Theory of Analytical Chemistry

Use of pseudo-sample extraction and the projection technique to estimate the chemical rank of three-way data arrays

Determining the rank of a trilinear data array is a first step in subsequent trilinear component decomposition. Different from estimating the rank of bilinear data, it is more difficult to decide the significant number of component to fit the trilinear decompositions exactly. General methods of rank estimation utilize the information contained in the singular values but ignore information from eigenvectors. In this paper, a rank estimating method specifically for trilinear data arrays is proposed. It uses the idea of direct trilinear decomposition (DTLD) to compress the cube matrix into two pseudo sample matrices which are then decomposed by singular value decomposition. Two eigenvectors combined with the projection technique are used to estimate the rank of trilinear data arrays. Simulated trilinear data arrays with homoscedastic and heteroscedastic noise, different noise levels, high collinearity, and real three-way data arrays have been used to illustrate the feasibility of the proposed method. Compared with other factor-determining methods, for example use of the factor indication function (IND), residual percentage variance (RPV), and the two-mode subspace comparison approach (TMSC), the results showed that the new method can give more reliable answers under the different conditions applied.

Wet granulation in rotary processor and fluid bed: comparison of granule and tablet properties

The aim of the present study was to investigate and compare granule and tablet properties of granules prepared by wet granulation in a rotary processor or a conventional fluid bed. For this purpose the working range of selected process variables was determined and a factorial study with 3 factors (equipment type, filler type, and liquid addition rate) and 1 covariate (fluidizing air flow rate) was performed. Two grades of calcium carbonate with different size and shape characteristics were applied, and the liquid addition and fluidizing air flow rates were investigated in the widest possible range. Dry mixtures of microcrystalline cellulose, polyvinyl povidone, calcium carbonate, and riboflavin, in a 10:5:84:1 ratio, were granulated in both types of equipment. The granulation end point was determined manually in the fluid bed and by torque measurements in the rotary processor. The filler type had a more pronounced effect on granular properties in the fluid bed, but the rotary processor showed a higher dependency on the investigated process variables. The rotary processor gave rise to more dense granules with better flow properties, but the fluid bed granules had slightly better compressional properties. Furthermore, the distribution of a low-dose drug was found to be more homogeneous in the rotary processor granules and tablets. Generally, wet granulation in a rotary processor was found to be a good alternative to conventional fluid bed granulation, especially when cohesive powders with poor flow properties or formulations with low drug content are to be granulated by a fluidizing air technique.

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.

Determination of Daunomycin in Human Plasma and Urine by Using an Interference-free Analysis of Excitation-Emission Matrix Fluorescence Data with Second-Order Calibration

Daunorubicin (DNR) is a significant antineoplastic antibiotic, which is usually applied to a chemotherapy of acute lymphatic and myelogenous leukaemia. Unfortunately, cardiotoxicity research in animals has indicated that DNR is cardiotoxic. Therefore, it is important to quantify DNR in biological fluids. A new algorithm, the alternating fitting residue (AFR) method, and the traditional parallel factor analysis (PARAFAC) have been utilized to directly determine DNR in human plasma and urine. These methodologies fully exploit the second-order advantage of the employed three-way fluorescence data, allowing the analyte concentrations to be quantified even in the presence of unknown fluorescent interferents. Furthermore, in contrast to PARAFAC, more satisfactory results were gained with AFR.

Evaluation of partial least-squares with second-order advantage for the multi-way spectroscopic analysis of complex biological samples in the presence of analyte–background interactions

The combination of unfolded partial least-squares (U-PLS) with residual bilinearization (RBL) has not been properly exploited to process experimental second-order spectroscopic information, although it is able to achieve the important second-order advantage. Among other desirable properties, the technique can handle incomplete calibration information, i.e., when only certain analyte concentrations are known in the training set. It can also cope with analyte spectral changes from sample to sample, due to its latent variable structure. In this work, U-PLS/RBL has been successfully applied to experimental fluorescence excitation-emission matrix data aimed at the quantitation of analytes in complex samples: these were the antibiotic tetracycline and the anti-inflammatory salicylate, in both cases in the presence of human serum, where significant analyte-background interactions occur. The interactions of the analyte with the serum proteins modify their spectral fluorescence properties, making it necessary to employ training sets of samples where the biological background is present, possibly causing analyte spectral changes from sample to sample. The predictive ability of the studied model has been compared with that of parallel factor analysis (PARAFAC), as regards test samples containing different sera, and also other pharmaceuticals which could act as potential interferents.

Partial least-squares with residual bilinearization for the spectrofluorimetric determination of pesticides. A solution of the problems of inner-filter effects and matrix interferents

This paper demonstrates for the first time the power of a chemometric second-order algorithm for predicting, in a simple way and using spectrofluorimetric data, the concentration of analytes in the presence of both the inner-filter effect and unsuspected species. The simultaneous determination of the systemic fungicides carbendazim and thiabendazole was achieved and employed for the discussion of the scopes of the applied second-order chemometric tools: parallel factor analysis (PARAFAC) and partial least-squares with residual bilinearization (PLS/RBL). The chemometric study was performed using fluorescence excitation-emission matrices obtained after the extraction of the analytes over a C18-membrane surface. The ability of PLS/RBL to recognize and overcome the significant changes produced by thiabendazole in both the excitation and emission spectra of carbendazim is demonstrated. The high performance of the selected PLS/RBL method was established with the determination of both pesticides in artificial and real samples.

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.

Framework for multivariate selectivity analysis, part I: theoretical and practical merits

A number of definitions of multivariate selectivity have been proposed in the literature. Arguably, the one that enjoys the greatest chemometric attention has been the net analyte signal (NAS) based definitions of Lorber and Zinn. Recent works have suggested that similar inference can be made for inverse least-squares calibration methods (e.g., principal components regression). However, the properties of inverse calibration methods are markedly different than classical methods, so in many practical cases involving inverse models classically derived figures of merit cannot be transparently interpreted. In Part I of this work, we discuss a selectivity framework that is theoretically consistent regardless of the calibration method. Importantly, it is also experimentally measurable, either through controlled selectivity experiments, or through analysis on opportunistically acquired sample measurements. It is statistically advantageous to use the former if such control is achievable. Selectivity is defined to be a function of the change in predicted analyte concentration that will result from a change in the concentration of an interferant, an approach consistent with traditional definitions of analytical selectivity and National Committee for Clinical Laboratory Standards recommendations for interference testing. Unlike the NAS-based definition of selectivity, the definition discussed herein is relevant to only a particular analyte-interferant pair. The theoretical and experimental aspects of this approach are illustrated with simulated data herein and in Part II of this paper, which investigates several experimental near-infrared data sets.

Resolution of overlapping capillary electrophoresis peaks by using chemometric analysis: Quantification of the components in compound reserpine tablets

The application of multivariate curve resolution with alternating least squares (MCR-ALS) methods to second-order data from capillary electrophoresis with diode array detector (CE-DAD) is reported. Initial qualitative solutions obtained by evolving factor analysis (EFA) and pure-variable detection method can be further optimized by a simultaneous analysis of multiple electrophoresis run data with ALS regression. While unknown samples are analyzed simultaneously against the corresponding standards in different composition ratios, the exact amounts of common components in different CE runs can be determined by the traditional calibration curve method, and quantification can thus be achieved. The above methods are applied to the determination of the components in compound reserpine tablets in overlapping peaks from CE. The quantification results are compared with those of the first derivative of the electropherogram method and artificial neural network (ANN) method.

Evaluation of complex spectral-pH three-way arrays by modified bilinear least-squares: determination of four different dyes in interfering systems

This article reports on the first application of a modified version of the bilinear least-squares model to absorbance-pH second-order data recorded for complex samples. The latter are composed of fruit drink powders, where four different analytes and additional background components occur. The analytes are the common juice colorants tartrazine, yellow sunset, allura red and indigo carmine. The data have been measured after generating a double pH gradient within a flow injection system. The selected chemometric methodology adequately exploits the second-order advantage, needed to take into account the background interferents present in real samples. Due to severe spectral overlapping between the acid and basic forms of each of the colorants in the working pH range, other second-order multivariate calibration methods such as parallel factor analysis and multivariate curve resolution-alternating least-squares could not be successfully applied to the presently studied samples. Recoveries of 94.8, 104.7, 109.3 and 105.3% were obtained for yellow sunset, indigo carmine, allura red and tartrazine respectively in the real test samples.

Analysis of volatile components from Cortex cinnamomi with hyphenated chromatography and chemometric resolution

In this paper, the combination of hyphenated chromatography and chemometric resolution was investigated as a method to qualitatively and quantitatively determine volatile components in Cortex cinnamomi from four main producing areas. With the help of chemometric resolution approaches, whether the chromatographic elution of chemical components is featured by "first-in-first-out" or embedded peaks could be determined. Upon this useful information obtained, the matrix data generated by hyphenated chromatography could be uniquely resolved into pure chromatogram and spectrum of each chemical component involved followed by qualitative and quantitative analysis. The results obtained in this work showed that, 94, 88, 93 and 89 volatile components were separated and 63, 60, 60 and 58 of them qualitatively and quantitatively determined representing about 93.39, 93.62, 92.03 and 92.59% of the total relative content, respectively. The combination of hyphenated chromatography with chemometric resolution could greatly enhance the chromatographic separation and spectral qualitatively determination ability so as to qualitatively and quantitatively detect many more volatile components and improve the analysis accuracy.

Quantification of naphthalenes in jet fuel with GC x GC/Tri-PLS and windowed rank minimization retention time alignment

Comprehensive, two-dimensional gas chromatography (GC x GC) is used in conjunction with trilinear partial least squares (Tri-PLS) to quantify the percent weight of naphthalenes (two-ring aromatic compounds) in jet fuel samples. The increased peak capacity and selectivity of GC x GC makes the technique attractive for the rapid, and possibly less tedious analysis of jet fuel. The analysis of complex mixtures by GC x GC is further enhanced through the use of chemometric techniques, including those designed for use on 2-D data such as Tri-PLS. Unfortunately, retention time variation, unless corrected, can be an impediment to chemometric analysis. Previous work has demonstrated that the effects of retention time variation can be mitigated in sub-regions of GC x GC chromatograms through the application of an objective retention time alignment algorithm based on rank minimization. Building upon this previous work, it is demonstrated here that the effects of retention time variation can be mitigated throughout an entire GC x GC chromatogram with an objective retention time alignment algorithm based on windowed rank minimization alignment. A significant decrease in calibration error is observed when the algorithm is applied to chromatograms prior to construction of Tri-PLS models. Fourteen jet fuel samples with known weight percentages of naphthalenes (ASTM D1840) were obtained. Each sample was subjected to five replicate five-minute GC x GC separations over a period of two days. A subset of nine samples spanning the range of weight percentages of naphthalenes was chosen as a calibration set and Tri-PLS calibration models were subsequently developed in order to predict the naphthalene content of the samples from the GC x GC chromatograms of the remaining five samples. Calibration models constructed from GC x GC chromatograms that were retention time corrected are shown to exhibit a root mean square error of prediction of roughly half that of calibration models constructed from uncorrected chromatograms. The error of prediction is lowered further to a value that nearly matches the uncertainty in the standard percent weight values (ca. 1% of the median percent volume value) when the aligned chromatograms are truncated to include only regions of the chromatogram populated by naphthalenes and compounds of similar polarity and boiling point.

Application of multi-way models to the time-resolved fluorescence of polycyclic aromatic hydrocarbons mixtures in water

The time-resolved laser-induced fluorescence of a series of polycyclic aromatic compounds (PAHs) and mixtures of these latter in aqueous solution was measured by means of an apparatus equipped with optical fibers, which allows their real time in situ monitoring. The potential of such spectroscopic technique, yielding 4-way fluorescence data arrays, together with the application of multi-way models to the matricized data, was tested for the resolution of complex aqueous mixtures containing low concentrations of PAHs, as typical fluorescent pollutants in aquatic systems. PARAllel FACtors analysis was employed for the qualitative resolution of PAHs mixtures and for calculating the fluorescence lifetimes of single PAHs; n-way partial least squares analysis was applied for evaluating the concentration of the single PAHs in the aqueous mixtures.

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.

Simultaneous Spectrophotometric Determination of p-Benzoquinone and Chloranil after Microcrystalline Naphthalene Extraction by Using Genetic Algorithm-Based Wavelength Selection-Partial Least Squares Regression

Microcrystalline naphthalene extraction has been used for the preconcentration of p-benzoquinone and tetrachloro-p-benzoquinone (chloranil), after their reaction by aniline, and later simultaneous spectrophotometric analysis by genetic algorithm-partial least squares (GA-PLS) calibration. The chemical variables affecting the analytical performance of the methodology were studied and optimized. Under the optimum conditions i.e., [aniline] = 0.05 M and [naphthalene] = 2.2% (w/v), preconcentration of 25 ml of sample solution permitted the detection of 0.32 and 0.23 microg ml(-1) for p-benzoquinone and chloranil, respectively. The predictive abilities of partial least squares regression (PLS) and genetic algorithm-partial least squares regression (GA-PLS) were examined for simultaneous determination of two quinones. The GA-PLS shows superiority over other PLS methods due to the wavelength selection in PLS calibration using a genetic algorithm without loss of prediction capacity, provides useful information about the chemical system.

An improved trilinear decomposition algorithm based on a Lagrange operator

An improved trilinear decomposition algorithm based on a Lagrange operator (LO) is developed in this paper, which introduces a Lagrange operator and penalty terms in the loss function to improve the performance of the algorithm. Compared to the traditional parallel factor (PARAFAC) algorithm, the algorithm not only may converge much faster, but also overcome the sensibility to estimate the number of components. A set of simulated and measured excitation/emission fluorescence data were treated by both the proposed and traditional PARAFAC algorithm to compare their efficiencies. The analytical results obtained with real chemical system containing aspirin and its metabolic products show that the trilinear decomposition methodology is a promising tool to obtain spectral and composition information from mixtures without chemical separation.

Spectrophotometric determination of sorbic and benzoic acids in fruit juices by a net analyte signal-based method with selection of the wavelength range to avoid non-modelled interferences

Sorbic (SOR) and benzoic (BEN) acids were determined in fruit juice samples by using a net analyte signal-based methodology named HLA/GO (an hybrid linear analysis presented by Goicoechea and Olivieri) applied to spectroscopic signals. The calibration set was built with several fruit juices in order to take into account the natural variability and concentrations of both analytes covering the range usually present in commercial samples. Relative errors of prediction (REP %) of 3.6 and 5.2% were calculated for SOR and BEN respectively. Several figures of merit were calculated-sensitivity, selectivity, analytical sensitivity, and limit of detection. The method is quantitative, with reasonably good recoveries and excellent precision (less than 1%). Wavelength selection was applied, based on the concept of net analyte signal regression, and it allowed us to improve the method performance in samples containing non-modelled interferences, e.g. fruit juices different to those used to build the calibration model.

Application of GRAM and TLD to the resolution and quantitation of real complex multicomponent mixtures by fluorescence spectroscopy

The application of the generalised rank annihilation method (GRAM) and the trilinear decomposition (TLD) method to the resolution and quantitation of fluorescence excitation-emission matrices of a ternary mixture of pesticides, carbendazim, fuberidazole, and thiabendazole, with overlapped spectra is described. The results obtained with both methods are compared and evaluated using measures of similarity (correlation coefficients) between the real and estimated spectra. Both approaches have been tested using augmented data matrices containing only two samples, but none of these methods succeeded completely in resolution of the system. When TLD was applied to augmented data matrices containing more than two samples better performance was achieved. To illustrate the application of both algorithms to real samples, they were used in the analysis of water samples containing the target pesticides. Again, TLD had an advantage over GRAM because the ability to analyse data from multiple (more than two) samples simultaneously allowed the resolution of the mixtures.

Using second-order calibration to identify and quantify aromatic sulfonates in water by high-performance liquid chromatography in the presence of coeluting interferences

We used the Generalized Rank Annihilation Method (GRAM), a second-order calibration method, to quantify aromatic sulfonates in water with high-performance liquid chromatography (HPLC) when interferences coeluted with the analytes of interest. With GRAM, we can quantify in only two chromatographic analyses, one for a calibration sample and one for the unknown sample. The calculated concentrations were not statistically different to those obtained when the chromatographic separation of the unknown sample was modified in order to completely separate the analyte from the interferences before univariate calibration. With GRAM, the concentrations are determined much more quickly because a complete resolution is not required.

Micellar electrokinetic chromatography with on-line Fourier transform infrared detection

Micellar electrokinetic chromatography (MEKC) was successfully coupled to Fourier transform infrared (FTIR) detection, using a micromachined IR-transparent flow cell with an optical path length of 15 micro m for the on-line detection of five neutral analytes. Tight connections between the flow cell and the capillaries were achieved by creating a small O-ring of UV-curing epoxy adhesive on the sharply cut capillary ends. The background electrolyte consisted of 15 mM phosphate buffer at pH 7 and 40 mM sodium dodecyl sulfate (SDS). Five analytes (paracetamol, caffeine, p-nitro benzyl alcohol, m-nitrophenol and p-nitrophenol) were successfully separated, yielding detailed IR stack plots that could be used for quantification and identification. Linear calibration graphs were obtained for each individual analyte present in mixtures at concentrations up to 10 mM. The limit of detection (3 S/N) ranged between 1.1 and 1.5 mM (1.2-1.8 ng). Analytes were identified by comparing spectra obtained during the MEKC separation with those resulting from completely filling the capillary with each individual analyte dissolved in the micelle-containing electrolyte. Information on the specific functional groups of all analytes could be elucidated from the spectra. Since FTIR is a nondestructive detection technique, a conventional on-line UV detector was introduced directly after the developed IR flow cell to test the system's performance and to demonstrate that tandem FTIR and UV detection is feasible.