Probability of failure of the watershed algorithm for peak detection in comprehensive two-dimensional chromatography

The watershed algorithm is the most common method used for peak detection and integration in two-dimensional chromatography. However, the retention time variability in the second dimension may render the algorithm to fail. A study calculating the probabilities of failure of the watershed algorithm was performed. The main objective was to calculate the maximum second-dimension retention time variability, Δ²t_R,crit, above which the algorithm fails. Several models to calculate Δ²t_R,crit were developed and evaluated: (a) exact model; (b) simplified model and (c) simple-modified model. Model (c) gave the best performance and allowed to deduce an analytical expression for the probability of failure of the watershed algorithm as a function of experimental Δ²t_R, modulation time and peak width in the first and second dimensions. It could be demonstrated that the probability of failure of the watershed algorithm under normal conditions in GC × GC is around 15–20%. Small changes of Δ²t_R, modulation time and/or peak width in the first and second dimension could induce subtle changes in the probability of failure of the watershed algorithm. Theoretical equations were verified with experimental results from a diesel sample injected in GC × GC and were found to be in good agreement with the experiments.     

Peak clustering in two-dimensional gas chromatography with mass spectrometric detection based on theoretical calculation of two-dimensional peak shapes: the 2DAid approach

A method is presented to facilitate the non-target analysis of data obtained in temperature-programmed comprehensive two-dimensional (2D) gas chromatography coupled to time-of-flight mass spectrometry (GC×GC-ToF-MS). One main difficulty of GC×GC data analysis is that each peak is usually modulated several times and therefore appears as a series of peaks (or peaklets) in the one-dimensionally recorded data. The proposed method, 2DAid, uses basic chromatographic laws to calculate the theoretical shape of a 2D peak (a cluster of peaklets originating from the same analyte) in order to define the area in which the peaklets of each individual compound can be expected to show up. Based on analyte-identity information obtained by means of mass spectral library searching, the individual peaklets are then combined into a single 2D peak. The method is applied, amongst others, to a complex mixture containing 362 analytes. It is demonstrated that the 2D peak shapes can be accurately predicted and that clustering and further processing can reduce the final peak list to a manageable size.     

Probabilistic peak detection in CE‐LIF for STR DNA typing

In this work, we present a novel probabilistic peak detection algorithm based on a Bayesian framework for forensic DNA analysis. The proposed method aims at an exhaustive use of raw electropherogram data from a laser‐induced fluorescence multi‐CE system. As the raw data are informative up to a single data point, the conventional threshold‐based approaches discard relevant forensic information early in the data analysis pipeline. Our proposed method assigns a posterior probability reflecting the data point's relevance with respect to peak detection criteria. Peaks of low intensity generated from a truly existing allele can thus constitute evidential value instead of fully discarding them and contemplating a potential allele drop‐out. This way of working utilizes the information available within each individual data point and thus avoids making early (binary) decisions on the data analysis that can lead to error propagation. The proposed method was tested and compared to the application of a set threshold as is current practice in forensic STR DNA profiling. The new method was found to yield a significant improvement in the number of alleles identified, regardless of the peak heights and deviation from Gaussian shape.     

A continuous wavelet transform algorithm for peak detection

Contactless conductivity detector technology has unique advantages for microfluidic applications. However, the low S/N and varying baseline makes the signal analysis difficult. In this paper, a continuous wavelet transform-based peak detection algorithm was developed for CE signals from microfluidic chips. The Ridger peak detection algorithm is based on the MassSpecWavelet algorithm by Du et al. [Bioinformatics 2006, 22, 2059-2065], and performs a continuous wavelet transform on data, using a wavelet proportional to the first derivative of a Gaussian function. It forms sequences of local maxima and minima in the continuous wavelet transform, before pairing sequences of maxima to minima to define peaks. The peak detection algorithm was tested against the Cromwell, MassSpecWavelet, and Linear Matrix-assisted laser desorption/ionization-time-of-flight-mass spectrometer Peak Indication and Classification algorithms using experimental data. Its sensitivity to false discovery rate curve is superior to other techniques tested.     

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.     

Characterization of peak purity by fast multiscan circular dichroism detection

Summary A method has been developed to detect inhomogeneity of apparently homogeneous peaks of very similar analytes. The method utilizes the rapid scan feature of state-of-the-art spectrometers/detectors that allow the recording of up to 30 spectra in a single chromatographic peak. Sensitivity and selectivity are enhanced by chiroptical/optical detection. Thus, identification of “front” and “rear” components of the peak can be carried out. The method is exemplified by mixtures of codeine, hydrocodone and oxycodone as analytes. Presented at: Balaton Symposium on High-Performance Separation Methods, Siófok, Hungary, September 3–5, 1997     

Algorithms for the assessment of peak purity in liquid chromatography with photodiode-array detection. Part II

Two modifications of the algorithm based on the Gram-Schmidt orthogonalization technique for the assessment of peak purity are presented. The performance of this approah is investigated for liquid chromatography with photodiode-array detection (LC-DAD) data, although its applicability is not restricted to this experimental model. This method is applied to simulated and experimental data where two compounds are eluting, but can be applied when more compounds are eluting. The results are compared with the ones obtained previously with the first version of this algorithm.     

Computer-aided multichannel detection in high-performance liquid chromatography

Summary The development of a computer-aided rapid-scanning detector for HPLC based on the linear photodiode array UV-visible spectrophotometer is described. Chomatograms monitored at up to three wavelengths, with automatic capture of spectra for eluted peaks and post-run processing of spectral data to generate log₁₀ (A) spectra, second derivative and fourth derivative spectra, are described. Methods are reported for the analysis of forensic samples of diacetylmorphine (heroin) in the presence of the degradation products and potential contaminants caffeine, papaverine, 6-acetylcodeine, thebaine, 6-acetyl-morphine, procaine and morphine separated by HPLC. The novel use of second and higher derivative spectra for the qualitative characterisation of drugs and contaminants separated by HPLC is described.Presented at the 14th International Symposium on Chromatography London, September, 1982     

The system evaluation strategy in practice,allowing direct estimation of peak heights and limits of detection in HPLC

Summary The novel system evaluation strategy recently developed describes an HPLC system in terms of two parameters, that ideally are independent of the test conditions. These describe the peak height response, or dilution, occurring in the column and the system. Limits of detection (LOD’s) can thus also be calculated. System parameters, (e.g. cell length, external dispersion), chromatographic parameters (e.g. retention, column length, flow-rate), and sample parameters (e.g. sample volume & absorptivity), are all included. Consequently this approach is applicable to the chromatographer and LC system designer alike. The system evaluation strategy was previously demonstrated under typical chromatographic conditions, on two HPLC systems, and systematic changes were studied. In principle this is applicable to any compound under any chromatographic conditions, on any column. This is now to be investigated further, under a wide range of conditions, and applied to the calculation of an LOD in a real LC analysis.     

Comparison of methods to enhance flame ionization detector (FID) signals in gas chromatography

The performances of some numerical methods to improve the signal to noise ratio are compared and applied to enhance noisy signals obtained in gas chromatography with capillary columns and a flame Ionization detector. Several methods have been considered: cutoffs In the Fourier transform of the recorded signal; real time numerical filtering; theoretical model curve fitting; and the correlation of a chromatogram recorded from a pseudorandomly injected sample with the pseudorandom injection function. Numerical real time filtering is shown to be the most convenient method when the main periodic component of the noise has been determined by Fourier analysis.     

Automatic data processing in chromatography — A mixed blessing

Summary Possible changes in chemical analysis as a result of the introduction of microprocessors are discussed. Many of the problems associated with mini-computer systems for GC arise from putting too many facilities into small systems because of price constraints. These should disappear with widespread use of microprocessors. The problems of inadequate or inappropriate software are a little more intractable. However, the software industry has learnt a lot in the past decade and, while bad software continues to be produced in some quantity, the tools to construct good programs are becoming readily available, and should give rise to improved systems.     

Achieving high peak capacity production for gas chromatography and comprehensive two-dimensional gas chromatography by minimizing off-column peak broadening

By taking into consideration band broadening theory and using those results to select experimental conditions, and also by reducing the injection pulse width, peak capacity production (i.e., peak capacity per separation time) is substantially improved for one dimensional (1D-GC) and comprehensive two dimensional (GC×GC) gas chromatography. A theoretical framework for determining the optimal linear gas velocity (the linear gas velocity producing the minimum H), from experimental parameters provides an in-depth understanding of the potential for GC separations in the absence of extra-column band broadening. The extra-column band broadening is referred to herein as off-column band broadening since it is additional band broadening not due to the on-column separation processes. The theory provides the basis to experimentally evaluate and improve temperature programmed 1D-GC separations, but in order to do so with a commercial 1D-GC instrument platform, off-column band broadening from injection and detection needed to be significantly reduced. Specifically for injection, a resistively heated transfer line is coupled to a high-speed diaphragm valve to provide a suitable injection pulse width (referred to herein as modified injection). Additionally, flame ionization detection (FID) was modified to provide a data collection rate of 5kHz. The use of long, relatively narrow open tubular capillary columns and a 40°C/min programming rate were explored for 1D-GC, specifically a 40m, 180μm i.d. capillary column operated at or above the optimal average linear gas velocity. Injection using standard auto-injection with a 1:400 split resulted in an average peak width of ～1.5s, hence a peak capacity production of 40peaks/min. In contrast, use of modified injection produced ～500ms peak widths for 1D-GC, i.e., a peak capacity production of 120peaks/min (a 3-fold improvement over standard auto-injection). Implementation of modified injection resulted in retention time, peak width, peak height, and peak area average RSD%'s of 0.006, 0.8, 3.4, and 4.0%, respectively. Modified injection onto the first column of a GC×GC coupled with another high-speed valve injection onto the second column produced an instrument with high peak capacity production (500-800peaks/min), ～5-fold to 8-fold higher than typically reported for GC×GC.     

Essential peak area normalisation for quantitative impurity content determination by capillary electrophoresis

Summary A number of papers have been published [1–5] which mention that normalisation of CE peak areas (ie division of peak areas by migration time) is necessary to ensure correct quantitation. However, there is a general unawareness of the impact of not performing this simple data manipulation upon impurity results when expressed as % area/area. An exercise has been conducted to exemplify the need for this normalisation using the separation of selected pharmaceuticals as illustrative examples. The impact of normalisation on % area/area results was demonstrated using the pharmaceutical ranitidine, and a synthetic precusor, as test solutes. The UV absorbance of each compound was determined and found to be equivalent. A solution of ranitidine hydrochloride was the spiked with a weighed amount of precursor. The % area/area CE results, when normalised, mateched the known weighed radio. Use of uncorrected peak area data in this instance would have resulted in a severe underestimation of impurity levels. A quantitative analysis of drug related impurities was conducted at three levels of operating voltage whilst keeping all other operating parameters constant. This produced electropherograms having identical peak profiles but each peak having a different retention time and peak area. However, when normalised, the results were identical at each level of operating voltage confirming the validity and necessity of normalisation. A chiral separation of a racemic pharmaceutical was conducted. The uncorrected peak area data indicated the test sample was not racemic whilst the corrected data correctly confirmed that the compound was racemic. The significance and impact upon reported purity data of not normalising peak area data has been clearly demonstrated in this paper.     

Modeling of analytical peaks: peaks properties and basic peak functions

The general approach to the detailed characterizing of peak properties based on the use of characteristic points on a peak contour located at the certain levels is proposed. Three basic functions of peaks have been chosen which are submitted in normalized form on height and width. The ability to characterize a peaks shape of a certain analytical series is shown by an example of series of analytical peaks of thallium obtained by stripping voltammetry at linear and step potential sweep. Also the proposed shape parameters are studied for groups of stripping voltammetry and chromatographic peaks.     

Investigation of peak compression effects in packed column supercritical fluid chromatography using chemometrics

Summary In this paper chemometrics have been used to study and characterize peak compression phenomena in packed column SFC. A carbon dioxide/2-methyl-1-propanol mobile phase was used in the experimental design (modifier concentration, temperature and pressure) and modelling part of the investigation. A cubic interaction term was needed in the model to obtain a reasonable fit, suggesting that all three parameters are of significance in terms of controlling peak compression. At the optimum conditions derived from the model a narrow peak was obtained as predicted.     

Factors affecting peak shape in comprehensive two-dimensional gas chromatography with non-focusing modulation

In the case of a non-focusing modulator for comprehensive two-dimensional gas chromatography (GC × GC), the systematic distortions introduced when the modulator loads the second-dimension column give rise to a characteristic peak shape. Depending on the operating conditions this systematic distortion can be the dominant component of the second-dimension elution profiles in the GC × GC peak. The present investigation involved a systematic investigation of peak shape in pulsed-flow modulation (PFM)–GC × GC. It is shown that low flow ratio can lead to significant peak skewing and increasing the flow ratio reduces the magnitude of peak skewing. Validation of the peak shape model is made by comparison with experimental data. The residuals from the fitting process (normalised to the maximum detector response) vary between –1.5% and +2.6% for an isothermal model and between –1.0% and +3.0% for a temperature-programmed model.     

Calculation of retention indices and peak widths in temperature programmed gas-liquid chromatography

Summary Isothermal chromatographic measurements lead directly to H _v ^o and A (entropy term) of solutes, and three constants of an empirical relationship between peak width and column temperature. From the thermodynamic parameters H _v ^o and A retention temperatures have been computed by means of a theoretical model including temperature dependence of carrier gas viscosity, and subsequently retention times; programmed retention indices have been determined by linear and polynomial interpolations. By substituting the value of the calculated retention temperature in the above-mentioned relationship, peak width at half-height for a linear temperature may be estimated. Predicted retentions correlate with observed data, with a P-value 0.01; simulation accuracy is generally 6–10% for peak widths.Retention indices of some organochlorine species, separated on an OV-101 capillary column, may differ by as much as 26 units depending on the method of calculation. Polynomial-calculated indices are more consistent with the retention index scheme, and have smaller standard deviations and better constancy at different heating rates.     

Studies on thermionic ionisation detection in comprehensive two-dimensional gas chromatography

This study explores the application of specific thermionic ionisation detection in comprehensive 2-D GC (GC x GC) and represents the first report of GC x GC with nitrogen phosphorus detection (GC x GC-NPD). Of particular interest is the performance of the NPD with respect to peak parameters of asymmetry and sensitivity. Since GC x GC produces much narrower peaks than obtained with fast GC (e.g. 100 ms vs. <1 s) the effect of detector response time and any lack of symmetry arising from the detection step is important if peak separation (resolution) is to be maintained. It was observed that detector gas flows had a significant impact on peak asymmetry and peak magnitude, and that optimisation of the detector was critical, particularly for complex sample analysis by GC x GC-NPD. Peak asymmetries ranging from As = 1.8 to 8.0 were observed under different conditions of detector gas flows. Comparison of GC x GC-NPD with GC x GC-flame ionisation detection (FID) showed the former to be approximately 20 times more sensitive for the detection of nitrogen-containing methoxypyrazines analytes, and GC x GC-NPD had a larger linear detection range compared to GC x GC-FID. Furthermore, comparison of GC x GC-NPD and GC x GC-TOFMS chromatograms for the analysis of coffee head-space demonstrated the benefits of selective detection, ultimately realised in a comparatively simplified contour plot.