## 3 Results
### Permeation Studies of Naproxen from the Topical Compositions Based on Pentravan(r)
Figure 4: Permeation profiles of naproxen through human skin from topical compositions based on Pentravan®: (**A**)—with acid form of naproxen, NAP; (**B**)—with salt of naproxen, [ProDiPr][NAP], in the presence of chemical enhancers: menthol (green line), TinCap (red line) or without enhancer (dark blue line). NAP is as follows Pen + NAP < Pen + menthol + NAP < Pen + TinCap + NAP (12.9; 34.5 and 47.9 \(\upmu\)g NAP cm\({}^{-2}\) h\({}^{-1}\) respectively). Different permeation results of drug through human skin were obtained when naproxen salt [ProOiPr][NAP] was used instead of acid naproxen (Figure 4B). The application of the composition Pen + [ProOiPr][NAP] on the skin ensured the highest flux 91.14 \(\pm\) 2.7 \(\upmu\)g NAP cm\({}^{-2}\) h\({}^{-1}\), during the first five hours. However, after five hours of permeation, the diffusion of the naproxen from Pen + [ProOiPr][NAP] composition through the skin slowed down and continued, but with a significantly lower flux. The addition of the TinCap to the composition comprising [ProOiPr][NAP] caused only a slightly decreased amount of the drug to permeate into the receptor fluid within the first five hours compared to the composition without tincture. However, from the third hour following application to the skin up to the 24 h limit of the test duration, the naproxen permeates through the skin from the composition Pen + TinCap + [ProOiPr][NAP] with a steady-state flux 66.8 \(\upmu\)g NAP cm\({}^{-2}\) h\({}^{-1}\). Ultimately, with the addition of TinCap, the cumulative mass of naproxen in the receptor fluid after 24 h was twice as high (1613.2 \(\pm\) 114.3 \(\upmu\)g NAP cm\({}^{-2}\)) compared to the one (791.2 \(\pm\) 83.8 \(\upmu\)g NAP cm\({}^{-2}\)) without enhancer in the composition (Table 2, Figure 4B). Figure 5 shows cluster analysis in which the cumulative mass of compounds from all-time points during the 24 h experiment was considered. The cluster analysis distinguished three groups that differed significantly from each other. The largest group, ensuring the similar penetration, are the compositions: Pen + [ProOiPr][NAP], Pen + Men + [NAP] and Pen + TinCap + [NAP]. On the other hand, the composition Pen + TinCap+[ProOiPr][NAP] comprising naproxen salt, constitutes a separate group characterized by the highest penetration, considering all time points\". Figure 5: Cluster analysis graph for the mean cumulative mass of naproxen (for all-time points) during 24 h permeation study from topical Pentravan® based compositions comprising two forms of naproxen and without or with penetration enhancers. Compounds with similar permeation are marked with various separate circles (blue circle—the greatest permeation, green circle—the lowest permeation). Figure 6 presents a box plot of the mean flux (in \(\upmu\)g NAP cm\({}^{-2}\) h\({}^{-1}\)) calculated for time intervals between subsequent experimental points during the 24 h study--for example, between the first and second hour of the experiment, between the second and third hour of the experiment, and so on. The mean flux value for each composition is shown in the graph as a point within a box, the standard error as an area, and the standard deviation as a pair of \"whiskers\". These results clearly indicate that the compositions containing the naproxen salt provided the highest naproxen permeation rate over the entire time range. However, for the composition Pen + TinCap + [ProCiPr][NAP], each individual flux values at subsequent experimental points during the 24 h study tends to be clustered closer to the mean than for Pen + [ProCiPr][NAP]. This means that the permeation rate is more uniform over the entire time range for Pen + TinCap + [ProCiPr][NAP].