Multivariate Curve Resolution Methods Research Articles

On the factor ambiguity of MCR problems for blockwise incomplete data sets

Multivariate curve resolution (MCR) methods are sometimes faced with missing or erroneous data, e.g., due to sensor saturation. In some cases, an estimation of the missing data is possible, but often MCR works with the largest submatrix without missing entries. This ignores all rows and columns of the data matrix that contain missing values. A successful approach to deal with incomplete data multisets has been proposed by Alier and Tauler (2013), but it does not include a factor ambiguity analysis. Here, the missing data problem is addressed in combination with a factor ambiguity analysis. An approach is presented that minimizes the factor ambiguity by extracting a maximum of spectral information even from incomplete rows and columns of the spectral data matrix. The method requires a high signal-to-noise ratio. Applications are presented for UV/Vis and HSI data.

Visualization and identification of components in a gigantic spherical dolomite concretion by Raman imaging in combination with MCR or CLS methods

The combination of Raman imaging and multivariate curve resolution (MCR) or classical least squares (CLS) has allowed us to explore the distribution and identification of components in a gigantic spherical dolomite concretion. It has been found by the MCR and CLS analyses of imaging data that the concretion contains dolomite, kerogen, anatase, quartz, plagioclase, and carbon materials with considerably large distribution of dolomite. The existence of these components has also been confirmed by the point-by-point analysis of imaging data. The distributions of these components were clearly observed by Raman images. Of note is that the amount of carbon materials is considerably large, and they are buried among the matrix sedimentary grains in the concretion, suggesting that there exist soft tissues with biological origin. Moreover, one of the loading spectra of CLS shows intense bands in the region of 3000–2800 cm−1, and bands at ca. 1658, ca. 1585, 1455, 1323, and 1261 cm−1. These bands indicate the existence of decomposed organic materials in the concretion. Raman imaging of concretions provides direct evidence that concretions are of biological organic origin.

Chemometric enhancement for blind signal resolution from non-invasive spatially offset Raman spectra

Spatially offset Raman spectroscopy (SORS) is a promising spectroscopic technique that enables the collection of Raman signals from deeper layers of materials compared to conventional Raman spectroscopy. SORS equipment allows acquiring Raman spectra of substances through packaging, making it a non-invasive analytical technique. Note that the acquired spectrum is always the result of mixing two contributions: (1) the spectrum of the container material, and (2) the spectrum of the substance inside the container. Nowadays, SORS equipment are supported by software capable of removing the surface contribution from the recorded spectral data. However, the optimal extraction of this contribution is not achieved in all cases. This study explored the potential of two chemometric methods, Multivariate Curve Resolution (MCR) and Independent Components Analysis (ICA), for resolving the mixed spectra acquired by Vaya Raman equipment (Agilent) of four standard substances (sucrose, anhydrous sodium sulphate, ethanol 96% and glycerol) analyzed through containers of two different plastic materials (polypropylene and polyethylene terephthalate). The two resulting resolved spectra (by MCR and by ICA) and the one resolved by the equipment software were compared by similarity analysis with the Raman spectra of the standard substances available in recognized databases intended as target spectra. Similarity analysis was performed by calculating four similarity indexes, namely: cosine, arccosine, coefficient of determination and nearness index. Both MCR and ICA methods successfully extracted pure Raman spectra of the test substances more similar to the standard substances than the spectra resolved by the equipment software. These results highlighted the potential of both methods for resolving complex mixed signals, such as those acquired through the SORS technique, thereby enhancing its utility.

Chemometric Exploration of Photostability of Ornidazole in Aqueous Solution with Soft and Hard Modelling Multivariate Curve Resolution Method

The photodegradation study of ornidazole in an aqueous solution was performed by using the multivariate curve resolution-alternative least square technique. The sample solution was exposed to direct sunlight for 42 hours, and the spectroscopic data was obtained at predetermined intervals of wavelengths. MCR-ALS, which is a chemometric technique, was applied to the data set. Initially, soft modeling was used, followed by hard modeling. The results show that ornidazole undergoes photodegradation via a two-step process in an aqueous medium, with three species involved in the degradation process. The initial concentration of pure ornidazole decreases while the concentration of intermediate start increasing and the concentration of intermediate falls with the formation of a new product. Thus, we have got three pure spectra in the MCR-ALS process. The reaction kinetics was performed with the hard modeling technique using kinetic constrain and the rate constant of the reaction was found to be k1 = 0.0955 and k2 = 1.287, respectively.

Application of ultramicrotomy and infrared imaging to the forensic examination of automotive paint

AbstractIn several previously published studies, Lavine and coworkers have demonstrated that infrared (IR) spectra from all layers of an intact multilayered automotive paint chip can be collected in a single analysis by scanning across each layer of a cross sectioned paint chip using a Fourier transform IR imaging microscope. Applying alternating least squares to the spectral data, the IR spectrum of each layer of an original equipment manufacturer paint chip can be extracted from a line map of the spectral image. To further develop this imaging technique for automotive paint analysis, the capability to cross section “small” paint chips (1 mm or less) using an ultramicrotome has been incorporated into our current imaging methodology. An ultramicrotome does not require epoxy or other embedding media for the paint chip and will simplify the analysis. However, extracting the IR spectra for each layer of an original equipment manufacturer paint chip by alternating least squares can be problematic for thin peels (less than one micron thickness), necessitating the use of target testing factor analysis to determine whether a specific layer is present in the line map and modified alternating least squares to recover the IR spectrum of the layer. Using a new sample preparation technique and the appropriate multivariate curve resolution methods, high quality IR spectra of the layers of a modern automotive paint system can be obtained from paint fragments that are smaller than what is practical to analyze by conventional Fourier transform IR spectroscopy.

Two‐ and Three‐Dimensional Strategies for Determining Consecutive Acidity Constants of Ciprofloxacin and Enrofloxacin Using Fluorescent Excitation‐Emission Measurements

AbstractMultidimensional analysis is getting more popular by the day thanks to technical improvements of analytical instruments and development of chemometric methods. Here, we describe the application of two different chemometric methods to the analysis of three‐dimensional spectrofluorimetric dataset for green determination of dissociation constants of ciprofloxacin and enrofloxacin with minimal use of consumables. Three‐dimensional spectrofluorimetric datasets of both drugs were obtained by recording excitation‐emission matrices of only six sample solutions having different pH values. Parallel factor analysis (PARAFAC) and multivariate curve resolution (MCR) methods with the use of three components were used to decompose three‐dimensional excitation‐emission‐pH arrays. The number of components support the presence of two pKa values. The individual profiles of H2A, HA− and A2− species in excitation, emission and pH modes were obtained by the application of PARAFAC and MCR. The intersection points in the pH modes were used to predict pKa values. pKa1 and pKa2 of ciprofloxacin was reported as 6.35, 9.15 and 6.42, 9.40 by PARAFAC and MCR‐ALS, respectively. For enrofloxacin, consecutive pKa values were predicted as 6.11 and 9.06 by PARAFAC and 6.10 and 9.10 by MCR. A detailed comparison to literature was done for the estimated pKa values.

Investigating the High-Temperature Water/MgCl2 Interface through Ambient Pressure Soft X-ray Absorption Spectroscopy

Magnesium chloride is a prototypical deliquescent material whose surface properties, although central for Ziegler-Natta cataysis, have so far remained elusive to experimental characterization. In this work, we use surface-selective X-ray absorption spectroscopy (XAS) at ambient pressure in combination with multivariate curve resolution, molecular dynamics, and XAS theoretical methods to track in real time and accurately describe the interaction between water vapor and the MgCl2 surface. By exposing MgCl2 to water vapor at temperatures between 595 and 391 K, we show that water is preferentially adsorbed on five-coordinated Mg2+ sites in an octahedral configuration, confirming previous theoretical predictions, and find that MgCl2 is capable of retaining a significant amount of adsorbed water even under prolonged heating to 595 K. As a consequence, our work provides first experimental insights into the unique surface affinity of MgCl2 for atmospheric water. The developed technique is proven highly sensitive to the modifications induced by adsorbates on a given low-Z metal based surface and may be useful in the toolbox required to disentangle the mechanisms of interfacial chemical processes.

Regions of Interest Multivariate Curve Resolution Liquid Chromatography with Data-Independent Acquisition Tandem Mass Spectrometry

New data-independent acquisition (DIA) modes coupled to chromatographic separations are opening new perspectives in the processing of massive mass spectrometric (MS) data using chemometric methods. In this work, the application of the regions of interest multivariate curve resolution (ROIMCR) method is shown for the simultaneous analysis of MS1 and MS2 DIA raw data obtained by liquid chromatography coupled to quadrupole-time-of-flight MS analysis. The ROIMCR method proposed in this work relies on the intrinsic bilinear structure of the MS1 and MS2 experimental data which allows us for the fast direct resolution of the elution and spectral profiles of all sample constituents giving measurable MS signals, without needing any further data pretreatment such as peak matching, alignment, or modeling. Compound annotation and identification can be achieved directly by the comparison of the ROIMCR-resolved MS1 and MS2 spectra with those from standards or from mass spectral libraries. ROIMCR elution profiles of the resolved components can be used to build calibration curves for the prediction of their concentrations in complex unknown samples. The application of the proposed procedure is shown for the analysis of mixtures of per- and polyfluoroalkyl substances in standard mixtures, spiked hen eggs, and gull egg samples, where these compounds tend to accumulate.

An upgrade of MVC2, a MATLAB graphical user interface for second-order multivariate calibration: Beyond trilinear models

In the present report, an upgrade of a MATLAB graphical user interface (GUI) toolbox for implementing second-order multivariate calibration models is presented, named Multivariate Calibration 2 (MVC2). Due to the advances in the chemometric field, this software has undergone numerous changes since its last release in 2009. The new freely available MVC2 incorporates novel features and models that make it a very practical tool for data processing. Overall, the current version presents different types of algorithms, designed to provide specific degrees of model flexibility for different multi-way data scenarios: in addition to trilinear decomposition (TLD) and residual bilinearization (RBL) models, which were previously included in the 2009 version, parallel factor analysis 2 (PARAFAC2) and multivariate curve resolution (MCR) methods are now available. All these chemometric methodologies are integrated in the software for quantitative purposes, and if needed, they permit to exploit the so-called analytical second-order advantage. The program offers practical tools for data loading and visualization, model development and validation, and prediction in unknown samples. The software output also includes a comprehensive report on the analytical figures of merit (AFOMs) applicable to second-order calibration models. Specifically, a tool was incorporated for the diagnosis of the remaining rotational ambiguity in the MCR solutions. In the present report, the new features of MVC2 are illustrated through simulated examples and real calibration datasets.

Gas chromatography/mass spectrometry with chemometric methods for the determination of fatty acid profiles in herbal oils.

The conventional method for analyzing fatty acid is gas chromatography (GC) with polar capillary columns. However, owing to the high cost and the sensitivity of these columns to the presence of water and oxygen, these columns are not the best choice for separation. Also, analyzing long-chain acids (>C28) with polar columns is impossible. On the other hand, complete separation with nonpolar columns is not possible for some saturated, unsaturated and long-chain fatty acids. Therefore, in this study, with the help of chemometric methods, a method was developed using GC/mass spectrometry (MS) with a nonpolar column to resolve the peaks to completely separate and accurately identify and quantify fatty acids. Using this method, the fatty acid profiles of the seed oils of Sesamum indicum L, Nigella sativa, Pimpinella anisum, Linum asitatissimum L, Silybum marianum and Amygdalus communis L. var. Amara and var. Dulcis were identified. Through applying the multivariate curve resolution method after GC/MS, the C-18 fatty acids such as α-linolenic, linoleic, oleic and stearic acids were separated and quantified. Also, the total percentages of identified fatty acids increased by 1-6% after resolving overlapping peaks. Finally, the obtained percentages of saturated and unsaturated fatty acids were confirmed by reference reports.

Kinetic Model of Diclofenac Degradation Developed Using Multivariate Curve Resolution Method.

This study presents the kinetic modeling of the natural long-term aging of the pharmaceutical substance as well as the intact tablets of Diclofenac. Datasets are collections of near-infrared spectra acquired from the intact tablets packed in plastic blisters and the spectra of the pure substance. Fresh samples and samples at different stages of degradation are analyzed. No methods of accelerated aging were applied. Multi-step application of MCR-ALS in its soft version followed by the kinetic modeling of the results helps to propose a generic degradation mechanism; which includes: a global kinetic model; approximations of the NIR spectra of the intermediate and product; rough estimates of rate constants. We study tablets in blister packs; exactly as they are presented in pharmacies; and this is important from a practical point of view.

The water structure around chloride ion investigated from D2O ↔ H2O substitution effect

The Raman spectra for (D2O + H2O) − NaCl solutions (nH2O/nD2O = 0/1, 1/4, 1/1, 4/1 and 1/0) were measured at temperatures from 293 to 573 K. We further discuss the water structure in the solutions based on the solute-correlated (SC) OD/OH stretch bands obtained from the Multivariate Curve Resolution method. The most prominent effect of H ↔ D substitution is raising the relative intensity of the high-wavenumber modes. The ∼ 2660 cm−1/∼3635 cm−1 mode can become the main peak when isotopic substitution ratio is 80 % at temperatures over 493 K. The spectral features suggest a flexible water structure in the Cl− hydration shell where most hydrating water molecules are engaged in hydrogen bonding configurations of single donor (SD) and single hydrogen-bond water (SHW). The increase of isotopic substitution ratio leads to the structural transition of SD → SHW → FW (free water) so that FW is greatly increased at isotopic substitution ratio of 80 % and temperatures over 493 K. Moreover, the estimated hydrogen bond number for hydrating water indicates a stronger D2O − Cl− interaction than H2O − Cl− interaction in the hydration shell.

An active constraint approach to identify essential spectral information in noisy data

Multivariate curve resolution (MCR) methods aim at extracting pure component profiles from mixed spectral data and can be applied to high-dimensional data, e.g., from process spectroscopy or hyperspectral imaging techniques. One often observes that some parts of this data, namely certain rows and columns of the data matrix, are considered essential for MCR outcomes, while other parts are of minor importance. Some methods for determining essential data are known, but all have different disadvantages concerning the application for noisy data. This work presents a new approach on how to detect the essential information for noisy, experimental spectral data. Active nonnegativity constraints in combination with duality arguments are the key ingredients for determining essential spectra and frequency channels. The new approach is conceptually simple, computationally cheap and stable with respect to noise. The algorithm is tested for noisy experimental Raman, UV–Vis and FTIR-SEC data.

A temperature‐dependent hydrating structure around SO42− investigated from Raman spectroscopy

AbstractThe Raman spectra of H2O/D2O−Na2SO4 solutions are measured at temperatures (T) up to 573 K. The hydrating structure of SO42− is investigated based on the solute‐correlated (SC) OD/OH stretch bands obtained by the multivariate curve resolution method. Remaining a nearly constant wavenumber of the main peak with increasing temperature, the SC OD/OH bands are narrowed first due to the reduced relative intensity of the shoulder at 2395/~3245 cm−1 when T < ~473 K/~513 K but then because the OD/OH bands get sunken around 2610/3580 cm−1 above ~473/~513 K (letting the ~2660/~3635 cm−1 mode be more prominent and even a separate peak). These spectral features incline to support a temperature‐dependent water structure in the SO42− hydration shell balanced by the SO42−···H2O(D2O) and O–H(D)···O hydrogen bonds (those with D are stronger) as well as the electrostatics. Most hydrating water molecules are engaged in hydrogen bonding configurations of single donor (SD) and single hydrogen‐bond water (SHW). As temperature rises, the average number of hydrogen bonds per hydrating water molecule decreases below ~373 K because of the SD → SHW transition and increases afterward owning to the rapid increase of the ion pairs, and SO42− changes its role from structure breaker to structure maker above ~453 K. The temperature‐dependent solubility behavior of Na2SO4 in H2O can be rationalized by the ion pairing effect and temperature‐dependent structure details in SO42− hydration shell.

Predicting the uniqueness of single non-negative profiles estimated by multivariate curve resolution methods

In many kinds of chemical data, one or more species are unknown and the only efficient way to identify and/or quantify them is by mathematical resolution of the mixture spectra. The major problem with such mathematical decompositions is the possibility of obtaining a range of feasible solutions instead of a unique solution due to insufficient prior information about the system under study. However, even with the minimal non-negativity assumptions, there may be some levels of uniqueness, i.e., full/partial/fractional, in the results of the bilinear decomposition of chemical data which is very important to detect. In this study, a procedure is proposed to predict the uniqueness of the resolved non-negative profiles obtained by MCR-ALS (or analogous methods like NMF, EFA, SIMPLISMA, ITTFA, HELP, etc.). This uniqueness prediction is based on the data-based uniqueness (DBU) theorem and the general rule of uniqueness (GRU) presented in previous studies. The proposed procedure is easy to implement, has no additional computational cost, and is general for different systems with any number of components. Several simulated and experimental datasets containing different numbers of components were used to examine and evaluate the proposed procedure.

Understanding temporal and spatial changes of O3 or NO2 concentrations combining multivariate data analysis methods and air quality transport models

The application of the multivariate curve resolution method to the analysis of temporal and spatial data variability of hourly measured O3 and NO2 concentrations at nineteen air quality monitoring stations across Catalonia, Spain, during 2015 is shown. Data analyzed included ground-based experimental measurements and predicted concentrations by the CALIOPE air quality modelling system at three horizontal resolutions (Europe at 12 × 12 km2, Iberian Peninsula at 4 × 4 km2 and Catalonia at 1 × 1 km2). Results obtained in the analysis of these different data sets allowed a better understanding of O3 and NO2 concentration changes as a sum of a small number of different contributions related to daily sunlight radiation, seasonal dynamics, traffic emission patterns, and local station environments (urban, suburban and rural). The evaluation of O3 and NO2 concentrations predicted by the CALIOPE system revealed some differences among data sets at different spatial resolutions. NO2 predictions, showed in general a better performance than O3 predictions for the three model resolutions, specially at urban stations. Our results confirmed that the application of the trilinearity constraint during the multivariate curve resolution factor analysis decomposition of the analyzed data sets is a useful tool to facilitate the understanding of the resolved variability sources.

Solute-induced changes in the water H-bond network of different alcohol-aqueous systems

In this work, alcohol-water solutions for eight monohydric and two polyhydric alcohols at different concentrations and temperatures were analyzed by infrared spectroscopy to investigate the perturbation of the structure of water surrounding the amphiphilic alcohol molecule. The solute-induced structural changes of water were studied based on the solute-correlated spectral component, which reflects the vibrational properties of the solute and the water molecules perturbed by the solute. This component was obtained from the spectral decomposition using the vibrational multivariate curve resolution method. We used the HOH bending mode as the main probe to investigate the water hydrogen bonding network and estimate the number of water molecules perturbed by the solute molecule. In addition, the CH and CO stretching modes were analyzed to gain a more comprehensive insight into the hydration of these amphiphilic molecules and to provide a reasonable explanation for the observed phenomena.The blue shifts we identified in the HOH bending frequency from the solute-correlated spectra can be attributed to the water molecules with strengthened hydrogen bonds (i.e., the water molecules perturbed by the solute). The perturbation of the water H-bond network is found to depend on the size and shape of the hydrophobic moiety of alcohol, although the differences are small, i.e., the number of perturbed water molecules per alcohol molecule varies depending on the type of alcohol, but is generally between 1 and 3. It seems that this small perturbation of the solvent–water structure does not occur at the immediate water contacts, but rather at the distances beyond the immediate neighbor contact distance. A strong indication of the latter is the relatively large fraction of the bulk-like water (compared to the fraction of perturbed water) still present even in the highly concentrated alcohol solutions. In summary, the number of perturbed water molecules testifies to the fact that it is unlikely that hydration of alcohols at atmospheric pressure and at room temperature and above will result in larger distorted structural units of water different from those found in bulk water.

Pheomelanin subunit non-destructive quantification by Raman spectroscopy and multivariate curve resolution-alternating least squares (MCR-ALS)

To date no direct methods are available for the subunit quantification of pheomelanin, the sulfur-containing melanin form whose structure increases melanoma risk. Here we apply Raman spectroscopy combined with chemometrics (MCR-ALS method) to quantify benzothiazine (BT) and benzothiazole (BZ), the constituent monomers of pheomelanin. The Raman spectra of synthetic pheomelanins only composed of BT or BZ were markedly different from those of natural pheomelanins composed of mixed BT-BZ, indicating the necessity of using a multivariate curve resolution method to extract the pure profiles of these monomers in complex samples. MCR-ALS with correlation constraint was applied to the Raman spectra of pheomelanized feathers from 26 bird species to predict BT-BZ concentrations. The methodology was able to quantify BT with R2 ​= ​0.91 and a relative error of 9%, for the range of 100–1000 ​ng/mg. However, the model did not perform well for BZ quantification. In addition, the MCR-ALS model could retrieve a pure profile associated to keratin, a major component (interference) in feathers. The deconvolution of Raman spectra, which predicts total pheomelanin content, combined with MCR-ALS, which predicts BT content, can therefore provide a complete pheomelanin determination at the monomeric level. This represents a direct and non-destructive analytical method for pheomelanin subunits, opening the door to investigate the differential cytotoxicity of these subunits in a high diversity of biological samples, including melanoma.

Morphotropic phase boundaries of (1−x)Pb(Zn1/3Nb2/3)O3–xPbTiO3 probed by Raman spectroscopy at high temperature

Morphotropic phase boundaries (MPBs) in relaxor Pb(Zn1/3Nb2/3)O3–ferroelectric PbTiO3 systems were investigated by means of angle-resolved polarized Raman spectroscopy at 800 K in the paraelectric phase. The features of the spectra represented by contour maps were extracted through the multivariate curve resolution (MCR) method, rendering the comparison among the data with six compositions more accurate and convenient. The result indicates that the structure becomes unstable at x = 0.07, which is slightly smaller than the MPB occurring at x = 0.09. The additional analysis using the MCR method to investigate the x dependence of the extracted Raman spectra shows anomalies at the MPB. The information related to the MPB near room temperature could be extracted through Raman spectroscopy even in a simple high-temperature paraelectric phase.

Soft Modelling of the Photolytic Degradation of Moxifloxacin Combining Surface enhanced Raman Spectroscopy and Multivariate Curve Resolution

The antibiotic moxifloxacin had a recent surge in its use due to its broad spectrum of activity. However, due to the low metabolization inside the organism, it became an environmental concern. Here, the photolytic degradation of moxifloxacin antibiotic in alkaline medium was carried out and monitored through SERS spectroscopy. Multivariate curve resolution method was applied to extract quantitative and kinetic information about the whole process, using correlation constraint to simultaneously quantify the variation of moxifloxacin concentration. The results showed that the photolysis follows an apparent first order kinetics with half-life of 47.5 min. Also, SERS spectrum along with the calculated Raman spectra suggest that cleavage of the diazabicyclonyl substituent is the preferred photodegradation pathway, in agreement with previous reports.