## 3 Results and Discussion  
### Development of the Ultrasound-Assisted Extraction Using Box-Behnken Design  
Multivariate techniques are used very effectively to optimize the extraction method from complex plant matrices such as food products and by-products [36]. Among the different multivariate techniques, when three factors are considered, the Behnken-Box design is one of the most effective techniques [36; 37]. The Behnken-Box matrix is a spherical and rotating design, which, viewed on a cube, consists of the central point and the middle of the edges [36; 37]. Many parameters can influence the extraction of phenolic compounds from plant matrices [38], but three parameters are very widely distinguished when developing an USAE method: the type of solvent used, the frequency of ultrasound applied and the extraction time [11; 21; 30]. The choice of solvent is a crucial parameter to define when developing an extraction method. Various solvents, including methanol, ethanol, or acetone, are regularly used for the extraction of plant polyphenols [28; 39]. Here, given our objective of developing an extraction method in accordance with green chemistry principles for future nutraceuticalul and/or cosmeceutical applications of the resulting extract, EtOH was considered as an extraction solvent. First, EtOH is one of the less toxic solvents for humans and more respectful of the environment than other organic solvents such as methanol for example [38; 40]. In addition, its extraction capacity can easily be modulated by addition of water, making it an ideal solvent for the extraction of a wide range of variable polarity polyphenols. Finally, these two universal solvents (i.e., EtOH and water) are already widely used for various food and/or cosmetic applications [11; 28; 30; 38; 40]. US frequency is a crucial parameter to consider because of its significant impact on the extraction efficiency. Indeed, this parameter modulates the cavitation effect as well as the diffusion coefficient of the target compound in the extraction solvent. Consequently, it improves the solubilization of the compound in the extraction solvent, thus increasing the extraction efficiency [28]. In addition, increasing US frequency can also lead to a drastic reduction in extraction time, thereby reducing energy consumption, which is in accordance with the green chemistry principles [41]. However, depending on the compound and the plant matrix subjected to the extraction, application of high US frequency can alter the native structure of the compound, which not only decreases the extraction yield, but also considerably reduces its biological activity, thus negating any valuation interest [30]. Therefore, during the development of an USAE method, US frequency must be optimized very carefully depending on the compound, and the plant matrix subjected to the extraction. Finally, regarding the extraction time, it is important to consider that its increase does not necessarily lead to any improvement in extraction yield, since, contrarily, a prolonged exposure to US can lead to the increased degradation of the compound [30]. In addition, in order to reduce the impact of energy consumption in the green chemistry context, optimizing the extraction time also appears to be essential [41]. Having these considerations in mind, in order to develop a rapid, green and efficient USAE of TPC for the valorization of AOR, we therefore considered a Behnken-Box matrix with the following three parameters: aqEtOH concentration (X\({}_{1}\)), ultrasound (US) frequency (X\({}_{2}\)), and extraction duration (X\({}_{3}\)) as described in Table 1.  
Table 2 presents the experimental and predicted TPC obtained from almond oil residues for the 18 different observations (run ID) corresponding the different USAE conditions of the Behnken-Box matrix having been determined randomly (run order) after an _in silico_-assisted procedure generated by the XL-Stat2019.4.1 software.