#### 2.2. Statistical Analysis and Model Fitting

To optimize the operating parameters, 30 random sequential experiments were performed under the designed UAE conditions based on the ranges of every single factor (independent variable) determined above to study the reciprocal influence of independent variables (i.e., solvent concentration, material-to-liquid ratio, extraction temperature and ultrasonic power) on the two dependent (response) variables (i.e., phenolic yield and its corresponding antioxidant activity). The experimental values, together with predicted values obtained by their response surface central composite design, are presented in

Table 1.

The final quadratic equation obtained in terms of actual factors upon applying multiple regression analysis to the experimental data is given below:

When the phenolic extraction efficiencies (

Y_{1}) were considered as the response:

When the antioxidant capacities (

Y_{2}) were considered as the response:

where,

X_{1},

X_{2},

X_{3},

X_{4},

Y_{1},

Y_{2} are the aqueous ethanol concentration, material-to-liquid ratio, extraction temperature, ultrasonic power, phenolic yield response and antioxidant activity response, respectively.

The linear effect of solvent concentration (X_{1}) was found to be significant for both response variables while X_{4} was only significant for phenol yield (Y_{1}), and X_{2} and X_{3} were only significant for antioxidant activity (Y_{2}). It can be concluded that solvent concentration was the vital parameter in both responses. However, the quadratic effect (X_{1}^{2}, X_{2}^{2}, X_{3}^{2}) was found to produce extremely significant (p < 0.01) positive effect on both Y_{1} and Y_{2}, but X_{4}^{2} was only significant for Y_{2}.

ANOVA results for multiple regression analysis and response surface quadratic model of

Y_{1} and

Y_{2} were evaluated using the corresponding

F and

p values (

Table 2).

F values of

Y_{1} and

Y_{2} were calculated to be 25.95 and 50.34, both leading to a

p value < 0.0001, suggesting that both the models were statistically extremely significant. The models’ coefficient of determination (

R^{2}) were 0.9604 and 0.9792, indicating that more than 96.04% and 97.92% of the response variability is explained, and supporting a good accuracy and ability of the established model within the range limits used [

47]. Correlation coefficients of 0.9800 and 0.9898 also indicate a good positive correlation between the actual data and the predicted values obtained using CCD. The

F-values of Lack of Fit of

Y_{1} and

Y_{2} were 0.6032 and 0.2015, respectively, implying that the Lack of Fit is not significant relative to the pure error, thus the model can be used to predict the phenol yield and corresponding antioxidant activity of ATL. In addition, Adj-

R^{2}, Pre-

R^{2} and the coefficient of variation (C.V.) were calculated to check the model’s adequacy. Pre-

R^{2} of

Y_{1} and

Y_{2} were 0.8341 and 0.8968, which were in reasonable agreement with their Adj-

R^{2} of 0.9233 and 0.9597, respectively (Adj-

R^{2} − Pre-

R^{2} < 0.2), indicating a high degree of correlation between the measured and predicted data from the regression model [

48]. The C.V. expressed the standard deviation as a percentage of the mean, and was found to be 1.5169% (<5.00%) for the phenolic yield, and 2.3491% (<5.00%) for antioxidant activity, implying that the models were reproducible [

24]. Adequate precision measures the signal to noise ratio, which is desirable when the value is larger than 4.

The ratios of 22.3775 and 28.1801 both referred an adequate signal and illustrated that the models (

Y_{1} and

Y_{2}) were applicative for the present UAE process [

49]. These correlation analyses between predicted values and actual data can be used to evaluate the suitability of the response surface model [

50]. Thus, the model can be used to predict the phenolic yield and corresponding antioxidant activity under various extraction conditions during UAE process. As shown in

Table 1, the levels of phenolic yield ranged from 5783.04 to 7591.30 mg GAE/100 g d.w., and the levels of antioxidant activity ranged from 42,030.84 to 73,849.78 μmol TE/100 g d.w. The highest levels of phenolic yield (7256.52 to 7587.83 mg GAE/100 g d.w.) and antioxidant activity (70,844.41 to 73,849.78 μmol TE /100 g d.w.) were obtained under the center point combinations of 70% ethanol, material-to-liquid ratio of 1:20 g/mL, 240 W, 50 °C, and 30 min. Moreover, the conditions involving a solvent concentration of 66.21%, material-to-liquid ratio of 1:15.31 g/mL, ultrasonic temperature 60 °C, power 267.30 W, and extraction time of 30 min were predicted to provide the highest phenolic yield, together with the highest antioxidant activity according to the fitted models. Ratios of DPPH activity/total phenols were calculated and we found that these ratios ranged between 7.29 and 9.91, which means the phenolic components extracted in all 30 runs were similar. Moreover, the ratios of six repetitions with the condition at the central point (9.60–9.91) were higher than those of the others, further indicating that the antioxidant activity of phenolics extracted under the condition represented by the central point was superior and the results of single factor experiments were reliable. Total phenols of the leaves collected in April optimized with UAE in the present study was lower than those (93.08 mg/g, i.e., 9308 mg/100 g) of fallen leaves reported by Cai et al. [

51] prepared with a microwave method. However, according to another study conducted by ourselves [

52],

Acer truncatum fallen leaves naturally possessed a much higher total phenols and radical scavenging activity than those collected in other seasons such as in April. Considering the difference in sampling seasons mentioned above, the data discrepancy between our two studies might be considered to be within a reasonable range.

To further verify the models obtained from RSM, ATL was extracted under the predicted optimal UAE conditions, and its phenolic yield and antioxidant ability were evaluated and compared to the predicted maximum yield. For operational convenience, the optimal parameters were modified slightly in the verification experiment as follows: solvent concentration 66.20%, material-to-liquid ratio 1:15.30 g/mL, ultrasonic power 270.00 W, temperature 60 °C, and extraction time 30 min. The predicted phenolic yield and antioxidant activity under the optimal conditions were 7589.19 mg GAE/100 g and 74,010 μmol TE/ 100 g, and the experimental values under the optimal conditions were 7579.56 ± 354.44 mg GAE/100 g and 73,585.78 ± 790.74 μmol TE/100 g, respectively. No significant differences were observed between predicted and experimental values (p > 0.05), indicating that the experimental results confirmed the adequate fitness of the predicted model.

#### 2.3. Effect of Interactions Among Variables on Phenolic Yield and Antioxidant Activity in ATL

To visualize the interactions of two operational parameters on extraction efficiency, the responses were generated as planar contour plots (

Figure 2). Two variables unshown in the Figures were kept constant at their respective central experimental values and the other two variables presented on the two horizontal axis varied within their experimental ranges in order to understand their main and interactive effects on the dependent variables.

Figure 2a–f show the results of interactive influence of solvent concentration, material-to-liquid ratio, extraction temperature, and ultrasonic power on phenolic yield, while

Figure 2g–h exhibit the impact of these variables on antioxidant activity.

Figure 2a–c, g–i show the phenols and antioxidant activities as responses of aqueous ethanol concentration (

X_{1}) and the other factors (

X_{2},

X_{3},

X_{4}). The extraction efficiencies first increased then decreased with increase of aqueous ethanol concentration from 50% to 90%, material-to-liquid ratio from 1:10 to 1:30 g/mL, ultrasonic power from 180 to 300 W, and extraction temperature from 30 to 70 °C.

The interaction of solvent concentration and material-to-liquid ratio (

X_{1}X_{2}) showed an extremely significant positive effect (

p < 0.001) on both responses (see

Table 2). At lower ethanol concentration with increasing material-to-liquid ratio, total phenols and antioxidant activity kept generally mild. However, the total phenols with antioxidant activity first increased, then decreased at lower material-to-liquid ratio with increasing ethanol concentration (

Figure 2a,g).

The possible interaction mechanism between solvent concentration and material-to-liquid ratio might be interpreted as that the positive interaction caused by appropriate solvent concentration and material-to-liquid ratio affected the polarity and viscosity of aqueous ethanol and solubility of target phenolic compounds in the extraction solvent, thus influenced the yield of phenols.

As shown in

Figure 2f,l, the interaction between sonication power and temperature (

X_{3}X_{4}) also showed a significant positive effect (

p < 0.05) on total phenols and antioxidant activity (

Figure 2f). The possible interaction mechanism between temperature and power may be the change of cavitation threshold affected by changing temperature, which is responsible for acoustic cavitation and also results in the formation of a cavitational nucleus. The influence of relatively greater forces ruptures and erupts the formed cavitational nucleus and disrupts the cell tissues during extraction, which in turn enhances the mass transfer rate [

38].

With respect to antioxidant activity (

Y_{2}), the interaction effect of solvent concentration and sonication power (

X_{1}X_{4}) was also found to be significant (

p < 0.05). According to the study of Hemwimol et al. [

43], only a small fraction of the electric energy from the ultrasound actually entered the extraction solvent in the ultrasonic bath system, and most of it was absorbed by the water in the bath. Under this circumstances, the rise of the solvent concentration might increase the utilization efficiency of the limited electric energy, thus playing a vital role in the improvement of the extraction yield.