## 3 Results
### Permeation Studies of Naproxen from the Topical Compositions Based on Pentravan(r)  
In vitro permeation tests evaluated the effect of two naproxen forms used in the Pentravan(r) based topical compositions and two penetration enhancers--menthol and TinCap, on the penetration of the drug through human skin using Franz diffusion cells. Permeation parameters, including the cumulative permeation mass of naproxen (Q), a steady-state flux (JSS), and the quantity of permeated naproxen as percentage of the applied dose over 24 h (%AD), were determined for five topical compositions (Table 2). The permeation profiles are presented in Figure 4. Only the topical composition Pen + menthol + [ProCiPr][NAP] was not used in these tests due to its instability and the liquid phase separation immediately after preparation, as described above. Figure 3: The plot of viscosity (at 30 \({}^{\circ}\)C) vs. shear rate for the Pentravan® and the topical compositions comprising acid naproxen (NAP) or its salt [ProCiPr][NAP], with and without permeation enhancers. As shown in Figure 4A when the topical compositions comprising the acid form of naproxen were applied, both enhancers increased the percutaneous permeation of naproxen compared with the control (Pen + NAP). In the initial five hours, the drug penetrated the skin in the largest amounts from the composition Pen + menthol + NAP comprising the menthol. When the composition Pen + TinCap + NAP was used, in the first two hours, the percutaneous permeation of NAP was like the control, but after that time, the permeation increased with TinCap significantly. Thus, after eight hours the cumulative amount of NAP, with use of menthol and TinCap in topical composition, was similar, 243.4 \(\pm\) 16.8 \(\upmu\)g NAP cm\({}^{-2}\) and 252.8 \(\pm\) 22.1 \(\upmu\)g NAP cm\({}^{-2}\), respectively. However, without any enhancer, the acid naproxen permeated much slower and after eight hours, the cumulative mass was twice lower (116.1 \(\pm\)7.6 \(\upmu\)g NAP cm\({}^{-2}\)). Finally, after 24 h, when the topical composition with TinCap was used, the cumulated mass of naproxen in the receptor fluid was 1079.1 \(\pm\) 137.1 \(\upmu\)g NAP cm\({}^{-2}\) and was over three times higher than without any penetration enhancer 339.7 \(\pm\) 16.3 \(\upmu\)g NAP cm\({}^{-2}\) (Table 2). It can be assumed that for each topical Pentravan(r) composition comprising NAP, the dependence of cumulative mass of naproxen on time has a typical _J_-shape, and steady-state flux was reached after three hours. The steady-state flux for the time interval from three to 24 h are presented in Table 2. The ascending order of flux for the topical compositions with \begin{table}
\begin{tabular}{c c c c} \hline
**Formulation** & **Q** & **\%AD** & **Jss,** \\  & **(\(\upmu\)g NAP cm\({}^{-2}\))** & **(\(\upmu\)g NAP cm\({}^{-2}\) h\({}^{-1}\))** \\ \hline Pen + NAP & 339.7 \(\pm\) 16.3  & 0.33 \(\pm\) 0.02  & 12.9 \(\pm\) 0.6  \\ Pen + menthol + NAP & 847.9 \(\pm\) 117.1  & 0.85 \(\pm\) 0.12  & 34.5 \(\pm\) 1.6  \\ Pen + TinCap + NAP & 1079.1 \(\pm\) 137.1  & 1.08 \(\pm\) 0.12  & 47.9 \(\pm\) 1.9  \\ Pen + [ProDiPr][NAP] & 791.2 \(\pm\) 83.8  & 0.79 \(\pm\) 0.08  & 91.14 \(\pm\) 2.7  **,d \\ Pen + TinCap + [ProDiPr][NAP] & 1613.2 \(\pm\) 114.3  & 1.61 \(\pm\) 0.11  & 68.8 \(\pm\) 1.0  *,e \\ \hline \end{tabular}  
Q—the cumulative mass of naproxen permeating through the human skin after 24 h; %AD—Q as the percentage of the applied dose; Jss—steady-state flux determined from the slope of the linear portion of the profiles; flux determined for permeation interval time: * 3–24 h; * 1–5 h; * 6, * 6, * 6 different letters indicate significant differences \(p\) < 0.001, \(\alpha\) = 0.05, mean \(\pm\) SD, n = 3. The statistically significant difference was estimated by ANOVA using the Tuckey’s test.  
\end{table} 
Table 2: Permeation parameters of naproxen through the human skin from different compositions.