## 3 Results and Discussion
### Optimisation of the Processing Parameters  
A numerical method was applied to compute the maximum value of polyphenols and the antioxidant activity by the DPPH assay value, the FRAP assay value, and the ABTS assay value. The optimal conditions for each response were listed in (Table 12). The highest total content of polyphenols determined on the basis of the developed models was 12.48 mg GAE/g for the vessel with a diameter of 35 mm and 11.68 mg GAE/g for the vessel with a diameter of 25 mm. The optimal extraction conditions for both models were very similar in terms of the ultrasound time and amplitude. The greatest discrepancies were obtained for the concentration of the solvent, amounting to about 34.23%. The highest antioxidant activity estimated by the DPPH value was 79.58 umol TE/g for model 1 and 75.90 umol TE/g for model 2. The optimum extraction conditions for both models were very similar and amounted to 15 min for the time, 36 um for the ultrasound amplitude, and 60% for the solvent concentration. The highest antioxidant activity estimated by the FRAP value was 120.65 umol TE/g for the vessel with a diameter of 35 mm and 155.54 umol TE/g for the vessel with a \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Source** & **Sum of Squares** & **DF** & **Mean Square** & **F-Value** & **\(p\)-Value** \\ \hline Model & 2.70 & 1 & 2.70 & 1602.88 & \textless{}0.0001 & significant \\ \(X_{3}\) & 2.70 & 1 & 2.70 & 1602.88 & \textless{}0.0001 & \\ \hline Residual & 0.0219 & 13 & 0.0017 & & \\ \hline Lack of Fit & 0.0211 & 11 & 0.0019 & 4.42 & 0.1990 & not significant \\ \hline Pure Error & 0.0009 & 2 & 0.0004 & & \\ \hline Total & 2.72 & 14 & & & \\ \hline \hline \multicolumn{6}{l}{\(R^{2}=0.9920\), adj \(R^{2}=0.9913\), CV = 0.94, Adeq Precision 77.53} \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Effect of the independent variables on the dependent variables and statistical significance for \(pH_{2}\) of extracts obtained in vessels with a diameter of 25 mm. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline \multirow{2}{*}{**Optimised Condition**} & \multicolumn{3}{c}{**Extraction Variables**} & \multicolumn{3}{c}{**Yield of Extraction**} \\ \cline{2-7}  & \(\mathbf{X_{1}}\) & \(\mathbf{X_{2}}\) & \(\mathbf{X_{3}}\) & **Predicted** & **Experimental** & **Predictive Capacity (\%)** \\ \hline \(TPC_{1}\) & 14.34 & 25.20 & 59.74 & 12.48 & 10.51 & 84.27 & \\ \(TPC_{2}\) & 14.71 & 27.28 & 39.29 & 11.68 & 10.16 & 86.98 & \\ \(DPPH_{1}\) & 15.00 & 36.00 & 60.00 & 79.58 & 68.34 & 85.87 & \\ \(DPPH_{2}\) & 15.00 & 35.83 & 55.26 & 75.90 & 65.87 & 86.78 & \\ \(FRAP_{1}\) & 11.02 & 33.07 & 53.53 & 120.65 & 100.45 & 83.27 & \\ \(FRAP_{2}\) & 14.98 & 35.89 & 30.05 & 155.54 & 120.54 & 77.49 & \\ \(ABTS_{1}\) & 14.20 & 34.73 & 66.05 & 126.54 & 104.49 & 82.52 & \\ \(ABTS_{2}\) & 11.54 & 34.55 & 47.95 & 120.49 & 111.12 & 91.39 & \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Experimental and predicted values of response variables under optimum conditions. diameter of 25 mm. There were also significant differences regarding the optimal extraction conditions. The largest difference observed in the solvent concentration was over 43.86%. The highest antioxidant activity estimated by the ABTS value was 126.54 umol TE/g for the vessel with a diameter of 35 mm and 120.49 umol TE/g for the vessel with a diameter of 25 mm. The optimal extraction conditions were similar for the ultrasound amplitude and different for time and solvent concentration. The difference between the optimal solvent concentration for the tested vessel was 27.40%. Based on the calculated optimal parameters, experimental values were determined for each of the responses. The predictive capacity of the models was calculated as the ratio of the experimental values to the predicted values. For most models, the value of this indicator ranged from 80 to 90%, which is considered a good level.