## 3 Results and Discussion  
The contents of chlorophyll a (Y) for each experiment were estimated under the various extraction conditions designed by the CCD (Table 1). In general, the amounts of chlorophyll a were increased the most by an increase in the frequency, followed by the process time; however, there was not much effect for an increase in the extraction temperature, possibly due to the destruction of the chlorophyll at higher temperatures. The highest chlorophyll a content, 18.09 (mg/g), was obtained for the extraction at 40 kHz and 40 \({}^{\circ}\)C for 4 h, and this value was much higher than 13.81 (mg/g) from a most conventional extraction process such as 70% ethanol at 80 \({}^{\circ}\)C for 24 h (data not shown). This concentration was also found to be higher than those reported from conventional extractions from _Spirulina_ and even other plants [26; 27]. This result strongly implies that the optimized ultrasonification extraction is an effective process for extracting chlorophyll a from natural resources, and the optimized conditions of this method can be expected to yield high amounts of intact chlorophyll. Tables 2 and 3 show the results of the ANOVA analysis and the RSM model, using the following equation:  
\[ \begin{split} Y=13.749+0.8014X_{1}+0.1448X_{2}+0.0041X_{3}-0.0653{ X_{1}}^{2}-0.0023{X_{2}}^{2}-0.0001{X_{3}}^{2}\\ +0.0001X_{1}X_{2}-0.0048X_{1}X_{3}+0.0004X_{2}X_{3},\end{split}  \tag{2}\]  
where, the regression coefficient (R2) was 0.969, which indicates that this model is a good fit. The linear, quadratic and total model regressions were also highly significant (\(p<0.001\)), 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 1 also illustrates the three-dimensional response surfaces and contour plots for the chlorophyll a contents as a function of ultrasonic frequency, temperature and extraction time. As already demonstrated in Table 1, the amount of chlorophyll a in the extracts was most significantly increased with an increase in the frequency in the range of 20 to 40 kHz, and chlorophyll a also increased with an increase in the process time from 3 to 5 h, while chlorophyll a was less significantly increased with the increase of the temperature from 30 to 40 \({}^{\circ}\)C. This could be caused by the breakdown of the chlorophylls in _Spirulina_ at higher temperatures since chlorophylls are known to be heat sensitive and similar data were also reported [28]. In contrast, the results clearly proved that ultrasonification is very effective in extracting heat labile components, requiring a lower process temperature and shorter process time. Similar results were also found elsewhere [28; 29]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Factor 1** & **DF 2** & **Sum of Squares** & **F-Value** \\ \hline X\({}_{1}\) & 4 & 0.323 & 0.15 \\ X\({}_{2}\) & 4 & 7.6606 & 45.96 ***,3 \\ X\({}_{3}\) & 4 & 0.055 & 0.02 * \\ \hline \end{tabular} \({}^{1}\) X\({}_{1}\): Process time (h), X\({}_{2}\): Temperature (\({}^{\circ}\)C), X\({}_{3}\): Frequency (kHz); 2 DF: degrees of freedom; 3.* Significant at \(p<0.05\), *** Significant at \(p<0.001\).  
\end{table} 
Table 2: Analysis of variance for chlorophyll a contents in the extracts of marine _Spirulina maxima_. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter 1** & **DF 2** & **Coefficient** & **_t-Value_** & **_p-Value_** \\ \hline Intercept & 1 & 13.749 & 8.348 & 0 \\ X\({}_{1}\) & 1 & 0.8014 & 2.087 & 0.063 \\ X\({}_{2}\) & 1 & 0.1448 & 3.603 & 0.005 \\ X\({}_{3}\) & 1 & 0.0041 & 0.215 & 0.834 \\ X\({}_{1}\) X\({}_{1}\) & 1 & \(-\)0.0653 & \(-\)2.045 & 0.068 To evaluate the predictive model, Table 4 shows the results of the determination of an optimal extraction condition by the ridge analysis (Minitab release 14.12.1, Minitab Inc., State College, PA, USA, 2004) compared with the values from the model with the experimental data.