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Kañiwa (Chenopodium pallidicaule), an Andean pseudocereal, exhibits significant potential as a source of bioactive compounds, particularly phenolic constituents, whose efficient recovery is essential for food industry applications. In this study, the extraction of total polyphenols was optimized through a Simplex Lattice Mixture Design, enabling the assessment of synergistic effects among solvents with varying polarities and the establishment of conditions for exhaustive extraction. The design incorporated distilled water, methanol, ethanol, and acetone as acidified extractants (0.1 mL HCl PA per 5 mL solvent). Extraction was performed using 0.2 g of kañiwa flour and 1.5 mL of extracting solution, followed by sonication at 40 kHz (100 W) for 5 minutes and centrifugation at 5,000 RCF for 10 minutes and 5 °C, after which the supernatant was adjusted to 2 mL. Total polyphenol content was quantified via the Folin– Ciocalteu method at 750 nm. Exhaustive extraction was achieved through eight consecutive cycles using the optimized solvent under reduced sonication time (5 minutes per cycle). The absorbances ranged from 0.242 ± 0.001 to 0.552 ± 0.006 and the quadratic model exhibited satisfactory adjustment (R² = 0.854; P < 0.001). The ethanol–acetone binary mixture (50:50) yielded the highest absorbance, closely followed by the quaternary mixture containing 12.5% water, 12.5% methanol, 12.5% ethanol, and 62.5% acetone (0.547), corresponding to increases of 62.4% and 60.9%, respectively, compared with pure water (0.340). Significant individual effects were detected for acetone (0.430, P < 0.001) and ethanol (0.422, P < 0.001), while synergistic binary interactions were observed for ethanol–acetone (0.593, P = 0.006) and methanol–acetone (0.451, P = 0.028). Antagonistic interactions involving water were also identified (−0.429, P = 0.035; −0.503, P = 0.016). Response surface analysis revealed an optimal region comprising 50–60% acetone and 40–50% ethanol, associated with absorbance values above 0.55. The optimized extracting solution was composed of 1.27% water, 2.17% methanol, 43.28% ethanol, and 53.30% acetone (desirability = 1.00), exhibiting a relative deviation of 1.47%. The exhaustive extraction process demonstrated that 95% recovery was achieved within seven cycles. The predominance of semipolar solvents in the optimal mixture suggests that kañiwa polyphenols exhibit intermediate polarity, a key finding for designing industrial-scale extraction systems. Overall, the Simplex Lattice Mixture Design proved to be an innovative and effective approach for optimizing bioactive compound extraction from emerging Andean grains.
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