Multivariate Curve Resolution-alternating Least Squares Research Articles

The Fe4+/3+ Redox Mechanism in NaFeO2: A Simultaneous Operando Nuclear Resonance and X‐ray Scattering Study

AbstractSimultaneous operando Nuclear Forward Scattering and transmission X‐ray diffraction and 57Fe Mössbauer spectroscopy measurements were carried out in order to investigate the electrochemical mechanism of NaFeO2 vs. Na metal using a specifically designed in situ cell. The obtained data were analysed using an alternative and innovative data analysis approach based on chemometric tools such as Principal Component Analysis (PCA) and Multivariate Curve Resolution ‐ Alternating Least Squares (MCR‐ALS). This approach, which allows the unbiased extraction of all possible information from the operando data, enabled the stepwise reconstruction of the independent “real” components permitting the description of the desodiation mechanism of NaFeO2. This wealth of information allows a clear description of the electrochemical reaction at the redox‐active iron centres, and thus an improved comprehension of the cycling mechanisms of this material vs. sodium.

Surface chemistry investigation of froth flotation products of lead-zinc sulfide ore using ToF-SIMS and multivariate analysis

In complex flotation circuits of lead-zinc sulfide ore, selective adsorption of flotation reagents (e.g., collectors, depressants, and regulators) and solution components onto different mineral surfaces are involved. This work aimed to study the surface chemistry differences between minerals in lead concentrate and those in tailings by time-of-flight secondary ion mass spectrometry (ToF-SIMS) and multivariate analysis to understand the flotation behavior of minerals. Specifically, multivariate curve resolution-alternating least squares (MCR-ALS) and principal component analysis (PCA) were used to process ToF-SIMS image datasets of flotation products to enhance mineral identification. The results show that MCR-ALS was more successful than PCA in identifying minerals of ToF-SIMS images from flotation products. Further PCA of the spectra obtained from the specific mineral surfaces in the lead concentrate and tailings revealed surface chemistry reasons for the poor mineral separation. The main finding of this study was that the adsorption of lead ions onto the surfaces of sphalerite, pyrite, calcite, and quartz was an important reason for the failed separation of these minerals from galena in high-alkaline lime systems. The surface chemical evidence provided by this study helps to better understand the selective separation mechanism of lead-zinc sulfide ores.

Modeling and optimization of simultaneous degradation of rhodamine B and acid red 14 binary solution by homogeneous Fenton reaction: a chemometrics approach

This study aimed to propose a mathematical method to investigate and optimize the simultaneous elimination process of multiple organic pollutants using the Fenton process. Hence, the treatment of rhodamine B (RB) and acid red 14 (AR14) dyes in their binary solution was studied. Multivariate curve resolution alternating least square (MCR-ALS), a novel chemometric method, was applied along with correlation constraints to resolute the UV-Vis spectrophotometric data, enabling quantification of investigated dyes despite a high spectral overlapping. Response surface methodology was adopted to assess the model and optimize individual and interactive effects of three independent factors (Fe2+, H2O2 and initial pH) on the simultaneous elimination of RB and AR14. The values of the regression coefficient for RB and AR14 were determined as 98.48 and 98.67 percent, respectively, revealing the reliability of the obtained polynomial models to predict decolorization efficiencies. Desirability function was employed to optimize the independent variables to attain the highest possible degradation performance for both dyes in their binary solution. At the optimum point of operation ([Fe2+] = 143.88 mg/L, [H2O2] = 126.89 mg/L and pH = 3.71), degradation efficiencies of RB and AR14 were found as 81.58% and 80.22%, respectively, which were nearly identical to the experimental results.

Visible, near- and mid-infrared spectroscopy coupled with an innovative chemometric strategy to control apple puree quality

Vis-NIRS, MIRS, and a combination of both coupled with PLS and machine learning were applied to i) trace the composed proportions of different apple varieties in formulated purees and ii) predict the quality characteristics of formulated purees from spectral information of initial puree cultivars. The PLS models could estimate proportions of each apple cultivar in puree mixtures using MIR spectra (RMSEP<8.1%, RPD> 3.6), especially for Granny Smith (RMSEP = 2.7%, RPD = 11.4). The concentration profiles from multivariate curve resolution-alternative least squares (MCR-ALS) made possible to reconstruct spectra of formulated purees. MIRS technique was evidenced to predict the final puree quality, such as viscosity (RPD>4.0), contents of soluble solids (RPD = 4.1), malic acid (RPD = 4.7) and glucose (RPD = 4.3), based only on the spectral data of composed puree cultivars. Infrared technique should be a powerful tool for puree traceability, even for multicriteria optimization of final products from the characteristics of composed puree cultivars before formulation.

Raman mapping coupled to self-modelling MCR-ALS analysis to estimate active cosmetic ingredient penetration profile in skin.

Confocal Raman mapping (CRM) is a powerful, label free, non-destructive tool, enabling molecular characterization of human skin with applications in the dermo-cosmetic field. Coupling CRM to multivariate analysis can be used to monitor the penetration and permeation of active cosmetic ingredients (ACI) after topical application. It is presently illustrated how multivariate curve resolution alternating least squares (MCR-ALS) can be applied to detect and semi-quantitatively describe the diffusion profile of Delipidol, a commercially available slimming ACI, from Raman spectral maps. Although the analysis outcome can be critically dependent on the a priori selection of the number of regression components, it is demonstrated that profiling of the kinetics of diffusion into the skin can be established with or without additionnal spectral equality constraints in the multivariate analysis, with similar results. Ultimately, MCR-ALS, applied without spectral equality contraints, specifically identifies the ACI as one of main spectral components enabling to investigate its distribution and penetration into the stratum corneum and underlying epidermis layers.

Extraction of information about structural changes in a semisolid pharmaceutical formulation from near‐infrared and Raman images by multivariate curve resolution–alternating least squares and ComDim

AbstractSolid dispersions are an interesting option to improve the solubility of Class II (high permeability, low water solubility) drugs of the Biopharmaceutical Classification System without the use of organic solvents. However, structural changes (polymorphism) may be present in both active pharmaceutical ingredients (API) and excipients, which require evaluation during pharmaceutical development. Thus, the aim of this work was to demonstrate the feasibility of using Raman and near‐infrared (NIR) mapping associated with multivariate curve resolution–alternating least squares (MCR‐ALS) and common components and specific weights analysis (CCSWA or ComDim) chemometric methods to assess the solid dispersions of atorvastatin calcium in Gelucire® 48/16 under controlled (3.0 ± 1.0°C, sealed flask) and accelerated (33.0 ± 1.0°C, 75% of relative humidity, open flask) aging conditions. MCR‐ALS allowed the identification of the amorphous and crystalline fractions of the drug within the solid dispersion, which is not easily achieved by traditional techniques such as differential scanning calorimetry and X‐ray diffraction, especially for semisolid formulations. ComDim results indicated that Raman seemed more sensitive to the presence of the API, whereas NIR was found to be more sensitive to alterations in the spectra of the excipient. The use of the ComDim method is not yet widespread in the pharmaceutical area; therefore, this paper shows its potential to support pharmaceutical development in preformulation stages for stability studies.

Three-dimensional voltammetry: Use of chronoamperometric E-t-i data to achieve second-order advantage

This work studied the use of three-dimensional voltammetry, particularly potential-time-current (E-t-i) data, on the development of electroanalytical methods. E-t-i data was obtained by taking chronoamperograms at potentials applied as pulses on a staircase waveform. By using this three-way kind of data and appropriate calibration algorithms, the possibility of achieving the second-order advantage was evaluated in the determination of ferrocyanide in the presence of the uncalibrated interference hydroquinone as a model system. The determination of acetaminophen in urine samples, where ascorbic acid and uric acid play the major roles as interferents was also studied. Parallel factor analysis (PARAFAC) and multivariate curve resolution alternating least-squares (MCR-ALS) were the algorithms employed in this work. Both algorithms successfully achieved the second-order advantage by correctly predicting the concentrations of the validation synthetic samples. Excellent predictions were obtained in the direct analysis of acetaminophen-spiked urine samples by E-t-i data and MCR-ALS.

Effect of physicochemical factors and use of milk powder on milk rennet-coagulation: Process understanding by near infrared spectroscopy and chemometrics

The effect of physicochemical factors and use of skim milk powder on milk rennet-coagulation was investigated combining near infrared (NIR) spectroscopic monitoring and Multivariate Curve Resolution - Alternating Least Squares (MCR-ALS). Coagulum formation has been studied by reference approaches (Formagraph and fundamental rheology) and with NIR spectroscopy on unaltered reconstituted milk samples, pasteurized samples, samples with calcium chloride addition and samples of reconstituted milk mixed with fresh milk. The MCR-ALS models successfully described the process evolution, explaining more than 99.9% of variance. The MCR-ALS profiles revealed to be significantly directly correlated with Formagraph and rheological data (p < 0.001) and allowed assessing the significant effect (p < 0.05) of the milk powder type on the coagulation occurrence and the non-significance (p > 0.05) of the CaCl2 concentration level added and the heat treatment applied. The MCR-ALS models calculated for the coagulation trials of pasteurized skimmed milk mixed with reconstituted milk samples highlighted shorter coagulation times with the increasing of reconstituted milk amount (from 4.3-6.6 min to 2–5 min). Profiles extracted from MCR-ALS models developed for a wide range of coagulation conditions proved to be suitable non-destructive, non-invasive and on-line tools to evaluate the rennet-induced coagulation of reconstituted milks.

Multivariate curve resolution of multiway data using the multilinearity constraint

AbstractThe extension of Multivariate Curve Resolution‐Alternating Least Squares (MCR‐ALS) to the analysis of multiway data using the multilinearity constraint is described in detail as one step forward of previous implementations of the trilinearity and quadrilinearity constraints for the analysis of three‐ and four‐way data sets, respectively. As in previous cases, the implementation of the multilinear model for multiway data sets is done algorithmically, within the frame of the alternating least squares (ALS) optimization in the MCR‐ALS method. This implementation is tested using multiway data sets of different complexity, and the obtained results have confirmed the adequacy of the proposed approach. Special advantages of the proposed methodology are that it allows for the implementation of the constraint separately for the different components in their different modes and that it also allows for the introduction of different levels of complexity of the multilinear model, including mixed multilinear models. These two features are especially relevant because they are not present in most of the most used multiway data analysis methods at present.

Detection of chocolate powder adulteration with peanut using near-infrared hyperspectral imaging and Multivariate Curve Resolution

This study aims to detect peanut flour adulteration in chocolate powder using near-infrared (NIR) hyperspectral imaging. Fifteen samples were prepared by mixing both food products in different proportions (0%, 0.1%, 1%, 10% and 100% of peanut) and measured using the hyperspectral camera. A preliminary Principal Component Analysis (PCA) was performed to investigate the structure of the data. Next, the Multivariate Curve Resolution - Alternating Least Squares (MCR-ALS) chemometric method combined with a selectivity constraint in the concentration matrix was applied to untangle the spectral data into a set of components representative of the main constituents found in the samples. Moreover, a detection algorithm based on the calculation of the Mahalanobis distance for every pixel to the model distribution of chocolate powder was implemented. This analysis revealed the complexity of the unmixing problem, allegedly due to the spectral signature overlap in the pixel field of view and because the pure products presented similar spectral signatures. MCR-ALS results were improved after the application of a selectivity constraint, which resulted in a higher performance of the detection algorithm. MCR-ALS detected from 0% to 2.2% of adulterated pixels in mixed samples. On the other hand, the selectivity-constrained MCR-ALS method provided detections from 0.03% to 17.0% in those samples. This pipeline showed that peanut adulteration can be detected even for the lowest concentration level tested (0.1% of peanut). This work highlights the potential of NIR hyperspectral imaging combined with chemometrics for detection purposes.

MCR-ALS analysis of 1H NMR spectra by segments to study the zebrafish exposure to acrylamide.

Metabolomics is currently an important field within bioanalytical science and NMR has become a key technique for drawing the full metabolic picture. However, the analysis of 1H NMR spectra of metabolomics samples is often very challenging, as resonances usually overlap in crowded regions, hindering the steps of metabolite profiling and resonance integration. In this context, a pre-processing method for the analysis of 1D 1H NMR data from metabolomics samples is proposed, consisting of the blind resolution and integration of all resonances of the spectral dataset by multivariate curve resolution-alternating least squares (MCR-ALS). The resulting concentration estimates can then be examined with traditional chemometric methods such as principal component analysis (PCA), ANOVA-simultaneous component analysis (ASCA), and partial least squares-discriminant analysis (PLS-DA). Since MCR-ALS does not require the use of spectral templates, the concentration estimates for all resonances are obtained even before being assigned. Consequently, the metabolomics study can be performed without neglecting any relevant resonance. In this work, the proposed pipeline performance was validated with 1D 1H NMR spectra from a metabolomics study of zebrafish upon acrylamide (ACR) exposure. Remarkably, this method represents a framework for the high-throughput analysis of NMR metabolomics data that opens the way for truly untargeted NMR metabolomics analyses. Graphical abstract.

Untargeted metabolomics changes on Gammarus pulex induced by propranolol, triclosan, and nimesulide pharmaceutical drugs

The presence of pharmaceuticals and personal care products (PPCPs) in natural water resources due to incomplete removal in Wastewater Treatment Plants (WWTPs) is a serious environmental concern at present. In this work, the effects of three pharmaceuticals (propranolol, triclosan, and nimesulide) on Gammarus pulex metabolic profiles at different doses and times of exposure have been investigated by liquid chromatography coupled to high-resolution mass spectrometry (LC-HRMS). The complex data sets generated in the different exposure experiments were analyzed with the ROIMCR procedure, based on the selection of the MS regions of interest (ROI) data and on their analysis by the Multivariate Curve-Resolution Alternating Least Squares (MCR-ALS) chemometrics method. This approach, allowed the resolution and identification of the metabolites present in the analyzed samples, as well as the estimation of their concentration changes due to the exposure experiments. ANOVA Simultaneous Component Analysis (ASCA) and Partial Least Squares Discriminant Analysis (PLS-DA) were then conducted to assess the changes in the concentration of the metabolites for the three pharmaceuticals at the different conditions of exposure. The three tested pharmaceuticals changed the concentrations of metabolites, which were related to different KEGG functional classes. These changes summarize the biochemical response of Gammarus pulex to the exposure by the three investigated pharmaceuticals. Possible pathway alterations related to protein synthesis and oxidative stress were observed in the concentration of identified metabolites.

Near‐infrared multivariate model transfer for quantification of different hydrogen bonding species in aqueous systems

AbstractIt is challenging to achieve consistent quantification of hydrogen‐bonded water species by fitting Gaussian bands on spectra collected from different instruments, especially when the spectral resolution is low. Therefore, this work aims to propose a near‐infrared (NIR) multivariate calibration model transfer method to obtain reliable, consistent, and reproducible results from different spectroscopic instruments. A composite method of Gaussian deconvolution, multivariate curve resolution‐alternating least squares (MCR‐ALS), and partial least squares (PLS) was developed to quantify five water species (labeled as C1, C2, C3, C4, and C5), respectively, assigned to non‐hydrogen‐bonded, singly hydrogen‐bonded, doubly and triply hydrogen‐bonded species, distorted ice‐like structures in the liquid phase, and fully hydrogen‐bonded species showing ice‐like structure. Primary instrument (iS50) was selected due to the highest spectral resolution and spectra (7500–5845 cm−1 with spectral resolution of 0.5 cm−1) were acquired from four types of salt solutions. The developed PLS model yielded a high prediction performance when applied on two independent prediction sets with R2P higher than 0.95 and RMSEP less than 0.009 for prediction of C1‐5. Model built with primary spectra was successfully transferred to spectra of secondary instrument (iN10), producing RMSEP less than 0.010. Transferred model applied on secondary instruments (NIRECO and MPA) showed that fully H‐bonded species in deionized water decreased as temperature increased, while non‐hydrogen‐bonded and singly hydrogen‐bonded demonstrated an opposite temperature dependence. Our results confirmed that it is promising to transfer the calibration model from a sophisticated spectrometer to a simple spectroscopic instrument in terms of quantification of hydrogen‐bonded water species.

Raman Microspectroscopy and Imaging Reveal Novel Biomarkers Specific for Thoracic Aortic Aneurysms

Aortic rupture and dissection are life-threatening complications of ascending thoracic aortic aneurysms (aTAAs) and the risk assessment has been largely based on the monitoring of a lumen size enlargement. Temporal changes of the extracellular matrix (ECM), which has a critical influence on aortic remodeling, are not routinely evaluated nor cardiovascular biomarkers exist to predict aTAA formation. Here, we performed Raman microspectroscopy and imaging and identified marker spectra specific for aTAAs in mice and humans by multivariate data analysis (MVA). Multivariate curve resolution-alternating least squares (MCR-ALS) combined with Lasso regression successfully identified elastic fiber-derived Ce1 and collagen fiber-derived Cc6 components, which were significantly increased in aTAA lesions of murine and human aortic tissues. Cc6 detected the changes in amino acid residues, including phenylalanine, tyrosine, tryptophan, cysteine, aspartate, and glutamate. Ce1 and Cc6 may serve as a diagnostic Raman spectral marker that detects alterations of amino acids derived from aneurysm lesions.

3D and 4D Image Fusion: Coping with Differences in Spectroscopic Modes among Hyperspectral Images.

Image fusion is often oriented to solve differences in spatial scale and orientation among different spectroscopic platforms. However, an additional problem arises when the nature of the spectroscopic information differs in dimensionality as well. Indeed, most imaging systems, e.g., Raman, IR, MS, etc., allow acquisition of 3D images, with a linear spectrum per pixel, but new platforms have emerged, such as the recent excitation-emission fluorescence imaging platforms that provide 4D images, with a 2D spectral landscape per pixel. A proper 3D/4D image fusion needs to take into account the difference in the dimension of the spectral information and in the underlying models of both measurements (bilinear for 3D images and trilinear for 4D images). This work solves this image fusion problem through a new dedicated variant of the multivariate curve resolution-alternating least squares (MCR-ALS) algorithm for multiset analysis based on the incorporation of a hybrid bilinear/trilinear model that can handle the image fused structure preserving the natural behavior of the 3D and 4D imaging techniques coupled. The example is illustrated on the fusion of real 3D Raman and 4D fluorescence images recorded on cross sections of rice leaf samples.

Spectrophotometric and Multivariate Calibration Techniques for Simultaneous Determination of Different Drugs in Pharmaceutical Formulations and Human Urine: Evaluation of Greenness Profile.

Eco-friendly, rapid, and cost-effective two spectrophotometric methods were developed and validated for the determination of atenolol, paracetamol, hydrochlorothiazide, and levofloxacin. The first method is the newly developed extended derivative ratio (EDR) and the second method is multivariate curve resolution—alternating least squares (MCR-ALS). In the EDR method, the extended derivative ratio amplitudes at 281.6, 237.6, 279.2, and 282.8 nm were used for quantification of atenolol, paracetamol, hydrochlorothiazide, and levofloxacin, respectively. In the MCR-ALS method, calibration model was developed and correlation constraint was employed. External validation data set composed of seven mixtures was used, and different figures of merits such as root mean square error of prediction, standard error of prediction, bias, and relative error of prediction were calculated, and satisfactory results were obtained. Both methods provided comparable results. The methods were validated and applied for the determination of the target analytes in dosage forms, spiked and real human urine. Thereafter, the obtained results were statistically compared to the published methods and revealed no significant difference regarding accuracy and precision. Furthermore, the greenness profile of the methods was evaluated using the National Environmental Methods Index “NEMI” and Analytical Eco-Scale. The developed methods can be used as a valid eco-friendly and simple cost-effective alternative to the commonly used chromatographic methods for the routine analysis of the studied drugs in dosage forms and human urine.

Initialization effects in two-component second-order multivariate calibration with the extended bilinear model

Bilinear decomposition of an augmented data matrix is usually complicated by the phenomenon of rotational ambiguity. If the latter is significant, quantitative and qualitative information of the recovered profiles may be less useful. Although constraints can reduce the extent of feasible regions and the degree of rotational ambiguity, the estimation of initial parameters to start the decomposition is an important phase in multivariate curve resolution-alternating least-squares (MCR-ALS) studies. Dealing with a bilinear decomposition of an augmented data matrix where rotational ambiguity persists, the question remains whether it is possible to still develop a successful calibration protocol. Indeed, literature reports indicate that various analytical systems have been experimentally developed, in which substantial rotational ambiguity exists, yet the experimental results confirmed that accurate analyte quantitation was possible. In this research, we further investigate on the effect of the initialization step for a two-component second-order multivariate calibration with the extended bilinear model. It is shown that the selection strategy based on the so-called purest variables can be helpful in achieving a correct profile resolution, depending on which data direction it is applied. Finally, some data-driven guidelines for analytical chemists are suggested, to identify the potential degree of rotational ambiguity and the correct choice of the initialization strategy.

A New Parameter for Measuring the Prediction Uncertainty Produced by Rotational Ambiguity in Second-Order Calibration with Multivariate Curve Resolution.

Multivariate curve resolution-alternating least-squares (MCR-ALS) is the model of choice when dealing with matrix data that cannot be arranged into a trilinear three-way array, that is, mostly from chromatographic origin with spectral detection. A range of feasible solutions may be found in MCR studies, due to the phenomenon of rotational ambiguity associated with bilinear decompositions of matrices. The application of chemically driven constraints is vital to achieving an adequate solution and minimizing the degree of rotational ambiguity present in the system. However, when studying complex samples, it may not be possible to recover unique solutions, even under the application of proper constraints. In such cases, it is important to be able to assess the propagation of rotation uncertainty to the estimated analyte concentrations, which stems from the existence of a finite range of feasible solutions. In this work, we present a new analytical parameter to estimate the potential uncertainty in analyte prediction brought about by rotational ambiguity, in the form of an associated root-mean-square error, named RMSERA. The proposed parameter comes in the form of a range of values, whose limits are δRA/(12)1/2 and δRA/(3)1/2, with δRA being defined as the difference between the maximum and minimum values of the analyte concentration that would be predicted by the MCR model from its concentration profiles lying in the range of feasible solutions, and corresponding to maximum and minimum area, respectively. We support our proposal on extensive simulations for systems of varying composition, and demonstrate its application on experimental data aimed at the determination of four pollutants in environmental water samples.

Parametric optimization and MCR-ALS kinetic modeling of electro oxidation process for the treatment of textile wastewater

Kinetic modeling using multivariate curve resolution-alternating least squares (MCR-ALS) was performed successfully for the electro oxidation (EO) treatment of textile wastewater. The present study represents the monitoring of the % degradation and kinetics of the EO reaction during the treatment of textile effluent. Optimum condition was found to be t ​= ​130 ​min, i ​= ​1.41 A, pH ​= ​5.41 and Retention time ​= ​143 ​min. At this optimum condition, the degradation suggested by response surface methodology (RSM) under central composite design (CCD) was 86%. A good correlation was observed between the predicted and experimental % degradation at the optimum value of process parameters. Spectrophotometric data of EO process during the treatment of textile effluent was analyzed during MCR-ALS. ALS optimization was performed by applying a series of constraints. The initial and final concentration of the pollutants along with the kinetic parameters were successfully resolved. The performance of kinetic modeling on predicting EO treatment was evaluated by a lack of fit in % experimental (1.215) and explained variance (99.98%).

Real-time monitoring of multi-layered film coating processes using Raman spectroscopy

Raman spectroscopy was used as an in-line PAT tool to predict the applied coating mass of three different coating layers on caffeine cores. The different coating suspensions contained titanium dioxide in the anatase and rutile modification and iron oxide as Raman markers. Partial least squares-regression (PLSR) and multivariate curve resolution-alternating least squares (MCR-ALS) were used for multivariate analysis. The acquired Raman spectra were correlated to the applied coating mass. MCR-ALS models were built and applied offline, while PLS-regression was implemented in the coating process to enable a real-time monitoring. Inline-measurements were optimized by a higher frequency of the spectral measurements and the implementation of a moving average. By PLS-regression analysis, all three layers could be predicted with root mean square errors (RMSEP) of less than 2.3%. Inline implementation and optimization resulted in RMSEPs less than 1.9%. MCR-ALS analysis was able to predict the application of the first and the second layer with RMSEPs less than 2.9%, but failed in predicting the application of the third layer. In conclusion, a real-time monitoring of a multi-layered coating process was achieved, PLS-regression was found to be superior to MCR-ALS and smoothing by the implementation of a moving average enhanced the predictability.