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.     

Automatic program for peak detection and deconvolution of multi-overlapped chromatographic signals part II: peak model and deconvolution algorithms

Several interlinked algorithms for peak deconvolution by non-linear regression are presented. These procedures, together with the peak detection methods outlined in Part I, have allowed the implementation of an automatic method able to process multi-overlapped signals, requiring little user interaction. A criterion based on the evaluation of the multivariate selectivity of the chromatographic signal is used to auto-select the most efficient deconvolution procedure for each chromatographic situation. In this way, non-optimal local solutions are avoided in cases of high overlap, and short computation times are obtained in situations of high resolution. A new algorithm, fitting both the original signal and the second derivatives is proved to avoid local optima in intermediate coelution situations. This allows achieving the global optimum without the need of background knowledge by the user. A previously reported peak model, a Gaussian with a polynomial standard deviation whose complexity can be modulated to enhance the fitting quality, was applied. However, the original formulation was modified to account baseline outside the peak region. Also, the optimal model complexity was auto-selected via error propagation theory. The method is able to process simultaneously several related chromatograms. The software was tested with both simulated and experimental chromatograms obtained with monolithic silica columns.     

Kalman filter deconvolution after cubic splines background removal in the HPLC determination of Cr(III) and Al(III) as 8-hydroxyquinolines

Summary A procedure for the simultaneous quantitation of Al(III) and Cr(III) ions by reversed-phase HPLC, after pre-column complexation with 8-hydroxyquinoline, is described. The deconvolution of the partially overlapped peaks was by the Kalman filter method which yielded accurate and precise results. Background removal from the chromatograms was by a new approach employing cubic splines as interpolators between the peak valleys. Finally, it is shown that the Kalman filter deconvolution, after subtraction of the background by cubic spline interpolation, allowed quantitation of Al(III) and Cr(III) down to 25 ppb for each metal. These concentrations were not detectable by conventional integration methods due to a very low signal-to-noise ratio.     

Net analyte signal as a deconvolution-oriented resolution criterion in the optimisation of chromatographic techniques

The performance of two multivariate calibration measurements, multivariate selectivity (SEL(s)) and scalar net analyte signal (scalar NAS), as chromatographic objective functions (COFs), was investigated. Since both assessments are straightforwardly related to the quantification of analytes in the presence of interferents, they were expected to confer new features in the optimisation of compound resolution, not present in conventional assessments. These capabilities are especially interesting in situations of low resolution, where peak deconvolution becomes an attractive alternative. For comparison purposes, chromatographic resolution (R(s)) and peak purity (p(s)) were used as reference COFs. In order to correlate COFs with the probability of deconvolution error, an artificial peak crossing was used to generate 73 different peak arrangements, which were deconvolved using three different methods. SEL(s) exhibited the best correlation, which allowed predicting properly the risk of obtaining inaccurate deconvolutions. The optimisation of a poorly resolved mixture of 16 aromatic compounds by reversed-phase liquid chromatography with methanol-water and acetonitrile-water mobile phases was examined to investigate the differences in performance among the resolution criteria. In situations like these, SEL(s) tends to consider acceptable mobile phase compositions with partial coelution, which permits however the deconvolution with low errors. In contrast, p(s) selects compositions where the resolution of some compounds is sacrificed to enhance the separation of others. Scalar NAS was not so favourable as expected, since it depends on sampling frequency and peak widening. SEL(s) was not affected by these factors.     

An absorbance-based micro-fluidic sensor for diffusion coefficient and molar mass determinations

The H-Sensor reported herein is a micro-fluidic device compatible with flow injection analysis (FIA) and high performance liquid chromatography (HPLC). The device detects analytes at two separate off-chip absorbance flow cells, providing two simultaneous absorbance measurements. The ratio of these two absorbance signals contains analyte diffusion coefficient information. A theoretical model for the sensing mechanism is presented. The model relates the signal Ratio to analyte diffusion coefficient. The model is qualitatively evaluated by comparing theoretical and experimental signal Ratio values. Experimental signal Ratios were collected via FIA for a variety of analytes, including sodium azide, benzoic acid, amino acids, peptides, and proteins. Measuring absorbance at multiple wavelengths provides higher order data allowing the analyte signals from mixtures to be deconvolved via classical least squares (CLS). As a result of the H-Sensor providing two simultaneous signals as a function of time for each sample injection, two simulated second-order HPLC chromatograms were generated using experimental H-Sensor data. The chemometric deconvolution method referred to as the generalized rank annihilation method (GRAM) was used to demonstrate chromatographic and spectroscopic deconvolution. GRAM also provides the signal Ratio value, therefore simultaneously obtaining the analyte diffusion coefficient information during deconvolution. The two chromatograms successfully serve as the standard and unknown for the GRAM deconvolution. GRAM was evaluated on chromatograms at various chromatographic resolutions. GRAM was found to function to a chromatographic resolution at and above 0.25 with a percent quantitative error of less then 10%.     

Automated gas chromatography with cryogenic/sorbent trap for the measurement of volatile organic compounds in the atmosphere

An automated gas chromatographic system was constructed to easily adapt either the cryogenic trap or chemical sorbent trap for preconcentrating ambient levels of volatile organic compounds. Remarkable similarity in chromatograms from C3 to C10 was found between these two enrichment methods, except that the sorbent trap did not quantitatively trap the C2-hydrocarbons. In contrast to cryogenic trapping, the chromatographic conditions for more volatile compounds were substantially improved using the sorbent trap. Water interference on the porous-layer open tubular column was also better managed using the sorbent trap for the continuous analysis of humid room air. The similarity in peak profiles between the GC-flame ionization detection (FID) and a commercial GC-MS system, regardless of concentration levels, facilitated compound identification on the FID chromatograms based on a field mission involving analysis of 106 air samples.     

Longest distance shifting: A simple and efficient approach for the alignment of shifted chromatographic peaks

The preprocessing of chromatograms, such as the alignment of retention time shifts, is often a crucial step in the proper data analysis chain. Here, an efficient approach to align shifted chromatographic signals, longest distance shifting, is presented and highlighted. The performance of this novel strategy was demonstrated by using both simulated chromatograms that covered the different kinds of retention time shifts and the real experimental chromatograms of Pudilan Xiaoyan Tablets obtained by high‐performance liquid chromatography with photodiode array detection. The averaged correlation coefficient for experimental chromatograms were in the range of 0.9517–0.9840 and the peak factor was 0.9989. As a comparison, all the chromatograms have also been aligned using correlation optimized warping and Interval Correlation Optimized Shifting algorithms. The obtained results indicate that the longest distance shifting algorithm is simpler, faster and more effective, and will be potentially suitable for the alignment of other types of signals.     

Pressure‐Tunable Dual‐Column Ensembles for High‐Speed GC and GC/MS

A series‐coupled ensemble of two capillary GC columns of different selectivity with an adjustable pressure at the column junction point is used to obtain tunable selectivity for high‐speed GC and GC/TOFMS. An electronic pressure controller with a 0.1‐psi step size is used to obtain numerous computer‐selected unique selectivities. System configurations for conventional, atmospheric‐pressure outlet operation with flame ionization detection and for vacuum‐outlet operation with photoionization detection are described for GC‐only experiments. Polydimethylsiloxane is used as the non‐polar column and polyethylene glycol (atmospheric outlet) or triflouropropylpolysiloxane (vacuum outlet) is used as the polar column. For GC/TOFMS experiments, 5% phenyl polydimethylsiloxane was used as the non‐polar column, and polyethylene glycol was used as the polar column. The time‐of‐flight mass spectrometer can acquire up to 500 complete mass spectra per second. Since spectral continuity is achieved across the entire chromatographic peak profile, severely overlapping peaks can be spectrally deconvoluted for high‐speed characterization of completely unknown mixtures. For mixture components with significantly different fragmentation patterns, spectral deconvolution can be achieved for chromatographic peak separations of as little as 6.0 ms. This can result is very large peak capacity for time compressed (not completely resolved) chromatograms. The use of columns with tunable selectivity allows for precise peak‐position control, which can result in more efficient utilization of available peak capacity and thus further time compression of chromatograms. The limits of tunability and deconvolution are tested for near co‐elutions of different classes of hydrocarbon compounds as well as for more multi‐functional mixtures.     

Qualitative evaluation of chromatographic data from quality control schemes using a support vector machine

The qualitative evaluation of chromatographic data in the framework of external quality assurance schemes is considered in this paper. The homogeneity in the evaluation of chromatographic data among human experts in samples with analytes close to the limit of detection of analytical methods was examined and also a Support Vector Machine (SVM) was developed as an alternative to experts for a more homogeneous and automatic evaluation. A set of 105 ion chromatograms obtained by anti-doping control laboratories was used in this study. The quality of the ion chromatograms was evaluated qualitatively by nine independent experts (associating a score from 0 to 4) and also more objectively taking into account chromatographic parameters (peak width, asymmetry, resolution and S/N ratio). Results obtained showed a high degree of variability among experts when judging ion chromatograms. Experts applying extremely outlying evaluation criteria were identified and excluded from the data used to develop the SVM. This machine was built providing the system with qualitative information (scores assigned by experts) and with objective data (parameters) of the ion chromatograms. A seven-fold cross-validation approach was used to train and to evaluate the predictive ability of the machine. According to the results obtained, the SVM developed was found to be close to the reasoning process followed by the homogeneous human expert group. This machine also could provide a scoring system to sort laboratories according to the quality of their results. The qualitative evaluation of analytical records using a scoring system allowed the identification of the main factors affecting the quality of chromatographic analytical data, such as the specific analytical technique applied and the adherence to guidelines for reporting positive results.     

A new statistical method for the automated detection of peaks in UV-DAD chromatograms of a sample mixture

One of the major issues within the context of the fully automated development of chromatographic methods consists of the automated detection and identification of peaks coming from complex samples such as multi-component pharmaceutical formulations or stability studies of these formulations. The same problem can also occur with plant materials or biological matrices. This step is thus critical and time-consuming, especially when a Design of Experiments (DOE) approach is used to generate chromatograms. The use of DOE will often maximize the changes of the analytical conditions in order to explore an experimental domain. Unfortunately, this generally provides very different and “unpredictable” chromatograms which can be difficult to interpret, thus complicating peak detection and peak tracking (i.e. matching peaks among all the chromatograms). In this context, Independent Components Analysis (ICA), a new statistically based signal processing methods was investigated to solve this problem. The ICA principle assumes that the observed signal is the resultant of several phenomena (known as sources) and that all these sources are statistically independent. Under those assumptions, ICA is able to recover the sources which will have a high probability of representing the constitutive components of a chromatogram. In the present study, ICA was successfully applied for the first time to HPLC–UV-DAD chromatograms and it was shown that ICA allows differentiation of noise and artifact components from those of interest by applying clustering methods based on high-order statistics computed on these components. Furthermore, on the basis of the described numerical strategy, it was also possible to reconstruct a cleaned chromatogram with minimum influence of noise and baseline artifacts. This can present a significant advance towards the objective of providing helpful tools for the automated development of liquid chromatography (LC) methods. It seems that analytical investigations could be shortened when using this type of methodologies.     

Correction of retention time shifts for chromatographic fingerprints of herbal medicines

In this study, the combination of chemometric resolution and cubic spline data interpolation was investigated as a method to correct the retention time shifts for chromatographic fingerprints of herbal medicines obtained by high-performance liquid chromatography-diode array detection (HPLC-DAD). With the help of the resolution approaches in chemometrics, it was easy to identify the purity of chromatographic peak clusters and then resolve the two-dimensional response matrix into chromatograms and spectra of pure chemical components so as to select multiple mark compounds involved in chromatographic fingerprints. With these mark components determined, the retention time shifts of chromatographic fingerprints might be then corrected effectively. After this correction, the cubic spline interpolation technique was then used to reconstruct new chromatographic fingerprints. The results in this work showed that, the purity identification of the chromatographic peak clusters together with the resolution of overlapping peaks into pure chromatograms and spectra by means of chemometric approaches could provide the sufficient chromatographic and spectral information for selecting multiple mark compounds to correct the retention time shifts. The cubic spline data interpolation technique was user-friendly to the reconstruction of new chromatographic fingerprints with correction. The successful application to the simulated and real chromatographic fingerprints of two Cortex cinnamomi, fifty Rhizoma chuanxiong, ten Radix angelicae and seventeen Herba menthae samples from different sources demonstrated the reliability and applicability of the approach investigated in this work. Pattern recognition based on principal component analysis for identifying inhomogenity in chromatographic fingerprints from real herbal medicines could further interpret it.     

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.     

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.     

Chemometric analysis of high performance liquid chromatography-diode array detection-electrospray mass spectrometry of 2- and 3-hydroxypyridine

Triply coupled high performance liquid chromatography using diode array detection and positive ion electrospray mass spectrometry of 2- and 3-hydroxypyridine is presented. Considerations of the physical method for coupling the two detectors, the influence of pH on retention times, the cone voltage of the mass spectrometer and the linear concentration ranges are described. Data from both detectors are aligned and interpolated. The analyte mass spectra are reduced to 20 significant masses. Principal components plots on the raw, normalised and standardised data, derivatives to determine composition 1 regions, deconvolution and procrustes analysis to compare data from both detectors are discussed. Common trends in both mass spectral and diode array chromatograms are interpreted. This paper represents a new approach to common processing of chromatographic data from two detectors.     

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.