Improving signal-to-noise ratios of liquid chromatography-tandem mass spectrometry peaks using noise frequency spectrum modification between two consecutive matched-filtering procedures

This paper reports a simple chemometric technique to alter the noise spectrum of liquid chromatography-tandem mass spectrometry (LC-MS-MS) chromatogram between two consecutive matched filter procedures to improve the peak signal-to-noise (S/N) ratio enhancement. This technique is to multiply one match-filtered LC-MS-MS chromatogram with another artificial chromatogram added with thermal noises prior to the second matched filter. Because matched filter cannot eliminate low-frequency components inherent in the flicker noises of spike-like sharp peaks randomly riding on LC-MS-MS chromatograms, efficient peak S/N ratio improvement cannot be accomplished using one-step or consecutive matched filter procedures to process LC-MS-MS chromatograms. In contrast, when the match-filtered LC-MS-MS chromatogram is conditioned with the multiplication alteration prior to the second matched filter, much better efficient ratio improvement is achieved. The noise frequency spectrum of match-filtered chromatogram, which originally contains only low-frequency components, is altered to span a boarder range with multiplication operation. When the frequency range of this modified noise spectrum shifts toward higher frequency regime, the second matched filter, working as a low-pass filter, is able to provide better filtering efficiency to obtain higher peak S/N ratios. Real LC-MS-MS chromatograms containing random spike-like peaks, of which peak S/N ratio improvement is less than four times with two consecutive matched filters typically, are remedied to accomplish much better ratio enhancement approximately 16-folds when the noise frequency spectrum is modified between two matched filters.     

Improving liquid chromatography–tandem mass spectrometry determinations by modifying noise frequency spectrum between two consecutive wavelet-based low-pass filtering procedures

This paper employs one chemometric technique to modify the noise spectrum of liquid chromatography–tandem mass spectrometry (LC–MS/MS) chromatogram between two consecutive wavelet-based low-pass filter procedures to improve the peak signal-to-noise (S/N) ratio enhancement. Although similar techniques of using other sets of low-pass procedures such as matched filters have been published, the procedures developed in this work are able to avoid peak broadening disadvantages inherent in matched filters. In addition, unlike Fourier transform-based low-pass filters, wavelet-based filters efficiently reject noises in the chromatograms directly in the time domain without distorting the original signals. In this work, the low-pass filtering procedures sequentially convolve the original chromatograms against each set of low pass filters to result in approximation coefficients, representing the low-frequency wavelets, of the first five resolution levels. The tedious trials of setting threshold values to properly shrink each wavelet are therefore no longer required. This noise modification technique is to multiply one wavelet-based low-pass filtered LC–MS/MS chromatogram with another artificial chromatogram added with thermal noises prior to the other wavelet-based low-pass filter. Because low-pass filter cannot eliminate frequency components below its cut-off frequency, more efficient peak S/N ratio improvement cannot be accomplished using consecutive low-pass filter procedures to process LC–MS/MS chromatograms. In contrast, when the low-pass filtered LC–MS/MS chromatogram is conditioned with the multiplication alteration prior to the other low-pass filter, much better ratio improvement is achieved. The noise frequency spectrum of low-pass filtered chromatogram, which originally contains frequency components below the filter cut-off frequency, is altered to span a broader range with multiplication operation. When the frequency range of this modified noise spectrum shifts toward the high frequency regimes, the other low-pass filter is able to provide better filtering efficiency to obtain higher peak S/N ratios. Real LC–MS/MS chromatograms, of which typically less than 6-fold peak S/N ratio improvement achieved with two consecutive wavelet-based low-pass filters remains the same S/N ratio improvement using one-step wavelet-based low-pass filter, are improved to accomplish much better ratio enhancement 25-folds to 40-folds typically when the noise frequency spectrum is modified between two low-pass filters. The linear standard curves using the filtered LC–MS/MS signals are validated. The filtered LC–MS/MS signals are also reproducible. The more accurate determinations of very low concentration samples (S/N ratio about 7–9) are obtained using the filtered signals than the determinations using the original signals.     

Optimisation of data handling and detection conditions for automated chromatographic assay software

Summary The principle of automated chromatographic peak detection and analysis software is summarized, and critical steps are systematically studied. As the only parameter to be entered is the acquisition frequency, evaluation of its effect on software performance is discussed. In the case of relatively noisy chromatograms, it is shown experimentally that numerous points per peak have to be taken, leading to quite fast computer acquisition procedures. The use of discrete Fourier transform filtration techniques can modify peak shapes and a comparative study evaluates the relative errors induced in the shapes and characteristics of the chromatographic profiles. Optimisation of filtering conditions is achieved and it is shown that for a filter position only 2% of the Nyquist frequency no deformation occurs in the chromatographic profile. Detection of the start and finish of chromatographic peaks is optimized according to a simple four step iterative procedure. In the case of simulations, the difference between the values used to simulate peaks and those calculated by the software are less than 1%.     

High-throughput automated post-processing of separation data

The development of an efficient method for high-throughput analysis of multiple electropherograms or chromatograms collected in series is presented. The method, encoded in a computer program designated "Cutter", utilizes batch processing for determining chromatographic figures of merit (CFOM) including peak centroid times, heights, areas, signal-to-noise ratios (S/N), variance (sigma2), skew, excess, and plate number (N) across a set of separations collected serially. The software was validated using simulated data with varying S/N, skew, and excess. The accuracy of the analysis was comparable to or improved over commercial software with area calculation relative errors (RE) below 5% for simulated data with S/N = 5. File sets containing 1300 electropherograms were analyzed in 5 min, representing a nearly 200-fold reduction in analysis time from other methods. Incorporated within the program is a novel method for automated peak deconvolution using an Empirically Transformed Gaussian function. Area measurements of deconvoluted peaks were within 3% of the true value of a simulated data set with S/N = 5 and resolution (R(S)) = 1 for equivalent peaks, and within 10% when the ratio of the overlapped peak heights was 10:1.     

Application of the stochastic resonance algorithm to the simultaneous quantitative determination of multiple weak peaks of ultra-performance liquid chromatography coupled to time-of-flight mass spectrometry

The stochastic resonance algorithm (SRA) has been developed as a potential tool for amplifying and determining weak chromatographic peaks in recent years. However, the conventional SRA cannot be applied directly to ultra-performance liquid chromatography/time-of-flight mass spectrometry (UPLC/TOFMS). The obstacle lies in the fact that the narrow peaks generated by UPLC contain high-frequency components which fall beyond the restrictions of the theory of stochastic resonance. Although there already exists an algorithm that allows a high-frequency weak signal to be detected, the sampling frequency of TOFMS is not fast enough to meet the requirement of the algorithm. Another problem is the depression of the weak peak of the compound with low concentration or weak detection response, which prevents the simultaneous determination of multi-component UPLC/TOFMS peaks. In order to lower the frequencies of the peaks, an interpolation and re-scaling frequency stochastic resonance (IRSR) is proposed, which re-scales the peak frequencies via linear interpolating sample points numerically. The re-scaled UPLC/TOFMS peaks could then be amplified significantly. By introducing an external energy field upon the UPLC/TOFMS signals, the method of energy gain was developed to simultaneously amplify and determine weak peaks from multi-components. Subsequently, a multi-component stochastic resonance algorithm was constructed for the simultaneous quantitative determination of multiple weak UPLC/TOFMS peaks based on the two methods. The optimization of parameters was discussed in detail with simulated data sets, and the applicability of the algorithm was evaluated by quantitative analysis of three alkaloids in human plasma using UPLC/TOFMS. The new algorithm behaved well in the improvement of signal-to-noise (S/N) compared to several normally used peak enhancement methods, including the Savitzky-Golay filter, Whittaker-Eilers smoother and matched filtration.     

A software package for the orthogonal polynomial approximation of analytical signals,including a simulation program for chromatograms and spectra

The computer package calculates the coefficients of the terms of orthogonal polynomial series used to approximate the analytical signal. Two different polynomial series (Hermite and Chebyshev) are used, depending on the number of peaks and spreading of the error of the approximation over the interval. The package is applied for data reduction and filtering of the analytical signal. Part of the package facilitates optimization in chromatography, by calculating the effect of varying chromatogram parameters on polynomial terms. Some scaling methods for the analytical signal are discussed. For testing purposes, a program that generates chromatograms is added to the computer package. The program simulates chromatographic peaks with user-defined peak parameters; noise can be added. The theoretical background is described and some results are presented.     

自适应形态滤波器用于色谱信号的处理

建立了一种能自适应地调整尺度的形态滤波器对色谱信号中混杂的离散冲型噪声加以滤除的方法。结果表明,自适应形态滤波器在滤除脉冲型噪声进,比目前文献报道的中值滤波方法呈现出更好的效果,它能保存高度完整的信号信息,是处理色谱信号脉冲型噪声的有力工具。     

Combined Kalman filtering and steepest descent minimization for quantitative analysis of unresolved misaligned chromatographic peaks. The resolution of alternariol and altenuisol mycotoxins in mixtures by HPLC

Summary The potential of a computational approach for the quantitative resolution of seriously overlapping chromatographic peaks when there is loss of collinearity between the pure component peaks and the mixture peak has been explored. The program makes iterative use of the Kalman filter algorithm for resolving the mixture peak with the component peaks aligned according to some values of the position parameters, and of a steepest descent minimization procedure to find the optimal alignment. This combined procedure has been applied to the quantitive resolution of the HPLC chromatograms of alternariol and altenuisol mycotoxins in synthetic mixtures and in real samples.     

Application of static signal-to-noise theory to the detection and integration of dynamic signals

Static, time-independent noise terms are combined to estimate the noise and signal-to-noise ratio (S/N) of dynamic, time-dependent methods. Simplified S/N equations for shot-noise-limited and flicker-noise-limited analyte signals with and without background signal noises are given. The intuitive aspects of peak integration are justified by these equations. For an ideal Gaussian peak, the equations are used to derive the chromatographic limit of detection (LOD). A comparison of the chromatographic detection limit with the detection limit for a static system using the same amount of sample predicts poorer chromatographic detection limits because of peak broadening. A possible determinate error in area measurement is shown to result when integration limits are chosen on the basis of the static detection limit.     

Matched filtering with background suppression for improved quality of base peak chromatograms and mass spectra in liquid chromatography-mass spectrometry

A time domain filter that combines the properties of matched filtering and two-fold differentiation is presented. The filter coefficients are given by the second derivative of a Gaussian model peak, controlled by the setting of two parameters related to the chromatographic system. The fundamental characteristics of the filter were derived, and its applicability demonstrated for real liquid chromatography-mass spectrometry (LC-MS) data. The filter is primarily intended as a fast pre-processing step, for a mass chromatogram with 320 scans over 700 mass channels the computation time was 0.6 s on a standard PC. Base peak chromatograms with improved peak detection capability and mass spectra useful for compound identification were obtained with filtered data. The most significant effect of the described filter is background reduction due to the differentiation, which in combination with the matched filter can be performed with maintained or even improved signal-to-noise ratio.     

Semi-automated alignment and quantification of peaks using parallel factor analysis for comprehensive two-dimensional liquid chromatography–diode array detector data sets

Parallel factor analysis was used to quantify the relative concentrations of peaks within four-way comprehensive two dimensional liquid chromatography–diode array detector data sets. Since parallel factor analysis requires that the retention times of peaks between each injection are reproducible, a semi-automated alignment method was developed that utilizes the spectra of the compounds to independently align the peaks without the need for a reference injection. Peak alignment is achieved by shifting the optimized chromatographic component profiles from a three-way parallel factor analysis model applied to each injection. To ensure accurate shifting, components are matched up based on their spectral signature and the position of the peak in both chromatographic dimensions. The degree of shift, for each peak, is determined by calculating the distance between the median data point of the respective dimension (in either the second or first chromatographic dimension) and the maximum data point of the peak furthest from the median. All peaks that were matched to this peak are then aligned to this common retention data point. Target analyte recoveries for four simulated data sets were within 2% of 100% recovery in all cases. Two different experimental data sets were also evaluated. Precision of quantification of two spectrally similar and partially coeluting peaks present in urine was as good as or better than 4%. Good results were also obtained for a challenging analysis of phenytoin in waste water effluent, where the results of the semi-automated alignment method agreed with the reference LC–LC MS/MS method within the precision of the methods.     

计算机快速富里叶变换应用于气相色谱痕量分析

将计算机快速富里叶变换(FFT)应用于高分辨率气相色谱痕量分析中，以增加色谱峰的S／N比(信号与噪声比)，提高分析精度，对S／N非常低的色谱峰采用的这种计算机快速富里叶变换平滑新方法，可以提取出几乎被噪声淹没的色谱信号，使S／N比提高12倍以上，而色谱峰面积误差非常小。     

Peak alignment using wavelet pattern matching and differential evolution

Retention time shifts badly impair qualitative or quantitative results of chemometric analyses when entire chromatographic data are used. Hence, chromatograms should be aligned to perform further analysis. Being inspired and motivated by this purpose, a practical and handy peak alignment method (alignDE) is proposed, implemented in this research for one-way chromatograms, which basically consists of five steps: (1) chromatogram lengths equalization using linear interpolation; (2) accurate peak pattern matching by continuous wavelet transform (CWT) with the Mexican Hat and Haar wavelets as its mother wavelets; (3) flexible baseline fitting utilizing penalized least squares; (4) peak clustering when gap of two peaks is smaller than a certain threshold; (5) peak alignment using differential evolution (DE) to maximize linear correlation coefficient between reference signal and signal to be aligned. This method is demonstrated with both simulated chromatograms and real chromatograms, for example, chromatograms of fungal extracts and Red Peony Root obtained by HPLC-DAD. It is implemented in R language and available as open source software to a broad range of chromatograph users (http://code.google.com/p/alignde).     

An automatic peak finding method for LC‐MS data using Gaussian second derivative filtering

A highly automated procedure for localising and characterising peaks in the chromatographic time domain of LC‐MS data has been developed. The work was initiated by an identified need to facilitate the detection and tracking of chromatographic peaks during method development for the analysis of impurities in pharmaceutical products. The algorithm is mainly based on a digital filter for which the settings are automatically adapted to the data set under study. The procedure was evaluated for synthetic data sets with various S/N levels, peak widths and baseline properties. It was found that even for the worst case tested with S/N=10 and a high variability in the baseline, 94% of the simulated analytical peaks could be detected without producing any false‐positive identifications. Furthermore, the number of correctly estimated peak heights and peak widths falling within a 10% error of the true values were 94 and 91%, respectively. For experimental data sets, peak height, and width estimations were more difficult, but the processed reconstructions showed an excellent agreement with the analytical signals of the raw data, and also a clearly improved visualisation in total ion‐ and base‐peak chromatograms.     

基于分形维数的分析信号自适应中值滤波

提出一种面向分析仪器谱图信号处理的分形维自适应中值波方法（AMeFFD）。该法延拓运用分形理论，定义了相对点盒维数概念，由此建立建立判定脉冲型噪声的特异性指标，从而可自动调节中值滤波窗口宽度，有效地滤除脉冲型噪声及其它类噪声。对仿真色谱信号及实测色谱图的处理结果表明：AMeFFD法克服了经典中值滤波算法的缺陷，无论在信号的均方根偏差还是谱峰差等指标上，均明显优于后者，能在确保谱峰不畸变的同时更有效地滤除脉冲型常见噪声，是处理化学谱图信号的有力工具。     

Segmented post-column analyte addition; a concept for continuous response control of liquid chromatography/mass spectrometry peaks affected by signal suppression/enhancement

A novel technique, "segmented post-column analyte addition", is proposed to visualize and compensate signal suppression/enhancement effects in electrospray ionization tandem mass spectrometry (ESI-MS/MS). Instead of delivering a constant flow of analyte solution between the liquid chromatography (LC) column exit and the ESI interface into the eluent resulting from LC separation of analyte-free matrix in order to determine retention time widows in which suppression/enhancement is unimportant (King et al., J. Am. Soc. Mass Spectrom. 2000; 11: 942), segmented packets of analyte-containing solvent and analyte-free solvent were infused into an LC eluent resulting from separation of an analyte-containing sample. The obtained, superimposed, periodic spikes are much narrower than the analyte peak eluting from the column. The height of the spikes is affected by signal suppression phenomena to the same extent as the analyte signal, and hence variations of the spike height can be used to correct the peak area of analyte peaks affected by signal suppression/enhancement.     

Interpretation on Band‐Broadening in Chromatography with Spatial Peak Profiles Obtained Using Whole‐Column Detection

Fifteen liquid chromatographic experiments were investigated using a whole‐column detection (WCD) system and a conventional post‐column UV/Vis detector. The peak widths obtained from chromatograms were found dependent on the retention factor; the larger the retention factor was the greater the peak width. However, the on‐column spatial peak widths were dependent on the locations where they were measured in the column. The peak widths monitored at 17 cm from the column inlet were found essentially the same no matter what their retention factors were. In addition, a linear relationship was found between the chromatographic peak width and the reciprocal of the average linear rate of the solute migration. The peak widths on chromatograms did not reflect how they appeared in the column; instead, the widths were determined by the solute speed passing the detector.     

自适应中值滤波用于色谱信号去噪的研究

在分析化学领域中，如何从被干扰的信号中有效去除噪声并恢复有用信号，具有重要的意义。此文从中值滤波基本概念出发，针对经典中值滤波器滑动窗口长度固定对信号去噪的影响，提出了自适应中值滤波器，通过对某元素色谱曲线进行去噪处理，并与移动均值法和小波变换法进行比较表明，此方法不仅能有效地滤除脉冲和高斯噪声，而且使色谱峰的边缘得到良好保护，从而提高了色谱数据分析的精确性。     

Enhancement of Signal-to-Noise Ratios in Capillary Gas Chromatography by Using a Longitudinally Modulated Cryogenic System

A Longitudinally Modulated Cryogenic System (LMCS) was evaluated for its use in detection enhancement in capillary gas chromatography. The mechanism for chromatographic re-elution for the LMCS is substantially different to other cryogenic devices. The cooled region of the capillary column in which chromatographic bands may be focused is heated by the surrounding oven temperature either by moving the trap along the column, or by moving the column out of the trap. By continually modulating the LMCS at the detector end of the capillary column, signal-to-noise ratios of routine chromatograms can be readily increased by a factor of ten, thus enhancing chromatographic detection. Base widths of peaks, which are often about 2–3 s or more can be easily reduced to 0.3 s when the LMCS is employed in the detection enhancement mode, thus offering a simple avenue to improved peak height sensitivity in capillary gas chromatography.     

Deconvolution method for accurate determination of overlapping peak areas in chromatograms.

A method is described for deconvoluting chromatograms which contain overlapping peaks. Parameters can be selected to ensure that attenuation of peak areas is uniform over any desired range of peak widths. A simple extension of the method greatly reduces the negative overshoot frequently encountered with deconvolutions. The deconvoluted chromatograms are suitable for integration by conventional methods.