## 5 Permeability Study with Franz Cells  
After formulating the cold cream and developing a reliable analytical method, an in vitro penetration study of APIs was performed using vertical Franz cells and a cellulose membrane setup. Although cellulose is generally characterized as a polar membrane, on its surface contains OH and carbonyl groups as functional groups and a carbon skeleton (CH2) that give it a partially amphiphilic character. We could say that the hydrophobic nature of the glycopyanose plane allows the cellulose chains to stack through hydrophobic interactions, creating a polymer-like structure. Thus, its structural similarity to biological membranes (phospholipid bilayer) allows cellulose to be used as a marker of drug permeation in in vitro studies [42]. [PERSON] et al. reveal that a hydrophilic artificial membrane simulates more closely drug permeation into tissue at levels comparable to Caco-2 permeation and is significantly superior to in silico techniques [43]. It should, of course, be noted that the epidermis, due to the existence of keratinocytes on its surface, is a special category of tissue and needs additional ex vivo and in vivo experiments in order to be studied thoroughly. In the present permeation study, comparative experiments were performed using two different carriers, cold cream and an aqueous suspension. Both formulations, since the five actives were incorporated, were studied in Franz cells in triplicate. After sampling, and to remove PBS salts, samples were lyophilized and reconstituted with methanol. Supplementary Table S1 provides an overall presentation of the most important physicochemical properties of the five drugs under study, which determine the permeability (paracellular, intercellular, and intercellular) of a molecule through a tissue or membrane. The profile of the cumulative amount of each compound that permeated per unit area (mg\(\cdot\)cm\({}^{-2}\)), at the sampling times, is illustrated in Figure 5, while their steady-state flux Jss and Papp coefficient values are recorded in Table 9.  
Figure 5: Permeability study of ferulic acid, resveratrol, and quercetin (**a**) cream, (**b**) suspension. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{5}{c}{**\% Recovery**} \\ \cline{2-6}
**Sample** & **RSV** & **FERA** & **QR** & **RTN** & **\(\alpha\)-TOC** \\ \hline
1 & 98.9 & 99.9 & 98.6 & 100.9 & 99.3 \\
2 & 99.4 & 99.4 & 99.5 & 102.9 & 100.8 \\
3 & 99.3 & 100.0 & 98.9 & 102.5 & 100.0 \\
4 & 99.1 & 99.7 & 98.5 & 101.3 & 99.7 \\
5 & 98.5 & 99.1 & 97.7 & 101.1 & 99.0 \\ \hline \%RSD & 0.4 & 0.4 & 0.6 & 0.9 & 0.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: % recovery values (\(\
u\) = 5) applying the proposed purification procedure. According to the results, the substance with the greatest tendency to penetrate the membrane is ferulic acid, followed by resveratrol and quercetin, while the two vitamins show no activity. This behavior was partly expected since ferulic acid is the most polar substance and has the lowest molecular weight. In fact, its high solubility in water indicates that the aqueous carrier is the most effective. RSV, although more lipophilic than QR, is more membrane permeable due to its smaller size (MW). Furthermore, it appears that quercetin, when incorporated into the suspension, barely penetrates the membrane, while when present in the cream, its penetration is more significant. This is probably due to the fact that it is more soluble in the cold cream (due to coconut and almond oils) than in the aqueous suspension [44]. Regarding the two vitamins, it was found that due to their high lipophilicity and molecular weight, they do not penetrate the membrane in either of the two carriers. The different penetration abilities of the five substances are desirable since they must act both on the layers of the epidermis and on the inner layers of the skin. Given that they have a similar and/or complementary action, they can treat, in this way, the problem of aging.