118 JOURNAL OF COSMETIC SCIENCE Tang et al. also showed that for the PBS control contacting solution containing Na+ and c1- ions, and also for the mannitol aqueous solution, the Debye-Hi.ickel screening length "S:.7 A, which is much smaller than the typical average skin aqueous pore radii, that is, than the sizes of the aqueous pores, of approximately 15-25 A (7). The quantities, v and D: 1n appearing in C refer to the permeant and to the ion infinite-dilution diffusion coefficients, respectively (note that these quantities correspond typically to the bulk diffusion coefficients of the permeant and of the ion in the dilute donor contacting solutions used in the in vitro transdermal permeability and electrical resistivity mea­ surements). According to the hindered-transport theory (42), the hindrance factor for permeant or ion transport, H(A), is a function of both the permeant/ion type and of the skin membrane characteristics. The four intrinsic membrane characteristics of the skin barrier are: (i) the porosity, B, which is the fraction of the skin area occupied by the aqueous pores, (ii) the tortuosity, T, which is the ratio of the permeant diffusion path length within the skin barrier to the skin barrier thickness, (iii) the average pore radius, r po w and (iv) the skin barrier thickness, LlX. Based on these four membrane characteristics, one can express the permeability, P, of a hydrophilic permeant, such as mannitol, through the skin aqueous pores as follows (6,7,42): (6) Therefore, from equations 4-6, once one can determine P and R upon exposure of p-FTS to contacting aqueous solutions of SDS and SDS + 10 wt% glycerol, one can also determine the radius of the aqueous pores as the average skin pore radius, r por e' and the ratio of porosity-to-tortuosity, defined as BIT, if all the other parameters, such as LlX, are known (see Appendix, where we illustrate how to deduce r pore and BIT when p-FTS is contacted with SDS aqueous solutions). The porosity-to-tortuosity ratio, BIT, corre­ sponds to the number of tortuous aqueous pores per unit volume of the SC, that is, to the pore number density (6,7,42). In the context of the hindered-transport aqueous porous pathway model of the SC, an increase in the porosity, B, and/or a decrease in the tortuosity, T, which increases the porosity-to-tortuosity ratio, BIT, of the aqueous pores, can be interpreted as an increase in the number of aqueous pores per unit volume of the SC (7-9,42). A harsh surfactant like SDS can induce skin barrier perturbation by modifying the SC aqueous porous pathways as follows: (i) increasing the size of the existing aqueous pores in the SC, and/or (ii) increasing the number density of the existing aqueous pores in the SC, or both. It then follows, in the context of the hindered-transport aqueous porous pathway model, that mechanism (i) involves increasing r po re, while mechanism (ii) involves increasing BIT [6-9,42}. In Table I, we report r pore values resulting from the exposure of p-FTS to contacting solutions of: (a) SDS in water, (b) SDS + 10 wt% glycerol in water, (c) PBS control, and (d) 10 wt% glycerol in water. Note that in Table I, we have reported the BIT values resulting from the exposure of p-FTS to the contacting solutions (a-d) normalized by the BIT value resulting from the exposure of p-FTS to contacting solution (c), which we have denoted as (B/T)normal· It then follows that when (B/T)00rmal 1, it indicates that the contacting solution creates more aqueous pores in the

SDS MICELLES IN SKIN BARRIER PERTURBATION Table I Skin Aqueous Pore Characteristics Induced by Various Skin Contacting Solutions Type of aqueous contacting solution (a) SDS (6) SDS + 10 wt% glycerol (c) PBS control (d) 10 wt% glycerol Average pore radius, r por ,· (A) 33 ± 5 20 ± 5 20 ± 3 11 ± 4 Normalized pore number density, (e/T)normal 7 ± 1 3 ± 1 1 0.5±0.1 119 The hindered-transport aqueous porous pathway model was used, along with the in vitro mannitol trans­ dermal permeability and average skin electrical resistivity measurements, to determine the average pore radius, r pore , and the pore number density, e!T, resulting from skin exposure to the four aqueous contacting solutions considered: (a) SDS, (6) SDS + 10 wt% glycerol, (c) PBS control, and (d) 10 wt% glycerol. Note that we have reported e/T values resulting from the exposure of p-FTS to the contacting solutions a-d normalized by the e!T value resulting from the exposure of p-FTS to contacting solution (c), which we have denoted as (e/T)normal· SC relative to those created by the PBS control, while when (s/T) normal 1, it indicates that the contacting solution creates fewer aqueous pores relative to those created by the PBS control. RESULTS AND DISCUSSION EFFECT OF GLYCEROL ON SDS-INDUCED SKIN BARRIER PERTURBATION In order to quantify the effect of the SDS concentration in the skin aqueous contacting solution on the skin barrier in the absence and in the presence of glycerol, we utilized the in vitro transdermal permeability and the skin electrical current measurements discussed above. The physical basis for these measurements is as follows: a large skin electrical current or transdermal permeability, which results from a high transfer rate of permeant molecules (mannitol in our case) or of ions, respectively, across the skin, is indicative of a large extent of skin barrier perturbation in vitro (1-7). Therefore, if upon exposure of the skin to an aqueous contacting solution of SDS or of SDS + 10 wt% glycerol, one observes a high skin electrical current (corresponding to a low average skin electrical resistivity) or permeability, one may conclude that the contacting solution has induced skin barrier perturbation, thereby compromising the skin barrier. With the above expectation in mind, we conducted skin electrical current measurements for aqueous contacting solutions of SDS ranging in SDS concentrations from 1 mM to 200 mM.2 The results of these measurements are shown as striped bars in Figure 2. As can be seen, the extent of skin barrier perturbation, quantified in terms of the skin electrical current, continues to increase, with an increase in the SDS concentration in the contacting solution above the CMC of SDS (8.7 mM).3 According to the monomer 2 Note that 1 wt% SDS = 35 mM, and that the CMC of SDS = 8.7 mM = 0.25 wt%. 3 Recall that the CMC is the threshold total surfactant concentration above which the concentration of the surfactant monomers remains approximately constant, while that of the surfactant micelles increases upon increasing the total surfactant concentration. This is because, above the CMC, any new surfactant molecules added to the solution self-assemble to form micelles, a process that is thermodynamically more favorable than to remain as free monomers in the surfactant solution.