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.     

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.     

An approach for simultaneous estimation of reaction kinetics and curve resolution from process and spectral data

Parameter estimation of reaction kinetics from spectroscopic data remains an important and challenging problem. This study describes a unified framework to address this challenge. The presented framework is based on maximum likelihood principles, nonlinear optimization techniques, and the use of collocation methods to solve the differential equations involved. To solve the overall parameter estimation problem, we first develop an iterative optimization‐based procedure to estimate the variances of the noise in system variables (eg, concentrations) and spectral measurements. Once these variances are estimated, we then determine the concentration profiles and kinetic parameters simultaneously. From the properties of the nonlinear programming solver and solution sensitivity, we also obtain the covariance matrix and standard deviations for the estimated kinetic parameters. Our proposed approach is demonstrated on 7 case studies that include simulated data as well as actual experimental data. Moreover, our numerical results compare well with the multivariate curve resolution alternating least squares approach.     

ICE: a new method for the multivariate curve resolution of hyperspectral images

The iterated constrained endmembers (ICE) algorithm is a new method of unmixing hyperspectral images that combines aspects of multivariate curve resolution (MCR) methods in chemometrics and unmixing algorithms in remote sensing. Like many MCR methods, ICE also estimates pure components, or endmembers, via alternating least squares; however, it is explicitly based on a convex geometry model and estimation is carried out in a subspace of reduced dimensionality defined by the minimum noise fraction (MNF) transform. In this paper, we describe the ICE algorithm and its properties. We also illustrate its use on a hyperspectral image of cervical tissue. The unmixing of hyperspectral images presents some unique challenges, and we also outline where further development is required. © 2008 John Wiley & Sons, Ltd.     

Multivariate curve resolution of rapid-scan FTIR difference spectra of quinone photoreduction in bacterial photosynthetic membranes

Photosynthetic reaction centres and membranes are systems of particular interest and are often taken as models to investigate the molecular mechanisms of selected bioenergetic reactions. In this work, a multivariate curve resolution by alternating least squares procedure is detailed for resolution of time-resolved difference FTIR spectra probing the evolution of quinone reduction in photosynthetic membranes from Rhodobacter sphaeroides under photoexcitation. For this purpose, different data sets were acquired in the same time range and spectroscopic domain under slightly different experimental conditions. To enable resolution and provide meaningful results the different data sets were arranged in an augmented matrix. This strategy enabled recovery of three different species despite rank-deficiency conditions. It also results in better definition (identity and evolution) of the contributions. From the resolved spectra, the species have been attributed to: 1. the formation of ubiquinol, more precisely the disappearance of Q/appearance of QH₂; 2. conformational change of the protein in the surrounding biological medium; 3. oxidation of diaminodurene, a redox mediator. Because, moreover, results obtained from augmented data sets strategies enable quantitative and qualitative interpretation of concentration profiles, other effects, for example the consequence of repeated light excitation of the same sample, choice of illumination power, or the number of spectra accumulated could be compared and discussed.     

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.     

Curing reaction of glycidylthioether resins: Kinetic model study by near infrared spectroscopy and multivariate curve resolution

The reactivity of sulfur‐based epoxy monomers was studied by monitoring of a model system involving phenylglycidylthioether and aniline. The reaction was carried out under isothermal conditions and monitored in situ by near infrared spectroscopy. Using multivariate curve resolution‐alternating least squares made it possible to obtain the concentration and spectral profiles of each species throughout the reaction. To obtain the kinetic rate constants, the values of the recovered concentration profiles were fitted to a kinetic model proposed for the reaction. Reactivity was evaluated by comparing the concentration profiles and kinetic rate constants obtained with the same parameters obtained for phenylglycidylether/aniline as a reference system. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4846–4856, 2006     

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 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.     

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.     

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.     

Reactivity of silicon‐based epoxy monomers as studied by near‐infrared spectroscopy and multivariate curve resolution methods

The reaction of glycidyloxydimethylphenyl silane with aniline was used as a model system to study the reactivity of silicon‐based epoxy monomers. The reaction was monitored online by near‐infrared spectroscopy, and the evolution of the concentration of each species throughout the reaction was determined by the application of multivariate curve resolution/alternating least squares to the set of recorded spectra. The reactivity was evaluated by a comparison of the concentration profiles obtained for the glycidyloxydimethylphenyl silane/aniline system with those of phenylglycidyl ether/aniline as a reference system. The results confirmed that the reactivity of the silicon‐based epoxy monomer was higher and that its ring opening reaction was faster because of electronic effects. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1447–1456, 2006     

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.     

Estimation of rotation ambiguity in multivariate curve resolution with charged particle swarm optimization (cPSO‐MCR)

Rotation ambiguity (RA) in multivariate curve resolution (MCR) is an undesirable case, when the physicochemical constraints are not sufficiently strong to provide a unique resolution of the data matrix of the mixtures into spectra and concentration profiles of individual chemical components. RA is often met in MCR of overlapped chromatographic peaks, kinetic and equilibrium data, and fluorescence two‐dimensional spectra. In case of RA, a single candidate solution has little practical value. So, the whole set of feasible solutions should be characterized somehow. It is a quite intricate task in a general case. In the present paper, a method was proposed to estimate RA with charged particle swarm optimization (cPSO), a population‐based algorithm. The criteria for updating the particles were modified, so that the swarm converged to the steady state, which spanned the set of feasible solutions. The performance of cPSO‐MCR was demonstrated on test functions, simulated datasets, and real‐world data. Good accordance of the cPSO‐MCR results with the analytical solutions (Borgen plots) was observed. cPSO‐MCR was also shown to be capable of estimating the strength of the constraints and of revealing RA in noisy data. As compared with analytical methods, cPSO‐MCR is simpler to implement, expands to more than three chemical compounds, is immune to noise, and can be easily adapted to virtually all types of constraints and objective functions (constraint based or residue based). cPSO‐MCR also provides natural visual information about the level of RA in spectra and concentration profiles, similar to the methods of two extreme solutions (e.g., MCR‐BANDS). Copyright © 2014 John Wiley & Sons, Ltd.     

Application of maximum likelihood multivariate curve resolution to noisy data sets

In this work, two different maximum likelihood approaches for multivariate curve resolution based on maximum likelihood principal component analysis (MLPCA) and on weighted alternating least squares (WALS) are compared with the standard multivariate curve resolution alternating least squares (MCR‐ALS) method. To illustrate this comparison, three different experimental data sets are used: the first one is an environmental aerosol source apportionment; the second is a time‐course DNA microarray, and the third one is an ultrafast absorption spectroscopy. Error structures of the first two data sets were heteroscedastic and uncorrelated, and the difference between them was in the existence of missing values in the second case. In the third data set about ultrafast spectroscopy, error correlation between the values at different wavelengths is present. The obtained results confirmed that the resolved component profiles obtained by MLPCA‐MCR‐ALS are practically identical to those obtained by MCR‐WALS and that they can differ from those resolved by ordinary MCR‐ALS, especially in the case of high noise. It is shown that methods that incorporate uncertainty estimations (such as MLPCA‐ALS and MCR‐WALS) can provide more reliable results and better estimated parameters than unweighted approaches (such as MCR‐ALS) in the case of the presence of high amounts of noise. The possible advantage of using MLPCA‐MCR‐ALS over MCR‐WALS is then that the former does not require changing the traditional MCR‐ALS algorithm because MLPCA is only used as a preliminary data pretreatment before MCR analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Quantitative analysis of the hydration of lithium salts in water using multivariate curve resolution of near-infrared spectra

The hydration process of lithium iodide, lithium bromide, lithium chloride and lithium nitrate in water was analyzed quantitatively by applying multivariate curve resolution alternating least squares (MCR-ALS) to their near infrared spectra recorded between 850 nm and 1100 nm. The experiments were carried out using solutions with a salt mass fraction between 0% and 72% for lithium bromide, between 0% and 67% for lithium nitrate and between 0% and 62% for lithium chloride and lithium iodide at 323.15 K, 333.15 K, 343.15 K and 353.15 K, respectively. Three factors were determined for lithium bromide and lithium iodide and two factors for the lithium chloride and lithium nitrate by singular value decomposition (SVD) of their spectral data matrices. These factors are associated with various chemical environments in which there are aqueous clusters containing the ions of the salts and non-coordinated water molecules. Spectra and concentration profiles of non-coordinated water and cluster aqueous were retrieved by MCR-ALS. The amount of water involved in the process of hydration of the various salts was quantified. The results show that the water absorption capacity increases in the following order LiI < LiBr < LiNO₃ < LiCl. The salt concentration at which there is no free water in the medium was calculated at each one of the temperatures considered. The values ranged between 62.6 and 65.1% for LiBr, 45.5–48.3% for LiCl, 60.4–61.2% for LiI and 60.3–63.7% for LiNO₃. These values are an initial approach to determining the concentration as from which crystal formation is favored.     

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.     

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.     

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.