Probabilistic peak detection for first-order chromatographic data

We present a novel algorithm for probabilistic peak detection in first-order chromatographic data. Unlike conventional methods that deliver a binary answer pertaining to the expected presence or absence of a chromatographic peak, our method calculates the probability of a point being affected by such a peak. The algorithm makes use of chromatographic information (i.e. the expected width of a single peak and the standard deviation of baseline noise). As prior information of the existence of a peak in a chromatographic run, we make use of the statistical overlap theory. We formulate an exhaustive set of mutually exclusive hypotheses concerning presence or absence of different peak configurations. These models are evaluated by fitting a segment of chromatographic data by least-squares. The evaluation of these competing hypotheses can be performed as a Bayesian inferential task. We outline the potential advantages of adopting this approach for peak detection and provide several examples of both improved performance and increased flexibility afforded by our approach.     

Time-resolved cryogenic modulation reveals isomer interconversion profiles in dynamic chromatography.

The dynamic chromatographic study of interconversion of E and Z forms of oximes has been investigated by using a novel cryogenic modulation method in a two-dimensional gas chromatographic array. The primary column is a conventional capillary GC column on which the molecular interconversion proceeds. In this case, the molecular dynamical process leads to a peak profile describing the kinetics and thermodynamics of the interconverting molecules during its chromatographic elution. Thus an interconversion region intercedes the elution of the individual stereoisomers of the reaction. Since the molecules are isomers, classical molecular identification methods such as gas chromatography-mass spectrometry are unable to study the individual instantaneous amounts of each of the compounds. Hence the infinitesimal profiles of interconversion along the entire column have never been experimentally observed; rather the total profile is normally subjected to mathematical modelling studies in order to match experiment with theory, and to gain the kinetic parameters of the process. In the present study, an instantaneous ratio of the individual isomers can be found during the chromatographic elution by direct measurement. This is achieved by using a cryogenic zone focussing process, with rapid longitudinal modulation of a cold trap and continual pulsing of collected zones into a fast-analysis high-resolution capillary column on which isomer interconversion is minimized. The data can be displayed as a two-dimensional contour plot to demonstrate the individual isomer profiles. The two-dimensional analysis also allows easy measurement of the peak ratios of the two isomers which is an indicator of the extent of interconversion that has taken place. Two model systems, acetaldoxime and butyraldoxime, were chosen to illustrate the use of the cryogenic modulation procedure. It is anticipated that the procedure could be applied to other molecules which exhibit gas-phase isomerizations or reactions.     

Automated optimization and construction of chemometric models based on highly variable raw chromatographic data

Direct chemometric interpretation of raw chromatographic data (as opposed to integrated peak tables) has been shown to be advantageous in many circumstances. However, this approach presents two significant challenges: data alignment and feature selection. In order to interpret the data, the time axes must be precisely aligned so that the signal from each analyte is recorded at the same coordinates in the data matrix for each and every analyzed sample. Several alignment approaches exist in the literature and they work well when the samples being aligned are reasonably similar. In cases where the background matrix for a series of samples to be modeled is highly variable, the performance of these approaches suffers. Considering the challenge of feature selection, when the raw data are used each signal at each time is viewed as an individual, independent variable; with the data rates of modern chromatographic systems, this generates hundreds of thousands of candidate variables, or tens of millions of candidate variables if multivariate detectors such as mass spectrometers are utilized. Consequently, an automated approach to identify and select appropriate variables for inclusion in a model is desirable. In this research we present an alignment approach that relies on a series of deuterated alkanes which act as retention anchors for an alignment signal, and couple this with an automated feature selection routine based on our novel cluster resolution metric for the construction of a chemometric model. The model system that we use to demonstrate these approaches is a series of simulated arson debris samples analyzed by passive headspace extraction, GC-MS, and interpreted using partial least squares discriminant analysis (PLS-DA).     

三元重叠色谱峰面积的定量方法

本从色谱峰的ＥＭＧ模型出发，通过对重叠色谱峰的模拟和回归分析，提出了一种三元重叠色谱峰的面积的定量方法，三元重叠色谱峰的每一个峰面积可以由峰面积比和总面积求得，此法所需的数据都由实验色谱图上测得，峰面积计算结果的相对误差小于±５％，适用于相对峰谷为５０％－９５％的三元重叠色谱峰面积的定量。     

Chromatographic quantitation using fractions of the peak areas

Quantitative chromatographic analysis is liable to errors due to peak asymmetry because the uncertainty in the detected position of the end of the peak tail decreases the reliability of the computed peak area. This dependence may be a severe drawback whenever peaks of different areas must be compared, as in the case of calibration curves. A new approach to overcome the uncertainties of area calculation due to peak asymmetry is reported in this paper. The approach consists of calculating only the area included between the start and the maximum of the chromatographic peak. Simulated and experimental chromatographic data were used in this study. Both the peak start-to-peak maximum area (SMA) and the start-to-end or total area (TA) were calculated and the quantitative results were compared. Within the scope of this work it is concluded that the SMA yields calibration curves that are more linear and have intercepts closer to zero than the calibration curves obtained using the TA.     

The stochastic resonance algorithm with the direct current signal as external force and its application to the detection of weak chromatographic peaks

As a potential tool for amplifying weak chromatographic peaks, the stochastic resonance algorithm was developed based upon a counterintuitive physical phenomenon. Therefore, the essential step, parameter optimization, was perplexing and difficult for analysts. In order to avoid optimizing the system parameters on a case‐by‐case basis, an improved algorithm was proposed by introducing a constant or direct current signal into the signal to be measured as the external force. The weak chromatographic peak can be amplified and detected by the new algorithm using the same set of parameters. Two sets of our previous experimental data were reanalyzed by using the developed algorithm and the results were satisfactory. A generalized solution was expected to come into being on account of the new algorithm.     

The utility of statistical moments in chromatography using trapezoidal and Simpson's rules of peak integration

Modern chromatographic data acquisition softwares often behave as black boxes where the researchers have little control over the raw data processing. One of the significant interests of separation scientists is to extract physico‐chemical information from chromatographic experiments and peak parameters. In addition, column developers need the total peak shape analysis to characterize the flow profile in chromatographic beds. Statistical moments offer a robust approach for providing detailed information for peaks in terms of area, its center of gravity, variance, resolution, and its skew without assuming any peak model or shape. Despite their utility and theoretical significance, statistical moments are rarely incorporated as they often provide underestimated or overestimated results because of inappropriate choice of the integration method and selection of integration limits. The Gaussian model is universally used in most chromatography softwares to assess efficiency, resolution, and peak position. Herein we present a user‐friendly, and accessible approach for calculating the zeroth, first, second, and third moments through more accurate numerical integration techniques (Trapezoidal and Simpson's rule) which provide an accurate estimate of peak parameters as compared to rectangular integration. An Excel template is also provided which can calculate the four moments in three steps with or without baseline correction.     

Renaissance of gas chromatography-time-of-flight mass spectrometry. Meeting the challenge of capillary columns with a beam deflection instrument and time array detection

This report describes the use of a unique beam deflection time-of-flight mass spectrometer to address some of the demands made on mass spectrometry by new developments in high-resolution capillary column gas chromatography. An integrating transient recorder is used in combination with this beam deflection time-of-flight instrument to apply the concept of time array detection in capturing all of the mass spectral information available from the ion source, thereby greatly enhancing the signal-to-noise ratio quality of the mass spectral data. The applicability of the time array detection approach to gas chromatography-mass spectrometry is demonstrated in the context of an analysis of the standard Grob mixture for assessing performance of capillary column chromatography. During analysis of the Grob mixture by gas chromatography-mass spectrometry, mass spectra were recorded at a rate of 20 scan files per second. The data indicate that this rate of mass spectral scan file generation is adequate to provide a suitable data base for reconstruction of the chromatographic profile. In addition, the effective scan rate is high enough that there is no distortion in the relative peak intensities throughout the individual mass spectra of components regardless of the relatively high dynamic changes in partial pressure of the analyte as reflected by the sharp peaks in the chromatographic profile. The experimental results indicate that the beam deflection time-of-flight mass spectrometer can provide mass spectra at a scan file generation rate much higher than that possible with the conventional quadrupole or magnetic sector mass spectrometer, but at comparable detection limits.     

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.     

An integrated method for spectrum extraction and compound identification from gas chromatography/mass spectrometry data

A method is presented for extracting individual component spectra from gas chromatography/mass spectrometry (GC/MS) data files and then using these spectra to identify target compounds by matching spectra in a reference library. It extends a published “model peak” approach which uses selected ion chromatograms as models for component shape. On the basis of this shape, individual mass spectral peak abundance profiles are extracted to produce a “purified” spectrum. In the present work, ion-counting noise is explicitly treated and a number of characteristic features of GC/MS data are taken into account. This allows spectrum extraction to be reliably performed down to very low signal levels and for overlapping components. A spectrum match factor for compound identification is developed that incorporates a number of new corrections, some of which employ information derived from chromatographic behavior. Test results suggest that the ability of this system to identify compounds is comparable to that of conventional analysis.     

Estimation of chromatographic parameters on two silica-based columns connected in series under nonaqueous reversed phase liquid chromatographic conditions

Empirical equations were produced to relate important chromatographic parameters on two silica-based columns serially linked, in isocratic nonaqueous RP HPLC, to retention times and peak widths of the separated compounds on the individual columns. These equations were derived because the experimental data seemed to deviate from the values expected, applying basic chromatographic theoretical equations. The chromatographic parameters studied were retention time, peak width, resolution, number of theoretical plates, capacity factor, and separation factor. In addition, empirical linear relationships were produced for the estimation of the above mentioned parameters of the serial systems, in direct and reverse order, relating them to those obtained on each column, separately. The experimentally obtained values were in good agreement with those estimated by the derived equations.     

Multi-parameter investigation of tandem mass spectrometry in a linear ion trap using response surface modelling

The feasibility of experimental design in combination with subsequent response surface modelling was illustrated for the prediction and interpretation of tandem mass spectrometric (MS/MS) fragmentation data using a linear quadrupole ion trap under various experimental conditions. The instrumental parameters included were (i) the pressure of the collision gas, (ii) the collision energy, (iii) the fill time of the linear ion trap and (iv) the scan rate. The spectral intensity and width of five fragment ions of the doubly charged neuro-active peptide bombesin were used for evaluation, and all experiments were performed so as to resemble the results obtained from a liquid chromatographic peak. The reported results show how fairly simple mathematical tools can be utilized successfully to describe fundamental mechanisms associated with multiple collisional activation and collision-induced dissociation processes without an extensively controlled experimental environment. Most beneficial, using the suggested approach, is the ability to study interaction (synergistic) effects between various parameters. As was realized from the results, many interaction effects are indeed significant. For example, the effect on the signal intensity of different collision gas pressure settings is strongly dependent on the settings of the other parameters. The described approach can easily be adopted for optimization purposes of any MS/MS experiment.     

Investigation of interpolation techniques for the reconstruction of the first dimension of comprehensive two-dimensional liquid chromatography-diode array detector data

Simulated and experimental data were used to measure the effectiveness of common interpolation techniques during chromatographic alignment of comprehensive two-dimensional liquid chromatography-diode array detector (LC×LC-DAD) data. Interpolation was used to generate a sufficient number of data points in the sampled first chromatographic dimension to allow for alignment of retention times from different injections. Five different interpolation methods, linear interpolation followed by cross correlation, piecewise cubic Hermite interpolating polynomial, cubic spline, Fourier zero-filling, and Gaussian fitting, were investigated. The fully aligned chromatograms, in both the first and second chromatographic dimensions, were analyzed by parallel factor analysis to determine the relative area for each peak in each injection. A calibration curve was generated for the simulated data set. The standard error of prediction and percent relative standard deviation were calculated for the simulated peak for each technique. The Gaussian fitting interpolation technique resulted in the lowest standard error of prediction and average relative standard deviation for the simulated data. However, upon applying the interpolation techniques to the experimental data, most of the interpolation methods were not found to produce statistically different relative peak areas from each other. While most of the techniques were not statistically different, the performance was improved relative to the PARAFAC results obtained when analyzing the unaligned data.     

On the equations describing chromatographic peaks and the problem of the deconvolution of overlapped peaks

The problem of the appropriate choice of the function that describes a chromatographic peak is examined in combination with the deconvolution of overlapped peaks by means of the non-linear least-squares method. It is shown that the majority of the functions proposed in the literature to describe chromatographic peaks are not suitable for this purpose. Only the polynomial modified Gaussian function can describe almost every peak but it is mathematically incorrect unless it is redefined properly. Two new functions are proposed and discussed. It is also shown that the deconvolution of an overlapping peak can be done with high accuracy using a non-linear least-squares procedure, like Microsoft Solver, but this target is attained only if we use as fitted parameters the position of the peak maximum and the peak area (or height) of every component in the unresolved chromatographic peak. In case we use as fitted parameters all the parameters that describe each single peak enclosed in the multi-component peak, then Solver leads to better fits, which though do not correspond to the best deconvolution of the peak. Finally, it is found that Solver gives much better results than those of modern methods, like the immune and genetic algorithms.     

Calculations of the energy distribution from perturbation peak data--a new tool for characterization of chromatographic phases

The calculation of the adsorption energy distribution (AED) was recently introduced as an important tool for the chromatographic community for characterization of modern phases. The AED-calculations, provides model-independent information about the numbers of different adsorption sites and their respective energy-levels, prior to the selection of an adsorption isotherm model which narrows the number of possible rival models. The selection of a proper model for the fitting of the determined raw data is crucial; if the wrong model is selected misleading information about the retention mechanism may be drawn. The AED-calculations require raw adsorption isotherm data (i.e. data points) which is unfortunately not obtained by the newly validated perturbation peak method. In this study, we developed mathematical expression allowing the use of the raw tangential slope provided by the perturbation peak method for AED calculations. The approach worked excellently and was verified against both computer-generated adsorption isotherm data as well as experimentally determined data, using three different experimental systems. It was found that the calculations of the AED, as based on perturbation peak data, converts faster and are not more sensitive to experimental noise as compared to the classical AED calculations using raw adsorption isotherm data.     

Modulation-induced error in comprehensive two-dimensional gas chromatographic separations

There is a fundamental difference between data collected in comprehensive two-dimensional gas chromatographic (GCxGC) separations and data collected by one-dimensional GC techniques (or heart-cut GC techniques). This difference can be ascribed to the fact that GCxGC generates multiple sub-peaks for each analyte, as opposed to other GC techniques that generate only a single chromatographic peak for each analyte. In order to calculate the total signal for the analyte, the most commonly used approach is to consider the cumulative area that results from the integration of each sub-peak. Alternately, the data may be considered using higher order techniques such as the generalized rank annihilation method (GRAM). Regardless of the approach, the potential errors are expected to be greater for trace analytes where the sub-peaks are close to the limit of detection (LOD). This error is also expected to be compounded with phase-induced error, a phenomenon foreign to the measurement of single peaks. Here these sources of error are investigated for the first time using both the traditional integration-based approach and GRAM analysis. The use of simulated data permits the sources of error to be controlled and independently evaluated in a manner not possible with real data. The results of this study show that the error introduced by the modulation process is at worst 1% for analyte signals with a base peak height of 10xLOD and either approach to quantitation is used. Errors due to phase shifting are shown to be of greater concern, especially for trace analytes with only one or two visible sub-peaks. In this case, the error could be as great as 6.4% for symmetrical peaks when a conventional integration approach is used. This is contrasted by GRAM which provides a much more precise result, at worst 1.8% and 0.6% when the modulation ratio (MR) is 1.5 or 3.0, respectively for symmetrical peaks. The data show that for analyses demanding high precision, a MR of 3 should be targeted as a minimum, especially if multivariate techniques are to be used so as to maintain data density in the primary dimension. For rapid screening techniques where precision is not as critical lower MR values can be tolerated. When integration is used, if there are 4-5 visible sub-peaks included for a symmetrical peak at MR=3.0, the data will be reasonably free from phase-shift-induced errors or a negative bias. At MR=1.5, at least 3 sub-peaks must be included for a symmetrical peak. The proposed guidelines should be equally relevant to LCxLC and other similar techniques.     

Spectral correlative chromatography and its application to analysis of chromatographic fingerprints of herbal medicines

A signal-processing method known as spectral correlative chromatography (SCC) for two-dimensional data obtained from hyphenated chromatography is developed and applied to chemical chromatographic fingerprint data sets of herbal medicine under specific experimental conditions. The method can judge the presence or absence of a spectral correlative peak among the spectrochromatograms. A local least squares regression model (LLS) is constructed in a piecewise manner to correct the shifts of retention time of some peaks of interest in the chromatograms of various test samples. The results compare favorably with those obtained by a two-point calibrated algorithm. It is shown that performing SCC and LLS on the piecewise clusters of various chromatographic fingerprints is more helpful in practice in revealing their common nature and for characterizing the chemical constituents. This approach holds great potential for facilitating quality control of herbal medicines.     

Fast quantitative characterisation of differential mobility responses

A chromatography-based method for producing mass flux-response surfaces for differential mobility spectrometers is described as a replacement for exponential dilution and mixing approaches. An exponential dilution or mixing experiment typically takes 150 min; while the exponential function in the Gaussian elution profile obtained from linear chromatography may be exploited in approximately 10 s. The approach was demonstrated with a gas chromatograph-mass spectrometer and the correlation of the calibration results to nominal on-column masses was within experimental error for 19 separate analyses. The method was then applied to a gas chromatographic (10.6 eV UV) differential mobility spectrometer. Mass fluxes in the range 10 pg s(-1) to 250 ng s(-1) were generated over the 5 s to 10 s associated with the elution of a chromatographic peak. The characterisations were repeated for a range of electrical field strengths from 10 kV cm(-1) to 30 kV cm(-1). Triplicate runs indicated that the approach was reproducible and that response surfaces could be generated rapidly from chromatographic data. The effects of trace impurities associated with the chromatographic eluent on the relationship between compensation voltage and electrical field strength was observed. This emphasised the importance of managing this aspect of the operation if reliable estimates of alpha functions for the compounds under study were to be obtained. Application of this approach to other detection systems with an 85% reduction in the analytical operations required to produce a reliable calibration function was also noted.     

Voltammetric/amperometric detection for liquid chromatography

A voltammetric/amperometric detector based on a dual-electrode electrochemical detector is described for liquid chromatography. The detector combines the advantages of both voltammetric and amperometric detection. A three-dimensional data array of current response as a function of both time (chromatographic domain) and potential (electrochemical domain) is obtained. From the chromatographic point of view, this allows post-experimental choice of the optimal detection potential. Different detection potentials can even be chosen for each chromatographic peak. Having the voltammetric data as well as the chromatographic data provides ready identification of chromatographically unresolved compounds and the ability to resolve such co-eluting compounds voltammetrically. The voltammetric data also provide a second method of peak identification for greater certainty in peak assignments. Voltammetric detection limits of less than 10 pmol of material injected on the column were achieved with this detection method. From the electrochemical perspective, voltammetric/amperometric detection provides a technique for obtaining hydrodynamic voltammograms with small amounts or small volumes of sample. Voltammograms can also be obtained for the individual components of complex mixtures without the need for isolation steps.