## 3 Results and Discussion
### Optimization of UAE of the Antioxidant Bioactive Compounds  
A BBD was used to optimize the UAE, considering three factors: amplitude, time and the sample/solvent ratio. Fifteen runs of the experiments were conducted (Table 1). The TPC obtained from the RP and the WP in these experiments ranged from 3.69 to 48.48 mg GAE/g dw and 16.05 to 44.68 mg GAE/g dw, respectively, while the FRAP ranged from 14.45 to 105.64 mg TE/g dw and 36.17 to 102.59 mg TE/g dw, respectively. The highest TPC and FRAP were obtained at an amplitude of 40%, using an extraction time of 25 min and at a sample/solvent ratio of 1:30 for both types of SGP. For all variable responses obtained in the experimental matrix, Table 2 shows the results of conducting a regression analysis and an ANOVA in adapting the model design to determine whether the terms were statistically significant. As shown in Table 3, for the RP, amplitude, quadratic interactions (AA) and ratio-time interactions (AC) significantly influenced (\(p<0.05\)) both the TPC and the FRAP. The sample/solvent ratio also significantly affected the FRAP (\(p<0.05\)). For the WP, the amplitude had a significant effect (\(p<0.05\)) on both the TPC and the FRAP. In terms of FRAP, for WP as well as RP, the sample/solvent ratio, quadratic interactions (AA) and ratio-time interactions (AC) also had significant effects (\(p<0.05\)). Indeed, other recent studies on the optimization of the extraction parameters in UAE for the recovery of polyphenonic compounds from plant matrices and by-products have also reported significant (\(p<0.05\)) impacts of factors such as the amplitude used and/or time-ratio interactions [38; 39; 40; 41]. The second-order predictive polynomial equations obtained by applying quadratic regression models to the experimental values to represent the empirical relationship between the TPC and the FRAP and the operating conditions are shown below (Equations (3)-(6)): \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & & & & & **RP** & & **WP** \\ \hline
**Runs** & \(\mathbf{X_{1}}\) & \(\mathbf{X_{2}}\) & \(\mathbf{X_{3}}\) & **TPC** & **FRAP** & **TPC** & **FRAP** \\ \hline
1 & 25 & 17.5 & 1:30 & 26.60 \(\pm\) 1.78 & 78.98 \(\pm\) 4.85 & 31.07 \(\pm\) 2.94 & 86.76 \(\pm\) 1.61 \\
2 & 10 & 17.5 & 1:10 & 25.84 \(\pm\) 0.66 & 53.31 \(\pm\) 1.84 & 29.25 \(\pm\) 0.84 & 36.17 \(\pm\) 3.08 \\
3 & 25 & 10 & 1:10 & 27.50 \(\pm\) 1.22 & 54.77 \(\pm\) 2.37 & 32.95 \(\pm\) 2.03 & 58.00 \(\pm\) 13.70 \\
4 & 25 & 25 & 1:10 & 3.69 \(\pm\) 0.58 & 14.45 \(\pm\) 0.75 & 32.82 \(\pm\) 4.50 & 50.61 \(\pm\) 2.98 \\
5 & 25 & 10 & 1:50 & 18.83 \(\pm\) 0.11 & 77.90 \(\pm\) 4.90 & 21.91 \(\pm\) 2.36 & 48.78 \(\pm\) 7.47 \\
6 & 25 & 25 & 1:50 & 24.80 \(\pm\) 5.02 & 89.75 \(\pm\) 1.82 & 34.83 \(\pm\) 0.91 & 88.23 \(\pm\) 3.23 \\
7 & 10 & 17.5 & 1:50 & 8.74 \(\pm\) 1.33 & 63.39 \(\pm\) 0.51 & 16.05 \(\pm\) 0.92 & 55.32 \(\pm\) 2.61 \\
8 & 25 & 17.5 & 1:30 & 33.61 \(\pm\) 0.93 & 77.86 \(\pm\) 4.96 & 35.44 \(\pm\) 5.89 & 89.17 \(\pm\) 2.50 \\
9 & 40 & 10 & 1:30 & 32.99 \(\pm\) 1.36 & 82.03 \(\pm\) 1.01 & 40.63 \(\pm\) 0.39 & 101.24 \(\pm\) 0.64 \\
10 & 40 & 17.5 & 1:50 & 28.95 \(\pm\) 0.56 & 81.99 \(\pm\) 7.70 & 35.93 \(\pm\) 4.98 & 98.32 \(\pm\) 1.57 \\
11 & 40 & 17.5 & 1:10 & 33.80 \(\pm\) 0.83 & 64.39 \(\pm\) 4.61 & 38.24 \(\pm\) 1.09 & 86.57 \(\pm\) 7.06 \\
12 & 10 & 25 & 1:30 & 20.73 \(\pm\) 3.73 & 57.52 \(\pm\) 9.44 & 17.63 \(\pm\) 0.15 & 64.16 \(\pm\) 1.20 \\
13 & 40 & 25 & 1:30 & 48.48 \(\pm\) 5.24 & 105.64 \(\pm\) 8.41 & 44.68 \(\pm\) 2.96 & 102.59 \(\pm\) 1.99 \\
14 & 10 & 10 & 1:30 & 11.42 \(\pm\) 1.56 & 50.62 \(\pm\) 4.34 & 27.88 \(\pm\) 1.64 & 87.09 \(\pm\) 0.93 \\
15 & 25 & 17.5 & 1:30 & 34.79 \(\pm\) 2.60 & 94.59 \(\pm\) 3.56 & 29.05 \(\pm\) 1.70 & 79.51 \(\pm\) 4.83 \\ \hline \end{tabular}
\end{table} 
RP  
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