Multivariate Curve Resolution-alternating Least Squares Research Articles

Unlocking New Capabilities in the Analysis of GC × GC‐TOFMS Data With Shift‐Invariant Multi‐Linearity

ABSTRACTThis paper introduces a novel deconvolution algorithm, shift‐invariant multi‐linearity (SIML), which significantly enhances the analysis of data from two‐dimensional gas chromatography instruments coupled to a time‐of‐flight mass spectrometer (GC × GC‐TOFMS). Designed to address the challenges posed by retention time shifts and high noise levels, SIML incorporates wavelet‐based smoothing and Fourier‐transform based shift‐correction within the multivariate curve resolution‐alternating least squares (MCR‐ALS) framework. We benchmarked the SIML algorithm against non‐negativity constrained MCR‐ALS and parallel factor analysis 2 with flexible coupling (PARAFAC2 × N) using both simulated and real GC × GC‐TOFMS datasets. Our results demonstrate that SIML provides unique solutions with significantly improved robustness, particularly in low signal‐to‐noise ratio scenarios, where it maintains high accuracy in estimating mass spectra and concentrations. The enhanced reliability of quantitative analyses afforded by SIML underscores its potential for broad application in complex matrix analyses across environmental science, food science, and biological research.

Hyperspectral Raman imaging with multivariate curve resolution-alternating least square (MCR-ALS) analysis for xylazine-containing drug mixtures

Xylazine, increasingly implicated in illicit opioid overdose deaths, poses a significant public health threat due to its synergistic effects with fentanyl and resistance to naloxone reversal. Despite its rising prevalence, xylazine is not classified as a controlled substance, leading to its exclusion from routine forensic screening. This study introduces a novel analytical method combining Raman hyperspectral imaging with Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) to detect xylazine in drug mixtures containing common excipients such as acetaminophen, dipyrone, and mannitol. Utilizing only non-negativity constraints, MCR-ALS successfully resolved the Raman spectrum of xylazine at levels as low as 5 % without reference spectra. The method demonstrated robust performance, with percent variance explained (R²) values of 99.60 %, 99.80 %, and 99.91 % for the drug mixtures containing 25 %, 10 %, and 5 % xylazine, respectively.

Chemometric modeling of spectroscopic data for characterizing the visible-light-driven photocatalytic N-dealkylation of rhodamine B on a TiO2 film.

The green-light driven photocatalytic N-deethylation reaction of Rhodamine B (RhB) on a TiO2 film was investigated by UV-vis absorption and fluorescence emission spectroscopies, in addition to HPLC and HR-MS, to ascertain the nature of the reaction products. The evolution of the photocatalytic reaction was chemometrically analyzed using Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) of the spectroscopic data to obtain the kinetic and spectral decomposition of the RhB derivatives involved in the reaction. This was then compared with the results obtained by standard HPLC analysis. The MCR-ALS analysis yielded satisfactory spectral and kinetic profiles for RhB and the fully deethylated product, Rhodamine 110. However, the spectral profiles for the N-triethyl (3EtRh) and the mixture of the two isomeric N-diethyl (2EtRh) derivatives exhibited some spectral distortions due to significant spectral overlap between these compounds. In contrast to the HPLC analysis, the MCR-ALS could not resolve the N-ethylrhodamine (EtRh) derivative. The deethylation reactions occurred via independent zero-order steps at the surface of TiO2, indicating that the RhB degradation reaction is governed by the adsorption-desorption equilibrium of the dye and derivatives on the photocatalyst surface, thereby enhancing the diffusion of compounds on the surface.

Simultaneously quantifying a novel five-component anti- migraine formulation containing ergotamine, propyphenazone, caffeine, camylofin, and mecloxamine using UV spectrophotometry and chemometric models

This study presents a new method for simultaneously quantifying a complex anti-migraine formulation containing five components (ergotamine, propyphenazone, caffeine, camylofin, and mecloxamine) using UV spectrophotometry and chemometric models. The formulation presents analytical challenges due to the wide variation in component concentrations (ERG: PRO: CAF: CAM: MEC ratio of 0.075:20:8:5:4) and highly overlapping UV spectra. To create a comprehensive validation dataset, the Kennard-Stone Clustering Algorithm was used to address the limitations of arbitrary data partitioning in chemometric methods. Three different chemometric models were evaluated: Classical Least Squares (CLS), Partial Least Squares (PLS), and Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS). Among these, MCR-ALS demonstrated excellent performance, achieving recovery values of 98–102% for all components, accompanied by minimal root mean square errors of calibration (0.072–0.378) and prediction (0.077–0.404). Moreover, the model exhibited high accuracy, with relative errors ranging from 1.936 to 3.121%, bias-corrected mean square errors between 0.074 and 0.389, and a good sensitivity (0.2097–1.2898 μg mL−1) for all components. The Elliptical Joint Confidence Region analysis further confirmed the predictive performance of the models, with MCR-ALS consistently showing the smallest ellipses closest to the ideal point (slope = 1, intercept = 0) for most analytes, indicating superior accuracy and precision. The approach's sustainability was rigorously assessed using six advanced metrics, validating its environmental friendliness, economic viability, and practical application. This approach effectively resolves complex pharmaceutical formulations, contributing to sustainable development objectives in quality control processes.

Analytical Figures of Merit in Univariate, Multivariate, and Multiway Calibration: What Have We Learned? What Do We Still Need to Learn?

ABSTRACTAn overview of the status of the research in analytical figures of merit is provided, including all calibration scenarios from univariate to multivariate and multiway analytical protocols. Both linear and nonlinear multivariate models are considered. Starting with the simplest multivariate model, inverse least‐squares regression, the basic concepts of sensitivity, sample leverage, and limit of detection are introduced. The extension to other multivariate models is discussed, as well as to nonlinear models based on radial basis functions, kernel partial least‐squares, and multilayer feed‐forward artificial neural networks. Finally, multiway calibration models are discussed, including multilinear decomposition models such as parallel factor analysis (PARAFAC) and multivariate curve resolution–alternating least‐squares (MCR‐ALS). In the latter case, recent developments concerning the pervasive phenomenon of rotational ambiguity are discussed. Unfinished works and areas where further research efforts are needed to develop closed‐form expressions and to fully understand their meaning are included.

Machine Learning and Hyperspectral Imaging for Analysis of Human Papillomaviruses (HPV) Vaccine Self-Healing Particles.

Human papillomaviruses (HPV) are known to cause a variety of diseases, including cervical cancer and genital warts. HPV is a highly prevalent virus and is considered the most common sexually transmitted disease. Because of the risks associated with HPV, Gardasil, a quadrivalent recombinant vaccine, was developed by Merck & Co., Inc., Rahway, NJ, USA, and approved by the Food and Drug Administration (FDA) in 2006. The second generation of the vaccine, Gardasil9, was subsequently approved by the FDA in 2014, providing significant protection against HPV. The HPV vaccine may be given as 2 or 3 doses; however, vaccine administration as a single dose with a sustained release mechanism may potentially offer benefits to meet emerging health needs. To explore this, HPV vaccines were formulated within microporous self-healing particles (SHPs) to enable potential controlled release of HPV virus-like particle (VLP) antigen. Machine learning, in the form of multivariate curve resolution-alternating least-squares (MCR-ALS), with Raman hyperspectral imaging was used to determine the molecular identity and spatial distribution of all relevant species within this HPV vaccine formulation. The results indicate that machine learning with Raman hyperspectral imaging was able to spatially resolve HPV VLP antigens within SHP vaccines for the first time, providing crucial information necessary for vaccine development.

Investigating In Vivo Tumor Biomolecular Changes Following Radiation Therapy Using Raman Spectroscopy.

Treatment resistance is a major bottleneck in the success of cancer therapy. Early identification of the treatment response or lack thereof in patients can enable an earlier switch to alternative treatment strategies that can enhance response rates. Here, Raman spectroscopy was applied to monitor early tumor biomolecular changes in sensitive (UM-SCC-22B) and resistant (UM-SCC-47) head and neck tumor xenografts for the first time in in vivo murine tumor models in response to radiation therapy. We used a validated multivariate curve resolution-alternating least-squares (MCR-ALS) model to resolve complex multicomponent Raman spectra into individual pure spectra and their respective contributions. We observed a significant radiation-induced increase in the contributions of lipid-like species (p = 0.0291) in the radiation-sensitive UM-SCC-22B tumors at 48 h following radiation compared to the nonradiated baseline (prior to commencing treatment). We also observed an increase in the contribution of collagen-like species in the radiation-resistant UM-SCC-47 tumors at 24 h following radiation compared to the nonradiated baseline (p = 0.0125). In addition to the in vivo analysis, we performed ex vivo confocal Raman microscopic imaging of frozen sections derived from the same tumors. A comparison of all control and treated tumors revealed similar trends in the contributions of lipid-like and collagen-like species in both in vivo and ex vivo measurements; however, when evaluated as a function of time, longitudinal trends in the scores of collagen-like and lipid-like components were not consistent between the two data sets, likely due to sample numbers and differences in sampling depth at which information is obtained. Nevertheless, this study demonstrates the potential of fiber-based Raman spectroscopy for identifying early tumor microenvironmental changes in response to clinical doses of radiation therapy.

Comprehensive characterization of volatile compounds in Iranian black teas using chemometric analysis of GC-MS fingerprints

Black tea, a widely popular non-alcoholic beverage, is renowned for its unique aroma and has attracted significant attention due to its complex composition. However, the chemical profile of Iranian tea remains largely unexplored. In this research, black tea samples from key tea cultivation regions in four geographical areas in northern Iran were firstly analyzed using headspace solid-phase microextraction followed by gas chromatography–mass spectrometry (HS-SPME-GC–MS) to separate, identify, and quantify their volatile organic compounds. Subsequently, employing a robust investigative strategy, we utilized for the first time the well-known multivariate curve resolution-alternating least square (MCR-ALS) method as a deconvolution technique to analyze the complex GC–MS peak clusters of tea samples. This approach effectively addressed challenges such as severe baseline drifts, overlapping peaks, and background noise, enabling the identification of minor components responsible for the distinct flavors and tastes across various samples. The MCR-ALS technique significantly improved the resolution of spectral and elution profiles, enabling both qualitative and semi-quantitative analysis of tea constituents. Qualitative analysis involved comparing resolved peak profiles to theoretical spectra, along with retention indices, while semi-quantification was conducted using the overall volume integration (OVI) approach for volatile compounds, providing a more accurate correlation between peak areas and concentrations. The application of chemometric tools in GC–MS analysis increased the number of recognized components in four tea samples, expanding from 54 to 256 components, all with concentrations exceeding 0.1 %. Among them, 32 volatile compounds were present in every tea sample. Hydrocarbons (including alkenes, alkanes, cycloalkanes, monoterpenes and sesquiterpenes), esters and alcohols were the three major chemical classes, comprising 78 % of the total relative content of volatile compounds. Analyzing black teas from four distinct regions revealed variations not only in their volatile components but also in their relative proportions. This integrated approach provides a comprehensive understanding of the volatile chemical profiles in Iranian black teas, enhances knowledge about their unique characteristics across diverse geographical origin, and lays the groundwork for quality improvement.

Determination of DEET, Icaridin, and IR3535 in insect repellents using excitation-emission matrix (EEM) fluorescence spectroscopy and multiway calibration

Due to rising temperatures in recent years, there has been an increase in outbreaks of arboviral diseases like Dengue, chikungunya, Zika, and yellow fever, which are primarily transmitted by two Aedes mosquitos. The outbreak has sparked significant concern among the population and prompted countries to heighten their precautions, specially by increasing the use of insects repellents. Regarding the regulatory demands of these products, this study develops a novel analytical method for the determination of DEET, Icaridin, and IR3535 in insect repellents combining excitation-emission matrix (EEM) fluorescence spectroscopy with higher-order multivariate calibration techniques. For this purpose, a dataset comprising 21 samples containing the studied active ingredients was used to construct Parallel Factor Analysis (PARAFAC) and Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) models. As a result, DEET, Icaridin, and IR3535 were quantified with a RMSEP lower than 1.84% for PARAFAC and below 11.30% for MCR-ALS. The EJCR test confirmed the accuracy of the proposed methods, which agreed with the high-performance liquid chromatography reference method at a 95% confidence level. These findings suggest that developing multiway calibration models using EEM proves to be accurate and cost-effective for quality control in repellent-based products.

Eco-friendly chemometric analysis: Sustainable quantification of five pharmaceutical compounds in bulk, tablets, and spiked human plasma

The development of sustainable chemometric methodologies is crucial in pharmaceutical analysis to ensure accurate chemical quantification with little environmental effect. This study introduces novel chemometric techniques for the simultaneous measurement of Rabeprazole (RAB), Lansoprazole (LAN), Levofloxacin (LEV), Amoxicillin (AMO), and Paracetamol (PAR) in various samples, including lab-prepared mixtures, tablets, and spiked human plasma. Taguchi L25 (5^5) orthogonal array design to construct the calibration and validation sets was employed, the techniques used named Principal Component Regression (PCR), Partial Least Squares (PLS-2), Artificial Neural Networks (ANNs), and Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS). The models were validated for their effectiveness in resolving complex spectra from overlapping components, the models achieving high correlation coefficients (R≥0.9997) and the relative error of prediction (REP) and root mean square error of prediction (RMSEP), were (0.2221 to 0.8022) and (0.0352 to 0.1767), respectively. The bias-corrected mean square error of prediction (BCMSEP) was (−0.00065 to 0.00166). The application of various assessment tools for evaluating greenness, blueness, and whiteness offered valuable insights into the environmental impact and sustainability of the developed methods compared to the reported ones. According to the Need Quality Sustainability (NQS) index, the developed methods align with sustainable analytical practices and support the United Nations Sustainable Development Goals (UN-SDGs).

In Situ Raman Hyperspectral Analysis of Microbial Colonies for Secondary Metabolites Screening.

Since the discovery of penicillin, a vast array of microbial antibiotics has been identified and applied in the medical field. Globally, the search for drug candidates via microbial screening is ongoing. Traditional screening methods, however, are time-consuming and require labor-intensive sample processing, significantly reducing throughput. This research introduces a Raman spectroscopy-based screening system tailored to the in situ analysis of microbial colonies on solid culture media. Employing multivariate curve resolution-alternating least-squares (MCR-ALS) for spectral decomposition, our approach reveals the production of secondary metabolites at the single colony level. We enhanced the microbial culture method, enabling direct, high signal-to-noise (S/N) ratio Raman spectroscopic measurements of colonies of Escherichia coli and actinomycetes species. Through semisupervised MCR analysis using the known spectra of actinorhodin and undecylprodigiosin as references, we accurately assessed the production of these compounds by Streptomyces coelicolor A3(2). Furthermore, we herein successfully detected the production of amphotericin B by Streptomyces nodosus, even in the absence of prior spectral information. This demonstrates the potential of our technique in the discovery of secondary metabolites. In addition to enabling the detection of the above-mentioned compounds, this analysis revealed the heterogeneity of the spatial distribution of their production in each colony. Our technique makes a significant contribution to the advancement of microbial screening, offering a rapid, efficient alternative to conventional methods and opening avenues for secondary metabolites discovery.

Multivariate curve resolution-alternating least-squares and second-order advantage in first-order calibration. A systematic characterisation for three-component analytical systems

BackgroundRecent interest has been focused on the application of multivariate curve resolution-alternating least-squares (MCR-ALS) to systems involving the measurement of first-order and non-bilinear second-order data. The latter pose important challenges to bilinear decomposition models, due to the phenomenon of rotational ambiguity in the solutions, even under the application of the full set of chemical constraints that is usually employed in MCR-ALS calibration. ResultsAfter the analysis of several simulated and experimental datasets, important conclusions regarding the role of the selectivity patterns in the constituent spectra have been drawn concerning the achievement of the second-order advantage. Theoretical considerations based on the calculation of the areas of feasible solutions helped to support the observations regarding the predictive ability of MCR- ALS in the various datasets. SignificanceThe understanding of the impact of rotational ambiguity in obtaining the second-order advantage with both first-order and non-bilinear second-order data is of paramount importance in the future development of analytical protocols of complex samples.

Investigating the quality of extraction and quantification of bioactive compounds in berries through liquid chromatography and multivariate curve resolution

Berries are a rich source of natural antioxidant compounds, which are essential to profile, as they add to their nutritional value. However, the complexity of the matrix and the structural diversity of these compounds pose challenges in extraction and chromatographic separation. By relying on multivariate curve resolution alternating least squares (MCR-ALS) ability to extract components from complex spectral mixtures, our study evaluates the contributions of various extraction techniques to interference, extractability, and quantifying different groups of overlapping compounds using liquid chromatography diode array detection (LC-DAD) data. Additionally, the combination of these methods extends its applicability to evaluate polyphenol degradation in stored berry smoothies, where evolving factor analysis (EFA) is also used to elucidate degradation products. Results indicate that among the extraction techniques, ultrasonication-assisted extraction employing 1% formic acid in methanol demonstrated superior extractability and selectivity for the different phenolic compound groups, compared with both pressurized liquid extraction and centrifugation of the fresh berry smoothie. Employing MCR-ALS on the LC-DAD data enabled reliable estimation of total amounts of compound classes with high spectral overlaps. Degradation studies revealed significant temperature-dependent effects on anthocyanins, with at least 50% degradation after 7 months of storage at room temperature, while refrigeration and freezing maintained fair stability for at least 12 months. The EFA model estimated phenolic derivatives as the main possible degradation products. These findings enhance the reliability of quantifying polyphenolic compounds and understanding their stability during the storage of berry products.Graphical abstract

Visible-short wavelength near infrared hyperspectral imaging coupled with multivariate curve resolution-alternating least squares for diagnosis of breast cancer

This study investigates the application of visible-short wavelength near-infrared hyperspectral imaging (Vis-SWNIR HSI) in the wavelength range of 400–950 nm and advanced chemometric techniques for diagnosing breast cancer (BC). The research involved 56 ex-vivo samples encompassing both cancerous and non-cancerous breast tissue from females. First, HSI images were analyzed using multivariate curve resolution-alternating least squares (MCR-ALS) to exploit pure spatial and spectral profiles of active components. Then, the MCR-ALS resolved spatial profiles were arranged in a new data matrix for exploration and discrimination between benign and cancerous tissue samples using principal component analysis (PCA) and partial least squares-discriminant analysis (PLS-DA). The PLS-DA classification accuracy of 82.1 % showed the potential of HSI and chemometrics for non-invasive detection of BC. Additionally, the resolved spectral profiles by MCR-ALS can be used to track the changes in the breast tissue during cancer and treatment. It is concluded that the proposed strategy in this work can effectively differentiate between cancerous and non-cancerous breast tissue and pave the way for further studies and potential clinical implementation of this innovative approach, offering a promising avenue for improving early detection and treatment outcomes in BC patients.

Green highly sensitive and selective spectroscopic detection of guaifenesin in multiple dosage forms and spiked human plasma

Guaifenesin (GUA) is determined in dosage forms and plasma using two methods. The spectrofluorimetric technique relies on the measurement of native fluorescence intensity at 302 nm upon excitation wavelength “223 nm”. The method was validated according to ICH and FDA guidelines. A concentration range of 0.1–1.1 μg/mL was used, with limit of detection (LOD) and quantification (LOQ) values 0.03 and 0.08 µg/mL, respectively. This method was used to measure GUA in tablets and plasma, with %recovery of 100.44% ± 0.037 and 101.03% ± 0.751. Furthermore, multivariate chemometric-assisted spectrophotometric methods are used for the determination of GUA, paracetamol (PARA), oxomemazine (OXO), and sodium benzoate (SB) in their lab mixtures. The concentration ranges of 2.0–10.0, 4.0–16.0, 2.0–10.0, and 3.0–10.0 µg/mL for OXO, GUA, PARA, and SB; respectively, were used. LOD and LOQ were 0.33, 0.68, 0.28, and 0.29 µg/mL, and 1.00, 2.06, 0.84, and 0.87 µg/mL for PARA, GUA, OXO, and SB. For the suppository application, the partial least square (PLS) model was used with %recovery 98.49% ± 0.5, 98.51% ± 0.64, 100.21% ± 0.36 & 98.13% ± 0.51, although the multivariate curve resolution alternating least-squares (MCR-ALS) model was used with %recovery 101.39 ± 0.45, 99.19 ± 0.2, 100.24 ± 0.12, and 98.61 ± 0.32 for OXO, GUA, PARA, and SB. Analytical Eco-scale and Analytical Greenness Assessment were used to assess the greenness level of our techniques.

Insights into the Structure and Activity of Bimetallic Au/Cu2O Catalysts during CO2 Electroreduction to C2 products

Despite its promising performance for C2+ product formation in electrochemical reduction of CO2 (CO2RR), Cu-based catalysts exhibit a relatively poor selectivity towards important chemical intermediates such as ethylene and ethanol. Up to 16 different products can typically be formed during CO2RR.1 Cu is the only element that can form C-C bonds at an appreciable rate.2 Therefore, it is critical to better understand the active sites of Cu-based electrocatalysts, as it can lead to better catalyst design with improved selectivity towards desired products. A common approach is to investigate the reactivity of well-defined surface terminations of Cu, which can be achieved by employing shape-controlled (nano)particles.3 Here, we expanded on such studies by evaluating the impact of Au on well-defined Cu2O surfaces for the electrochemical reduction of CO2. This promoter metal was chosen, because it can reduce CO2 to CO, which is widely accepted as the key intermediate for C-C coupling.2,4 In this study, 40 nm Cu2O nanocubes that predominantly expose the (100) facet were synthesized with a ligand-free method. The (100) facet is more active in the production of ethylene at the expense of unwanted methane formation, which takes place predominantly at the (111) facet.3 The surface of the nanocubes was decorated with Au nanoparticles by a galvanic replacement reaction. HAADF-STEM images of the catalysts with various Au loadings are shown in Figure 1a-d. After addition of Au nanoparticles, the shape of the Cu2O nanocubes was preserved. However, the Au nanoparticles were highly dispersed at low loadings (1 mol % Au) whereas Au clusters were observed at higher loadings (10 mol % Au). This result was in line with synchrotron X-ray diffraction (XRD) results, whereby the Au(111) reflection appears for the 10Au/Cu2O sample. Besides, the formation of a Au-Cu alloy and CuO phase was confirmed as well. The highly dispersed nature of the Au nanoparticles at low loadings was further established by Au 4f X-ray photoelectron spectroscopy (XPS), whereby a shift towards higher binding energies was observed as compared to the samples with higher Au loadings. The electrocatalytic performance of the catalysts was assessed over a range of potentials in neutral electrolyte (0.1 M KHCO3) in H-cell configuration. With highly dispersed Au as promotor, we found that the formation of ethylene and ethanol was significantly enhanced (Figure 1e-f). More specifically, the Faradaic effiency towards ethanol increased by roughly 1.5 times by introducing 1 mol % Au to the Cu2O nanocubes. Surprisingly, the 10Au/Cu2O sample displayed the lowest Faradaic efficiency for C2 products. We believe that the dispersion of Au on the Cu2O surface plays an important role in the product formation, whereby CO can be formed at Au sites and diffuse to Cu sites in proximity for further reduction to C2 products (CO spillover). To further study structure-activity relationships, we performed in-situ X-ray absorption spectroscopy (XAS) measurements. Figure 1g shows the normalized Cu K-edge X-ray absorption near-edge structure (XANES) of the Cu2O and Au/Cu2O samples in the final state. The evolution of the Cu(0), Cu(I) and Cu(II) fractions was followed by Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) analysis. This analysis revealed that the final oxidation state of the catalysts is different. The Cu(I)/Cu(0) ratio shows the following trend 1Au/Cu2O > 5Au/Cu2O > Cu2O > 10Au/Cu2O. Based on these observations, we hypothesize that the oxidation state of Cu affects the product distribution and in particular, the formation of oxygenates. The presence of Cu(I) species and the formation of Cu(0) species during CO2 electroreduction was further confirmed with in-situ XRD measurements. Finally, we performed quasi in-situ XPS measurements to study the reduction of the surface of the catalysts. Acknowledgements This publication is part of the research programme 'Reversible Large-scale Energy Storage' (RELEASE) with project number 17621 which is financed by the Dutch Research Council (NWO).

Flexible Trilinearity Alignment (FTA) and Shift Invariant Transformation (SIT) Constraints in Three‐Way Multivariate Curve Resolution Data Analysis

ABSTRACTIn this work, two alternative ways of analyzing three‐way data with multivariate curve resolution alternating least squares (MCR‐ALS) using the trilinearity constraint are described and compared. Different synthetic datasets and experimental three‐way datasets covering different scenarios are analyzed, and the results obtained are compared. The two new different ways of applying the trilinearity constraint are named flexible trilinearity alignment (FTA) and shift invariant transformation (SIT). The effects of noise in the application of both types of constraints are investigated in detail. Results show that both approaches are particularly adequate for those cases like in gas chromatography and especially in liquid chromatography where the elution profiles of the same chemical component in different chromatographic runs are not totally reproducible because they are time shifted, although they preserve their shape. When strong time shifts and co‐elution occur, then the “standard” trilinear model does not work, and alternative approaches should be used, such as the MCR extended bilinear model to multiset (multirun) data, or the proposed relaxation of the trilinearity constraint in the FTA and SIT methods to capture the time drift changes produced in the elution profiles of the resolved components.

Molecular Fingerprinting of Mouse Brain Using Ultrabroadband Coherent Anti-Stokes Raman Scattering (CARS) Microspectroscopy Empowered by Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS).

The Raman fingerprint spectral region provides abundant structural information on molecules. However, analyzing vibrational images within this region using coherent Raman imaging remains challenging due to the small Raman cross section and congested spectral features. In this study, we combined ultrabroadband coherent anti-Stokes Raman scattering (CARS) microspectroscopy across the spectral range of 500-4000 cm-1 with multivariate curve resolution-alternating least-squares (MCR-ALS) to reveal hidden Raman bands in the fingerprint region. Applying this method to mouse brain tissue, we extracted information on cholesterol and collagen, leveraging their distinctive molecular signatures, as well as on key molecules such as lipids, proteins, water, and nucleic acids. Moreover, the simultaneous detection of second harmonic generation facilitated label-free visualization of organelles, including arachnoid membrane and Rootletin filaments.

Serum Raman spectroscopy: Unearthing the snapshot of distinct metabolic profile in patients with congenital heart defects (CHDs)

In the present study, efficacy of minimally-invasive serum Raman spectroscopy (SRS) in stratification of congenital heart diseases was explored. Blood was collected from 62 subjects [42 congenital heart defect (CHD) patients (19 with atrial septal defect, 13 with ventricular septal defect and 10 with tetralogy of fallot) and 20 controls], and serum separated. Raman spectra of sera were recorded, pre-processed and subjected to spectral and multivariate analyses. Multivariate curve resolution-alternating least squares (MCR-ALS) analyses indicated alterations in lipid and protein levels between the study groups. Principal Component Analysis (PCA) and Principal Component based Linear Discriminant Analysis (PC-LDA), cross-validated with Leave-one-out cross validation (LOOCV), were employed to study stratification between the different groups. CHD could be classified from controls with 76 % efficiency. The different CHD subtypes could be distinguished with efficiencies as high as ∼90 %. To the best of our knowledge, differentiation between controls and CHDs as well as the stratification between controls and CHDs subtypes was for the first time successfully accomplished by serum-based Raman spectroscopy.

Exploratory analysis of hyperspectral imaging data

Characterizing sample composition and visualizing the distribution of its chemical compounds is a prominent topic in various research and applied fields. Integrating spatial and spectral information, hyperspectral imaging (HSI) plays a pivotal role in this pursuit. While self-modelling curve resolution techniques, like multivariate curve resolution - alternating least squares (MCR-ALS), and clustering methods, such as K-means, are widely used for HSI data analysis, their effectiveness in complex scenarios, where the structure of the data deviates from the models’ assumptions, deserves further investigation. The choice of a data analysis method is most often driven by research question at hand and prior knowledge of the sample. However, overlooking the structure of the investigated data, i.e. linearity, geometry, homogeneity, might lead to erroneous or biased results. Here, we propose an exploratory data analysis approach, based on the geometry of the data points cloud, to investigate the structure of HSI datasets and extract their main characteristics, providing insight into the results obtained by the above-mentioned methods. We employ the principle of essential information to extract archetype (most linearly dissimilar) spectra and archetype single-wavelength images. These spectra and images are then discussed and contrasted with MCR-ALS and K-means clustering results. Two datasets with varying characteristics and complexities were investigated: a powder mixture analyzed with Raman spectroscopy and a mineral sample analyzed with Laser Induced Breakdown Spectroscopy (LIBS). We show that the proposed approach enables to summarize the main characteristics of hyperspectral imaging data and provides a more accurate understanding of the results obtained by traditional data modelling methods, driving the choice of the most suitable one.