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.

Chemometric evaluations of repeatability and detection limit in high-performance liquid chromatography with electrochemical detection.

The function of mutual information (FUMI) theory proposes that it is possible to obtain a relative standard deviation (RSD) of the peak area of an analyte from baseline noises and a signal on a single chromatogram when the analyte concentrations are proportional to their peak areas. In this study, we demonstrate that the FUMI theory using noise parametrization by the difference method is applicable for the evaluations of repeatability and detection limit (DL) in high-performance liquid chromatography with electrochemical detection (HPLC-ECD). HPLC-ECD for determining vincristine (VCR) was taken as an example, and VCR was detected on a glassy carbon surface at +0.8 V vs. Ag/AgCl. In the comparisons of precision profiles (plots of RSD of peak area against concentrations of an analyte), the stochastically estimated RSD (N = 1) by the FUMI theory fell within the 95% confidence intervals of statistically estimated RSD (N = 6) by repetitive measurements. Furthermore, the DL obtained by the FUMI theory (3.3×SD) was almost the same value as that by the signal-to-noise ratio (S/N) = 3. Moreover, we introduced a manual method for signal-noise resolution to obtain noise parameters from a chromatogram with low-pass Bessel filter processing. In conclusion, our results show that the FUMI theory using noise parametrization by the difference method can be applied to the evaluations of repeatability and DL in HPLC-ECD without and with a low-pass Bessel filter.

Effects of sampling rate and noise filter processing on repeatability assessment in UHPLC with ultraviolet detection based on the ISO 11843-7.

The present study examines whether short measurement time and noise filter processing in an ultra-high-performance liquid chromatography with ultraviolet detection (UHPLC-UV) contribute to limitations for repeatability assessment based on the ISO 11843 part 7 (ISO 11843-7), which can stochastically provide a measurement standard deviation (SD) caused by baseline noise (SB). In this study, ergosterol was used as an example in UHPLC-UV analysis. From the results of power spectrum analysis of baseline noise, 1024 consecutive digital data points provided a suitable SB. Thus, it was found that an SB can be obtained from about 1 min of baseline when a chromatogram was recorded at sampling rate of 20 points s-1 in the present UHPLC-UV system. The relative SDs (RSDs) of the peak area obtained by the ISO 11843-7 were within 95% of the confidential intervals of the RSDs obtained by repetitive measurements, indicating the ISO 11843-7 is applicable to estimate repeatability in a UHPLC-UV system. In a similar way, we found that the RSD of the peak area obtained from a chromatogram with noise filter processing in UHPLC-UV could also be estimated by the ISO 11843-7. In conclusion, we experimentally demonstrate that short measurement time and noise filter processing are not limitations for repeatability assessment based on the ISO 11843-7.

A simple method for daily inspections of gas chromatography-mass spectrometry systems with an instrumental detection limit as an indicator.

The purpose of this paper is to propose a simple method for daily inspections of a gas chromatography-mass spectrometry (GC-MS) system with an instrumental detection limit (IDL) as an indicator. A definition of DLs by ISO is 3.3σ where σ denotes the standard deviation (SD) of blank measurements. Estimation of σ is carried out according to the function of mutual information (FUMI) theory and actually with commercial software (TOCO19). An IDL which is a combination of a signal area, width and noise level is concluded to be a good indicator for daily inspections compared with each of its constituents. Methyl stearate is used as a standard material for the daily inspection of a programmed-temperature GC-MS system. A short chromatogram of 1800 data points (1.5 min) containing a target signal and background noise is fit for the IDL prediction by TOCO19. The relative SDs (RSDs) based on the theoretically estimated σ are shown to coincide with statistical results from repeated measurements within 95% confidence intervals. Column temperature is observed to affect IDLs through background fluctuation and then temperature-IDL relationship is examined in a range from 170 to 270 °C. Actual daily inspections over a month are demonstrated.

Chemometric evaluation of repeatability of internal standard methods in high-performance liquid chromatography with a Japanese pharmacopoeia assay for indomethacin as an example.

The purpose of this study is to elucidate uncertainty structures of internal standard (IS) methods as compared with absolute calibration methods in liquid chromatography. A quantitative test of indomethacin with butyl 4-hydroxybenzoate as an IS in high-performance liquid chromatography with ultra-violet detection is taken here as an example. The repeatability is evaluated by both a usual statistical method of repetition and a theoretical approach, called the function of mutual information (FUMI) theory. The latter predicts the precision from noise and signals of instrumental output. Plots of relative standard deviations (RSDs) of measurements against analyte amounts, called precision profiles, are compared between the IS methods for indomethacin and their corresponding absolute calibration methods over a wide range of amount. Sample injection errors are observed to be effectively eliminated at high amounts by the IS methods, but at low amounts where background random noise dominates over the other error, the superiority of the IS methods is overshadowed and the precision of both the methods is almost comparable. The smallest possible amount of IS material without spoiling the integrity of analysis is estimated from the precision profiles.

An automated assessment system of limits of detection and quantitation in gradient high-performance liquid chromatography with ultraviolet detection.

A previous paper of this series of study put forward a basic model of an automated system for predicting detection limits and showed its application to a simple example of isocratic high-performance liquid chromatography (HPLC). This paper describes an expansion of the basic system into gradient HPLC. The most serious problem with the expansion is a long-term variation in backgrounds, called gradient baseline drifts, which in theory cannot be covered by a noise model (stationary random process) of the original system. This paper demonstrates that the above problem can be solved with modifying a parametrization procedure of the noise model. The essential role of the system is to predict the standard deviation (SD) of measurements at low concentrations from a chromatogram without repeated measurements of real samples. Laboratory-made software enables the automated assessment of the limits of detection and quantitation for each of chromatographically separated signals in a single run. Simulated background noise which consists of the stationary noise model with linear slopes is used to confirm the accuracy and reproducibility of the automated prediction. A gradient HPLC determination for cefaclor is taken as an example. The parametrization modification improves the correlation coefficient, r2, between the observed and theoretical distributions of the area measurements from 0.373 to 0.966. The statistical confidence levels of the theoretically predicted relative SDs for cefaclor were verified by comparing them with those obtained by repeated experiments (r2 = 0.989). The limits of detection (= 3.3 × SD = 18.0 µg/L) and quantitation (= 10 × SD = 54.7 µg/L) for cefaclor have signal-to-noise ratios close to the commonly adopted values, 3 and 10, respectively.

An automated system for predicting detection limit and precision profile from a chromatogram.

This paper presents a basic model of an automated system for predicting the detection limit and precision profile (plot of relative standard deviation (RSD) of measurements against concentration) in chromatography. The fundamental assumption is that the major source of response errors at low sample concentrations is background noise and at high concentrations, it is the volumes injected into an HPLC system by a sample injector. The noise is approximated by the mixed random processes of the first order autoregressive process AR(1) and white noise. The research procedures are: (1) the description of the standard deviation (SD) of measurements in terms of the parameters of the mixed random processes; (2) the algorithm for the parameter estimation of the mixed processes from actual background noise; (3) the mathematical distinction between noise and signal in a chromatogram. When compounds are chromatographically separated, each obtained signal is given the detection limit and precision profile on laboratory-made software. A file of a chromatogram is the only requirement for the theoretical prediction of measurement uncertainty and therefore the repeated measurements of real samples can be dispensed with. The theoretically predicted RSDs are verified by comparing them with the statistical RSDs obtained by repeated measurements. Signal shapes on noise are illustrated at the detection limit and quantitation limit, the signal-to-noise ratios of which are close to the widely adopted values, 3 and 10, respectively.

Chemometric Evaluation of Repeatability Using the Autocorrelation Method in High-Performance Liquid Chromatography with Ultraviolet Detection.

The mixed random processes of the first order autoregressive process (AR(1)) and white noise have been proved to provide a good approximation of baseline noise in a variety of analytical instruments, and may therefore be useful for estimating precision profiles. This study aims to examine a recently proposed autocorrelation method for estimating three noise parameters involved in the mixed processes (two for AR(1) and one for white noise) of HPLC, which can then be used to calculate the precision profile. This chemometric method was applied to repeatability evaluations of estriol determination using HPLC with UV detection (HPLC-UV). The relative standard deviations (RSDs) of peak area measurements for 5.0 mg/L estriol were observed to be 1.42% for the autocorrelation method and 1.63% for actual repeated measurements of real samples (n = 6). The theoretical RSDs of the autocorrelation method fell within the 95% confidence intervals of the repeated measurements. It is found that the noise parameters are obtained from real chromatographic baseline via the autocorrelation method. Moreover, the instrumental detection limit of estriol based on ISO 11843 was obtained from the precision profile (plot of RSD of measurements against concentration). This is the first paper to describe the autocorrelation method is a practically useful technique for evaluating the precision profile of HPLC-UV analyses without recourse to the repeated measurements of real samples.

Assessment of Repeatability in Supercritical Fluid Chromatography with Electrochemical Detection Based on the ISO 11843 Part 7.

The present study proposes a method for the assessment of repeatability in supercritical fluid chromatography with electrochemical detection (SFC-ECD), based on the ISO 11843 part 7 (ISO 11843-7:2018) which can theoretically provide detection limits and standard deviation (S.D.) through the stochastic properties of baseline noise without repetitive measurements of real samples. On the baseline noise of SFC-ECD, large-amplitude and periodic noises with less than 0.05 Hz were observed, and the power spectrum of the baseline noise showed 1/f fluctuation (f = frequency). It was found that the present power spectrum analysis, according to the law of error propagation, can provide suitable noise parameters to calculate S.D. of baseline noise and a relative S.D. (RSD) of peak area by ISO 11843-7. The chromatographic determinations of α-, ß-, γ- and δ-tocopherol have been taken as examples. In the present SFC-ECD, the RSDs of peak areas for α-, ß-, γ- and δ-tocopherol obtained by ISO 11843-7 were within 95% confidence intervals of the RSD of them obtained by repetitive measurements (n = 6). Thus, we found that ISO 11843-7 is applicable to the assessment of repeatability in SFC-ECD for determining tocopherols without repetitive measurements.

Theoretical repeatability assessment without repetitive measurements in gradient high-performance liquid chromatography.

This paper puts forward a time and material-saving method for evaluating the repeatability of area measurements in gradient HPLC with UV detection (HPLC-UV), based on the function of mutual information (FUMI) theory which can theoretically provide the measurement standard deviation (SD) and detection limits through the stochastic properties of baseline noise with no recourse to repetitive measurements of real samples. The chromatographic determination of terbinafine hydrochloride and enalapril maleate is taken as an example. The best choice of the number of noise data points, inevitable for the theoretical evaluation, is shown to be 512 data points (10.24s at 50 point/s sampling rate of an A/D converter). Coupled with the relative SD (RSD) of sample injection variability in the instrument used, the theoretical evaluation is proved to give identical values of area measurement RSDs to those estimated by the usual repetitive method (n=6) over a wide concentration range of the analytes within the 95% confidence intervals of the latter RSD. The FUMI theory is not a statistical one, but the "statistical" reliability of its SD estimates (n=1) is observed to be as high as that attained by thirty-one measurements of the same samples (n=31).

Determination of Detection Limits and Quantitation Limits for Compounds in a Database of GC/MS by FUMI Theory.

The aim of this paper is to propose a stochastic method for estimating the detection limits (DLs) and quantitation limits (QLs) of compounds registered in a database of a GC/MS system and prove its validity with experiments. The approach described in ISO 11843 Part 7 is adopted here as an estimation means of DL and QL, and the decafluorotriphenylphosphine (DFTPP) tuning and retention time locking are carried out for adjusting the system. Coupled with the data obtained from the system adjustment experiments, the information (noise and signal of chromatograms and calibration curves) stored in the database is used for the stochastic estimation, dispensing with the repetition measurements. Of sixty-six pesticides, the DL values obtained by the ISO method were compared with those from the statistical approach and the correlation between them was observed to be excellent with the correlation coefficient of 0.865. The accuracy of the method proposed was also examined and concluded to be satisfactory as well. The samples used are commercial products of pesticides mixtures and the uncertainty from sample preparation processes is not taken into account.

[Estimation of the Health Status of People in the Vicinity of Pharmacies Using Pharmacy Big Data].

The purpose of this study was to propose a method for visualizing the patterns of the geographical propagation of influenza infection, and to elaborate parameters for the characterization of these patterns. First, a motion picture was prepared for the quotidian propagation of influenza infection in the Greater Tokyo Metropolitan area, which is considered a typical epidemic area for the 2012/2013 flu season. Second, hebdomadal recordings of patients with influenza infection in the 47 prefectures of Japan were grouped into 3 categories (1-peak, 2-peak, or multi-peak). The prefectures were arranged according to the weeks with the maximum number of patients, to examine variations in the temporal infection order of the districts among the flu seasons. These characteristics were analyzed using Cramer's coefficient of association and Spearman's rank correlation coefficient. Finally, the propagation of influenza infection was compared between urban and remote areas: the Greater Tokyo Metropolitan area and Tochigi prefecture. Regarding influenza virus infection, differences in population density, public transportation systems, and lifestyles between the urban and rural areas were found to lead to distinct endemic patterns of infection. Emphasis was placed on the so-called big data hubris.

Evaluation of Measurement Precision from Stationary Baseline Noise in Instrumental Analyses.

This paper provides two approaches to estimate the standard deviation of measurements from baseline noise in instrumental output when (i) in theory, the noise can be approximated by a well-established random process in statistics and mathematics, referred to as a stationary process and (ii) in practice, the baseline noise is the predominant source of measurement error. For the first approach proposed, a general evaluation equation for measurement precision, when the baseline noise can be treated as a stationary process, is derived as a function of the process autocorrelations and process variance of the noise. In particular, for the second approach, when the baseline noise is a mixed random process of white noise and a first order autoregressive (AR(1)) process, the corresponding equation for the precision is also derived. The equations derived in the present paper include some results published elsewhere as special cases. For illustration, an example is presented.

Repeatability Assessment by ISO 11843-7 in Quantitative HPLC for Herbal Medicines.

We have proposed an assessment methods to estimate the measurement relative standard deviation (RSD) of chromatographic peaks in quantitative HPLC for herbal medicines by the methodology of ISO 11843 Part 7 (ISO 11843-7:2012), which provides detection limits stochastically. In quantitative HPLC with UV detection (HPLC-UV) of Scutellaria Radix for the determination of baicalin, the measurement RSD of baicalin by ISO 11843-7:2012 stochastically was within a 95% confidence interval of the statistically obtained RSD by repetitive measurements (n = 6). Thus, our findings show that it is applicable for estimating of the repeatability of HPLC-UV for determining baicalin without repeated measurements. In addition, the allowable limit of the "System repeatability" in "Liquid Chromatography" regulated in a pharmacopoeia can be obtained by the present assessment method. Moreover, the present assessment method was also successfully applied to estimate the measurement RSDs of quantitative three-channel liquid chromatography with electrochemical detection (LC-3ECD) of Chrysanthemi Flos for determining caffeoylquinic acids and flavonoids. By the present repeatability assessment method, reliable measurement RSD was obtained stochastically, and the experimental time was remarkably reduced.

Selection of the optimal solvent grade for the mobile phase in HPLC with electrochemical detection based on FUMI theory.

The optimum conditions of the mobile phase for HPLC with electrochemical detection (HPLC-ECD) were selected from among solvents of different grades with the standard deviation (SD) of area measurements based on FUMI (function of mutual information) theory as a criterion. In HPLC-ECD for determining baicalin and baicalein using a phosphoric acid-methanol-water mixture (0.5:60:40, v/v/v) as a mobile phase, the effects of three grades of phosphoric acid, of five grades of methanol, and of seven grades of water on the measurement precision were examined. The mixture, if characterized by the minimum SD of measurements, was selected as the optimal mobile phase. This selection method saves considerable amounts of chemicals and experimental time, and would be a useful exploration technique for the routine check and troubleshooting of HPLC-ECD.

Detection limit used for early warning in public health surveillance.

A theory of detection limit, developed in analytical chemistry, is applied to public health surveillance to detect an outbreak of national emergencies such as natural disaster and bioterrorism. In this investigation, the influenza epidemic around the Tokyo area from 2003 to 2006 is taken as a model of normal and large-scale epidemics. The detection limit of the normal epidemic is used as a threshold with a specified level of significance to identify a sign of the abnormal epidemic among the daily variation in anti-influenza drug sales at community pharmacies. While auto-correlation of data is often an obstacle to an unbiased estimator of standard deviation involved in the detection limit, the analytical theory (FUMI) can successfully treat the auto-correlation of the drug sales in the same way as the auto-correlation appearing as 1/f noise in many analytical instruments.

Optimization of capillary liquid chromatography with electrochemical detection for determining femtogram levels of baicalin and baicalein on the basis of the FUMI theory.

Capillary liquid chromatography with electrochemical detection (CLC-ECD) was developed for determining the femtogram levels of baicalin and baicalein. The CLC-ECD system and the experimental conditions were optimized based on the precision (=information content) phi and efficiency (=information content/time) theta, which were calculated from a relative standard deviation (R.S.D.) by a chemometric tool called the FUMI theory. When CLC-ECD was established using a capillary column (Inertsil ODS-3, 150 mm x 0.2 mm i.d.), a sample injector fitted with a 0.2 microL injection loop, an applied potential of +650 mV vs. Ag/AgCl, and a flow rate at 1.8 microL/min, baicalin and baicalein were determined at femtogram levels. Moreover, the present method was validated using a chemometric tool and a conventional method. Since the FUMI theory makes it possible to predict R.S.D. without repetitive measurements, the chemometric tool saves considerable amounts of chemicals and experimental time, and was found to be useful for the optimization of conditions and validation for determination by CLC-ECD. The present method was applied to the analysis of Japanese Pharmacopoeia Scutellaria Root and Scutellaria baicalensis Georgi for determining baicalin and baicalein.

Detection limit of measurement of pharmaceuticals labeled with short-lived isotopes in HPLC with flow-through gamma-counter.

This paper proposes a method for estimating the detection limit, which is defined as 3.3 times the standard deviation (S.D.) of blank measurements under the situations where the repetition of measurement is difficult or impossible because of a short half-life of radioactivity. The FUMI theory, which can estimate an S.D. value without repetition in various instrumental analyses, is adopted and proved here to be available in a radio-HPLC system as well. (99m)Tc-ECD (T(1/2)=360.6 min) that is a lipophilic compound for the diagnosis of regional brain perfusion is taken as an example.

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.