## 3 Results and Discussion  
### Optimisation of the Extraction Performance  
The process implemented was designed to appraise the effect of three crucial extraction variables, \(C_{\text{CD}}\), R\({}_{\text{I/S}}\), and pH, and to identify possible synergistic functions between them. Evaluation of the fitted model and the suitability of response surface were based on the ANOVA and lack-of-fit test (Table 2), by considering the closeness of the predicted and measured values (Table 3). The second-degree polynomial equations (mathematical models), considering only the significant terms, are presented in Table 4, along with the square correlations coefficients (R\({}^{2}\)) of the models, which are indicators of the total variability around the mean determined by the model. Because all total R\({}^{2}\) of the models were equal or higher than 0.97, and the \(p\)-value for lack of fit (assuming a confidence interval of 95%) was highly significant for all models, it can be argued that equations exhibited excellent fit to the experimental data. The contour plots constructed on the basis of the models, which are presented on a comparative arrangement in Figure 2, provide an at-a-glance image of how the experimental variables affected response (Y\({}_{\text{TP}}\)), but also illustrate the differences between the three CDs used. For the extraction with \(\beta\)-CD, \(C_{\text{CD}}\) was found to exert a non-significant effect, suggesting that any shift in \(C_{\text{CD}}\) within the range tested cannot impact Y\({}_{\text{TP}}\). The same was observed for HP-\(\beta\)-CD, but for m-\(\beta\)-CD, this variable was highly significant (\(p\) = 0.0047). This outcome strongly indicated that the nature of the CD used may play a key role in extraction. On the other hand, no cross term between m-\(\beta\)-CD concentration and either R\({}_{\text{I/S}}\) or pH was significant, showing that combined effects did not occur. Contrary to those, for the extractions performed with any CD, both R\({}_{\text{I/S}}\) and pH were significant. Quadratic effects of these variables were also significant for the extractions with \(\beta\)-CD and m-\(\beta\)-CD, but for HP-\(\beta\)-CD, a significant quadratic effect was seen only for pH. Moreover, for HP-\(\beta\)-CD and m-\(\beta\)-CD, cross terms of R\({}_{\text{I/S}}\) and pH were significant too, demonstrating that combinations of these two variables may have either a negative (HP-\(\beta\)-CD) or positive (m-\(\beta\)-CD) influence on the extraction yield. The desirability function (Figure 3) enabled the estimation of the optimal predicted response for each CD tested (Table 5). The Y\({}_{\text{TP}}\) achieved with HP-\(\beta\)-CD and m-\(\beta\)-CD were identical and significantly higher than that obtained with \(\beta\)-CD (\(p\) < 0.05). This finding highlighted the prominent role of the nature of the CD used for the extraction. In support of this are pertinent results on the extraction of olive pomace polyphenols, where HP-\(\beta\)-CD exhibited superior extraction capacity compared with either m-\(\beta\)-CD or \(\gamma\)-CD [11]. Data on polyphenol extraction from pomegranate fruit were in the same line [12], stressing the superiority of HP-\(\beta\)-CD against \(\beta\)-CD as a polyphenol extraction booster. In opposition, anthocyanin extraction was more efficient with \(\beta\)-CD rather than HP-\(\beta\)-CD [13]. Such discrepancies might emerge from the different encapsulating capacity of the CDs used towards structurally unrelated polyphenolic constituents. Indeed, examinations with pure polyphenols (catechin) demonstrated a more efficient encapsulation with \(\beta\)-CD than HP-\(\beta\)-CD or m-\(\beta\)-CD [14]. Therefore, the higher-performance extraction of _S. fruticosa_ polyphenols observed with m-\(\beta\)-CD might reflect the manifestation of such phenomena. Given that the modelling performed revealed significant effect of \(C_{\text{CD}}\) only for m-\(\beta\)-CD, then it could be postulated that m-\(\beta\)-CD interacted more strongly with _S.