# Physicochemical Properties and In Vivo Hepatoprotective Effect of Polysaccharides from Grape Pomace
## 3 Results and Discussion
### Response Surface Analysis  
Based on the findings of 17 random BBD test points, the encompassing design and experimental values are indicated in Table 2. The GPP extraction rate and projected response Y may be fitted to the following second-order polynomial equation using experimental data from multiple regression analysis:  
\[ \begin{split}\text{Y}=8.14+0.12\times\text{A}-0.071\times\text{B}- 0.039\times\text{C}-0.023\times\text{AB}-2.500\text{E}-003\times\text{AC}-0.05 5\times\text{BC}\\ -1.76\times\text{A}^{2}-0.46\times\text{B}^{2}-0.71\times\text{C} ^{2}\end{split} \]  
where Y is the extraction yield of GPPs (%); and A, B and C are the liquid-to-solid ratios, ultrasound power and extraction time, respectively. \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multicolumn{3}{c}{**Coded Factor Level**} \\ \cline{2-4}  & \(-\mathbf{1}\) & \(\mathbf{0}\) & \(\mathbf{1}\) \\ \hline Liquid–solid ratio (mL/g) (A) & 2 & 3 & 4 \\ Ultrasound power (W) (B) & 200 & 300 & 400 \\ Extraction time (min) (C) & 30 & 40 & 50 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Factors and level values of Box–Behnken. Figure 1: Single-factor experiment results and response surface plots showing the effects of interactions among different selected factors on the extraction yield of grape pomace polysaccharides (GPPs). (**A–C**) Effects of different liquid–solid ratio (**A**), ultrasound power (**B**) and extraction time (**C**) on the yield of GPPs in single-factor experiments. (**D–I**) Three- and two-dimensional plots showing the effects of liquid–solid ratio (**D**,**G**), ultrasound power (**E**,**H**) and extraction time (**F**,**I**) on extraction yield of GPPs, respectively. \begin{table}
\begin{tabular}{c c c c c} \hline
**Run** & \begin{tabular}{c} **Liquid–Solid** \\ **Ratio (A)** \\ \end{tabular} & \
\begin{tabular}{c} **Ultrasonic** \\ **Power (B)** \\ \end{tabular} &
\begin{tabular}{c} **Extraction Time** \\ **(C)** \\ \end{tabular} & \multirow{2}{*}{**Yield (\%)**} \\ \hline
1 & 0 & \(-1\) & \(-1\) & 7.02 \\
2 & \(-1\) & \(1\) & 0 & 5.77 \\
3 & 0 & \(-1\) & 1 & 7.1 \\
4 & 0 & 0 & 0 & 8.14 \\
5 & 0 & 0 & 0 & 8.17 \\
6 & \(-1\) & 0 & 1 & 5.5 \\
7 & 0 & 1 & 1 & 6.81 \\
8 & 1 & 0 & 1 & 5.72 \\
9 & 1 & \(-1\) & 0 & 6.11 \\
10 & \(-1\) & \(-1\) & 0 & 5.83 \\
11 & 0 & 0 & 0 & 8.13 \\
12 & \(-1\) & 0 & \(-1\) & 5.62 \\
13 & 1 & 0 & \(-1\) & 5.85 \\
14 & 0 & 0 & 0 & 8.08 \\
15 & 0 & 1 & \(-1\) & 6.95 \\
16 & 1 & 1 & 0 & 5.96 \\
17 & 0 & 0 & 0 & 8.2 \\ \hline \end{tabular}
\end{table} 
Table 2: Box–Behnken design (BBD) matrix of the three variables in coded units and response values for the extraction rate of GPPs. The ANOVA for this model is shown in Table 3. Lack of fit can be used to judge the validity of the model; as shown in Table 3, the lack-of-fit value of the mathematical model of 0.2766 was insignificant relative to the pure error. The high absolute F-value of 878.22 and the low \(p\)-value (\(p<0.0001\)) indicated a significant model. Moreover, the high R\({}^{2}\) score (R\({}^{2}\) = 0.9991) suggested that this model could be adequately explained by 99.91% of the variability and accuracy of the response. Additionally, R\({}^{2}\)A\({}_{\text{Adj}}\) was 0.9980, which implied that the model was highly correlated with the experimental data and the theoretical values of extraction yield of GPPs. There was a relatively low value of the coefficient of variation (C.V. = 0.70%), which reflected high reproducibility and reliability of the experimental values. In order to predict the relationship between independent variables and dependent variables, Design-Expert (version 8.0) software was used to establish the 3D response surface and contour maps as presented in Figure 1D-I. The interaction effects of liquid-to-solid ratio (A) and ultrasound power (B) are shown in Figure 1D,G, and the extraction yield increased with the increase in liquid-to-solid ratio and ultrasonic power.