Model inversion and three-way decompositions in the analytical quality by design strategy for the determination of...

In this work, strategies within Analytical Quality by Design (AQbD) with tools of the Process Analytical Technology (PAT) were used in the development of a head space-solid phase microextraction-gas chromatography-mass spectrometry (HS-SPME-GC-MS) procedure for the multiresidue analysis of four phthalic acid esters, benzyl butyl phthalate, bis(2-ethylhexyl) phthalate, dibutyl phthalate and diethyl phthalate (regulated by Commission Regulation (EU) No 10/2011). The approach is based on the fact that the intended quality of the resulting chromatograms is defined in terms of the loadings on the sample mode of a Parallel Factor Analysis (PARAFAC2) decomposition. These loadings are the ones used for the inversion of a Partial Least Squares (PLS2) prediction model that has been previously fitted. The inversion gives the experimental conditions that represent a compromise solution in terms of the desired or target values of the responses (Critical Quality Attributes, CQAs), while guaranteeing that these experimental conditions are inside the experimental domain of the Control Method Parameters (CMPs). This strategy results in experimental conditions of extraction time and temperature that lead to a chromatogram of predefined quality for the four analytes together, with the subsquent saving of time and energy. The experimental conditions achieved have been experimentally verified and figures of merit of the analytical method have been determined. The method has been applied to a case study, bottled natural and flavoured mineral water. Concentrations around 0.3 μg L^-1 of dibutyl phthalate have been found in 5 of the 22 bottles of water analysed.