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.     

Parametric studies of matched filters to enhance the signal-to-noise ratios of LC-MS-MS peaks

Chromatographic parameters of reference signals employed in matched filter methods have been studied using numerical experiments to improve the signal-to-noise (S/N) ratios of small liquid chromatography (LC) peaks obtained with electrospray tandem mass spectrometers (MS-MS). These parameters include the width, shape, and S/N ratios of chromatographic peaks used as the reference signal profiles. Our results show the effect of reference peak widths on improving the S/N ratio of chromatographic peaks; the influence of reference peak shapes is negligible. To verify simulation results, various reference signals, including analyte peaks of high concentration standards, internal standard peaks, and artificial Gaussian peaks of different widths, have been employed to enhance signal peaks on real liquid chromatography-tandem mass spectrometry (LC-MS-MS) chromatograms via matched filter methods. Our experimental results demonstrate that the S/N ratio enhancement of chromatographic peaks agree with the simulation predictions. These findings, therefore, suggest that regardless of peak shape, a well-smooth peak with a width close to that of the analyte peak is an adequate reference signal, when matched filter methods are used to improve LC-MS-MS chromatograms. Nevertheless, all methods processed LC-MS-MS peaks in this study do not achieve the ideal improvement ratios estimated with simulation results. We attribute this deficiency to spike-like noise, which have considerable low frequency components riding on LC-MS-MS chromatograms. Matched filtering, which works as a low-pass filter in the frequency domain, cannot effectively eliminate low frequency flicker noise contributed by these spikes. In addition, simple median filtering does not provide adequate improvement despite being able to smooth out most spikes in the chromatograms.     

Tailoring noise frequency spectrum to improve NIR determinations

Near infrared spectroscopy (NIR) contains excessive background noise and weak analytical signals caused by near infrared overtones and combinations. That makes it difficult to achieve quantitative determinations of low concentration samples by NIR. A simple chemometric approach has been established to modify the noise frequency spectrum to improve NIR determinations. The proposed method is to multiply one Savitzky-Golay filtered NIR spectrum with another reference spectrum added with thermal noises before the other Savitzky-Golay filter. Since Savitzky-Golay filter is a kind of low-pass filter and cannot eliminate low frequency components of NIR spectrum, using one step or two consecutive Savitzky-Golay filter procedures cannot improve the determination of NIR greatly. Meanwhile, significant improvement is achieved via the Savitzky-Golay filtered NIR spectrum processed with the multiplication alteration before the other Savitzky-Golay filter. The frequency range of the modified noise spectrum shifts toward higher frequency regime via multiplication operation. So the second Savitzky-Golay filter is able to provide better filtering efficiency to obtain satisfied result. The improvement of NIR determination with tailoring noise frequency spectrum technique was demonstrated by both simulated dataset and two measured NIR spectral datasets. It is expected that noise frequency spectrum technique will be adopted mostly in applications where quantitative determination of low concentration sample is crucial.     

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.     

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。     

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。     

An objective comparison of pre-processing methods for enhancement of liquid chromatography-mass spectrometry data

Four data pre-processing methods have been applied with different settings to data sets obtained from the analysis of a pharmaceutical drug and its degradation products by liquid chromatography-mass spectrometry (LC-MS). The methods compared were the frequently used component detection algorithm (CODA) and three kinds of digital filters--matched filtration (MF), Gaussian second derivative (GSD) and Savitzky-Golay. The aim was to evaluate the performance and robustness of these methods for extracted ion chromatogram (XIC), total ion chromatogram (TIC) and base peak chromatogram (BPC) in the presence of different types of noise. In accordance with theory, the best improvements in signal-to-noise ratio (S/N) of the XICs were obtained with MF under the ideal case with random white noise. However, when highly coloured noise was present, it was found that no improvements in XIC S/N could be obtained with any of the pre-processing methods studied. GSD and CODA did, however, improve the S/N for both TIC and BPC. GSD and CODA also significantly reduced the background in the spectral domain, thereby facilitating the interpretation of the mass spectra. Another advantage associated with CODA and to some extent also with GSD is their data reduction ability.     

The usefulness of the deconvolution of chromatograms into orthogonal polynomials for characterizing the quality of separation

Simulated chromatograms are deconvoluted into series of orthogonal polynomials. The number of terms necessary to achieve a preset goodness of fit, the reproducibility of coefficients in the presence of noise and the effects of signal-to-noise ratio, peak-height ratio and peak asymmetry on the value of coefficients from the deconvolution are investigated. A convenient method for the deconvolution of real chromatograms is described in order to characterize the quality of separation in the chromatogram. A known quality criterion is modified by using coefficients from the deconvolution in order to enhance its performance. Performance is tested on a simulated separation of five sulfa drugs on a reversed- phase column.     

Inverse Optimal Filtering Method for the Instrumental Spreading Correction in Size Exclusion Chromatography

Abstract

The Kalman filter based techniques are adapted to solve the most general form of Tung's integral formula, i. e. when a non-uniform, non-symmetric calibration model is employed to correct chromatograms obtained in size exclusion chromatography from instrumental broadening errors. Through this method, the inverse smoothing of a chromatogram contaminated with measurement noise of known statistics is optimally performed by minimizing the estimation error variance. The method is numerically very “robust”, improves the signal to noise ratio, provides good validation checks, and does not involve any previous parameter estimation procedure.     

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.     

Monolithic silica columns for high-efficiency chromatographic separations

A deconvolution methodology for overlapped chromatographic signals is proposed. Several single-wavelength chromatograms of binary mixtures, obtained in different runs at diverse concentration ratios of the individual components, were simultaneously processed (multi-batch approach), after being arranged as two-way data. The chromatograms were modelled as linear combinations of forced peak profiles according to a polynomially modified Gaussian equation. The fitting was performed with a previously reported hybrid genetic algorithm with local search, leaving all model parameters free. The approach yielded more accurate solutions than those found when each experimental chromatogram was fitted independently to the peak model (single-batch approach). The improvement was especially significant for those chromatograms where the peaks were severely affected by the tails of the preceding compounds. Peak shifts among chromatograms, which are a usual source of non-bilinearity, were modelled in a continuous domain instead of in a discrete way, which avoided some drawbacks associated with latent variable methods. An experimental design involving simulated chromatograms was applied to check the method performance. Five main factors affecting the deconvolution were examined: concentration pattern, chromatographic resolution, number of batches and replicates, and noise level, which were evaluated using first- and second-order figures of merit. The method was also tested on three real samples containing compounds showing different overlap. Four multi-batch deconvolution methods were considered differing in the nature of the processed information and kind of peak matching among chromatograms. In all cases, the multi-batch deconvolution yielded better performance than the single-batch approach.     

Enhancement of chromatographic detail using infrared spectra from chromatography/infrared spectrometer systems

Working with chromatography/infrared spectroscopy data, the technique of local baseline correction in the calculation of the chromatographic intensities from each spectrum is used to provide improved chromatographic detection. The technique reduces chromatographic baseline drift, and produces broad-band (universal) chromatograms with noise levels approaching those obtained from narrow-band specific chromatograms. Chromatograms produced from the ratio of two selected band chromatograms can quickly profile a trend in a homologous series of compounds, test a chromatographic peak for compositional uniformity, or show shifts in composition across a polymer chromatographic series.     

Wavelet transforms in separation science for denoising and peak overlap detection

Wavelet transform is a versatile time‐frequency analysis technique, which allows localization of useful signals in time or space and separates them from noise. The detector output from any analytical instrument is mathematically equivalent to a digital image. Signals obtained in chemical separations that vary in time (e.g., high‐performance liquid chromatography) or space (e.g., planar chromatography) are amenable to wavelet analysis. This article gives an overview of wavelet analysis, and graphically explains all the relevant concepts. Continuous wavelet transform and discrete wavelet transform concepts are pictorially explained along with their chromatographic applications. An example is shown for qualitative peak overlap detection in a noisy chromatogram using continuous wavelet transform. The concept of signal decomposition, denoising, and then signal reconstruction is graphically discussed for discrete wavelet transform. All the digital filters in chromatographic instruments used today potentially broaden and distort narrow peaks. Finally, a low signal‐to‐noise ratio chromatogram is denoised using the procedure. Significant gains (>tenfold) in signal‐to‐noise ratio are shown with wavelet analysis. Peaks that were not initially visible were recovered with good accuracy. Since discrete wavelet transform denoising analysis applies to any detector used in separation science, researchers should strongly consider using wavelets for their research.     

Validation of a chromatography data analysis software

The performance of chromatography data analysis software packages is of cardinal importance when the precision and the accuracy of a chromatographic system are evaluated. Users cannot rely on a procedure generating chromatographic data of known accuracy. Holistic approaches cannot always be entirely trusted. We propose a new method consisting in validating a data analysis package against computer generated chromatograms of exactly known characteristics by feeding these chromatograms into the vendor supplied software and comparing the results supplied by the software and the exact answers. We simulated symmetrical and tailing chromatograms and processed these signals with the Agilent Technologies (formerly Hewlett-Packard) ChemStation software. The noise profile (i.e. the power spectrum of the baseline) was determined for a HPLC UV detector prior to the calculations, and chromatograms of different signal-to-noise ratios were used for the analysis. For every chromatogram, we simulated 25 replicates with identical signal-to-noise ratios but different noise sequences. In this manner, both the random and the systematic errors of the retention data and peak shape characteristics can be evaluated. When analyzing tailing peaks, we simulated the effects of extra-column band broadening and those of column overload. Our calculations show that the general performance of the data analysis system studied is excellent. The contribution of the random error originating from the data analysis procedure is in most cases negligible compared to the repeatability of the chromatographic measurement itself.     

一种基于光谱信息计算解析的液相色谱滤噪新方法

提出一种基于光谱信息计算解析的高效液相色谱滤噪新方法.对于HPLC/DAD所获得的二维量测数据,取半峰高以上色谱数据点所对应的各列光谱数据进行计算处理,求得在检测波长下的单位标准光谱,并根据光谱维数据与单位标准光谱的关系,采用最小二乘法重构计算求出色谱维数据,从而去除色谱噪声.仿真实验和实测谱图的滤噪结果表明,该方法能有效滤除常见噪声,与中值滤波算法相比较,滤噪性能明显优于后者,是提高色谱定量分析准确度的有力工具.     

小波变换用于高效液相色谱的噪声滤除

根据小波变换将信号分频的性质，用Ｈａａｒ小波成功地解决了高效液相色谱中噪音的扣除问题，并应用于乳酸－稀土络合物体系的色谱数据，得到的色谱曲线平滑且峰位置不变，大葱旁氡群徒档土思觳庀蕖?     

A comparison of some electronic filters for use in noise suppression circuitry of HPLC detectors

Summary Four electronic filters suitable for baseline noise suppression in HPLC detectors were compared for their response and peak distortion characteristics under conventional HPLC conditions. The filters were designed to be white noise equivalent and the types of filter used were lag, lag-lag, critically damped lag and chain, these being representative of common, simple filter configurations. These filters were evaluated for speed of response to an optical step input signal and also for the effects of their level of noise suppression on peak height, retention time, peak asymmetry and apparent column efficiency. The critically damped lag filter was superior to the other filters in almost all respects and its use considerably enhanced detector performance.     

基于小波理论的化学谱图数据自适应滤波方法研究

运用小波理论,利用噪声与真实信号小波变换极大模性态之间的显著差异,提出了一类新的化学谱图数据自适应滤波算法,从根本上突破了现有算法均依据信噪频率特性进行滤波的传统模式.经大量色谱谱图数据处理试验证明,这种算法具有无需设置初始参数,消除人为误差因素对分析计算结果的影响,信噪分离性能好及峰位和峰高保持不变等一系列优点,其鲁棒性、自适应性和谱峰保真度完全符合仪器分析信号处理的要求.     

Reconstructed Mass Spectra,A Novel Approach for the Utilization of Gas Chromatograph—Mass Spectrometer Data

Abstract

Peak profile analysis of each of the few hundred mass chromatograms generated during a complete GC-MS experiment identifies all m/e values which maximize at any of the few hundred consecutive mass spectra recorded during the gas chromatogram. The resulting sets of data correspond to the mass spectrum of each eluting component (even very minor ones) practically free of the contributions of unresolved companion substances, tailing fractions, column bleed, etc. These “reconstructed mass spectra” are therefore more easily interpreted or automatically identified than the mass spectra originally recorded. A plot of the summed abundance of the ions that maximize at a given spectrum index number (“mass resolved gas chromatogram”) results in a gas chromatogram of dramatically improved apparent resolution.     

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.