Determination of pesticides and metabolites in wine by high performance liquid chromatography and second-order calibration methods

The models parallel factor analysis (PARAFAC) and the recently introduced bilinear least squares (BLLS) were applied to develop second-order calibration methods to high performance liquid chromatography with diode array detection (HPLC-DAD) data, where overlap of interferences with the compounds of interest was observed, making the determination and resolution of the analytes possible. In this work, the simultaneous determination of five pesticides and two metabolites in wine samples by HPLC-DAD was performed, using the second-order advantage. The results of two chromatographic methods were compared, involving either isocratic or gradient elution. An appropriate preprocessing method was necessary to correct the effects of time shifts, baseline variations and background. BLLS presented results that were of the same quality as PARAFAC in five cases, but in two other situations only PARAFAC enabled analyte quantitation. Relative errors of prediction lower than 10% for all compounds were obtained, indicating that the methodology employing HLPC-DAD and second-order calibration can handle complex analytical systems.     

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.     

Core consistency diagnostic in PARAFAC2

PARAFAC2 is applied in multiple research areas, for example, where data containing shifts are analysed, but it is a challenge to determine the appropriate number of components in the model. In this paper, it is hypothesized that the core consistency diagnostic, which is currently applied in, for example, PARAFAC1 can be used to determine model complexity in PARAFAC2. Theoretically, a PARAFAC1 model is fitted ‘inside’ the PARAFAC2 algorithm, and it should therefore be possible to apply the core consistency diagnostic from PARAFAC1 in PARAFAC2. To support this hypothesis, three different datasets, as well as simulated datasets, have been evaluated by means of PARAFAC2, and the core consistencies have been investigated. There is a general trend that if the core consistency is low, the model is overfitted as in PARAFAC1. Also, core consistency captures the true variation in the data, whereas small peaks are easily overlooked by visual inspection of noisy models. However, for determining the number of components in a PARAFAC2 model, we suggest usage of the core consistency in combination with other model parameters such as residuals, loadings, and split‐half analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Comparison of PARAFAC and PARALIND in modeling three‐way fluorescence data array with special linear dependences in three modes: a case study in 2‐naphthol

Owing to excited‐state proton transfer in 2‐naphthol solutions, the fluorescence excitation–emission matrices (EEMs) have factors that are highly dependent in three modes. For the first time such EEMs are used to compare the capability of PARALIND (PARAFAC with linear dependence) and conventional PARAFAC in modeling three‐way EEMs having linearly dependent factors in three modes. Two primary conclusions have been drawn. First, the results indicate that a 3‐factor PARAFAC model fit the data better than two PARALIND models (type 1 and 2) in this case while equally well with a specially PARALIND model (type 3); second, a negative core consistency (CC) in the 3‐factor PARAFAC model is reported but the type 3 PARALIND model reports a nearly 100 CC. This work has demonstrated that a properly constrained PARALIND can fit the very special EEMs of 2‐naphthol. The presence of negative CC associated with a perfect PARAFAC model would imply the presence of very special linear dependences in EEMs, which would be used as an “alarm” for the investigators to interpret the data more carefully when dealing with complicated environmental EEMs in the absence of a priori knowledge. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Matrix-free analysis of aflatoxins in pistachio nuts using parallel factor modeling of liquid chromatography diode-array detection data

In the present study a second-order calibration strategy for high performance liquid chromatography with diode-array detection (HPLC-DAD) has been developed using parallel factor analysis (PARAFAC) and has been applied for simultaneous determination of aflatoxins B₁, B₂, G₁ and G₂ in pistachio nuts in the presence of matrix interferences. Sample preparation was based on solvent extraction (SE) followed by solid phase extraction (SPE) on Bond Elut C18 cartridges. Since the sample preparation procedure was not selective to the analytes of interest, exploiting second-order advantage to obtain concentrations of individual analytes in the presence of uncalibrated interfering compounds seemed necessary. Appropriate pre-processing steps have been applied to correct background signals and the effect of retention time shifts. Transferred calibration data set obtained from standardization of solvent based calibration data has been used in prediction step. The results of PARAFAC on a set of spiked and naturally contaminated pistachio nuts indicated that the four aflatoxins could be successfully determined. The method was validated and multivariate analytical figures of merit were calculated. The advantages of the proposed method are using a low-cost SPE step relative to standard method of aflatoxin analysis (immune affinity column assay), a unique and simple isocratic elution program for all samples and a calibration transfer for saving both chemicals and time of analysis. This study show that coupling of SPE-HPLC-DAD with PARAFAC as a powerful second-order calibration method can be considered as an alternative method for resolution and quantification of aflatoxins in the presence of unknown interferences obtained through analysis of highly complex matrix of pistachio samples and cost per analysis can be reduced significantly.     

Enantioseparation of chiral aromatic acids by multiple dual mode counter‐current chromatography using hydroxypropyl‐β‐cyclodextrin as chiral selector

This work concentrates on extending the utilization of multiple dual mode (MDM) counter‐current chromatography in chiral separations. Two aromatic acids, 2‐(6‐methoxy‐2‐naphthyl)propionic acid (NAP) and 2‐phenylpropionic acid (2‐PPA), were enantioseparated by MDM counter‐current chromatography using hydroxypropyl‐β‐cyclodextrin (HP‐β‐CD) as chiral selector. The two‐phase solvent systems consisting of n‐hexane/ethyl acetate 0.1 mol/L phosphate buffer pH 2.67 containing 0.1 mol/L HP‐β‐CD (7.5:2.5:10 for NAP and 7:3:10 for 2‐PPA, v/v/v) were used. Conventional MDM and modified MDM were compared according to peak resolution under current separation mechanism. The influence of elution time after the first‐phase inversion and number of cycles for MDM were investigated. Peak resolution of NAP and 2‐PPA increased from 0.62 to 1.05 and 0.72 to 0.84, respectively, using optimized MDM conditions. Being an alternative elution method for counter‐current chromatography, MDM elution greatly improved peak resolution in chiral separations.     

Application of artificial neural networks for gradient elution retention modelling in ion chromatography

Gradient elution in ion chromatography (IC) offers several advantages: total analysis time can be significantly reduced, overall resolution of a mixture can be increased, peak shape can be improved (less tailing) and effective sensitivity can be increased (because there is little variation in peak shape). More importantly, it provides the maximum resolution per time unit. The aim of this work was the development of a suitable artificial neural network (ANN) gradient elution retention model that can be used in a variety of applications for method development and retention modelling of inorganic anions in IC. Multilayer perceptron ANNs were used to model the retention behaviour of fluoride, chloride, nitrite, sulphate, bromide, nitrate and phosphate in relation to the starting time of gradient elution and the slope of the linear gradient elution curve. The advantage of the developed model is the application of an optimized two-phase training algorithm that enables the researcher to make use of the advantages of first- and second-order training algorithms in one training procedure. This results in better predictive ability, with less time required for the calculations. The number of hidden layer neurons and experimental data points used for the training set were optimized in terms of obtaining a precise and accurate retention model with respect to minimization of unnecessary experimentation and time needed for the calculation procedures. This study shows that developed, ANNs are the method of first choice for retention modelling of inorganic anions in IC.     

Designing polymer matrix for microchip-based double-stranded DNA capillary electrophoresis

An optimization strategy for ternary solvent-strength gradient elution RP chromatography is described in which a two-dimensional model of gradient time (2 levels) against ternary proportions of organic modifiers (4 levels) was constructed. From the resolution surface the optimum ratio of organic modifiers could be selected. Excellent retention time and acceptable peak width and resolution simulations were obtained. The separation could be further optimized from the same input data by using a standard one-dimensional model in order to optimize for gradient slope, duration and shape. Excellent retention time and acceptable peak width and resolution simulations were obtained (< 1, 2 and 6% error, respectively).     

Determination of phenol in the presence of its principal degradation products in water during a TiO2-photocatalytic degradation process by three-dimensional excitation-emission matrix fluorescence and parallel factor analysis

This paper describes a simple and rapid way of monitoring a photocatalytic degradation of phenol in aqueous suspensions of TiO₂. A three-way analytical methodology based on fluorescence excitation-emission matrix (EEM) and parallel factor analysis (PARAFAC) was developed to resolve the species present in the reaction mixture and quantify the concentration of phenol and its principal degradation products throughout the degradation. Parameters such as core consistency, fit% and correlation coefficients between recovered and pure spectra were used to determine the appropriate number of factors for the PARAFAC model. The accuracy of the model was evaluated by the root mean square error of prediction (RMSEP). Using a four-factors PARAFAC model, phenol, hydroquinone, resorcinol and catechol, were satisfactorily determined. The proposed method is an interesting alternative to the traditional techniques normally used for monitoring degradation reactions.     

Approaching the direct exponential curve resolution algorithm from a maximum likelihood perspective

The implementation of maximum likelihood parallel factor analysis (MLPARAFAC) in conjunction with the direct exponential curve resolution algorithm (DECRA) is described. DECRA takes advantage of the intrinsic exponential structure of some bilinear data sets to produce trilinear data by a simple shifting scheme, but this manipulation generates an error structure that is not optimally handled by traditional three-way chemometrics methods such as TLD and PARAFAC. In this work, the effects of these violations are studied using simulated and experimental data used in conjunction with the well-established TLD and PARAFAC. The results obtained by both methods are compared with the results obtained by MLPARAFAC, which is a method designed to optimally accomodate a variety of measurement error structures. The impact on the estimates of different parameters linked to the data sets and the DECRA method is investigated using simulated data. The results indicate that PARAFAC produces estimates of much poorer quality than TLD and MLPARAFAC. Also, it was found that the quality TLD estimates was comparable or only marginally poorer than the MLPARAFAC estimates. A number of commonly used algorithms were also compared to MLPARAFAC using two sets of published experimental data from kinetic studies. The MLPARAFAC estimates of rate constants were more precise than the other methods examined.     

On uniqueness and selectivity in three-component parallel factor analysis

Unambiguous recovery of profiles is a distinguishable advantage of Parallel Factor Analysis (PARAFAC) as a trilinear model and has made it a promising exploratory tool for data analysis. Linear dependency in profiles destroys trilinearity and will increase ambiguity in the curve resolution of three-way data sets. PARAFAC uniqueness deteriorates totally or partially in data sets with linearly dependent loadings. Exploiting a reliable method for determination and direct visualization of feasible bands in the PARAFAC model can be helpful not only in full characterization of uniqueness conditions but also in the investigation of the effects of constraints on the PARAFAC feasible solutions. The purpose of this paper is twofold. First, the calculation of rotational ambiguity in the PARAFAC model extends to three components system. The principle behind the algorithm is described in detail and tested for simulated and real data sets. Completely general and thoroughly investigated results are presented for the three component cases. Secondly, the effects of selective regions in the profiles on the resolution of systems that suffered from the rank deficiency problem, due to rank overlap, are emphasized. In the case of two-way data sets the effect of selectivity constraint on the unique recovery of profiles was investigated and applied. However, to our knowledge, in this report, for the first time, the effect of the presence of selective windows in the profiles, on the unique resolution of three-way data sets has been systematically investigated.     

An alternative quadrilinear decomposition algorithm for four-way calibration with application to analysis of four-way fluorescence excitation–emission–pH data array

A novel quadrilinear decomposition algorithm for four-way calibration (third-order tensor calibration), which was called as regularized self-weighted alternating quadrilinear decomposition (RSWAQLD), has been developed in this work. It originates from the alternating trilinear decomposition (ATLD) algorithm, inherits the philosophy behind self-weighting operation from the self-weighted alternating trilinear decomposition (SWATLD) algorithm. The RSWAQLD algorithm is based on a nearby least-squares scheme, in which two extra terms are added to each loss function, making it more stable and flexible. Experiment shows that RSWAQLD has the features of fast convergence and being insensitive to the excess estimated factors in the model. Owing to its unique optimizing approach, RSWAQLD is much more efficient than four-way PARAFAC. Moreover, the performance of RSWAQLD is quit stable as the number of factors used in calculation varies (as long as it is no less than the true number of factors). Such a feature will simplify the analysis of four-way data arrays, since it is unnecessary to spend a lot of time and effort on accurately determining the appropriate number of factors in the matrix. In addition, the result of four-way fluorescence excitation–emission–pH data, as well as that of simulated data, illustrated that RSWAQLD can not only remain the “higher-order advantage” but also provide a satisfying result even in high collinear systems.     

Multivariate curve resolution based chromatographic peak alignment combined with parallel factor analysis to exploit second-order advantage in complex chromatographic measurements

In the present contribution, a new combination of multivariate curve resolution-correlation optimized warping (MCR-COW) with trilinear parallel factor analysis (PARAFAC) is developed to exploit second-order advantage in complex chromatographic measurements. In MCR-COW, the complexity of the chromatographic data is reduced by arranging the data in a column-wise augmented matrix, analyzing using MCR bilinear model and aligning the resolved elution profiles using COW in a component-wise manner. The aligned chromatographic data is then decomposed using trilinear model of PARAFAC in order to exploit pure chromatographic and spectroscopic information. The performance of this strategy is evaluated using simulated and real high-performance liquid chromatography-diode array detection (HPLC-DAD) datasets. The obtained results showed that the MCR-COW can efficiently correct elution time shifts of target compounds that are completely overlapped by coeluted interferences in complex chromatographic data. In addition, the PARAFAC analysis of aligned chromatographic data has the advantage of unique decomposition of overlapped chromatographic peaks to identify and quantify the target compounds in the presence of interferences. Finally, to confirm the reliability of the proposed strategy, the performance of the MCR-COW-PARAFAC is compared with the frequently used methods of PARAFAC, COW-PARAFAC, multivariate curve resolution-alternating least squares (MCR-ALS), and MCR-COW-MCR. In general, in most of the cases the MCR-COW-PARAFAC showed an improvement in terms of lack of fit (LOF), relative error (RE) and spectral correlation coefficients in comparison to the PARAFAC, COW-PARAFAC, MCR-ALS and MCR-COW-MCR results.     

Handling within run retention time shifts in two-dimensional chromatography data using shift correction and modeling

The use of PARAFAC for modeling GC × GC-TOFMS peaks is well documented. This success is due to the trilinear structure of these data under ideal, or sufficiently close to ideal, chromatographic conditions. However, using temperature programming to cope with the general elution problem, deviations from trilinearity within a run are more likely to be seen for the following three cases: (1) compounds (i.e., analytes) severely broadened on the first column hence defined by many modulation periods, (2) analytes with a very high retention factor on the second column and likely wrapped around in that dimension, or (3) with fast temperature program rates. This deviation from trilinearity is seen as retention time-shifted peak profiles in subsequent modulation periods (first column fractions). In this report, a relaxed yet powerful version of PARAFAC, known as PARAFAC2 has been applied to handle this shift within the model step by allowing generation of individual peak profiles in subsequent first column fractions. An alternative approach was also studied, utilizing a standard retention time shift correction to restore the data trilinearity structure followed by PARAFAC. These two approaches are compared when identifying and quantifying a known analyte over a large concentration series where a certain shift is simulated in the successive first column fractions. Finally, the methods are applied to real chromatographic data showing severely shifted peak profiles. The pros and cons of the presented approaches are discussed in relation to the model parameters, the signal-to-noise ratio and the degree of shift.     

An algorithm for three-way data analysis that alternatively minimizes coupled vector (COV) resolution error and PARAFAC error.

A novel algorithm, alternatively minimizing coupled vector (COV) resolution error and PARAFAC error algorithm, is proposed in this paper. This algorithm can overcome the problem of slow convergence and is insensitive to the estimation of component number, such problems are unavoidable while using the traditional parallel factors analysis (PARAFAC) algorithm. In other words, this algorithm is capable of improving the computing speed and providing accurate resolutions provided that the number of factors used in the computation is no less than that of the actual underlying ones. The characteristic performances were demonstrated with a novel fluorescence data array.     

Parallel factor analysis and trilinear partial least squares applied to the UPLC-PDA data array for the quantification of brimonidine tartrate and timolol maleate in an eye drop formulation

Simultaneous quantification of brimonidine tartrate (BRI) and timolol maleate (TIM) in an eye drop formulation was performed by applying parallel factor analysis (PARAFAC) and trilinear (three way) partial least squares to the ultra performance liquid chromatography-photodiode array (UPLC-PDA) data array. In PARAFAC and 3 W-PLS1 applications, the co-elution of the related compounds in their chromatograms obtained in the presence of ornidazole as an internal standard (IS) was resolved, and then analyses were performed. On the other hand, a new conventional ultra performance liquid chromatography (UPLC) method was developed after long and tedious studies to get desirable elution of BRI and TIM in a chromatogram using different column and mobile phase system than that of chromatographic conditions of PARAFAC and 3 W-PLS1 applications. The performance and validity of all the proposed methods were confirmed by analyzing independent validation samples consisting of synthetic mixture, intraday and interday samples, and standard addition samples. Analysis results of BRI and TIM in eye drop samples by chemometric PARAFAC and 3 W-PLS1, and conventional UPLC were statistically compared to each other. It was concluded that PARAFAC and 3 W-PLS1 have shortest analysis time and lower cost than the developed conventional UPLC method for the analysis of the related compounds in commercial eye drop preparation with adequate selectivity and sensitivity.     

Diagnosis of early stage nasopharyngeal carcinoma using ultraviolet autofluorescence excitation-emission matrix spectroscopy and parallel factor analysis

We report the diagnostic ability of ultraviolet (UV)-excited autofluorescence (AF) excitation-emission matrix (EEM) spectroscopy associated with parallel factor (PARAFAC) analysis for differentiating cancer from normal nasopharyngeal tissue. A bifurcated fiber-optic probe coupled with an EEM system was used to acquire tissue AF EEMs using excitation wavelengths between 260 and 400 nm, and emission collection between 280 and 500 nm. A total of 152 AF EEM landscapes were acquired from 13 normal and 16 nasopharyngeal carcinoma (NPC) thawed ex vivo tissue samples from 23 patients. PARAFAC was introduced for curve resolution of individual AF EEM landscapes associated with the endogenous tissue constituents. The significant factors were further fed to a support vector machine (SVM) and cross-validated to construct diagnostic algorithms. Both the EEM intensity landscapes and the PARAFAC model revealed tryptophan, collagen, and elastin to be the three major endogenous fluorophores responsible for the AF signal from normal and NPC tissues. The EEM intensity distribution and PARAFAC factors suggest an increase of tryptophan and a decrease of collagen and elastin in NPC tissues compared to the normal. The classification results obtained from the PARAFAC-SVM modeling yielded a diagnostic accuracy of 94.7% (sensitivity of 95.0% (76/80); specificity of 94.4% (68/72)) for normal and NPC tissue differentiation. This study suggests that UV-excited AF EEM spectroscopy integrated with PARAFAC algorithms has the potential to provide clinical diagnostics of early onset and progression of NPC.     

Usefulness of a PARAFAC decomposition in the fiber selection procedure to determine chlorophenols by means SPME-GC-MS

In this work, a procedure based on solid-phase microextraction and gas chromatography coupled with mass spectrometry is proposed to determine chlorophenols in water without derivatization. The following chlorophenols are studied: 2,4-dichlorophenol; 2,4,6-trichlorophenol; 2,3,4,6-tetrachlorophenol and pentachlorophenol. Three kinds of SPME fibers, polyacrylate, polydimethylsiloxane, and polydimethylsiloxane/divinylbenzene are compared to identify the most suitable one for the extraction process on the basis of two criteria: (a) to select the equilibrium time studying the kinetics of the extraction, and (b) to obtain the best values of the figures of merit. In both cases, a three-way PARAllel FACtor analysis decomposition is used. For the first step, the three-way experimental data are arranged as follows: if I extraction times are considered, the tensor of data, X, of dimensions I × J × K is generated by concatenating the I matrices formed by the abundances of the J m/z ions recorded in K elution times around the retention time for each chlorophenol. The second-order property of PARAFAC (or PARAFAC2) assesses the unequivocal identification of each chlorophenol, as consequence, the loadings in the first mode estimated by the PARAFAC decomposition are the kinetic profile. For the second step, a calibration based on a PARAFAC decomposition is used for each fiber. The best figures of merit were obtained with PDMS/DVB fiber. The values of decision limit, CCα, achieved are between 0.29 and 0.67 μg L⁻¹ for the four chlorophenols. The accuracy (trueness and precision) of the procedure was assessed. This procedure has been applied to river water samples.     

Hard–soft modeling parallel factor analysis to solve equilibrium processes

PARAFAC model is the most famous model for analyzing three‐way data. However, this method does not converge to chemically meaningful solutions when applied to three‐way problems involving rank overlap profiles at least in one mode. Rank overlap can be simply found where components have similar spectral profiles or analytes appearing in identical proportions throughout an experiment. However, an appropriate selection of the initial parameters and constraints such as non‐negativity and unimodality can still make PARAFAC model useful in this regard. Although such constraints reduce rotational freedom in PARAFAC solution, they are generally insufficient to wholly eliminate the rotational problem. The goal of the present paper is to incorporate hard modeling constraint in the soft‐modeled PARAFAC algorithm to overcome non‐uniqueness problem in the equilibrium processes involving linearly dependent factors at least in one mode. The hard constraint is introduced to force some or all of the concentration profiles to fulfill an equilibrium model that is refined at each iteration cycle of the optimization process of PARAFAC. The proposed approach is called hard–soft PARAFAC (HSPARAFAC). When the rank overlap species obeys equilibrium model in HSPARAFAC, the unique results are obtained even in the presence of non‐modeled interferences. The new modification in the treatment of equilibrium data sets yields more satisfactory results than the exclusive PARAFAC algorithm. Simulated and real examples with rank overlap problem are used to confirm this statement. Copyright © 2011 John Wiley & Sons, Ltd.