Response surface models fitting
The effects of three main variables on UAE of carotenoids from palm fronds was simultaneously investigated using a threefactor design with three levels for each factor (low [−], medium [0], and high [+]). The main aim of the optimization process was to maximize the UAE of βcarotene (Y_{1}), lutein (Y_{2}), and zeaxanthin (Y_{3}) concentrations in ethanolic extracts of OPF. In optimizing the UAE, the effect of three main independent variables namely ultrasonic temperature of 30–70°C, extraction time of 10–50 min, and solvent:sample ratio of 10:1–50:1 mL/g was simultaneously studied using threefactor (X_{1}, X_{2}, X_{3}), three levels for each factor (−1, 0, +1) (Table 1) to determine the responses (concentrations of βcarotene, lutein, and zeaxanthin), which resulted in 17 experiments. The data obtained in the Box–Behnken experiment were converted into secondorder polynomial equation with three independent variables and three responses (Y values) as described by equations (5)(7) for βcarotene, lutein, and zeaxanthin, respectively:
 (5)
 (6)
 (7)
Table 1. Observed and predicted values of carotenoid concentrations obtained by Box–Behnken experimentFactor  Codes  Levels 

Low (−1)  Medium (0)  High (+1) 

Temperature (°C)  X _{1}  30  50  70 
Time (min)  X _{2}  10  30  50 
Solvent:sample ratio  X _{3}  10  30  50 
Carotenoids concentration, μg/g DW 

Standard order  X _{1}  X _{2}  X _{3}  Observed value  Predicted value 

βcarotene  Lutein  Zeaxanthin  βcarotene  Lutein  Zeaxanthin 


1  30 (−1)  10 (−1)  30 (0)  12.99  212.97  24.29  13.55  219.33  24.77 
2  70 (+1)  10 (−1)  30 (0)  12.17  211.64  24.63  11.87  206.43  24.45 
3  30 (−1)  50 (+1)  30 (0)  16.14  244.78  28.82  16.44  249.99  29.00 
4  70 (+1)  50 (+1)  30 (0)  12.22  211.99  24.35  11.66  205.63  23.87 
5  30 (−1)  30 (0)  10 (−1)  17.95a  261.99b  29.99c  17.06  253.92  29.12 
6  70 (+1)  30 (0)  10 (−1)  13.32  225.11  25.67  13.29  228.60  25.45 
7  30 (−1)  30 (0)  50 (+1)  15.67  256.11  26.94  15.71  252.62  27.16 
8  70 (+1)  30 (0)  50 (0)  12.12a  212.61b  24.51c  13.02  220.68  25.38 
9  50 (0)  10 (−1)  10 (−1)  12.01  212.08  24.37  12.35  213.80  24.77 
10  50 (0)  50 (+1)  10 (−1)  13.74  225.97  25.89  14.34  228.83  26.59 
11  50 (0)  10 (−1)  50 (+1)  12.78  212.15  24.44  12.19  209.29  23.75 
12  50 (0)  50 (+1)  50 (+1)  13.21  225.83  25.98  12.88  224.12  25.58 
13  50 (0)  30 (0)  30 (0)  16.84  258.28  28.99  16.87  258.40  28.88 
14  50 (0)  30 (0)  30 (0)  16.87  257.77  28.76  16.87  258.40  28.88 
15  50 (0)  30 (0)  30 (0)  16.85  258.79  28.98  16.87  258.40  28.88 
16  50 (0)  30 (0)  30 (0)  16.88  258.97  28.88  16.87  258.40  28.88 
17  50 (0)  30 (0)  30 (0)  16.89  258.17  28.79  16.87  258.40  28.88 
The predicted and observed (experimental) values were close to each other (Table 1), making the models precisely adequate. By applying ANOVA for the three regression equations (5)(7), the models were found to be significant (P < 0.05), thus very useful in predicting the effects of the three different level factors on carotenoid concentrations for all the three responses (Table 2). However, for βcarotene and zeaxanthin, solventtosample ratio (X_{3}) as well as all the interaction parameters (X_{1}X_{2}, X_{1}X_{3}, X_{2}X_{3}) were insignificant (P > 0.05). All the interaction parameters for lutein were also insignificant (P > 0.05) and not the linearterm coefficients (X_{1}, X_{2}, X_{3}) and quadraticterm coefficients (X_{1}^{2}, X_{2}^{2}, X_{3}^{2}) (Table 2). The models also showed that the extraction temperatures were the most significant single parameter which influenced the sonication of OPF for all the considered carotenoids, followed by extraction times and solventtosample ratios. The predicted and observed coefficients of determination (R^{2}) values for the above regressions were close to each other (Table 2), indicating that the model adequately fits the real relationship between the parameters chosen in this study. The “fitness” of the models was studied using the lackoffit test (P > 0.05), which must be insignificant to show the suitability of the models to predict the variations correctly. The Pvalues of the lackoffit for the models are 0.0611, 0.0512, and 0.0506 for βcarotene, lutein, and zeaxanthin, respectively. The results again indicate that the effect of all the independent variables were major contributors to the carotenoid concentrations of OPF by UAE.
Table 2. Analysis of variance for response surface methodology quadratic model for carotenoid concentrations from ethanolic extracts of oil palm frondsCarotenoid  Source  Sum of squares  Degree of freedom  Mean squares  Fvalue  Pvalue 


βcarotene  Model  71.70  9  7.97  16.67  0.0006 
Sonication temperature X_{1}  20.87  1  20.87  43.65  0.0003 
Extraction time, X_{2}  3.59  1  3.59  7.51  0.0289 
Solvent:sample ratio, X_{3}  1.31  1  1.31  2.75  0.1415 
X _{1} ^{2}  2.89  1  2.89  6.04  0.0436 
X _{2} ^{2}  29.75  1  29.75  62.23  0.0001 
X _{3} ^{2}  6.82  1  6.82  14.27  0.0069 
X _{1} X _{2}  2.40  1  2.40  5.03  0.0599 
X _{1} X _{3}  0.29  1  0.29  0.61  0.4604 
X _{2} X _{3}  0.42  1  0.42  0.88  0.3784 
Residual  3.35  7  0.48   
Correlation total  75.04  16    
R ^{2}  0.9554     
Adjusted R^{2}  0.8981     
Adequate precision  10.174a     
Lutein  Model  7061.11  9  784.57  17.55  0.0005 
Sonication temperature X_{1}  1638.78  1  1638.78  36.65  0.0005 
Extraction time, X_{2}  445.96  1  445.96  9.97  0.0160 
Solvent:sample ratio, X_{3}  42.55  1  42.55  0.95  0.3618 
X _{1} ^{2}  344.99  1  344.99  7.72  0.0274 
X _{2} ^{2}  3540.87  1  3540.87  79.19  0.0001 
X _{3} ^{2}  454.47  1  454.47  10.16  0.0153 
X _{1} X _{2}  247.43  1  247.43  5.53  0.0500 
X _{1} X _{3}  10.96  1  10.96  0.25  0.6357 
X _{2} X _{3}  0.011  1  0.011  0.00024  09879 
Residual  312.98  7  44.71   
Correlation total   16    
R ^{2}  0.9576     
Adjusted R^{2}  0.9030     
Adequate precision  10.288a     
Zeaxanthin  Model  68.89  9  7.65  15.46  0.0008 
Sonication temperature X_{1}  14.80  1  14.80  29.88  0.0009 
Extraction time, X_{2}  6.68  1  6.68  13.49  0.0079 
Solvent:sample ratio, X_{3}  2.05  1  2.05  4.14  0.0813 
X _{1} ^{2}  3.22  1  3.22  6.51  0.0380 
X _{2} ^{2}  25.95  1  25.95  52.39  0.0002 
X _{3} ^{2}  6.34  1  6.34  12.81  0.0090 
X _{1} X _{2}  5.78  1  5.78  11.68  0.0112 
X _{1} X _{3}  0.89  1  0.89  1.80  0.2212 
X _{2} X _{3}  0.0001  1  0.0001  0.0002  0.9891 
Residual  3.47  7  0.50   
Correlation total  72.36  16    
R ^{2}  0.9521     
Adjusted R^{2}  0.8905     
Adequate precision  9.951a     
Taking the Fvalues (16.67, 17.55, and 15.46 for βcarotene, lutein, and zeaxanthin, respectively) into consideration, the models were significant (Table 2). The predicted residual sum of squares for all the models were 53.51, 4994.09, and 54.82 for βcarotene, lutein, and zeaxanthin, respectively, which implies that the models fit each point in the design. Coefficient of variation (CV) describes the extent to which the experimental data are dispersed and in the models developed in this study, CV values were 4.73, 2.83, and 2.63% for βcarotene, lutein, and zeaxanthin, respectively. Low values of the CV (between 1.54% and 9.55%) indicate good precision and reliability of the experiments (Khuri and Cornell 1996; Kuehl 2000; Ahmad et al. 2005); hence, the models are reliable and reproducible. Adequate precision is a measure of the range in predicted response relative to its associated error. It measures the signaltonoise ratio; thus, values of 4 and above are considered desirable (Mason et al. 2003). The adequate precision for all the models (10.174, 10.288, and 9.951 for βcarotene, lutein, and zeaxanthin, respectively) was desirable (Table 2).
Effects of extraction parameters on carotenoid concentrations
The experimental values compared with the predicted ones of carotenoids concentrations obtained with the different combinations of independent variables for βcarotene (12.12–17.95 μg/g DW and 11.66–17.06 μg/g DW, respectively), lutein (211.61–261.99 μg/g DW and 205.63–258.40 μg/g DW, respectively), and zeaxanthin (24.51–29.99 μg/g DW and 23.75–29.12 μg/g DW, respectively) were close to each other.
Extraction temperature is one of the important factors affecting the extraction of carotenoids from plant materials. At higher temperature (above 30.14°C) with UAE, a lower content of carotenoids are obtained as opposed to the conventional maceration, which releases carotenoids at high temperatures yet with minimal yield. However, carotenoid concentrations were found to decrease at elevated temperatures during the preliminary extraction for solvent selection. Pingret et al. (2012) have also reported the degradation of lipids at high ultrasonic temperatures. The concentration of βcarotene increased with increase in extraction temperature and extraction time until 30.14°C and 37.11 min, respectively, and then decreased significantly (P < 0.05) at temperatures between 40 and 70°C and extraction time from 30 to 50 min. However, there was no significant increase of βcarotene concentration in the solvent:sample ratio (Fig. 3a–c). Carotenoids are found to degrade at elevated temperatures (Gang and Zora 2001; MeléndezMartínez et al. 2007); thus, this study corresponds to the report by Gu et al. (2008) who also reported an optimum temperature of 30°C for carotenoid extraction. The optimum conditions for βcarotene extraction were determined to be 30.14°C, 37.11 min, and 23.18 mL/g for an optimal concentration of 17.95 μg/g DW.
Lutein and zeaxanthin followed almost the same trend as βcarotene. Temperatures above 30.00°C and 30.15°C led to decrease in concentration of lutein and zeaxanthin, respectively. Solventtosample ratio did not affect the lutein concentration significantly (P > 0.05), but was significantly affected with zeaxanthin concentration (P < 0.05). The optimal concentrations of lutein (261.99 μg/g DW) and zeaxanthin (29.99 μg/g DW) were obtained at 30.00°C, 39.07 min and 19.22 mL/g for lutein; and 30.15°C, 36.85 min and 22.74 mL/g for zeaxanthin. It is evident from this study that, generally, lutein, zeaxanthin, and βcarotene are optimally extracted at low temperatures (30.00–30.15°C), short extraction time (36.85–39.07 min), and low solventtosample ratio (19.22:1–23.18:1 mL/g). Extraction temperature was the most significant parameter (P < 0.001 for lutein and βcarotene; P < 0.005 for zeaxanthin) in the UAE of carotenoid from OPF.
Figures 4–6 represent the response surface plots (for βcarotene, lutein, and zeaxanthin, respectively), which explain the effects of the linear, quadratic, and interactive parameters on carotenoid extraction by UAE. The contour and 3D surface plots show the effects of two factors on the response at a time with the other factor kept at zero level.
Figures 4a–c, 5a–c, and 6a–c represent the effects of extraction temperature, extraction time, and their reciprocal interactions on the extraction of βcarotene, lutein, and zeaxanthin, respectively. An increase in carotenoid concentration was observed with the increase of extraction temperature and extraction time at first, but the carotenoid concentration started to decrease when the extraction temperature and extraction time went past a certain value. Extraction time exhibited an important effect on βcarotene concentration which was significant (P < 0.05), which was opposite to solventtosample ratio.
Verification of optimized parameters for carotenoid extraction
In order to validate the adequacy of the model equations (eqs. (3)(7)), additional experiments were carried out using the predicted optimized conditions (30°C, 37 min, and 22:1 mL/g for βcarotene; 30°C, 37 min, and 23:1 mL/g for lutein, and; 30°C, 39 min, and 20:1 mL/g for zeaxanthin) to verify the predicted values for βcarotene, lutein, and zeaxanthin. These conditions were used to run fresh experiments and the observed mean values (16.94 ± 0.07, 263.22 ± 3.23, and 31.84 ± 0.27 μg/g DW for βcarotene, lutein, and zeaxanthin, respectively) obtained from these experiments validated the RSM model, which shows that the model was adequate for the extraction process. Predicted carotenoid concentrations obtained from the models were 17.95, 261.99, and 29.99 μg/g DW for βcarotene, lutein, and zeaxanthin, respectively. The good correlation between these results confirmed that the predicted responses for the models were adequate for reflecting the observed optimization; hence, the models are reproducible. This study shows that RSM is one of the suitable methods to optimize the operating conditions of sonication for extraction of carotenoids from ethanolic extracts of OPF in order to maximize their concentrations.