Flexible Implementation of the Trilinearity Constraint in Multivariate Curve Resolution Alternating Least Squares (MCR-ALS) of Chromatographic and Other Type of Data

Abstract

Multivariate Curve Resolution Alternating Least Squares (MCR-ALS) can analyze three-way data under the assumption of a trilinear model using the trilinearity constraint. However, the rigid application of this constraint can produce unrealistic solutions in practice due to the inadequacy of the analyzed data to the characteristics and requirements of the trilinear model. Different methods for the relaxation of the trilinear model data requirements have been proposed, like in the PARAFAC2 and in the direct non-trilinear decomposition (DNTD) methods. In this work, the trilinearity constraint of MCR-ALS is adapted to different data scenarios where the profiles of all or some of the components of the system are shifted (not equally synchronized) or even change their shape among different slices in one of their data modes. This adaptation is especially useful in gas and liquid chromatography (GC and LC) and in Flow Injection Analysis (FIA) with multivariate spectroscopic detection. In a first data example, a synthetic LC-DAD dataset is built to investigate the possibilities of the proposed method to handle systematic changes (shifts) in the retention times of the elution profiles and the results are compared with those obtained using alternative methods like ATLD, PARAFAC, PARAFAC2 and DNTD. In a second data example, multiple wine samples were simultaneously analyzed by GC-MS where elution profiles presented large deviations (shifts) in their peak retention times, although they still preserve the same peak shape. Different modelling scenarios are tested and the results are also compared. Finally, in the third example, sample mixtures of acid compounds were analyzed by FIA under a pH gradient and monitored by UV spectroscopy and also examined by different chemometric methods using a different number of components. In this case, however, the departure of the trilinear model comes from the acid base speciation of the system depending on the pH more than from the shifting of the FIA diffusion profiles.