Abstract
Background. Ultrasound-assisted extraction is the dominant green route to recovering polyphenols from fruit processing by-products, and response surface methodology is the near-universal tool for optimising it. Individual studies report optimal conditions for a single matrix, but the fitted surfaces themselves are rarely interrogated, and the results have never been placed on a common scale. Objective. To refit published response surface designs for ultrasound-assisted extraction of polyphenols from agro-industrial fruit waste, establish the geometry of each fitted surface, compare factor effects across studies on a common coded scale, and test whether reported optima are consistent with the models from which they were derived. Methods. Five published designs covering orange by-products, apple peel, pomegranate peel, grape pomace and apple pomace, comprising 105 experimental runs, were transcribed in full from their source publications. Full second-order models were refitted by ordinary least squares in coded units, with analysis of variance, lack-of-fit testing where replication permitted, and leave-one-out predicted coefficients of determination. Every surface was subjected to canonical analysis. Linear coefficients were standardised against the mean response of their own design. Multi-response optimisation used the Derringer-Suich desirability function constrained to the experimental region. Results. Mean ordinary coefficient of determination across the five phenolic models was 0.9240, but the mean predicted coefficient of determination was 0.5379, falling to 0.0050 in one design, and 2 of 5 fell below one half. Canonical analysis classified 4 of 5 phenolic surfaces as saddle points with stationary points outside the studied region; only 1 possessed an interior maximum. Solvent variables dominated: solvent-to-material ratio carried a standardised effect of -0.4721 and ethanol concentration a mean of -0.2048 across two designs, whereas extraction time averaged 0.0370 across 5 designs and ultrasonic amplitude 0.0019. One reported optimum fell 2.8 per cent short of the maximum of its own refitted surface. Conclusion. Published optima in this field frequently derive from surfaces that possess no interior optimum, and ordinary coefficients of determination substantially overstate predictive capability. Solvent composition, not sonication intensity or duration, governs phenolic recovery across matrices.