## 3 Results and Discussion
### Model Fitting and Statistical Analysis
Therefore, increasing the temperature leads to an increase in the extraction yield. However, high temperature led to the decrease of surface tension and the increase of vapor pressure within micro bubbles, causing the damping of the ultrasonic wave. This tendency is in agreement with other reports in extracting polysaccharides [8; 33]. The ratio of water to raw material is one of the most important parameters from economical point of view. Generally, a larger ratio of water to raw material can dissolve target compounds more effectively. 3D response surface plot at varying ultrasonic power and ratio of water to raw material ratio at fixed sonication time (50 min) and extraction temperature (60 \({}^{\circ}\)C) is shown in Figure 1D. It can be seen that extraction yield of GPPP increased with increase of sonication power from 50 to 100 W, then did not further increase with increasing sonication power, and reached the maximum value when ratio of water to raw material at 30 mL/g, and beyond this level, extraction yield of GPPP was constant. Figure 1: Response surface plots showing the effects of independent variables on the extraction yield of GPPP: (**A**) Extraction yield vs. sonication time (min) and ultrasonic power (W); (**B**) Extraction yield vs. ratio (mL/g) and sonication time (min); (**C**) Extraction yield vs. ultrasonic power (W) and temperature (\({}^{\circ}\)C); (**D**) Extraction yield vs. ratio (mL/g) and ultrasonic power (W); (**E**) Extraction yield vs. temperature (\({}^{\circ}\)C) and sonication time (min); (**F**) Extraction yield vs. temperature (\({}^{\circ}\)C) and ratio (mL/g). The contact area between material and water increased with increasing ratio of water to raw material, fully dissolving the polysaccharide from the material and leading to higher diffusion, but distribution of ultrasonic energy density in the extraction solution decreased at a higher ratio (>30:1 mL/g), resulting in no obvious change in the extraction yield of polysaccharide from 30:1 to 40:1 mL/g. Moreover, it is pointed out that the distance of diffusion towards the interior tissues was prolonged at a high ratio of water to raw material [36]. The same tendency was also reported for polysaccharide extraction from mulberry leaves [36] and _Nephelium lapaceum_ L. fruit peel [13]. Figure 1E shows the 3D response surface plot at varying extraction temperatures and extraction times at fixed sonication power (100 W) and ratio of water to raw material (30 mL/g). The extraction yield of GPP increased within the extraction temperature from 40 to 60 \({}^{\circ}\)C, and the extraction yield also increased with the increase of the extraction time from 20 to 50 min, and beyond these levels did not further increase. Finally, a 3D response surface plot at varying extraction temperatures and ratios of water to raw material at fixed sonication power (100 min) and extraction time (50 min) is shown in Figure 1F. The result showed that extraction yield of GPPP increased with the increasing of extraction temperature from 40 to 60 \({}^{\circ}\)C, but beyond this level, extraction yield of GPPP was constant with the increase of extraction temperature. Furthermore, extraction yield of GPPP was also increased when the ratio of water to raw material was increased in the range from 20 to 30 mL/g. The result of numerical optimization showed that the optimized conditions were ultrasonic power of 135.34 W, extraction time of 48.61 min, ratio of water to raw material 33.6:1 mL/g and extraction temperature of 68.25 \({}^{\circ}\)C. Under these conditions, the maximum extraction yield predicted by the model was 7.20%. However, considering the operability in actual production, the optimal conditions can be modified as follows: ultrasonic power of 135 W, sonication time of 50 min, ratio of water to raw material of 30 mL/g and extraction temperature of 68 \({}^{\circ}\)C. Triplicate experiments at the modified optimal extraction conditions were carried out to compare the predicted results with the experimental value.