## 3 Results and Discussion
### Water Extraction Experiments and Response Surface Analysis  
#### 3.2.1 Water Extraction  
In Table 4 are listed the results obtained for the inulin extraction experiments from the dried RSW. It is observed that the maximum inulin content was obtained at the experimental conditions of the center point (75 \({}^{\circ}\)C and 75 min; runs No. 1, 6, 8, 11 and 13), with an average value of 44.72 mg glu eq/g artichoke (d.b.). On the contrary, the lowest inulin content was obtained at the lowest temperature, 54 \({}^{\circ}\)C. For TPC and Aox, average values for the central points were 10.54 mg GAE/g artichoke (d.b.) and 40.28 mM trolox/g artichoke (d.b. ), respectively. Maximum values of Aox are associated with the maximum TPC content. Table 5 shows the ANOVA results considering the quadratic model indicated in Equation (3). For inulin content, it is observed that for a confidence level of 95%, the only non-significant term is the combined term for time and temperature (Figure 1a). The response surface based on the quadratic model (Equation (4)) is shown in Figure 1b. This trend for inulin extraction is agreement with the results obtained by [PERSON] et al. [36], who reported that, initially, an increase in the extraction temperature facilitates the recovery of carbohydrates, but that overly high temperatures lead to a reduction in the extraction yield, likely due the hydrolysis of inulin [37]. This fact may explain the negative quadratic effect of temperature (Equation (4)). The optimum value of inulin content is 47.8 mg glu eq/g artichoke (d.b.) for the experimental conditions of 98.8 min and 79 \({}^{\circ}\)C. Fit results of the quadratic model are shown in Equation (4), which explains 96% of the total variability (r\({}^{2}\) = 96%; r\({}^{2}\)(adl) = 93%). \[\text{Inulin content }(\text{mg gluc eq/g }(\text{d.b.}))=-389.849+10.34\cdot\text{T}+0.597 1\cdot\text{t}-0.0672\cdot\text{T}^{2}+0.0028\cdot\text{T}\cdot\text{t}-0.004 1\cdot\text{t}^{2} \tag{4}\] \begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Run No.**} & **Inulin Content** & **Total Polyphenol Content, TPC** & **Antioxidant Activity, Aox** \\ \cline{2-4}  & **mg glu eq/g (d.b.)** & **mg GAE/g (d.b.)** & **mM trolox/g (d.b.)** \\ \hline
1 & 41.89 \(\pm\) 5.50 & 10.89 \(\pm\) 0.13 & 37.84 \(\pm\) 2.83 \\
2 & 11.03 \(\pm\) 1.47 & 13.18 \(\pm\) 0.97 & 48.33 \(\pm\) 0.89 \\
3 & 19.13 \(\pm\) 5.03 & 12.87 \(\pm\) 0.32 & 45.14 \(\pm\) 0.88 \\
4 & 1.60 \(\pm\) 0.35 & 10.17 \(\pm\) 0.23 & 39.17 \(\pm\) 1.56 \\
5 & 13.74 \(\pm\) 4.12 & 12.49 \(\pm\) 0.35 & 48.56 \(\pm\) 1.53 \\
6 & 42.99 \(\pm\) 5.37 & 10.22 \(\pm\) 0.23 & 37.31 \(\pm\) 1.08 \\
7 & 23.88 \(\pm\) 3.32 & 9.50 \(\pm\) 0.23 & 39.55 \(\pm\) 1.80 \\
8 & 42.00 \(\pm\) 3.51 & 10.30 \(\pm\) 0.23 & 37.97 \(\pm\) 1.07 \\
9 & 24.19 \(\pm\) 4.90 & 12.03 \(\pm\) 0.81 & 47.06 \(\pm\) 1.54 \\
10 & 39.44 \(\pm\) 5.25 & 11.16 \(\pm\) 0.40 & 47.30 \(\pm\) 2.39 \\
11 & 52.00 \(\pm\) 8.31 & 10.27 \(\pm\) 0.26 & 39.24 \(\pm\) 2.10 \\
12 & 37.69 \(\pm\) 5.31 & 11.66 \(\pm\) 0.67 & 46.54 \(\pm\) 2.40 \\
13 & 44.72 \(\pm\) 3.20 & 11.00 \(\pm\) 0.13 & 49.04 \(\pm\) 0.90 \\ \hline \end{tabular}
\end{table} 
Table 4: Results of water extraction experiments from dried RSW. For the total polyphenol content, the only significant terms are the lineal and quadratic time coefficients (\(p<0.95\)) (Table 5 and Figure 1c). The related response surface is shown in Figure 1d. It has been found that the optimized TPC in the studied ranges of time and temperature would be 14.18 mg acid gallic eq/g artichoke (d.b.) at 11 min and 54 \({}^{\circ}\)C. Fitted results are shown in Equation (5) and explain 81% of the total variability (r\({}^{2}\) = 81%; r\({}^{2}\)(adj) = 67.5%). \[\text{TPC (mg ac.gallic eq/g(d.b.))}=23.2465-0.2236\cdot\text{T}-0.1301\cdot \text{t}+0.0013\cdot\text{T}^{2}+0.0007\cdot\text{T}\cdot\text{t}+0.0004\cdot \text{t}^{2} \tag{5}\]  
The response surface for the antioxidant activity is shown in Figure 1f. The optimized Aox would be 54.5 mM trolox/g artichoke (d.b.)