# Somatotropin Penetration Testing from Formulations Applied Topically to the Skin
## 3 Results
### Permeation Kinetics  
To define the kinetics of the permeation process, a kinetic model was then fitted based on the amount of STH permeated (at 6 h for cellulose membrane and 24 h for porcine skin) (Table 3).  
The STH permeation process was assumed to follow first-order kinetics. To calculate the rate constant of the STH permeation process, a formula based on the first-order kinetics model was used (R\({}^{2}\) = 0.9768 for the cellulose membrane and R\({}^{2}\) = 0.9812 for the skin). In a test of STH permeation through the cellulose membrane, STH permeated most rapidly from formulation F-3, containing STH and ALB in a 1:2 ratio. ALB increased the permeation rate with respect to the formulation without ALB by 1.4-fold. For the F-4 formulation, it  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{3}{*}{**Formulations**} & \multicolumn{3}{c}{**Kinetics Release Models**} & \multicolumn{3}{c}{**Kinetics Parameters**} \\ \cline{2-6}  & \begin{tabular}{c} **Higuchi** \\ **R\({}^{2}\)** \\ \end{tabular} & \begin{tabular}{c} **[PERSON]-** \\ **[PERSON]** \\ \end{tabular} & \begin{tabular}{c} **First Order** \\ **R\({}^{2}\)** \\ \end{tabular} & \
\begin{tabular}{c} **K** \\ **R\({}^{2}\)** \\ \end{tabular} &
\begin{tabular}{c} **Permation** \\ **Half-Life** \\ **t\({}_{\text{80\% }}\) **(h)** \\ \end{tabular} \\ \hline \multicolumn{6}{c}{Spectra/Por} \\ \hline F-1 & 0.9999 & 0.9955 & 0.9996 & 0.314 \(\pm\) 0.029 & 2.22 \(\pm\) 0.21 \\ F-2 & 0.9197 & 0.9426 & 0.9688 & 0.100 \(\pm\) 0.034 1 & 7.58 \(\pm\) 1.75 1 \\ F-3 & 0.9733 & 0.9683 & 0.9620 & 0.451 \(\pm\) 0.029 1 & 1.54 \(\pm\) 0.10 1 \\ F-4 & 0.9864 & 0.9939 & 0.9616 & 0.351 \(\pm\) 0.098 & 2.08 \(\pm\) 0.61 \\ Average R\({}^{2}\) & 0.9698 & 0.9751 & 0.9768 & & \\ \hline \multicolumn{6}{c}{Membrane} \\ \hline F-1 & 0.9772 & 0.9785 & 0.9885 & 0.601 \(\pm\) 0.082 & 1.17 \(\pm\) 0.16 \\ F-2 & 0.9634 & 0.9750 & 0.9869 & 0.108 \(\pm\) 0.046 1 & 7.40 \(\pm\) 1.47 1 \\ F-3 & 0.9113 & 0.9457 & 0.9770 & 0.131 \(\pm\) 0.055 1 & 6.07 \(\pm\) 0.80 1 \\ F-4 & 0.9663 & 0.9251 & 0.9841 & 0.077 \(\pm\) 0.007 1 & 9.10 \(\pm\) 0.83 1 \\ Average R\({}^{2}\) & 0.9546 & 0.9561 & 0.9812 & & \\ \hline \hline \end{tabular}  
* F-1\(-\)STH 0.1%; F-2\(-\)STH / ALB 1:1 (0.1%\(\times\)0.1%); F-3\(-\)STH / ALB 1:2 (0.1%\(\times\)0.2%); F-4\(-\)STH / ALB 1:5 (0.1%\(\times\)0.5%). \({}^{1}\)—statistically significant difference with respect to the rate of penetration of STH from the F-1 formulation (STH 0.1%), \(p<\) 0.05.  
\end{table}
Table 3: Permeation rates and R\({}^{2}\) regression coefficients for the prepared MC-based hydrogel formulations containing STH.  
only slightly increased the permeation rate (1.1-fold). In contrast, ALB added in a 1:1 ratio to STH reduced the permeation rate by three-fold.  
In the STH skin permeation test, STH permeated most rapidly from the formulation without ALB (F-1), while the addition of ALB reduced the permeation rate in all formulations: most significantly in formulation F-4 by approximately 8-fold, in F-2 by 5.5-fold and in formulation F-3 by 4.5-fold. ALB increased the half-life of STH permeation. When tested over 24 h, the longest \(\mathrm{t}_{50\%}=9.10\)\(\pm\) 0.83 (h) was observed for the formulation with the highest ALB content (0.5%), while the shortest half-life was observed for the STH-containing hydrogel without ALB, which was \(\mathrm{t}_{50\%}=1.17\)\(\pm\) 0.16 (h).