A New Parameter for Measuring the Prediction Uncertainty Produced by Rotational Ambiguity in Second-Order Calibration with Multivariate Curve Resolution.

Multivariate curve resolution-alternating least-squares (MCR-ALS) is the model of choice when dealing with matrix data that cannot be arranged into a trilinear three-way array, that is, mostly from chromatographic origin with spectral detection. A range of feasible solutions may be found in MCR studies, due to the phenomenon of rotational ambiguity associated with bilinear decompositions of matrices. The application of chemically driven constraints is vital to achieving an adequate solution and minimizing the degree of rotational ambiguity present in the system. However, when studying complex samples, it may not be possible to recover unique solutions, even under the application of proper constraints. In such cases, it is important to be able to assess the propagation of rotation uncertainty to the estimated analyte concentrations, which stems from the existence of a finite range of feasible solutions. In this work, we present a new analytical parameter to estimate the potential uncertainty in analyte prediction brought about by rotational ambiguity, in the form of an associated root-mean-square error, named RMSERA. The proposed parameter comes in the form of a range of values, whose limits are δRA/(12)1/2 and δRA/(3)1/2, with δRA being defined as the difference between the maximum and minimum values of the analyte concentration that would be predicted by the MCR model from its concentration profiles lying in the range of feasible solutions, and corresponding to maximum and minimum area, respectively. We support our proposal on extensive simulations for systems of varying composition, and demonstrate its application on experimental data aimed at the determination of four pollutants in environmental water samples.

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.

Quantifying the Prediction Error in Analytical Multivariate Curve Resolution Studies of Multicomponent Systems.

In multivariate curve resolution (MCR) analysis, a range of feasible solutions is often encountered, because of the rotational ambiguities associated with the bilinear decomposition of data matrices. For quantitative purposes, the analysis is usually applied to a carefully designed set of calibration and test samples having uncalibrated interferents. Under the usual minimal constraints (non-negativity, unimodality, species correspondence, etc.), concentration and spectral profiles of the analyte in the test samples are not univocally recovered, unlike those in the calibration samples, especially when profile overlapping with the interferents is significant and selective regions do not exist for the analyte. In this report, a quantitative measure of the prediction errors due to rotational ambiguities is discussed, based on the calculation of the differences between the maximum and minimum area under the analyte concentration profiles calculated by the MCR-BANDS procedure. This methodology can be applied in different analytical scenarios with any number of analytes and interferents. Both absolute and relative quantitative errors due to rotation ambiguities are estimated and discussed in both simulated and experimental examples derived from liquid chromatography with diode array detection. The proposed procedure can be generalized to most of the analytical situations where every instrumentally measured sample produces a data table or data matrix.

The effect of constraints on the analytical figures of merit achieved by extended multivariate curve resolution-alternating least-squares.

Multivariate curve resolution-alternating least-squares (MCR-ALS) is the model of choice when dealing with some non-trilinear arrays, specifically when the data are of chromatographic origin. To drive the iterative procedure to chemically interpretable solutions, the use of constraints becomes essential. In this work, both simulated and experimental data have been analyzed by MCR-ALS, applying chemically reasonable constraints, and investigating the relationship between selectivity, analytical sensitivity (γ) and root mean square error of prediction (RMSEP). As the selectivity in the instrumental modes decreases, the estimated values for γ did not fully represent the predictive model capabilities, judged from the obtained RMSEP values. Since the available sensitivity expressions have been developed by error propagation theory in unconstrained systems, there is a need of developing new expressions or analytical indicators. They should not only consider the specific profiles retrieved by MCR-ALS, but also the constraints under which the latter ones have been obtained.

Online Third-Order Liquid Chromatographic Data with Native and Photoinduced Fluorescence Detection for the Quantitation of Organic Pollutants in Environmental Water.

Third-order liquid chromatographic data were generated online for the simultaneous quantitation of six organic environmental pollutants. The employed strategy consists in reducing the linear flow rate at the column outlet. A postcolumn UV reactor and a fluorimetric detector allowed to properly record both photoinduced and native excitation-emission fluorescence matrices (EEPIFMs and EEFMs, respectively). The obtained third-order liquid chromatography data were chemometrically processed with the multivariate curve resolution-alternating least-squares model. The sensitivity of the overall analytical method was enhanced by a very simple solid-phase extraction with C18 membranes, to be able to successfully apply it to natural water samples tested as real matrices. Favorable detection limits for the investigated pollutants, ranging from 0.02 to 0.27 ng mL-1, were attained, with relative prediction errors between 2 and 7%. Since the studied samples contain uncalibrated interferents, the applied strategy achieves the second-order advantage. Implications regarding the potential achievement of the third-order advantage are discussed.

Advantages of Data Fusion: First Multivariate Curve Resolution Analysis of Fused Liquid Chromatographic Second-Order Data with Dual Diode Array-Fluorescent Detection.

For the first time, liquid chromatography-diode array detection (LC-DAD) and liquid-chromatography fluorescence detection (LC-FLD) second-order data, collected in a single chromatographic run, were fused and chemometrically processed for the quantitation of coeluting analytes. Two different experimental mixtures composed of fluorescent and nonfluorescent endocrine disruptors were analyzed. Adequate pretreatment of the matrices before their fusion was crucial to attain reliable results. Multivariate curve resolution-alternating least-squares (MCR-ALS) was applied to LC-DAD, LC-FLD, and fused LC-DAD-FLD data. Although different degrees of improvement are observed when comparing the fused matrix results in relation to those obtained using a single detector, clear benefits of data fusion are demonstrated through: (1) the obtained limits of detection in the ranges 2.1-24 ng mL-1 and 0.9-6.3 ng mL-1 for the two evaluated systems and (2) the low relative prediction errors, below 7% in all cases, indicating good recoveries and precision. The feasibility of fusing data and its advantages in the analysis of real samples was successfully assessed through the study of spiked tap, underground, and river water samples.

Development of an ionic-liquid-based dispersive liquid-liquid microextraction method for the determination of antichagasic drugs in human breast milk: Optimization by central composite design.

Chagas disease constitutes a major public health problem in Latin America. Human breast milk is a biological sample of great importance for the analysis of therapeutic drugs, as unwanted exposure through breast milk could result in pharmacological effects in the nursing infant. Thus, the goal of breast milk drug analysis is to inquire to which extent a neonate may be exposed to a drug during lactation. In this work, we developed an analytical technique to quantify benznidazole and nifurtimox (the two antichagasic drugs currently available for medical treatment) in human breast milk, with a simple sample pretreatment followed by an ionic-liquid-based dispersive liquid-liquid microextraction combined with high-performance liquid chromatography and UV detection. For this technique, the ionic liquid 1-octyl-3-methylimidazolium hexafluorophosphate has been used as the "extraction solvent." A central composite design was used to find the optimum values for the significant variables affecting the extraction process: volume of ionic liquid, volume of dispersant solvent, ionic strength, and pH. At the optimum working conditions, the average recoveries were 77.5 and 89.7%, the limits of detection were 0.06 and 0.09 µg/mL and the interday reproducibilities were 6.25 and 5.77% for benznidazole and nifurtimox, respectively. The proposed methodology can be considered sensitive, simple, robust, accurate, and green.

Partition coefficients of organic compounds between water and imidazolium-, pyridinium-, and phosphonium-based ionic liquids.

The partition coefficients, P IL/w, of several compounds, some of them of biological and pharmacological interest, between water and room-temperature ionic liquids based on the imidazolium, pyridinium, and phosphonium cations, namely 1-octyl-3-methylimidazolium hexafluorophosphate, N-octylpyridinium tetrafluorophosphate, trihexyl(tetradecyl)phosphonium chloride, trihexyl(tetradecyl)phosphonium bromide, trihexyl(tetradecyl)phosphonium bis(trifluoromethylsulfonyl)imide, and trihexyl(tetradecyl)phosphonium dicyanamide, were accurately measured. In this way, we extended our database of partition coefficients in room-temperature ionic liquids previously reported. We employed the solvation parameter model with different probe molecules (the training set) to elucidate the chemical interactions involved in the partition process and discussed the most relevant differences among the three types of ionic liquids. The multiparametric equations obtained with the aforementioned model were used to predict the partition coefficients for compounds (the test set) not present in the training set, most being of biological and pharmacological interest. An excellent agreement between calculated and experimental log P IL/w values was obtained. Thus, the obtained equations can be used to predict, a priori, the extraction efficiency for any compound using these ionic liquids as extraction solvents in liquid-liquid extractions.