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.     

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.     

Multivariate curve resolution: a method of evaluating the kinetics of biotechnological reactions

In biotechnology, strong emphasis is placed on the development of wet chemical analysis and chromatography to separate target components from a complex matrix. In bioprocessing, the development of single compound biosensors is an important activity. The advantages of these techniques are their high sensitivity and specificity. Inline or online monitoring by means of spectroscopy has the potential to be used as an “all-in-one” analysis technique for biotechnological studies, but it lacks specificity. Multivariate curve resolution (MCR) can be used to overcome this limitation. MCR is able to extract the number of components involved in a complex spectral feature, to attribute the resulting spectra to chemical compounds, to quantify the individual spectral contributions, and to use this quantification to develop kinetic models for the process with or without a priori knowledge. After a short introduction to MCR, two applications are presented. In the first example, the spectral features of hemp are monitored and analysed during growth. MCR provides unperturbed spectra on the activity of, for example, lignin and cellulose during plant development. In a second example, the kinetics of a laccase enzyme-catalysed degradation of aromatic hydrocarbons are calculated from UV/VIS spectra.     

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.     

Hyphenated techniques of thermal analysis for characterisation of soil humic substances

Our aim was to investigate the thermal behaviour of humic substances extracted from temperate and tropical soils by means of hyphenated techniques of thermal analysis (e. g. simultaneous thermal analysis DSC/TG coupled with mass spectrometry, MS, for the analysis of evolved gas, EGA) in order (i) to verify whether the chemical composition of isolated humic substances also reflected the differences in microbial parameters previously measured in related soil samples and (ii) to identify suitable indices of thermal stability. Our results show that the investigation of humic substances by thermal methods can provide information on soil organic matter dynamics. Differences in thermal behaviour between the two groups of soils were found. The indices of thermal stability here proposed, IR (index of thermal recalcitrance), and ID (index of thermal decomposability) clearly showed that in humic substances from tropical soils the thermally recalcitrant organic fraction dominated, whilst in temperate humic substances the opposite held. This agrees with previous results on the microbial dynamics and organic matter turnover of the respective soils and indicates that these indices of thermal stability could represent a useful tool in soil environmental quality investigations.     

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.     

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.     

Study of acid-base properties of fulvic acids using fluorescence spectrometry and multivariate curve resolution methods

Samples of fulvic acids obtained from cultivated calcareous soils are analyzed using acid-base titrations with spectrofluorimetric detection. Observed changes in both synchronous and emission spectra of fulvic acids when pH is changed are explained in terms of a limited number of fluorescent contributions each defined by its specific fluorescent spectrum and a concentration profile (species distribution) recovered from the multivariate curve resolution analysis of experimental data. Information on equilibrium is estimated from concentrations of the acid-base species.     

Multivariate curve resolution based chromatographic peak alignment combined with parallel factor analysis to exploit second-order advantage in complex chromatographic measurements

In the present contribution, a new combination of multivariate curve resolution-correlation optimized warping (MCR-COW) with trilinear parallel factor analysis (PARAFAC) is developed to exploit second-order advantage in complex chromatographic measurements. In MCR-COW, the complexity of the chromatographic data is reduced by arranging the data in a column-wise augmented matrix, analyzing using MCR bilinear model and aligning the resolved elution profiles using COW in a component-wise manner. The aligned chromatographic data is then decomposed using trilinear model of PARAFAC in order to exploit pure chromatographic and spectroscopic information. The performance of this strategy is evaluated using simulated and real high-performance liquid chromatography-diode array detection (HPLC-DAD) datasets. The obtained results showed that the MCR-COW can efficiently correct elution time shifts of target compounds that are completely overlapped by coeluted interferences in complex chromatographic data. In addition, the PARAFAC analysis of aligned chromatographic data has the advantage of unique decomposition of overlapped chromatographic peaks to identify and quantify the target compounds in the presence of interferences. Finally, to confirm the reliability of the proposed strategy, the performance of the MCR-COW-PARAFAC is compared with the frequently used methods of PARAFAC, COW-PARAFAC, multivariate curve resolution-alternating least squares (MCR-ALS), and MCR-COW-MCR. In general, in most of the cases the MCR-COW-PARAFAC showed an improvement in terms of lack of fit (LOF), relative error (RE) and spectral correlation coefficients in comparison to the PARAFAC, COW-PARAFAC, MCR-ALS and MCR-COW-MCR results.     

Multivariate curve resolution of incomplete fused multiset data from chromatographic and spectrophotometric analyses for drug photostability studies

An advanced and powerful chemometric approach is proposed for the analysis of incomplete multiset data obtained by fusion of hyphenated liquid chromatographic DAD/MS data with UV spectrophotometric data from acid–base titration and kinetic degradation experiments. Column- and row-wise augmented data blocks were combined and simultaneously processed by means of a new version of the multivariate curve resolution-alternating least squares (MCR-ALS) technique, including the simultaneous analysis of incomplete multiset data from different instrumental techniques. The proposed procedure was applied to the detailed study of the kinetic photodegradation process of the amiloride (AML) drug. All chemical species involved in the degradation and equilibrium reactions were resolved and the pH dependent kinetic pathway described.     

Multivariate curve resolution in liquid chromatography—resolving two-way multi-component data using a Varimax extended rotation

The Varimax extended rotations (VER) have been proposed as a new method to mathematically resolve severely overlapped peaks in chromatographic experiments that produce bilinear data. VER employs a four-step procedure to determine the relative concentration and identity of the components that comprise a severely overlapped chromatographic peak. In the first step, the data are pre-processed to ensure that they are in a form suitable for multivariate curve resolution. The second step involves principal component analysis, which reduces the dimensionality of the data matrix while simultaneously retaining the information present in the data. In the third step, a new coordinate system is developed for the data using a Varimax rotation followed by a so-called extended rotation, which assists in identifying the so-called pure regions in the peak. Identifying these regions is crucial to rotating the concentration and spectral matrices towards a solution. The fourth step utilizes alternating least squares (ALS) to improve the estimates of the concentration and spectral profiles of each component. Results from real and simulated data are used to illustrate the efficacy and simplicity of the proposed method.     

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.     

Electrospray ionization mass spectrometry of terrestrial humic substances and their size fractions

Electrospray ionization mass spectrometry (ESI-MS) was used to evaluate the average molecular mass of terrestrial humic substances, such as humic (HA) and fulvic (FA) acids from a soil, and humic acid from a lignite (NDL). Their ESI mass spectra, by direct infusion, gave average molecular masses comparable to those previously obtained for aquatic humic materials. The soil HA and FA were further separated in size-fractions by preparative high performance size exclusion chromatography (HPSEC) and analyzed with ESI-MS by both direct infusion and a further on-line analytical HPSEC. Unexpectedly, their average molecular mass was only slightly less than for the bulk sample and, despite different nominal molecular size, did not substantially vary among size-fractions. The values increased significantly (up to around 1200 Da) after on-line analytical HPSEC for the HA bulk sample, at both pH 8 and 4, and for the HA size-fractions when pH was reduced from 8 to 4. It was noticed that HA size-fractions at pH 8 were separated by on-line HPSEC in further peaks showing average masses which progressively increased with elution volume. Furthermore, when the HA and NDL bulk samples were sequentially ultracentrifuged at increasing rotational speed, their supernatants showed mass values which were larger than bulk samples and increased with rotational speed. These variations in mass values indicate that the electrospray ionization is dependent on the composition of the humic molecular mixtures and increases when their heterogeneity is progressively reduced. It is suggested that the dominance of hydrophobic compounds in humic supramolecular associations may inhibit the electrospray ionization of hydrophilic components. Our results show that ESI-MS is reasonably applicable to humic substances only after an extensive reduction of their chemical complexity.     

Chemistry at level of individual aerosol particle using multivariate curve resolution of confocal Raman image

Airborne particles with aerodynamic diameter in the 10-1 microm range have been collected in an industrial/urban zone by impaction and have been investigated by automated confocal Raman microspectrometry. The computer-microcontrolled XY scanning and Z focusing of Raman images provided many pixel Raman spectra which are characteristics of complex mixture at level of individual particle. The large heterogeneity was not resolved by the spatial resolution of the instrument which is limited by the optical diffraction. The severe spectral overlaps generated by heterogeneity were resolved by multivariate curve resolution (MCR) methods. The purity based method (SIMPLISMAX) was used to resolve both luminescence spectra and pure Raman spectra without prior information. The MCR-alternating least square (ALS) was used as a refined method of both spectra and spectral concentrations. The reconstructing Raman images of the respective spectral contribution supply a versatile potential to characterize the chemistry of atmospheric aerosols at the level of the individual particles.     

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.     

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.     

Application of multivariate curve resolution to the voltammetric study of the complexation of fulvic acids with cadmium(II) ion

The interaction of fulvic acids with Cd(II) ions has been studied by differential pulse anodic stripping voltammetry (ASV), at pH 7.0 and 0.1 M KNO₃. Voltammetric data obtained during the titration of mixtures of Cd(II) and fulvic acids at different concentrations have been analyzed using multivariate curve resolution (MCR). The application of this method allowed the resolution of the major contributions involved in the titration experiments. Apart from free Cd(II), two more contributions related with the complexation process were detected and resolved, and their corresponding pure voltammograms and concentration profiles were estimated. Simultaneous analysis of independent voltammetric titrations using the proposed MCR methods is shown extremely recommended because it overcame some of the limitations observed in the analysis of individual titrations.     

Resolution of overlapped NMR spectra by two-way multivariate curve resolution alternating least squares with imbedded kinetic fitting

This paper describes the investigation of the hydrolysis of Ally, which is a sulfonylurea (SU) herbicide. The hydrolysis of this compound was observed in situ by nuclear magnetic resonance (NMR) spectroscopy. The data were analyzed using a two-way, multivariate curve resolution (MCR) technique. The resolution of the overlapping aromatic region of the product and the reactant was of special interest. The reactant, product and intermediate spectra were successfully resolved and the rate constants for the degradation of the herbicide under these conditions were simultaneously determined. The results of the chemometric resolution of the overlapped NMR data were compared to the rates found by using a liquid chromatographic method with diode array detection.     

Comparison of voltammetric detection assisted by multivariate curve resolution with amperometric detection in liquid chromatographic analysis of cysteine-containing compounds

A voltammetric detection mode (VD) in conjunction with multivariate curve resolution with alternating least squares (MCR-ALS) method is applied to the analysis of cysteine-containing compounds and compared with a well established amperometric detection (AD) mode in a thin-layer dual Hg/Au cell. VD-MCR-ALS provides an increase in selectivity for cases where satisfactory separation of electroactive compounds is not allowed. However, concentrations needed for a good quantification in VD are higher than in AD due to much large contribution of background in VD.