Statistical Modeling and Numerical Optimization of Ultrasound-Assisted Phenolic and Flavonoid Extraction from Momordica charantia Fruit

This study modeled ultrasound-assisted extraction (UAE) of total phenolic content (TPC) and total flavonoid content (TFC) from Momordica charantia fruit using a three-factor Box–Behnken design. Ethanol concentration (0–96%), liquid-to-solid ratio (10–40 mL/g), and extraction time (5–30 min) were evaluated at a fixed bath temperature of 50 °C. Box–Cox-guided square-root and log₁₀ transformations were applied to TPC and TFC, respectively. The selected linear models were significant (p < 0.0001), with R²/adjusted R²/predicted R² of 0.9582/0.9469/0.9264 for TPC and 0.9129/0.8892/0.8148 for TFC. Liquid-to-solid ratio significantly affected TPC, whereas ethanol concentration and liquid-to-solid ratio significantly affected TFC; extraction time was not significant. TPC showed significant lack-of-fit (p = 0.0426), while TFC lack-of-fit was not significant (p = 0.0636). Joint numerical optimization predicted 95.994% ethanol, 40.000 mL/g, and 5.000 min (desirability = 0.955), with bias-corrected mean predictions of 109.054 mg GAE/g dry extract and 123.371 mg QE/g dry extract. This boundary solution was not experimentally confirmed. At a separate confirmation location (82.8208%, 37.4455 mL/g, 26.3205 min), TPC was substantially underpredicted, whereas TFC agreed more closely with the model. These findings identify a preliminary operating direction for UAE but indicate that the TPC model requires additional design points, stronger replication, and assay-specific verification before confirmatory or scale-up use.