Third order chromatographic-excitation–emission fluorescence data: Advances, challenges and prospects in analytical applications

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.

Exploring the potential of combining chemometric approaches to model non-linear multi-way data with quantitative purposes - A case study

Second-order based calibration methods have been widely investigated capitalizing on the inherent benefits of the data structure and the decomposition models, demonstrating that second-order advantage is a property that conspires to a high likelihood success in the resolution of systems of varying complexity. This work aims to demonstrate the applicability of a combined chemometric strategy to solve non-linear multivariate calibration systems in the presence of non-multilinear multi-way data. The determination of histamine by differential pulse voltammetry at different pH is presented as case study. The experimental system has the outstanding difficulty arisen from the large displacement along the potential axis by the pH, which was successfully overcome by implementation of the presented combined strategy. For data modeling, MCR-ALS, U-PLS/RBL and U-PCA/RBL-RBF were used. MCR-ALS allowed unraveling the non-linear behavior between the signal and the concentration, and extracting the underlying profiles of the constituent. Quantitative analysis was performed through the three models, and a comparative evaluation of the predictive performance was done. The best results were achieved with U-PCA/RBL-RBF (mean recovery = 101%) whereas, MCR-ALS yield the lowest mean recovery for all samples (70%).

Novel Approach to the Analysis of Chemical Third-Order Data

For the more complex samples, chemical higher-order data can be collected from various information sources, which become the necessary foundation of accurate analysis. In this article, the Tchebichef cubic moment (TCM) was developed for the analysis of chemical third-order data for the first time. Then, the proposed TCM approach was applied to the fluorescence excitation-emission time data for the analysis of adrenaline and noradrenaline in urinary samples (Data I) and the data fusion of the excitation-emission matrix (EEM), NMR, and liquid chromatography-mass spectrometry (LC-MS) spectra for the determination of the five target components (Data II). For Data I, all of the cross-validation correlation coefficients (R_cv²) of the obtained linear models on the calibration set were more than 0.9937 and the prediction root-mean-square errors (RMSE_p) of the external independent test samples were less than 0.0250 μM. For Data II, all of the R_cv² were higher than 0.9846 and RMSE_p were less than 0.2267 μM. Compared with several conventional methods, the proposed method was more convenient and accurate. This study provides another effective approach to the analysis of complex samples based on their chemical third-order data.

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.

Online Third-Order Liquid Chromatographic Data with Native and Photoinduced Fluorescence Detection for the Quantitation of Organic Pollutants in Environmental Water

Third-order liquid chromatographic data were generated online for the simultaneous quantitation of six organic environmental pollutants. The employed strategy consists in reducing the linear flow rate at the column outlet. A postcolumn UV reactor and a fluorimetric detector allowed to properly record both photoinduced and native excitation-emission fluorescence matrices (EEPIFMs and EEFMs, respectively). The obtained third-order liquid chromatography data were chemometrically processed with the multivariate curve resolution-alternating least-squares model. The sensitivity of the overall analytical method was enhanced by a very simple solid-phase extraction with C18 membranes, to be able to successfully apply it to natural water samples tested as real matrices. Favorable detection limits for the investigated pollutants, ranging from 0.02 to 0.27 ng mL^-1, were attained, with relative prediction errors between 2 and 7%. Since the studied samples contain uncalibrated interferents, the applied strategy achieves the second-order advantage. Implications regarding the potential achievement of the third-order advantage are discussed.