## 3 Results and Discussion
### Microstructural Properties of R. typhina Fruits Using SEM Analysis
#### 3.2.2 UAE Optimization Using the Response Surface Design  
The significance of an independent variable effect on a response variable is given both by the probability value (\(p\)! 0.05) [70] and by the regression coefficients (Coef.) strongly different from zero [71]. The Coef. and \(p\)-values of the measured TAC, TPC, TFC, TTC, and carotenoids, and antioxidant activities of \(R\). _torphina_ fruit extracts at different UAE parameters (solvent concentration, solvent/solid ratio, extraction time) are presented in Table 6.  
Solvent concentration significantly influenced the content of anthocyanins (\(p\) = 0.018 *), tannins (\(p\) = 0.012 *), flavonoids (\(p\) = 0.014 *), and carotenoids (\(p\) = 0.006 ***), but not the content of total phenolics (\(p\)! 0.05). Antioxidant activity measured using FRAP and DPPH assays was not significantly affected by the variations of this factor (\(p\)! 0.05). Moreover, the square of solvent concentration had a more significant impact compared to the simple factor on anthocyanins (\(p\) = 0.003 *), tannins (\(p\) = 0.033 *), flavonoids (\(p\) = 0.006 **), and carotenoids (\(p\) = 0.002 **), but also had a marginally significant impact on the phenolic content (\(p\) = 0.082). The solvent/solid ratio showed the strongest effect on TPC (\(p\)! 0.001 ***), carotenoid content (\(p\) = 0.001), FRAP activity (\(p\)! 0.001), and DPPH capacity (\(p\)! 0.001 ***). Also, this factor had a marginally significant influence on the TTC (\(p\) = 0.083). Its squared value also had a decreased significance, influencing only the TPC (\(p\) = 0.048 *) and the carotenoid content (\(p\) = 0.005 **). TTC and the content of carotenoids were the only variables significantly influenced by the extraction time (\(p\) = 0.002 ** in both cases). However, the square of the time factor remained significant only for the carotenoid content (\(p\) = 0.048 *) but became marginally significant for TPC (\(p\) = 0.060). Figure 4: Boxplot representations of antioxidant activities of \(R\). _torphina_ fruit UAE extracts according to the solvent/solid ratio. Distinct letters (a, b) on top of the boxes indicate significant differences between values. The interaction between these factors significantly affected some of the responses. Thus, TAC and TPC were related to the interaction between solvent concentration and extraction time (\(p\) = 0.042 * and 0.035 *, respectively), while the interaction between solvent concentration and solvent/solid ratio affected only the TPC (\(p\) = 0.045 *). The content in carotenoids and the DPPH capacity were influenced by the interaction of extraction time and solvent/solid ratio (\(p\) = 0.012 *). The study by [PERSON] et al. (2010) [31] on the optimization of the phenolic content of an ethanolic extract of _R. typhina_ fruits, prepared using the maceration technique, showed that optimum values were obtained at a 15/1 solvent/solid ratio and decreased slightly at a 20/1 ratio. A variance analysis was conducted. The results of the models for response variables are indicated in Table 7.  
All models were significant (\(p\) < 0.05). R\({}^{2}\) and adjusted R\({}^{2}\) values higher than 0.8 suggest a valid model [71] with a significantly strong correlation between the predicted and the real responses [72]. Also, the low values of \(p\) (< 0.05) confirmed the significance of the models. The equation models for TAC (\(Y\)I), TPC (\(Y\)Z), TTC (\(Y\)3), TFC (\(Y\)4), Carotenoids (\(Y\)5), FRAP (\(Y\)6), and DPPH (\(Y\)7) were fitted as follows:  
\[Y \tag{3}\] \[Y\] (4) \[Y\] (5) \[Y\] (6) \[Y\] (7) \[Y\] (8) \[Y\] (9) Figure 4:0 (10) Figure 4:1 (11) Figure 4:2 (12) Figure 4:3  
Desirability values between 0 and 1 indicate how much the optimal values for factors are effective in achieving the results-related objectives [73]. In the present case, the individual desirability values indicate that the solvent concentration, extraction time, and solvent/solid ratio values are more effective for TPC and FRAP maximization (d = 0.9547 and 0.9220, respectively).