Multivariate curve resolution strategy for non-quadrilinear type 4 third-order/four way liquid chromatography–excitation-emission fluorescence matrix data

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

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.

Chromatographic Applications in the Multi-Way Calibration Field

In this review, recent advances and applications using multi-way calibration protocols based on the processing of multi-dimensional chromatographic data are discussed. We first describe the various modes in which multi-way chromatographic data sets can be generated, including some important characteristics that should be taken into account for the selection of an adequate data processing model. We then discuss the different manners in which the collected instrumental data can be arranged, and the most usually applied models and algorithms for the decomposition of the data arrays. The latter activity leads to the estimation of surrogate variables (scores), useful for analyte quantitation in the presence of uncalibrated interferences, achieving the second-order advantage. Recent experimental reports based on multi-way liquid and gas chromatographic data are then reviewed. Finally, analytical figures of merit that should always accompany quantitative calibration reports are described.

Standardization of chromatographic signals - Part II: Expanding instrument-agnostic fingerprints to reverse phase liquid chromatography

There is a large amount of literature relating to multivariate analytical methods using liquid chromatography together with multivariate chemometric/data mining methods in the food science field. Nevertheless, dating the obtained results cannot be compared as they are based on data acquired by a particular analytical instrument, thus they are instrument-dependant. Therefore, this creates difficulties in generating a database large enough to gather together all the variability of the samples. The solution to this problem is to obtain an instrument-agnostic chromatographic signal that is independent of the chromatographic state, i.e., measuring instrument or particular condition of the same instrument from which it was acquired. This paper describes the methodology to be followed to obtain standardized instrumental fingerprints when liquid chromatography is used for prior separation. For this purpose both internal and external chemical standards series are used as references. As an application example, we have applied this methodology for the determination of biophenols in olive oil by liquid chromatography coupled to ultraviolet-visible detector (LC-UV), using three different LC-UV instruments. The instrument-agnostic fingerprints obtained show a high grade of similarity, regardless of the state of the chromatographic system or the time of acquisition.

Multiblock modelling on the study of the kinetic degradation of rosuvastatin calcium in the presence of retention time shifts and rank deficiency

In pharmaceutical development, forced degradation studies are mandatory before the commercialization of any drug product. They aim at identifying the possible degradation routes and the potential products that may be formed during drug product shelf life. The most widely used techniques for monitoring this in the pharmaceutical industry are hyphenated techniques such as Liquid Chromatography coupled to ultraviolet diode array detector (LC-DAD). There are however some drawbacks, such as long analysis times required for the elution of all compounds and coelution, which is not easily detected since degradation products usually have spectra very similar to that of the drug. Chemometrics methods applied to LC-DAD data are capable of solving this issue, but the approaches described in the literature first require peak alignment to solve the rank deficiency problem, which is a delicate preprocessing method for high order data. The present work describes another approach where extra information - the kinetic degradation profiles - is included for the modelling, generating a third-order data set for each sample, resulting in a four-way array (sample x retention times x spectra x degradation profile). This approach has the advantage of using the information in the third mode to solve the peak co-elution problem without the need for peak alignment among samples. With the proposed approach, it was possible to study the degradation of calcium rosuvastatin, a modern cholesterol lowering drug, using a 2 min-run, despite all the challenges in the modelling of this data. The proposed strategy was compared to an approach based on augmenting the matrix in the spectral/kinetic modes (second order modelling strategy).

Four- and five-way excitation-emission luminescence-based data acquisition and modeling for analytical applications. A review

The latest advances in both theory and experimental procedures on third-order/four-way and fourth-order/five-way calibration methods are discussed. This report is focused on excitation-emission (fluorescence and phosphorescence) matrices generation, employing different variables as the third data mode (time retention in chromatography, pH gradient, fluorescence/phosphorescence lifetime, kinetics, or other chemical treatments). Fully capitalizing on the second-order advantage, it has been possible to develop appealing analytical applications in spite of the complexity of the data. Extraction of the significant chemical information about the system under study as well as the individual abundance of the contributing constituents after proper higher-order data decomposition has allowed to analytical researchers performing quantitative analysis of complex samples. The experimental works reported up to the present are introduced and discussed in order to illustrate concepts. Throughout this work, the analytical benefits achieved by modeling third- and fourth-order data are exposed, attempting to contribute to the ongoing debate in the chemometric community regarding the existence and the true nature of the third-order advantage.