Singular spectrum analysis for an automated solvent artifact removal and baseline correction of 1D NMR spectra

NMR spectroscopy in biology and medicine is generally performed in aqueous solutions, thus in (1)H NMR spectroscopy, the dominant signal often stems from the partly suppressed solvent and can be many orders of magnitude larger than the resonances of interest. Strong solvent signals lead to a disappearance of weak resonances of interest close to the solvent artifact and to base plane variations all over the spectrum. The AUREMOL-SSA/ALS approach for automated solvent artifact removal and baseline correction has been originally developed for multi-dimensional NMR spectroscopy. Here, we describe the necessary adaptations for an automated application to one-dimensional NMR spectra. Its core algorithm is still based on singular spectrum analysis (SSA) applied on time domain signals (FIDs) and it is still combined with an automated baseline correction (ALS) in the frequency domain. However, both steps (SSA and ALS) have been modified in order to achieve optimal results when dealing with one-dimensional spectra. The performance of the method has been tested on one-dimensional synthetic and experimental spectra including the back-calculated spectrum of HPr protein and an experimental spectrum of a human urine sample. The latter has been recorded with the typically used NOESY-type 1D pulse sequence including water pre-saturation. Furthermore, the fully automated AUREMOL-SSA/ALS procedure includes the managing of oversampled, digitally filtered and zero-filled data and the correction of the frequency domain phase shift caused by the group delay time shift from the digital finite response filtering.     

Signal identification in NMR spectra with coupled evolution periods

Novel multidimensional NMR experiments rely on modified time-domain sampling schemes to provide significant savings of experimental time. Several approaches are based on the coupling of evolution times resulting in a reduction of the dimensionality of the recorded spectra, and a concomitant saving of experimental time. We present a consistent and general tool, called EVOCOUP, for the analysis of these reduced dimensionality spectra. The approach is flexible in the sense that the input can consist of various forms of reduced dimensionality spectra, that any piece of information can be removed (provided enough information is left), e.g., signals undetectable due to poor signal-to-noise or covered by artifacts, and that it can be applied to spectra involving any number of nuclei. The use of a general optimization procedure and an appropriate target function provides for a robust approach with well-defined results and ensures optimal use of redundant information normally present in the input. Spectral overlap in the directly detected dimension is resolved in a fully automated manner, avoiding the assessment of signal quality and its use in combinatorial trials. The positions of all peaks in a corresponding full-dimensional spectrum are obtained without need for reconstruction of this spectrum. In a systematic analysis of a complete spectrum recorded for the 14 kDa protein azurin and involving five different nuclei, only four spin systems were missed and no false spins systems were detected.     

Robust baseline correction algorithm for signal dense NMR spectra

This paper outlines a fully automated algorithm for baseline correction. Based on our experience with NMR spectra of complex mixtures, this algorithm is designed to automatically differentiate signal points from baseline points. The algorithm's strength is its ability to accurately determine baseline points in very dense spectra, without destroying the line shapes of prominent peaks. The algorithm described is implemented in Chenomx NMR Suite 4.6. It is demonstrated here using two separate spectra acquired on two different NMR spectrometers.     

Bayesian Estimation of NMR Spectral Parameters Under Low Signal-to-Noise Conditions

The Bayesian statistical method of spectral estimation is applied to NMR free induction decay signals at various values of signal-to-noise ratio (SNR). The frequency and amplitude estimates from the Bayesian calculations are more accurate than those from the commonly used fast Fourier transformation (FFT) of the same data sets. Both real and synthetic data sets are examined with the Bayesian results being superior in all cases. In addition to the superior performance at low SNR the Bayesian derived amplitudes and frequency estimates were not as affected by signal decay as in Fourier Transformed spectra. Finally, the amplitudes obtained are equal to the FFT integrated intensities resulting in an apparent frequency domain signal-to-noise ratio (SNR) greater than the FFT SNR by a factor proportional to the FFT frequency domain linewidth. For typical high resolution spectra this improvement was approximately a factor of 2.5. Even greater improvement is obtained when rapidly decaying signals are analyzed. Bayesian computation time for the 6 line p-chloroanaline and chloroform spectrum was approximately 12 minutes on a modern computer work station.     

一种核磁共振波谱谱峰对齐及谱峰提取的方法

在代谢组学研究方法中,对一组具有生物学意义且平行的核磁共振波谱数据进行处理是其方法研究的关键,其中包含谱峰对齐、谱峰提取、噪音去除等几个步骤。该文提出了一种全新且快速有效的核磁共振波谱批量处理方法。其原理主要为：在保持波谱形状不发生变化的同时,通过平移目标谱使其与参考谱达到最大程度的相关,从而实现谱峰对齐及利用谱峰最大值的判断来实现谱峰变量的提取。此外,该文还结合大鼠尿样和血样的分析结果,详细地说明了算法的准确性及其它优点。该文所涉及的算法是基于Matlab程序进行编译的,可以结合不同实验进行改编,具有良好的扩展性。     

Rapid construction of solid-state magnetic resonance powder spectra from frequencies and amplitudes as applied to ESEEM

In many Fourier-transform spectroscopies, such as pulse magnetic resonance (NMR, EPR), time-domain signals are acquired. Parameters are extracted from these signals by fitting numerical simulations to the experimental data. At present, simulations are often performed in frequency domain (FD). These computations generate a list of frequencies and amplitudes associated with the complex exponential components evolving during one or several variable time intervals. In order to compare simulations with experiments, this peak list is converted to a finite-length time-domain (TD) signal. This can be achieved either by directly evoluting the exponentials in time (direct method) or by rounding their frequencies and binning their amplitudes into a frequency-domain array (histogram method). The first approach is equivalent to a brute-force TD simulation and is slow for a large number of peaks. The second approach is a fast, but very crude approximation and is usually applied without considering in detail the errors involved. A third method introduced and illustrated here is based on the convolution and deconvolution of a short finite impulse response filter kernel. This convolution approach is much faster than the direct method and by orders of magnitude more accurate than the histogram method. For both TD and FD signals a detailed analysis of the errors and of the associated computational costs is presented. The convolution approach is applicable to any simulation problem where TD signals consist of a large number of complex exponentials. In particular, it is the method of choice for simulating 1D and 2D electron spin echo envelope modulation (ESEEM) spectra of disordered systems.     

A new general-purpose fully automatic baseline-correction procedure for 1D and 2D NMR data

A new procedure for automatic baseline correction of NMR data sets is presented. It is based on an improved automatic recognition of signal-free regions that uses a Continuous Wavelet transform derivative calculation, followed by a baseline modelling procedure based on the Whittaker smoother algorithm. The method has been proven to automatically flatten 1D and 2D NMR spectra with large baseline distortions arising from different sources, is tolerant to low signal-to-noise ratio spectra, and to signals of varying widths in a single spectrum. Even though this procedure has so far only been applied to NMR spectra, we believe it to also be applicable to other spectroscopies having relatively narrow peaks (e.g., mass spectrometry), and potentially to those with broad peaks (e.g., near infrared or ultraviolet).     

Line shape considerations in ultrafast 2D NMR

We have recently proposed and demonstrated an approach that enables the acquisition of 2D nuclear magnetic resonance (NMR) spectra within a single scan. The approach is based on spatially encoding the spins' evolution along the indirect domain with the aid of a magnetic field gradient, and subsequently decoding this information numerous times over the course of the signal acquisition while spins are subject to a train of gradient echoes. The present paper discusses further considerations pertaining the 2D line shapes arising from this new way of collecting NMR data. Specific issues that are hereby addressed include (i) the effects introduced by fast relaxation onto the spatial encoding process, particularly the line widths and line shapes that will then arise in the frequency domain; (ii) approaches capable of correcting for the mixed-phase kernels resulting in these fast-relaxation cases, corresponding in essence to spatially encoded analogs of the TPPI and hypercomplex time-domain acquisition procedures; (iii) the enveloping characteristics imposed by the use of discrete excitation pulses on the attainable spectral widths along the indirect domain; and (iv) an analysis of the signal-to-noise characteristics of the methodology, with experimental corroborations of theoretical predictions and an illustration of the method's capabilities to analyze protein solutions in the mM-range concentration.     

Sequentially acquired two-dimensional NMR spectra from hyperpolarized sample

A scheme capable of acquiring heteronuclear 2D NMR spectra of hyperpolarized sample is described. Hyperpolarization, the preparation of nuclear spins in a polarized state far from thermal equilibrium, can increase the NMR signal by several orders of magnitude. It presents opportunities to apply NMR spectroscopy to dilute samples that would otherwise yield insufficient signal. However, conventional 2D NMR spectroscopy, which is commonly applied for the determination of molecular structure, relies on the recovery of the initial polarization after each transient. For this reason, it cannot be applied directly to a sample that has been hyperpolarized once. With appropriately modified pulse schemes, two-dimensional NMR spectra an however be acquired sequentially by utilizing a small portion of the hyperpolarized signal in every scan, while keeping the remaining polarization for future scans. We present heteronuclear multi-quantum spectra of single hyperpolarized samples using this technique, and discuss different options for distributing the polarization among different scans. This robust method takes full advantage of Fourier NMR to resolve overlapping chemical shifts, and may prove particularly useful for the structural elucidation of compounds in mass-limited samples.     

A model for domain and domain wall NMR signals in magnetic materials

Spin echo NMR signals in magnetic materials (simple metals, alloys or intermetallic compounds) generally result from mixed contributions of distinct magnetic regions of the sample, the magnetic domains and the domain walls. The amplitude of the signal is proportional to the so-called enhancement factor which in most of the cases greatly differs in these two regions, depending upon the wall mobility, the magnetic anisotropy, etc. The experimental access to domain and domain walls is possible, in principle, by a careful control of the RF power applied to the sample. In this paper a simple superposition model is proposed which includes both contributions to the NMR signal. We calculate the amplitude of the spin echo in magnetic powder samples and compare it with experimental situations where it has been possible to separate different contributions to the signal. This has been done in some RCo₂ magnetic rare-earth intermetallic compounds by analyzing the spectral line widths and the curve of the spin echo amplitude versus the applied RF field. Despite its simplicity, the present model allows the understanding of the main features of the NMR spectra and the dependence of the echo amplitude with the RF power in these compounds.     

On the accuracy of thickness measurements in impact-echo testing of finite concrete specimens--numerical and experimental results

In impact-echo testing of finite concrete structures, reflections of Rayleigh and body waves from lateral boundaries significantly affect time-domain signals and spectra. In the present paper we demonstrate by numerical simulations and experimental measurements at a concrete specimen that these reflections can lead to systematic errors in thickness determination. These effects depend not only on the dimensions of the specimen, but also on the location of the actual measuring point and on the duration of the detected time-domain signal.     

Application of the Filter Diagonalization Method to One- and Two-Dimensional NMR Spectra

A new non-Fourier data processing algorithm, the filter diagonalization method (FDM), is presented and applied to phase-sensitive 1D and 2D NMR spectra. FDM extracts parameters (peak positions, linewidths, amplitudes, and phases) directly from the time-domain data by fitting the data to a sum of damped complex sinusoids. Grounded in a quantum-mechanical formalism, FDM shares some of the features of linear prediction and other linear algebraic approaches, but is numerically more efficient, scaling like the fast Fourier transform algorithm with respect to data size, and has the ability to correctly handle spectra with thousands or even millions of lines where the competing methods break down. Results obtained on complex spectra are promising.     

The equilibrium unfolding of MerP characterized by multivariate analysis of 2D NMR data

A general problem when analysing NMR spectra that reflect variations in the environment of target molecules is that different resonances are affected to various extents. Often a few resonances that display the largest frequency changes are selected as probes to reflect the examined variation, especially in the case, where the NMR spectra contain numerous resonances. Such a selection is dependent on more or less intuitive judgements and relying on the observed spectral variation being primarily caused by changes in the NMR sample. Second, recording changes observed for a few (albeit significant) resonances is inevitably accompanied by not using all available information in the analysis. Likewise, the commonly used chemical shift mapping (CSM) [Biochemistry 39 (2000) 26, Biochemistry 39 (2000) 12595] constitutes a loss of information since the total variation in the data is not retained in the projection into this single variable. Here, we describe a method for subjecting 2D NMR time-domain data to multivariate analysis and illustrate it with an analysis of multiple NMR experiments recorded at various folding conditions for the protein MerP. The calculated principal components provide an unbiased model of variations in the NMR spectra and they can consequently be processed as NMR data, and all the changes as reflected in the principal components are thereby made available for visual inspection in one single NMR spectrum. This approach is much less laborious than consideration of large numbers of individual spectra, and it greatly increases the interpretative power of the analysis.     

High-resolution 2D NMR spectra in inhomogeneous fields based on intermolecular multiple-quantum coherences with efficient acquisition schemes

High-resolution 2D NMR spectra in inhomogeneous fields can be achieved by the use of intermolecular multiple-quantum coherences and shearing reconstruction of 3D data. However, the long acquisition time of 3D spectral data is generally unbearable for in vivo applications. To overcome this problem, two pulse sequences dubbed as iDH-COSY and iDH-JRES were proposed in this paper. Although 3D acquisition is still required for the new sequences, the high-resolution 2D spectra can be obtained with a relatively short scanning time utilizing the manipulation of indirect evolution period and sparse sampling. The intermolecular multiple-quantum coherence treatment combined with the raising and lowering operators was applied to derive analytical signal expressions for the new sequences. And the experimental observations agree with the theoretical predictions. Our results show that the new sequences possess bright perspective in the applications on in vivo localized NMR spectroscopy.     

Missing first points and phase artifact mutually entangled in FT NMR data--noniterative solution

Even moderate distortion at the beginning of the NMR signal contributes significantly to the baseline in the reciprocal domain, when the FID-type experiment is considered. If constant phase artifact is also involved, the net problem cannot be resolved accurately, according to its constituents considered in separation. This issue is particularly severe for powder patterns in solids, featuring complex broadband spectra, which substantially mask the baseline behavior. The complete correction procedure should intrinsically deal with both artifacts, due to the mutual dependency. The aim of this work is to indicate the possibility for the exact treatment of baseline and constant phase artifacts together, providing precise measure whether the correction is successful. We have found the analytical, noniterative solution for this coupled problem in the closed form. In this paper, we introduce the correction efficiency concept in order to have the measure for the correction reliability of the resulting spectrum. Relevant efficiency parameter eta is the subject for quantitative analysis resulting in certain constraints for the measurement. We have determined exemplar trends for this parameter as a function of experimental variables such as signal-to-noise ratio and missing points number. The method is model-free and drawn from the origin of the baseline artifact; therefore has potential to work for a broad range of applications.     

基于衰减全反射式太赫兹时域光谱技术的食用油光谱特性研究

食用油是人类营养和能量的重要来源,为人体提供必需的脂肪酸,研究食用油在太赫兹波段光学特性,对食用油成分分析及品质评价具有重要价值。衰减全反射式太赫兹时域光谱技术是一种新型的太赫兹时域光谱技术,通过样品与倏逝波的相互作用,获取样品的太赫兹光谱。与透射式或反射式太赫兹时域光谱技术相比,该技术能有效地避免测量食用油等液体样品时样品池对光学参数的影响,并能获得样品的精确光学参数。分别利用透射式太赫兹时域光谱技术和衰减全反射式太赫兹时域光谱技术测量了大豆油的吸收光谱。结果表明,与透射式太赫兹时域光谱技术相比,衰减全反射式太赫兹时域光谱技术能更有效地提取大豆油的吸收系数、吸收峰分布等光学特性。进一步利用衰减全反射式太赫兹时域光谱技术研究了大豆油、核桃油、葡萄籽油在太赫兹波段的光学特性,获得了三种食用油在1~1.8 THz范围内的折射率谱和吸收光谱。利用密度泛函理论计算了食用油中四种主要成分(软脂酸、硬脂酸、油酸和亚油酸)在太赫兹波段的振动、转动模式,理论计算结果同实验测量结果吻合较好。研究表明,在太赫兹波段食用油的吸收峰与所含脂肪酸分子种类与含量有关,其主要来源为脂肪酸分子的低频振动和转动。研究成果对食用油成分定性定量分析及品质检测等具有指导意义。     

基于噪声预估计的DPOAE最小二乘估计方法*

针对畸变产物耳声发射(distortion product otoacoustic emission, DPOAE)信号比较微弱,估计结果的准确性对信噪比依赖性强的特点,本文给出一种新的DPOAE信号最小二乘估计(least square estimation, LSE)方法。该方法先估计本底噪声,将本底噪声的影响体现于估计模型中,再估计DPOAE信号。记录信号经过一定的预处理后,利用频域加窗法估计本底噪声并进行噪声衰减;利用IFFT变换后的信号估计DPOAE信号的模型参数,给出DPOAE的强度和相位。仿真和实验结果表明,该方法相对于传统的最小二乘拟合(least-square-fit, LSF)法,对DPOAE的估计更加准确,抗噪声干扰能力更强。     

Spectral restoration from low signal-to-noise,distorted NMR signals: application to hyphenated capillary electrophoresis-NMR

In capillary electrophoresis separations coupled to NMR signal detection using small solenoidal coils, electrophoretic currents cause substantial distortion in the NMR spectral linewidths and peak heights, distortions which cannot be fully counteracted through shimming. The NMR spectra also have a low signal-to-noise ratio due to the small amounts of material, typically <1nmol, associated with such microseparations. This study proposes a two-step, signal processing method to restore spectral lines from the distorted NMR spectrum. First, a reference signal is acquired to estimate the broadening function, as a combination of several Lorentzian functions, using a gradient descent method. Then multi-resolution wavelet analysis is applied to the distorted spectrum to determine an initial estimate of the frequencies of the spectral lines. Convergence to the final spectrum, a second set of Lorentzians, involves deconvolution with the estimated broadening function using a gradient descent method. Experimental CE-NMR data show that considerable improvements in spectral quality are possible using this approach, although fine splittings can not be resolved if the broadening function is large.