## 3 Results and Discussion
### Results of Ultrasound-Assisted Extraction
#### 3.2.1 UAE Extracts of Chicory and Fennel By-Products  
Regarding TPC, the following effects were significant (\(p<0.05\)): linear effects of'solid-water ratio' and 'treatment time'; interactive effects of'solid-water ratio'-temperature','solid-water ratio'-power', and 'temperature'-time'; quadratic effects of 'po wer'. Based on the \(F\) values, the major impacts on TPC were exerted by 'temperature'-time' interaction,'solid-water ratio', and 'time'. The TPC of chicory extract is described by Equation (4):  
\[TPC=+1.5710A-0.3426C+0.0003D^{2}-0.0241 AB-0.0044 AD+0.0087 BC \tag{4}\]  
where \(A\), solid-water ratio (g/100 mL); \(B\), temperature (\({}^{\circ}\)C); \(C\), time (min); \(D\), power (W). According to the equation, the TPC of the extracts increased mainly with the increase in the 'temperature'-time' interaction, and'solid-water ratio', while the increase in 'time' determined its reduction. To facilitate the graphic visualization of the effects of the inde pendent variables on the TPC, the application of RSM gave rise to six surfaces and related equations that plotted two independent variables at a time, keeping fixed the other two factors at the central value of the experimental design (Figure 1). Concerning the antioxidant activity, the following were significant effects (\(p<0.05\)): interactive effects of'solid-water ratio'-'temperature'; quadratic effects of'solid-water ratio' and 'temperature'. The extraction time did not exert significant effects. According to the \(F\) values, the major impacts on AA were exerted by both the quadratic 'temperature' term and the interactive'solid-water ratio'-'temperature' term. The AA of chicory extract is described by Equation (5):  
\[AA=0.0244+0.00009A^{2}+0.00001B^{2}-0.00008 AB \tag{5}\]  
where \(A\), solid-water ratio (g/10 mL); \(B\), temperature (\({}^{\circ}\)C). Figure 1: Three-dimensional response surface plots for TPC (mg gallic acid/g dm) of chicory extracts obtained through UAE: effect of solid–water ratio (A), temperature (B), extraction time (C), power (D), and their interactions. Based on the equation, the antioxidant activity mainly increased with 'temperature' and decreased as the'solid-water ratio'-'temperature' interaction increased. The corresponding six-response surfaces and equations are reported in Figure S1. Concerning fennel, statistically significant effects (\(p<0.05\)) on TPC were exerted by the linear term 'power' and the interactive term of'solid-water ratio'-'power'. Based on the \(F\) values, their impacts were similar. The interactions'solid-water ratio'-'time' and 'temperature'-'time' were not statistically significant. The TPC of fennel extract is described by Equation (6), while the response surfaces are shown in Figure S2. \[\text{TPC}=4.9733-0.0463\text{D}+0.0039\text{AD} \tag{6}\]  
where A, solid-water ratio (g/100 mL); D, power (W). According to Equation (6), the total phenolic content of fennel extracts decreased with the increasing values of 'power', and increased with the increase in the'solid-water ratio'-'power' interactive term. Concerning the antioxidant activity of fennel extracts, significant effects (\(p<0.05\)) were exerted by the linear and quadratic'solid-water ratio' term, the linear 'time' term and the interactive'solid-water ratio'-'time' term. The linear and quadratic 'power' terms were not statistically significant. According to the \(F\) values, the major impacts on AA were exerted by the quadratic'solid/water' term, followed by the linear'solid-water ratio' and 'time' terms and their interaction. The AA of fennel extract is described by Equation (7), which shows that the antioxidant activity increased with the increase in the quadratic'solid-water ratio' and the linear 'time' terms, and decreased with the increase in the linear'solid-water ratio' term and in the interaction between'solid-water ratio' and 'time'. The response surfaces obtained with the application of RSM are shown in Figure S3.