Prediction of precision from signal and noise measurement in liquid chromatography: Mathematical relationship between integration domain and precision

Summary The precision of integration over noisy instrumental output for quantitative analysis is studied. A probability theory is developed to predict the relative standard deviation (RSD) of integration results over an integration domain from one-point integation (peak height measurement) to entire area integration in HPLC. Common integration modes of horizontal zero line and oblique zero line are taken into account, but no peak overlap is assumed. The question of the analytical superiority of peak height measurement or integration for quantitation is answered. In the HPLC apparatus used, the minimum RSD of measurements is found in the integration domain of ca. ±0.5 for analytes [peaks are approximated by the Gaussian signal of width, (standard deviation)]. The RSD of integration measurements is also shown to depend on the stochastic properties of back-ground noise (uncorrelated noise and correlated 1/f type noise). The theoretical conclusion is verified by Monte Carlo simulation and HPLC experiments for some aromatic compounds.Second Part of series cited as Ref. [1].     

Prediction of precision from signal and noise measurement in liquid chromatography: Limit of detection

Summary A method to determine the limit of detection (LOD) in high performance liquid chromatography (HPLC) is described. The power spectral density of instrumental baseline variation is fitted by the simplex least squares methods with a mixed random process of white noise and Markov process as a model. The white noise is characterized by standard deviation (SD),; the Markov process by the SD, , and auto-correlation degree, ρ. All required parameters for calculating the LOD signal are obtained by experiment without repeat measurements. No arbitrary constants are needed. The LOD signal is uniquely determined and is characterized by 33.3 % relative standard deviation (RSD) of analyte measurements and 0.13 % of the error of the first type. This signal also specifies that the signal-to-noise ratio =3, using the definition of noise originating from the white noise and Markov process. The theoretical conclusion is verified by the Monte Carlo simulation using real baseline and peaks. The LOD concentrations for naphthalene, acenaphthene, pyrene and perylene are given. First part of series cited as Ref. [1].     

Deductive prediction of measurement precision and optimization of integration time and wavelength in capillary electrophoreses

Summary This paper demonstrates that the relative standard deviation (RSD) of measurements in a capillary electrophoresis system can be predicted theoretically from the baseline and the signal shape at low sample concentration. The only requirements for prediction of the uncertainty are the Fourier transform of the baseline (here 2048 data points) and the observation of signal shape. The micellar electrokinetic chromatography (MEKC) of acetaminophen and caffeine is taken as an example. The optimum is defined here as the condition of the lowest RSD or highest precision. The optimum single wavelength is selected from between 220 and 350 nm for the MEKC system equipped with a photodiode array detector. The optimum time domain of signal integration is shown to be even narrower than the entire signal region, providing an RSD value about half that for integration of the entire region. The theory is in good agreement with observed RSD values.     

Prediction of precision from signal and noise measurement in liquid chromatography: Limit of detection

Summary A method to determine the limit of detection (LOD) in high performance liquid chromatography (HPLC) is described. The power spectral density of instrumental baseline variation is fitted by the simplex least squares methods with a mixed random process of white noise and Markov process as a model. The white noise is characterized by standard deviation (SD), w; the Markov process by the SD, m, and auto-correlation degree, . All required parameters for calculating the LOD signal are obtained by experiment without repeat measurements. No arbitrary constants are needed. The LOD signal is uniquely determined and is characterized by 33.3% relative standard deviation (RSD) of analyte measurements and 0.13% of the error of the first type. This signal also specifies that the signal-to-noise ratio=3, using the definition of noise originating from the white noise and Markov process. The theoretical conclusion is verified by the Monte Carlo simulation using real baseline and peaks. The LOD concentrations for naphthalene, acenaphthene, pyrene and perylene are given.First part of series cited as Ref. [1].     

Prediction of measurement precision of apparatus using a chemometric tool in electrochemical detection of high-performance liquid chromatography

The relative standard deviation (RSD) of measurements in high-performance liquid chromatography with electrochemical detection (HPLC-ECD) was predicted by a chemometric tool based on the 1/f fluctuation model which is made up of white noise and a Markov process, called the Function of Mutual Information (FUMI) theory. FUMI theory can provide aprecise and reliable detection limit from a single measurement of noise and signal in HPLC-ECD. To obtain RSD (n = 5) for determination of (-)-epicatechin at five concentrations required 12.5 h, while the predicted RSD by FUMI theory required only 0.5 h (one measurement). Moreover, to trace the source of instrumental noise, power spectra of chromatographic baseline were used. Selection of a suitable apparatus in HPLC-ECD system, acquisition of RSD, and detection limits for determination of catechins by HPLC-ECD were simply and easily made by this chemometric tool within a very short time. The use of the FUMI theory for the prediction of measuring precision was more efficient and the optimization was less time-consuming to be suited for determination.     

High precision retention time measurements in gas chromatography. I. A simple differentiating time printer for large sample sizes

Summary A differentiating time printer (DTP) apparatus has been constructed from standard laboratory equipment by connecting a differentiating CR circuit via an operational amplifier to an electronic temperature regulator that triggers the print out of a line frequency driven register. The electronic resolution is 0.1 s, giving a relative standard deviation _rel, which is determined by the stability of the line frequency at sufficiently long retention times. In Lund this corresponds to a best _rel = 0.02% and to a mean _rel = 0.03%. For late and broad peaks in real GC the noise caused the print-out of extra time values, especially with fronting peaks from ordinary 1/8 columns. However, a comparison with the simultaneously recorded chromatograms was generally sufficient to pick out the proper retention times. For large sample sizes the corrected retention time t increased with peak height, the later the peak in the chromatogram. The In t _n+1 /t _n values from a series of n-paraffins showed good linear correlations with peak height h_n+1 and peak area A_n+1, giving standard deviations around the line approaching that expected from _rel. The accuracy of the system was mainly determined by the effect of a non-zero triggering level on the derived signal and by the time displacement expected from a large time constant. A rough estimate of the time error was made by simulating GC peaks with a cosine wave generator.     

Use of a spectrally segmented photodiode-array spectrometer for inductively coupled plasma atomic-emission spectroscopy Examination of procedures for the evaluation of detection limits

The utility of a spectrally segmented photodiode array spectrometer was examined by using inductively coupled plasma atomic-emission spectrometry (ICP-AES). The spectrometer used in this study is capable of high resolution (reciprocal linear dispersion of approximately 0.08 nm/mm at 300 nm) over a wide spectral range (190-415 nm). The effect of using spectral peak areas instead of peak heights as a signal definition was examined by using the emission signals from 10 molybdenum lines obtained with various photodiode-array integration periods. In addition, a procedure to determine the detection limits obtainable with such a spectrometer is proposed. It was found that a signal definition involving a summation over a range of 5 pixels offered the best signal-to-noise ratio when the noise was defined as the standard deviation of the residual values from the line fitted to the sideband background level. A detection limit of 6 ng/ml was determined in this way for molybdenum. The multichannel capability of the spectrometer was found to permit continuous background correction, thereby reducing errors caused by low-frequency noise or plasma drift. The linearity of response was found to extend over three orders of magnitude with use of a single integration period. However, by use of different integration periods, the linear range of the detector could be extended to at least four orders of magnitude. The precision (RSD) of the spectrometer for a molybdenum concentration of 0.5 mug/ml was found to be about 3-4% for molybdenum peaks where the background emission was relatively low.     

A Rapid Analytical Method for Free Choline by LC and Its Application for Bacterial Culture Medium Samples

A rapid, and inexpensive analytical method for free choline is described here. Choline was derivatized with benzoyl chloride and analyzed by HPLC with UV detection. Choline samples in the micro-molar range were determined with good repeatability. The precision (RSD) was not greater than 10%. The quantification limit was 10 μM (3σ), and the linear calibration range was between 10 and 1,500 μM. This method was applied to the measurement of free choline in a culture medium of bacteria and was shown to be suitable for aqueous samples with a wide concentration range and for routine analyses.     

The development of an automated continuous measurement system for the monitoring of HCHO and CH3CHO in the atmosphere by using an annular diffusion scrubber coupled to HPLC

An automated continuous measurement system for the monitoring of formaldehyde (HCHO) and acetaldehyde (CH₃CHO) in the urban atmosphere was developed by using an annular diffusion scrubber in conjunction with a high-performance liquid chromatograph (HPLC). With this technique, atmospheric HCHO and CH₃CHO were effectively collected by the annular diffusion scrubber which consists of a porous polytetrafluoroethylene (PTFE) tube disposed concentrically within a Pyrex-glass tube and a scrubbing solution. 2,4-Dinitrophenylhydrazine (DNPH) was selected as the scrubbing solution for collecting HCHO and CH₃CHO, which are derivatized to 2,4-dinitrophenylhydrazone-formaldehyde (DNPH-HCHO) and 2,4-dinitrophenylhydrazone-acetaldehyde (DNPH-CH₃CHO), respectively. An aliquot of the sample solution was automatically injected into an HPLC equipped with a semi-micro ODS column and a UV-VIS detector for separating and determining DNPH-HCHO and DNPH-CH₃CHO. All the operations are sequenced by a programmable controller, and automated continuous measurements are performed with a typical temporal resolution of 1 h. The collection efficiencies of HCHO and CH₃CHO were about 97% and 93%, respectively, at an air flow rate of 0.2 L/min. The lower detection limits (3σ of the blank hydrazones) of HCHO and CH₃CHO were 0.05 ppbv and 0.10 ppbv, respectively, in the case of 12-L air sample volume. Analytical response of a standard solution of DNPH-HCHO and DNPH-CH₃CHO by the HPLC during a 10-day continuous measurement was unchanged and the relative standard deviation (RSD) was < 1.0%. Interferences from O₃ and NO₂ were insignificant in this annular diffusion scrubber method. Both for HCHO and CH₃CHO measurements, concentrations from this developed system well agreed with those measured by a DNPH Silica cartridge method. Received: 15 July 1998 / Revised: 5 October 1998 / Accepted: 7 October 1998     

Development and validation of a stability-indicating HPLC method for the determination of degradation products in dipyridamole injection

Summary The development and subsequent validation of an isocratic high-performance liquid chromatographic (HPLC) procedure employing ultraviolet (UV) detection for the determination of degradation products in Dipyridamole Injection is reported. The development of this assay involved the evaluation of several factors including buffer type, ionic strength, pH, organic composition, and column type. The described method is simple, reproducible, accurate, and selective. The precision, relative standard deviation (RSD), amongst five sample preparations for total degradation products was not more than (NMT) 10.2 %, while the individual degradation products were NMT 12.1%. Intermediate precision, as determined from fifteen sample preparations, generated by two Analysts on different HPLC systems over three days, exhibited an RSD for total and individual degradation products of 8.2 % and NMT 27.5 %, respectively. The mean absolute recovery of dipyridamole using the described method is 102.1±1. 9%, (mean±SD, n=12) over the concentration range of 0.03 % to 5.0 % of its label claim of 5 mg mL⁻¹. The limit of detection and limit of quantitation were 0.1 and 0.3 μg mL⁻¹, respectively. The linearity of the peak response was verified with respect to dipyridamole concentration over a range of 0.3 and 50 μg mL⁻¹ (0.03 % to 5.0 % label claim). The Standard and Assay Preparations are stable for up to 48 hours at room temperature. The selectivity was evaluated by subjecting the finished product (Dipyridamole Injection) to thermal, acidic, basic, oxidative and fluorescent radiation stress conditions. No interference in the analysis of degradation products was observed, showing the method is stability-indicating.     

Baseline noise and measurement uncertainty in liquid chromatography.

The stochastic properties of baseline noise in HPLC systems with a UV photo-diode array, photo-multiplier and gamma-ray detector were examined by dividing the noise into auto-correlated random process (Markov process) and an independent process (white noise). The present work focused on the effect of the stochastic noise properties on a theoretical estimation of the standard deviation (SD) of area measurements in instrumental analyses. An estimation theory, called FUMI theory (Function of Mutual Information), was taken as an example. A computer simulation of noise was also used. It was shown that the reliability (confidence intervals) of theoretical SD estimates mainly depends on the following factors: the ratio of the white noise and Markov process occurring in the baselines; the number of data points used for the estimation; the width of a target peak for which the SD is estimated.     

Effects of digital processing on repeatability assessment of a multiple reaction monitoring liquid chromatography–tandem mass spectrometry system by ISO 11843-7

ISO 11843 part 7 (ISO 11843-7) can provide a standard deviation (SD) of area measurements of a target peak through the stochastic behaviors of instrumental noises. The purpose of this study is to demonstrate that ISO 11843-7 can be applied to assess repeatability in an isocratic liquid chromatography–tandem mass spectrometry (LC–MS/MS) system without repetitive measurements. The relative standard deviation (RSD) of the peak area of ergosterol picolinyl ester, which was used as an example, on a multiple reaction monitoring (MRM) chromatogram was determined by ISO 11843-7. The RSD by ISO 11843-7 (N = 1) was within a 95% confidence band of the RSD by repetitive measurements (N = 6). Moreover, the effects of digital smoothing, such as moving average, were also examined on the repeatability assessment in LC–MS/MS by ISO 11843-7. From the results of the comparisons of the RSDs obtained by ISO 11843-7 and the repetitive measurements, it was shown that suitable RSDs of the peak area were obtained from the smoothed MRM chromatograms by the moving average for narrow data point windows (e.g., one-sixth of the peak width). In conclusion, the utility of repeatability assessment based on ISO 11843-7 has been expanded for the validation of an LC–MS/MS system.     

Stereospecific determination of cis- and trans-resveratrol in rat plasma by HPLC: application to pharmacokinetic studies

A simple, accurate, precise, specific and reproducible high-performance liquid chromatography (HPLC) method was developed for simultaneous determination of resveratrol isomers in rat plasma. Cis-resveratrol was made by exposure of a trans-resveratrol solution to sunlight for 5 days followed by separation by HPLC and identification by mass spectrometry (MS). The assay procedure involved simple liquid-liquid extraction of resveratrol isomers and internal standard (IS, caffeine) from a small plasma volume directly into acetonitrile. The supernatant liquid was added an equal volume of water and injected onto a Hypersil ODS(2) C(18) column (5 microm, 4.6 x 250 mm). Mobile phase consisting of methanol and distilled water was used at a flow rate of 1.0 mL/min for the effective separation of cis-, trans-resveratrol and caffeine (IS). The detection of the analyte peak was achieved by monitoring the eluate using a UV detector set at 303 nm. The ratio of peak area of analyte to IS was used for quantification of plasma samples. Nominal retention times of cis-, trans-resveratrol and IS were 3.2, 4.3 and 6.1 min, respectively. The calibration curve was linear ranging from 0.066 to 6.64 and 0.134 to 13.4 microg/mL with correlation coefficients of 0.9998 and 0.9997 for trans and cis isomers, respectively. The absolute recovery of both isomers was more than 85%. The inter- and intra-day precisions in the measurement of quality control (QC) samples, 0.066, 0.664 and 6.64 microg/mL of trans-resveratrol, were in the range 2.37-6.95% relative standard deviation (RSD) and 0.77-6.97% RSD, respectively. The inter- and intra-day precisions in the measurement of quality control (QC) samples, 0.134, 1.34 and 13.4 microg/mL of cis-resveratrol, were in the range 1.93-3.72% relative standard deviation (RSD) and 1.13-6.57% RSD, respectively. Both analytes and IS were stable in the battery of stability studies and freeze-thaw cycles. Resveratrol isomers were found to be stable for a period of 30 days on storage at -20 degrees C. The application of the assay to determine the pharmacokinetic disposition after a single oral dose to rats is described.     

Characterization of heteroscedastic measurement noise in the absence of replicates

A method is described for the characterization of measurement errors with non-uniform variance (heteroscedastic noise) in contiguous signal vectors (e.g., spectra, chromatograms) that does not require the use of replicated measurements. High-pass digital filters based on inverted Blackman windowed sinc smoothing coefficients are employed to provide point estimates of noise from measurement vectors. Filter parameters (number of points, cutoff frequency) are selected based on the amplitude spectrum of the signal in the Fourier domain. Following this, noise estimates from multiple signals are partitioned into bins based on a variable that correlates with the noise amplitude, such as measurement channel or signal intensity. The noise estimates in each bin are combined to estimate the standard deviation and, where appropriate, a functional model of the noise can be obtained to characterize instrumental errors (e.g., shot noise, proportional noise). The proposed method is demonstrated and evaluated with both simulated and experimental data sets, and results are compared with replicated measurements. Experimental data includes fluorescence spectra, ion chromatograms from liquid chromatography/mass spectrometry, and UV–vis absorbance spectra. The limitations and advantages of the new method compared to replicate analysis are presented.     

Validated HPLC–MS–MS method for simultaneous determination of atorvastatin and 2-hydroxyatorvastatin in human plasma—pharmacokinetic study

Cholesterol-reducing statin drugs are the most frequently prescribed agents for reducing morbidity and mortality related to coronary heart disease. In this publication a validated, highly sensitive, and selective isocratic HPLC method is reported for quantitative determination of the major statin drug atorvastatin (ATV) and its metabolite 2-hydroxyatorvastatin (HATV). Detection was performed with an electrospray ionization triple-quadrupole mass spectrometer equipped with an ESI interface operating in positive-ionization mode. Multiple reaction monitoring (MRM) was used for MS–MS detection. The calibration plot was linear in the concentration range 0.10–40.00 ng mL⁻¹ for both ATV and HATV. Inter-day and intra-day precision and accuracy of the proposed method were characterized by measurement of relative standard deviation (RSD) and percentage deviation, respectively; both were less than 8% for both analytes. The limit of quantitation was 0.02 ng mL⁻¹ for ATV and 0.07 ng mL⁻¹ for HATV. The method was used for pharmacokinetic study of ATV and HATV. Pharmacokinetic data for all analytes are also reported.     

Quantification of mercury in soils and sediments – acid digestion versus pyrolysis

Mercury (Hg) pyrolysis techniques allow the differentation of Hg-binding forms in contaminated soils and sediments. However, data about reproducibility and accuracy of the results concerning quantification of single Hg-compounds and total Hg-concentrations are rare. Therefore the total mercury concentration of different contaminated soils and sediments determined by using a pyrolysis technique were compared to those obtained after aqua regia digestion and cold vapor atomic absorption spectroscopy Hg detection. Twenty replicates of four soil and two sediment samples containing different Hg-compounds were investigated by both methods. All samples were analyzed without any pretreatment. For most of the samples total Hg-concentrations determined by pyrolysis show lower values, and up to threefold higher relative standard deviation(s) (RSD) than those obtained after wet digestion. Soil samples containing specified Hg-compounds like metallic Hg (Hg⁰) or cinnabar (α-HgS) show by far higher RSD by means of both methods than samples containing only matrix-bound Hg-compounds. Single peak integration indicate that the distribution of Hg⁰ and cinnabar is usually heterogeneous resulting in RSD of up to 85%, whereas RSD of matrix-bound Hg-compounds were always distinctly lower. Besides the higher standard deviation the pyrolysis technique has been found to be reliable for screening contaminated soils and sediments due to the important additional information about occurring Hg-binding forms. Received: 13 February 1997 / Revised: 13 March 1997 / Accepted: 17 March 1997     

高效液相色谱法测定家蝇细胞色素P450O-脱甲基活性

建立了以乙酸乙酯/正己烷为终止剂(含1% H3PO4)和萃取剂,利用高效液相色谱,ZORBAX Eclipse XDB C18色谱柱,梯度洗脱,在316 nm检测,外标法分析对硝基苯酚的生成量,表征家蝇粗酶液中细胞色素P450催化的对硝基苯甲醚 O-脱甲基活性的新方法.本方法的检出限为0.1 ng; 分析精密度的RSD为1.02%; 0.351, 1.755和8.755 μg对硝基苯酚3个添加水平的回收率为92.34%～87.60%; 回收率的RSD为2.64%～5.90%;对硝基苯酚在9.72～486 ng范围内,线性关系良好, r=0.9995.应用本方法比较了家蝇吡虫啉抗性品系与敏感品系细胞色素P450的活性差异.结果表明,家蝇抗性品系的P450 O-脱甲基活性是敏感品系的3.34倍; 细胞色素P450活性的提高是家蝇对吡虫啉产生抗性的一个重要机制.     

Spark ablation-inductively coupled plasma spectrometry for analysis of geologic materials

Spark ablation-inductively coupled plasma (SA-ICP) spectrometry is applied to the measurement of hafnium-zirconium ratios in zircons and to the determination of cerium, cobalt, iron, lead, nickel and phosphorus in ferromanganese nodules. Six operating parameters used for the high-voltage spark and argon-ICP combination are established by sequential simplex optimization of both signal-to-background ratio and signal-to-noise ratio. The time-dependences of the atomic emission signals of analytes and matrix elements ablated from a finely pulverized sample embedded in a pressed disk of copper demonstrate selective sampling by the spark. Concentration ratios of hafnium to zirconium in zircons are measured with a precision of 4% (relative standard deviation, RSD). For ferromanganese nodules, spectral measurements based on intensity ratios of analyte line to the Mn(II) 257.610 nm line provide precisions of analysis in the range from 7 to 14% RSD. The accuracy of analysis depends on use of standard additions of the reference material USGS Nod P-1, and an independent measurement of the Mn concentration.     

Fast quantitation of 5-hydroxymethylfurfural in honey using planar chromatography

An approach for rapid quantitation of 5-hydroxymethylfurfural (HMF) in honey using planar chromatography is suggested for the first time. In high-performance thin-layer chromatography (HPTLC) the migration time is approximately 5 min. Detection is performed by absorbance measurement at 290 nm. Polynomial calibration in the matrix over a range of 1:80 showed correlation coefficients, r, of ≥ 0.9997 for peak areas and ≥ 0.9996 for peak heights. Repeatability in the matrix confirmed the suitability of HPTLC–UV for quantitation of HMF in honey. The relative standard deviation (RSD, %, n = 6) of HMF at 10 ng/band was 2.9% (peak height) and 5.2% (peak area); it was 0.6% and 1.0%, respectively, at 100 ng/band. Other possible detection modes, for example fluorescence measurement after post-chromatographic derivatization and mass spectrometric detection, were also evaluated and can coupling can be used as an additional tool when it is necessary to confirm the results of prior quantitation by HPTLC–UV. The confirmation is provided by monitoring the HMF sodium adduct [M + Na]⁺ at m/z 149 followed by quantitation in TIC or SIM mode. Detection limits for HPTLC–UV, HPTLC–MS (TIC), and HPTLC–MS (SIM) were 0.8 ng/band, 4 ng/band, and 0.9 ng/band, respectively. If 12 μL honey solution was applied to an HPTLC plate, the respective detection limits for HMF in honey corresponded to 0.6 mg kg⁻¹. Thus, the developed method was highly suitable for quantitation of HMF in honey at the strictest regulated level of 15 mg kg⁻¹. Comparison of HPTLC–UV detection with HPTLC–MS showed findings were comparable, with a mean deviation of 5.1 mg kg⁻¹ for quantitation in SIM mode and 6.1 mg kg⁻¹ for quantitation in TIC mode. The mean deviation of the HPTLC method compared with the HPLC method was 0.9 mg kg^-1 HMF in honey. Re-evaluation of the same HPTLC plate after one month showed a deviation of 0.5 mg kg⁻¹ HMF in honey. It was demonstrated that the proposed HPTLC method is an effective method for HMF quantitation in honey.      

Determination of total cholesterol in serum by high-performance liquid chromatography with electrochemical detection

A simple and sensitive HPLC method that does not require derivatization for determining cholesterol has been developed. Investigation of voltammetric behavior of cholesterol showed that cholesterol could be oxidized on a glassy carbon electrode in non-aqueous solvents. This was applied to the development of a method by HPLC with electrochemical detection (HPLC-ED). The HPLC-ED was optimized using the separation of cholesterol and oxysterols including 26-hydroxycholesterol and 24S-hydroxycholesterol. The separation was carried out with a Develosil C30-UG-3 column; acetonitrile-2-propanol (9:1, v/v) containing 50mM LiClO(4) as a mobile phase; and an applied potential at 1.9V versus Ag/AgCl. The current peak height was linearly related to the amount of cholesterol injected from 0.5-100 microM (r>0.999). The detection limit (S/N=3) of cholesterol was 0.36 microM (1.8 pmol). Cholesterol at 100 microM was directly detected with a relative standard deviation (RSD) of less than 1.0% (n=8). Total cholesterol and free cholesterol in control human serum were determined by the present method with the recovery of more than 90% and the RSD (n=6) of less than 3.0%.