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.     

Limits of detection and decision. Part 4

Probability density functions (PDFs) have been derived for a number of commonly used limit of detection definitions, including several variants of the Relative Standard Deviation of the Background–Background Equivalent Concentration (RSDB–BEC) method, for a simple linear chemical measurement system (CMS) having homoscedastic, Gaussian measurement noise and using ordinary least squares (OLS) processing. All of these detection limit definitions serve as both decision and detection limits, thereby implicitly resulting in 50% rates of Type 2 errors. It has been demonstrated that these are closely related to Currie decision limits, if the coverage factor, k, is properly defined, and that all of the PDFs are scaled reciprocals of noncentral t variates. All of the detection limits have well-defined upper and lower limits, thereby resulting in finite moments and confidence limits, and the problem of estimating the noncentrality parameter has been addressed. As in Parts 1–3, extensive Monte Carlo simulations were performed and all the simulation results were found to be in excellent agreement with the derived theoretical expressions. Specific recommendations for harmonization of detection limit methodology have also been made.     

Statistical behavior of ten million experimental detection limits

Using a lab-constructed laser-excited fluorimeter, together with bootstrapping methodology, the authors have generated many millions of experimental linear calibration curves for the detection of rhodamine 6G tetrafluoroborate in ethanol solutions. The detection limits computed from them are in excellent agreement with both previously published theory and with comprehensive Monte Carlo computer simulations. Currie decision levels and Currie detection limits, each in the theoretical, chemical content domain, were found to be simply scaled reciprocals of the non-centrality parameter of the non-central t distribution that characterizes univariate linear calibration curves that have homoscedastic, additive Gaussian white noise. Accurate and precise estimates of the theoretical, content domain Currie detection limit for the experimental system, with 5% (each) probabilities of false positives and false negatives, are presented.     

Detection limits and quantitation limits in the view of international harmonization and the consequences for analytical laboratories

 In the literature and in daily work there exist many different models to describe detection limits and quantitation limits in the chemical measurement process (CMP). It is still an open question whether the evaluation of detection and quantitation limits should be an one-off process carried out during the validation of a CMP, or whether it should be a continuous process. Because of these reasons many laboratories have difficulties to interprete such values. It is necessary that the official standardization bodies should do some efforts in the international harmonization of the special standards concerning detection and quantitation limits. Received: 3 November 1997 · Accepted: 25 January 1998     

Limits of detection and decision. Part 3

It has been shown that the MARLAP (Multi-Agency Radiological Laboratory Analytical Protocols) for estimating the Currie detection limit, which is based on ‘critical values of the non-centrality parameter of the non-central t distribution’, is intrinsically biased, even if no calibration curve or regression is used. This completed the refutation of the method, begun in Part 2. With the field cleared of obstructions, the true theory underlying Currie's limits of decision, detection and quantification, as they apply in a simple linear chemical measurement system (CMS) having heteroscedastic, Gaussian measurement noise and using weighted least squares (WLS) processing, was then derived. Extensive Monte Carlo simulations were performed, on 900 million independent calibration curves, for linear, “hockey stick” and quadratic noise precision models (NPMs). With errorless NPM parameters, all the simulation results were found to be in excellent agreement with the derived theoretical expressions. Even with as much as 30% noise on all of the relevant NPM parameters, the worst absolute errors in rates of false positives and false negatives, was only 0.3%.     

Effects of Different Extraction Methods in Pharmacopoeia on the Content and Structure Transformation of Ginsenosides

Ginseng (Panax ginseng C. A. Meyer), a perennial herb, possesses immunostimulatory, anticarcinogenic, antiemetic, and antioxidative biological activities. In recent years, more and more people have paid attention to the extraction methods and quality evaluation of ginseng. China, the United States, Europe, Japan, and Korea have all had the quality standards and content determination methods of ginseng. The different treatment methods are adopted before the determination of ginseng samples and the content limits of the index components, such as ginsenoside Rb₁, ginsenoside Rg₁, and ginsenoside Re exist differences. The similarities and differences of ginseng content detection methods in pharmacopoeias of different countries have been analyzed by a research group, but the comparison of the effects of different methods on the ginsenoside content and structural transformation has not been reported. In this paper, ginsenosides in ginseng were extracted according to four national pharmacopoeias and analyzed quantitatively and qualitatively by UPLC-Q-Exactive-MS and HPLC-UV. It was illustrated that the pretreatment method has a significant influence on the content determination of ginseng. The yield of rare saponins was increased by heating concluded from both the qualitative and quantitative comparison. Finally, a simple and feasible extraction method was optimized by response surface method at room temperature. The analysis of the preparation method and process optimization of the four pharmacopoeias can provide important reference information for the revision of ginseng standards.     

Voltammetric Determination of Maleic and Fumaric Acids at an In Situ Renewed Graphite Electrode

It was shown that a graphite electrode renewed by cutting a thin surface layer immediately before each measurement can be used for the voltammetric determination of maleic and fumaric acids. The mechanical renewal of the electrode by polishing did not give a reliable signal. The relative standard deviation in the determination of maleic and fumaric acids at the in situ renewed graphite electrode was 3–6%, and the detection limits for both acids were 0.4 mg/L. The deaeration of the solutions is not needed before the determination, which increases the rapidity of the method.     

A tutorial review of some elementary concepts in the statistical evaluation of trace element measurements

This tutorial review discusses the concepts of limit of detection, C_L, limit of identification (=limit of guarantee for purity), C_I, and limit of determination, C_D, from an elementary, statistical point of view. The interrelation between the limit of detection and the limit of identification is treated in terms of α and β errors. It is emphasized that limits of detection, though they are useful figures of merit of a complete analytical procedure, represent safeguards only to not mistaking random fluctuations of the blank for true analyte signals (“α error”). Customers of analytical chemists, however, intuitively want to be informed about the maximum concentrations present in their samples that might escape attention (“β error”), and therefore they are inclined to interpret the limits of detection stated in reports of analytical chemists as if they were limits of identification. The paper further elaborates the dependence of C_L and C_I on two distinct numbers of measurements, viz. the number (N) that underlies the determination of standard deviations (s) and the number (n) that underlies the determination of means. It is illustrated that limits of identification are at least a factor of 3 to 4 above the “2σ limits of detection” commonly reported in the literature. The author concludes that, in spite of the fact that the basic concepts concerning the definition, determination and interpretation of detection limits are well established, psychological barriers remain to be removed before these concepts can be fully implemented in analytical chemistry.     

A passive chemical dosimeter for assessing long-term exposure in air containing aniline and aniline derivatives

A passive chemical dosimeter for assessing long-term exposure to toxic substances (aniline and its derivatives) in the atmosphere of inhabitable premises was described. The compounds to be determined were accumulated on an absorption filter due to a chemical reaction with a selective agent upon the many-hour exposure of the device. Analytical performance of chemical dosimeters (diffusion coefficients, chemisorption pre-concentration rate, and detection limits) was evaluated. The concentrations of aniline, p-chloroaniline, 3,4-dichloroaniline, and o-toluidine in the air of chemical laboratories and smoking rooms were determined.     

A new HPLC-DAD-MS/MS method for the simultaneous determination of major compounds in the crude extract of Lychnophora salicifolia Mart. (Brazilian arnicão) leaves: Application to chemical variability evaluation

Lychnophora salicifolia Mart., which occurs in the Brazilian Cerrado in the states of Bahia and Minas Gerais as well as in the southeast of the state of Goiás, is the most widely distributed and also the most polymorphic species of the genus. This plant is popularly known to have anti-inflammatory and analgesic activities. In this work, we have studied the variation in terms of polar metabolites of ninety-three Lychnophora salicifolia Mart. specimens collected from different regions of the Brazilian Cerrado. Identification of the constituents of this mixture was carried out by analysis of the UV spectra and MS data after chromatographic separation. Twenty substances were identified, including chlorogenic acid derivatives, a flavonoid C-glucoside, and other sesquiterpenes. The analytical method was validated, and the reliability and credibility of the results was ensured for the purposes of this study. The concentration range required for analysis of content variability within the analyzed group of specimens was covered with appropriate values of limits of detection and quantitation, as well as satisfactory precision and recovery. A quantitative variability was observed among specimens collected from the same location, but on average they were similar from a chemical viewpoint. In relation to the study involving specimens from different locations, there were both qualitative and quantitative differences among plants collected from different regions of Brazil. Statistical analysis revealed that there is a correlation between geographical localization and polar metabolites profile for specimens collected from different locations. This is evidence that the pattern of metabolites concentration depends on the geographical distribution of the specimens.     

The determination of natural uranium in human tissues by recovery corrected kinetic phosphorescence analysis

Two typical methods used for the determination of uranium in human autopsy tissues are kinetic phosphorescence analysis (KPA) and alpha-spectrometry, both of which have significant limitations and advantages. KPA is limited because of the amount of sample used (1–10 ml for sample digestion followed by one ml KPA aliquots), no isotopic information is provided, phosphorescence degradation by salts in solution, and even more importantly, it does not provide chemical recovery information. For samples with sub ng uranium concentrations per g of inorganic material, preconcentration is necessary, which may require chemical recovery (other than simple evaporation). While alpha-spectrometry has very good radiometric detection limits for ²³⁸U, the very long half-life of ²³⁸U (4.468·10⁹ y) restricts its mass detection limit (27 ng). KPA, on the other hand, has a detection limit three orders of magnitude lower (0.02 ng) for natural uranium. A recovery corrected method for the determination of natural uranium in human tissues was developed combining preconcentration of human tissues dissolved in 6M HCl by anion exchange with alpha-spectrometry and kinetic phosphorescence analysis, utilizing ²³²U as a tracer. Solution aliquots containing up to 6 g of bone ash were pre-concentrated for KPA measurement thereby allowing the use of up to 25% of the original sample solution weight for analysis by KPA. The radiochemical yield of ²³²U was determined by alpha-spectrometry and the uranium content was determined by KPA. The mean radiochemical yields obtained for human tissue samples range from 65% to 106% with a mean of 85%±8%.     

Detection and identification of bacteria using direct injection inductively coupled plasma mass spectroscopy

In this study, an inductively coupled plasma mass spectrometer (ICP-MS) was used for the inorganic chemical characterization of biological materials by direct injection. ICP-MS has the advantage of sub-nanogram/gram detection limits for most elements making it a sensitive tool for the detection and characterization of aerosolized biological material. Suspended, microgram-sized samples of Bacillus subtilis spores (BG), Bacillus subtilis vegetative cells (Bg), and Bacillus thuringiensis (Bt) were analyzed via direct injection and they exhibit unique chemical signatures reflecting the processing history of each organism.     

Direct detection of benzene, toluene, and ethylbenzene at trace levels in ambient air by atmospheric pressure chemical ionization using a handheld mass spectrometer

The capabilities of a portable mass spectrometer for real-time monitoring of trace levels of benzene, toluene, and ethylbenzene in air are illustrated. An atmospheric pressure interface was built to implement atmospheric pressure chemical ionization for direct analysis of gas-phase samples on a previously described miniature mass spectrometer (Gao et al. Anal. Chem. 2006, 78, 5994–6002). Linear dynamic ranges, limits of detection and other analytical figures of merit were evaluated: for benzene, a limit of detection of 0.2 parts-per-billion was achieved for air samples without any sample preconcentration. The corresponding limits of detection for toluene and ethylbenzene were 0.5 parts-per-billion and 0.7 parts-per-billion, respectively. These detection limits are well below the compounds’ permissible exposure levels, even in the presence of added complex mixtures of organics at levels exceeding the parts-per-million level. The linear dynamic ranges of benzene, toluene, and ethylbenzene are limited to approximately two orders of magnitude by saturation of the detection electronics.     

Detecting the quality of glycerol monolaurate: A method for using Fourier transform infrared spectroscopy with wavelet transform and modified uninformative variable elimination

Glycerol monolaurate (GML) products contain many impurities, such as lauric acid and glucerol. The GML content is an important quality indicator for GML production. A hybrid variable selection algorithm, which is a combination of wavelet transform (WT) technology and modified uninformative variable eliminate (MUVE) method, was proposed to extract useful information from Fourier transform infrared (FT-IR) transmission spectroscopy for the determination of GML content. FT-IR spectra data were compressed by WT first; the irrelevant variables in the compressed wavelet coefficients were eliminated by MUVE. In the MUVE process, simulated annealing (SA) algorithm was employed to search the optimal cutoff threshold. After the WT-MUVE process, variables for the calibration model were reduced from 7366 to 163. Finally, the retained variables were employed as inputs of partial least squares (PLS) model to build the calibration model. For the prediction set, the correlation coefficient (r) of 0.9910 and root mean square error of prediction (RMSEP) of 4.8617 were obtained. The prediction result was better than the PLS model with full-spectra data. It was indicated that proposed WT-MUVE method could not only make the prediction more accurate, but also make the calibration model more parsimonious. Furthermore, the reconstructed spectra represented the projection of the selected wavelet coefficients into the original domain, affording the chemical interpretation of the predicted results. It is concluded that the FT-IR transmission spectroscopy technique with the proposed method is promising for the fast detection of GML content.     

连续流动法同时测定污水中氨氮和总磷

采用连续流动分析法测定污水中氨氮、总磷的含量。比较了污水样品不同的稀释倍数对测定结果的影响。实验结果表明:氨氮和总磷的质量浓度在0.1~8 mg/L范围内线性良好,线性相关系数均为0.99997;测量结果的相对标准偏差分别为2.01%,0.84%(n=7);方法检出限分别为0.012,0.009 mg/L;质控样测量值均在标示值范围内;样品加标回收率为93.4%~101.1%。污水的洁净程度对测定结果影响较大。洁净度高的污水,直接测定与稀释后测定,测定值无显著性差异;而洁净度低的污水,直接测定与稀释后测定结果差异比较大。该法采用全谱直读CCD检测方式,灵敏度高,稳定性好,无光谱干扰,且支持氨氮和总磷同时测定,方便快捷,适合污水中氨氮和总磷的测定。     

A method for dating small amounts of uranium

In this study we describe a method for uranium dating (i.e. determination of the date of the last chemical purification undergone by the material) by measurement of the ²³⁰Th/²³⁴U ratio, applicable to sub-microgram quantities. The chosen protocol (AG1x8 resin in hydrochloric acid medium) has been tested on separation microcolumns (100 μl). This ‘microchemistry’ technique considerably limits the risks of contamination by reagents or the environment. Thorium extraction efficiencies were greater than 90 % and reproducible. The quantities of ²³⁰Th introduced by the chemical purification procedure were negligible. Using an ultra-sensitive inductively coupled plasma mass spectrometry measurement technique, detection limits of the order of femtograms (10^?15 g) of ²³⁰Th were obtained. The complete procedure, chemical separation and isotope measurement, was successfully tested and validated on a few micrograms of uranium.     

Some problems of the emission spectral analysis theory

Over the past 50 years spectral analysis has grown from a semi-empirical method to an independent discipline based on a well-developed theory and having the disposal of various experimental techniques. What is the aim of the spectral analysis theory? Spectral analysis, unlike, for example, classical chemical gravimetric methods, is a relative method. The measured analytical signal T_L is connected with the quantity to be determined, i.e. the element content (C) in the analysis sample by calibration with reference samples. The author believes that the spectral analysis theory should be aimed not at establishing this connection with such an accuracy that it would allow in the end to abandon the reference samples, but at elucidating the role of those physical factors which form the basis of all the links of the spectral analytical procedure, so that a rational choice can be made for obtaining optimum results.It is from this point of view that the problems of atom excitation and ionization, intensity of spectral lines, detection limits and entry of sample into the excitation source are schematically discussed.     

GC-MS analysis of ethanol and other volatile compounds in micro-volume blood samples—quantifying neonatal exposure

A static headspace gas chromatography coupled mass spectrometry (GC-MS) method was developed and fully validated for the quantitative measurement of acetaldehyde, acetone, methanol, ethanol and acetic acid in the headspace of micro-volumes of blood using n-propanol as an internal standard. The linearity of the method was established over the range 0.2–100 mg/L (R ²?>?0.99) and the limits of detection were 0.1–0.2 mg/L and lower limits quantification 0.5–1 mg/L. Precision and accuracies fell within acceptable limits (20 % for LLOQ and 15 %) for both intra- and inter-day analyses for all compounds except acetaldehyde which had inter-day variability of ≤25 %. The method was applied to analyse blood samples from neonatal patients receiving courses of ethanol excipient containing medications. Baseline levels of acetaldehyde, acetone, methanol and ethanol could be measured in patients before dosing commenced and an increase in levels of some volatiles were observed in several neonates after receiving ethanol-containing medications.     

New approach for sensitive photothermal detection of C60 and C70 fullerenes on micro-thin-layer chromatographic plates

In this paper the pulse thermovision (photothermal) detection and quantification methods of C60 and C70 fullerenes are presented. Quantification results are compared with optical and fluorescence measurements. Target components were separated under isothermal conditions (30 °C) on micro-TLC plates (RP18WF₂₅₄S) using n-hexane as the mobile phase. The principle of described analytical protocol is based on sensitive measurement of the temperature contrast generated within TLC stationary phase and fullerenes spots after white light pulse excitation. It has been demonstrated that observed temperature contrast is mainly driven by the optical properties of fullerenes (UV–vis absorption spectra). Contrary to the commonly applied optical reflection or transmission techniques the proposed thermovision method involves dissipated light. The results of presented experimental work have revealed that both types of quantitative measurements provide similar outcome despite the key differences in the signal origin. However, it has been found that thermovision method was characterized by smaller value of LOD, particularly for C60 molecule. We demonstrated that application of correlation technique to post-acquisition analysis of the sequence of temperature contrast images significantly increase detection limits of fullerenes, even in comparison to fluorescence quenching detection mode. Moreover, the thermal contrast images and particularly, computed correlation image, allow detection of stationary phase layer nonuniformities, including changes in the adsorbent thickness and thermal conductivity. Therefore, invented pulsed thermovision methodology can be additionally used for fast quality screening of home made and commercially available TLC plates.     

Quantification of nanodiamonds in aqueous solutions by spectrophotometry and thermal lens spectrometry

Spectrophotometry and thermal lens spectrometry were used to study solutions of several commercial detonation nanodiamonds. It was found that the absorption spectra of solutions of all studied nanodiamond samples obey the Bouger-Lambert-Beer law, which ensures the precise determination of the total mass concentration of unknown nanodiamond solutions using a calibration plot. It was shown that the absorption spectra of nanodiamond solutions exhibit both absorption and scattering components, both significantly affecting signal formation. Conditions were proposed for the spectrophotometric determination of nanodiamonds at 250 nm (l = 1.0 cm). The detection limits were from 60 ng/mL to 2 ??g/mL, depending on the nanodiamond type. Limits of detection of SDND nanodiamonds by spectrophotometry and thermal lens spectrometry were calculated for identical conditions of sample preparation and measurements (488 nm, l = 1.0 cm). These were 10 and 0.6 ??g/mL for spectrophotometry and thermal lens spectrometry, respectively (power of excitation radiation 150 mW).