Method operable design region obtained with a partial least squares model inversion in the determination of ten...

A chromatographic method with the Analytical Quality by Design (AQbD) methodology is developed for the simultaneous determination by HPLC-FLD of ten PAHs (naphthalene, phenanthrene, anthracene, fluoranthene, pyrene, chrysene, benzo[a]anthracene, perylene, benzo[b]fluoranthene, and benzo[a]pyrene), widely spread in the environment. The construction of the Method Operable Design Region (MODR) is conducted, for the first time, via the inversion of a multiresponse Partial Least Squares (PLS2) model, which is needed to maintain the correlations among the Critical Method Parameters (CMP), among the Critical Quality Attributes (CQA), and the covariance between one another. The five CMP considered were the composition of the mobile phase (water, methanol, acetonitrile), flow rate, and column temperature. The eight CQA were linked to resolution between peaks recorded in the same emission wavelength (greater than 1.4) and the total time (less than 15 minutes). By systematic use of experimental design and parallel coordinates plots to explore the Pareto optimal front obtained with the PLS2 model inversion, the computed MODR is formed by convex combinations of eight specific settings of Critical Method Parameters that have a mobile phase with percentages of water between 37 and 38 %, of methanol from 13 and 22 %, and of acetonitrile between 41 and 49 %, together with a flow rate between 1.47 and 1.50 mL min^-1, and column temperature between 41.9 and 44.0 °C in their adequate combinations. All the chromatographic peaks are well resolved, with total time varying between 12.96 and 15.66 min inside the estimated MODR and the analytical method is accurate with CCβ between 0.9 and 7.0 µg L^-1 with probability of both false positive and false negative equal to 0.05.