## 3 Results and Discussion
### Model Fitting and Statistical Analysis
Analysis of Response Surfaces, Optimization of Extraction Parameters and Validation of the Predictive Model  
Three-dimensional (3D) response surface plots were generated to visualize the effects of experimental levels of each variable on the response, the type of interactions between of two independent variables, and to determine the optimum level of each independent variables for maximum extraction yield of GPPP. In each plot, the interaction of two independent variables was investigated simultaneously, while the others were fixed constant at zero level. The 3D response surface plots were presented in Figure 1A-F.  
Ultrasonic power is one of the most important parameters affecting the extraction yield of polysaccharide and cost of the process especially at industrial scale. The extraction yield of GPPP as a function of sonication time and ultrasonic power at fixed extraction temperature (60 \({}^{\circ}\)C) and ratio of water to raw material (30 mL/g) is given in Figure 1A. It can be seen that extraction yield of GPPP increased with increasing sonication time up to 35 min, and the extraction yield of GPPP was also found to increase with the increase of ultrasonic power up to 100 W. The higher extraction yield at high sonication power could be attributed to different mechanisms such as the creation and collapse of more bubbles resulting in swelling of the materials, solvent uptake and enlargement of the pores in the materials and washing out of cell content due to generation of strong liquid microjets and acoustic streaming rupturing the cells [33; 34]. The extraction yield was no longer changed when the ultrasound power exceeded 100 W. These results could be attributed to the intensive cavitation, turbulence shear, and instantaneous high pressure drop involved in processing. With the increase in ultrasonic intensity and treatment time, the ultrasonic energy was sufficient to break down the strong bonds, such as glycosidic linkages, connecting the sugar units. It was pointed out that intense ultrasonic power would result in degradation and decomposition of the polysaccharide [35; 36]. This result was in accordance with other reports for polysaccharide extraction from various raw materials [8; 33; 37]. Generally, a long extraction time favored polysaccharide production. On the other hand, long extraction time may induce decomposing and structural destruction of polysaccharides [37]. The extraction yield of GPPP at varying sonication times and ratios of water to raw material at fixed extraction temperature (60 \({}^{\circ}\)C) and ultrasonic power (100 W) is shown in Figure 1B. It is obvious that the extraction yield of GPPP increased within the ratio of water to raw material up to 35 mL/g and the extraction yield increased with the increase of the extraction time up to 60 min. Ultrasonic waves facilitated the release of polysaccharides through ruptured cells at the early period of extraction. The current finding seems to be consistent with other researches [8; 33; 38]. Usually, in the solid-liquid extraction process, the higher temperature could enhance the recovery of target compounds from raw materials. However, the degradation reaction was also reported. The 3D response surface plot at varying extraction temperature and ultrasonic power at fixed sonication time (50 min) and ratio of water to raw material (30 mL/g) is shown in Figure 1C. The extraction yield of GPPP increased with increasing the extraction temperature up to 65 \({}^{\circ}\)C, and no further changes were observed beyond the temperature of 70 \({}^{\circ}\)C while the extraction yield of GPPP increased with the increase of the ultrasonic power to 100 W. It was pointed out that the solvent viscosity decreases and the cavitation and vapor pressure of solvent increases within the tissue with increasing temperature (up to 65 \({}^{\circ}\)C) so that the area of contact between the particles and solvent is maximized [39]. Moreover, the mass transfer increased with increasing extraction temperature due to the increase of the polysaccharide solubility [40].