Sequential surrogate optimization for supercritical fluid extraction - Supercritical fluid chromatography - Tandem...

Supercritical fluid extraction coupled on-line with supercritical fluid chromatography creates a powerful multidimensional analysis platform, but its adoption is limited by the resource-heavy process of method development. This research presents a surrogate optimization approach as a better alternative to traditional design of experiments and response surface methodology. Unlike fixed experimental designs, the surrogate model iteratively updates the response surface after each run, facilitating effective global optimization through continuous exploration and exploitation. The study adjusts both SFE- and SFC-specific variables-such as back-pressure regulation and split flow-to reduce peak FWHM and enhance extraction efficiency. Analytes, specifically reserpine, vigabatrin, hydromorphone, and hydrocodone, covering diverse physicochemical profiles, were optimized sequentially, guided by a molecular similarity metric, to broaden the design space. The surrogate model identified critical factors, including modifier concentration, chromatography pressure, dynamic extraction time, and flow rate, with adjusted coefficient of determination (R²) values reaching 0.97 as more data was collected and the model was refined. Response surface and parallel coordinate analyses showed that hydrocodone, hydromorphone, and vigabatrin favored high modifier concentrations, while reserpine had a distinct optimum more sensitive to static extraction time. Sensitivity analysis over 62.5-1000 ng mL^-1 yielded detection limits/quantification limits of 6.9/23.0 and 2.4/8.1 ng mL^-1 for hydrocodone and reserpine, respectively. Sequential optimization enhanced sensitivity by 15%, demonstrating the scalability and transferability of the surrogate optimization framework for developing SFE-SFC methods.