## 3 Results and Discussion  
Table 1 shows the results for estimating the content of C3G (Y) for each experiment under the various extraction conditions as independent variables (\(X_{1}\), \(X_{2}\), and \(X_{3}\)), as designed by the CCD. In general, the amount of C3G in the extracts was increased the most by an increase in the ultrasonic frequency, followed by an increase in the process time, while the yield of C3G was sharply decreased as the temperature was increased. This result confirmed the susceptibility of C3G to heat, with serious destruction occurring at 35 \({}^{\circ}\)C. The highest C3G content, 12.88 mg/g, was obtained from the extraction at 60 kHz and 20 \({}^{\circ}\)C for 5 h, and this value was much higher than the 10.01 mg/g C3G in the juice extract powder reportedly obtained from a conventional method of processing aronia [11; 13; 31]. Similarly, the concentration of C3G in the extract from the optimized process was also found to be higher than 3.0-10.5 mg/g from other extraction processes with water or 70% ethanol, even though  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & \multicolumn{2}{c}{**Level**} & & & & \\ \cline{2-7}  & \(\mathbf{\mathrm{-2}}\) & \(\mathbf{\mathrm{-1}}\) & \(\mathbf{\mathrm{0}}\) & \(\mathbf{\mathrm{1}}\) & \(\mathbf{\mathrm{2}}\) \\ \hline
**Extraction Time \(\mathbf{X_{1}}\) (h)** & 2 & 3 & 4 & 5 & 6 \\
**Temperature \(\mathbf{X_{2}}\) (\({}^{\circ}\)C)** & **15** & **20** & **25** & **30** & **35** \\
**Frequency \(\mathbf{X_{3}}\) (kHz)** & **20** & **40** & **60** & **80** & **100** \\ \hline \hline \multirow{2}{*}{**Variables**} & \multicolumn{4}{c}{**Coded Variables**} & \multicolumn{4}{c}{**Uncoded Variables**} \\ \cline{2-7}  & \(\mathbf{X_{1}}\) & \(\mathbf{X_{2}}\) & \(\mathbf{X_{3}}\) & \(\mathbf{X_{1}}\) & \(\mathbf{X_{2}}\) & \(\mathbf{X_{3}}\) & \(\mathbf{Y}\) (mg/g) \\ \hline
**1** & 1 & 1 & 0 & 5 & 20 & 60 & 12.88 \(\pm\) 1.07 \\
**2** & 1  
some of the results showed exceptionally high concentrations of above 15 mg/g in their extracts, values of which were not often reproducible [32]. This result strongly implies that the ultrasonic extraction is an effective process for extracting C3G from aronia at low temperatures, and this optimized process can yield high amounts of intact C3G. Tables 2 and 3 show the results of the ANOVA and the RSM model, resulting in the following quadratic Equation (2). \[ \begin{array}{c}Y=-6.19705+0.94378X_{1}+1.81871X_{2}-0.12436X_{3}-0.00673{X_{1 }}^{2}-0.04127{X_{2}}^{2}-\\ 0.00083{X_{3}}^{2}-0.09196X_{1}X_{2}+0.02641X_{1}X_{3}+0.00522X_{2}X_{3}\end{array}  \tag{2}\]  
where the regression coefficient (R\({}^{2}\)) of this quadratic model was estimated as 0.956, which tells us this model was a good fit. The linear, quadratic, and total model regressions were also highly significant (\(p<0.05\)), except for the cross-products, such as \(X_{1}X_{2}\) (\(p<0.01\)), \(X_{1}X_{3}\) (\(p<0.01\)), and \(X_{2}X_{3}\) (\(p<0.05\)). Figure 2 also illustrates the three-dimensional response surfaces and contour plots for the C3G contents as a function of the three variables ultrasonic frequency, process temperature, and extraction time. The saddle point of each plot well represented the optimal conditions that can obtain the highest concentration of C3G in the extract, considering each of two processes. As shown in Table 1, the amount of C3G in the extracts was most significantly increased by an increase in the frequency in the range of 20 to 60 kHz, but the extraction was not much more effective at frequencies above 80 kHz. The contents of C3G were also increased as the process time increased from 3 to 6 h, which shows that longer process times can be helpful to increase the yield of C3G. However, the concentrations of C3G in the extracts were significantly decreased by an increase in the temperature from 30 to 35 \({}^{\circ}\)C. This result could have been due to the breakdown of C3G in the extracts at higher temperatures, as similar results have been reported elsewhere [11; 14].