## 3 Results
### Model Fitting
There was a significant (\(p<0.05\)) interaction between MAE time and microwave power (X\({}_{1}\)X\({}_{2}\)). MAE times between 18 and 25 min combined with microwave power levels of 70-250 W tended to yield the highest extraction yield, achieving yields of over 18%, as shown in Figure 3a. The increase in microwave power, along with longer extraction time, led to a higher extraction yield. This phenomenon can be attributed to the enhanced mass transfer rate and solubility of phenolic compounds, resulting from the reduced surface tension and solvent viscosity. These effects improve sample wetting and facilitate better matrix penetration, respectively. At a microwave-assisted extraction (MAE) time of 18-25 min and a microwave power exceeding 250 W, the extraction yield decreases due to the degradation of certain polyphenol compounds [9]. TPC: The microwave power (X\({}_{2}\)), and solid-liquid ratio (X\({}_{3}\)) were significant (\(p<0.05\)). The quadratic effect (X\({}_{3}\)\({}^{2}\)) was also significant (\(p<0.05\)). The second-order polynomial equation of TPC is shown as Equation (5). \[\mathrm{Y_{2}=23.052+0.917X_{2}+1.108X_{3}-3.339X_{3}{}^{2}} \tag{5}\]  
The impacts of the MAE independent variables and their interactions on TPC are illustrated in the 3D response surface plots shown in Figure 3d-f. However, the interaction term is not significant for TPC. TFC: The microwave power (X\({}_{2}\)) and solid-liquid ratio (X\({}_{3}\)) were significant (\(p<0.05\)). The quadratic effect (X\({}_{2}\)\({}^{2}\) and X\({}_{3}\)\({}^{2}\)) was also significant (\(p<0.05\)). The second-order polynomial equation of TPC is shown as Equation (6). \[\mathrm{Y_{3}=13.342+0.901X_{2}-0.475X_{3}-0.956X_{2}{}^{2}-1.366X_{3}{}^{2}+ 0.444X_{1}X_{3}} \tag{6}\]  
There was a significant (\(p<0.05\)) interaction between the MAE time and the solid-liquid ratio (X\({}_{1}\)X\({}_{3}\)). The influence of the MAE independent variables and their interactions on TPC is depicted in the 3D response surface plots presented in Figure 3g-i. Using an extraction time of 5-11 min with a solid-liquid ratio of 1:60-1:210 g/mL or an extraction time of 20-25 min with a solid-liquid ratio of 1:110-1:250 g/mL is likely to maximize the total flavonoid content, exceeding 14 mg QE/g, as illustrated in Figure 3h. A solid-to-liquid ratio greater than 1:250 results in a decrease in TPC. In MAE, a higher solvent volume \begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**Source**} & \multicolumn{2}{c}{**Y\({}_{1}\)—Yield**} & \multicolumn{2}{c}{**Y\({}_{2}\)—TPC**} & \multicolumn{2}{c}{**Y\({}_{3}\)—TFC**} & \multicolumn{2}{c}{**Y\({}_{4}\)—IC\({}_{50}\)**} \\ \cline{2-9}  & \(\boldsymbol{F}\)**-Value** & \(\boldsymbol{p}\)**-Value** & \(\boldsymbol{F}\)**-Value** & \(\boldsymbol{p}\)**-Value** & \(\boldsymbol{F}\)**-Value** & \(\boldsymbol{p}\)**-Value** & \(\boldsymbol{F}\)**-Value** & \(\boldsymbol{p}\)**-Value** \\ \hline X\({}_{2}\) X\({}_{3}\) & 0.51 & 0.493 \({}^{\mathrm{NS}}\) & 1.65 & 0.228 \({}^{\mathrm{NS}}\) & 0.63 & 0.445 \({}^{\mathrm{NS}}\) & 5.65 & 0.039 \({}^{\mathrm{a}}\) \\ \hline Lack of Fit & 0.77 & 0.610 \({}^{\mathrm{NS}}\) & 1.63 & 0.511 \({}^{\mathrm{NS}}\) & 2.30 & 0.191 \({}^{\mathrm{NS}}\) & 2.18 & 0.363 \({}^{\mathrm{NS}}\) \\ \hline R\({}^{2}\) & 0.9497 & & 0.9494 & & 0.9199 & & 0.9570 \\ \hline Adj-R\({}^{2}\) & 0.9044 & & 0.9038 & & 0.8479 & & 0.9183 \\ \hline Pred-R\({}^{2}\) & 0.7752 & & 0.6009 & & 0.5181 & & 0.7673 \\ \hline \end{tabular} \({}^{\mathrm{a}}\)\(p<0.05\); \({}^{\mathrm{NS}}\) not significant.  
\end{table} 
Table 3: _Cont._can lead to lower recoveries because it reduces the solvent's ability to effectively extract flavonoids [24]. DPPH: The extraction time (X1), microwave power (X2), and solid-liquid ratio (X3) were significant (_p_ < 0.05). The quadratic effect (X12 and X22) was also significant.