## 3 Results and Discussion
### Optimization of MAE Extraction Conditions
#### 3.2.1 Optimization of Extraction Conditions for the Content of Total Compounds
This could be because prolonging the exposure to the extraction microwave could lead to degradation of the compounds with overheating of the solvent [42]. A Box-Behnken design was used to maximize the content of these compounds with the capacity to activate the AMPK pathway. Table 4 includes the results of the ANOVA test of the regression model for the response variable (total AMPK bioactive compounds). The results indicated that the value of the regression coefficient (R\({}^{2}\)) was 98.47%. This value justified a considerable part of the variance within data. Lack of fit for this model has a \(p\)-value greater than 0.05 (\(p\) = 0.3957). Therefore, the model seems to be adequate for the data observed at the 95.0% confidence level. The obtained parameters of ANOVA confirmed that this model provides a suitable approach to the experimental conditions. Temperature (X\({}_{1}\)) (\(p\) = 0.0091), quadratic of temperature (X\({}_{11}\)) (\(p\) = 0.0038) and the quadratic of time (X\({}_{33}\)) (\(p\) = 0.0104) were the significant variables (\(p\) \(\leq\) 0.05). In Figure 3, the surface response plots show the effect of temperature with % EtOH (a), temperature with time (b), and % EtOH with time (c) on total AMPK bioactive compounds. The significant effect of temperature on the content of total AMPK bioactive compounds can be observed, with the maximum value appearing at 90-130 \({}^{\circ}\)C, after which this response decreases (Figure 3a). Figure 3b shows that the maximum content of total AMPK bioactive compounds is in the range of 100-130 \({}^{\circ}\)C and 20-30 min. Figure 3c shows that the maximum value of this response was obtained in the range of 15-30 min, after which it decreases, whereas the % EtOH did not has a significant effect on this response. This is because high temperatures of 100-130 \({}^{\circ}\)C increase the solubility of these compounds so they have a similar solubility in different ethanol compositions, while an extraction time higher than 20-30 min results in a decrease in content. This is probably because these compounds were degraded due to thermal degradation after a prolonged period of microwave radiation [43]. \begin{table}
\begin{tabular}{c c c c c c} \hline \multicolumn{6}{c}{**Total AMPK Bioactive Compounds**} \\ \hline
**Source** & **SS** & **DF** & **MS** & **F-Value** & \(p\)**-Value** \\ \hline X\({}_{1}\) & 15.41 & 1 & 15.41 & 108.22 & 0.0091 \({}^{*}\) \\ X\({}_{2}\) & 0.40 & 1 & 0.40 & 2.79 & 0.2366 \\ X\({}_{3}\) & 0.16 & 1 & 0.16 & 1.11 & 0.4033 \\ X\({}_{11}\) & 37.2 & 1 & 37.2 & 261.32 & 0.0038 \({}^{*}\) \\ X\({}_{12}\) & 0.75 & 1 & 0.75 & 5.25 & 0.1490 \\ X\({}_{13}\) & 0.07 & 1 & 0.07 & 0.48 & 0.5612 \\ X\({}_{22}\) & 0.29 & 1 & 0.29 & 2.06 & 0.2874 \\ X\({}_{23}\) & 0.10 & 1 & 0.10 & 0.70 & 0.4922 \\ X\({}_{33}\) & 13.50 & 1 & 13.50 & 94.82 & 0.0104 \({}^{*}\) \\ Lack of fit & 0.71 & 3 & 0.24 & 1.67 & 0.3957 \\ Pure error & 0.28 & 2 & 0.14 & & \\ Total (corr.) & 65.46 & 14 & & & \\ R\({}^{2}\) & 98.47 & & & & \\ Adj R\({}^{2}\) & 95.73 & & & & \\ \hline \end{tabular} \(X_{1}\): temperature, X\({}_{2}\): % EtOH, X\({}_{3}\): Time, SS: Sum of squares, DF: Degree of freedom, MS: Mean square, R\({}^{2}\): Quadratic correlation coefficient; Adj R\({}^{2}\): Quadratic correlation coefficient adjusted, \({}^{*}\) Significant (\(p\) < 0.05).  
\end{table} 
Table 4: ANOVA test for the response variable of total AMPK bioactive compounds. The fitted equation of the model for total AMPK bioactive compounds (Equation (2) includes the significant effects of temperature (\(X_{1}\)), quadratic of temperature (\(X_{11}\)) and quadratic of time (\(X_{33}\)). The model also considers the linear effect of time (\(X_{3}\)). Total AMPK bioactive compounds = \(-9.84797+0.280015X_{1}+0.285851X_{3}-0.00126127X_{11}-0.00617407X_{33}\)  
Considering the equation to explain the model for total AMPK bioactive compounds behavior and understanding the influence of each independent variable, an optimization of conditions to obtain the highest content of these compounds was proposed.