Chemometrics applied to unravel multicomponent processes and mixtures: Revisiting latest trends in multivariate resolution

Progress in the analysis of multicomponent processes and mixtures relies on the combination of sophisticated instrumental techniques and suitable data analysis tools focused on the interpretation of the multivariate responses obtained. Despite the differences in compositional variation, complexity and origin, the raw measurements recorded in a multicomponent chemical system can be very often described with a simple model consisting of the composition-weighted sum of the signals of their pure compounds.

Multivariate resolution methods have been the tools designed to unravel this pure compound information from the non-selective mixed original experimental output. The evolution of these chemometric approaches through the improvement of exploratory tools, the adaptation to work with complex data structures, the ability to introduce chemical and mathematical information in the algorithms and the better quality assessment of the results obtained is revisited. The active research on these chemometric area has allowed the successful application of these methodologies to chemical problems as complex and diverse as the interpretation of protein folding processes or the resolution of spectroscopic images.     

Self-modeling curve resolution method applied for the evaluation of dissolution testing data: A case study of meloxicam-mannitol binary systems

This paper introduces some chemometric methods, i.e., self-modeling curve resolution (SMCR), multivariate curve resolution-alternating least squares (MCR-ALS) and parallel factor analysis (PARAFAC and PARAFAC2), which are used to evaluate in vitro dissolution testing data detected by a UV-vis spectrophotometer on meloxicam-mannitol binary systems. These systems were chosen because of their relative simplicity to apply as part of the validation process illustrating the effectiveness of the developed and applied chemometric method. The paper illustrates the failure of PARAFAC methods used before for pharmaceutical data evaluations as well, and we suggest application of the feasible band form given by SMCR as a more general procedure.Steps to improve the dissolution behavior of drugs have become among the most interesting aspects of pharmaceutical technology, and our results show that a larger particle size of meloxicam is advantageous for dissolution. Instead of the use of only one characteristic wavelength, appropriate chemometric methods can furnish more information from dissolution testing data, i.e., the individual dissolution rate profiles and the individual spectra for all the components can be obtained without resorting to any separation techniques such as HPLC.     

Multivariate data analysis for Raman imaging of a model pharmaceutical tablet

Spectroscopic imaging techniques provide spatial and spectral information about a sample simultaneously and are finding ever-increasing application in the pharmaceutical industry. Effective extraction of chemical information from imaging data sets is a crucial step during the application of imaging techniques. Multivariate imaging data analysis methods have been reported but few applications of these methods for pharmaceutical samples have been demonstrated. In this study, a bilayer model tablet consisting of avicel, lactose, sodium benzoate, magnesium stearate and red dye was prepared using custom press tooling, and Raman mapping data were collected from a 400 μm × 400 μm area of the tablet surface. Several representative multivariate methods were selected and used in the analysis of the data. Multivariate data analysis methods investigated include principal component analysis (PCA), cluster analysis, direct classical least squares (DCLS) and multivariate curve resolution (MCR). The relative merits and drawbacks of each technique for this application were evaluated. In addition, some practical issues associated with the use of these methods were addressed including data preprocessing, determination of the optimal number of clusters in cluster analysis and the optimization of window size in second derivative calculation.     

Analysis of Complex Molecular Systems: The Impact of Multivariate Analysis for Resolving the Interactions of Small Molecules with Biopolymers – a Review

This review is focused on the impact of chemometrics for resolving data sets collected from investigations of the interactions of small molecules with biopolymers. These samples have been analyzed with various instrumental techniques, such as fluorescence, ultraviolet–visible spectroscopy, and voltammetry. The impact of two powerful and demonstrably useful multivariate methods for resolution of complex data—multivariate curve resolution–alternating least squares (MCR–ALS) and parallel factor analysis (PARAFAC)—is highlighted through analysis of applications involving the interactions of small molecules with the biopolymers, serum albumin, and deoxyribonucleic acid. The outcomes illustrated that significant information extracted by the chemometric methods was unattainable by simple, univariate data analysis. In addition, although the techniques used to collect data were confined to ultraviolet–visible spectroscopy, fluorescence spectroscopy, circular dichroism, and voltammetry, data profiles produced by other techniques may also be processed. Topics considered including binding sites and modes, cooperative and competitive small molecule binding, kinetics, and thermodynamics of ligand binding, and the folding and unfolding of biopolymers. Applications of the MCR–ALS and PARAFAC methods reviewed were primarily published between 2008 and 2013.     

Photochemistry and chemometrics—An overview

Photochemistry has made significant contributions to our understanding of many important natural processes as well as the scientific discoveries of the man-made world. The measurements from such studies are often complex and may require advanced data interpretation with the use of multivariate or chemometrics methods. In general, such methods have been applied successfully for data display, classification, multivariate curve resolution and prediction in analytical chemistry, environmental chemistry, engineering, medical research and industry. However, in photochemistry, by comparison, applications of such multivariate approaches were found to be less frequent although a variety of methods have been used, especially with spectroscopic photochemical applications. The methods include Principal Component Analysis (PCA; data display), Partial Least Squares (PLS; prediction), Artificial Neural Networks (ANN; prediction) and several models for multivariate curve resolution related to Parallel Factor Analysis (PARAFAC; decomposition of complex responses). Applications of such methods are discussed in this overview and typical examples include photodegradation of herbicides, prediction of antibiotics in human fluids (fluorescence spectroscopy), non-destructive in- and on-line monitoring (near infrared spectroscopy) and fast-time resolution of spectroscopic signals from photochemical reactions. It is also quite clear from the literature that the scope of spectroscopic photochemistry was enhanced by the application of chemometrics.To highlight and encourage further applications of chemometrics in photochemistry, several additional chemometrics approaches are discussed using data collected by the authors. The use of a PCA biplot is illustrated with an analysis of a matrix containing data on the performance of photocatalysts developed for water splitting and hydrogen production. In addition, the applications of the Multi-Criteria Decision Making (MCDM) ranking methods and Fuzzy Clustering are demonstrated with an analysis of water quality data matrix. Other examples of topics include the application of simultaneous kinetic spectroscopic methods for prediction of pesticides, and the use of response fingerprinting approach for classification of medicinal preparations. In general, the overview endeavours to emphasise the advantages of chemometrics’ interpretation of multivariate photochemical data, and an Appendix of references and summaries of common and less usual chemometrics methods noted in this work, is provided.     

Multivariate curve resolution–alternating least squares (MCR-ALS) applied to spectroscopic data from monitoring chemical reactions processes

This paper overviews the application of multivariate curve resolution (optimized by alternating least squares) to spectroscopic data acquired by monitoring chemical reactions and other processes. The goals of the resolution methods and the principles for understanding their applications are described. Some of the problems arising from these evolving systems and the limitations of the multivariate curve resolution methods are also discussed. This article reviews most of the applications of multivariate curve resolution applied to reacting systems published between January 2000 and June 2007. Some basic papers dated before 2000 have also been included.     

Multivariate curve resolution: A review of advanced and tailored applications and challenges

Multivariate curve resolution (MCR) is a widespread methodology for the analysis of process data in many different application fields. This article intends to propose a critical review of the recently published works. Particular attention will be paid to situations requiring advanced and tailored applications of multivariate curve resolution, dealing with improvements in preprocessing methods, multi-set data arrangements, tailored constraints, issues related to non-ideal noise structure and deviation to linearity. These analytical issues are tackling the limits of applicability of MCR methods and, therefore, they can be considered as the most challenging ones.     

The role of chemometrics in single and sequential extraction assays: a review. Part II. Cluster analysis, multiple linear regression, mixture resolution, experimental design and other techniques

Single and sequential extraction procedures are used for studying element mobility and availability in solid matrices, like soils, sediments, sludge, and airborne particulate matter. In the first part of this review we reported an overview on these procedures and described the applications of chemometric uni- and bivariate techniques and of multivariate pattern recognition techniques based on variable reduction to the experimental results obtained. The second part of the review deals with the use of chemometrics not only for the visualization and interpretation of data, but also for the investigation of the effects of experimental conditions on the response, the optimization of their values and the calculation of element fractionation. We will describe the principles of the multivariate chemometric techniques considered, the aims for which they were applied and the key findings obtained. The following topics will be critically addressed: pattern recognition by cluster analysis (CA), linear discriminant analysis (LDA) and other less common techniques; modelling by multiple linear regression (MLR); investigation of spatial distribution of variables by geostatistics; calculation of fractionation patterns by a mixture resolution method (Chemometric Identification of Substrates and Element Distributions, CISED); optimization and characterization of extraction procedures by experimental design; other multivariate techniques less commonly applied.     

Multivariate concentration determination using principal component regression with residual analysis

Data analysis is an essential tenet of analytical chemistry, extending the possible information obtained from the measurement of chemical phenomena. Chemometric methods have grown considerably in recent years, but their wide use is hindered because some still consider them too complicated. The purpose of this review is to describe a multivariate chemometric method, principal component regression, in a simple manner from the point of view of an analytical chemist, to demonstrate the need for proper quality-control (QC) measures in multivariate analysis and to advocate the use of residuals as a proper QC method.     

Hybrid approach combining chemometrics and likelihood ratio framework for reporting the evidential value of spectra

Many chemometric tools are invaluable and have proven effective in data mining and substantial dimensionality reduction of highly multivariate data. This becomes vital for interpreting various physicochemical data due to rapid development of advanced analytical techniques, delivering much information in a single measurement run. This concerns especially spectra, which are frequently used as the subject of comparative analysis in e.g. forensic sciences. In the presented study the microtraces collected from the scenarios of hit-and-run accidents were analysed. Plastic containers and automotive plastics (e.g. bumpers, headlamp lenses) were subjected to Fourier transform infrared spectrometry and car paints were analysed using Raman spectroscopy. In the forensic context analytical results must be interpreted and reported according to the standards of the interpretation schemes acknowledged in forensic sciences using the likelihood ratio approach. However, for proper construction of LR models for highly multivariate data, such as spectra, chemometric tools must be employed for substantial data compression. Conversion from classical feature representation to distance representation was proposed for revealing hidden data peculiarities and linear discriminant analysis was further applied for minimising the within-sample variability while maximising the between-sample variability. Both techniques enabled substantial reduction of data dimensionality. Univariate and multivariate likelihood ratio models were proposed for such data. It was shown that the combination of chemometric tools and the likelihood ratio approach is capable of solving the comparison problem of highly multivariate and correlated data after proper extraction of the most relevant features and variance information hidden in the data structure.     

Investigation of the equality constraint effect on the reduction of the rotational ambiguity in three-component system using a novel grid search method

The obtained results by soft modeling multivariate curve resolution methods often are not unique and are questionable because of rotational ambiguity. It means a range of feasible solutions equally fit experimental data and fulfill the constraints. Regarding to chemometric literature, a survey of useful constraints for the reduction of the rotational ambiguity is a big challenge for chemometrician. It is worth to study the effects of applying constraints on the reduction of rotational ambiguity, since it can help us to choose the useful constraints in order to impose in multivariate curve resolution methods for analyzing data sets. In this work, we have investigated the effect of equality constraint on decreasing of the rotational ambiguity. For calculation of all feasible solutions corresponding with known spectrum, a novel systematic grid search method based on Species-based Particle Swarm Optimization is proposed in a three-component system.     

Chemometrics in pharmaceutical analysis: an introduction, review, and future perspectives

Chemometrics is the application of statistical and mathematical methods to analytical data to permit maximum collection and extraction of useful information. The utility of chemometric techniques as tools enabling multidimensional calibration of selected spectroscopic, electrochemical, and chromatographic methods is demonstrated. Application of this approach mainly for interpretation of UV-Vis and near-IR (NIR) spectra, as well as for data obtained by other instrumental methods, makes identification and quantitative analysis of active substances in complex mixtures possible, especially in the analysis of pharmaceutical preparations present in the market. Such analytical work is carried out by the use of advanced chemical instruments and data processing, which has led to a need for advanced methods to design experiments, calibrate instruments, and analyze the resulting data. The purpose of this review is to describe various chemometric methods in combination with UV-Vis spectrophotometry, NIR spectroscopy, fluorescence spectroscopy, electroanalysis, chromatographic separation, and flow-injection analysis for the analysis of drugs in pharmaceutical preparations. Theoretical and practical aspects are described with pharmaceutical examples of chemometric applications. This review will concentrate on gaining an understanding of how chemometrics can be useful in the modern analytical laboratory. A selection of the most challenging problems faced in pharmaceutical analysis is presented, the potential for chemometrics is considered, and some consequent implications for utilization are discussed. The reader can refer to the citations wherever appropriate.     

Application of a novel chemometric approach to the determination of aqueous photolysis rates of organic compounds in natural waters

The utility of multivariate optimization methods in the determination of aqueous photolysis rates of organic compounds is examined in this study. A basic pursue was to designate the appropriate experimental design plan that extend the analytical utility of multivariate methods from qualitative data interpretation approaches, as applied thus far, to quantitative estimation methods. A three-level second-order central composite design with parameter concentrations (factor levels) beyond the environmental realistic concentrations was employed for that purpose enabling statistically significant effects to be determined. Method application is demonstrated in the first photodegradation study of two UV absorbing chemicals in natural waters. The results suggest that the proposed approach of enables a good approximation of the real behavior in terms of both qualitative and quantitative data interpretation with minimal loss of information.     

Efficient recovery of electrophoretic profiles of nucleoside metabolites from urine samples by multivariate curve resolution

Chemometric techniques usually employed in purity assessment and resolution of multicomponent peaks have been applied to analytical data from complex biological samples obtained with CE‐DAD. In the assessment of the purity of the electrophoretic peaks, the orthogonal projection approach, the orthogonal projection approach with Durbin–Watson criterion, and the simple‐to‐use interactive self‐modeling mixture analysis method have been employed. Multivariate curve resolution with alternating least squares has been successfully implemented to resolve co‐migrating peaks of metabolites in CE‐DAD and to recover qualitative and quantitative information about co‐migrating components of urine extract. The main challenge consisted of developing high‐quality multivariate curve resolution with alternating least squares models of multicomponent peaks acquired during the CE analysis of nucleoside patterns in 18 urine samples. The recovered ultraviolet visible (UV–Vis) spectra have been employed to identify additional nucleosides, such as 1‐methylinosine, 2‐methylguanosine, and 1‐methylguanosine, whose presence in the metabolic profile produced by the applied CE‐DAD method has not yet been recognized. Concentration profiles of these compounds can be used in metabonomic studies.     

Chemometrics in near-infrared spectroscopy

Spectroscopy methods of chemical analysis are excellent for the application of chemometric methods, because the measurements at many different wavelengths provide inherently multivariate data. The chemist generally requires three categories of information from specimens under investigation: quantitative data, qualitative data, and fundamental information on the properties of the material. Spectroscopy has long been used for all three purposes; the recent application of chemometric algorithms has assisted greatly in these endeavors. Although there is some overlap, three chemometric methods correspond to the three types of information: multiple regression, discriminant analysis, and principal components analysis. The basis of these chemometric methods and some of their strengths and limitations in application to near-infrared spectroscopy are discussed.     

Chemometric tools in electroanalytical chemistry: Methods for optimization based on factorial design and response surface methodology

The aim of this paper is to give a brief overview of chemometric techniques based on factorial designs and response surface methodologies used in the optimization of electroanalytical methods. Chemometric techniques have several important advantages over one-way optimization for analytical applications, including a relatively low cost, a reduced number of experiments, and possibilities to evaluate interactions among variables. These techniques also enable the selection of optimal experimental conditions, helping to avoid trivial mistakes during optimization. Despite these facts, chemometric techniques have rarely been applied to electroanalytical data, especially in comparison with their use in spectroscopy. The application of chemometric methods in electroanalytical chemistry has been mostly used for solving overlapping signals, multivariate calibration methods, model identification and optimization of analytical procedures. This review is focused on the latter applications and overviews the role of full or fractional factorial designs (first-order designs), as well as second-order designs, such as central composite, Doehlert and Box-Behnken designs, for optimization of electroanalytical methods. A discussion of chemometric-related advantages is also given for stripping analyses, flow injection systems with amperometric detection, differential pulse voltammetry, square wave voltammetry and electrochemical sensor preparation.     

Enhancement of analyte detectability in isotachophoresis exploiting spectrophotometric diode‐array detection with chemometric data processing

The potentialities of capillary ITP combined with diode‐array detection (DAD) with subsequent chemometric data processing have been investigated in this work. A series of different migration configurations were created using model analytes, interferents and appropriate spacers. Special attention has been paid not only to constituents migrating in fully developed ITP zones but also to the spike mode of ITP migration. The purity assessment and identity confirmation of model analytes migrating in both modes were performed by means of multivariate curve resolution and target transformation factor analysis (TTFA). Their successful applications have revealed a smart way to increase in the analytical information obtained by ITP separation even in the instance of trace analysis.     

An advanced multivariate approach for processing X-ray fluorescence spectral and hyperspectral data from non-invasive in situ analyses on painted surfaces

In the last decades, in situ non-invasive analytical techniques have been widely used for the analysis of paintings. These techniques are useful to extensively map the surface in a non-invasive way, in order to identify the most representative areas to be sampled. When spectroscopic investigations, such as X ray fluorescence (XRF), are conducted, they usually imply the acquisition of a huge amount of measurements. Subsequently, all these data should be processed in situ, in order to immediately support the sampling strategies. To this aim, an appropriate and fast strategy for multivariate treatment of XRF spectral and hyperspectral data sets is presented, able to account for inter-correlation among variables, which is an issue of high importance for elemental analyses. The main advantage of the approach is that XRF spectral profiles are analysed directly, without computation of derived parameters, by means of principal component analysis (PCA). This procedure allows a fast interpretation of results that can be accomplished in situ. Particular attention was paid to the selection of proper spectral pre-treatments to be applied on data together with the use of several chemometric tools (peak alignment, spectra normalisation and exploratory analysis) aimed at improving the interpretation of XRF results. In addition, the application of multivariate exploratory analysis on XRF hyperspectral maps was studied by using an interactive brushing procedure. The multivariate approach was validated on data obtained from the analysis of the famous Renaissance panel painting “The Ideal City”, exhibited in Palazzo Ducale of Urbino, Italy.     

Comparison of various chemometric evaluation approaches for on-line FT-NIR transmission and FT-MIR/ATR spectroscopic data of methyl methacrylate solution polymerization

For the evaluation of vibrational spectroscopic data acquired on-line to a chemical reaction a broad range of different chemometric algorithms is available. The present study reports the comparative results obtained by different chemometric techniques from the data acquired by light-fiber coupled Fourier-transform near infrared (FT-NIR) transmission spectroscopy and Fourier-transform mid-infrared (FT-MIR) spectroscopy in the attenuated total reflection (ATR) mode to monitor the solution polymerization of methyl methacrylate (MMA). We have found that the results obtained by the application of multivariate curve resolution (MCR) methods to the MIR spectral data acquired during the polymerization of MMA are quite comparable to the results derived by partial least-squares calibration. In the case of the NIR data univariate calibration yields somewhat poorer results than multivariate calibration and MCR, but still inside an acceptable range.     

The role of chemometrics in single and sequential extraction assays: a review: part I. Extraction procedures, uni- and bivariate techniques and multivariate variable reduction techniques for pattern recognition

Element mobility and availability in natural solid matrices can be studied with single and sequential extraction procedures; such procedures provide reliable and useful information only if the experiments are correctly planned and executed and the results are properly interpreted. Chemometrics can be a valuable tool for these aims, especially taking into account the large amounts of data generated with extraction essays and the complexity of the processes under investigation. This review deals with the application of chemometrics in research studies involving single and sequential extractions on soils or sediments, for several purposes: the development and optimization of the extraction conditions, the calculation of element fractionation, the visual illustration of the experimental results, the acquisition of different areas of information, including relationships among variables, similarities and differences among samples, causes of the observed behaviour (e.g. source identification), risk assessment, models and predictions of future events. In Part I of the review, following an overview on extraction procedures, the applications of univariate and bivariate chemometric methods are reported; then the principles of multivariate techniques for pattern recognition based on variable reduction, their applications and the main findings obtained are addressed.