Binding the gap between experiments, statistics, and method comparison: A tutorial for computing limits of detection and quantification in univariate calibration for complex samples.

The present tutorial aims to review the most frequently reported criteria for the calculation of the limits of detection (LOD) and quantification (LOQ) in univariate calibration, summarizing their fundamentals, advantages, and limitations. The current criteria for estimating LOD and LOQ are based on diverse theoretical and/or empirical assumptions and require different amounts of experimental data, making the calculation rather complex in some cases. Moreover, alternative forms for calculating LOD/LOQ frequently lead to dissimilar results. This scenario might worsen in the case of complex analytical systems. Throughout this tutorial, different forms of calculating LOD/LOQ are illustrated using previously reported experimental datasets in the environmental chemistry field as examples. The influence of the sample matrix during the estimation of LOD/LOQ parameters is investigated through one calibration approache. The discrepancies in the obtained results with different criteria for the calculation of LOD/LOQ are highlighted. Finally, general guidelines and recommendations regarding experimental and data processing issues are proposed, aiming to promote fair criteria for the comparison of different analytical methodologies in terms of prediction ability and detection capability.

Modeling four and three-way fast high-performance liquid chromatography with fluorescence detection data for quantitation of fluoroquinolones in water samples.

This paper presents a study regarding the acquisition and analytical utilization of four and three-way data, acquired by following the excitation-emission fluorescence matrices at different elution times, in a fast liquid chromatographic HPLC procedure. This kind of data were implemented for first time for quantitative purposes, and applied to the determination of two fluoroquinolones in tap water samples, as a model to show the potentiality of the proposed strategy of four-way data generation. The data were modeled with three well-known algorithms: PARAFAC, U-PLS/RTL and MCR-ALS, the latter conveniently adapted to model third-order data. The second-order advantage was exploited when analyzing samples containing uncalibrated interferences. PARAFAC and MCR-ALS were the algorithms that better exploited the second-order advantage when no peak time shifts occurred among samples. On the other hand, when the quadrilinearity was lost due to the occurrence of temporal shifts, MCR-ALS furnished the better results. Relative error of prediction (REP%) obtained were 9.9% for ofloxacin and 14.0% for ciprofloxacin. In addition, a significant enhancement in the analytical figures of merit was observed when going from second- to third-order data (reduction of ca. 70% in LODs).

Second- and higher-order data generation and calibration: a tutorial.

An introduction to multi-way calibration based on second- and higher-order data generation and processing is provided, with emphasis on practical experimental aspects. After a discussion concerning a proper nomenclature scheme, a suitable classification of the obtainable data, and the general features of the available algorithms and their underlying models, a series of examples is discussed in detail, with the purpose of illustrating the great potentiality of the field for the analytical community. Emphasis is directed toward the most popular multi-way data, i.e., second-order or matrix data, which can be conveniently measured in a variety of instruments. Third-order data are being increasingly studied and are also discussed, along with the less explored field of fourth-order data. The estimation of figures of merit, which analysts need to report during method development, is now sufficiently mature to be provided for the general audience.

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 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.