Varimax extended rotation applied to multivariate spectroscopic image analysis

A new approach for spectral image analysis called the Varimax extended rotation (VER) has been developed. VER employs a four-step procedure to resolve image data. In the first step, the data are pretreated to ensure they are is in a form suitable for principal component analysis. The second step involves reducing the dimensionality of the data using principal component analysis. In the third step, the significant principal components are rotated to identify single component regions in the spectral image. The fourth step uses alternating least squares (ALS) to improve the estimates of the spectral profiles of each component. Results from simulated and real Raman imaging data of water in oil emulsions demonstrate the efficacy and efficiency of the proposed method.     

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.     

Recent trends in application of multivariate curve resolution approaches for improving gas chromatography-mass spectrometry analysis of essential oils

Essential oils (EOs) are valuable natural products that are popular nowadays in the world due to their effects on the health conditions of human beings and their role in preventing and curing diseases. In addition, EOs have a broad range of applications in foods, perfumes, cosmetics and human nutrition. Among different techniques for analysis of EOs, gas chromatography-mass spectrometry (GC-MS) is the most important one in recent years. However, there are some fundamental problems in GC-MS analysis including baseline drift, spectral background, noise, low S/N (signal to noise) ratio, changes in the peak shapes and co-elution. Multivariate curve resolution (MCR) approaches cope with ongoing challenges and are able to handle these problems. This review focuses on the application of MCR techniques for improving GC-MS analysis of EOs published between January 2000 and December 2010. In the first part, the importance of EOs in human life and their relevance in analytical chemistry is discussed. In the second part, an insight into some basics needed to understand prospects and limitations of the MCR techniques are given. In the third part, the significance of the combination of the MCR approaches with GC-MS analysis of EOs is highlighted. Furthermore, the commonly used algorithms for preprocessing, chemical rank determination, local rank analysis and multivariate resolution in the field of EOs analysis are reviewed.     

Application of multivariate self-modeling curve resolution to the quantitation of trace levels of organophosphorus pesticides in natural waters from interlaboratory studies

Multivariate self-modeling curve resolution is applied to the quantitation of coeluted organophosphorus pesticides: fenitrothion, azinphos-ethyl, diazinon, fenthion and parathion-ethyl. Analysis of these pesticides at levels of 0.1 to 1 μg/l in the presence of natural interferences is achieved using automated on-line liquid-solid extraction (Prospekt) coupled to liquid chromatography and diode array detection followed by a recently developed multivariate self-modeling curve resolution method. The proposed approach uses only 100 ml of natural water sample and has improved resolution of the coeluted organophosphorus insecticides and their quantitation at trace level. The results have been compared with those obtained by different laboratories participating in the Aquacheck interlaboratory exercise (WRC, Medmenham, UK) where more conventional analytical techniques are being used.     

Problem of mixtures with known compositions and IRONFLEA method for multivariate curve resolution

A special case of gray spectral data systems [(a) F.-T. Chau, Y.-Z. Liang, J. Gao, X.-G. Shao (Eds.), Chemometrics: From Basics to Wavelet Transform, Chemical Analysis Series, vol. 164, John Wiley & Sons, Inc., 2004; (b) Y.Z. Liang, O.M. Kvalheim, R. Manne, Chemom. Intell. Lab. Syst. 18 (1993) 235-250] is discussed here and the least-squares method for the multivariate curve resolution (MCR) named IRONFLEA is proposed. The system under consideration is the bilinear spectral data of the samples with known chemical compositions and unknown concentration matrix. If the spectra of samples (A_i) and (Q + A_i) (i = 1, …, n, n ≥ 2) are available, then the spectrum and the concentrations of Q could be found and the solution is unique. A practical chemical model for this problem could be mixtures, polymers, peptides, oligosaccharides, or supramolecular formations made of a limited number of monomeric components. In the cases of polymeric or oligomeric samples the spectral contributions and the concentrations of the particular monomeric units are extracted. The method is capable of extracting chemically meaningful spectra of components. The method is implemented in SAS IML code and tested for the deconvolution of spectra of polymers made of styrene derivatives with known monomeric compositions [(a) H. Fenniri, L. Ding, A.E. Ribbe, Y. Zyrianov, J. Am. Chem. Soc. 123 (2001) 8151-8152; (b) H. Fenniri, S. Chun, L. Ding, Y. Zyrianov, K. Hallenga, J. Am. Chem. Soc. 125 (2003) 10546-10560]. The method performs calculations fast enough to allow the incorporation of leave-one-out outlier removal procedure.     

The evolution of chemometrics

Chemometrics is the application of statistical and mathematical methods to chemical problems to permit maximal collection and extraction of useful information. The development of advanced chemical instruments and processes has led to a need for advanced methods to design experiments, calibrate instruments, and analyze the resulting data. For many years, there was the prevailing view that if one needed fancy data analyses, then the experiment was not planned correctly, but now it is recognized that most systems are multivariate in nature and univariate approaches are unlikely to result in optimum solutions. At the same time, instruments have evolved in complexity, computational capability has similarly advanced so that it has been possible to develop and employ increasing complex and computationally intensive methods. In this paper, the development of chemometrics as a subfield of chemistry and particularly analytical chemistry will be presented with a view of the current state-of-the-art and the prospects for the future will be presented.     

Interpreting Analytical Chemistry Data: Recent Advances in Curve Resolution with the Aid of Chemometrics

This overview summarizes the application and impact of chemometrics on the extraction and interpretation of analytical data with the use of curve resolution methods from about 2005 onward. The development and usage of well-known and novel chemometric methods have been described and approximately 85 papers have been referenced. Many suggested improvements to some well-known methods, for example, multivariate curve resolution, have been noted as well as the growing software for such methods. Also, these high dimensional resolution methods have found significant application and, arguably, have opened up a new perspective in calibration, that is, extraction of otherwise unobtainable analytical information from strongly overlapping profiles in the presence of interferences. Recent literature suggests that the use of chemometric methods in analytical chemistry for data extraction and interpretation provides indispensable tools for multivariate data processing and extraction of hidden information, which otherwise would be difficult to obtain.     

Increasing the scope and power of flow-injection analysis through chemometric approaches

The objective of this paper is to illustrate how chemometrics can enhance the scope and power of flow injection analysis (FIA) by considering a few simple but representative cases where the ability of chemometrics to improve performance is not readily apparent. In principle, there are two phases when chemometrics can be usefully combined with FIA: first when developing an FIA method and, second, when treating raw data acquired from an FIA detection system. The most obvious application of chemometrics for the FIA practitioner is to use experimental design to replace the obsolete, but too often used one-variable-at-a-time approach when optimising an FIA method. Therefore, methods for screening variables and system optimisation are discussed. Raw data acquired from most FIA systems are first-order data, containing information about the dispersed sample plug. However, the information that is extracted when using FIA for routine purposes is of zero-order: predominantly peak height values. It is shown by a simple example that a chemometric approach in such cases can again provide additional useful information about the sample. First-order spectral data and second-order data more or less require a chemometrics approach for successful analysis, and examples of such applications are briefly discussed.     

Study of the degradation of 5-azacytidine as a model of unstable drugs using a stopped-flow method and further data analysis with multivariate curve resolution

A general strategy for the study of degradation processes of drugs based on stopped-flow monitoring in a flow system is proposed. The flow system consists of a two-channel manifold for pumping sample and buffer solutions, which join and mix in a PTFE coil (57 cm × 0.7 mm i.d). The flow is stopped when the sample reaches the detection cell and, then, the corresponding kinetic processes are monitored in the spectral range 200-300 nm using a UV-vis diode array spectrophotometer. 5-Azacytidine has been chosen as a model of unstable drugs to illustrate the possibilities of the procedure. Kinetic runs have been developed at temperatures in the range 25-80 °C and pH values from 2 to 11 in order to investigate the influence of these factors on the degradation of the pharmaceutical agent. Multivariate curve resolution based on alternating least squares has been used for the data treatment in order to obtain the kinetic and spectral profiles of species involved in the degradation as well as to calculate the kinetic constants. Results indicate that 5-azacytidine is moderately stable in acid solutions while quickly decomposes in alkaline media. In addition, the degradation is dramatically accelerated with increasing temperature.     

Multi-analyte quantification in bioprocesses by Fourier-transform-infrared spectroscopy by partial least squares regression and multivariate curve resolution

This paper presents the quantification of Penicillin V and phenoxyacetic acid, a precursor, inline during Pencillium chrysogenum fermentations by FTIR spectroscopy and partial least squares (PLS) regression and multivariate curve resolution – alternating least squares (MCR-ALS). First, the applicability of an attenuated total reflection FTIR fiber optic probe was assessed offline by measuring standards of the analytes of interest and investigating matrix effects of the fermentation broth. Then measurements were performed inline during four fed-batch fermentations with online HPLC for the determination of Penicillin V and phenoxyacetic acid as reference analysis. PLS and MCR-ALS models were built using these data and validated by comparison of single analyte spectra with the selectivity ratio of the PLS models and the extracted spectral traces of the MCR-ALS models, respectively. The achieved root mean square errors of cross-validation for the PLS regressions were 0.22 g L⁻¹ for Penicillin V and 0.32 g L⁻¹ for phenoxyacetic acid and the root mean square errors of prediction for MCR-ALS were 0.23 g L⁻¹ for Penicillin V and 0.15 g L⁻¹ for phenoxyacetic acid. A general work-flow for building and assessing chemometric regression models for the quantification of multiple analytes in bioprocesses by FTIR spectroscopy is given.     

Multivariate curve resolution combined with gas chromatography to enhance analytical separation in complex samples: A review

This review describes the major advantages and pitfalls of iterative and non-iterative multivariate curve resolution (MCR) methods combined with gas chromatography (GC) data using literature published since 2000 and highlighting the most important combinations of GC coupled to mass spectrometry (GC–MS) and comprehensive two-dimensional gas chromatography with flame ionization detection (GC × GC-FID) and coupled to mass spectrometry (GC × GC–MS). In addition, a brief summary of some pre-processing strategies will be discussed to correct common issues in GC, such as retention time shifts and baseline/background contributions. Additionally, algorithms such as evolving factor analysis (EFA), heuristic evolving latent projection (HELP), subwindow factor analysis (SFA), multivariate curve resolution-alternating least squares (MCR-ALS), positive matrix factorization (PMF), iterative target transformation factor analysis (ITTFA) and orthogonal projection resolution (OPR) will be described in this paper. Even more, examples of applications to food chemistry, lipidomics and medicinal chemistry, as well as in essential oil research, will be shown. Lastly, a brief illustration of the MCR method hierarchy will also be presented.     

Extension and application of multivariate curve resolution-alternating least squares to four-way quadrilinear data-obtained in the investigation of pollution patterns on Yamuna River,India—A case study

This study focuses on the development and extension of Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) to the analysis of four-way datasets. The proposed extension of the MCR-ALS method with non-negativity and the newly developed quadrilinear constraints can be exploited to summarize and manage huge multidimensional datasets and resolve their four way component profiles. In this study, its application is demonstrated by analyzing a four-way data set obtained in a long term environmental monitoring study (15 sampling sites × 9 variables × 12 months × 7 years) belonging to the Yamuna River, one of the most polluted rivers of India and the largest tributary of the Ganges river. MCR-ALS resolved pollution profiles described appropriately the major observed changes on pH, organic pollution, bacteriological pollution and temperature, along with their spatial and temporal distribution patterns for the studied stretch of Yamuna River. Results obtained by MCR-ALS have also been compared with those obtained by another multi-way method, PARAFAC. The methodology used in this study is completely general and it can be applied to other multi-way datasets.     

Multivariate curve resolution applied to in situ X-ray absorption spectroscopy data: An efficient tool for data processing and analysis

Large datasets containing many spectra commonly associated with in situ or operando experiments call for new data treatment strategies as conventional scan by scan data analysis methods have become a time-consuming bottleneck. Several convenient automated data processing procedures like least square fitting of reference spectra exist but are based on assumptions. Here we present the application of multivariate curve resolution (MCR) as a blind-source separation method to efficiently process a large data set of an in situ X-ray absorption spectroscopy experiment where the sample undergoes a periodic concentration perturbation. MCR was applied to data from a reversible reduction–oxidation reaction of a rhenium promoted cobalt Fischer–Tropsch synthesis catalyst. The MCR algorithm was capable of extracting in a highly automated manner the component spectra with a different kinetic evolution together with their respective concentration profiles without the use of reference spectra. The modulative nature of our experiments allows for averaging of a number of identical periods and hence an increase in the signal to noise ratio (S/N) which is efficiently exploited by MCR. The practical and added value of the approach in extracting information from large and complex datasets, typical for in situ and operando studies, is highlighted.     

Multivariate calibration: What is in chemometrics for the analytical chemist?

Chemometrics has been used for some 30 years but there is still need for disseminating the potential benefits to a wider audience. In this paper, we claim that proper analytical chemistry (1) must in fact incorporate a chemometric approach and (2) that there are several significant advantages of doing so. In order to explain this, an indirect route will be taken, where the most important benefits of chemometric methods are discussed using small illustrative examples. Emphasis will be on multivariate data analysis (for example calibration), whereas other parts of chemometrics such as experimental design will not be treated here. Four distinct aspects are treated in detail: noise reduction; handling of interferents; the exploratory aspect and the possible outlier control. Additionally, some new developments in chemometrics are described.     

Influence of selectivity and sensitivity parameters on detection limits in multivariate curve resolution of chromatographic second-order data

We have established a procedure for calculating limits of detection for second-order data. One of the steps involves curve resolution by iterative target transformation factor analysis (ITTFA) and we have checked some experimental factors that affect the efficiency of resolution by ITTFA. Therefore, they directly affect the estimation of the limits of detection (LOD). In this paper, we describe the quality of the LOD estimator as a function of the performance characteristics of a determination with high performance liquid chromatography (HPLC)-diode array detection (DAD) (sensitivity and selectivity of spectra and chromatograms) and advise the end user about how he can improve it by modifying these experimental variables.     

Handling time misalignment and rank deficiency in liquid chromatography by multivariate curve resolution: Quantitation of five biogenic amines in fish

Biogenic amines (BAs) are used for identifying spoilage in food. The most common are tryptamine (TRY), 2-phenylethylamine (PHE), putrescine (PUT), cadaverine (CAD) and histamine (HIS). Due to lack of chromophores, chemical derivatization with dansyl was employed to analyze these BAs using high performance liquid chromatography with a diode array detector (HPLC-DAD). However, the derivatization reaction occurs with any primary or secondary amine, leading to co-elution of analytes and interferents with identical spectral profiles, and thus causing rank deficiency. When the spectral profile is the same and peak misalignment is present on the chromatographic runs, it is not possible to handle the data only with Multivariate Curve Resolution and Alternative Least Square (MCR-ALS), by augmenting the time, or the spectral mode. A way to circumvent this drawback is to receive information from another detector that leads to a selective profile for the analyte. To overcome both problems, (tri-linearity break in time, and spectral mode), this paper proposes a new analytical methodology for fast quantitation of these BAs in fish with HPLC-DAD by using the icoshift algorithm for temporal misalignment correction before MCR-ALS spectral mode augmented treatment. Limits of detection, relative errors of prediction (REP) and average recoveries, ranging from 0.14 to 0.50 µg mL⁻¹, 3.5–8.8% and 88.08%–99.68%, respectively. These are outstanding results obtained, reaching quantification limits for the five BAs much lower than those established by the Food and Agriculture Organization of the United Nations and World Health Organization (FAO/WHO), and the European Food Safety Authority (EFSA), all without any pre-concentration steps. The concentrations of BAs in fish samples ranged from 7.82 to 29.41 µg g⁻¹, 8.68–25.95 µg g⁻¹, 4.76–28.54 µg g⁻¹, 5.18–39.95 µg g⁻¹ and 1.45–52.62 µg g⁻¹ for TRY, PHE, PUT, CAD, and HIS, respectively. In addition, the proposed method spends less than 4 min in an isocratic run, consuming less solvent in accordance with the principles of green analytical chemistry.     

Detection of malathion in food peels by surface-enhanced Raman imaging spectroscopy and multivariate curve resolution

An analytical methodology was developed for detection of malathion in the peels of tomatoes and Damson plums by surface-enhanced Raman imaging spectroscopy and multivariate curve resolution. To recover the pure spectra and the distribution mapping of the analyzed surfaces, non-negative matrix factorization (NMF), multivariate curve calibration methods with alternating least squares (MCR-ALS) and MCR with weighted alternating least square (MCR-WALS) were utilized. Error covariance matrices were estimated to evaluate the structure of the error over all the data. For the tomato data, NMF-ALS and MCR-ALS presented excellent spectral recovery even in the absence of initial knowledge of the pesticide spectrum. For the Damson plum data, owing to heteroscedastic noise, MCR-WALS produced better results. This methodology enabled detection below to the maximum residue limit permitted for this pesticide. This approach can be implemented for in situ monitoring because it is fast and does not require extensive manipulation of samples, making its use feasible for other fruits and pesticides as well.     

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 curve resolution applied to the simultaneous analysis of electrochemical and spectroscopic data: study of the Cd(II)/glutathione-fragment system by voltammetry and circular dichroism spectroscopy

Multivariate curve resolution with alternating least squares (MCR-ALS) is applied for the first time to the simultaneous analysis of electrochemical and spectroscopic data. Then, a data analysis is done with augmented matrices constituted by Differential Pulse Polarography and Circular Dichroism data submatrices. The use of proper, and different for each submatrix, constrains in the iterative ALS optimization allows to obtain chemically meaningful results constituted by a common matrix containing the concentration profiles, and two matrices with the pure electrochemical and spectroscopic signals. MCR-ALS is applied to the study of the complexation of Cd by Cys-Gly, a glutathione-fragment of great interest for understanding metal-phytochelatins complexation.     

Multivariate curve resolution applied to Fourier transform infrared spectra of macromolecules: structural characterisation of the acid form and the salt form of humic acids in interaction with lead

The significance of evolving mixtures structural spectroscopic studies might appear limited when the experimental spectra do not present a sufficient quality for a precise interpretation. It is the case when the chemical behaviour of macromolecules is studied on the basis of infrared spectra. If the effective resolution is low, the spectral profiles appear similar despite the applied chemical conditions change. This makes impossible the interpretation of the raw spectra and mathematical treatments are required to separate the different contributions that overlap.To determine the behaviour of the reactive sites of humic acids in the binding with heavy metals, infrared spectra are recorded under various chemical conditions. The cation to be considered is Pb²⁺ and the two chemical variables to be studied are pH and initial lead concentration. Four series of FTIR spectra are recorded, but no visible difference can be directly assigned to the different chemical states of the macromolecules. Multivariate self-modelling curve resolution is thus proposed as a tool for resolving these complex and strong overlapping datasets. First, initial estimates are obtained from pure variable detection methods: it comes out that two spectra are enough to reconstruct the experimental matrices. In a further step, the application of the multivariate curve resolution-alternating least squares (MCR-ALS) algorithm with additional constraints on each individual dataset, as well as on column-wise augmented matrices, allows to optimise the profiles and spectra that appear to be highly characterising the acid and the salt form of the molecule. Moreover, the concentrations profiles associated to these two limit spectral forms allow interpreting the analytical measurements made during the reactions between humic acids and H⁺ or Pb²⁺. Consequently, depending on the initial state of the humic acid, two distinct reactional mechanisms are proposed.