## 3 Results and Discussion
### Statistical Analysis  
Using analysis of variance, the software proposed the models presented in the Tables 5 and 6. For each model, the F-and \(p\)-values were determined. These values showed that the models were significant. Also, the lack of fit of the F-and \(p\)-values implied that lack of fit was not significant relative to the pure error. The \(p\)-values were determined for each coefficient, with values greater than 0.1000 indicating the model terms were not significant (Table 5). Using the models, we were able to describe the response surface for each variant. The charts were ternary, and because there was a large difference between the \(\alpha\)-hederin variation domains and the other two components, we had to present the larger diagrams in the so called concentration zone (Figure 3). \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{8}{c}{**Coefficients (Coded Equation) and \(p\)-Value**} \\ \cline{2-11}  & **A** & **B** & **C** & **AB** & **AC** & **BC** & **ABC** & **AB(A-B)** & **ACA(A-C)** & **ABC\({}^{\mathbf{2}}\)** & **A** \\ \hline NCTC & 18,786.6 & 70,9735 & 83.3454 & -20,732.2 & -19,596.5 & 15,8615 & - & - & - & - & 18,786.6 \\ \(p\)-values & \(<\)0.0001 & \(<\)0.0001 & \(<\)0.0001 & 0.5880 & 0.6085 & 0.1430 & - & - & - & - & \(<\)0.0001 \\ \hline In Hep-2 & 5,65986 & 4,51276 & 3,99676 & 8,53632 & 8,552 & 1.0551 & 5,7696 & 28,07669 & 2,89269 & - & 5,6968 \\ (MEM) & E+06 & & 2+06 & E+06 & 2+06 & 2+06 & 2+06 & E+06 & 2+06 & 2+06 \\ \(p\)-values & \(<\)0.0001 & \(<\)0.0001 & \(<\)0.0001 & 0.0052 & 0.0052 & 0.3829 & 0.0052 & 0.0053 & 0.0052 & - & \(<\)0.0001 \\ \hline Hep-2 & \multirow{2}{*}{\(-9343.646\)} & \multirow{2}{*}{\(-9343.646\)} & \multirow{2}{*}{\(-76.5045\)} & \multirow{2}{*}{\(88.9519\)} & \multirow{2}{*}{\(7533.95\)} & \multirow{2}{*}{\(6852.24\)} & \multirow{2}{*}{\(71.2811\)} & \multirow{2}{*}{-} & \multirow{2}{*}{-} & \multirow{2}{*}{-} & \multirow{2}{*}{0.0391} & \multirow{2}{*}{\(<\)0.0001} \\ (MEM + FBS) & & & & & & & & & & & \\ \(p\)-values & \(<\)0.0001 & \(<\)0.0001 & \(<\)0.0001 & 0.9173 & 0.9248 & 0.0152 & - & - & - & 0.0391 & \(<\)0.0001 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The model coefficients and associated \(p\)-values. Figure 3: Response surface for cell viability of NCTC fibroblasts ternary and concentration zone. Figure 5 presents the response area forthe experimental desirability and also for the cell viability of NCTC and Hep-2 treated cells. It maybe seen that there was a fairly restricted area around the experimental point 2, where the two conditions of cell viability were fulfilled, respectively: \(>\)79% were met for NCTC cells and \(<\)50% for Hep-2 cells. This area had the following coordinates: \(\alpha\)-hederin ranging between 3.44 and 3.96; hederagenin ranging from 100 to 116, and hederacoside C between 580 and 595. A statistical analysis of cell viability data was performed, showing that the funded solution with optimized ratio between the three saponins, \(\alpha\)-hederin, hederagenin, and hederacoside C, was the same variant found by restriction solution, in which the 3.863:100.000:596.137 (w/w/w) variant had induced cell viability results of 80% in normal NCTC cells, 35% in Hep-2 tumor cells cultivated in MEM, and 76% in Hep-2 tumor cells in MEM with FBS (Table 8). From the in vitro cytotoxicity experiments of the 14 variants obtained by mixture modeling using the Design Expert 11 software, the optimal variant of the saponin mixture, i.e., \(\alpha\)-hederin, hederagenin, and hederacoside C, (no.9, Table 4), induced similar values: 81% in normal NCTC cells, 36% in Hep-2 tumor cells cultivated in MEM, and 77% in Hep-2 tumor cells in MEM with FBS (Table 4). This saponin combination was biocompatible in NCTC fibroblast cells and had a strong antiproliferative activity in Hep-2 cells in MEM. In addition, it had a mild cytotoxic effect on Hep-2 tumor cells in MEM with FBS. All these data correspond to the response optimization procedures using the desirability function.