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.     

An absorbance-based micro-fluidic sensor for diffusion coefficient and molar mass determinations

The H-Sensor reported herein is a micro-fluidic device compatible with flow injection analysis (FIA) and high performance liquid chromatography (HPLC). The device detects analytes at two separate off-chip absorbance flow cells, providing two simultaneous absorbance measurements. The ratio of these two absorbance signals contains analyte diffusion coefficient information. A theoretical model for the sensing mechanism is presented. The model relates the signal Ratio to analyte diffusion coefficient. The model is qualitatively evaluated by comparing theoretical and experimental signal Ratio values. Experimental signal Ratios were collected via FIA for a variety of analytes, including sodium azide, benzoic acid, amino acids, peptides, and proteins. Measuring absorbance at multiple wavelengths provides higher order data allowing the analyte signals from mixtures to be deconvolved via classical least squares (CLS). As a result of the H-Sensor providing two simultaneous signals as a function of time for each sample injection, two simulated second-order HPLC chromatograms were generated using experimental H-Sensor data. The chemometric deconvolution method referred to as the generalized rank annihilation method (GRAM) was used to demonstrate chromatographic and spectroscopic deconvolution. GRAM also provides the signal Ratio value, therefore simultaneously obtaining the analyte diffusion coefficient information during deconvolution. The two chromatograms successfully serve as the standard and unknown for the GRAM deconvolution. GRAM was evaluated on chromatograms at various chromatographic resolutions. GRAM was found to function to a chromatographic resolution at and above 0.25 with a percent quantitative error of less then 10%.     

Outlier detection for the Generalized Rank Annihilation Method in HPLC-DAD analysis

The Generalized Rank Annihilation Method (GRAM) is a second-order calibration method that is used in chromatography to quantify analytes that coelute with interferences. For a correct quantification, the peak of the analyte in the standard and in the test sample must be aligned and have the same shape (i.e., have a trilinear structure). Variations in retention time and shape between the two peaks may cause the test sample to behave as an outlier and produce an incorrect prediction. This situation cannot be detected by checking the coincidence of the recovered spectrum with the known spectrum of the analyte because the spectral domain is not affected. It cannot be detected either by checking if the recovered profile is correct (i.e., unimodal and positive). Several plots are presented to detect such outliers. The first plot compares the particular elution profiles in the standard and in the test sample that are recovered by least-squares regression from the spectra estimated by GRAM. The calculated elution profiles from both peaks should coincide. A second plot uses the elution profiles and spectra calculated by GRAM to define the vector space spanned by the interferences. The measured peaks in the standard and in the test sample are projected onto the space that is orthogonal to the space spanned by the interferences. These projections are proportional (up to the noise) if data are trilinear. The proportionality is checked graphically from the first singular vector of the projected peaks, or from the plot of the orthogonal signal versus the net sensitivity. The use of these graphs is shown for simulated data and for the determination of 4-nitrophenol in river water samples with liquid chromatography/UV-Vis detection.     

Modulation-induced error in comprehensive two-dimensional gas chromatographic separations

There is a fundamental difference between data collected in comprehensive two-dimensional gas chromatographic (GCxGC) separations and data collected by one-dimensional GC techniques (or heart-cut GC techniques). This difference can be ascribed to the fact that GCxGC generates multiple sub-peaks for each analyte, as opposed to other GC techniques that generate only a single chromatographic peak for each analyte. In order to calculate the total signal for the analyte, the most commonly used approach is to consider the cumulative area that results from the integration of each sub-peak. Alternately, the data may be considered using higher order techniques such as the generalized rank annihilation method (GRAM). Regardless of the approach, the potential errors are expected to be greater for trace analytes where the sub-peaks are close to the limit of detection (LOD). This error is also expected to be compounded with phase-induced error, a phenomenon foreign to the measurement of single peaks. Here these sources of error are investigated for the first time using both the traditional integration-based approach and GRAM analysis. The use of simulated data permits the sources of error to be controlled and independently evaluated in a manner not possible with real data. The results of this study show that the error introduced by the modulation process is at worst 1% for analyte signals with a base peak height of 10xLOD and either approach to quantitation is used. Errors due to phase shifting are shown to be of greater concern, especially for trace analytes with only one or two visible sub-peaks. In this case, the error could be as great as 6.4% for symmetrical peaks when a conventional integration approach is used. This is contrasted by GRAM which provides a much more precise result, at worst 1.8% and 0.6% when the modulation ratio (MR) is 1.5 or 3.0, respectively for symmetrical peaks. The data show that for analyses demanding high precision, a MR of 3 should be targeted as a minimum, especially if multivariate techniques are to be used so as to maintain data density in the primary dimension. For rapid screening techniques where precision is not as critical lower MR values can be tolerated. When integration is used, if there are 4-5 visible sub-peaks included for a symmetrical peak at MR=3.0, the data will be reasonably free from phase-shift-induced errors or a negative bias. At MR=1.5, at least 3 sub-peaks must be included for a symmetrical peak. The proposed guidelines should be equally relevant to LCxLC and other similar techniques.     

Quantification from highly drifted and overlapped chromatographic peaks using second-order calibration methods

For determining low levels of pesticides and phenolic compounds in river and wastewater samples by high performance liquid chromatography (HPLC), solid phase extraction (SPE) is commonly used before the chromatographic separation. This preconcentration step is not necessarily selective for the analytes of interest and it may retain other compounds of similar characteristics as well. In this case, we present, humic and fulvic acids caused a large baseline drift and overlapped the analytes to be quantified. The inaccurate determinations of the area of the peaks of these analytes made it difficult to quantify them with univariate calibration. Here we compare three second-order calibration algorithms (generalized rank annihilation method (GRAM), parallel factor analysis (PARAFAC) and multivariate curve resolution-alternating least squares (MCR-ALS)) which efficiently solve this problem. These methods use second-order data, i.e., a matrix of responses for each peak, which is easily obtained with a high performance liquid chromatography-diode array detector (HPLC-DAD). With these methods, the area does not need to be directly measured and predictions are more accurate. They also save time and resources because they can quantify analytes even if the peaks are not resolved. GRAM and PARAFAC require trilinear data. Biased and imprecise concentrations (relative standard deviation, %R.S.D. = 34) were obtained without correcting the time-shift. Hence, a time-shift correction algorithm to align the peaks was needed to obtain accurate predictions. MCR-ALS was the most robust to the time-shift. All three algorithms provided similar mean predictions, which were comparable to those obtained when sulfite was added to the samples. However, the predictions for the different replicates were more similar for the second-order algorithms (%R.S.D. = 3) than the ones obtained by univariate calibration after the sulfite addition (%R.S.D. = 13).     

Enhancing the Limit of Detection for Comprehensive Two‐Dimensional Gas Chromatography (GC×GC) using Bilinear Chemometric Analysis

The chemometric method referred to as the generalized rank annihilation method (GRAM) is used to improve the precision, accuracy, and resolution of comprehensive two‐dimensional gas chromatography (GC×GC) data. Because GC×GC signals follow a bilinear structure, GC×GC signals can be readily extracted from noise by chemometric techniques such as GRAM. This resulting improvement in signal‐to‐noise ratio (S/N) and detectability is referred to as bilinear signal enhancement. Here, GRAM uses bilinear signal enhancement on both resolved and unresolved GC×GC peaks that initially have a low S/N in the original GC×GC data. In this work, the chemometric method of GRAM is compared to two traditional peak integration methods for quantifying GC×GC analyte signals. One integration method uses a threshold to determine the signal of a peak of interest. With this integration method only those data points above the limit of detection and within a selected area are integrated to produce the total analyte signal for calibration and quantification. The other integration method evaluated did not employ a threshold, and simply summed all the data points in a selected region to obtain a total analyte signal. Substantial improvements in quantification precision, accuracy, and limit of detection are obtained by using GRAM, as compared to when either peak integration method is applied. In addition, the GRAM results are found to be more accurate than results obtained by peak integration, because GRAM more effectively corrects for the slight baseline offset remaining after the background subtraction of data. In the case of a 2.7‐ppm propylbenzene synthetic sample the quantification result with GRAM is 2.6 times more precise and 4.2 times more accurate than the integration method without a threshold, and 18 times more accurate than the integration method with a threshold. The limit of detection for propylbenzene was 0.6 ppm (parts per million by mass) using GRAM, without implementing any sample preconcentration prior to injection. GRAM is also demonstrated as a means to resolve overlapped signals, while enhancing the S/N. Four alkyl benzene signals of low S/N which were not resolved by GC×GC are mathematically resolved and quantified.     

Simultaneous spectrofluorometric determination of piroxicam and pyridoxine using generalized rank annihilation method.

The application of generalized rank annihilation method (GRAM) to the analysis of fluorescence excitation-emission matrices of mixtures of piroxicam and pyridoxine is described. The input of GRAM consists of two bilinear data matrices, i.e. one for unknown and one for the calibration sample. The excitation wavelength range was from 290 to 340 nm and the emission was recorded from 370 to 560 nm. Piroxicam and pyridoxine were determined in the concentration ranges 0.33 - 4.00 microg ml(-1) and 0.66 - 8.00 microg ml(-1), respectively. To check the accuracy of the proposed method, several binary synthetic mixtures and one real sample were analyzed successfully. No matrix effect was observed in mixture analysis, so a single external calibration sample was used for each analyte. The ability of GRAM to quantify the studied compounds and the comparability of GRAM results were evaluated by comparing them with those of PLS regression as a standard first-order calibration.     

Evaluation of analyte protectants to improve gas chromatographic analysis of pesticides

A common problem in gas chromatography (GC) applications is the analyte losses and/or peak tailing due to undesired interactions with active sites in the inlet and column. Analytes that give poor peak shapes or degrade have higher detection limits, are more difficult to identify and integrate, and are more prone to interferences than stable analytes that give narrow peaks. For susceptible analytes, significant peak quality improvements are obtained when matrix components are present because they fill active sites, thus reducing analyte interactions. This phenomenon is called "matrix-induced chromatographic response enhancement." Several approaches have been proposed to minimize peak distortion phenomena and compensate for matrix-induced effects, which is especially important for accurate quantitation, but each approach has serious limitations for routine multi-pesticide analysis. In this study, we demonstrate the feasibility of using "analyte protectants" to provide a more convenient and effective solution to the problem than other approaches developed thus far. The protecting agents are added to extracts and matrix-free standards alike to provide the chromatographic enhancement effect even for the most susceptible analytes in a very dirty GC system. In this study, we evaluated 93 different compounds to find the most suitable ones for improving chromatographic quality of the signal. Because hydrogen bonding has been shown to be an important factor in analyte interactions with active sites, we mainly focused on additives with strong hydrogen bonding capabilities. Dramatic peak enhancements were achieved using compounds containing multiple hydroxy groups, such as sugars and sugar derivatives, and gulonolactone appears to be the most effective protecting agent for the most pesticides that we tested. The benefits of using analyte protectants versus alternative procedures for overcoming matrix-induced effects in quantitation include: (a) simpler procedure; (b) easier integration of peaks; (c) lower detection limits; (d) better quantitation; (e) less maintenance of the GC inlet; and (e) lower cost. However, long-term influences on the performance of the chromatographic system have yet to be established.     

Using calibration approaches to compensate for remaining matrix effects in quantitative liquid chromatography/electrospray ionization multistage mass spectrometric analysis of phytoestrogens in aqueous environmental samples

Signal suppression is a common problem in quantitative liquid chromatography/electrospray ionization multistage mass spectrometric (LC/ESI-MS(n)) analysis in environment samples, especially in highly loaded wastewater samples with highly complex matrix. Optimization of sample preparation and improvement of chromatographic separation are prerequisite to improve reproducibility and selectivity. Matrix components are reduced if not eliminated by optimization of sample preparation steps. However, extensive sample preparation may be time-consuming and risk the significant loss of some trace analytes. The best way to further compensate matrix effects is the use of an internal standard for each analyte. However, in a multi-component analysis, finding appropriate internal standards for every analyte is often difficult. In this present study, a more practical alternative option was sought. Matrix effects were assessed using the post-extraction addition method. By comparison of three different calibration approaches, it was found that matrix-matched calibration combined with one internal standard provides a satisfactory method for compensating for any residual matrix effects on all the analytes. Validating experiments on different sewage treatment plant (STP) influent samples analyzing for a range of phytoestrogens showed that this calibration method provided satisfactory results with concentration ratio 96.1-105.7% compared to those by standard addition.     

简化柱切换技术在高浓度基体存在下测定痕量离子的研究

 建立了适用于高浓度基体存在下测定痕量离子的简化柱切换技术。通过分析淋洗液浓度对待测离子色谱峰保留时间的影响 ,指出可使用高浓度淋洗液抑制色谱峰漂移 ,并通过实验案例提出了针对不同样品采取的不同策略。     

Evaluation of the interrelationship between mass resolving power and mass error tolerances for targeted bioanalysis using liquid chromatography coupled to high‐resolution mass spectrometry

The determination of acceptable mass error tolerances for high‐resolution mass spectrometry based signals has been evaluated in a comprehensive way. This was achieved by using a technical approach which is based on the post‐column infusion of an analyte containing solution. This well‐known experimental setup was not used to spot signal suppression regions of a particular analyte, but to spot regions of the chromatogram where a systematic mass drift of the analyte ion can be observed (isobaric interference plot). Not the changing signal intensity but the stability of the measured analyte mass was observed. A wide range of different analytes in combinations with potentially interfering matrices has been evaluated. Furthermore, different mass resolving power settings were evaluated. Isobaric interferences between matrix compounds and analytes were common at mass resolving powers <50 000 full width at half maximum. The proposed post‐column infusion technique is a useful tool for the determination of the assay and matrix‐specific mass error tolerances. It aims to ensure the highest possible selectivity, at the same time preventing the encounter of detrimental mass error related peak deformations as well as false negative findings. Unlike conventional matrix spiking approaches, isobaric interference plots provide information of potential interferences across the whole chromatographic time range. This becomes relevant when there is a relative retention time shift between the analyte and potential interfering matrix compounds. Furthermore, the described setup can be used to study how the mass accuracy of any mass spectrometer is affected by a widely varying total ion current. Copyright © 2012 John Wiley & Sons, Ltd.     

Evaluation of three calibration methods to compensate matrix effects in environmental analysis with LC-ESI-MS

In quantitative analysis of environmental samples using high-performance liquid chromatography–electrospray ionization mass spectrometry (HPLC-ESI-MS) one of the major problems is the suppression or, less frequently, the enhancement of the analyte signals in the presence of matrix components. Standard addition is the most suitable method for compensating matrix effects, but it is time-consuming and laborious. In this study we compare the potential of three calibration approaches to compensate matrix effects that occurred when seven analytes (naphthalene sulfonates) were quantified in time series samples of waters with different matrices (untreated and treated industrial wastewater). The data obtained by external calibration, internal calibration with one standard, and external sample calibration (corresponding to matrix-matched calibration) were compared with those obtained by standard addition. None of the three approaches were suitable for a sample series of highly loaded, untreated wastewater with highly variable matrix. For less heavily loaded and less variable samples (treated wastewater effluents), the external sample calibration provided reasonable results for most analytes with deviations mostly below 25% as compared to standard addition. External sample calibration can be suitable to compensate matrix effects from moderately loaded samples with more uniform matrices, but it is recommended to verify this for each sample series against the standard addition approach.     

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.     

Second-order standard addition for deconvolution and quantification of fatty acids of fish oil using GC-MS

In the present work two second-order calibration methods, generalized rank annihilation method (GRAM) and multivariate curve resolution-alternating least square (MCR-ALS) have been applied on standard addition data matrices obtained by gas chromatography-mass spectrometry (GC-MS) to characterize and quantify four unsaturated fatty acids cis-9-hexadecenoic acid (C16:1ω7c), cis-9-octadecenoic acid (C18:1ω9c), cis-11-eicosenoic acid (C20:1ω9) and cis-13-docosenoic acid (C22:1ω9) in fish oil considering matrix interferences. With these methods, the area does not need to be directly measured and predictions are more accurate. Because of non-trilinear conditions of GC-MS data matrices, at first MCR-ALS and GRAM have been used on uncorrected data matrices. In comparison to MCR-ALS, biased and imprecise concentrations (%R.S.D. = 27.3) were obtained using GRAM without correcting the retention time-shift. As trilinearity is the essential requirement for implementing GRAM, the data need to be corrected. Multivariate rank alignment objectively corrects the run-to-run retention time variations between sample GC-MS data matrix and a standard addition GC-MS data matrix. Then, two second-order algorithms have been compared with each other. The above algorithms provided similar mean predictions, pure concentrations and spectral profiles. The results validated using standard mass spectra of target compounds. In addition, some of the quantification results were compared with the concentration values obtained using the selected mass chromatograms. As in the case of strong peak-overlap and the matrix effect, the classical univariate method of determination of the area of the peaks of the analytes will fail, the “second-order advantage” has solved this problem successfully.     

Matrix sensitivity of solid sampling AAS. Determination of zinc in geological samples

Direct solid sampling techniques in AAS have several advantages over wet digestion methods such as small sample size requirements and simple calibration procedures. But some disadvantages also exist such as the sample in homogeneity and the matrix sensitivity of calibration. The calibration is commonly carried out by varying the sample mass and evaluating the peak intensity versus absolute analyte amount. It is shown here that this procedure must be considered doubtful when matrix effects are expected. In the case of zinc determination in geological samples it has been shown that calibration functions obtained by different reference materials differ significantly from each other. As an alternative a three-dimensional calibration technique can be applied that evaluates the peak intensity versus both analyte content and sample weight. The resulting calibration planes are expected to be hyperbolically curved. This three-dimensional calibration has been applied to the determination of Zn in geological samples and compared with classical solid sampling AAS calibration procedures.     

Using strong injection solvents with 100% aqueous mobile phase in RP-LC

When samples are dissolved for HPLC analysis, organic solvents are often used to enhance the solubility of the sample components. However, when the diluent becomes significantly stronger than the mobile phase, peak shape distortions may develop during injection. This is a serious problem for weakly retained analytes under 100% aqueous mobile phase conditions. Under these extreme conditions, even small amounts of solvent in the diluent can cause serious broadening or distortion effects. However, if the organic solvent used in the diluent elutes significantly after the analyte, the peak shape of the analyte will be relatively unaffected, even when a relatively strong solvent such as THF is used. This phenomenon is counterintuitive considering the usual practice of keeping the sample diluent as weak as possible. This report describes the potential analytical utility and limitations of this approach for the analysis of weakly retained analytes.     

Note on the Error Analysis of the Generalized Rankannihilation Method

ABSTRACT

The generalized rank annihilation method (GRAM) is a method for curveresolution and quantitation that uses two data matrices simultaneously, i.e., onefor the unknown and one for the calibration sample. Requirements have beenderived that ensure the unique resolution of the analyte of interest in thepresence of unknown interferences if the data matrices are free fromexperimental error. In this paper, it is shown that the same requirements allowfor correct determination of bias and variance in the quantitative results obtainedby GRAM if the data matrices are not free from experimental error.     

Alternative calibration approaches to compensate the effect of co-extracted matrix components in liquid chromatography-electrospray ionisation tandem mass spectrometry analysis of pesticide residues in plant materials

The aim of this study was to evaluate the applicability of different calibration approaches in a multi- and single-residue analysis of modern pesticides in plant matrices using liquid chromatography-electrospray mass spectrometry (HPLC-ESI-MS). In the first set of experiments the determination of eight pesticides representing different groups of polar/unstable pesticides (carbamates, benzimidazoles, azoles, benzoylphenylurea) in apple samples was performed. The trueness and precision of data obtained by using: (i) external solvent standard calibration, (ii) external matrix-matched standard calibration and (iii) echo-peak internal standard calibration was compared. The last mentioned method is a novel technique providing the possibility to inject internal standard of the same identity as a target analyte, so that its retention time is close to the analyte from the sample. According to expectation, when using external standard solvent calibration the results were under- or overestimated due to suppression or enhancement of analyte's signal by matrix components. On the other hand with the use of matrix-matched calibration accurate data were obtained. With echo-peak technique accurate results comparable to those obtained by matrix calibration were obtained for six out of eight pesticides. In the second set of experiment we used the echo-peak technique to overcome the problem with the response instability in the analysis of chlormequat in pear concentrate samples. As an internal standard method the echo-peak technique provided the possibility of monitoring of signal decrease during the analytical sequence and to compensate this decrease by relating sample peak area relatively to this internal standard.     

Matrix-induced peak enhancement of pesticides in gas chromatogrtaphy: Is there a solution?

In this study, it is shown that calibration solution prepared in control matrix extrix extract can be used to compensate for matrix-induced chromatographic response enhancement observed for certain pesticedes. This phenomenon is characterized by enhanced chromatographic response for certain pesticides in the presence of matrix du to reduced analyte loss during injection. Unacceptably high recoveries are seen for affected pesticides when maatrix-free solutions are used for reference and calibration. The effects of matrix concentration on overall enhancement and linear response were determined. When used as reference standards for the determination of recovery, matrix-standard solutions were found to provide acceptable recoveries for pesticides subject to matrix-induced chromatographic response enhancement along with other pesticides. General guidelines are presented for using matrix-standard calibration solutions in pesticide residue analysis.     

A sample preparation method for recovering suppressed analyte ions in MALDI TOF MS

In matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry (MALDI TOF MS), analyte signals can be substantially suppressed by other compounds in the sample. In this technical note, we describe a modified thin‐layer sample preparation method that significantly reduces the analyte suppression effect (ASE). In our method, analytes are deposited on top of the surface of matrix preloaded on the MALDI plate. To prevent embedding of analyte into the matrix crystals, the sample solution were prepared without matrix and efforts were taken not to re‐dissolve the preloaded matrix. The results with model mixtures of peptides, synthetic polymers and lipids show that detection of analyte ions, which were completely suppressed using the conventional dried‐droplet method, could be effectively recovered by using our method. Our findings suggest that the incorporation of analytes in the matrix crystals has an important contributory effect on ASE. By reducing ASE, our method should be useful for the direct MALDI MS analysis of multicomponent mixtures. Copyright © 2015 John Wiley & Sons, Ltd.