Time-alignment of bidimensional chromatograms in the presence of uncalibrated interferences using parallel factor analysis: Application to multi-component determinations using liquid-chromatography with spectrofluorimetric detection

A new methodology for the alignment of matrix chromatographic data is proposed, based on the decomposition of a three-way array composed of a test and a reference data matrix using a suitably initialized and constrained parallel factor (PARAFAC) model. It allows one to perform matrix alignment when the test data matrix contains unexpected chemical interferences, in contrast to most of the available algorithms. A series of simulated analytical systems is studied, as well as an experimental one, all having calibrated analytes and also potential interferences in the test samples, i.e., requiring the second-order advantage for successful analyte quantitation. The results show that the newly proposed method is able to properly align the different data matrix, restoring the trilinearity which is required to process the calibration and test data with second-order multivariate calibration algorithms such as PARAFAC. Recent models including unfolded partial least-squares regression (U-PLS) and N-dimensional PLS (N-PLS), combined with residual bilinearization (RBL), are also applied to both simulated and experimental data. The latter one corresponds to the determination of the polycyclic aromatic hydrocarbons benzo[b]fluoranthene and benzo[k]fluoranthene in the presence of benzo[j]fluoranthene as interference. The analytical figures of merit provided by the second-order calibration models are compared and discussed.     

Multiway partial least-squares coupled to residual trilinearization: a genuine multidimensional tool for the study of third-order data. Simultaneous analysis of procaine and its metabolite p-aminobenzoic acid in equine serum

A new third-order multivariate calibration approach, based on the combination of multiway-partial least-squares with a separate procedure called residual trilinearization (N-PLS/RTL), is presented and applied to multicomponent analysis using third-order data. The proposed chemometric algorithm is able to predict analyte concentrations in the presence of unexpected sample components, which require strict adherence to the second-order advantage. Results for the determination of procaine and its metabolite p-aminobenzoic acid in equine serum are discussed, based on kinetic fluorescence excitation-emission four-way measurements and application of the newly developed multiway methodology. Since the analytes are also the reagent and product of the hydrolysis reaction followed by fast-scanning fluorescence spectroscopy, the classical approach based on parallel factor analysis is challenged by strong linear dependencies and multilinearity losses. In comparison, N-PLS/RTL appears an appealing genuine multiway alternative that avoids the latter complications, yielding analytical results that are statistically comparable to those rendered by related unfolded algorithms, which are also able to process four-way data. Prediction was made on validation samples with a qualitative composition similar to the calibration set and also on test samples containing unexpected equine serum components.     

A versatile strategy for achieving the second-order advantage when applying different artificial neural networks to non-linear second-order data: Unfolded principal component analysis/residual bilinearization

Second-order instrumental signals showing a non-linear behaviour with respect to analyte concentration can still be adequately processed in order to achieve the important second-order advantage. The combination of unfolded principal component analysis with residual bilinearization, followed by application of a variety of neural network models, allows one to obtain the second-order advantage. While principal component analysis models the training data, residual bilinearization models the contribution of the potential interferents which may be present in the test samples. Neural networks such as multilayer perceptron, radial basis functions and support vector machines, are all able to model the non-linear relationship between analyte concentrations and sample principal component scores. Three different experimental systems have been analyzed, all requiring the second-order advantage: 1) pH–UV absorbance matrices for the determination of two active principles in pharmaceutical preparations, 2) fluorescence excitation–emission matrices for the determination of polycyclic aromatic hydrocarbons, and 3) UV-induced fluorescence excitation–emission matrices for the determination of amoxicillin in the presence of salicylate. In all cases, reasonably accurate predictions can be made with the proposed techniques, which cannot be reached using traditional methods for processing second-order data.     

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.     

Unfolded partial least-squares with residual quadrilinearization: A new multivariate algorithm for processing five-way data achieving the second-order advantage. Application to fourth-order excitation-emission-kinetic-pH fluorescence analytical data

Unfolded partial least-squares in combination with residual quadrilinearization (U-PLS/RQL), is developed as a new latent structured algorithm for the processing of fourth-order instrumental data. In order to check its analytical predictive ability, fluorescence excitation-emission-kinetic-pH data were measured and processed. The concentration of the fluorescent pesticide carbaryl was determined in the presence of the pesticides fuberidazole and thiabendazole as uncalibrated interferents, in the first example of fourth-order multivariate calibration. The hydrolysis of the analyte was followed at different pH values using a fast-scanning spectrofluorimeter, recording the excitation-emission fluorescence matrices during its evolution to produce 1-naphthol, which does also emit fluorescence. A set of test samples containing the above mentioned fluorescent contaminants was analyzed with the new model, comparing the results with those from parallel factor analysis (PARAFAC). The newly developed U-PLS/RQL model provides better figures of merit for analyte quantitation (average prediction error, 7 μg L⁻¹, relative prediction error, 5%, calibration range, 50-250 μg L⁻¹), and is considerably simpler than PARAFAC in its implementation. The latter, however, furnishes important physicochemical information regarding the chemical process under study, although this requires the data to be unfolded into an array of lower dimensions, due to the lack of quadrilinearity of the experimental data.     

New robust bilinear least squares method for the analysis of spectral-pH matrix data

A new second-order multivariate method has been developed for the analysis of spectral-pH matrix data, based on a bilinear least-squares (BLLS) model achieving the second-order advantage and handling multiple calibration standards. A simulated Monte Carlo study of synthetic absorbance-pH data allowed comparison of the newly proposed BLLS methodology with constrained parallel factor analysis (PARAFAC) and with the combination multivariate curve resolution-alternating least-squares (MCR-ALS) technique under different conditions of sample-to-sample pH mismatch and analyte-background ratio. The results indicate an improved prediction ability for the new method. Experimental data generated by measuring absorption spectra of several calibration standards of ascorbic acid and samples of orange juice were subjected to second-order calibration analysis with PARAFAC, MCR-ALS, and the new BLLS method. The results indicate that the latter method provides the best analytical results in regard to analyte recovery in samples of complex composition requiring strict adherence to the second-order advantage. Linear dependencies appear when multivariate data are produced by using the pH or a reaction time as one of the data dimensions, posing a challenge to classical multivariate calibration models. The presently discussed algorithm is useful for these latter systems.     

Nonlinear four-way kinetic-excitation-emission fluorescence data processed by a variant of parallel factor analysis and by a neural network model achieving the second-order advantage: malonaldehyde determination in olive oil samples

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.     

Second-order calibration of excitation-emission matrix fluorescence spectra for the determination of N-phenylanthranilic acid derivatives

A spectrofluorimetric method has been developed for the quantitative determination of mefenamic, flufenamic, and meclofenamic acids in urine samples. The method is based on second-order data multivariate calibration (unfolded partial least squares (unfolded-PLS), multi-way PLS (N-PLS), parallel factor analysis (PARAFAC), self-weighted alternating trilinear decomposition (SWATLD), and bilinear least squares (BLLS)). The analytes were extracted from the urine samples in chloroform prior to the determination. The chloroform extraction was optimized for each analyte, studying the agitation time and the extraction pH, and the optimum values were 10 minutes and pH 3.5, respectively. The concentration ranges in chloroform solution of each of the analytes, used to construct the calibration matrix, were selected in the ranges from 0.15 to 0.8 microg mL-1 for flufenamic and meclofenamic acids and from 0.25 to 3.0 microg mL-1 for mefenamic acid. The combination of chloroform extraction and second-order calibration methods, using the excitation-emission matrices (EEMs) of the three analytes as analytical signals, allowed their simultaneous determination in human urine samples, in the range of approximately 80 mg L-1 to 250 mg L-1, with satisfactory results for all the assayed methods. Improved results over unfolded-PLS and N-PLS were found with PARAFAC, SWATLD, and BLLS, methods that exploit the second-order advantage.     

Screening of oil samples on the basis of excitation-emission room-temperature phosphorescence data and multiway chemometric techniques. Introducing the second-order advantage in a classification study

Room-temperature phosphorescence excitation-emission matrices and multiway methods have been analyzed as potential tools for screening oil samples, based on full matrix information for polyaromatic hydrocarbons. Crude oils obtained from different sources of similar geographic origin, as well as light and heavy lubricating oils, were analyzed. The room-temperature phosphorescence matrix signals were processed by applying multilayer perceptron artificial neural networks, parallel factor analysis coupled to linear discriminant analysis, discriminant unfolded partial least-squares, and discriminant multidimensional partial least-squares (DN-PLS). The ability of the latter algorithm to classify the investigated oils into four categories is demonstrated. In addition, the combination of DN-PLS with residual bilinearization allows for a proper classification of oils containing unsuspected compounds not present in the training sample set. This second-order advantage concept is applied to a classification study for the first time. The employed approach is fast, avoids the use of laborious chromatographic analysis, and is relevant for oil characterization, identification, and determination of accidental spill sources.     

Analytical advantages of multivariate data processing. One, two, three, infinity?

Multidimensional data are being abundantly produced by modern analytical instrumentation, calling for new and powerful data-processing techniques. Research in the last two decades has resulted in the development of a multitude of different processing algorithms, each equipped with its own sophisticated artillery. Analysts have slowly discovered that this body of knowledge can be appropriately classified, and that common aspects pervade all these seemingly different ways of analyzing data. As a result, going from univariate data (a single datum per sample, employed in the well-known classical univariate calibration) to multivariate data (data arrays per sample of increasingly complex structure and number of dimensions) is known to provide a gain in sensitivity and selectivity, combined with analytical advantages which cannot be overestimated. The first-order advantage, achieved using vector sample data, allows analysts to flag new samples which cannot be adequately modeled with the current calibration set. The second-order advantage, achieved with second- (or higher-) order sample data, allows one not only to mark new samples containing components which do not occur in the calibration phase but also to model their contribution to the overall signal, and most importantly, to accurately quantitate the calibrated analyte(s). No additional analytical advantages appear to be known for third-order data processing. Future research may permit, among other interesting issues, to assess if this "1, 2, 3, infinity" situation of multivariate calibration is really true.     

Two multivariate strategies applied to three-way kinetic spectrophotometric data for the determination of mixtures of the pesticides carbaryl and chlorpyrifos

Two pesticides, carbaryl and chlorpyrifos, have been simultaneously determined using second-order kinetic spectrophotometric measurements upon alkaline oxidative degradation. In spite of the complexity of the system and of the serious spectral overlap among the reagents and products, calibration and prediction is possible thanks to the power of second-order multivariate techniques. Strategies such as parallel factor analysis (PARAFAC) and multivariate curve resolution coupled to alternating least-squares (MCR-ALS) have been employed, which adequately exploit the second-order advantage. They allow for a correct determination of the analytes both in synthetic binary samples and in a commercial formulation, in this latter case even in the presence of unmodeled interferents. Multi-way partial least-squares (n-PLS) produced good results only on synthetic binary mixtures but could not be applied to a commercial sample because it contained an uncalibrated component.     

Second-order advantage achieved with four-way fluorescence excitation-emission-kinetic data processed by parallel factor analysis and trilinear least-squares. Determination of methotrexate and leucovorin in human urine

Four-way fluorescence data recorded by following the kinetic evolution of excitation-emission fluorescence matrices (EEMs) have been analyzed by parallel factor analysis and trilinear least-squares algorithms. These methodologies exploit the second-order advantage of the studied data, allowing analyte concentrations to be estimated even in the presence of an uncalibrated fluorescent background. They were applied to the simultaneous determination of the components of the anticancer combination of methotrexate and leucovorin in human urine samples. Both analytes were converted into highly fluorescent compounds by oxidation with potassium permanganate, and the kinetics of the reaction was continuously monitored by recording full EEM of the samples at different reaction times. A commercial fast scanning spectrofluorometer has been used for the first time to measure the four-way EEM kinetic data. The rapid scanning instrument allows the acquisition of a complete EEM in 12 s at a wavelength scanning speed of 24 000 nm/min. The emission spectra were recorded from 335 to 490 nm at 5-nm intervals, exciting from 255 to 315 nm at 6-nm intervals. Ten successive EEMs were measured at 72-s intervals, to follow the fluorescence kinetic evolution of the mixture components. Good recoveries were obtained in synthetic binary samples and also in spiked urine samples. The excitation, emission, and kinetic time profiles recovered by both chemometric techniques are in good agreement with experimental observations.     

Interference-free analysis using three-way fluorescence data and the parallel factor model. Determination of fluoroquinolone antibiotics in human serum

Three-way fluorescence data and multivariate calibration based on parallel factor analysis (PARAFAC) are combined for the simultaneous quantitation of three fluoroquinolone anitibiotics (norfloxacin, enoxacin, and ofloxacin) in human serum samples. The three analytes can be adequately determined with limits of detection of 0.2, 3.0, and 0.5 microg L(-1), respectively, with minimum experimental effort. The selected analytical methodology fully exploits the so-called second-order advantage of the employed three-way data, allowing obtaining individual concentrations of calibrated analytes in the presence of any number of uncalibrated (serum) components. In contrast to PARAFAC, less satisfactory results were obtained with a multidimensional partial least-squares (nPLS) model trained with the same calibration set.     

Application of a combination of hard and soft modeling for equilibrium systems to the quantitative analysis of pH-modulated mixture samples

pH modulation of aqueous mixture samples combined with FT-IR detection and a powerful second-order resolution method is proposed for both resolution and quantitation of acid analytes in the presence of similarly behaving interferences. The proposed method allows for the analyte determination in mixtures using a single standard sample per analyte. Due to the very similar pKa values of the investigated analytes and interferences, the highly correlated concentration profiles of these compounds cannot be successfully resolved with pure soft-modeling second-order approaches. The inclusion of a hard-modeling constraint based on the acid-base equilibrium model in the soft-modeling curve resolution method has allowed for the unambiguous resolution of the analyte profiles and, as a consequence, for the correct quantitation of this compound in the mixture sample. A detailed discussion of the combined hard-soft-modeling approach as well as the analytical problem and the quantitation results is given. Also, strategies to overcome problems associated with variation in pKa values between different samples are addressed. Due to the flexible implementation of the hard-model equilibrium constraint in the multivariate curve resolution-alternating least squares method, this approach is expected to be useful also for analysis of other complex mixed equilibrium-based chemical systems.     

三维荧光二阶校正法用于水样中培氟沙星和 氧氟沙星的同时测定

提出三维荧光二阶校正法,用于环境水样中氟喹诺酮类抗生素培氟沙星和氧氟沙星的同时定量分析.即在激发波长为230～400 nm,发射波长为360～580 nm范围内,测定样品(包含校正样、验证样、测试样)的三维荧光光谱,构建三维荧光响应数据阵;经数据处理后,采用交替三线性分解算法进行分解,得到与物质相关的相对激发、相对发射和相对浓度谱信息;通过对浓度信息进行单变量校正,获得校正曲线,进一步预测真实浓度.结果表明,培氟沙星和氧氟沙星的平均回收率分别为(101.1±5.3)％,(99.7±4.7)％,检测限分别为2.14,4.34 ng/mL,定量限分别为6.49,13.16 ng/mL.三维荧光二阶校正法可以在未知干扰物共存下,同时定量分析环境水样中培氟沙星和氧氟沙星,实现二阶优势.     

Multiway calibration for creatinine determination in human serum using the Jaffé reaction

Second-order calibration and multivariate spectroscopic-kinetic measurements in the visible region are proposed to improve the Jaffé method for creatinine assay. Analyses performed on synthetic mixtures containing bilirubin, glucose, and albumin confirm that second-order calibration is useful for creatinine determination in human serum. Quantitative determinations of creatinine with the parallel factor analysis (PARAFAC) and direct trilinear decomposition (TLD) methods were compared. It is shown that both methods can be used for creatinine determination in human serum, with an SEP (standard error of prediction) of 2.22 and coefficient of variability of 6.14% for PARAFAC, and an SEP of 2.38 and coefficient of variability of 6.57% for TLD [corrected].     

Monitoring of welding aerosol compositions (a review)

Physicochemical properties inherent in the solid component of welding aerosols (SCWA) are characterized. The features of SCWA sampling are considered. Methods are indicated which are most commonly used for the analysis of SCWA in Russian and foreign analytical practice. Destructive and nondestructive methods of SCWA analysis are compared, and their advantages and disadvantages are noted. By particular examples, it is shown that because of the complexity of phase and chemical composition of SCWA samples, rather frequently, one observes a loss of monitored elements in the course of the decomposition of exposed filters. Techniques for making synthetic calibration samples are considered for both classes of methods. In the case of using the X-ray fluorescence method, it is difficult to prepare calibration samples adequate to real SCWA samples collected on a filter. The comparative variant of neutron activation analysis involves synthetic mixtures for the calculation of the content of analytes containing one or two components. Metrological characteristics are presented for SCWA analysis techniques.     

Pure component selectivity analysis of multivariate calibration models from near-infrared spectra

A novel procedure is proposed as a method to characterize the chemical basis of selectivity for multivariate calibration models. This procedure involves submitting pure component spectra of both the target analyte and suspected interferences to the calibration model in question. The resulting model output is analyzed and interpreted in terms of the relative contribution of each component to the predicted analyte concentration. The utility of this method is illustrated by an analysis of calibration models for glucose, sucrose, and maltose. Near-infrared spectra are collected over the 5000-4000-cm(-)(1) spectral range for a set of ternary mixtures of these sugars. Partial least-squares (PLS) calibration models are generated for each component, and these models provide selective responses for the targeted analytes with standard errors of prediction ranging from 0.2 to 0.7 mM over the concentration range of 0.5-50 mM. The concept of the proposed pure component selectivity analysis is illustrated with these models. Results indicate that the net analyte signal is solely responsible for the selectivity of each individual model. Despite strong spectral overlap for these simple carbohydrates, calibration models based on the PLS algorithm provide sufficient selectivity to distinguish these commonly used sugars. The proposed procedure demonstrates conclusively that no component of the sucrose or maltose spectrum contributes to the selective measurement of glucose. Analogous conclusions are possible for the sucrose and maltose calibration models.     

Procedure for the quantitative determination of mixtures of nucleic Acid components based on multivariate spectrophotometric Acid-base titrations

A new procedure for the quantitative determination of mixtures of nucleic acid components, based on continuous spectrophotometric acid-base titrations and multivariate curve resolution, is proposed. The procedure simultaneously takes into account the spectroscopic and acid-base properties of the compounds, which leads to a higher selectivity. Furthermore, quantitative determination of an analyte in a complex mixture is performed using a synthetic solution as standard containing only the analyte of interest. An intrinsic difficulty in the analysis of spectrometric titration data is the presence of rank deficiency due to closure for the mixtures of two or more compounds. An additional problem can be encountered in some mixtures if species spectra or species concentration profiles are practically identical (rank overlap). However, even in the presence of these rank difficulties, accurate quantitation with prediction errors lower than 5% was obtained. The presence of unknown and uncalibrated interferences in the samples does not affect the quantitative determination of the analyte of interest. The proposed procedure was successfully applied to the analysis of real samples (pharmaceuticals) using synthetic external standards.     

Chemometric study of excitation-emission matrix fluorescence data: quantitative analysis of petrol-kerosene mixtures

Products of petroleum crude are multifluorophoric in nature due to the presence of a mixture of a variety polycyclic aromatic hydrocarbons (PAHs). The use of excitation-emission matrix fluorescence (EEMF) spectroscopy for the analysis of such multifluorophoric samples is gaining progressive acceptance. In this work, EEMF spectroscopic data is processed using chemometric multivariate methods to develop a reliable calibration model for the quantitative determination of kerosene fraction present in petrol. The application of the N-way partial least squares regression (N-PLS) method was found to be very efficient for the estimation of kerosene fraction. A very good degree of accuracy of prediction, expressed in terms of root mean square error of prediction (RMSEP), was achieved at a kerosene fraction of 2.05%.