## 3 Results and Discussion
### Response Surface Methodology (RSM) Analysis for the TSPs and FLAs from Pigmented Corn Powder
In the case of a 1:1 s on/off pulse cycle, 100% ultrasound power for 4 min is required for the extraction of a high content of TSPs (Figure 2a), while for FLAs, 100% ultrasound power for at least 6 min is necessary for a high content of FLAs (Figure 2b). Nevertheless, with a 2:1 s on/off pulse cycle, the highest STP content can be achieved at 100% or 80% ultrasound power for 4 or 6 min extraction time, respectively (Figure 2c). In contrast, for FLAs, 80% of ultrasound power for 6 min is necessary (Figure 2d). On the other hand, under a 3:1 s on/off pulse cycle, 100% ultrasound power for 3 min is required for the extraction of a high content of TSPs (Figure 2e), while 80% ultrasound power for 6 min is needed for a high FLA content (Figure 2f). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Source**} & \multicolumn{2}{c}{**Total Soluble Phenols**} & \multirow{2}{*}{**Source**} & \multicolumn{2}{c}{**Total Flavonoids**} \\ \cline{2-2} \cline{4-6}  & \(\beta\)**-Coefficient** & \(p\)**-Value** & & \(\beta\)**-Coefficient** & \(p\)**-Value** \\ \hline Mean/Interc & 256.32 & \textless{}0.0001 \({}^{+}\) & Mean/Interc & 449.70 & \textless{}0.0001 \({}^{+}\) \\ \(X_{ET}\) & –81.21 & \textless{}0.0001 \({}^{+}\) & \(X_{ET}\) & –25.47 & \textless{}0.0001 \({}^{+}\) \\ \(X_{ET}{}^{2}\) & 10.55 & \textless{}0.0001 \({}^{+}\) & \(X_{ET}\)\({}^{2}\) & 3.88 & \textless{}0.0001 \({}^{+}\) \\ \(X_{PC}\) & 6.46 & 0.2133 \({}^{++}\) & \(X_{PC}\) & 18.85 & \textless{}0.0001 \({}^{+}\) \\ \(X_{PC}{}^{2}\) & –1.63 & 0.0975 \({}^{++}\) & \(X_{PC}\)\({}^{2}\) & –3.81 & 0.0851 \({}^{++}\) \\ \(X_{UP}\) & –3.73 & \textless{}0.0001 \({}^{+}\) & \(X_{UP}\)\({}^{-}\) & –9.35 & \textless{}0.0001 \({}^{+}\) \\ \(X_{UP}\)\({}^{2}\) & 0.01 & \textless{}0.0001 \({}^{+}\) & \(X_{UP}\)\({}^{2}\) & 0.049 & \textless{}0.0001 \({}^{+}\) \\ \(X_{ET}{}^{*}X_{PC}\) & 8.48 & \textless{}0.0001 \({}^{+}\) & \(X_{ET}{}^{*}X_{PC}\) & –0.54 & 0.4900 \({}^{++}\) \\ \(X_{ET}{}^{*}X_{PC}\) & –0.01 & 0.9419 \({}^{++}\) & \(X_{ET}{}^{*}X_{PC}\)\({}^{2}\) & 0.85 & \textless{}0.0001 \({}^{+}\) \\ \(X_{ET}{}^{*}X_{PC}\) & –0.56 & \textless{}0.0001 \({}^{+}\) & \(X_{ET}{}^{2*}X_{PC}\) & –4.13 & \textless{}0.0001 \({}^{+}\) \\ \(X_{ET}{}^{*}X_{UP}\) & 0.82 & \textless{}0.0001 \({}^{+}\) & \(X_{ET}{}^{*}X_{UP}\) & 0.28 & \textless{}0.0001 \({}^{+}\) \\ \(X_{ET}{}^{*}X_{UP}\) & –0.10 & \textless{}0.0001 \({}^{+}\) & \(X_{ET}{}^{2*}X_{UP}\) & –0.03 & \textless{}0.0001 \({}^{+}\) \\ \(X_{PC}{}^{*}X_{UP}\) & –0.10 & 0.0034 \({}^{+}\) & \(X_{PC}{}^{*}X_{UP}\) & –0.10 & \textless{}0.0001 \({}^{+}\) \\ \hline \hline \end{tabular} Extraction time (\(X_{ET}\)); pulse cycle (\(X_{PC}\)); ultrasonic power (\(X_{UP}\)); \({}^{+}\) significant (\(p\) < 0.01), \({}^{++}\) non-significant (\(p\) > 0.01).  
\end{table} 
Table 3: Regression coefficients for total soluble phenol and total flavonoid contents extracted by ultrasound from native Mexican pigmented corn kernel powder. Figure 2: Response surface plots and Pareto Chart indicating the effect of ultrasound-assisted extraction on the total soluble phenols (**a**,**c**,**c**,**e**,**g**) and total flavonoids (**b**,**d**,**f**,**h**) contents from native Mexican pigmented corn kernel powder at 1:1, 2:1, and 3:1 second on/off pulse cycle. Extraction time (\(X_{ET}\)); pulse cycle (\(X_{PC}\)); ultrasonic power (\(X_{UP}\)). Additionally, the Pareto Chart reveals the effect of independent variables in the polynomial equation on extracting TSPs (Figure 2f) and FLAs (Figure 2g) at a confidence level of 99%. The most important parameter during the UAE of TSPs was the interaction between extraction time and ultrasound power (\(X_{ET}\)2*\(X_{UP}\)). It has been reported that ultrasonic power significantly influenced the effectiveness of ultrasound extraction; the increase in released compounds is attributable to acoustic cavitation by increasing mass transfer [51]. However, the extraction time is an important parameter because long extraction times can promote the degradation of bioactive compounds.