Three-way calibration using PARAFAC and MCR-ALS with previous synchronization of second-order chromatographic data through a new functional alignment of pure vectors for the quantification in the presence of retention time shifts in peak position and shape

Iterative Regression of Corrective Baselines (IRCB): A New Model for Quantitative Spectroscopy

In this work, a new model with broad utility for quantitative spectroscopy development is reported. A primary objective of this work is to create a novel modeling procedure that may allow for higher automation of the model development process. The fundamental concept is simple yet powerful even for complex spectra and is employed with no additional preprocessing. This approach is applicable for several types of spectroscopic data to develop regression models that have similar or greater quality than the current methods. The key modeling steps are a matrix transformation and subsequent feature selection process that are collectively referred to as iterative regression of corrective baselines (IRCB). The transformed matrix (Xtransform) is a linearized form of the original X data set. Features from Xtransform that are predictive of Y can be ranked and selected by ordinary least-squares regression. The best features (rows of Xtransform) are linear depictions of Y that can be utilized to develop regression models with several machine learning models. The IRCB workflow is first detailed by using a case study of Fourier transform infrared (FTIR) spectroscopy for prepared solutions of a three-component mixture. Next, IRCB is applied and compared to benchmark results for the 2006 "Chimiométrie" near-infrared spectroscopy (NIR) soil composition challenge and Raman measurements of a simulated nuclear waste slurry.

Application of smart chemometric models for spectra resolution and determination of challenging multi-action quaternary mixture: statistical comparison with greenness assessment

A multivariate spectrophotometric method is a potential approach that enables discrimination of spectra of components in complex matrices (e.g., pharmaceutical formulation) serving as a substitution method for chromatography. Four green smart multivariate spectrophotometric models were proposed and validated, including principal component regression (PCR), partial least-squares (PLS), multivariate curve resolution-alternating least squares (MCR-ALS), and artificial neural networks (ANN). The developed chemometric models were compared to resolve highly overlapping spectra of Paracetamol (PARA), Chlorpheniramine maleate (CPM), Caffeine (CAF), and Ascorbic acid (ASC). The four multivariate calibration models were assessed via recoveries percent, and root mean square error of prediction. Hence, the proposed models were efficiently applied with no need for any preliminary separation step. The models were utilized to analyze the studied components in their combined pharmaceutical formulation (Grippostad® C capsules). Analytical GREEnness Metric Approach (AGREE) and eco-scale tools were applied to assess the greenness of the established models and found to be 0.77 and 85, respectively. Moreover, the proposed models have been compared to official ones showing no considerable variations in accuracy and precision. Therefore, these models can be highly advantageous for conducting standard pharmaceutical analysis of the substances researched within product testing laboratories.

Excitation-emission fluorescence spectroscopy coupled with PARAFAC and MCR-ALS with area correlation for investigation of jet fuel contamination

The contamination of jet fuel has gained attention in the past years as a notable factor in aircraft accidents. Identifying the contamination sources is still a challenge, especially when they have a similar composition to the fuel, such as kerosene solvent (KS). A novel analytical methodology was developed by combining a set of excitation-emission matrix (EEM) fluorescence to area constrained multivariate curve resolution with alternating least-squares (MCR-ALS) and PARAllel FACtor (PARAFAC) analysis, in order to identify KS in blends with JET-A1. For this purpose, a dataset with 50 samples (KS and JET-A1 blends, 2.0-100% v/v) was used to build the multivariate models. Both PARAFAC and MCR-ALS allowed fuel quantification with 4.64% and 3.46% RMSEP, respectively; both models (PARAFAC and MCR-ALS) could quantify KS with high accuracy (RMSEP <5.36%). In addition, MCR-ALS model was able to recover the pure spectral profiles of KS, JET-A1 and interferers. GC-MS data of the samples proved the composition similarities between both petroleum distillates, thus being inefficient for identifying the contamination. These results indicate that the development of multivariate models using EEM was the key for contributing with a new low-cost and accurate method for on-line screening of jet fuel contamination.

A tutorial on multi-way data processing of excitation-emission fluorescence matrices acquired from semiconductor quantum dots sensing platforms

This tutorial demonstrates how to exploit the second-order advantage on excitation-emission fluorescence matrices (EEFMs) acquired from sensing platforms based on analyte-triggered semiconductor quantum dots (QDs) fluorescence modulation (quenching/enhancing). The advantage in processing such second-order EEFMs data from complex samples, seeking successful quantification, is comprehensively addressed. It is worth emphasizing that, aiming to exploit the second-order advantage, the selection of the most appropriate advanced chemometric model should rely on the matching between the data structure and the physicochemical chemometric model assumption. In this sense, the achievement of second-order advantage after EEFMs' processing is extensively addressed throughout this tutorial taking into consideration three different analytical situations, each involving a specific data structure: i) parallel factor analysis (PARAFAC), which is applied in a real dataset stacked in a three-way data array containing a trilinear data structure acquired from QDs-based detection with non-selective species; ii) multivariate curve resolution - alternating least-squares (MCR-ALS), which is also employed in a real dataset arranged in an augmented data matrix containing non-trilinear data structure acquired from QDs-based detection with a single breaking mode caused by background signals; iii) unfolded partial least-squares with residual bilinearization (U-PLS/RBL), which is applied in a dataset containing non-trilinear data acquired from a classical fluorescence system with two breaking modes caused by inner filter effect (IFE) in both instrumental modes (excitation and emission). The latter challenging data structure can be acquired via fluorescence quenching from IFE-based sensing platforms and chemometrically handled in two main steps. First, a set of calibration EEFMs data is converted into an unfolded data matrix during the unfolding process, followed by applying U-PLS model. Second, a post-calibration procedure using RBL analysis is applied to a test sample of EEFM maintained in its matrix form, in order to handle potential interferents. In the last section, the state-of-the-art of second-order EEFMs data acquired from semiconductor QDs-based sensing platforms and coupled to multi-way fluorescence data processing to accomplish a successful quantification, even with substantial interfering species, is critically reviewed.

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.

Restoring trilinearity with the purpose of advanced modeling: towards a more effective analysis of Pericarpium Citri Reticulatae during storage periods

To accurately quantify Pericarpium Citri Reticulatae samples, trilinear structure was restored in the stacked fingerprints for more robust modeling. Initially, liquid chromatography - diode array detector - mass spectrometry (LC-DAD-MS) and head space-solid phase micro extraction coupled to gas chromatography - mass spectrometry (HS-SPME/GC-MS) were utilized to analyze Pericarpium Citri Reticulatae. Faced with the time-shifts in two-dimensional (2D) matrices across different samples, three algorithms were developed to synchronize them. Furthermore, bilinear and trilinear models were used to realize the quantifications with different principles. Through real cases based on LC-DAD, the advantages and disadvantages of trilinear decomposition over multivariate curve resolution-alternating least-squares can be clarified in the quantification of raw or synchronized fingerprints. Also in the data processing, a modification version of multi-scale peak alignment (^mMSPA) was proved to be more suitable for trilinearity restoring than the other two algorithms. Recognizing these facts, restoring trilinearity were developed for more robust modeling in the application of the Pericarpium Citri Reticulatae fingerprints from different storage periods. After effective analysis, the upward/downward trend of 13 flavonoids were drawn accurately; and several flavour components having the highest contribution rate during storage were outlined reasonably. In conclusion, more robust modeling can be realized in trilinear data synchronized by appropriate algorithms, leading to an accurate quantification in herbal quality researches.