Optimization and Mathematical Modeling of Biocompound Extraction from Pterocaulon Species Using Deep Eutectic Solvents

Species from the genus Pterocaulon are recognized for their pharmacological relevance attributed to the presence of coumarins and phenolic compounds such as flavonoids and phenolic acids. This study aimed to optimize the extraction of these compounds using deep eutectic solvents (DES) via a Box–Behnken experimental design. For the Pterocaulon species (P. Polystachyum, P. balansae, and P. lorentzii), extraction time, ultrasonic power, and ultrasonic probe pretreatment cycles were evaluated. The regression models obtained showed good fits for P. lorentzii (R2 = 96.09%), whereas for P. polystachyum and P. balansae, the models were less predictive, reflecting the influence of the specific characteristics of each plant matrix. Optimal extraction conditions within the investigated range varied among the species, notably involving maximum ultrasonic power (275 W) and a 90 min extraction time for the Pterocaulon species studied, at a fixed temperature of 40 °C and a solid-to-liquid ratio of 0.05 (g/mL). Total phenolic content (TPC) was quantified using UV-Vis spectrophotometry. The chromatographic analysis (UFLC-DAD) showed the presence of the coumarins previously reported for the species under study, which were tentatively identified based on their retention times and UV absorption spectra. The main compounds tentatively identified were sabandinol in P. lorentzii; prenyletin-methyl-ether and 5-methoxy-6,7-methylenedioxycoumarin in P. polystachyum; and 5,6-dimethoxy-7-(2′,3′-epoxy-3-methylbutyloxy)coumarin, followed by 5-methoxy-6,7-methylenedioxycoumarin in P. balansae. In the extracts of the three species, compounds with the UV profile of phenolic acids were detected. The extraction kinetics were adequately described (R2 = 0.954–0.960 for P. balansae, 0.953 for P. lorentzii, and 0.918–0.923 for P. polystachyum) by a diffusion model with time-varying boundary conditions associated with the interfacial condition represented by different types of adsorption isotherms. These findings suggest that ultrasound-assisted extraction using DES (betaine:ethylene glycol 1:3) is an efficient and sustainable strategy for obtaining extracts rich in bioactive compounds of potential pharmaceutical and cosmetic interest.