## 3 Results and Discussion
### Set Point Identification  
The optimal values of control variables were determined by using a central composite face-centered (CCF) design; the two limits'max' and'min' of the three factors (\(T_{\text{min}}\), \(T_{\text{max}}\)), (\(n_{\text{min}}\), \(n_{\text{max}}\)), and (\(C_{\text{min}}\), \(C_{\text{max}}\)) are established in the previous section and are presented below.  
\[T_{\text{c}}=(T_{\text{min}}+\ T_{\text{max}})/2=\frac{25+75}{2}=50\ \text{\mu s} \tag{1}\]  
\[n_{\text{c}}=(n_{\text{min}}+n_{\text{max}})/2=\frac{200+400}{2}=300 \tag{2}\]  
\[C_{\text{c}}=(C_{\text{min}}+C_{\text{max}})/2=\frac{20+60}{2}=40\% \tag{3}\]  
The results of the CCF design experiments are presented in Table 1.  
MODDE 5.0 software (Umetrics, Stockholm, Sweden), that is a Windows programme dedicated to the experimental designs, was used [34]. The programme calculates mathematical model coefficients and identifies the best adjustments of the factors to optimise the response. Moreover, the programme estimates two important statistical criteria that determine whether the mathematical model is valid, symbolised as R\({}^{2}\) and Q\({}^{2}\). To validate a mathematical model, both criteria should be equal or very close to the unit.  
The mathematical models of the three responses, namely the extraction yield values of total phenol content, total flavonoid content, and condensed tannin content, were given by MODDE 5.0 and plotted, as shown in Figure 5. Because both criteria R\({}^{2}\) and Q\({}^{2}\) were very close to the unit, the three models were validated and therefore used for optimisation and prediction analyses.  
Figure 5: Coefficients of mathematical models plotted by MODDE. (**a**) Total phenols; (**b**) Total flavonoids; (**c**) Condensed tannins.  
According to the obtained mathematical models (Figure 5), the coefficients of the three factors had an almost similar effect on the amount of phenol and flavonoid extracted. The effect of pulse width was negative, whereas the effects of pulse number and ethanol concentration were positive. Therefore, the phenol and flavonoid amounts decreased with the pulse width and increased with both pulse number and ethanol concentration. These results remain valid only within the variation domain of each factor defined previously. As observed in the results, the disruption of cell membranes increased with an increase in the number of pulses. The increased electroporation of cell membranes leads to the transfer of intracellular components from the disrupted cells [35]. Submitting the plant tissues in the PEF increased cell wall permeability and thus the extraction of intercellular products. Low-energy PEF for a short period results in the electroporation of cell membranes with minimum deterioration of the quality of plant compounds extracted [36]. Electroporation of the cell membrane by PEF causes a high extraction yield of the phenolic compounds. When subjected to a PEF, a transmembrane electric voltage is thus created on the extremities of the cell membrane thereby causing the separation of molecules on the charge mass basis [37].  
On the other hand, for tannins, the coefficients associated with factors T and [C] were nonsignificant; tannins were indeed little influenced by PEF.