Mathematical solution of Fick’s second law determines dermato-pharmacokinetic param- eters of UV fi lters, K, and D/L2, as follows (Crank, 1975): 2 1 2 veh veh 1 sin expž n x KC n x D C x KC n L n L L2 d  ｬ  ｬ  ｬ ž ž Q2tｭ, ｭ ｭ ž ž ž ｮ ｮ Ÿ ｮ Q œ where Cveh is the permeant’s concentration in the vehicle, K is the partition coeffi cient of the chemical between the SC surface and the vehicle, and L and D are the diffusion path- length and the coeffi cient of diffusion of the chemical across the SC, respectively. T he validity of equation https://www.sciencedirect.com/science/article/pii/S037851731400 9235?via%3Dihub - eq0015 also assumes that (i) all transport of chemical substance across the SC takes place by passive diffusion, (ii) the vehicle in which the chemical is presented to the SC does not modify the membrane or act as a carrier for the compound, and (iii) that no others skin layers contribute to the total barrier (37). P resently used sun fi lters are lipophilic molecules with relatively low molecular weight and because of their physicochemical characteristics possess a good potential to penetrate into the deep strata of the skin and to be systemically absorbed. I t has also been proven that there are some factors that designate differences between various formulations. These factors include penetration into the skin, permeation through it, and retention of UV fi lters in the skin from topical products. The formulation type infl uences the UV fi lter diffusion on the epidermis. Roussel et al. (38), conducted a study according to which they managed to predict and defi ne bioavailability of the following sunscreen agents: BP-3, 2-ethylhexyl salicylate (EHS), and OMC. The epidermis of four human volunteers was treated with petrolatum and emulsion-based formulations, which remained on the skin for 7 and 30 min. The composition of three sunscreen products ap- plied on human volunteers included a commercial Daylong 15 formulation (i.e., BP-3, 2-EHS, and OMC-loaded liposomes in oil/water emulsion gel, Galderma-Spirig, Egerkin- gen, Switzerland) and 2 laboratory-produced petrolatum jellies including BP-3, OS, and OMC. All sunscreen products respected the maximal concentrations authorized by the directive adopted by the European Union (Cosmetic Directive 76/768/EEC, Annex VII. Part I). Profi les of sunscreen agents through the SC, derived from the assessment of chem- ical amounts in SC layers collected by successive adhesive tape stripping, were success- fully fi tted to Fick’s second law of diffusion. Therefore, permeability coeffi cients of sunscreen agents were found lower with petrolatum than with emulsion-based formula- tions, confi rming the crucial role of vehicle in topical delivery. Although no signifi cant difference was shown for K values, likely because of the small number of volunteers, higher partition of chemicals between SC and emulsion-based vehicle was evidenced than petrolatum formulations, confi rming the crucial role of physicochemical properties of vehicle for the topical delivery of lipophilic compounds. This assumption was confi rmed by the comparison of permeability coeffi cients of UV fi lters showing higher values for emulsion than petrolatum formulations. M ARGIN OF SAFETY R esearchers calculated the margin of safety of UV fi lters by comparing the potential human SED with the NOAEL from in vivo toxicity studies DISTRIBUTION OF UV FILTERS ON THE SKIN 307

 ｬ žMoS ｭ ž ｮ NOAEL SED (39) see below. T he accepted safety limit of an MoS value should be equal or more than 100. During in vitro studies, avobenzone, octinoxate, OCR, oxybenzone, and padimate O, using mineral oil as carrier, were assessed, with respect to their skin penetration properties, and were found to cause no harm to the underlying cells of the epidermis (40). As sunscreen effi cacy may depend on vehicle formulation, some researchers investigated the vehicle effects on UV fi lter skin penetration and permeation. In vitro release and skin permeation of two widely used UV fi lters, OMC (5% w/w) and BMBM (1% w/w), form topical formulations with different features [oil-in-water (O/W) emulsions with different viscosity, water-in-oil (W/O) emulsion, and oils with different lipophilicities]. To mimic in-use conditions, experiments were carried out repeating sunscreen application on the skin surface for three consecutive days. BMBM release from all these vehicles was very low, thus leading to poor skin permeation. The vehicle composition signifi cantly affected OMC release and skin permeation, and slight increases of OMC permeation were ob- served after repeated applications. From skin permeation data, SED and MoS values of BMBM and OMC were calculated for all the investigated formulations after a single ap- plication and repeated applications. SE D was estimated, as reported by Søeborg et al. (41) and by the Scientifi c Commit- tee on Consumer Safety (2016), using the following equation: 3 2 1 2 mg mg DA 10 SSA cm day Kg body weight cm SED , day 60 kg a F  ｬ  ｬ Ng ž ž q q ｭ ｭq ž ž ｮ Ng ｭ ž ｭ ｭ ž ｭ ž wh er e DAa (μg/cm2) is the dermal absorption reported as amount/cm2, resulting from in vitro skin permeation experiments SSA is the skin surface area, expected to be treated with the formulation under investigation F is the frequency of application of the inves- tigated formulation and 60 kg is the default human body weight. The r esults showed that both vehicle composition and the pattern of application affected BMBM and OMC skin permeation. However, all formulations investigated could be con- sidered safe under in-use conditions (42). UV FI LTER SUBSTANCE CLASSIFICATION INORG ANIC UV FILTERS There are two inorganic fi lters (also known as mineral fi lters): titanium dioxide (TiO2) and zinc oxide (ZnO) both are metal oxide particles. These molecules absorb, refl ect, and refract UV photons but function in photoprotection primarily by absorbing UV radiation. The initial formulations of mineral fi lter–containing sunscreens often left a white, chalky JOURNAL OF COSMETIC SCIENCE 308