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In the present report, a chemometrics-assisted second-order kinetic-spectrophotometric method has been developed for determining reducing sugars, glucose, fructose and lactose, in food samples, based on the reaction with hexacyanoferrate, HCF, at 70 °C in alkaline medium. A suitable experimental design helped us to establish the conditions (pH, temperature, and HCF concentration) for optimal sensitivity and selectivity among analytes. Second order data were recorded by measuring the absorbance of unreacted HCF in the spectral range of 370 to 470 nm for five minutes using a diode array. A calibration set of samples was prepared according to a central composite design containing the three sugars for training the algorithms. Validation samples containing only the analytes were prepared for checking the reliability of the algorithms. In this particular system, identical profiles for sample components are obtained in the spèctral dimension corresponding to unreacted HCF. Moreover, two kinds of interferents may be present: sample components active in the spectral region at which HCF absorbs as well as potential reducing interferents, causing linear dependence, since they provide identical profiles in spectral dimension to those of the analytes of interest. In the present work, MCR-ALS in the spectral augmentation mode was the only algorithm that could successfully resolve linear dependence. Satisfactory results were obtained by applying MCR-ALS in the spectral augmentation mode in order to achieve a second order advantage for the determination of fructose and glucose in validation samples, in test samples containing the two kinds of interferents and in real food samples, providing LODs of 4.0 and 5.0 mg L-1, respectively. However, bad results were obtained for lactose which may be due to its low sensitivity in the augmented dimension. Good results were also obtained by applying U-PLS/RBL and N-PLS/RBL for determining simultaneously the three sugars in validation samples and in test samples containing only active spectral interferents. Finally, lactose and also, glucose and fructose, were successfully quantified in real milk samples, with LODmin = 1.0 mg L-1, 1.0 mg L-1 and 0.1 mg L-1 and LODmax = 3.5, 3.8 and 4.4 mg L-1, respectively, using UPLS/RBL, and LODmin of 1.3, 1.1 and 0.1 mg L-1 and LODmax of 4.0, 4.3 and 4.9 mg L-1 for lactose, glucose and fructose, respectively, for NPLS/RBL. Results for real samples in all cases were statistically comparable to those obtained by applying a reference method based on HPLC (High Performance Liquid Chromatography).

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Quantitative analytical works developed by processing second- and third-order chromatographic data are reviewed. The various modes in which data of complex structure can be measured are discussed, with chromatographic separation providing either one or two of the data dimensions. This produces second-order data (matrices from uni-dimensional chromatography with multivariate detection or from two-dimensional chromatography) or third-order data (three-dimensional data arrays from two-dimensional chromatography with multivariate detection). The available algorithms for processing these data are classified and discussed, regarding their ability to cope with the ubiquitous phenomenon of retention time shifts from run to run. A summary of relevant works applying this combination of techniques is presented, with focus on quantitative analytical results. Special attention is paid to works achieving the full potentiality of the multidimensional data, i.e., the second-order advantage.

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A second-order multivariate calibration method based on a combination of unfolded partial least-squares (U-PLS) with residual bilinearization (RBL) has been applied to second-order data obtained from excitation-emission fluorescence matrices for determining atenolol in human urine, even in the presence of background interactions and fluorescence inner filter effects, which are both sample dependent. Atenolol is a cardioselective beta-blocker, which is considered a doping agent in shoot practice, so that its determination in urine can be required for monitoring the drug. Loss of trilinearity due to analyte-background interactions which may vary between samples, as well as inner filter effects, precludes the use of methods like parallel factor analysis (PARAFAC) that cannot handle trilinearity deviations, and justifies the employment of U-PLS. Successful analysis required to include the background in the calibration set. Unexpected components appear in new urine samples, different from those used in calibration set, requiring the second-order advantage which is obtained from a separate procedure known as residual bilinearization (RBL). Satisfactory results were obtained for artificially spiked urines, and also for real urine samples. They were statistically compared with those obtained applying a reference method based on high-performance liquid chromatography (HPLC).

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Liquid chromatographic-diode array detection data recorded for aqueous mixtures of 11 pesticides show the combined presence of strongly coeluting peaks, distortions in the time dimension between experimental runs, and the presence of potential interferents not modeled by the calibration phase in certain test samples. Due to the complexity of these phenomena, data were processed by a second-order multivariate algorithm based on multivariate curve resolution and alternating least-squares, which allows one to successfully model both the spectral and retention time behavior for all sample constituents. This led to the accurate quantitation of all analytes in a set of validation samples: aldicarb sulfoxide, oxamyl, aldicarb sulfone, methomyl, 3-hydroxy-carbofuran, aldicarb, propoxur, carbofuran, carbaryl, 1-naphthol and methiocarb. Limits of detection in the range 0.1-2 µg mL(-1) were obtained. Additionally, the second-order advantage for several analytes was achieved in samples containing several uncalibrated interferences. The limits of detection for all analytes were decreased by solid phase pre-concentration to values compatible to those officially recommended, i.e., in the order of 5 ng mL(-1).

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Four-way data were obtained by recording the kinetic evolution of excitation-emission fluorescence matrices for samples containing the analytes carbaryl and 1-naphthol, two widely employed pesticides, in the concentration ranges 0-363 µg L(-1) and 0-512 µg L(-1), respectively. The reaction followed was the alkaline hydrolysis of carbaryl to produce 1-naphthol, a fact which introduced strong linear dependencies and multi-linearity losses in the analyzed system. Data processing was performed with unfolded partial least-squares combined with residual trilinearization (U-PLS/RTL) and also with a suitably initialized and restricted parallel factor model (PARAFAC), combined with calibration based on multi-linear regression. U-PLS/RTL is shown to be significantly simpler in its implementation and to provide similar figures of merit. The applied chemometric strategy is able to successfully determine the analytes in water samples containing uncalibrated interferences, such as other commonly employed agrochemicals and also a naturally occurring background signal.

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Synchronous fluorescence spectra measured in a flow-injection system with double pH gradient modulation constitute a new second-order signal which is herein studied for the quantitative determination of three fluoroquinolone antibiotics in spiked human urine samples. Because calibration is done using aqueous solutions of each of the three analytes ciprofloxacin, norfloxacin and ofloxacin, the fluorescent urine background makes it necessary to achieve the second-order advantage. Several second-order multivariate calibration algorithms were evaluated for this purpose: parallel factor analysis, unfolded and multiway partial least-squares with residual bilinearization, and multivariate curve resolution-alternating least-squares. The best analytical figures of merit, a root mean square error of 4-6 mg L(-1) (corresponding to a relative error of 4-6% for a calibration range from 0 to 200 mg L(-1) for each analyte), and a limit of detection of 4 mg L(-1) were obtained using partial least-squares (in the specific unfolded version) combined with residual bilinearization. Reasons for the improved success of this latter technique are provided on the basis of the analysis of simulated second-order data.

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Four-way data were obtained by recording the kinetic evolution of excitation-emission fluorescence matrices for the product of the Hantzsch reaction between the analyte malonaldehyde and methylamine. The reaction product, 1,4-disubstituted-1,4-dihydropyridine-3,5-dicarbaldehyde, is a highly fluorescent compound. The nonlinear nature of the kinetic fluorescence data has been demonstrated, and therefore the four-way data were processed with parallel factor analysis combined with a nonlinear pseudounivariate regression, based on a quadratic polynomial fit, and also with a recently introduced neural network methodology, based on the combination of unfolded principal component analysis, residual trilinearization, and radial basis functions. The applied chemometric strategies are not only able to adequately model the nonlinear data but also to successfully determine malonaldehyde in olive oil samples. This is possible since the experimentally recorded four-way data, modeled with the above-mentioned advanced chemometric approaches, permit the achievement of the second-order advantage. This allows us to predict the analyte concentration in a complex background, in spite of the nonlinear behavior and in the presence of uncalibrated interferences. The present work is a new example of the use of higher-order data for the resolution of a complex nonlinear system, successfully employed in the context of food chemical analysis.

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Three different experimental systems have been studied regarding the determination of analytes in complex samples, using non-linear second-order instrumental data, which are intrinsically able to provide the second-order advantage. This permits the quantitation of calibrated analytes in the presence of unexpected sample components, although a suitable algorithm is required. The recently described combination of artificial neural networks with post-training residual bilinearization has been applied to the three data sets, with successful results concerning prediction accuracy and precision, as well as profile recovery for the potential interferents in test samples. The studies involve: (1) the determination of two pharmaceuticals in the presence of an unexpected excipient by absorbance-pH matrix measurements, (2) the quantitation of iron(II) by its catalytic effect on the kinetics of the bromate oxidation of a colorant in the presence of a second interfering organic dye, and (3) the analysis of the antibiotic amoxicillin by fluorescence excitation-emission matrices in the presence of a fluorescent anti-inflammatory. The prediction results were compared and shown to be significantly better than those yielded by the unfolded partial least-squares/residual bilinearization model, due to the non-linear nature of the studied data.

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Fluorescence excitation-emission data recorded for amoxicillin after photo-activated reaction with periodate have been processed by a novel second-order multivariate method based on the combination of artificial neural networks and residual bilinearization (ANN/RBL), since the signals bear a strong non-linear relation with the analyte concentration. The selected chemometric methodology is employed for the first time to evaluate experimental non-linear second-order spectral information. Due to severe overlapping between the emission profiles for the analyte reaction product and for the urine background, calibration was done using different spiked urine samples. This allowed for the determination of amoxicillin in test spiked urines, other than those employed for calibration. When new urine samples containing a fluorescent anti-inflammatory were analyzed, accurate prediction in the presence of unexpected components required the achievement of the second-order advantage, which is provided by the post-training RBL procedure. Amoxicillin was also determined by ANN/RBL in a series of real urine samples, which allowed one to perform a comparison study with the reference high-performance liquid chromatographic technique.

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The kinetic evolution of UV-visible absorption spectra of amoxicillin in the presence of copper(II) ions has been processed by the second-order multivariate methods parallel factor analysis (PARAFAC) and also by a novel approach based on partial least-squares with residual bilinearization (PLS/RBL). The latter one is employed for the first time to evaluate kinetic-spectral information. The mechanism of the analyte metal-catalyzed hydrolysis involves a reaction intermediate and a final reaction product, both with spectra which may allow for the determination of amoxicillin in human urine, even in the presence of unsuspected sample components. This is possible thanks to the second-order advantage exploited by the employed chemometric algorithms, among which PARAFAC and PLS/RBL gave the best results. Amoxicillin was determined in a series of spiked and real urine samples, which allowed to perform, respectively, a recovery study and a comparison with the reference high-performance liquid chromatographic technique. The best figures of merit were obtained with PLS/RBL, namely sensitivity, 0.5AUL mg(-1) (AU=absorbance units), analytical sensitivity, 500L mg(-1) and limit of detection, 6mg L(-1). Relative advantages and disadvantages of the employed algorithms are discussed.

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The simultaneous determination of levodopa and benserazide in pharmaceutical formulations is described, based on the application of multidimensional partial least-squares regression to the kinetic-spectrophotometric data provided by diode-array detection within a stopped-flow injection method where analytes react with periodate. Flow injection parameters were adequately optimized. Accurate analysis is performed with no sample pre-treatment steps, and with minimum experimental effort. Satisfactory recovery results were obtained on a number of synthetic and commercial samples, in the latter case including the comparison with liquid chromatography measurements.

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The analytical performances of two algorithms, the recently introduced bilinear least-squares (BLLS) and the popular parallel factor analysis (PARAFAC), are compared as regards second-order fluorescence data recorded for the determination of the fluoroquinolone antibiotic ciprofloxacin in human urine samples. The applied chemometric methodologies employ different strategies for exploiting the so-called second-order advantage, which allows one to obtain individual concentrations of calibrated analytes in the presence of any number of uncalibrated (urine) components. Analysis of a spiked urine test set (in the analyte concentration range 0-200 mg L(-1)) showed that BLLS provides results of slightly better quality than PARAFAC. Satisfactory results have been obtained on comparing the concentrations predicted for a series of real urine samples with those furnished by liquid chromatography. The limit of detection of the fluorescence-based methods is approximately 5 mg L(-1).

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A spectrophotometric method is described and applied to resolve ternary mixtures of the corticosteroid dexamethasone sodium phosphate and the vitamins B6 and B12. It involves multivariate calibration based on partial least-squares regression. The model was built with UV-vis absorption spectra, and was evaluated by cross-validation on a number of synthetic mixtures. Satisfactory results for both artificial and commercial samples were obtained. A spectrofluorometric method was also developed for the determination of B6 in the presence of vitamin B12 and dexamethasone. The results provided by both methods for pharmaceutical formulations were compared successfully. None of the described procedures require sample pre-treatment steps.

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