Second-order Multivariate Calibration Research Articles

Identification and quantification of ciprofloxacin, enrofloxacin and difloxacin residues in milk using excitation-emission fluorescence and second-order standard addition methods

In the presence of non-modeled components and analyte-matrix interaction in real samples, a combination of second-order multivariate calibration and standard addition is desired to achieve accurate results via second-order advantage. Enrofloxacin (ENR), Difloxacin (DIF), and Ciprofloxacin (CIP) are Fluoroquinolones widely considered antibiotic residues in milk. Excitation-emission fluorescence spectra of these antibiotics at pH = 9.1 provide second-order data for identifying and quantifying them in a mixture using second-order calibration modeling.Rank annihilation factor analysis (RAFA) and multivariate curve resolution-alternating least squares (MCR-ALS) with trilinearity constraints are applied to determine the CIP, ENR, and DIF residues in synthetic mixtures and milk using second-order excitation-emission fluorescence spectroscopy. In both methods, the trilinearity constraint guarantees a unique true solution to the spectral profiles of analytes. The combination of second-order standard addition and higher-order calibration modeling with RAFA and MCR-ALS supports the second-order advantage in milk analysis.

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

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

Authentication of honey of different nectar sources and antioxidant property evaluation by phenolic composition analysis with chemometrics

The chemometric second-order multivariate calibration method was applied to the qualitative and quantitative analysis of seven phenolic acids in honey samples with five different floral origins. First, based on the “second-order advantage,” reasonable resolutions and satisfactory quantitative results were obtained even in the presence of strong background interference and overlapping peaks in complex real honey samples. Average spike recoveries for the seven target analytes were in the range of 89.34–118.81%, with high correlation coefficient (r ≥ 0.9997), low limit of quantification (1.00–20.20 ng mL−1) and high sensitivity (0.135–0.375 mL ng−1). Second, the quantitative data of seven target analytes were analyzed by principal component analysis (PCA) on MATLAB software to classify honey of five nectar sources. These results indicated that there is a strong association between the content of major phenolic acids and the flower sources of honey. Third, the quantitative composition-antioxidant activity relationship analysis was evaluated by partial least squares (PLS) analysis and studied to provide reliable analysis of multi-marker antioxidant data. The results enable the continued exploitation and utilization of honey from different floral origins and further contribute to honey market development and choices in available honey for consumption.

Determination of ochratoxin A in coffee and tea samples by coupling second-order multivariate calibration and fluorescence spectroscopy

A new method to quantify the mycotoxin ochratoxin A (OTA) in coffee and tea samples is proposed based on second-order multivariate calibration and excitation-emission fluorescence matrix (EEFM) data. Experimental conditions were optimized by studying the effect of pH and various organized media on the fluorescence signal of OTA. For each analysed matrix (coffee grains and tea leaves), several sample pretreatments and calibration methods (external or standard addition) and data processing by chemometric models (e.g., parallel factor analysis/PARAFAC and multivariate curve resolution-alternating least squares/MCR-ALS) were evaluated and discussed. The MCR-ALS algorithm provided an adequate fit to the data for both samples, while PARAFAC was satisfactory only for the tea samples. Regarding the figures of merit, the limits of detection were in the range of 0.2–0.3 ng mL−1; furthermore, low relative prediction errors, between 2% and 4%, were achieved in both the fortified and real samples. Accordingly, the proposed methodology was applied to analyse fortified roasted and green coffee and real tea leaf samples. Satisfactory recoveries were achieved (ranging from 92 to 110%), and the obtained concentrations were in agreement with the values obtained by the reference method (based on high-performance liquid chromatography with fluorescence detection/HPLC-FLD). In addition, all samples contained OTA levels lower than the maximum permissible levels. Finally, the proposed strategy allows the use of green analytical chemistry principles; for instance, the use of organic solvents and the generation of waste products were significantly lower than for similar analytical methods reported in the literature.

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.

Comparison of three second-order multivariate calibration methods for the rapid identification and quantitative analysis of tea polyphenols in Chinese teas using high-performance liquid chromatography

Retention time shifts in second-order calibration-assisted chromatographic analysis seriously impact the modeling and quantitative accuracies in complex systems. In this work, three second-order methods, i.e. alternating trilinear decomposition (ATLD) algorithm, multivariate curve resolution-alternating least squares (MCR-ALS), alternating trilinear decomposition-assisted multivariate curve resolution (ATLD-MCR), were compared their performance to process liquid chromatographic data in the presence of retention time shifts and overlapped peaks. Firstly, the validation samples contain five tea polyphenols at three concentrate levels within the calibration ranges, helped to understand, visualize and interpret these features of three second-order multivariate methods. Secondly, experimental data were studied concerning the determination of polyphenols in Chinese tea samples by HPLC-DAD. The results showed that all three second-order multivariate methods realized satisfactory quantification for five targeted analytes in Pu-Er ripe tea samples and Green tea samples even with the interference of slight retention time shifts, average recoveries were 91.23% –113.16% for ATLD, 89.96%–115.96% for ATLD-MCR, 90.64%–117.60% for MCR-ALS, respectively. However, ATLD was disappointing in the case of larger time shifts (approx. 4.00 s and 6.40 s) occurring for the quantitative analysis of Black tea and Clinacanthus nutans tea, the average recoveries were just 67.33–84.05%. Relatively, MCR-ALS and ATLD-MCR were more significantly excellent, satisfactory results still can be obtained, the average recoveries for MCR-ALS and ATLD-MCR were in the range of 86.04–117.60% and 89.96–115.96%, respectively.

Evaluation of three-way fluorescence data-based for simultaneous determination of polycyclic aromatic hydrocarbons in tea infusion samples at sub-ppb levels by second-order multivariate calibration

In this work, two fast and low solvent-consumption analytical methods were evaluated for the determination of the eight polycyclic aromatic hydrocarbons (PAHs), commonly named PAH8, in tea infusion samples by second-order multivariate calibration. The analytical performance of the excitation-emission matrix fluorescence (EEMF) and retention time-emission spectra matrices (RTEFM) data was compared, and these methods were applied to the analysis of real samples. Better figures of merit were obtained with EEMF (detection limit: 0.05–0.22 μg L−1; analytical sensitivity: 14.8–68.9) than with those of RTEFM (detection limit: 1.5–12.1 μg L−1; analytical sensitivity: 0.4–4.9). However, in the analysis of tea infusion samples, the method based on RTEFM showed a lower prediction error (4.0–9.7%) and better accuracy than did the reference method. Finally, the proposed methods were applied to real tea infusions obtained from green and black tea samples containing PAHs at ng L−1 levels, including a preconcentration step on a C-18 SPE cartridge, demonstrating the analytical potential of these methods.

Contribution to second-order calibration based on multivariate curve resolution with and without previous chromatographic synchronization

Rotational ambiguity in the bilinear solutions provided by multivariate curve resolution - alternating least-squares (MCR-ALS) leads to an additional source of uncertainty in the estimation of analyte concentrations by second-order multivariate calibration. The phenomenon is particularly important when measuring matrix instrumental data derived from liquid chromatography with spectral detection, where elution time profiles usually vary from sample to sample both in position and shape. This makes the data non-trilinear, precluding the use of unique trilinear decomposition models. The present report compares some analytical results achieved by: (1) the usual MCR-ALS analysis of augmented matrices built from raw matrix data and (2) a previously reported procedure based on synchronizing the MCR-ALS elution time profiles using correlation optimized warping (COW), reconstructing the augmented matrix with the spectra and the aligned chromatograms, and then applying MCR-ALS again with the trilinearity constraint, leading to unique solutions, which is possible because the warping process restores the trilinearity of the data. We show that alternative (2) does not solve the rotational ambiguity issues and artificially modifies the original data, without significant improvements in analytical performance. In the simulated systems, the best average errors for alternative (1) were about 2%, whereas for alternative (2) they were in the range 4–11%. For the experimental system, the corresponding errors were 2–3% and 3–4% respectively, i.e. with no significant improvement in going to alternative (2). All efforts should be directed to reduce the degree of rotational ambiguity by applying a full battery of chemically reasonable constraints.

Simultaneous Determination of Pesticides in Fruits by Using Second-Order Fluorescence Data Resolved by Unfolded Partial Least-Squares Coupled to Residual Bilinearization

In the present work, a chemometric-assisted spectrofluorimetric method has been developed for the simultaneous determination of natural fluorescent pesticides, carbaryl, carbendazim, and thiabendazole, in orange and banana. Only a simple extraction with methanol was required as sample pretreatment. Emission-excitation fluorescence matrices were obtained and resolved by using a second-order multivariate calibration method based on unfolded partial least-squares combined with residual bilinearization (U-PLS/RBL) for achieving “second-order advantage.” In this way, pesticides were determined in fruits even in the presence of inner filter effects, background interactions, strong spectral overlapping, and unexpected components. U-PLS can cope with effects that cause trilinearity loss such as, inner filter effects, including background in the calibration set; meanwhile, RBL allows to resolve the presence of unexpected components. The extraction technique was validated against a commonly applied technique based on the use of ethyl acetate and sodium sulfate. Besides, results obtained for real samples were statistically compared with those obtained by using HPLC. LODs of 0.038, 0.054, and 0.018 mg·kg−1 and 0.044, 0.072, and 0.020 mg·kg−1 were obtained for carbaryl, carbendazim, and thiabendazole in banana and orange samples, respectively; values were in accordance with the MRLs (Maximum Residue Limits) established by different official control organizations such as National Food Safety and Quality Service (SENASA), Codex Alimentarius (based on Food and Agriculture Organization (FAO) of the United Nations and World Health Organization (WHO), and Environmental Protection Agency (EPA).

Dealing with overlapped and unaligned chromatographic peaks by second-order multivariate calibration for complex sample analysis: Fast and green quantification of eight selected preservatives in facial masks

The quantification of preservatives in cosmetics has attracted great attentions for their controversial and widespread use. HPLC is a prevailing method for preservatives determination among various analytical methods. However, it takes long time to fully separate these compounds because of the complexity of cosmetic matrices. In this study, a fast and green HPLC-DAD strategy assisted with second-order multivariate calibration methods based on alternating trilinear decomposition (ATLD) and multivariate curve resolution-alternating least squares (MCR-ALS) was developed for the simultaneous determination of eight selected preservatives in complex facial mask samples. This appealing strategy proved to be a useful tool for eliminating unknown interferences in complex matrices without complete separation, which benefited from the “second-order advantages” and thus made the determination of the eight analytes in facial mask samples shorten to 8.2 min under a fast elution program. In particular, for the first time, we focused on the applicability of ATLD method for modeling of HPLC-DAD data with severe signal overlapping and slight time shifts. The spiked recovery values were in the range of 71.4–124.6%, and the RMSEP and REP values ranged from 0.07 to 2.4 μg mL−1 and 1.3–14.5%, respectively, indicating that the ATLD method could provide satisfactory prediction. The resolved spectral profiles and concentration values were compared with those obtained by the MCR-ALS method, an excellent tool for modeling of data deviating from trilinearity. Both qualitative and quantitative results from the two methods were consistent with each other, which evidenced the competence of ATLD method in handling HPLC-DAD data with severe signal overlapping and slight time shifts.

Strategy To Obtain Accurate Analytical Solutions in Second-Order Multivariate Calibration with Curve Resolution Methods

A novel procedure is described for processing the second-order data matrices with multivariate curve resolution-alternating least-squares; while the data set is nontrilinear and severe profile overlapping occurs in the instrumental data modes. The area of feasible solutions can be reduced to a unique solution by including/considering the area correlation constraint, besides the traditional constraints (i.e., non-negativity, unimodality, species correspondence, etc.). The latter is implemented not only for the unknown samples but also for all calibration samples, regardless of their interferent content. The area of correlation constraint was specially designed to remove rotational ambiguity in the chemical data sets when information about calibration samples is at hand. In this contribution a comprehensive strategy is developed to uniquely unravel nontrilinear data sets or data sets with severely overlapped profiles in the instrumental data modes. The approach is illustrated with simulated and experimental data sets. Borgen plots are employed to adequately visualize the extent of rotational ambiguity under non-negativity constraint.

Functional data analysis, a new approach to aligning three-way liquid chromatographic with fluorescence detection data

Functional data analysis (FDA) arises as a promissory auxiliary methodology designed to help the analytical chemists, especially chemometricians. However, although the innovative ideas of this approach have barely spread into the chemical research field. In this work, a novel approach for aligning three-way chromatographic-spectral data based on FDA methodology is proposed. Unlike most of the available algorithms, this novel method allows performing data alignment when the test data matrix contains unexpected chemical interferences. Simulated and experimental analytical systems composed of calibrated analytes and potential interferents in the test samples are studied. The experimental system corresponds to the determination of the four polycyclic aromatic hydrocarbons (benzo[a]pyrene, dibenzo[a,h]anthracene, benzo[b]fluoranthene and benzo [k]fluoranthene) in the presence of benzo[j]fluoranthene and benzo[e]pyrene as potential interferences. These compounds are priority pollutants; hence, its reliable quantification in environmental samples is an analytical challenge. The method consists in decomposing the three-way data in each sensor mode and in making a functional alignment of the pure vectors obtained from the individual chromatograms of each analyte and interferent. The functional preprocessing step enables the analysis of the data set with second-order multivariate calibration algorithms, such as PARAFAC. The results illustrate that the proposed method restores the trilinearity of the three-way data, thus being able to successfully quantify the analytes in the presence of the interferences, that is, exploiting the second-order advantage. MCR-ALS is also applied to both simulated and experimental data to evaluate the performance of the PARAFAC second-order calibration model proposed. The performance of the PARAFAC and MCR-ALS models are compared and discussed.

Maximum likelihood unfolded principal component regression with residual bilinearization (MLU-PCR/RBL) for second-order multivariate calibration

A maximum likelihood model is described for performing second-order multivariate calibration with unfolded principal component regression with residual bilinearization (MLU-PCR/RBL). It differs from the conventional RBL models based on U-PCR or U-PLS (unfolded partial least-squares) in the incorporation of the measurement error information into both the U-PCR calibration and the RBL model phases. The error information is represented by the instrumental error covariance matrix. Simulations were made by adding correlated and proportional noise to synthetic systems consisting of one analyte in the presence of a calibrated and unexpected interferent, under different conditions of overlapping profiles, noise levels and noise types (correlated and proportional). The results show that MLU-PCR/RBL outperforms conventional RBL methods in prediction ability, as confirmed by a detailed study on validation samples through the average prediction error as a convenient figure of merit. Results obtained in experimental data set based on flow injection analysis and UV detection for determination of acetylsalicylic and ascorbic acids in pharmaceutical products also support the theoretical conclusions.

Photochemically induced fluorescence coupled to second-order multivariate calibration as analytical tool for determining imidacloprid in honeybees

This paper presents a method for the determination of imidacloprid in honeybees based on the measurement of excitation-emission spectra of photo-induced fluorescence (PIF-EEMs) associated to unfolded partial least squares coupled to residual bilinearization (U-PLS/RBL) algorithm. As a preliminary step, matrix solid phase dispersion (MSPD) using C18 as dispersant, combined on-line with a solid phase extraction (SPE) clean-up on graphitized carbon-amino propyl silica phase was applied to diminish the interferences presents in samples. A previous study on the photochemical induction of fluorescence of imidacloprid in presence of bee matrix was included. The second order advantage achieved with RBL permitted the determination of imidacloprid in the presence of interferences present in samples (unexpected compounds of bees), which also shows photo-induced or native fluorescence. The LOD was 20µgkg−1 (2.5ng per bee; four bees treated), which is suitable for detecting imidacloprid at the oral LD50 for the insect. The predicted U-PLS/RBL concentrations compared favorably with those measured using high-performance liquid chromatography with diode array detection. The PIF-EEMs coupled to U-PLS/RBL was applied for the determination of imidacloprid in honeybees collected in field hives. The work demonstrates the feasibility of the determination of imidacloprid in a highly complex sample matrix as bee through photochemically induced fluorescence spectroscopy coupled to multivariate calibration.

Area correlation constraint for the MCR−ALS quantification of cholesterol using EEM fluorescence data: A new approach

This work demonstrates the use of a new additional constraint for the Multivariate Curve Resolution−Alternating Least Squares (MCR−ALS) algorithm called “area correlation constraint”, introduced to build calibration models for Excitation Emission Matrix (EEM) data. We propose the application of area correlation constraint MCR−ALS for the quantification of cholesterol using a simulated data set and an experimental data system (cholesterol in a ternary mixture). This new constraint includes pseudo-univariate local regressions using the area of resolved profiles against reference values during the alternating least squares optimization, to provide directly accurate quantifications of a specific analyte in concentration units. In the two datasets investigated in this work, the new constraint retrieved correctly the analyte and interference spectral profiles and performed accurate estimations of cholesterol concentrations in test samples. This the first study using the proposed area constraint using EEM measurements. This new constraint approach emerges as a new possibility to be tested in general cases of second-order multivariate calibration data in the presence of unknown interferents or in more involved higher order calibration cases.

Second-order advantage in determining Co (II) in real samples using kinetic-spectrophotometric data matrices and multivariate curve resolution-alternating least square approach

In the present study, multivariate curve resolution coupled to alternating least-squares (MCR-ALS) was used to analyze kinetic-spectroscopic second-order data. The purpose of the study was to achieve important sec ond-order advantage under the conditions of extreme spectral overlapping among sample components. The obtained experimental data indicated that MCR-ALS, unlike other second-order multivariate calibration algorithms, can conveniently handle the investigated analytical problem provided that matrix augmentation is implemented in the spectral mode instead of the usual kinetic mode. In this work, row-wise augmentation was used to break rank deficiency under conditions of extreme spectral overlapping among sample components. The approach was applied to determine Cobalt (II) based on its oxidation reaction with Fe (III) and 1, 10-phenantroline in micellar media. The results indicated good analytical performance toward the analyte despite the intense spectral overlapping and the presence of unexpected constituents in the test samples. The maximum and minimum band boundaries of feasible solutions corresponding to the species profiles were estimated by multivariate curve resolution. The results of the study indicated that unique solution can be practically obtained using MCR-ALS under the selection of suitable constraints such as trilinearity.

A novel application of nylon membranes for tributyltin determination in complex environmental samples by fluorescence spectroscopy and multivariate calibration

The widely distributed pollutant tributyltin (TBT) was analyzed in different environmental samples (waters and sediments) combining preconcentration on a nylon membrane, excitation–emission fluorescence matrices directly measured over the membrane and second-order multivariate calibration. The latter was implemented using unfolded partial least-squares with residual bilinearization (U-PLS/RBL), a flexible algorithm achieving second-order advantage, even under severe spectral overlapping among sample components. Matrix-specific calibrations were required to overcome matrix effects, resulting in good analytical performance. TBT was determined in the concentration ranges 0.043–1.42ng Sn mL−1 in water and 24–400μg Sn kg−1 in sediments, with adequate detection limits in the range 0.03–0.15ng Sn mL−1.

Application of bilinear least squares/residual bilinearization in bulk liquid membrane system for simultaneous multicomponent quantification of two synthetic dyes

For the first time, this research reports a new application of bulk liquid membrane (BLM) with second-order calibration based on the bilinear least squares/residual bilinearization (BLLS/RBL) algorithm, as a novel method for simultaneous removal and quantification of allura red (AR) and sunset yellow (SY) as model compounds in soft drinks and food samples. Due to severe spectral overlapping between the AR and SY and strong colinearities present in the data set, common second-order multivariate calibration methods, such as parallel factor analysis (PARAFAC) and multivariate curve resolution-alternating least-squares (MCR-ALS), could not be successfully applied to the presently studied samples. At first, the basic experimental parameters affecting the transport of the target dyes were investigated and optimized. Then under the optimum conditions, we have explored an alternative use of BLLS/RBL methodology, which can work adequately with strongly overlapping spectra and colinearities problems. Satisfactory results were obtained for analysis of target analytes. The proposed method was validated by comparison with a reference method based on high-performance liquid chromatography-ultra violet detection (HPLC-UV) and no significant differences were found between the reference values and the ones obtained with the proposed method. Such a chemometrics-based protocol may be a very promising tool for more analytical applications in real samples monitoring, due to its advantages of easy sample pretreatment, accuracy, sufficient spectral resolution and concentration prediction even in the presence of unknown interferences.

Determination of imidacloprid in water samples via photochemically induced fluorescence and second-order multivariate calibration

This paper presents a new method for the determination of imidacloprid in water samples; one of the most widely used neonicotinoid pesticides in the farming industry. The method is based on the measurement of excitation–emission spectra of photo-induced fluorescence (PIF-EEMs) associated with second-order multivariate calibration with a parallel factor analysis (PARAFAC) and unfolded partial least squares coupled to residual bilinearization (U-PLS/RBL). The second order advantage permitted the determination of imidacloprid in the presence of potential interferences, which also shows photo-induced fluorescence (other pesticides and/or unexpected compounds of the real samples). The photoreaction was performed in 100-μl disposable micropipettes. As a preliminary step, solid phase extraction on C18 (SPE-C18) was applied to concentrate the analyte and diminish the limit of detection. The LOD was approximately 1ngmL−1, which is suitable for detecting imidacloprid in water according to the guidelines established in North America and Europe. The PIF-EEMs coupled to PARAFAC or U-PLS/RBL was successfully applied for the determination of imidacloprid in different real water samples, with an average recovery of 101±10%.

Second-order advantage maintenance with voltammetric data modeling for quantitation of ethiofencarb in the presence of interferences

This work presents the development of a method based on a voltammetric determination coupled to second-order data modeling with multivariate curve resolution-alternating least-square (MCR-ALS) and unfolded partial least squares regression followed by residual bilinearization (U-PLS/RBL) for the quantitation of the pesticide ethiofencarb in the presence of interferences in tap water.The determination of ethiofencarb by voltammetry is possible on the basis that this pesticide is hydrolysed in alkaline media giving rise to a compound which shows an oxidation peak at Ep=0.80V. But some other pesticides belonging to the same family can be considered as interferences due to the high overlapping in their signals. The two such interferences are fenobucarb and bendiocarb, which have not been included in the calibration step.The possibility of second-order multivariate calibration was studied by using the hydrolysis time as the third variable, and MCR-ALS and U-PLS/RBL. Good results were obtained in this determination in spite of the high overlapping in voltammetric signals.