Peak area measurement of severely overlapped pairs

Summary Based on the ratio of two apparent heights and an empirical correction factor, a method is presented for quantitation of peak areas of severely overlapped pairs. This method can be applied to a wide range of area ratios and peak asymmetries, provided there exists a clear and precise valley-except for shoulder peaks. The relative errors of the first peak are usually within ±3% and theoretical relative error limits are −7.0% to +5.5%. Peak asymmetry of a severely overlapped pair can be determined using the ratio of the front half-width to the rear half-width at 10% peak height of an overlapping profile. The asymmetry so determined is an apparent one and the relative errors are −4% to +5.3% for peaks with 90% relative valley, depending on area ratio, degree of overlap and asymmetry. An empirical area equation for the first peak involving area ratio, asymmetry, resolution and the area measured by a perpendicular drop algorithm is also developed.     

Robust interpretive optimisation in high-performance liquid chromatography considering uncertainties in peak position

In the context of interpretive chromatographic optimisation, robustness is usually calculated by introducing deliberated shifts in the nominal optimal conditions and evaluating their effects on the monitored objective function, mimicking thus the experimental procedures used in method validation. However, such strategy ignores a major source of error: the uncertainties associated to the modelling step, that may give rise to deceiving results when conditions that were expected to yield baseline separation are reproduced in the chromatograph. Two approaches, based on the peak purity concept, are here proposed to evaluate the robustness of the objective function under the perspective of measurement errors and modelling. The first approach implements these uncertainties as an extra band broadening for each chromatographic peak. The second one implements them as peak fluctuations in simulated replicated assays, which gives rise to a distribution of peak purities, easily computed through Monte-Carlo simulations. Both approaches predict satisfactorily a decreased separation capability, with respect to the conventional approach, for those situations where the uncertainties in peak position make the objective function critical. The first approach is less optimistic and formally less rigorous than the second one, but its computation is simpler. It can be used to map the critical resolution regions, to be comprehensively appraised further by the slower, although more rigorous, Monte-Carlo approach.     

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 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.     

Simultaneous deconvolution and re-construction of primary and secondary overlapping peak clusters in comprehensive two-dimensional gas chromatography

In this study, simultaneous deconvolution and reconstruction of peak profiles in the first ((1)D) and second dimension ((2)D) of comprehensive two-dimensional (2D) gas chromatography (GC×GC) is achieved on the basis of the property of this new type of instrumental data. First, selective information, where only one component contributes to the peak elution window of a given modulation event, is employed for stepwise stripping of each (2)D peak with the help of pure components corresponding to that compound from the neighbouring modulations. Simulation based on an exponentially modified Gaussian (EMG) model aids this process, where the EMG represents the envelope of all (2)D peaks for that compound. The peak parameters can be restricted by knowledge of the pure modulated (2)D GC peaks derived from the same primary compound, since it is modulated into several fractions during the trapping and re-focusing process of the cryogenic modulation system according to the modulation period. Next, relative areas of all pure (2)D components of that compound are considered for reconstruction of the primary peak. This strategy of exploitation of the additional information provided by the second dimension of separation allows effective deconvolution of GC×GC datasets. Non-linear least squares curve fitting (NLLSCF) allows the resolved 2D chromatograms to be recovered. Accurate acquisition of the pure profiles in both (1)D and (2)D aids quantification of compositions and prediction of 2D retention parameters, which are of interest for qualitative and quantitative analysis. The ratio between the sum of squares of deconvolution residual and original peak response (R(rr)) is employed as an effective index to evaluate the resolution results. In this work, simulated and experimental examples are used to develop and test the proposed approach. Satisfactory performance for these studies is validated by minimum and maximum R(rr) values of 1.34e-7% and 1.09e-2%; and 1.0e-3% and 3.0e-1% for deconvolution of (1)D and (2)D peaks, respectively. Results suggest that the present technique is suitable for GC×GC data processing.     

原料奶在HPLC-MS负离子模式下的指纹图谱研究

采用高效液相色谱质谱联用技术,在负离子扫描模式下建立了原料奶的乙腈提取成分的指纹图谱。采用乙腈和0.1％的乙酸为流动相进行二元梯度洗脱,柱温30℃,分析时间为85 min。确定了11个共有峰,以7号峰为参照物,通过相对峰面积和相对保留时间进行了方法学考察。结果表明,本方法具有良好的重现性,各指纹峰相对保留时间的RSD<0.79％,相对峰面积的RSD<2.84％。在原料奶指纹图谱基础上,选取有代表性有害物如防腐剂苯甲酸等进行了标准添加,建立了添加图谱,对沈阳地区超市的50个纯牛奶样品进行了筛查,取得初步应用结果。     

High precision instrumental neutron activation analysis of uranium by multiple gamma-ray peak ratio determination

The method of multiple γ-ray peak ratio determination has been applied to the nondestructive neutron activation analysis of uranium in rocks and ores. The photopeaks of²³⁹Np gamma-rays produced by the activation of²³⁸U and those of the fission products of²³⁵U are a measure of the quantity of uranium in the irradiated sample, provided that the uranium is of natural isotopic composition. The ratios between the integrated areas of the different photopeaks are calculated and compared with those obtained for a uranium standard. The uranium concentration in the sample is calculated from the photopeaks whose ratios correspond, within the error limits to those of pure natural uranium. High accuracy better than ±2% has been obtained.     

Correction method for quantitative area determination of overlapping chromatographic peaks based on the exponentially modified Gaussian (EMG) model

A simple method is presented for peak area correction of overlapping peaks. This correction is necessary for the normal approach of dealing with overlapping peaks by a vertical line at the valley point. The relative area errors caused by this vertical line are calculated as the correction factors in three dimensions of peak separation, peak ratio, and peak tailing skew. The calculation is based on the exponentially modified Gaussian asymmetric peak model.     

Linear peak capacity of a comprehensive multi-dimensional separation

In order to resolve (quantifiably and identifiably separate) the same number of peaks in the analysis of the same mixture yielding statistically uniform peak distribution, a comprehensive 2-D separation needs a two times larger peak capacity than a 1-D separation does. Each additional dimension further reduces the utilization of the peak capacity of comprehensive multi-dimensional (MD) separation by a factor of two per dimension. As a result, the same peak capacity means different things for separations with different dimensionalities. This complicates the use of the peak capacity for comparison of the potential separation performance of the separations with different dimensionalities. To facilitate the comparison, a concept of a linear peak capacity has been proposed. The linear peak capacity of an MD separation is the peak capacity of a 1-D separation that, in the analysis of the same mixture, is statistically expected to resolve the same number of peaks as the MD separation is. There are other factors that differently affect the performance of the separations that have different dimensionalities. Peak capacity of a 2-D separation with a rectangular separation space is 27% larger than the product of the peak capacities of its first and second dimension. This advantage of a 2-D separation is essentially nullified by the fact that the peak capacity of the first dimension of an optimized 2-D separation cannot be higher than 80% of the peak capacity of its first dimension standing alone. All in all, the incremental peak capacity gained from addition of a second dimension will not exceed 50% of the peak capacity of the added second dimension. All results are valid for arbitrarily shaped (not necessarily Gaussian) peaks.     

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.     

A Simple and Efficient Approach for Estimating Recovery of a Preparative Reversed Phase HPLC Purification

The widely applied reversed phase high-performance liquid chromatography (RP-HPLC) is an indispensable purification technique in drug discovery. During drug discovery, recovery was usually calculated based on the weight of the purified product after drying over the weight of the crude material multiplied by the assumed purity from HPLC/UV area percent of the product. Such a purity assumption can be off significantly when the crude material contains water, solvents, other UV-inactive impurities and inorganic salts. In this paper, we report a simple and efficient way to estimate recovery of preparative HPLC purification process. It is based on the ratio of the HPLC/UV peak area measured for the product in the crude solution and that in the final collected fraction with both accounted for their volumes. This approach eliminates not only the need for drying of the collected fraction to calculate recovery but also the inaccuracy associated with the true content in the crude sample using the traditional method. A systematic study was conducted to verify this method using caffeine mixed with various UV-active and -inactive impurities. The calculated recoveries using this approach were found to be consistent within 4% with the true recoveries based on dry weight estimation. The approach has been successfully applied for our in-house purifications. Furthermore, the approach was extended to library purifications, where in many cases heart-cutting the desired peaks is used to meet the purity requirements.

     

Influence of temperature on peak shape and solvent compatibility: implications for two-dimensional liquid chromatography

Solvent compatibility is a limiting factor for the success of two-dimensional liquid chromatography (2-D LC). In the second dimension, solvent effects can result in overpressures as well as in peak broadening or even distortion. A peak shape study was performed on a one-dimensional high-performance liquid chromatography (HPLC) system to simulate the impact of peak distorting solvent effects on a reversed-phase second dimension separation operated at high temperatures. This study includes changes in injection volume, solute concentration, column inner diameter, eluent composition and oven temperature. Special attention was given to the influence of high temperatures on the solvent effects. High-temperature HPLC (HT-HPLC) is known to enhance second dimension separations in terms of speed, selectivity and solvent compatibility. The ability to minimise the viscosity contrast between the mobile phases of both dimensions makes HT-HPLC a promising tool to avoid viscosity mismatch effects like (pre-)viscous fingering. In case of our study, viscosity mismatch effects could not be observed. However, our results clearly show that the enhancement in solvent compatibility provided by the application of high temperatures does not include the elimination of solvent strength effects. The additional peak broadening and distortion caused by this effect is a potential error source for data processing in 2-D LC.     

A study of the precision and accuracy of peak quantification in comprehensive two-dimensional liquid chromatography in time

Simulated chromatographic data were used to determine the precision and accuracy in the estimation of peak volumes (i.e., peak sizes) in comprehensive two-dimensional liquid chromatography in time (LC × LC). Peak volumes were determined both by summing the areas in the second dimension chromatograms and by fitting the second dimension areas to a Gaussian peak. The Gaussian method is better at predicting the peak volume than the moments method provided there are at least three second dimension injections above the limit of detection (LOD). However, when only two of the second dimension signals are substantially above baseline, the accuracy and precision of the Gaussian fit method become quite poor because the results from the fitting algorithm become indeterminate. Based on simulations in which the modulation ratio (M_R = 4¹σ/t_s) and sampling phase (?) were varied, we conclude for well-resolved peaks that the optimum precision in peak volumes in 2D separations will be obtained when the M_R is between two and five, such that there are typically four to ten second dimension peaks recorded over the eight σ width of the first dimension peak. This sampling rate is similar to that suggested by the Murphy–Schure–Foley criterion. This provides an RSD of approximately 2% for the signal-to-noise ratio used in the present simulations. The precision of the peak volume of experimental data was also assessed, and RSD values were in the range of 4–5%. We conclude that the poorer precision found in the LC × LC experimental data as compared to LC may be due to experimental imprecision in sampling the effluent from the first dimension column.     

Implications of column peak capacity on the separation of complex peptide mixtures in single- and two-dimensional high-performance liquid chromatography

Column peak capacity was utilized as a measure of column efficiency for gradient elution conditions. Peak capacity was evaluated experimentally for reversed-phase (RP) and cation-exchange high-performance liquid chromatography (HPLC) columns, and compared to the values predicted from RP-HPLC gradient theory. The model was found to be useful for the prediction of peak capacity and productivity in single- and two-dimensional (2D) chromatography. Both theoretical prediction and experimental data suggest that the number of peaks separated in HPLC reaches an upper limit, despite using highly efficient columns or very shallow gradients. The practical peak capacity value is about several hundred for state-of-the-art RP-HPLC columns. Doubling the column length (efficiency) improves the peak capacity by only 40%, and proportionally increases both the separation time and the backpressure. Similarly, extremely shallow gradients have a positive effect on the peak capacity, but analysis becomes unacceptably long. The model predicts that a 2D-HPLC peak capacity of 15,000 can be achieved in 8 h using multiple fraction collection in the first dimension followed by fast RP-HPLC gradients employing short, but efficient columns in the second dimension.     

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.     

A novel determination of peak areas for application on large computers

Summary A computer program with some new algorithms for the determination of peak areas of gas chromatograms has been developed which has been used for several years with a satellite computer system. In contrast to most gc-programs the first and second derivatives of the curve are not used for peak detection. The maximum of a peak is defined by ordinates of the sample points alone; the base line is constructed by drawing curves of higher order through those parts of the chromatogram which are defined to be base line by special criteria. Consequently, the peak areas on the tailing of a solvent are determined more correctly than with skimming and, furthermore, the calculated base line of chromatograms with temperature program and subsequent isothermal run can be approximated to the real base line. The base line divides the chromatogram into several peak groups which are further separated by the democratic distribution method. This program is best suited for nonroutine analysis in research laboratories, because only a few input parameters are necessary for peak area determination with unknown chromatograms.     

Computation of distribution of minimum resolution for log-normal distribution of chromatographic peak heights

General equations are derived for the distribution of minimum resolution between two chromatographic peaks, when peak heights in a multi-component chromatogram follow a continuous statistical distribution. The derivation draws on published theory by relating the area under the distribution of minimum resolution to the area under the distribution of the ratio of peak heights, which in turn is derived from the peak-height distribution. Two procedures are proposed for the equations' numerical solution. The procedures are applied to the log-normal distribution, which recently was reported to describe the distribution of component concentrations in three complex natural mixtures. For published statistical parameters of these mixtures, the distribution of minimum resolution is similar to that for the commonly assumed exponential distribution of peak heights used in statistical-overlap theory. However, these two distributions of minimum resolution can differ markedly, depending on the scale parameter of the log-normal distribution. Theory for the computation of the distribution of minimum resolution is extended to other cases of interest. With the log-normal distribution of peak heights as an example, the distribution of minimum resolution is computed when small peaks are lost due to noise or detection limits, and when the height of at least one peak is less than an upper limit. The distribution of minimum resolution shifts slightly to lower resolution values in the first case and to markedly larger resolution values in the second one. The theory and numerical procedure are confirmed by Monte Carlo simulation.     

Estimation of uncertainty in size-exclusion chromatography with a double detection system (light-scattering and refractive index)

Size-exclusion chromatography (SEC) coupled with online laser light-scattering (LS) and refractive index (RI) detection provides an excellent approach to determine the molecular weights (Mw) of proteins by the “two-detector” approach. Mw is determined only at the maximum of a peak, using either peak heights or area ratio from the two detectors. However, proper calibration of the SEC/LS/RI system is critical to obtain high precision.Today, an essential part of any analysis is to evaluate the uncertainty associated with the method. Basically, it is possible to distinguish between factors related to signal nature, precision and those due to signal processing. Given the signal of interest is the peak height or area ratio from two detectors, the signal ratio uncertainty was calculated using the random propagation of error formula. In this case, the effect of signal correlation was evaluated to avoid the uncertainty overestimation. In the second case, the sources of uncertainty affecting analytical measurement were estimated with the information from the precision assessment. For this, two designs with two-factor fully nested were followed for each method. Finally, the contributions from various uncertainty sources related with calibration are also analysed in detail. There are in fact only three main sources of measurement uncertainty: intermediate precision, calibration and repeatability. Of these, method precision is always the greatest, regardless of approach.For all proteins and peptides studied, the Mw calculated using both methods are close to the theoretical results, independently of the design, but the contributions of individual terms to combined uncertainty depend on both the design and method used. For example, the combined uncertainty varied between 223 and 813.2 Da for carbonic anhydrase, although higher values were found for human insulin and ovalbumin dimer. Other considerations that can have a significant impact on the results are discussed.The reproducibility of the two methods versus that based on ASTRA software used as reference method was performed using the concordance correlation coefficient. The methods’ reproducibility depends on the permitted losses in precision and accuracy.