF MICELLAR AND MONOMERIC SDS TO Cs•,n FROM SOLUTIONS OF SDS/C•2E 6 Figure 2 shows that as o• s decreases, the contribution of the SDS/C•2E 6 mixed micelies to Cs•i, , decreases. To quantify the relative contributions of SDS in mixed micelle form (o• m = 1, 0.83, and 0.50) and in monomeric form to Cs•i,,, we carried out a multiple linear regression analysis using all the experimental data, prior to averaging, that was used to generate Figure 2. The simplest relationship between the SDS concentrations in miceliar and monomeric form to C•,•i,, is a linear one. The basis for this linear relationship is that in Fickian diffusion from an infinite reservoir with a large concentration differ- ence, the net permeant flux at a given time is directly proportional to the initial permeant concentration (42). With this assumption in mind, we fitted C•,•i,, to the following expression: C,•i, = o• ß C•,so s + b' C(o• m = 1) + c' C(o• m = 0.83) + d' C(o• m = 0.50) (4) where a, b, c, and d are the regression coefficients that were determined from the regression analysis, Cj,so s is the SDS monomer concentration, C(O•m) is the SDS con- centration in micelies of composition O•m, and C,/•, is the SDS concentration in the epidermis (in units of mmols of SDS per gram of dry epidermis). For the regression analysis, Cj,so s = oqC• and C(o•,•) = oq•(C t - Cj)using the appropriate values of o•, o•m, and Cj reported in Tables I and II (30,31). In this manner, we were able to isolate the contributions to C.,•i , due to the miceliar SDS for the three micelie compositions ex- amined (reflected in b, c, and d), as well as due to the monomeric SDS (reflected in a). The following values of a, b, c, and d were obtained from the regression analysis: 4.1 +_ 1.0 C,/•i,/Cl,so s 0.032 +0.014 Cskin/C(O• m '- 1) 0.003 +0.012 C•/•i,/C(o• m = 0.83) 0.0009 +_ 0.0092 C,/•i,/C(o• m = 0.50) According to these regression results, the O• m = 0.50 micelies do not contribute to C,/•, at all, because d is essentially equal to zero. The o• m = 0.83 micelies contribute very little or not at all to C,/•i ,, because although the average value of c is not zero, the 95% confidence interval includes zero. On a per SDS molecule basis, the contribution of the SDS monomers is quite large, with one SDS molecule in monomeric form being 130 times more skin penetrating than one SDS molecule in a pure SDS micelie (o• m = 1). However, at the higher SDS concentrations, there is significantly more miceliar SDS than monomeric SDS, and as a result, the net contribution to C•/•i , due to the miceliar SDS may overwhelm that due to the SDS monomers.