An exhaustive analysis of the use of image moments for second-order calibration. A comparison with multivariate curve resolution-alternating least-squares.

BACKGROUND: the chemometric processing of second-order chromatographic-spectral data is usually carried out with the aid of multivariate curve resolution-alternating least-squares (MCR-ALS). Recently, an alternative procedure was described based on the estimation of image moments for each data matrix and subsequent application of multiple linear regression after suitable variable selection. RESULTS: The analysis of both simulated and experimental data leads to the conclusion that the image moment method, although can cope with chromatographic lack of reproducibility across injections, it only performs well in the absence of uncalibrated interferents. MCR-ALS, on the other hand, provides good analytical results in all studied situations, whether the test samples contain uncalibrated interferents or not. SIGNIFICANCE: The results are useful to assess the real usefulness of newly proposed methodologies for second-order calibration in the case of chromatographic-spectral data sets, especially when samples contain unexpected chemical constituents.

Three-way calibration using PARAFAC and MCR-ALS with previous synchronization of second-order chromatographic data through a new functional alignment of pure vectors for the quantification in the presence of retention time shifts in peak position and shape.

In the present contribution is shown the application of the recently developed functional alignment of pure vectors (FAPV) as a proper algorithm to align second-order chromatographic data with severe retention time shifts in peak position and shape. FAPV decomposed a three-way chromatographic data array in their three modes (sample, spectral and elution time vectors), using a basis function to pre-process the non-linear mode (elution time) and then it aligns the functionalized pure vectors and reshapes the transformed vectors into matrices, restoring the trilinearity of second-order chromatographic data. The well-aligned three-way chromatographic data array is then successfully decomposed by advanced chemometric models such as parallel factor analysis (PARAFAC) and multivariate curve resolution - alternating least-squares (MCR-ALS) with the trilinearity constraint. The performance of this innovative analytical strategy based on PARAFAC and MCR-ALS with previous synchronization of data through FAPV algorithm is properly evaluated using real second-order chromatographic data with multiple artifacts, i.e., shifts in peak position and shape for the simultaneous quantification of amoxicillin and potassium clavulanate in commercial medicinal drugs. The present contribution compares some analytical results achieved by: (1) the usual MCR-ALS as a bilinear model applied in augmented data matrix without previous synchronization and with interval correlation optimized shifting (ICOSHIFT) and FAPV and (2) trilinear models using PARAFAC with ICOSHIFT and FAPV and trilinearity constraint in MCR-ALS with FAPV. Available results suggest that these strongly shifted and warped elution time profiles cause for the loss of trilinearity, which can be adequately restored by FAPV algorithm. PARAFAC performed a successful trilinear decomposition of three-way chromatographic data array with law values of relative prediction error (REP) in the order of 1.34-1.42% in both analytes.

Multivariate analysis of organic acids in fermented food from reversed-phase high-performance liquid chromatography data.

Multivariate calibration coupled to RP-HPLC with diode array detection (HPLC-DAD) was applied to the identification and the quantitative evaluation of the short chain organic acids (malic, oxalic, formic, lactic, acetic, citric, pyruvic, succinic, tartaric, propionic and α-cetoglutaric) in fermented food. The goal of the present study was to get the successful resolution of a system in the combined occurrence of strongly coeluting peaks, of distortions in the time sensors among chromatograms, and of the presence of unexpected compounds not included in the calibration step. Second-order HPLC-DAD data matrices were obtained in a short time (10min) on a C18 column with a chromatographic system operating in isocratic mode (mobile phase was 20mmolL-1 phosphate buffer at pH 2.20) and a flow-rate of 1.0mLmin-1 at room temperature. Parallel factor analysis (PARAFAC) and unfolded partial least-squares combined with residual bilinearization (U-PLS/RBL) were the second-order calibration algorithms select for data processing. The performance of the analytical parameters was good with an outstanding limit of detection (LODs) for acids ranging from 0.15 to 10.0mmolL-1 in the validation samples. The improved method was applied to the analysis of many dairy products (yoghurt, cultured milk and cheese) and wine. The method was shown as an effective means for determining and following acid contents in fermented food and was characterized by reducibility with simple, high resolution and rapid procedure without derivatization of analytes.

A new modeling strategy for third-order fast high-performance liquid chromatographic data with fluorescence detection. Quantitation of fluoroquinolones in water samples.

Matrix augmentation is regularly employed in extended multivariate curve resolution-alternating least-squares (MCR-ALS), as applied to analytical calibration based on second- and third-order data. However, this highly useful concept has almost no correspondence in parallel factor analysis (PARAFAC) of third-order data. In the present work, we propose a strategy to process third-order chromatographic data with matrix fluorescence detection, based on an Augmented PARAFAC model. The latter involves decomposition of a three-way data array augmented along the elution time mode with data for the calibration samples and for each of the test samples. A set of excitation-emission fluorescence matrices, measured at different chromatographic elution times for drinking water samples, containing three fluoroquinolones and uncalibrated interferences, were evaluated using this approach. Augmented PARAFAC exploits the second-order advantage, even in the presence of significant changes in chromatographic profiles from run to run. The obtained relative errors of prediction were ca. 10 % for ofloxacin, ciprofloxacin, and danofloxacin, with a significant enhancement in analytical figures of merit in comparison with previous reports. The results are compared with those furnished by MCR-ALS.

Chemometric processing of second-order liquid chromatographic data with UV-vis and fluorescence detection. A comparison of multivariate curve resolution and parallel factor analysis 2.

Second-order liquid chromatographic data with multivariate spectral (UV-vis or fluorescence) detection usually show changes in elution time profiles from sample to sample, causing a loss of trilinearity in the data. In order to analyze them with an appropriate model, the latter should permit a given component to have different time profiles in different samples. Two popular models in this regard are multivariate curve resolution-alternating least-squares (MCR-ALS) and parallel factor analysis 2 (PARAFAC2). The conditions to be fulfilled for successful application of the latter model are discussed on the basis of simple chromatographic concepts. An exhaustive analysis of the multivariate calibration models is carried out, employing both simulated and experimental chromatographic data sets. The latter involve the quantitation of benzimidazolic and carbamate pesticides in fruit and juice samples using liquid chromatography with diode array detection, and of polycyclic aromatic hydrocarbons in water samples, in both cases in the presence of potential interferents using liquid chromatography with fluorescence spectral detection, thereby achieving the second-order advantage. The overall results seem to favor MCR-ALS over PARAFAC2, especially in the presence of potential interferents.

Second order multivariate curve resolution of Fourier transform infrared spectroscopic data of the photo-induced crosslinking of thymine functionalized polymers.

A meaningful characterization of the photo-induced curing process of materials based on styrene monomers functionalized with thymine and charged ionic groups was accomplished using FT-IR spectroscopy in combination with second-order multivariate calibration algorithms. The polymer composition as well as the irradiation dose effects on the photo-crosslinking of copolymer films was experimentally determined. Each FT-IR absorption spectra was decomposed into the contribution of individual species by means of chemometric algorithms. A second-order strategy involving a three-way array for each sample and analyzing all arrays simultaneously was used. Temperature and solvent frequently have a strong influence on the FT-IR peak producing shifts and trilinearity lost. A new methodology to properly pre-align the spectroscopic matrix data is used based on the decomposition of a three-way array via a suitably initialized and constrained PARAFAC model. The chemical reaction mechanism describing the underlying process in terms of identifiable steps was determined. Associated key parameters and equilibrium rate constants that characterize the interconversion and stability of diverse species were predicted. Additionally, it was possible to quantify all the species even in the presence of a non-calibrated compound.

Chemometrics-assisted fluorimetry for the rapid and selective determination of heavy polycyclic aromatic hydrocarbons in contaminated river waters and activated sludges.

The most concerned polycyclic aromatic hydrocarbons (PAHs) benzo[a]pyrene, dibenz[a,h]anthracene, chrysene, benzo[b]fluoranthene, benzo[k]fluoranthene and benz[a]anthracene were simultaneously determined in the presence of other 10 interfering PAHs, applying second-order multivariate calibration to the data obtained with a flow-through optosensor interfaced to a fast-scanning spectrofluorimeter. Using a sample volume of 2.5 mL, detection limits in the range 5-115 ng L(-1) were obtained in interfering samples, with a sample frequency of ca. 15 samples per hour, and with a minimum use of organic solvents, competing very favorably with chromatographic methods. The significance of this study lies in the solution of the quantitative analysis problem of six PAHs in real matrices of unknown composition. The unfolded partial least-squares/residual bilinearization (U-PLS/RBL) algorithm showed the best performance in resolving the complex studied system.

Non-trilinear chromatographic time retention-fluorescence emission data coupled to chemometric algorithms for the simultaneous determination of 10 polycyclic aromatic hydrocarbons in the presence of interferences.

Multivariate calibration coupled to high-performance liquid chromatography-fast scanning fluorescence spectroscopy (HPLC-FSFS) was employed for the analysis of 10 selected polycyclic aromatic hydrocarbons (PAHs), six of which correspond to heavy PAHs. The goal of the present study was the successful resolution of a system even in the presence of real interferences. Second-order HPLC-FSFS data matrices were obtained in a short time with a chromatographic system operating in isocratic mode. The difficulties in aligning chromatographic bands in complex systems, such as the ones presented here, are discussed. Two second-order calibration algorithms which do not require chromatographic alignment were selected for data processing, namely, multivariate curve resolution-alternating least-squares (MCR-ALS) and parallel factor analysis 2 (PARAFAC2). These algorithms did also achieve the second-order advantage, and therefore they were able to overcome the problem of the presence of unexpected interferences. The study was employed for the discussion of the scopes of the applied second-order chemometric tools, demonstrating the superiority of MCR-ALS to successfully resolve this complex system. The quality of the proposed techniques was assessed on the basis of the analytical recoveries from different types of water and olive oil samples after solid-phase extraction. The studied concentration ranges in water samples were 5.6 x 10(-3)-0.20 ng mL(-1) for heavy PAHs and 0.036-0.80 ng mL(-1) for light PAHs, while in oil samples the PAHs concentrations were 0.13-9.6 and 2.3-49.5 ng mL(-1) for heavy and light PAHS, respectively. All real samples were analyzed in the presence of the studied interferences.

Chemometrics-assisted excitation-emission fluorescence spectroscopy on nylon membranes. Simultaneous determination of benzo[a]pyrene and dibenz[a,h]anthracene at parts-per-trillion levels in the presence of the remaining EPA PAH priority pollutants as interferences.

This work presents a novel approach for the simultaneous ultratrace determination of benzo[ a]pyrene and dibenzo[ a,h]anthracene, the two most carcinogenic polycyclic aromatic hydrocarbons (PAHs), in a very interfering environment, combining the recently discovered ability of the nylon membrane to strongly retain and concentrate PAHs on its surface, the sensitivity of molecular fluorescence, and the selectivity of second-order chemometric algorithms. The fluorescence excitation-emission matrices, directly measured on a nylon-membrane surface, are processed by applying parallel factor analysis (PARAFAC) and unfolded partial least-squares coupled to residual bilinearization (U-PLS/RBL). The superiority of U-PLS/RBL to quantify BaP and DBA at concentrations below 10 ng L (-1) in the presence of the remaining 14 US EPA (United States Environmental Protection Agency) PAHs at total concentrations ranging from 1400 and 14,000 ng L (-1) is demonstrated. The present method successfully faces this complex challenge without using organic solvents, which are to known produce environmental contamination. Finally, the high sensitivity of the present method avoids preconcentration and elution steps, considerably decreasing the analysis time and the experimental errors. Because the instrumental involved in the determination is nonsophisticated, the experiments could be carried out in routine laboratories.