## 3 Results and Discussion
### Extraction Process Optimization  
Since LA-SCDB15 provided significantly higher Y\({}_{\text{TP}}\) compared to all other DES tested, this solvent was chosen to further optimize the extraction process. To this end, three process variables that can critically affect polyphenol extraction [16; 21; 24], namely the S\({}_{\text{S}}\), the \(C_{\text{DES}}\) and the \(t_{\text{US}}\), were included in the experimental design. The design deployed aimed at assessing the effect of the process variables and identifying any synergistic functions between them. The evaluation of model fitting and validity was based on the ANOVA and lack-of-fit test (Figure 4), taking into account the proximity of measured and predicted values (Table 2). The mathematical model derived after omitting non-significant terms, was as follows:  
\[\text{Y}_{\text{TP}}=78.34+1.31\text{X}_{1}+1.70\text{X}_{2}+1.09\text{X}_{2} \text{X}_{3}-3.86\text{X}_{2}{}^{2}\;(\text{R}^{2}=0.97,\,p=0.003) \tag{6}\]  
Figure 4: Statistics associated with model fitting, performed by implementing response surface methodology. (**A**), Desirability function; and (**B**), actual-by-predicted plot. Inset tables (lack-of-fit, parameter estimates and effect test) illustrate the effect of independent (process) variables on the response. Asterisk (*) on values in the “parameter estimates” and “test effects” inset tables signify statistically significant values (at least at a 95% significance level). The square correlation coefficient (R\({}^{2}\)) was a good indicator of the total variability around the mean provided by the Equation (6). Assuming a confidence interval of 95% and considering the R\({}^{2}\) the \(p\) value for lack-of-fit (Figure 4), it could be supported that the mathematical model displayed very satisfactory adjustment to the experimental data. The 3D graphs that represent a visualization of the model, can portray at-a-glance the effect of the process variables on the response (Y\({}_{\text{TP}}\)) (Figure 5). The desirability function (Figure 4) provided the theoretical optimized values for each of the variables considered, which were S\({}_{\text{S}}\) = 900 rpm, \(C_{\text{DES}}\) = 77% (_w/v_), and \(t_{\text{US}}\) = 15 min. By adjusting these optimal settings, the predicted maximum response was calculated to be 79.93 \(\pm\) 1.92 mg GAE g\({}^{-1}\) dm. To ascertain the validity of the model, three individual extracts were performed using the optimized values and the outcome was 78.39 \(\pm\) 2.96 mg GAE g\({}^{-1}\) dm, illustrating the accuracy of response prediction. The ANOVA results indicated that X\({}_{3}\) (\(t_{\text{US}}\)) was not statistically significant, as opposed to its cross term with X\({}_{2}\) (\(C_{\text{DES}}\)) (Figure 4). This finding pointed to a combined effect of these two variables and evidenced that the efficiency of the ultrasonication pretreatment might be dependent on the proportion of DES/water. On the other hand, X\({}_{1}\) (S\({}_{\text{S}}\)) had a clear positive effect on Y\({}_{\text{TP}}\), which showed that increased speed of agitation favored polyphenol extraction yield. Recent studies on the effect of S\({}_{\text{S}}\) on Y\({}_{\text{TP}}\) gave contradictory results, suggesting that the influence exerted by S\({}_{\text{S}}\) might not follow a specific pattern.