DEPLETION EFFECTS IN TOPICAL PREPARATIONS 167 MEASUREMENT OF MN PENETRATION (INFINITE DOSE) For the penetration study a recently developed glass chamber system was used (11). Briefly, two glass cells were fastened to both upper arms of each subject, allowing the examination of four MN preparations at the same time under occlusion conditions. The glass cells were filled with MN solutions of equal permeant activity, emptied after one-hour time periods, and refilled with the initial MN solutions. The MN concentra- tion of the donor phase samples was measured spectrophotometrically. Because the concentration decrease in each one-hour time interval was •10%, zero-order kinetics were assumed. MN disappearance rates were calculated from the concentration differ- ences between the initial solution and the samples obtained after every hour. CALCULATIONS AND DATA TREATMENT Bioavailability factors fandf3. Using Fick's first law of diffusion, bioavailability factors f may be obtained by calculating the ratios of the first order penetration rate constants of the test vehicles R T and the standard vehicle RST: f RT/RsT (Eq. la) where the penetration rate constant R is defined as follows: R D B ø A' PCB/v/(dB ß V) (Eq. lb) where D B is the diffusion coefficient of the permeant in the barrier stratum corneum, A is the application area, PCB/v is the stratum corneum/vehicle partition coefficient of the permeant, d B is the thickness of the stratum corneum, and V is the volume of the applied preparation. The ratio V/A is an expression of the thickness h of the ointment layer. In the case of penetration rate data, bioavailability factors may be determined as the ratio of the penetration rate constants R obtained with the test vehicles and with the standard vehicle. Penetration rate constants are calculated as the quotient of the steady-state penetration rate and the permeant amount in the vehicle. From the horizontal distance between the parallel portions of the dose-response curves of a standard preparation (ST) and a test preparation (T) at a certain response level Resp%, the bioavailability factor f is determined as follows (Figure 1): log f = log doSeResp%S T - log doSeResp%T (Eq. 2a) f dOSeResp%ST/dOSeResp%T (Eq. 2b) In practice, the shape of the dose-response curves is sigmoidal for the response parameter 1/LT. A plateau is reached as soon as the permeant solubility limit in the vehicle is exceeded (Figure 2a). This plateau may be elevated under the influence of penetration enhancers. With the response parameter D, a sigmoidal shape of the curves cannot be expected because the pharmacodynamic effect will last as long as the amount of dissolved permeant in the vehicle, and thus the penetration rate is high enough, no matter if permeant solutions or suspensions are applied. In addition, the more R decreases, the more pronounced the reservoir function of the applied preparation will become and the higher the gradient of the curve will be, which at a certain dose level even leads to an intersection of the test and the standard curve (Figure 2b). Therefore, the determination

168 JOURNAL OF COSMETIC SCIENCE 100,,, so- tes log f 0 log dose standard Figure 1. Determination of the bioavailability factor f from the dose/response curves of a test and a standard preparation. log dose log dose Figure 2. Typical dose-response curves obtained with the response parameters 1/time until onset (a) and duration (b) of an effect. The curves resulting from. two different R values were simulated with the Bateman equation assuming an open one-compartment model and a negligible lag time. of bioavailability factors is more accurate in the lower part of the curves, where the duration of the effect is short (12). It has to be mentioned that in the case of dose-response curves, f also depends on the volume of the applied vehicles. The use of concentration-response curves mathematically eliminates the influence on f of the preparation volume and, assuming equal areas of