Univariate analytical calibration methods and procedures. A review

An original focus on univariate calibration as an experimental process of quantitative analysis is presented. A novel classification system is introduced against the background of the present situation concerning nomenclature of calibration methods. Namely, it has been revealed that four methods well-known in analytical chemistry: the conventional method, the internal standard method, the indirect method and the dilution method, can be split into those carried out in both the interpolative and the extrapolative mode. It is then shown that the basic procedures of all these methods can be modified including different approaches, such as matrix-matched technique, spiking the sample with a reactant, bracketing calibration, and others. For the first time (as compared to monographies dealing with univariate calibration) it is reviewed how the methods are mixed and integrated with one another thereby creating new calibration strategies of extended capabilities in terms of enhanced resistance to the interference and non-linear effects – as the main sources of systematic calibration errors. As additional novelty, rationally possible combinations of the calibration methods – not met hitherto in the literature – have been predicted. Finally, some general rules relating to calibration are formulated and the main calibration problems that still need to be solved are displayed.     

Applications of inductively coupled plasma mass spectrometry and laser ablation inductively coupled plasma mass spectrometry in materials science

Inductively coupled plasma mass spectrometry (ICP-MS) and laser ablation ICP-MS (LA-ICP-MS) have been applied as the most important inorganic mass spectrometric techniques having multielemental capability for the characterization of solid samples in materials science. ICP-MS is used for the sensitive determination of trace and ultratrace elements in digested solutions of solid samples or of process chemicals (ultrapure water, acids and organic solutions) for the semiconductor industry with detection limits down to sub-picogram per liter levels. Whereas ICP-MS on solid samples (e.g. high-purity ceramics) sometimes requires time-consuming sample preparation for its application in materials science, and the risk of contamination is a serious drawback, a fast, direct determination of trace elements in solid materials without any sample preparation by LA-ICP-MS is possible. The detection limits for the direct analysis of solid samples by LA-ICP-MS have been determined for many elements down to the nanogram per gram range. A deterioration of detection limits was observed for elements where interferences with polyatomic ions occur. The inherent interference problem can often be solved by applying a double-focusing sector field mass spectrometer at higher mass resolution or by collision-induced reactions of polyatomic ions with a collision gas using an ICP-MS fitted with collision cell. The main problem of LA-ICP-MS is quantification if no suitable standard reference materials with a similar matrix composition are available. The calibration problem in LA-ICP-MS can be solved using on-line solution-based calibration, and different procedures, such as external calibration and standard addition, have been discussed with respect to their application in materials science. The application of isotope dilution in solution-based calibration for trace metal determination in small amounts of noble metals has been developed as a new calibration strategy. This review discusses new analytical developments and possible applications of ICP-MS and LA-ICP-MS for the quantitative determination of trace elements and in surface analysis for materials science.     

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.     

Modeling the analytical response of optical fiber sensors for aromatic compounds determination

In recent years, there has been an increasing interest in the application of optical fiber sensors for in situ monitoring of chemical pollutants, including volatile organic compounds, regarding air quality assurance. In order to enhance the usefulness and applicability of this methodology to environmental analysis, a proper study of the analytical signal and an adequate calibration model are required. This contribution is focused on the model for optical fiber sensors calibration, discussing some problems associated with the estimates of the figures of merit of these analytical systems. We also suggest and discuss a calibration model based on a cumulative symmetric double sigmoidal (SDS) function, as a suitable and general alternative to the more limited and classical linear calibration model.     

Screening procedures for simultaneous detection of several drug classes used for high throughput toxicological analyses and doping control. A review

This paper reviews high throughput screening procedures for the simultaneous detection of several drug classes relevant to clinical and forensic toxicology or doping control in urine or blood using gas chromatography-mass spectrometry (GC-MS), liquid chromatography coupled with a diode-array detector (LC-DAD) or mass spectrometry (LC-MS). Basic information describing these systematic toxicological analysis (STA) procedures such as the analytes, the biosample, work-up, separation column, mobile phase or separation buffer, detection mode and detection limits are summarized in tables arranged according to the analytical method. Examples of typical applications are presented in 2 figures. Analysis of alternative matrices, like sweat, saliva, nails or hair, was not reviewed.     

The Integrated Calibration Method: Comparison of Various Flow Approaches

The integrated calibration method (ICM) is a novel calibration approach merging interpolative and extrapolative modes in a single procedure. Thanks to this strategy, chemical analysis can be performed along with a diagnosis of systematic calibration errors that leads to better accuracy of analytical results. The paper describes how the ICM can be adapted to different flow techniques: continuous flow, flow-injection, and sequential-injection ones. Instrumental systems dedicated to each flow technique have been presented and their operation has been explained. The systems were used for UV/VIS chromium determination in water samples and compared with each other in terms of precision and accuracy of the obtained results along with time and reagent consumption.     

New validated liquid chromatographic and chemometrics-assisted UV spectroscopic methods for the determination of two multicomponent cough mixtures in syrup

Multivariate spectrophotometric calibration and liquid chromatographic (LC) methods were applied to the determination of 2 multicomponent mixtures containing diprophylline, guaiphenesin, methylparaben, and propylparaben (Mixture 1), or clobutinol, orciprenaline, saccharin sodium, and sodium benzoate (Mixture 2). For the multivariate spectrophotometric calibration methods, principal component regression (PCR) and partial least-squares regression (PLS-1), a calibration set of the mixtures consisting of the components of each mixture was prepared in 0.1 M HCl. Analytical figures of merit such as sensitivity, selectivity, limit of quantitation, and limit of detection were determined for both PLS-1 and PCR. The LC separation was achieved on a reversed-phase C18 analytical column by using isocratic elution with 20 mM potassium dihydrogen phosphate, pH 3.3-acetonitrile (55 + 45, v/v) as the mobile phase and UV detection at 260 and 220 nm for Mixture 1 and Mixture 2, respectively. The proposed methods were validated and successfully applied to the analysis of pharmaceutical formulations and laboratory-prepared mixtures containing the 2 multicomponent combinations.     

A combined application of thermal desorber and gas chromatography to the analysis of gaseous carbonyls with the aid of two internal standards

In this study, a series of GC calibration experiments were conducted to examine the feasibility of the thermal desorption approach for the quantification of five carbonyl compounds (acetaldehyde, propionaldehyde, butyraldehyde, isovaleraldehyde, and valeraldehyde) in conjunction with two internal standard compounds. The gaseous working standards of carbonyls were calibrated with the aid of thermal desorption as a function of standard concentration and of loading volume. The detection properties were then compared against two types of external calibration data sets derived by fixed standard volume and fixed standard concentration approach. According to this comparison, the fixed standard volume-based calibration of carbonyls should be more sensitive and reliable than its fixed standard concentration counterpart. Moreover, the use of internal standard can improve the analytical reliability of aromatics and some carbonyls to a considerable extent. Our preliminary test on real samples, however, indicates that the performance of internal calibration, when tested using samples of varying dilution ranges, can be moderately different from that derivable from standard gases. It thus suggests that the reliability of calibration approaches should be examined carefully with the considerations on the interactive relationships between the compound-specific properties and the operation conditions of the instrumental setups.     

Simultaneous determination of tyrosine and dopamine in urine samples using excitation-emission matrix fluorescence coupled with second-order calibration

A "green" and quick analytical method for complex compounds was developed for simultaneous determination of tyrosine (Tyr) and dopamine (DA) in urine samples in this paper. The three-way responsive data recorded by excitation-emission matrix fluorescence (EEM) spectrometer was analyzed using second-order calibration methods based on both parallel factor analysis (PARAFAC) and selfweighted alternating trilinear decomposition (SWATLD) algorithms. The EEM spectra of the analytes were overlapped with the background in urine samples. However the second-order advantage of both PARAFAC and SWATLD methods was exploited, even in the presence of unknown interferences and the satisfactory results can be obtained. Furthermore, the linear ranges of Tyr and DA were determined to be 0.042-6.42 μg/mL and 0.18-4.43 μmg/mL, respectively, and the accuracies of both methods were validated by the analytical figures of merit (FOM).     

Design and model of calibration for chemical measurements

The international standard ISO 11843 specifies basic methods to design experiments for estimation of critical values referring to the capability of detection. The detection capability depends on the experimental design, the calibration model used, and the errors of the measurement process. This study reports how the specification of the calibration points within the calibration range can be used as a-priori information for evaluation of calibration uncertainty without any consideration of the response variables of the calibration. As result of investigation of the experimental designs, calibration points within the calibration range can be omitted without significant changes of calibration uncertainty. The approach is demonstrated at a practical example, the determination of arsenic in surface water samples taken from a river in Germany.     

Generalized Calibration Strategy in Analytical Chemistry

A novel calibration methodology named ‘the generalized calibration strategy’ (GCS) is presented that is aimed at verifying and improving the accuracy of analytical determinations. It is based on integration of calibration methods together with such operations as standard addition and sample dilution. At each stage of the sample dilution, the analytical result is estimated on the basis of six values, which are differently resistant to errors caused by interference and non-linearity effects. The process of stepwise elimination of both effects is controlled by comparison of these values. A dedicated flow system is presented. The GCS can be adapted to calibration by all well-known methods: conventional, internal standard, and indirect. This novel calibration strategy has been tested on indirect determination of chlorites in water samples by UV/Vis spectrophotometry.     

Determination of analytical limits in solid sampling ETAAS: a new approach towards the characterization of analytical quality in rapid methods

In the present study the lower analytical limits of solid sampling electrothermal atomization atomic absorption spectrometry (SS-ETAAS) were characterized by means of blank measurements and – for the first time – by means of the calibration curve method, where a calibration near the range of these limits (limit of decision, detection and quantification) was performed. The limit of decision as derived from blank measurements was calculated according to the 3σ-criterion to be 0.003 and 0.019 ng for Cd and Pb, respectively. For Pb and Cd a roughly threefold increase of these limits was observed when the calibration method according to DIN 32 645 was applied. When solid reference material was used, only a slight increase could be observed. The analytical limits were 2 to 20 times lower than reported for sample decomposition methods. The blank measurement and conventional calibration curve method, however, do not account for factors relating to solid sampling such as sample mass and matrix. Therefore, the calibration curve model was applied to data derived from comparisons between direct solid sampling ETAAS and a compound reference method (ETAAS following sample homogenization and digestion). The observed analytical limits were not found to be substantially increased if enough samples with low element contents were available for calibration. Coupling of the calibration curve model with the comparison of methods included real test samples and thus the relevant maximum sample mass and analyte content in the range of the lower analytical limits. As validation procedures frequently include comparisons of methods, the present approach might prove to be of some general interest for the characterization of analytical quality in rapid methods.     

Determination of analytical limits in solid sampling ETAAS: a new approach towards the characterization of analytical quality in rapid methods

In the present study the lower analytical limits of solid sampling electrothermal atomization atomic absorption spectrometry (SS-ETAAS) were characterized by means of blank measurements and--for the first time--by means of the calibration curve method, where a calibration near the range of these limits (limit of decision, detection and quantification) was performed. The limit of decision as derived from blank measurements was calculated according to the 3sigma-criterion to be 0.003 and 0.019 ng for Cd and Pb, respectively. For Pb and Cd a roughly three-fold increase of these limits was observed when the calibration method according to DIN 32 645 was applied. When solid reference material was used, only a slight increase could be observed. The analytical limits were 2 to 20 times lower than reported for sample decomposition methods. The blank measurement and conventional calibration curve method, however, do not account for factors relating to solid sampling such as sample mass and matrix. Therefore, the calibration curve model was applied to data derived from comparisons between direct solid sampling ETAAS and a compound reference method (ETAAS following sample homogenization and digestion). The observed analytical limits were not found to be substantially increased if enough samples with low element contents were available for calibration. Coupling of the calibration curve model with the comparison of methods included real test samples and thus the relevant maximum sample mass and analyte content in the range of the lower analytical limits. As validation procedures frequently include comparisons of methods, the present approach might prove to be of some general interest for the characterization of analytical quality in rapid methods.     

Determination of carbendazim, thiabendazole and fuberidazole using a net analyte signal-based method

The net analyte signal (NAS)-based method HLA/GO, modification of the original hybrid linear analysis (HLA) method, has been used to determine carbendazim, fuberidazole and thiabendazole in water samples. This approach was used after a solid-phase extraction (SPE) step, using the native fluorescence emission spectra of real samples, previously standardized by piecewise direct standardization (PDS). The results obtained show that the modification of HLA performs in a similar way that partial least-squares method (PLS-1). The NAS concept was also used to calculate multivariate analytical figures of merit such as limit of detection, selectivity, sensitivity and analytical sensitivity (γ⁻¹). With this purpose, blanks of methanol and ternary mixtures, with the target analyte at low concentration and the other two ranging according to the calibration matrix, were used, with different results. Detection limits calculated in the last way are more realistic and show the influence of the other components in the sample. Selectivity for carbendazim is higher than the corresponding values for fuberidazole and thiabendazole, whereas sensitivity, as well as the values obtained for their detection limits, are lower for carbendazim, followed by thiabendazole and fuberidazole. Results obtained by modification of HLA vary in the same way that the ones obtained by PLS-1.     

A comprehensive approach to method validation based on object technology

 Method validation procedure requires a strategy for collecting those validation data that are best adapted to the analytical technique used. A flexible and general approach based on Object Linking and Embedding technology is proposed. It allows a traceable validation strategy using modular objects which encapsulate documentation, analytical data and processing logic. The contents of these objects are accessible through a standard user interface. This paper demonstrates how this can reduce experiment time, simplify evaluation efforts, and increase the ease of use of validation figures of merit. An illustration using Microsoft Visual Basic for Applications is presented, and some specific aspects are described. It consists of the evaluation of a time domain NMR technique for determining the moisture content of foods involving a multivariate calibration step. This study also illustrates how guidelines such as Good Validation Practices could be defined to present all validation documents in a standardised manner. Received: 3 September 1996 Accepted: 14 October 1996     

An evaluation of the analytical performance of collinear multi-pulse laser induced breakdown spectroscopy

A detailed study of the relevant analytical figures of merit for time- and spatially integrated multi-pulse laser induced breakdown spectroscopy (MP-LIBS) was performed. Laser bursts containing up to 6, ns-range duration collinear pulses, separated by 20–40 μs interpulse gaps were used in the experiments, and the effect of the number of pulses within the burst on the analytical parameters was investigated. Signal enhancement, repeatability, matrix effects, background signals, sensitivity, linear dynamic range and limits of detection were studied for 20 lines of 11 elements in different solid matrices. It was established that all analytical figures of merit significantly improved with respect to those of single- or double-pulse LIBS as a result of the use of multiple laser pulses. For example, six-pulse limits of detection values were found to be with a factor of 4.2–16.7 lower than for double-pulses and calibration plots were found to be linear up to several tens of percents concentrations in some alloys.     

Molecularly imprinted solid-phase extraction and high-performance liquid chromatography with ultraviolet detection for the determination of urinary trans,trans-muconic acid: a comparison with ionic exchange extraction

A new molecularly imprinted polymer (MIP) has been synthesized for the selective extraction of trans,trans-muconic acid (ttMA) from urine samples, followed by high-performance liquid chromatography analysis with ultraviolet detection. The synthesis was based on non-covalent interactions, and 4-vinylpyridine was used as a functional monomer. The analytical calibration curve was prepared using a pool of five urine samples of non-smokers spiked with ttMA standards with concentrations that ranged from 0.3 to 10 mg L(-1) (r(2) = 0.999). The limit of quantification was 0.3 mg L(-1) (lower than the biological exposure limits suggested by the ACGIH). The within-day and between-day precision and accuracy presented relative standard deviations and relative errors of less than 15%. The analytical frequency was 4 h(-1) (considering extraction and separation/quantification steps), and the same MIP cartridge was efficiently used for approximately 100 cycles. All figures of merit were similar or better than those obtained by the procedure based on ionic exchange extraction. The proposed method could be an interesting alternative for the routine analysis of ttMA in urine for biological monitoring procedures of human exposure to benzene.     

Novel Approach to Two-Component Analysis Based on the Generalized Calibration Strategy

The generalized calibration strategy (GCS), developed and previously applied to chemical analysis, has been adapted to two-component (2C) analysis. According to the 2C-GCS procedure, a set of 10 calibration solutions containing a sample and standards of two analytes in well-defined composition was diluted. The measurements performed at a given dilution stage allow the concentration of both analytes in a sample to be evaluated with six apparent concentrations calculated with various mathematical approaches. As a result, the method allows the detection, examination, and elimination of nonlinear and interference effects with multiplicative and additive characteristics. To perform 2C-GCS automatically and effectively, a dedicated flow sequential injection system was designed to be fully controlled by a computer. Caffeine and paracetamol were determined in synthetic and pharmaceutical samples using this calibration approach. The analytes were determined with good precision and accuracy with low consumption of sample and standard solutions. On the basis of this experimental model, the influence of effects and tendencies in the examined analytical system was detected and evaluated.     

Multi-way partial least-squares and residual bi-linearization for the direct determination of monohydroxy-polycyclic aromatic hydrocarbons on octadecyl membranes via room-temperature fluorescence excitation emission matrices

Multi-way partial least-squares (N-PLS) is combined to the residual bi-linearization procedure (RBL) for the direct analysis of metabolites of polycyclic aromatic hydrocarbons in urine samples. Metabolite analysis is carried out via a two-step experimental procedure based on solid-phase extraction and room temperature fluorescence spectroscopy. Excitation-emission matrices are recorded from octadecyl (C18) membranes that serve as solid substrates for sample extraction and spectroscopic measurements. Excellent metabolite recoveries were obtained in all cases, which varied from 96.2 ± 1.35% (9-hydroxyphenanthrene) to 99.7 ± 0.49% (3-hydroxybenzo[a]pyrene). Background correction of extraction membranes is carried out with a new alternating least-squares (ALS) procedure adapted to second order data. The performance of N-PLS/RBL is compared to the well-established multivariate curve resolution-alternating least-squares (MCR-ALS) algorithm. Both algorithms provided similar analytical figures of merit, including their ability to handle unknown interference in urine samples. With only 10 mL of sample, the limits of detection varied between 0.06–0.08 ng mL⁻¹ (1-hydroxypyrene) and 0.016–0.018 ng mL⁻¹ (2-hydroxyfluorene). When compared to previously reported univariate calibration data, the limits of detection via N-PLS/RBL and MCR-ALS are approximately one order of magnitude higher. This was somehow expected due to the effect of unexpected components in multivariate figures of merit, i.e. a more realistic approach to the analysis of metabolites in human urine samples.