## 3 Results and Discussion
The results imply that ultrasonic treatment is an effective process to obtain heat-labile components from natural sources with a lower temperature and shorter time than those of conventional methods. To validate the model of Equation (2), Table 4 compares the contents of C3G from experimental results with the predictive model, operated under the optimal conditions determined by ridge analysis \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Factor 1** & **DF 2** & **Sum of Squares** & **_F-Value_** \\ \hline \(X_{1}\) & 1 & 1.353 & 0.63 \\ \(X_{2}\) & 1 & 889.08 & 51.47 **3** \\ \(X_{3}\) & 1 & 3691.5 & 4.07 **3** \\ \hline \end{tabular} \({}^{1}\)\(X_{1}\), Process time (hr); \(X_{2}\), Temperature (\({}^{\circ}\)C); \(X_{3}\), Frequency (kHz). 2 DF: degree of freedom. 3* Significant at \(p<0.05\), ** Significant at \(p<0.001\).  
\end{table} 
Table 2: Results of analysis of variance for C3G contents in the extracts of aronia. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter 1** & **DF 2** & **Coefficient** & **_t-Value_** & **_p-Value_** \\ \hline
**Intercept** & 1 & \(-\)6.19705 & \(-\)0.922 & 0 \\ \(X_{1}\) & 1 & 0.94378 & 1.061 & 0.014 \\ \(X_{2}\) & 1 & 1.81871 & 2.272 & 0.005 \\ \(X_{3}\) & 1 & \(-\)0.12436 & \(-\)0.996 & 0.009 \\ \(X_{1}\)**-\(X_{1}\)** & 1 & \(-\)0.00673 & \(-\)0.058 & 0.001 \\ \(X_{2}\)**-\(X_{2}\)** & 1 & \(-\)0.04127 & \(-\)2.722 & 0.087 \\ \(X_{3}\)**-\(X_{3}\)** & 1 & \(-\)0.00083 & \(-\)1.602 & 0.370 \\ \(X_{1}\)**-\(X_{2}\)** & 1 & \(-\)0.09196 & \(-\)1.703 & 0.819 \\ \(X_{1}\)**-\(X_{3}\)** & 1 & 0.02641 & 1.982 & 0.126 \\ \(X_{2}\)**-\(X_{3}\)** & 1 & 0.00522 & 1.760 & 0.109 \\ \hline \hline \end{tabular} \({}^{1}\)\(X_{1}\), Process time (hr); \(X_{2}\), Temperature (\({}^{\circ}\)C); \(X_{3}\), Frequency (kHz). 2 DF: degree of freedom  
\end{table} 
Table 3: The results of estimating regression coefficients of the second order polynomials for C3G contents in the extracts. (Minittab release ver. 14.12.1, Minitab Inc., State College, PA, USA, 2015). The model estimated a concentration of 13.70 mg/g of C3G under optimal conditions, and from the experiment with those same conditions, 13.01 mg/g of C3G was obtained, which is within ca. 95% similarity. Therefore, this result clearly confirms that the proposed quadratic model was well designed. The amount of C3G from this optimal extraction condition was also the highest concentration obtained from aronia, as compared to the concentrations estimated in Table 1. This concentration was similar to or even higher than other reported data from various extraction conditions [6; 33]. Figure 3 compares the HPLC chromatograms of C3G in the extracts from the conventional juice extraction process and this optimized ultrasonic process. It was very clear that higher amounts of C3G were obtained from the optimal extraction process than from conventional juice extraction even though the minor tailing of the peaks of the standard C3G was observed in Figure 3a, which would not much affect the measurement of actual concentrations of C3G in the extracts. Therefore, it can be concluded that this optimized process can be employed to yield a high quality extract containing high amounts of intact C3G, which can possibly reduce the production costs of purifying C3G and increase the efficacy of the extract itself. To confirm this hypothesis, Figure 4 compares the antioxidant activities of the extracts from the two different processes. The activities were also compared with the data from adding 13 mg/mL of C3G alone as a positive control, whose concentration was equivalent to the amount of C3G present in 1.0 mg/mL of the extracts, based on the results of Table 4. In general, the higher the concentration of C3G used in the treatment, the better the antioxidant activity. Specifically, even at the same dose of 1.0 mg/mL, the extract from the optimal conditions had higher activity than that from a conventional juice extraction, 89.5% vs. 71.3%, respectively.