130 JOURNAL OF COSMETIC SCIENCE that the addition of 10 wt% glycerol prevents SDS micelles from penetrating into the skin barrier by: (a) reducing the radius of the skin aqueous pores induced by the SDS aqueous contacting solution, from 33 ± 5A to 20 ± 5A, such that an SDS micelle of radius 18.5 ± 1A in an aqueous SDS micellar solution with 10 wt% added glycerol experiences steric hindrance and cannot penetrate into the SC, and (b) reducing the number density of the skin aqueous pores by more than 50%, thereby further reducing the ability of the SDS micelles to penetrate into the SC and induce skin barrier pertur­ bation. APPENDIX DETERMINATION OF THE RADIUS AND THE NUMBER DENSITY OF THE SKIN AQUEOUS PORES RESULTING FROM EXPOSURE OF p-FTS TO SDS AQUEOUS CONTACTING SOLUTIONS Average skin electrical resistivities, R! and mannitol-skin permeabilities, P! were mea­ sured upon exposure of p-FTS to SDS aqueous contacting solutions, as discussed in the text, and the resulting log P vs log R plot is shown in Figure 6 (see diamonds and the dashed line). It is noteworthy that the slope of the best-fit straight line (the dashed line) through the diamonds in Figure 6 is 0.98 ± 0.06, which is statistically similar to the theoretical value of -1 (see equation 4). The R 2 value is 0.96, which is close to 1. Hence, these results lend further support to the validity of the hindered-transport skin aqueous porous pathway model developed by Tang et al. (7). The intercept value in Figure 6 is -2.90 ± 0.03. The infinite-dilution diffusion coefficient of mannitol, v , is 0.672 x 10- 5 cm2/s at 25°C (6,7). The hydrodynamic radius of mannitol, r p , is 4.44 A (6,7). Because skin electrical currents were measured in PBS that contained Na + and Cl - as the dominant ions, the Na+ ions were used to model the current-carrying ions present in the solution. The infinite-dilution diffusion coefficient of the Na+ ions, v: n , is 1.33 x 10- 5 cm2/s at 25°C (7). The hydrodynamic radius of the Na + ion, r io n, is 2.2 A (7). In addition, we have used the following parameter values in C (see equation 4) in the Theoretical section): k 8 = 1.38 x 10- 23 J/K (Boltzmann constant), T = 298 K, F = 9.6485 x 104 C/mol (Faraday constant), z = 1 (in the PBS solution, since NaCl is the dominant electrolyte), c ion = 0.137 M, and e 0 = 1.6 x 10- 19 C. Using these parameter values, along with the experimentally determined value of C, we were able to determine the value of the ratio: H(A p )/H(A ion ) (see the expression for C in the Theoretical section). Next, using: (i) equation 5, (ii) the hydrodynamic radii values of mannitol and Na+, that is, 4.44 and 2.2 A, and (iii) the value of the ratio H(A p )/H(A ion ), we were able to numerically solve for the average pore radius, r pore · The average pore radius, r pore was found to be 33 ± 5 A, which we have taken as the radius of the skin aqueous pores. Note that H(A p ) and H(A i01,) are each less than 0.4, which is necessary for equation 5 to be valid (6,7,42). Having determined the aqueous pore radius, r pore ' the pore number density was determined using equation 6, in which all the parameters, except for e!T, the pore number density, are known in advance (since .6.X = 15µm) (6,7). The aqueous pore number density, e!T, for p-FTS exposed to the PBS control aqueous solution was determined using a calculation similar to the one for p-FTS exposed to the

SDS MICELLES IN SKIN BARRIER PERTURBATION 131 SDS aqueous contacting solutions presented in this appendix. Finally, the aqueous pore number density (e/'T) value resulting from the exposure of p-FTS to the SDS aqueous contacting solutions was normalized by the el'T value resulting from the expo­ sure of p-FTS to the PBS control aqueous solution. We calculated this normalized value, (e!T)n ormal • to be 7 ± 1 (see Table I). ACKNOWLEDGMENTS We thank Dr. Sidney Hornby and Dr. Yohini Appa from Neutrogena Corporation for useful discussions, and for providing partial financial support for this work. REFERENCES (1) R. Scheuplein, and I. Blank, Permeability of the skin, Physiol. Rev., 702, 702-747 (1971). (2) P. M. Elias, Lipids and the epidermal permeability barrier, Arch. Dermatol. Res., 270, 95-117 (1981). (3) P. W. Wertz and D. E. Downing, "Stratum Corneum: Biological and Biochemical Considerations," in Transdermal Drug Delivery: Developmental Issues and Research Initiatives, J. Hadgraft and R. H. Guy, Eds. (Marcel Dekker, New York, 1989), pp. 1-22. (4) R. L. Bronaugh and H. I. Maibach, "In Vitro Models for Human Percutaneous Absorption," in Models in Dermatology, H. I. Maibach et al., Eds. (Karger, Bassel, 1985), Vol. 2, pp. 178-188. (5) M. Heisig, R. Lieckfeldt, G. Wittum, G. Mazurkevich, and G. Lee, Non steady-state descriptions of drug permeation through stratum corneum. I. The biphasic brick-and-mortar model, Pharm. Res., 13, 421-426 (1996). (6) K. D. Peck, A.H. Ghanem, and W. I. Higuchi, Hindered diffusion of polar molecules through and effective pore radii estimates of intact and ethanol treated human epidermal membrane, Pharm. Res., 11, 1306-1314 (1994). (7) H. Tang, S. Mitragotri, D. Blankschtein, and R. Langer, Theoretical description of transdermal transport of hydrophilic permeants: Application to low-frequency sonophoresis,]. Pharm. Sci., 90, 545-568 (2001). (8) K. D. Peck, A.H. Ghanem, and W. I. Higuchi, The effect of temperature upon the permeation of polar and ionic solutes through human epidermal membrane, J. Pharm. Sci., 84, 975-982 (1995). (9) A. Tezel, A. Sens, and S. Mitragotri, Description of transdermal transport of hydrophilic solutes during low-frequency sonophoresis based on a modified porous pathway model,]. Pharm. Sci., 92, 381-393 (2003). (10) G. K. Menon, and P. M. Elias, Morphologic basis for a pore-pathway in mammalian stratum corneum, Skin Pharmacol., 10, 235-246 (1997). (11) P. Moore, S. Puvvada, and D. Blankschtein, Challenging the surfactant monomer skin penetration model: Penetration of sodium dodecyl sulfate micelles into the epidermis,]. Cosmet. Sci., 54, 29-46 (2003). (12) L. D. Rhein, F. A. Simion, R. L. Hill, R.H. Cagan, J. Mattai, and H. I. Maibach, Human cutaneous response to a mixed surfactant system: Role of solution phenomenon in controlling surfactant irrita­ tion, Dermatologica, 180, 18-23 (1990). (13) T. Agner and J. Setup, Sodium lauryl sulphate for irritant patch testing-A dose-response study using bioengineering methods for determination of skin irritation,]. Invest. Dermatol., 95, 543-547 (1990). (14) L. D. Rhein, "In Vitro Interactions: Biochemical and Biophysical Effects of Surfactants on Skin," in Surfactants in Cosmetics, M. M. Rieger and L. D. Rhein, Eds. (Marcel Dekker, New York, 1997), pp. 397-426. (15) K. P. Ananthapadmanabhan, C. L. Meyers, and M. P. Aronson, Binding of surfactants to stratum corneum,J. Soc. Cosmet. Chem., 47, 185-200 (1996). (16) J. A. Faucher and E. D. Goddard, Interaction of keratinous substrates with sodium lauryl sulfate. I. Sorption, J. Soc. Cosmet. Chem., 29, 323-337 (1978). (17) J. A. Faucher and E. D. Goddard, Interaction of keratinous substrates with sodium lauryl sulfate. II. Permeation through stratum corneum,J. Soc. Cosmet. Chem., 29, 339-352 (1978).