Time Shift Correction Research Articles

AntDAS-GCMS: A New Comprehensive Data Analysis Platform for GC-MS-Based Untargeted Metabolomics with the Advantage of Addressing the Time Shift Problem.

Over the years, a number of state-of-the-art data analysis tools have been developed to provide a comprehensive analysis of data collected from gas chromatography-mass spectrometry (GC-MS). Unfortunately, the time shift problem remains unsolved in these tools. Here, we developed a novel comprehensive data analysis strategy for GC-MS-based untargeted metabolomics (AntDAS-GCMS) to perform total ion chromatogram peak detection, peak resolution, time shift correction, component registration, statistical analysis, and compound identification. Time shift correction was specifically optimized in this work. The information on mass spectra and elution profiles of compounds was used to search for inherent landmarks within analyzed samples to resolve the time shift problem across samples efficiently and accurately. The performance of our AntDAS-GCMS was comprehensively investigated by using four complex GC-MS data sets with various types of time shift problems. Meanwhile, AntDAS-GCMS was compared with advanced GC-MS data analysis tools and classic time shift correction methods. Results indicated that AntDAS-GCMS could achieve the best performance compared to the other methods.

A SiPM-based dual and triple coincidence system for positron annihilation lifetime measurement

Positron annihilation lifetime (PAL) spectroscopy is a powerful non-destructive method to study defects in materials. Silicon photomultipliers (SiPMs) have emerged as promising photodetector alternatives for PAL systems. However, further research is needed to fully optimize SiPM arrays for PAL applications. In this study, a dual and triple coincidence system has been developed based on four 1 × 4 SiPM arrays with resistor-chain readout, and initial results of PAL measurement have been obtained. A pixel-by-pixel time shift correction method was proposed and successfully applied using triple γ coincidence for summing 128 PAL spectra in one measurement. The system provides position, timing, and energy information for both 1275 and 511 keV γ-rays. The use of SiPM arrays and the pixel-by-pixel time shift correction method have enabled precise and reliable measurements of PALs in single-crystal silicon and yttria-stabilized zirconia samples. The developed SiPM-array-based PAL system also offers a technical solution to measure angular correlations of positron annihilation radiation, with the potential for further improvements.

Spatio-temporal PV power forecasting considering the time-shift correction and the information fusion strategy of multi-stations

Accurate prediction of PV power is essential to ensuring the safe and economic operation of power systems with high PV penetration. The current PV power prediction scheme considering the spatio-temporal correlation characteristics is relatively simple in data processing, resulting in low prediction accuracy; at the same time, the missing data also poses a great problem to the prediction. Therefore, in order to improve the prediction accuracy and solve the problem of missing data, this paper proposes a PV power spatio-temporal prediction model considering time-shift correction and a multi-station information fusion strategy Firstly, relevant power station clusters are constructed using hierarchical clustering, and a similar daily data filtering model considering the variation characteristics of daily power characteristic curves is proposed to filter the data; Secondly, multiple BP neural network models are constructed and multiple reference power stations with high relevance are predicted using irradiance information; Thirdly, the prediction results of multiple reference power stations are input to the data processing module for time-shift analysis and spatial correlation information fusion correction, which solves the missing data problem of the target power station to be predicted. Finally, it is input to One-dimensional Convolutional Neural Network(1DCNN) to achieve the power prediction of the target power station with missing data. The simulation analysis shows that the root mean square error (RMSE) of a sunny day forecast is 3.31%; the RMSE of a non-sunny day forecast is 9.65%, which proves the accuracy of this two-layer neural network is higher compared to other model structures, so the proposed scheme has certain reliability and accuracy in the prediction of PV power with missing data.

Time-lapse seismic imaging using shot gathers with nonrepeatable source wavelets

In time-lapse seismic applications, the signal produced by changes in the properties of subsurface rocks is generally obscured by noise associated with imperfect repeatability between surveys. A particularly important obstacle in the formation of time-lapse difference images is variation in the effective source wavelet between baseline and monitoring data sets. However, the partially separable influence of the wavelet within Green’s function model of seismic data permits two frequency-domain matching filters to be designed, which act to reduce source wavelet nonrepeatability. One is based on the spectral ratio of the baseline and monitoring wavelets and can be applied when prior estimates of the wavelets are available; the other is the average spectral ratio of the baseline and monitoring traces and can be applied when prior estimates are unavailable. After balancing the data sets with either of these filters, we further prepare for the imaging step with time-shift corrections, using a published fast local crosscorrelations algorithm, preparing the difference data for use in an imaging algorithm. Reverse time migration is engaged for the imaging task, but we observe that residual repeatability errors tend to be magnified at this stage when source-normalized crosscorrelation imaging conditions are used. Testing indicates that replacing this with a Poynting vector imaging condition strongly suppresses remaining errors in a robust manner. This includes stability within simulated data environments to noise-free data and data with random noise, up to signal-to-noise ratios of roughly one. Furthermore, our method illustrates better performance when compared with the conventional least-squares matching filter and common-depth-point-domain warping. At present, there is no common workflow for seismic imaging directly using time-lapse shot gathers. Our research contribution lies not only in the two matching filters but also in a novel workflow for time-lapse seismic imaging.

A study of skin marker alignment using different diamond-shaped light fields for prone breast external-beam radiation therapy.

For breast cancer patients treated in the prone position with tangential fields, a diamond-shaped light field (DSLF) can be used to align with corresponding skin markers for image-guided radiation therapy (IGRT). This study evaluates and compares the benefits of different DSLF setups. Seventy-one patients who underwent daily tangential kilovoltage (kV) IGRT were categorized retrospectively into four groups: (1) DSLF field size (FS)=10×10cm2 , gantry angle=90° (right breast)/270° (left breast), with the same isocenter as treatment tangential beams; (2) same as group 1, except DSLF FS=4×4cm2 ; (3) DSLF FS=4×4-6×8cm2 , gantry angle=tangential treatment beam, off-isocenter so that the DSLF was at the approximate breast center; and (4) No-DSLF. We compared their total setup time (including any DSLF/marker-based alignment and IGRT) and relative kV-based couch shift corrections. For groups 1-3, DSLF-only dose distributions (excluding kV-based correction) were simulated by reversely shifting the couch positions from the computed tomography plans, which were assumed equivalent to the delivered dose when both DSLF and IGRT were used. For patient groups 1-4, the average daily setup time was 2.6, 2.5, 5.0, and 8.3min, respectively. Their mean and standard deviations of daily kV-based couch shifts were 0.64±0.4, 0.68±0.3, 0.8±0.6, and 1.0±0.6cm. The average target dose changes after excluding kV-IGRT for groups 1-3 were-0.2%, -0.1%, and +0.4%, respectively, whereas DSLF-1 was most efficient in sparing heart and chest wall, DSLF-2 had lowest lung Dmax ; and DSLF-3 maintained the highest target coverage at the cost of highest OAR dose. In general, the use of DSLF greatly reduces patient setup time and may result in smaller IGRT corrections. If IGRT is limited, different DSLF setups yield different target coverage and OAR dose sparing. Our findings will help DSLF setup optimization in the prone breast treatment setting.

A new platform for untargeted UHPLC-HRMS data analysis to address the time-shift problem

Substantial deviations in retention times among samples pose a great challenge for the accurate screening and identifying of metabolites by ultrahigh-performance liquid chromatography high-resolution mass spectrometry (UHPLC-HRMS). In this study, a coarse-to-refined time-shift correction methodology was proposed to efficiently address this problem. Metabolites producing multiple fragment ions were automatically selected as landmarks to generate pseudo-mass spectra for a coarse time-shift correction. Refined peak alignment for extracted ion chromatograms was then performed by using a moving window-based multiple-peak alignment strategy. Based on this novel coarse-to-refined time-shift correction methodology, a new comprehensive UHPLC-HRMS data analysis platform was developed for UHPLC-HRMS-based metabolomics. Original datasets were employed as inputs to automatically extract and register features in the dataset and to distinguish fragment ions from metabolites for chemometric analysis. Its performance was further evaluated using complex datasets, and the results suggest that the new platform can satisfactorily resolve the time-shift problem and is comparable with commonly used UHPLC-HRMS data analysis tools such as XCMS Online, MS-DIAL, Mzmine2, and Progenesis QI. The new platform can be downloaded from: http://www.pmdb.org.cn/antdas2tsc.

Technical note: Novel triple O<sub>2</sub> sensor aquatic eddy covariance instrument with improved time shift correction reveals central role of microphytobenthos for carbon cycling in coral reef sands

Abstract. The aquatic eddy covariance technique stands out as a powerful method for benthic O2 flux measurements in shelf environments because it integrates effects of naturally varying drivers of the flux such as current flow and light. In conventional eddy covariance instruments, the time shift caused by spatial separation of the measuring locations of flow and O2 concentration can produce substantial flux errors that are difficult to correct. We here introduce a triple O2 sensor eddy covariance instrument (3OEC) that by instrument design eliminates these errors. This is achieved by positioning three O2 sensors around the flow measuring volume, which allows the O2 concentration to be calculated at the point of the current flow measurements. The new instrument was tested in an energetic coastal environment with highly permeable coral reef sands colonised by microphytobenthos. Parallel deployments of the 3OEC and a conventional eddy covariance system (2OEC) demonstrate that the new instrument produces more consistent fluxes with lower error margin. 3OEC fluxes in general were lower than 2OEC fluxes, and the nighttime fluxes recorded by the two instruments were statistically different. We attribute this to the elimination of uncertainties associated with the time shift correction. The deployments at ∼ 10 m water depth revealed high day- and nighttime O2 fluxes despite the relatively low organic content of the coarse sediment and overlying water. High light utilisation efficiency of the microphytobenthos and bottom currents increasing pore water exchange facilitated the high benthic production and coupled respiration. 3OEC measurements after sunset documented a gradual transfer of negative flux signals from the small turbulence generated at the sediment–water interface to the larger wave-dominated eddies of the overlying water column that still carried a positive flux signal, suggesting concurrent fluxes in opposite directions depending on eddy size and a memory effect of large eddies. The results demonstrate that the 3OEC can improve the precision of benthic flux measurements, including measurements in environments considered challenging for the eddy covariance technique, and thereby produce novel insights into the mechanisms that control flux. We consider the fluxes produced by this instrument for the permeable reef sands the most realistic achievable with present-day technology.

Transmission-based surface-consistent framework for residual statics, deconvolution, and FWI: A new paradigm for near-surface analysis

We developed a novel surface-consistent processing framework that applies to transmitted wavefields (e.g., diving waves/refracted waves). Automatic velocity estimation from traveltime and full-waveform inversion, residual time shift corrections, and near-surface amplitude deconvolution are performed on the raw seismic gathers with minimal data preconditioning. In this implementation of the transmission-based surface-consistent analysis, we introduce a complete prestack and preprocessing workflow to fully analyze the near surface and enable highly specialized processes for what concerns land data imaging and reservoir characterization. Billions of traveltimes and traces can be analyzed automatically, providing enormous benefits in the execution time and in the accuracy and robustness of obtained results. The new paradigm for near-surface analysis opens the door to a better utilization of land seismic data for reservoir imaging and characterization.

Gaussian Process Preintegration for Inertial-Aided State Estimation

In this letter, we present Gaussian Process Preintegration, a preintegration theory based on continuous representations of inertial measurements. A novel use of linear operators on Gaussian Process kernels is employed to generate the proposed Gaussian Preintegrated Measurements (GPMs). This formulation allows the analytical integration of inertial signals on any time interval. Consequently, GPMs are especially suited for asynchronous inertial-aided estimation frameworks. Unlike discrete preintegration approaches, the proposed method does not rely on any explicit motion-model and does not suffer from numerical integration noise. Additionally, we provide the analytical derivation of the Jacobians involved in the first-order expansion for postintegration bias and inter-sensor time-shift correction. We benchmarked the proposed method against existing preintegration methods on simulated data. Our experiments show that GPMs produce the most accurate results and their computation time allows close-to-real-time operations. We validated the suitability of GPMs for inertial-aided estimation by integrating them into a lidar-inertial localisation and mapping framework.

A comprehensive automatic data analysis strategy for gas chromatography-mass spectrometry based untargeted metabolomics

Automatic data analysis for gas chromatography-mass spectrometry (GC-MS) is a challenging task in untargeted metabolomics. In this work, we provide a novel comprehensive data analysis strategy for GC-MS-based untargeted metabolomics (autoGCMSDataAnal) by developing a new automatic strategy for performing TIC peak detection and resolution and proposing a novel time-shift correction and component registration algorithm. autoGCMSDataAnal uses original acquired GC-MS datafiles as input to automatically perform TIC peak detection, component resolution, time-shift correction and component registration, statistical analysis, and compound identification. We utilize standards and complex plant samples to comprehensively investigate the performance of autoGCMSDataAnal. The results suggest that the developed strategy is comparable with several state-of-the-art methods that are widely used in GC-MS-based untargeted metabolomics. Based on the proposed strategy, we develop a user-friendly MATLAB GUI for users who are unfamiliar with programming languages to facilitate their routine analysis, which can be freely downloaded at: http://software.tobaccodb.org/software/autogcmsdataanal.

Searching for g modes

Context. The recent claims of g-mode detection have restarted the search for these potentially extremely important modes. These claims can be reassessed in view of the different data sets available from the SoHO instruments and ground-based instruments. Aims. We produce a new calibration of the GOLF data with a more consistent p-mode amplitude and a more consistent time shift correction compared to the time series used in the past. Methods. The calibration of 22 yr of GOLF data is done with a simpler approach that uses only the predictive radial velocity of the SoHO spacecraft as a reference. Using p modes, we measure and correct the time shift between ground- and space-based instruments and the GOLF instrument. Results. The p-mode velocity calibration is now consistent to within a few percent with other instruments. The remaining time shifts are within ±5 s for 99.8% of the time series.

A robust surface-consistent residual phase correction method based on migrated gathers

Conventional residual static corrections determine the residual statics (time shifts) using common mid-point (CMP) gathers to estimate and correct anomalies induced by the near-surface. These time shifts disregard the phase errors existing in the data, which will reduce the resolution of the stacked image. Further errors result when reflection events in CMP gathers do not exhibit hyperbolic moveout. In order to solve these problems, we propose a robust surface-consistent residual phase correction method that simultaneously resolves both time shifts and constant phase rotations based on migrated gathers. The surface-consistent residual statics and phase are obtained from the migrated gathers expressed in terms of shot and receiver locations. We modified the standard technique of estimating the time shift corrections to include a surface-consistent constant phase rotation term. The proposed dual parameter algorithm (time shift and constant phase rotation) proved on a synthetic example that it was superior to conventional residual statics for improving the coherence of trace gathers. The computational effort can be reduced by generating migrated gathers and estimating the dual parameters in a spatially varying time window. We applied the proposed method to both synthetic and real data, and improved results were obtained with both.

Direct Classification of GC × GC-Analyzed Complex Mixtures Using Non-Negative Matrix Factorization-Based Feature Extraction.

Complex chemical mixtures need to be evaluated to, for example, aid in medical diagnoses, assess product quality, and assess environmental conditions. Two-dimensional gas chromatography (GC × GC), which is a comprehensive analytical technique, combined with data classification techniques, has attracted great interest for assessing mixtures. In this study, a nontarget cross-sample analysis-based unsupervised direct classification method using non-negative matrix factorization was developed for assessing mixtures analyzed by GC × GC. The method was developed using GC × GC data for more than 30 river water samples as image data. The retention time shift correction data processing step was important to the classification accuracy because the compound signals were found at slightly different times for different samples. The maximum likelihood estimates of the matching ratios for the 30 samples, with retention time shift correction, were 86.8% and 77.0% using two and three ranks, respectively. The method is easy to perform and intuitive, requiring no specific knowledge or labeled data. This direct classification method will therefore be particularly useful for performing initial screens of large numbers of samples and for identifying major differences between samples.

AntDAS: Automatic Data Analysis Strategy for UPLC-QTOF-Based Nontargeted Metabolic Profiling Analysis.

High-quality data analysis methodology remains a bottleneck for metabolic profiling analysis based on ultraperformance liquid chromatography-quadrupole time-of-flight mass spectrometry. The present work aims to address this problem by proposing a novel data analysis strategy wherein (1) chromatographic peaks in the UPLC-QTOF data set are automatically extracted by using an advanced multiscale Gaussian smoothing-based peak extraction strategy; (2) a peak annotation stage is used to cluster fragment ions that belong to the same compound. With the aid of high-resolution mass spectrometer, (3) a time-shift correction across the samples is efficiently performed by a new peak alignment method; (4) components are registered by using a newly developed adaptive network searching algorithm; (5) statistical methods, such as analysis of variance and hierarchical cluster analysis, are then used to identify the underlying marker compounds; finally, (6) compound identification is performed by matching the extracted peak information, involving high-precision m/z and retention time, against our compound library containing more than 500 plant metabolites. A manually designed mixture of 18 compounds is used to evaluate the performance of the method, and all compounds are detected under various concentration levels. The developed method is comprehensively evaluated by an extremely complex plant data set containing more than 2000 components. Results indicate that the performance of the developed method is comparable with the XCMS. The MATLAB GUI code is available from http://software.tobaccodb.org/software/antdas .

Pixel-by-pixel correction of retention time shifts in chromatograms from comprehensive two-dimensional gas chromatography coupled to high resolution time-of-flight mass spectrometry

A pixel-by-pixel method for correcting retention time (RT) shifts in whole chromatograms from comprehensive two-dimensional gas chromatography coupled to high-resolution time-of-flight mass spectrometry (GC×GC-HRTOFMS) is introduced. A previously developed robust algorithm for correcting RT shifts was extended to high-resolution mass-spectral data. The performance of the new method in terms of decreasing RT shifts and peak volume changes was tested on GC×GC-HRTOFMS data. The RT shift correction algorithm, using linear interpolation for the 1st dimension and Sibson natural neighbor interpolation for the 2nd dimension, performed well for systematically shifted data acquired using two different temperature programs in terms of decreasing RT differences and alterations to the peak volumes and mass spectra. A modified RT shift correction algorithm, using Sibson natural neighbor for both dimensions, performed better for RT shifts caused by column damage, for which the original interpolation method did not appropriately correct RT shifts. Although further investigation would be required for more types of severe shifts, this study shows that the developed method is useful for correcting RT shifts with GC×GC-HRTOFMS.

A technique for rapid source apportionment applied to ambient organic aerosol measurements from a thermal desorption aerosol gas chromatograph (TAG)

Abstract. We present a rapid method for apportioning the sources of atmospheric organic aerosol composition measured by gas chromatography–mass spectrometry methods. Here, we specifically apply this new analysis method to data acquired on a thermal desorption aerosol gas chromatograph (TAG) system. Gas chromatograms are divided by retention time into evenly spaced bins, within which the mass spectra are summed. A previous chromatogram binning method was introduced for the purpose of chromatogram structure deconvolution (e.g., major compound classes) (Zhang et al., 2014). Here we extend the method development for the specific purpose of determining aerosol samples' sources. Chromatogram bins are arranged into an input data matrix for positive matrix factorization (PMF), where the sample number is the row dimension and the mass-spectra-resolved eluting time intervals (bins) are the column dimension. Then two-dimensional PMF can effectively do three-dimensional factorization on the three-dimensional TAG mass spectra data. The retention time shift of the chromatogram is corrected by applying the median values of the different peaks' shifts. Bin width affects chemical resolution but does not affect PMF retrieval of the sources' time variations for low-factor solutions. A bin width smaller than the maximum retention shift among all samples requires retention time shift correction. A six-factor PMF comparison among aerosol mass spectrometry (AMS), TAG binning, and conventional TAG compound integration methods shows that the TAG binning method performs similarly to the integration method. However, the new binning method incorporates the entirety of the data set and requires significantly less pre-processing of the data than conventional single compound identification and integration. In addition, while a fraction of the most oxygenated aerosol does not elute through an underivatized TAG analysis, the TAG binning method does have the ability to achieve molecular level resolution on other bulk aerosol components commonly observed by the AMS.

Fully automated near-surface analysis by surface-consistent refraction method

Industry practices for near-surface analysis indicate difficulties in coping with the increased number of channels in seismic acquisition systems, and new approaches are needed to fully exploit the resolution embedded in modern seismic data sets. To achieve this goal, we have developed a novel surface-consistent refraction analysis method for low-relief geology to automatically derive near-surface corrections for seismic data processing. The method uses concepts from surface-consistent analysis applied to refracted arrivals. The key aspects of the method consist of the use of common midpoint (CMP)-offset-azimuth binning, evaluation of mean traveltime and standard deviation for each bin, rejection of anomalous first-break (FB) picks, derivation of CMP-based traveltime-offset functions, conversion to velocity-depth functions, evaluation of long-wavelength statics, and calculation of surface-consistent residual statics through waveform crosscorrelation. Residual time lags are evaluated in multiple CMP-offset-azimuth bins by crosscorrelating a pilot trace with all the other traces in the gather in which the correlation window is centered at the refracted arrival. The residuals are then used to build a system of linear equations that is simultaneously inverted for surface-consistent shot and receiver time shift corrections plus a possible subsurface residual term. All the steps are completely automated and require a fraction of the time needed for conventional near-surface analysis. The developed methodology was successfully performed on a complex 3D land data set from Central Saudi Arabia where it was benchmarked against a conventional tomographic work flow. The results indicate that the new surface-consistent refraction statics method enhances seismic imaging especially in portions of the survey dominated by noise.

Technical note: Time lag correction of aquatic eddy covariance data measured in the presence of waves

Abstract. Extracting benthic oxygen fluxes from eddy covariance time series measured in the presence of surface gravity waves requires careful consideration of the temporal alignment of the vertical velocity and the oxygen concentration. Using a model based on linear wave theory and measured eddy covariance data, we show that a substantial error in flux can arise if these two variables are not aligned correctly in time. We refer to this error in flux as the time lag bias. In one example, produced with the wave model, we found that an offset of 0.25 s between the oxygen and the velocity data produced a 2-fold overestimation of the flux. In another example, relying on nighttime data measured over a seagrass meadow, a similar offset reversed the flux from an uptake of −50 mmol m−2 d−1 to a release of 40 mmol m−2 d−1. The bias is most acute for data measured at shallow-water sites with short-period waves and low current velocities. At moderate or higher current velocities (> 5–10 cm s−1), the bias is usually insignificant. The widely used traditional time shift correction for data measured in unidirectional flows, where the maximum numerical flux is sought, should not be applied in the presence of waves because it tends to maximize the time lag bias or give unrealistic flux estimates. Based on wave model predictions and measured data, we propose a new time lag correction that minimizes the time lag bias. The correction requires that the time series of both vertical velocity and oxygen concentration contain a clear periodic wave signal. Because wave motions are often evident in eddy covariance data measured at shallow-water sites, we encourage more work on identifying new time lag corrections.

Second-order calibration for simultaneous determination of pharmaceuticals in water samples by solid-phase extraction and fast high-performance liquid chromatography with diode array detector

A fast high-performance liquid chromatography–diode array detection (HPLC–DAD) approach combined to solid phase extraction (SPE) as a pre-concentration step is developed for simultaneous determination of five selected pharmaceuticals (carbamazepine, naproxen, diclofenac, gemfibrozil and mefenamic acid) in water samples. The effective factors on the efficiency of SPE procedure are optimized using faced-centered central composite design (FCCD). In addition, multi-response optimization by using Derringer's desirability function is used to find the optimum experimental conditions for extraction of analytes from well and river waters. Due to the complexity of water matrices and the presence of different chromatographic issues, new combination of multivariate curve resolution–correlation optimized warping to parallel factor analysis (MCR–COW–PARAFAC) and multivariate curve resolution-alternating least squares with trilinearity constraint (MCR–COW–MCRtril) is proposed for simultaneous determination of five target pharmaceuticals in these samples. This strategy allowed us to overcome matrix effects and to exploit second-order advantage. Recoveries ranging from 80.12% to 102.71% and relative standard deviations below 8.0% for all pharmaceuticals proved the accuracy and precision of the proposed method. In addition, the values of relative error in calibration curves (RE, %) were below 11.24% and 12.19% for MCR–COW–PARAFAC and MCR–COW–MCR, respectively. Furthermore, the values of detection limits (LODs) and quantification limits (LOQs) were between 0.02 to 0.32ngmL−1 and 0.07 to 1.07ngmL−1, respectively. In addition, analytical figures of merit using multivariate approaches were calculated for both methods. In this regard, the values of sensitivity, LOD and LOQ showed an improvement compared to univariate techniques. Inspection of the results showed that due to the efficient correction of elution time shifts using MCR–COW method and preserving trilinear data structure, both MCR–COW–PARAFAC and MCR–COW–MCRtril give similar results. These results confirmed that coupling optimized SPE–HPLC–DAD method with second-order calibration algorithms can be considered as an efficient method for fast, simple and cost effective quantification of pharmaceuticals in highly contaminated samples, such as river and well waters.

Simultaneous estimation of retention times of overlapping primary peaks in comprehensive two‐dimensional GC

A general approach is developed to estimate the retention time (t(R)) of overlapping primary peaks in comprehensive 2D GC without assumptions such as the limitation of modulation ratio or symmetry of the target primary peak. Accurate determination of t(R) can recover the original peak profile by using mathematical fitting. First, the modulation pattern of the first-dimension peak in the second dimension is summarized with the number of major modulation fractions equal to or less than four. A novel formula to derive t(R) is defined and separately investigated for cases of modulation number for 1-4, on the basis of the center of gravity of all fractions of the primary peak, in the second dimension. A moving-window search strategy is further developed for peak clusters overlapping in both separation dimensions, to extract first dimension tR of pure components with the same second dimension time after data pretreatment (background subtraction; time shift correction). Results are very close to the times of simulated comprehensive 2D GC separations. Compared to methods such as reconstruction of original chromatographic profiles to derive t(R), the proposed approach balances the precision, and ease of adaption to real applications.