## 3 Results
### Efficiency of Anthocyanins Extraction from Peels
#### 3.2.2 Development of the Response Surface Methodology  
From the results obtained in Section 3.2.1, a Box-Behnken experimental design was applied to develop the response surface of the total monomeric anthocyanin concentration. In this design, the independent variables were the significant variables resulting from the analysis of the screening design: solvent concentration, pH, and liquid-solid ratio. Levels of the independent variables are given in Table 4 and were chosen based on the behavior of the significant variables in the screening design (Figure 2B).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Independent Variable**} & \multicolumn{3}{c}{**Level**} \\ \cline{2-4}  & \(-\mathbf{1}\) & \(\mathbf{0}\) & \(\mathbf{1}\) \\ \hline Solvent concentration (\%) (\(\%\)) & 60 & 80 & 100 \\ pH & 3.50 & 4.75 & 6.00 \\ Liquid–solid ratio (mL/g) & 40 & 60 & 80 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Levels of the independent variables considered in the Box–Behnken design.  
Figure 2: (**A**) Pareto Chart of standardized effects. (**B**) Behavior of the model variables.  
A second-order polynomial equation was used to express the response surface:  
\[Y=\beta_{0}+\sum_{i=1}^{k}\beta_{i}x_{i}+\sum_{i=1}^{k}\beta_{ii}x_{i}^{2}+\sum_ {i=1}\sum_{<j=1}\beta_{ij}x_{i}x_{j}+\varepsilon \tag{1}\]  
where \(Y\) represents the total monomeric anthocyanin concentration of the kurugua peel extracts; \(x_{k}\) are the independent variables; \(k\) is the number of independent variables; \(\beta_{0},~{}\beta_{i},~{}\beta_{ii},\) and \(\beta_{ij}\) are the regression coefficients for intercept, linear, quadratic, and the interaction terms, respectively; and \(\varepsilon\) is the error [17].  
Table 5 details the conditions and results obtained by the Box-Behnken design; the content of total monomeric anthocyanins was found to range from 18.929 to 56.019 mg C3G/100 g DW. The maximum content obtained was obtained under the following conditions: 60% ethanol concentration, pH 4.75, and the liquid-solid ratio of 80 mL/g.  
The Pareto chart (Figure 3) and the ANOVA of this design (shown in Table S2 of the Supplementary Material) showed that the L-S ratio is the variable with the greatest significance on the extraction process, followed by the quadratic influence of the concentration and the interaction of the concentration. The model presented a coefficient of determination R\({}^{2}=91.65\%\) of the variance in the anthocyanin concentration and R\({}^{2}=83.29\%\), which  
Equation (2) expresses the regression of the model for the concentration of total monomeric anthocyanins (TMA) expressed in mg C3G/100 g DW. This equation predicts the TMA concentration and allows the response surface to be obtained, as shown in Figure 4.  
\[\begin{split} TMA=-394.883+6.646*Solvent\ concentration+22.475*pH+3.866*L-S\ ratio-0.262\\ *Solvent\ concentration*pH-0.022*Solvent\ concentration*L-S\ ratio-0.027\\ *Solvent\ concentration^{2}-0.014*L-S\ ratio^{2}\end{split} \tag{2}\]  
Figure 4A shows the response surface for the interaction between the solvent concentration and pH. As depicted, the concentration of anthocyanins extracted is favored with the increase in pH and the decrease in the concentration of the solvent.  
When running the response optimizer seeking to maximize the concentration of total monomeric anthocyanins, a predicted concentration of 61.9 mg C3G/100 g DW was obtained as a solution, under the conditions of solvent concentration equal to 60%, pH 6, and liquid-solid ratio equal to 80 mL/g. The contour plot is observed in Figure 4B. Therefore, ultrasound-assisted extraction was proposed under these conditions at 20 \({}^{\circ}\)C for 15 min for the characterization of the extract.