## 3 Results and Discussion
### Optimization of the Extraction Conditions  
Response surface methodology was employed to evaluate the combined effect of the four factors to maximize the extraction of the specific phenolic compounds under question, namely apigenin, caffeic acid, and luteolin. Figures 4-6 present the three-dimensional response surface plots that describe the interactive effect of the independent factors on the quantity of each studied phenolic that was extracted by UAE for the two more significant factors in each case. \begin{table}
\begin{tabular}{c c c} \hline
**Phenolic** & \multicolumn{2}{c}{**1 Predictive Equations**} \\ \hline Apigenin & (2) & Y\({}^{\lambda\lambda}=3.21-0.04X_{1}+0.01X_{3}-0.04X_{4}+0.0002\) X\({}_{1}^{2}+0.0004X_{2}^{2}+0.0008\) X\({}_{1}\)X\({}_{4}-0.0002\) X\({}_{3}\)X\({}_{4}\) \\ Caffeic acid & (3) & Y\({}^{\lambda\lambda\alpha}=1.02+0.04\) X\({}_{1}+0.01X_{2}+0.01X_{3}-0.11X_{4}+0.0001\) X\({}_{3}^{2}+0.0021\) X\({}_{4}^{2}-0.0005\) X\({}_{1}\)X\({}_{3}-0.0005\) X\({}_{2}\)X\({}_{4}\) \\ Luteolin & (4) & \((\gamma^{\lambda(1-1)})/(\lambda_{1}\times\mathrm{g}^{\ast(\lambda_{1}^{-1}-1)})=\) \\  & & \(9.80-0.34\) X\({}_{1}+0.08\) X\({}_{3}-0.19\) X\({}_{4}+0.0032\) X\({}_{1}^{2}+0.0048\) X\({}_{2}\)X\({}_{4}\) \\ \hline \end{tabular}  
* 1: Apigenin, caffeic acid, and luteolin are predicted in ug/g of dried parsley. \(\lambda_{\mathrm{a}}=0.38\); \(\lambda_{\mathrm{a}}=0.43\); \(\lambda_{\mathrm{t}}=2.89\); \(\mathrm{g}=17.59\) is the geometric mean of luteolin in ug/g DM. \(X_{\mathrm{t}}\): Temperature (T) in \({}^{\circ}\)C, X\({}_{2}\): Time in min, \(\chi_{3}\): ratio of solvent to dry parsley (LS ratio) in mL/g, X\({}_{4}\): Ethanol concentration (%, \(v/v\)).  
\end{table} 
Table 4: Quadratic models of polynomial predictive equations of response surface for apigenin, caffeic acid, and luteolin UAE from parsley. Figure 4: 3D response surface plot of the apigenin (response variable) in ug/g of dry matter (DM) of parsley as a function of Temperature (X\({}_{1}\)) in Celsius degrees (\({}^{\circ}\)C) and ratio of solvent to dry parsley (LSr) in mL/g while holding ethanol at 0% (\(v/v\)). Response surface methodology holds an important role in the exploration of the optimum conditions of independent variables that can contribute in order to achieve a maximum response [30; 31]. Response surface plots are useful for establishing the response values and operation conditions as required. They can also provide a method to visualize the results and help in processing the experimental levels of each variable and the types of interactions between them [32]. The 3D response surface plot in Figure 4 shows that extraction of apigenin is favored in high values of solvent to dry parsley ratio (LSr; \(X_{3}\)) and low values of temperature (T; \(X_{1}\)). Figure 5: 3D response surface plot of the caffeic acid (response variable) in \(\upmu\)g/g of dry matter (DM) of parsley as a function of Temperature (\(X_{1}\)) in Celsius degrees (\({}^{\circ}\)C) and ethanol concentration in \(\%\,v/v\) while holding time at 35 min and ratio of solvent to dry parsley (LSr) at 100. Figure 6: 3D response surface plot of luteolin (response variable) in \(\upmu\)g/g of dry matter (DM) of parsley as a function of Temperature (\(X_{1}\)) in Celsius degrees (\({}^{\circ}\)C) and ratio of solvent to dry parsley (LSr) in ml/g while holding ethanol at 0% (\(v/v\)). During the extraction of caffeic acid, as shown in Figure 5, high values of ratio of solvent to dry parley (LSr; X3) exert a positive effect while high values of temperature (T; X1) show a negative effect. Through the 3D response surface plot, Figure 6 indicates that higher luteolin extractability is achieved with high values of ratio of solvent to dry parley (LSr; X3) and low values of temperature (T; X1). Based on the experimental results of the luteolin, caffeic acid, and apigenin extracted amounts shown in Table 2, specific combination of the four factors lead to maximum extraction of the three studied phenolics.