Multi-way modeling of hydro-chemical data of an alluvial river system--a case study

A large data set pertaining to water quality of an alluvial river was analyzed using multi-way data analysis methods with a view to extract the hidden information, spatial and temporal variation trends in the river water quality. Four-way data (8 monitoring sites × 22 water quality variables × 10 monitoring years × 12 sampling months) analysis was performed using PARAFAC and Tucker3 models. A two component PARAFAC model, although explained 35.1% of the data variance, could not fit to the data set. Tucker3 model of optimum complexity (2,3,1,3) explaining 39.7% of the data variance, allowed interpretation of the data information in four modes. The model explained spatial and temporal variation trends in terms of water quality variables during the study period and revealed that sampling sites in mid-stretch of the river were dominated mainly by the variables of anthropogenic origin. The results delineated the mid stretch of the river as critical from pollution point of view and also identified summer months as having high influence on river water quality in this stretch. The information regarding spatial and temporal variations in water quality generated by the four-way modeling of data would be useful in developing long-term water resources management strategies in the river basin.     

Fast liquid chromatography-diode array detection assisted by chemometrics for quantification of seven ultraviolet filters in effluent wastewater

A fast chromatographic method is presented for simultaneous quantification of seven organic ultraviolet (UV) filters (benzophenone-3,4-methylbenzilidene camphor, octocrylene, 1-(4-tert-butylphenyl)-3-(4-methyoxyphenyl)1,3-propanedione), ethylhexyl methoxy cinnamate, ethylhexyl salicylate and homosalate) in effluent wastewater samples. The UV filters were pre-concentrated by Bond Elut-ENV cartridges and separated on an ODS column (15 cm × 0.46 cm, 5 μm) in less than 2.5 min using a non-aqueous mobile phase of methanol-acetonitrile (50:50, v/v) with flow-rate of 1.5 mL min⁻¹. Appropriate baseline correction through asymmetric least squares was applied to reduce the matrix of background signals in three way data. Then, second-order calibration based on multivariate curve resolution-alternating least squares (MCR-ALS) was implemented on the unfolded three-way data obtained from liquid chromatography with diode array detection (LC-DAD) through standard addition calibration method for handling co-eluted peaks, systematic and proportional errors. Recoveries ranging from 76% to 130% and %RSD values less than 11.2 for all UV filter shows the accuracy and precision of the proposed method in wastewater samples. In addition, statistical t-test as well as computed elliptical joint confidence region (EJCR) confirms the accuracy of the proposed method and indicates the absence of both constant and proportional errors in the predicted concentrations. This study demonstrates that coupling of the fast HPLC-DAD method with powerful algorithm of MCR-ALS can be considered as an efficient method for quantification of UV filters in highly contaminated samples of wastewaters where both time and cost per each analysis can be reduced significantly.     

Quantitative analysis of biodiesel in blends of biodiesel and conventional diesel by comprehensive two-dimensional gas chromatography and multivariate curve resolution

In this paper, a method to determine the composition of blends of biodiesel with mineral diesel (BXX) by multivariate curve resolution with Alternating Least Squares (MRC-ALS) combined to comprehensive two-dimensional gas chromatography with Flame Ionization Detection (GC × GC-FID) is presented. Chromatographic profiles of BXX blends produced with biodiesels from different sources were used as input data. An initial evaluation carried out after multiway principal component analysis (MPCA) was used to reveal regions of the chromatograms were the signal was likely to be dependent on the concentration of biodiesel, regardless its vegetable source. After this preliminary step MCR-ALS modeling was carried out only using relevant parts of the chromatograms. The resulting procedure was able to predict accurately the concentration of biodiesel in the BXX samples regardless of its origin.     

Trilinearity and component interaction constraints in the multivariate curve resolution investigation of NO and O<Subscript>3</Subscript> pollution in Barcelona

Multiway and multiset data analysis extensions of the multivariate curve resolution alternating least squares (MCR-ALS) method are proposed for the investigation of the temporal distribution of the pollution by nitric oxide (NO) and ozone (O₃) in one sampling station in the urban centre of Barcelona (Catalonia, Spain), during the years 2000–2006. Different specific studies were performed considering the annual and pluriannual contamination by these two contaminants, individually or in combination using different data matrix augmentation strategies and multiway and multiset data analysis models. Daily, hourly and annual profiles were estimated describing different patterns and summarising the main contamination processes. The daily and night trends found were mainly attributed to traffic and photochemical processes favoured by light radiation. Moreover, winter–summer seasonal trends were also clearly detected and their changes over different years assessed. The extension MCR-ALS method to multiset data analysis using different constraints like non-negativity, trilinearity and interaction among components is confirmed to be a powerful method to improve the interpretability of the different contamination patterns in atmospheric contamination studies.     

Resolution of phenol, and its di-hydroxyderivative mixtures by excitation-emission fluorescence using MCR-ALS: Application to the quantitative monitoring of phenol photodegradation

The photodegradation of phenol using TiO₂ as catalyst was studied and monitored by fluorescence excitation-emission matrix (EEM). Hydroquinone, catechol and resorcinol were the dihydroxyderivative intermediates although in lower concentrations than phenol. The data were analyzed using a three-way multivariate curve resolution alternating least squares method (MCR-ALS) and augmented matrices. The procedure was assessed using synthetic samples prepared with a {4,3} Simplex-lattice design that considered a representative range of analyte concentrations. The results were analyzed in terms of overall RMSEP for the overall data set. A detailed study was made of how the analytes behaved at each concentration level and how the concentration of the other species affected the process. The method was used to quantify phenol in photodegradation samples with an overall prediction error of 5.37%. The conversion values were fitted to pseudo first-order kinetics and the apparent rate constant was calculated to be −4.9 × 10⁻⁴ ± 5.2 × 10⁻⁵ min⁻¹.     

Second-order standard addition for deconvolution and quantification of fatty acids of fish oil using GC-MS

In the present work two second-order calibration methods, generalized rank annihilation method (GRAM) and multivariate curve resolution-alternating least square (MCR-ALS) have been applied on standard addition data matrices obtained by gas chromatography-mass spectrometry (GC-MS) to characterize and quantify four unsaturated fatty acids cis-9-hexadecenoic acid (C16:1ω7c), cis-9-octadecenoic acid (C18:1ω9c), cis-11-eicosenoic acid (C20:1ω9) and cis-13-docosenoic acid (C22:1ω9) in fish oil considering matrix interferences. With these methods, the area does not need to be directly measured and predictions are more accurate. Because of non-trilinear conditions of GC-MS data matrices, at first MCR-ALS and GRAM have been used on uncorrected data matrices. In comparison to MCR-ALS, biased and imprecise concentrations (%R.S.D. = 27.3) were obtained using GRAM without correcting the retention time-shift. As trilinearity is the essential requirement for implementing GRAM, the data need to be corrected. Multivariate rank alignment objectively corrects the run-to-run retention time variations between sample GC-MS data matrix and a standard addition GC-MS data matrix. Then, two second-order algorithms have been compared with each other. The above algorithms provided similar mean predictions, pure concentrations and spectral profiles. The results validated using standard mass spectra of target compounds. In addition, some of the quantification results were compared with the concentration values obtained using the selected mass chromatograms. As in the case of strong peak-overlap and the matrix effect, the classical univariate method of determination of the area of the peaks of the analytes will fail, the “second-order advantage” has solved this problem successfully.     

Multivariate resolution of rank-deficient near-infrared spectroscopy data from the reaction of curing epoxy resins using the rank augmentation strategy and multivariate curve resolution alternating least squares approach

A model of the curing reaction between phenyl glycidyl ether (PGE) and aniline as the curing agent was studied isothermally at 95 °C and monitored in situ by near-infrared spectroscopy (NIR). The spectra were recorded every 5 min. The ubiquitous problem of rank deficiency in reaction network systems was solved by assembling an augmented column-wise matrix containing five process runs from different initial conditions. The data were analyzed using a two-way multivariate curve resolution alternating least squares method (MCR-ALS). Initial estimates of spectra required by MCR-ALS were given by a SIMPLe-to-use Interactive Self-modeling Mixture Analysis (SIMPLISMA) approach. The reactants, product and intermediate spectra were successfully resolved and the concentration profiles properly represented the system studied. The performance of the model was evaluated by two parameters: ALS lack of fit (lof=0.88%) and explained variance (R²=99.99%). To validate the MCR-ALS results, the similarity coefficients (r) between the recovered spectra and the pure species spectra were calculated. These were: PGE (r=0.998), aniline (r=0.994) and tertiary amine (r=0.999).     

PARAFAC and PARAFAC2 calibration models for antihypertensor Nifedipine quantification

Two-way data structures were obtained by acquiring UV-vis spectra as function of the time of the alkaline hydrolysis reaction of the antihypertensor Nifedipine in dimethylsulfoxide (DMSO). Sets of three-way data structures were obtained from the analysis of solutions with different concentrations of Nifedipine generated by standard additions to DMSO, Nifedipine standard and a pharmaceutical formulation. PARAFAC and PARAFAC2 methods were used in the analysis of these multi-way data structures and calibration models were developed for Nifedipine quantification in pharmaceutical formulations. For all the three-way data structures a better model fit was found with the PARAFAC2 suggesting that the experimental data sets have deviations from trilinearity. The best concentrations estimations were found with the PARAFAC2 model in the analysis of a [concentration × time (s) × wavelength (nm)] three-way data structure which allows the quantification of Nifedipine in pharmaceutical formulations.     

Fast chromatographic method for the determination of dyes in beverages by using high performance liquid chromatography—Diode array detection data and second order algorithms

A fast chromatographic methodology is presented for the analysis of three synthetic dyes in non-alcoholic beverages: amaranth (E123), sunset yellow FCF (E110) and tartrazine (E102). Seven soft drinks (purchased from a local supermarket) were homogenized, filtered and injected into the chromatographic system. Second order data were obtained by a rapid LC separation and DAD detection. A comparative study of the performance of two second order algorithms (MCR-ALS and U-PLS/RBL) applied to model the data, is presented. Interestingly, the data present time shift between different chromatograms and cannot be conveniently corrected to determine the above-mentioned dyes in beverage samples. This fact originates the lack of trilinearity that cannot be conveniently pre-processed and can hardly be modelled by using U-PLS/RBL algorithm. On the contrary, MCR-ALS has shown to be an excellent tool for modelling this kind of data allowing to reach acceptable figures of merit. Recovery values ranged between 97% and 105% when analyzing artificial and real samples were indicative of the good performance of the method. In contrast with the complete separation, which consumes 10 mL of methanol and 3 mL of 0.08 mol L⁻¹ ammonium acetate, the proposed fast chromatography method requires only 0.46 mL of methanol and 1.54 mL of 0.08 mol L⁻¹ ammonium acetate. Consequently, analysis time could be reduced up to 14.2% of the necessary time to perform the complete separation allowing saving both solvents and time, which are related to a reduction of both the costs per analysis and environmental impact.     

Determination of interfacial tension of insulating oils by using image analysis and multi-way calibration

Power transformers are of great importance in the distribution of electrical energy. One of their most important parts is the insulating system, consisting of Kraft paper immersed in insulating oil. One of the most important parameters used for evaluating the degradation of this system is the oil interfacial tension. The aim of this study was to determine the interfacial tension in samples of insulating oils by using image analysis combined with a multi-way calibration method, N-PLS (multilinear PLS). Forty eight oil samples were obtained, whose values of interfacial tension were determined by a tensiometer, and divided into calibration (38) and validation (10) sets. Scanner images were obtained, converted to grey-scale, domain transformed and stacked in a three-way data array, before modelling. The best N-PLS model was obtained with mean centering and three latent variables and provided a RMSEP of 3 dyn cm^− 1. This model provided individual prevision errors between − 14 and 16%, which were acceptable for electric energy companies. The proposed method was rapid and non-destructive, showing great advantages over the traditional ones, which are slow and produce chemical waste.     

Multi-analyte quantification in bioprocesses by Fourier-transform-infrared spectroscopy by partial least squares regression and multivariate curve resolution

This paper presents the quantification of Penicillin V and phenoxyacetic acid, a precursor, inline during Pencillium chrysogenum fermentations by FTIR spectroscopy and partial least squares (PLS) regression and multivariate curve resolution – alternating least squares (MCR-ALS). First, the applicability of an attenuated total reflection FTIR fiber optic probe was assessed offline by measuring standards of the analytes of interest and investigating matrix effects of the fermentation broth. Then measurements were performed inline during four fed-batch fermentations with online HPLC for the determination of Penicillin V and phenoxyacetic acid as reference analysis. PLS and MCR-ALS models were built using these data and validated by comparison of single analyte spectra with the selectivity ratio of the PLS models and the extracted spectral traces of the MCR-ALS models, respectively. The achieved root mean square errors of cross-validation for the PLS regressions were 0.22 g L⁻¹ for Penicillin V and 0.32 g L⁻¹ for phenoxyacetic acid and the root mean square errors of prediction for MCR-ALS were 0.23 g L⁻¹ for Penicillin V and 0.15 g L⁻¹ for phenoxyacetic acid. A general work-flow for building and assessing chemometric regression models for the quantification of multiple analytes in bioprocesses by FTIR spectroscopy is given.     

A review on advanced oxidation processes: From classical to new perspectives coupled to two- and multi-way calibration strategies to monitor degradation of contaminants in environmental samples

This paper offers a critical review from classical to new perspectives of advanced oxidation processes (AOPs) coupled to two- and multi-way calibration strategies based on multivariate curve resolution – alternating least-squares (MCR-ALS) and parallel factory analysis (PARAFAC) with various analytical techniques to monitor the degradation of contaminants in environmental samples. It focuses on the generation of highly reactive hydroxyl (HO•) radicals (classical AOPs with emphasis on Fenton, photo-Fenton and ozonation processes) and emerging reactive sulphate (SO₄^•−) radicals (new perspectives of AOPs) for effective degradation of recalcitrant compounds. Other new perspectives of AOPs were also addressed, namely semiconductor photocatalysis (TiO₂/UV), combination of processes involving at least one AOP (hybrid or single-step processes and sequential or two-step processes), novel advanced electrochemical oxidation technologies (electro-Fenton and electro-photo-Fenton) and nanocatalytic heterogeneous Fenton technology with high specific surface area. Literature reports since 2008 for real applications in the environmental remediation based on AOPs (from classical to new perspectives) coupled to PARAFAC and MCR-ALS with first-, second- and third-order data were reviewed and the improvements obtained were briefly discussed. The two- and multi-way calibration strategies allow one the successful decomposition of first-, second- and third-order data collected from different analytical techniques. Therefore, the respective profiles obtained allowed qualitative (spectral profiles) and quantitative (concentration profiles) analysis of complex samples during the degradation of contaminants through the second-order advantage. Finally, trends of future research directions for AOPs coupled to various analytical techniques and advanced chemometric models were provided.     

Characterisation of hydrogen bond perturbations in aqueous systems using aquaphotomics and multivariate curve resolution-alternating least squares

Aquaphotomics is a new discipline that provides a framework for understanding changes in the structure of water caused by various perturbations, such as variations in temperature or the addition of solutes, using near infrared spectroscopy (NIRS). One of the main purposes of aquaphotomics is to identify water bands as main coordinates of future absorbance patterns to be used as biomarkers. These bands appear as consequence of perturbations in the NIR spectra. Curve resolution techniques may help to resolve and find new water bands or confirm already known bands. The aim of this study is to investigate the application of multivariate curve resolution-alternating least squares (MCR-ALS) to characterise the effects of various perturbations on the NIR spectra of water in terms of hydrogen bonding. For this purpose, the perturbations created by temperature change and the addition of four solutions of different ionic strength and Lewis acidity were studied (NaCl, KCl, MgCl₂ and AlCl₃, with concentrations ranging from 0.2 to 1 mol L⁻¹ in steps of 0.2 mol L⁻¹). Transmission spectra of all salt solutions and pure water were obtained at temperatures ranging from 28 to 45 °C. We have found that three distinct components with varying temperature dependence are present in water perturbed by temperature. The salt solutions studied exhibited similar trends with respect to the temperature perturbation, while the peak locations of their MCR-ALS pure components varied according to the ionic strength of the salt used.     

Profiling analysis of volatile compounds from fruits using comprehensive two-dimensional gas chromatography and image processing techniques

An image processing approach originating from the proteomics field has been transferred successfully to the processing of data obtained with comprehensive two-dimensional gas chromatographic separations data. The approach described here has proven to be a useful analytical tool for unbiased pattern comparison or profiling analyses, as demonstrated with the differentiation of volatile patterns (“aroma”) from fruits such as apples, pears, and quince fruit. These volatile patterns were generated by headspace solid phase microextraction coupled to comprehensive two-dimensional gas chromatography (HS-SPME-GC × GC). The data obtained from GC × GC chromatograms were used as contour plots which were then converted to gray-scale images and analyzed utilizing a workflow derived from 2D gel-based proteomics. Run-to-run variations between GC × GC chromatograms, respectively their contour plots, have been compensated by image warping. The GC × GC images were then merged into a fusion image yielding a defined and project-wide spot (peak) consensus pattern. Within detected spot boundaries of this consensus pattern, relative quantities of the volatiles from each GC × GC image have been calculated, resulting in more than 700 gap free volatile profiles over all samples. These profiles have been used for multivariate statistical analysis and allowed clustering of comparable sample origins and prediction of unknown samples. At present state of development, the advantage of using mass spectrometric detection can only be realized by data processing off-line from the identified software packages. However, such information provides a substantial basis for identification of statistically relevant compounds or for a targeted analysis.     

Spectrometric study of the interaction between Alpinetin and bovine serum albumin using chemometrics approaches

The binding interaction of Alpinetin (APT) with bovine serum albumin (BSA) was studied by fluorescence, UV-visible and synchronous fluorescence spectroscopy (SFS) under simulated physiological conditions. The measured complex spectra were resolved by multivariate curve resolution-alternating least squares (MCR-ALS), yielding a host of data and information, which otherwise would have been impossible to obtain. The extracted profiles corresponded to the spectra of the single species in the APT/BSA mixture. In addition, the presence of the APT-BSA complex was demonstrated, and it was shown that the associated quenching of the fluorescence from the BSA protein resulted from the formation of APT-BSA complex via a static mechanism. The binding constant (K_a(ave) = 2.34 × 10⁶ L mol⁻¹) and the number of sites (n = 1) were obtained by fluorescence methods as were the thermodynamic parameters (ΔH⁰, ΔS⁰ and ΔG⁰). This work suggested that the principal binding between APT to BSA was facilitated by hydrophobic interactions. The thermodynamic parameters for APT were compared to those from the structurally similar Chrysin and Wogonin molecules. It appeared that the entropy parameters were relatively more affected by the small structural changes. SFS from the interaction of BSA and APT showed that the ligand affected the conformation of BSA. The competitive interaction of APT and site makers with BSA indicated site I as the binding area of APT in BSA.     

Quantitative analysis of the effect of zidovudine,efavirenz, and ritonavir on insulin aggregation by multivariate curve resolution alternating least squares of infrared spectra

Quantification of the effect of antiretroviral drugs on the insulin aggregation process is an important area of research due to the serious metabolic diseases observed in AIDS patients after prolonged treatment with these drugs. In this work, multivariate curve resolution alternating least squares (MCR-ALS) was applied to infrared monitoring of the insulin aggregation process in the presence of three antiretroviral drugs to quantify their effect. To evidence concentration dependence in this process, mixtures at two different insulin:drug molar ratios were used. The interaction between insulin and each drug was analysed by ¹H NMR spectroscopy. In all cases, the aggregation process was monitored during 45 min by infrared spectroscopy. The aggregates were further characterised by scanning electron microscopy (SEM). MCR-ALS provided the spectral and concentration profiles of the different insulin–drug conformations that are involved in the process. Their feasible band boundaries were calculated using the MCR-BANDS methodology. The kinetic profiles describe the aggregation pathway and the spectral profiles characterise the conformations involved. The retrieved results show that each of the three drugs modifies insulin conformation in a different way, promoting the formation of aggregates. Ritonavir shows the strongest promotion of aggregation, followed by efavirenz and zidovudine. In the studied concentration range, concentration dependence was only observed for zidovudine, with shorter aggregation time obtained as the amount of zidovudine increased. This factor also affected the aggregation pathway.     

Multi-way partial least-squares and residual bi-linearization for the direct determination of monohydroxy-polycyclic aromatic hydrocarbons on octadecyl membranes via room-temperature fluorescence excitation emission matrices

Multi-way partial least-squares (N-PLS) is combined to the residual bi-linearization procedure (RBL) for the direct analysis of metabolites of polycyclic aromatic hydrocarbons in urine samples. Metabolite analysis is carried out via a two-step experimental procedure based on solid-phase extraction and room temperature fluorescence spectroscopy. Excitation-emission matrices are recorded from octadecyl (C18) membranes that serve as solid substrates for sample extraction and spectroscopic measurements. Excellent metabolite recoveries were obtained in all cases, which varied from 96.2 ± 1.35% (9-hydroxyphenanthrene) to 99.7 ± 0.49% (3-hydroxybenzo[a]pyrene). Background correction of extraction membranes is carried out with a new alternating least-squares (ALS) procedure adapted to second order data. The performance of N-PLS/RBL is compared to the well-established multivariate curve resolution-alternating least-squares (MCR-ALS) algorithm. Both algorithms provided similar analytical figures of merit, including their ability to handle unknown interference in urine samples. With only 10 mL of sample, the limits of detection varied between 0.06–0.08 ng mL⁻¹ (1-hydroxypyrene) and 0.016–0.018 ng mL⁻¹ (2-hydroxyfluorene). When compared to previously reported univariate calibration data, the limits of detection via N-PLS/RBL and MCR-ALS are approximately one order of magnitude higher. This was somehow expected due to the effect of unexpected components in multivariate figures of merit, i.e. a more realistic approach to the analysis of metabolites in human urine samples.     

Detection of explosives on the surface of banknotes by Raman hyperspectral imaging and independent component analysis

The aim of this study was to develop a methodology using Raman hyperspectral imaging and chemometric methods for identification of pre- and post-blast explosive residues on banknote surfaces. The explosives studied were of military, commercial and propellant uses. After the acquisition of the hyperspectral imaging, independent component analysis (ICA) was applied to extract the pure spectra and the distribution of the corresponding image constituents. The performance of the methodology was evaluated by the explained variance and the lack of fit of the models, by comparing the ICA recovered spectra with the reference spectra using correlation coefficients and by the presence of rotational ambiguity in the ICA solutions. The methodology was applied to forensic samples to solve an automated teller machine explosion case. Independent component analysis proved to be a suitable method of resolving curves, achieving equivalent performance with the multivariate curve resolution with alternating least squares (MCR-ALS) method. At low concentrations, MCR-ALS presents some limitations, as it did not provide the correct solution. The detection limit of the methodology presented in this study was 50 μg cm⁻².     

Fluorescence quantification of tetracycline in the presence of quenching matrix effect by means of a four-way model

In this work, a four-way tensor is used to model the quenching effect in fluorescent measurements. By means of the analysis of excitation-emission matrices obtained in the determination of tetracycline in tea, which acts as quencher, it is shown as the impossibility to use a calibration, or an addition standard based on a three-way model. It is analysed the quencher multiplicative effect made on the tetracycline signal by means of an ANOVA. However, by arranging the experimental data in a four-way tensor, it is viable to perform a calibration based on the parallel factor analysis, PARAFAC, decomposition and a four-way partial least squares, 4-PLS, regression to quantify the tetracycline in the presence of the matrix quencher effect. 4-PLS calibration provides better results. In the range from 40 to 220 μg L⁻¹ gives an average of relative errors in absolute value equal to 8.02% in prediction (3.40% in calibration). The repeatability as standard deviation in this range is 5.08 μg L⁻¹ and the method is accurate, slope and intercept being statistically equal to 1 and 0, respectively when a regression calculated versus true concentration is performed. Moreover, it has a decision limit (CCα) of 13.87 μg L⁻¹ for a probability of false positive, α, equal to 0.05 and a capability of detection (CCβ) of 26.63 μg L⁻¹ (for probabilities of false positive, α, false negative, β, equals to 0.05).