j. Cosmet. Sci., 54, 463-481 (September/October 2003) Efficiency of a continuous heioht distribution model of sunscreen film oeometry to predict a realistic sun protection factor L. FERRERO, M. PISSAVINI, S. MARGUERIE, and L. ZASTROW, Coty Beauty-Lancaster Group, International Research & Development Center, Athos Palace, 2, rue de la Lujernetta, MC 98000, Monaco. Accepted for publication June 16, 2003. Synopsis Irregularities in the geometry of sunscreen films spread on rough areas, like skin, is often presented as being the main cause of the degree of UV absorption achieved by the UV filters that are inside. Until now, only the step film, a model invented by O'Neill, was simple enough to calculate UV data close to in vitro experimental data, after determination of a limited number of fraction areas with their corresponding thickness. However, such models are obviously too simple to represent a real situation. In the present work, more complex distributions of film thickness were calculated, with an infinite number of individual heights. Realistic models were achieved via a probability function. The consequences for UV absorption were deduced, and the calculated UV data were compared to experimental in vitro data on sunscreen products measured after being spread on a roughened PMMA substrate. The latter substrate was previously selected for its ability to achieve a good correlation with in vivo SPF. An optimized version of the continuous mathematical model was finally determined in order to achieve UV curves, similar in shape and intensity to the experimental ones. The latter model can be used to predict realistic SPF values. INTRODUCTION Numerous attempts have been made to understand how sunscreen preparations protect against UV radiation (1-6). Normally, the final UV protection achieved by a sunscreen product should be the result of each filter UV absorption present in the preparation. However, it is now trivial to note the poor correlation between UV absorption of sunscreens diluted in alcohol solutions and the in vivo SPF. O'Neill (6) demonstrated in 1983 that a simple model of irregular film, a one-step film geometry, could satisfactorily account for the discrepancy between clinical results and simple spectrographic data. However, only a single wavelength calculation was possible in 1983. In previous pub- lications (7,8), we used the simple step film geometry proposed by O'Neill to success- fully calculate UV curves similar in shape and intensity to in vitro experimental ones. Our experimental data was collected by spreading different sunscreen formulations onto the well-known irregular transparent substrate Transpore © tape (3M Corporation) (9). Later, D. F. Tunstall (10) developed a similar mathematical analysis to demonstrate 463

464 JOURNAL OF COSMETIC SCIENCE that film thickness profiles can account for experimental variability in SPF measure- ment. UV data collected from Transpore © tape and Vitro-skin © served to validate the calculation. Recently, B. Herzog (11) also used the step film model to directly correlate calculated sun protection factors to in vivo data. However, the same simplistic model of sunscreen film geometry was postulated in all studies. The aim of the present work was to evaluate a more complex model, with a continuous height distribution, and to test its efficiency to predict realistic sun protection factors. EXPERIMENTAL DETAILS SUBSTRATE SELECTED FOR IN VITRO SPECTROSCOPY Sunscreen products should be applied to a UV-transparent substrate. It must be non- fluorescent, photostable, and nonreactive, and should distribute the product in a manner similar to human skin and so should have a textured upper surface. From our experience, a roughened Polymethylmethacrylate © plate (PMMA), with a reproducible roughness (measured R a of about 5-6 lam), is a very convenient material, and so it was chosen for this study (12). This substrate can be supplied by Helioscience under the trade name Helioplates ©. OPERATING CONDITIONS FOR IN VITRO SPECTROSCOPY A Labsphere © UV-1000 S transmittance analyzer was used. The principle of the method consisted in the determination of the diffuse transmission spectrum of the UV rays through the substrate, before and after application of the sunscreen. A PMMA plate covered with a film of solvent (glycerol) was used to obtain the blank transmittance (from 290 to 400 nm, each nm). A first study, performed in our laboratory on numerous products, showed that the best correlation with in vivo SPF was achieved for an application rate of 1.2 mg cm -2 (12). Then, 30 mg of sunscreen product was deposited onto the roughened PMMA surface (50 mm x 50 mm). The product was immediately spread over the whole surface, using light strokes with a gloved finger, until a uniform surface density distribution was achieved. The sample thus obtained was allowed to settle for 15 minutes at room temperature to ensure a self-leveling of the formula. Nine UV transmission spectra (from 290 to 400 nm, 5-nm increment steps) were taken on each substrate at different locations. Five different substrates were used for each sunscreen, to average the UV transmission data at each wavelength. OPERATING CONDITIONS FOR SPECTROSCOPY OF PURE UV FILTERS A UV-VIS spectrophotometer (Lambda 16 ©, Perkin Elmer) was used to collect UV data. An appropriate amount of pure UV filter was carefully diluted in a suitable solvent, and the transmittance spectrum of the solution was measured by using a UV quartz cuvette with a standardized optical pathlength. The absorbance data (400-290 nm, 5-nm in- crement steps) was normalized at 1 mg cm -3 and 1 cm optical pathlength (absortivities