The quality coefficient as performance assessment parameter of straight line calibration curves in relationship with the number of calibration points

Knowledge of the response function (y?=?f(x)) is essential in the validation of quantitative analysis methods as it describes the mathematical relationship between measurable responses and the concentrations or quantities of the analyte in the sample within a suitable range. The most common response function used is a straight line obtained by ordinary least squares (OLS) regression. Suitability of calibration lines obtained by OLS regression might be verified by calculation of a quality coefficient (QC_mean). Mathematical modelling performed previously showed that with respect to critical limit values for g, which controls the symmetry of the prediction interval of the abscissa value obtained from the confidence intervals around the OLS calibration curve, a corresponding quality coefficient value exists as a quality performance parameter which is related to the spread of the abscissa values around their mean. In this paper, new mathematical models are developed to demonstrate to which extend also the number n of calibration points (x _i ,y _i ) defines the required value for the quality coefficient (QC_mean) for different values of g. From these models, it could be established that the attribution of a critical limit value to QC_mean as a performance parameter for straight line calibration cannot be arbitrary chosen but has to rely on the mathematical model relating QC_mean, the g-value, the number n of calibration points and the spread of the x _i -values around their mean. Practical measures for analysts are provided which tend to lower the g-value of straight calibration lines beneath critical values and enable to improve the quality of the calibration line applied for analysis, as demonstrated in an elaborated example.     

Limits of detection and decision. Part 2

Extensive Monte Carlo studies of instrumental limits of detection (LODs) were performed on a simple univariate chemical measurement system having homoscedastic, Gaussian measurement noise and using ordinary least squares (OLS) processing of tens of millions of independent calibration curve data sets. It was found that experimental decision and detection limits in the content domain were distributed as scaled reciprocals of noncentral t variates. In the response domain, the decision and detection limits were distributed as scaled χ variates. Rates of false negatives were found to be as expected statistically and no bias was found. However, use of detection limit expressions based on critical values of the noncentrality parameter of the noncentral t distribution were found to be significantly biased, resulting in substantial bias in rates of false negatives.     

A Calibration‐Base Method for the Evaluation of the Detection Limit of an Electrochemical Biosensor

The method based on the confidence limits of a regression straight line is applied to the linear portion of the calibration curve of a biosensor in order to determine the limit of detection. A practical application gives a detection limit of an ethanol biosensor greater than that calculated by using the method of the signal‐to‐noise‐ratio, S/N=3, but the value is more reliable because it accounts for the variability in the response at analyte additions. A simple approximation of the method is also presented.     

Nachweis- und Bestimmungsgrenze beim direkt potentiometrischen Arbeiten mit ionensensitiven Elektroden

Summary Calibration of ion-sensitive electrodes using nonlinear regression analysis is combined with an increase of the working range to lower concentrations. It is possible to have statistically reliable results lower than the so-called limit of determination according to IUPAC. From these items the critical level, the limit of detection and the limit of determination are derived by the calibration function, its inverse (the function of analysis) and the confidence interval. The limit of detection is defined by the smallest detectable signal and the calibration function. The limit of determination is defined by the smallest concentration of an analysis that will be statistically significant with a preset probability of error differentiated from the concentration zero and the blind value of the potentiometric measurement. The limit of determination is therefore the smallest concentration of analysis that may be quantitatively determined.     

Coupling chemometrics and electrochemical-based sensor for detection of bacterial population

This work describes a home-made microelectrode array, based on reticulated vitreous carbon, which has been used to record the normal pulse voltammograms with the aim of obtaining the growth curves of Escherichia coli ATCC 13706 and Pseudomonas aeruginosa ATCC 27853 chosen as test microorganisms. The electrochemical signal data have been analysed with partial least squares (PLS) regression in order to highlight the useful analytical information and correlate with the data obtained from the aerobic plate counting. The obtained PLS models generally had a low root mean square error of cross-validation (RMSECV), a cross validated explained variance percentage near 90%.     

The performance of nu-support vector regression on determination of soluble solids content of apple by acousto-optic tunable filter near-infrared spectroscopy

The ν-support vector regression (ν-SVR) was used to construct the calibration model between soluble solids content (SSC) of apples and acousto-optic tunable filter near-infrared (AOTF-NIR) spectra. The performance of ν-SVR was compared with the partial least square regression (PLSR) and the back-propagation artificial neural networks (BP-ANN). The influence of SVR parameters on the predictive ability of model was investigated. The results indicated that the parameter ν had a rather wide optimal area (between 0.35 and 1 for the apple data). Therefore, we could determine the value of ν beforehand and focus on the selection of other SVR parameters. For analyzing SSC of apple, ν-SVR was superior to PLSR and BP-ANN, especially in the case of fewer samples and treating the noise polluted spectra. Proper spectra pretreatment methods, such as scaling, mean center, standard normal variate (SNV) and the wavelength selection methods (stepwise multiple linear regression and genetic algorithm with PLS as its objective function), could improve the quality of ν-SVR model greatly.     

Direct atomic absorption spectrometry determination of tin, lead, cadmium and zinc in high-purity graphite with flame furnace atomizer

This work described methodology of Sn, Pb, Cd and Zn impurities determination in high-purity graphite at direct atomic absorption spectrometry (AAS) with flame furnace (FF) atomizer. It was evidence that quality of AAS measurements are depended from sample amount, its homogeneity, particle size, as well as calibration procedure and operation parameters of FF atomizer. Prior to analysis the method has been developed and optimized with respect to the furnace heating temperature and flame composition of FF atomizer. Conditions of absorption peak areas (Q_A) formation to each element were studied on the basis of contribution into its value some of individual parameters of analytes, including mass-transporting process from increasing mass of graphite samples into gas phase. Because particle size and homogeneous distribution of analyte in powdered materials has an enormous influence on accuracy and precision of measurement results, graphite as well as appropriate series of powdered reference standards was previously ground and investigated. Graphite samples to be analyzed and standard reference materials with mass from 0.025 to 0.200 g was previously briquetted as pellet and insert on corresponding hole in furnace. The characteristic mass (g₀) of Sn, Pb, Cd and Zn were 0.35, 0.1, 0.008 and 0.025 ng, respectively, and relative standard deviation (S_r) not more than 20%.     

Validation of the membrane composition effect on the flow-injection signal profile of chalcogenide-based ion-selective sensors: a model study using electrochemical approach: Hg(II) flow-injection detector case

The membrane composition effect on signal profile of the combined ISE-flow-injection system is examined on the example of Hg(II) flow-injection potentiometric (FIP) detector based on the secondary response to Hg(II) of different thin layer silver chalcogenide membranes, obtained by cathodic electrodeposition at controlled potential. The potential of the electrochemical approach to produce a great diversity of membrane compositions and the possibility for fine tuning of their stoichiometry made it possible to select the stoichiometry with respect to silver (intrinsic defects factor) and the inclusion of dopant (extrinsic defects factor) as the two variable composition parameters. The following membranes have been tested: Ag₂Se_1−xTe_x, Ag₂Se, Ag_2+δSe and Ag_2+δSe_1−xTe_x (δ=0.24). The experimental conditions have been varied in a wide range to include four flow-rates (within the 2.5-6 ml min⁻¹ interval), and three typical carrier compositions to which either Ag(I) or Hg(II) have been added as pilot ions. The results obtained in this study show unambiguously that the membrane composition factors are an important figure of merit, the weight of which in some particular cases can be co-measurable with that of the flow manifold factors. A new important information concerning the active role of the “pilot ion” added to the carrier in controlling the rising part of the signal, through changing the membrane response rate order, is also provided.     

Analyse quantitative des hydrocarbures aromatiques polynucleaires par spectrofluorimetrie shpol'skii a 10 k: utilisation de la raie de mercure excitatrice diffusee par la matrice comme intensite lumineuse de reference

(Quantitative analysis by Shpol'skii spectrofluorimetry of polynuclear aromatic hydrocarbons at 10 K with the mercury excitation line scattered by the matrix used as a standard intensity.)High-resolution Shpol'skii spectrometry in a matrix is particularly suitable for the determination of trace polynuclear aromatic hydrocarbons in complex mixtures. In the usual technique, the method of standard additions is backed up by internal calibration, which is tedious. A direct calibration technique is proposed in which the mercury excitation line, scattered by the polycrystalline matrix, serves as the standard intensity. Detection limits vary from 0.3 ng ml^?1 for benzo(a)pyrene to 48 ng ml^?1 for pyrene, with linear response over about 2 orders of magnitude. The dynamics and a statistical analysis of the confidence interval for the results are discussed.     

Classification and quantification analysis of Radix scutellariae from different origins with near infrared diffuse reflection spectroscopy

A rapid near infrared spectroscopy analysis method was developed for the geographical origin discrimination and content determination of Radix scutellariae, a kind of Traditional Chinese Medicine (TCM). 81 R. scutellariae samples from six different origins were analyzed with HPLC-UV as reference method. The NIR spectra were collected in integrating-sphere diffused reflection mode and processed with different spectra pretreated methods. Discriminant analysis (DA) and discriminant partial least squares (DPLS) were applied to classify the geographical origins of those samples, and the latter had a better predictive ability with 100% accuracy after two exceptional samples eliminated from the calibration set. For the quantitative calibration, the samples were divided into calibration set and validation set by Kennard-Stone algorithm. The models of baicalin, wogonoside, baicalein, wogonin were established with partial least squares (PLS) algorithm and the optimal principal component (PC) numbers were selected with Leave-One-Out (LOO) cross-validation. The established models were evaluated with the root mean square error of prediction (RMSEP) and corresponding correlation coefficients. The correlation coefficients of all the four calibration models are above 0.920, and the RMSEPs of baicalin, wogonoside, baicalein and wogonin are 0.752%, 0.094%, 0.418% and 0.139%, respectively. This research indicated that the NIR diffuse reflection spectroscopy could be used for the rapid analysis of R. scutellariae, which is beneficial to the quality control of this raw material in TCM pharmaceutical factory, and will also help to solve analogous problems.     

Fluorescence quantification of tetracycline in the presence of quenching matrix effect by means of a four-way model

In this work, a four-way tensor is used to model the quenching effect in fluorescent measurements. By means of the analysis of excitation-emission matrices obtained in the determination of tetracycline in tea, which acts as quencher, it is shown as the impossibility to use a calibration, or an addition standard based on a three-way model. It is analysed the quencher multiplicative effect made on the tetracycline signal by means of an ANOVA. However, by arranging the experimental data in a four-way tensor, it is viable to perform a calibration based on the parallel factor analysis, PARAFAC, decomposition and a four-way partial least squares, 4-PLS, regression to quantify the tetracycline in the presence of the matrix quencher effect. 4-PLS calibration provides better results. In the range from 40 to 220 μg L⁻¹ gives an average of relative errors in absolute value equal to 8.02% in prediction (3.40% in calibration). The repeatability as standard deviation in this range is 5.08 μg L⁻¹ and the method is accurate, slope and intercept being statistically equal to 1 and 0, respectively when a regression calculated versus true concentration is performed. Moreover, it has a decision limit (CCα) of 13.87 μg L⁻¹ for a probability of false positive, α, equal to 0.05 and a capability of detection (CCβ) of 26.63 μg L⁻¹ (for probabilities of false positive, α, false negative, β, equals to 0.05).     

Investigation towards an efficient synthesis of benzo[g]isoquinoline-1,5,10(2H)-triones

As part of our research on 2-aza analogues of pentalongin, the active principle of Pentas longiflora Oliv., the first synthesis of 2,3-disubstituted benzo[g]isoquinoline-1,5,10(2H)-triones via 3,4-disubstituted 6-hydroxybenzo[g]furo[4,3,2-de]isoquinoline-2,5(4H)-diones as the key intermediates is reported. The latter compounds have been prepared by treating 2-methoxycarbonyl-1,4-naphthoquinone with N-substituted enaminoesters under acidic conditions. These reagents are easily accessible from readily available 1,4-dihydroxy-2-naphthoic acid, β-ketoesters and primary amines. Finally, a short synthesis of substituted benzo[g]isoquinoline-1,5,10(2H)-triones is achieved by an oxidative addition of N-substituted enaminoesters onto methyl 1,4-dihydroxynaphthalene-2-carboxylate.     

Uncertainties in Determination of pH

 A statistical analysis of multi-point calibration procedure for practical measurement of pH under laboratory conditions is given. The procedure is shown to provide the necessary elements for simple assignment of an uncertainty to a pH measurement – an essential element of quality control. Performance of ordinary least squares regression for prediction of confidence limits is compared to orthogonal regression, inverse regression and Monte Carlo simulations. In case of pH measurement by multi-point calibration procedure, methods considering uncertainties in both axes are found to be statistically more satisfactory than ordinary least squares regression. By analysis of 50 pH calibration data, randomly selected from 250 5-point glass electrode calibrations, it is found that the practical differences, however, are of minor importance. The significance of uncertainty in pH is demonstrated for an example from metal ion speciation in aqueous solution. Received September 20, 1999. Revision April 19, 2000.     

Multivariate methods on the excitation emission matrix fluorescence spectroscopic data of diesel-kerosene mixtures: a comparative study

Quantitative determination of kerosene fraction present in diesel has been carried out based on excitation emission matrix fluorescence (EEMF) along with parallel factor analysis (PARAFAC) and N-way partial least squares regression (N-PLS). EEMF is a simple, sensitive and nondestructive method suitable for the analysis of multifluorophoric mixtures. Calibration models consisting of varying compositions of diesel and kerosene were constructed and their validation was carried out using leave-one-out cross validation method. The accuracy of the model was evaluated through the root mean square error of prediction (RMSEP) for the PARAFAC, N-PLS and unfold PLS methods. N-PLS was found to be a better method compared to PARAFAC and unfold PLS method because of its low RMSEP values.     

Supercritical fluid extraction—Achiral liquid chromatography with circular dichroism detection for the determination of menthone enantiomers in natural peppermint oil samples

A simple and enantioselective method for the determination of menthone enantiomers in peppermint essential oil samples is proposed. The method involves the initial supercritical fluid extraction (SFE) to clean-up and extraction of analytes and their preconcentration on C₁₈ adsorption cartridges followed by achiral liquid chromatographic separation and direct circular dichroism (CD) detection. The calibration curve of the anisotropy factor (g) versus the enantiomeric excess was linear, with a correlation coefficient (R²) of 0.9970. The precision evaluated by UV peak area and CD peak area was suitable both in terms of intra- and inter-day precision (RSD < 5.1% in all cases). The usefulness of the proposed method was demonstrated by analyzing natural and spiked peppermint oil samples. This method has the advantages of being rapid and precise without using an expensive chiral column. It was demonstrated to be suitable for the simultaneous determination of both enantiomers and for assessing the chemical purity of menthone.     

Quantification of chlorpheniramine maleate enantiomers by ultraviolet spectroscopy and chemometric methods

Chlorpheniramine maleate (CLOR) enantiomers were quantified by ultraviolet spectroscopy and partial least squares regression. The CLOR enantiomers were prepared as inclusion complexes with β-cyclodextrin and 1-butanol with mole fractions in the range from 50 to 100%. For the multivariate calibration the outliers were detected and excluded and variable selection was performed by interval partial least squares and a genetic algorithm. Figures of merit showed results for accuracy of 3.63 and 2.83% (S)-CLOR for root mean square errors of calibration and prediction, respectively. The ellipse confidence region included the point for the intercept and the slope of 1 and 0, respectively. Precision and analytical sensitivity were 0.57 and 0.50% (S)-CLOR, respectively. The sensitivity, selectivity, adjustment, and signal-to-noise ratio were also determined. The model was validated by a paired t test with the results obtained by high-performance liquid chromatography proposed by the European pharmacopoeia and circular dichroism spectroscopy. The results showed there was no significant difference between the methods at the 95% confidence level, indicating that the proposed method can be used as an alternative to standard procedures for chiral analysis.     

Simultaneous quantification of three isoflavonoid glycosides in rabbit plasma after oral administration of Astragalus mongholicus extract by high-performance liquid chromatography coupled with electrospray ionization tandem mass spectrometry

A selective and sensitive liquid chromatography coupled with triple stage quadruple tandem mass spectrometry (HPLC/TSQ-MS/MS) was developed and validated for simultaneous quantification of calycosin-7-O-β-d-glycoside (CCSG), formononetin-7-O-β-d-glycoside (Ononin) and (6R,10R)-9,10-dimethoxypterocarpan-3-O-β-d-glycoside (DPG) in rabbit plasma. Plasma samples were extracted with solid-phase extraction (SPE), separated on an Inertsil ODS-3 column and detected by tandem mass spectrometry with electrospray ionization (ESI) interface in positive selective reaction monitoring (SRM) mode. 3,7,8-Trimethoxy-xanthone-1-O-primaverose was used as internal standard (IS) for quantitative measurement. For each analyte, one major product ion was chosen and used for screening of it. Calibration curves were generated over the range of 2-1000 ng mL⁻¹ with the correlation coefficients greater than 0.99 by using a weighted (1/χ) least squares linear regression. The method had the lower limit quantification of 0.15, 0.21 and 0.19 for CCSG, Ononin and DPG, respectively, with precision less than 20%. The intra- and inter-day precisions ranged from 2.48 to 6.38% and 4.81 to 11.78% (R.S.D.%), respectively. This assay is suitable for determining the above three trace glycosides in rabbit plasma simultaneously and thus investigating the pharmacokinetics of glycosides from Astragalus mongholicus extract in rabbits.     

De Novo Correction of Mass Measurement Error in Low Resolution Tandem MS Spectra for Shotgun Proteomics

We report an algorithm designed for the calibration of low resolution peptide mass spectra. Our algorithm is implemented in a program called FineTune, which corrects systematic mass measurement error in 1?min, with no input required besides the mass spectra themselves. The mass measurement accuracy for a set of spectra collected on an LTQ-Velos improved 20-fold from ?C0.1776?±?0.0010?m/z to 0.0078?±?0.0006?m/z after calibration (avg?±?95?% confidence interval). The precision in mass measurement was improved due to the correction of non-linear variation in mass measurement accuracy across the m/z range.     

Cytotoxic cembranoids from the Red Sea soft coral, Sarcophyton auritum

Chemical investigation of the Red Sea soft coral Sarcophyton auritum led to the isolation and structure elucidation of two new diterpene cembranoids; 2-epi-sarcophine (2) and (1R,2E,4S,6E,8R,11R,12R)-2,6-cembradiene-4,8,11,12-tetrol (4), as well as two known diterpene cembranoids, reported for the first time from this species, namely sarcophine (1) and (+)-7α,8β-dihydroxydeepoxysarcophine (3). Structure elucidation was achieved using spectroscopic techniques, including 1D and 2D NMR and HRMS. The isolated cembranoids were found to display high cytotoxicity against HepG2 (liver cancer cell line) and MCF-7 (breast cancer cell line).