WATER DIFFUSIVITY IN STRATUM CORNEUM 193 By keeping the difference in water conc__entration between Co and C h small, at first approximation, the mean concentration, C, may be assumed to be -- C = (C O q- Ch)/2. (5) The thickness of the membrane, H, is also a function of the water content in the tissue. Because Co and Ch are very close, it is assumed that the thickness may be defined by H = (Ho + Hh)/2, (6) where Ho and n h are the membrane thicknesses when the water concentrations throughout the membrane are uniformly Co and Ch, respectively. This assumption can be verified after D(C) is determined by using eq. 2 to calculate the thickness. -- D obtained from eq. 4, that is, from the measurement of F, H, Co and Ch, is then plotted against C. An empirical equation, D(C), describing the diffusivity-concentration relationship may be obtained from the plot. The form of the empirical equation was found to be D(C) = D O q- A C B (7) for the fetal hog periderm, where Do, A and B are constant parameters. This empirical equation is then inserted into Fick's equation (eq. 1) which may be integrated to give C as a function of position, x, in the membrane. The curve for C vs. x, that is, the water distribution profile, is then integrated to give the area under the pro- file. This area divided by the membrane thickness, H, yields the mean concentration C, __ of water in the membrane. Such calculated values for C are then compared with the -- values used to obtain D(C). If they are not_equal_, the assumed values of C are adjusted and a new D(C) is obtained from the new D rs. C plot. The process is repeated until the calculated and assumed values are equal or converge. This method may be carried out in vitro, because appropriate steps can be taken to keep the difference between Co and Ch small. However, in an in vivo situation, no control can be exerted on water concentration (Co) on the dermal side of the stratum corneum. Nevertheless, it is essentially constant. In contrast, the surface of the skin experiences a wide range of water concentrations (Ch) which depend largely on the ambient relative humidity. The difference between Co and Ch would be large, and the effective thickness of the tissue under these conditions would be unknown. Therefore, to apply the analytical technique used in the in vitro experiments to an in vivo situation some modifications in the analytical procedure were made. First, values for the mean -- concentration, C, and membrane thickness, H, were assumed before the iteration. Then the procedure used to obtain D(C) in vitro was followed. In subsequent approxima- tions, convergence between assumed and calculated values for both mean concentra- -- tion (C) and thickness (n) could be established. A danger with this approach is that, depending on the initial selection of the assumed -- values for C and H, there may be more than one explicit equation for D(C) which fits the experimental data. To avoid this pitfall, some restrictions were imposed before the iteration of the data analysis. Since human stratum corneum and fetal hog periderm are keratinous membranes, the functional forms for D(C) were assumed to be the same for both tissues (see eq. 7). The water diffusivity in human stratum corneum was known to

194 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS be an increasing function of the water concentration (4) therefore, the values for A and B must be positive. Also, the assumed values for the thickness H were confined to the range found in the literature. RESULTS AND DISCUSSION The data used to obtain the diffusivity of water in stratum corneum are shown in Table I. The rates of water loss (F) were taken from Goodman and Wolf (7). The surface water Table I Parameters Used To Obtain Diffusivity of Water in Human Stratum Corneum % RH Surface Water Concentration (g/ml) Rate of Water Loss* (g/cm 2 sec x 10 7) 0 0 2.32 29 0.051 1.80 54 0.078 1.60 80 0.15 1.48 88 0.22 1.22 *Ref. 7. concentrations (Ch) were calculated from the percentage weight gain of stratum corneum at different humidities (8) and the reported density of stratum corneum. A value of 1.3 g/ml (8) was used as the density at all relative humidities. It is known that the density for keratinous materials varies with humidity. The density of fetal hog periderm is 1.25 g/ml at 0% RH, 1.37 g/ml at 75% RH, and 1.26 g/ml at near 100 % RH (6). The density of human stratum corneum probably varies in the same range. If 1.25 or 1.35 g/ml for density was used to calculate Ch, the differences in Ch'S from those listed in Table I were less than 4%. This small difference should not affect the final equation for D(C). The water concentration in the stratum corneum at the dermal side (Co) was obtained from C O = K m C', (8) where K m is the partition coefficient of water in stratum corneum. Scheuplein (10) has suggested a value of 0.88 for Km. C' is the water concentration of body fluid in the underlying tissue. It was taken as 0.94 g/ml (11). From the data in Table I and the analytical procedures outlined previously, the water diffusivity in the stratum corneum of human volar forearm was determined to be the following function of the water concentration: D(C) = 1.6 x 10 -•ø + 5.1 x 10 -•ø C 2'7. (9) The calculated thickness of the stratum corneum and the mean water concentration in the tissue at various humidities are shown in Table II. The water concentration profiles in human stratum corneum at various ambient humidities are shown in Figure 1. For convenience of comparison, the figure is