## 3 Results and Discussion
### Analysis of the Optimal Extracts  
The extractions were carried out under these optimum UPAE conditions and were compared to the optimized conventional extraction method [20] under stirring, with water as the solvent at 40 \({}^{\circ}\)C for 2 h, as previously mentioned, to determine which one was more efficient. The results of the extractions are presented in Table 7, while Table 8 summarizes the results of the identification and quantification of the individual polyphenols through HPLC. Compared to Table 6, most of the experimental values do not deviate much from the predicted values. More specifically, the experimental TPC values of OM pulp and peels in Table 7 were \(\sim\)6% and \(\sim\)9% lower than predicted by the PLS values in Table 6. Moreover, both OM peel and pulp resulted in higher TPC values when subjected to UPAE rather than stirring. A possible mechanism could be due to acoustic cavitation bubbles that burst close to or even touch the solid surface. Shockwave damage and high-velocity jets of liquid into the surface are the results of a burst bubble. Localized erosion and the breaking apart of friable materials are possible outcomes of such impacts. These factors contribute to a decrease in particle size, which in turn increases the mass transfer of solid particles and generally improves media reactivity [29]. [PERSON] and [PERSON] [41] studied the optimal TPC of _Opuntia focus-indica_ fruits through Soxhlet and maceration, and the obtained TPC values were 1.46 and 1.15 mg GAE/g, significantly lower than the ones obtained in our study. Moreover, [PERSON] et al. [42] utilized ultrasonication bath extraction for 15 min, using a mixture of methanol and acetic acid as a solvent to assess the TPC on _Opuntia stria_. Their results yielded TPC 3.72 and 4.15 mg/g for pulp and peels, respectively; once again, significantly lower than in our study. These support the statement that _Opuntia macrorhiz_ might serve as a valuable substitute for _Opuntia focus-indica_ in food industries, and the use of ultrasound is not only beneficial for the environment but also for extraction efficiency. As for the BC, OM pulp yielded a \(\sim\)1.1% higher value than the predicted one, while OM peels yielded a \(\sim\)5.3% lower value. In both extraction techniques, the BC recovery from pulp and peels did not display statistically significant differences (\(p>0.05\)). In a similar study, [PERSON] et al. [43] studied the total betalains of two different red pickly pear varieties from Spain, _Sanguinos_, and Mexico, _Vigor_. The extraction technique employed was an ultrasonication bath, utilizing 50% \(v/v\) aqueous methanol as solvent. The BC values for peel ranged from 740 to 810 mg/g dw, and for the pulp ranged from 490 to 790 mg/g dw. The experimentally derived FRAP and DPPH values were slightly higher than the PLS model, except for the pulp DPPH value, which was slightly lower. This means that UPAE was successful in ensuring maximum antioxidant capacity (as defined by these two protocols) after optimization. It is worth noting that the values obtained from the optimized STE did not exhibit significant differences (\(p>0.05\)) with those of the UAE. In the previously mentioned study [38], the authors also quantified AAC from several _Opuntia_ spp. Pulp yielded 0.67-1.92 mg/g and peels yielded 1.19-1.72 mg/g, indicating that the several species had vast differences in terms of AAC. Finally, the color of the optimal UPAE peel and pulp extracts appeared slightly lighter than the STE ones. According to Table 8, the most abundant polyphenol in both OM pulp and peel appears to be pyrogallol, followed by syringe acid. Some polyphenic compounds determined by HPLC did not differ significantly (\(p\) > 0.05) between peel and pulp or between the two techniques. However, it was expected and observed that OM peels had higher polyphenic content than pulp, regardless of the extraction technique. [PERSON] et al. [44] also determined syringic acid in various _Oynthia_ species. Moreover, [PERSON] et al.