Noise Reduction in Solid-State NMR Spectra Using Principal Component Analysis

Multivariate Machine Learning Models of Nanoscale Porosity from Ultrafast NMR Relaxometry

Nanoporous materials are of great interest in many applications, such as catalysis, separation, and energy storage. The performance of these materials is closely related to their pore sizes, which are inefficient to determine through the conventional measurement of gas adsorption isotherms. Nuclear magnetic resonance (NMR) relaxometry has emerged as a technique highly sensitive to porosity in such materials. Nonetheless, streamlined methods to estimate pore size from NMR relaxometry remain elusive. Previous attempts have been hindered by inverting a time domain signal to relaxation rate distribution, and dealing with resulting parameters that vary in number, location, and magnitude. Here we invoke well-established machine learning techniques to directly correlate time domain signals to BET surface areas for a set of metal-organic frameworks (MOFs) imbibed with solvent at varied concentrations. We employ this series of MOFs to establish a correlation between NMR signal and surface area via partial least squares (PLS), following screening with principal component analysis, and apply the PLS model to predict surface area of various nanoporous materials. This approach offers a high-throughput, non-destructive way to assess porosity in c.a. one minute. We anticipate this work will contribute to the development of new materials with optimized pore sizes for various applications.

Sensitivity considerations on denoising series of spectra by singular value decomposition

When acquiring series of spectra ( T 1 , T 2 , CP buildup curves, etc.) on samples with poor SNR, we are usually faced with choosing between taking a few points with a large number of scans to maximize the SNR or more points with a smaller number of scans to maximize the information content. In this Letter, we show how low-rank decomposition can be used to denoise a series of spectra, reducing the trade-off between the number of scans and the number of experiments.

Deep Learning Methodology for Obtaining Ultraclean Pure Shift Proton Nuclear Magnetic Resonance Spectra

Nuclear magnetic resonance (NMR) is one of the most powerful analytical techniques. In order to obtain high-quality NMR spectra, a real-time Zangger-Sterk (ZS) pulse sequence is employed to collect low-quality pure shift NMR data with high efficiency. Then, a neural network named AC-ResNet and a loss function named SM-CDMANE are developed to train a network model. The model with excellent abilities of suppressing noise, reducing line widths, discerning peaks, and removing artifacts is utilized to process the acquired NMR data. The processed spectra with noise and artifact suppression and small line widths are ultraclean and high-resolution. Peaks overlapped heavily can be resolved. Weak peaks, even hidden in the noise, can be discerned from noise. Artifacts, even as high as spectral peaks, can be removed completely while not suppressing peaks. Eliminating perfectly noise and artifacts and smoothing baseline make spectra ultraclean. The proposed methodology would greatly promote various NMR applications.

DESPERATE: A Python library for processing and denoising NMR spectra

NMR spectroscopy is an inherently insensitive technique with respect to the amount of observable signal. A common element in all NMR spectra is random thermal noise that is often characterized by a signal-to-noise ratio (SNR). SNR can be generically improved experimentally with repetitive signal averaging or during post-processing with apodization; the former of which often results in long experimental times and the latter results in the loss of spectral resolution. Denoising techniques can instead be used during post-processing to enhance SNR without compromising resolution. The most common approach relies on the singular-value decomposition (SVD) to discard noisy components of NMR data. SVD-based approaches work well, such as Cadzow and PCA, but are computationally expensive when used for large datasets that are often encountered in NMR (e.g., Carr-Purcell/Meiboom-Gill and nD datasets). Herein, we describe the implementation of a new wavelet transform (WT) routine for the fast and robust denoising of 1D and 2D NMR spectra. Several simulated and experimental datasets are denoised with both SVD-based Cadzow or PCA and WT's, and the resulting SNR enhancements and spectral uniformity are compared. WT denoising offers similar and improved denoising compared with SVD and operates faster by several orders-of-magnitude in some cases. All denoising and processing routines used in this work are included in a free and open-source Python library called DESPERATE.

Parameter Visualization of Benchtop Nuclear Magnetic Resonance Spectra toward Food Process Monitoring

Low-cost and user-friendly benchtop low-field nuclear magnetic resonance (NMR) spectrometers are typically used to monitor food processes in the food industry. Because of excessive spectral overlap, it is difficult to characterize food mixtures using low-field NMR spectroscopy. In addition, for standard compounds, low-field benchtop NMR data are typically unavailable compared to high-field NMR data, which have been accumulated and are reusable in public databases. This work focused on NMR parameter visualization of the chemical structure and mobility of mixtures and the use of high-field NMR data to analyze benchtop NMR data to characterize food process samples. We developed a tool to easily process benchtop NMR data and obtain chemical shifts and T2 relaxation times of peaks, as well as transform high-field NMR data into low-field NMR data. Line broadening and time–frequency analysis methods were adopted for data processing. This tool can visualize NMR parameters to characterize changes in the components and mobilities of food process samples using benchtop NMR data. In addition, assignment errors were smaller when the spectra of standard compounds were identified by transferring the high-field NMR data to low-field NMR data rather than directly using experimentally obtained low-field NMR spectra.

Materials informatics approach using domain modelling for exploring structure-property relationships of polymers

In the development of polymer materials, it is an important issue to explore the complex relationships between domain structure and physical properties. In the domain structure analysis of polymer materials, ¹H-static solid-state NMR (ssNMR) spectra can provide information on mobile, rigid, and intermediate domains. But estimation of domain structure from its analysis is difficult due to the wide overlap of spectra from multiple domains. Therefore, we have developed a materials informatics approach that combines the domain modeling (http://dmar.riken.jp/matrigica/) and the integrated analysis of meta-information (the elements, functional groups, additives, and physical properties) in polymer materials. Firstly, the ¹H-static ssNMR data of 120 polymer materials were subjected to a short-time Fourier transform to obtain frequency, intensity, and T₂ relaxation time for domains with different mobility. The average T₂ relaxation time of each domain is 0.96 ms for Mobile, 0.55 ms for Intermediate (Mobile), 0.32 ms for Intermediate (Rigid), and 0.11 ms for Rigid. Secondly, the estimated domain proportions were integrated with meta-information such as elements, functional group and thermophysical properties and was analyzed using a self-organization map and market basket analysis. This proposed method can contribute to explore structure–property relationships of polymer materials with multiple domains.

Noise-Reduced Quantitative Fluorine NMR Spectroscopy Reveals the Presence of Additional Per- and Polyfluorinated Alkyl Substances in Environmental and Biological Samples When Compared with Routine Mass Spectrometry Methods

Per- and polyfluorinated alkyl substances (PFAS) are ubiquitous throughout the environment. Analysis of PFAS is commonly performed using both targeted and nontargeted mass spectrometry methods. However, it has been demonstrated that measurements of fluorinated compounds in the environment by mass spectrometry often fall short of the total fluorine concentration. In the present study, we employ a ¹⁹F NMR technique, which is capable of detailing fluorinated compounds in a sample while providing both quantitative and structural information. Inclusion of a noise-reduction strategy involving the acquisition of arrays of spectra with an increasing number of transients addresses the sensitivity challenges of environmental nuclear magnetic resonance (NMR), improving signal to noise. When this technique is applied to environmental and biological samples including rainwater, lake water, wastewater effluent, serum, and urine, the presence of PFAS, which may have been missed by routine mass spectrometric methods, is revealed. Important resonances in the ¹⁹F NMR spectrum such as that of trifluoroacetic acid are brought above the limit of quantification in all samples, allowing detection limits as low as 389 pg/L in rainwater. A liquid chromatography-tandem mass spectrometry (LC-MS/MS) method, which was used to analyze 47 PFAS compounds, accounts for only 3.7-27% of the total fluorine concentration as determined by the NMR strategy in the present study.

3D Relaxation-Assisted Separation of Wideline Solid-State NMR Patterns for Achieving Site Resolution

There are currently no methods for the acquisition of ultra-wideline (UW) solid-state NMR spectra under static conditions that enable reliable separation and resolution of overlapping powder patterns arising from magnetically...

Integrative measurement analysis via machine learning descriptor selection for investigating physical properties of biopolymers in hairs

Integrative measurement analysis of complex subjects, such as polymers is a major challenge to obtain comprehensive understanding of the properties. In this study, we describe analytical strategies to extract and selectively associate compositional information measured by multiple analytical techniques, aiming to reveal their relationships with physical properties of biopolymers derived from hair. Hair samples were analyzed by multiple techniques, including solid-state nuclear magnetic resonance (NMR), time-domain NMR, Fourier transform infrared spectroscopy, and thermogravimetric and differential thermal analysis. The measured data were processed by different processing techniques, such as spectral differentiation and deconvolution, and then converted into a variety of “measurement descriptors” with different compositional information. The descriptors were associated with the mechanical properties of hair by constructing prediction models using machine learning algorithms. Herein, the stepwise model refinement via selection of adopted descriptors based on importance evaluation identified the most contributive descriptors, which provided an integrative interpretation about the compositional factors, such as α-helix keratins in cortex; and bounded water and thermal resistant components in cuticle. These results demonstrated the efficacy of the present strategy to generate and select descriptors from manifold measured data for investigating the nature of sophisticated subjects, such as hair.

The exposome paradigm to predict environmental health in terms of systemic homeostasis and resource balance based on NMR data science

The environment, from microbial ecosystems to recycled resources, fluctuates dynamically due to many physical, chemical and biological factors, the profile of which reflects changes in overall state, such as environmental illness caused by a collapse of homeostasis. To evaluate and predict environmental health in terms of systemic homeostasis and resource balance, a comprehensive understanding of these factors requires an approach based on the "exposome paradigm", namely the totality of exposure to all substances. Furthermore, in considering sustainable development to meet global population growth, it is important to gain an understanding of both the circulation of biological resources and waste recycling in human society. From this perspective, natural environment, agriculture, aquaculture, wastewater treatment in industry, biomass degradation and biodegradable materials design are at the forefront of current research. In this respect, nuclear magnetic resonance (NMR) offers tremendous advantages in the analysis of samples of molecular complexity, such as crude bio-extracts, intact cells and tissues, fibres, foods, feeds, fertilizers and environmental samples. Here we outline examples to promote an understanding of recent applications of solution-state, solid-state, time-domain NMR and magnetic resonance imaging (MRI) to the complex evaluation of organisms, materials and the environment. We also describe useful databases and informatics tools, as well as machine learning techniques for NMR analysis, demonstrating that NMR data science can be used to evaluate the exposome in both the natural environment and human society towards a sustainable future.

Extraction of Weak Spectroscopic Signals with High Fidelity: Examples from ESR

Noise impedes experimental studies by reducing signal resolution and/or suppressing weak signals. Signal averaging and filtering are the primary methods used to reduce noise, but they have limited effectiveness and lack capabilities to recover signals at low signal-to-noise ratios (SNRs). We utilize a wavelet transform-based approach to effectively remove noise from spectroscopic data. The wavelet denoising method we use is a significant improvement on standard wavelet denoising approaches. We demonstrate its power in extracting signals from noisy spectra on a variety of signal types ranging from hyperfine lines to overlapped peaks to weak peaks overlaid on strong ones, drawn from electron-spin-resonance spectroscopy. The results show that one can accurately extract details of complex spectra, including retrieval of very weak ones. It accurately recovers signals at an SNR of ∼1 and improves the SNR by about 3 orders of magnitude with high fidelity. Our examples show that one is now able to address weaker SNR signals much better than by previous methods. This new wavelet approach can be successfully applied to other spectroscopic signals.

Exploring the potential of PCA-based quantitation of NMR signals in T1 relaxometry

Principal component analysis (PCA) has proved to be a powerful technique for processing NMR data. It is particularly useful in signal quantitation where it often provides better results compared to a direct integration of individual signals. In the present work, we recapitulate the principles and theoretical framework underlying PCA-based quantitation with a special focus on T₁ relaxometry. We show that under commonly encountered conditions, this approach can provide up to ~4-fold improvement in scatter of points in magnetization build-up curves compared to direct integration. Best practices to optimize the PCA performance in measuring the total magnetization are discussed, including minimization of the number of signal-related principal components and a proper selection of FT parameters and data quantitation intervals. For signals consisting of distinct relaxation components, formulas are provided for resolving the components relaxation and illustrated on a real-data example. In addition to the problem of quantitation, the use of PCA in denoising of partially relaxed spectra is discussed in connection with such applications as line shape analysis and monitoring relaxation of individual spectral components.

Signal Deconvolution and Generative Topographic Mapping Regression for Solid-State NMR of Multi-Component Materials

Solid-state nuclear magnetic resonance (ssNMR) spectroscopy provides information on native structures and the dynamics for predicting and designing the physical properties of multi-component solid materials. However, such an analysis is difficult because of the broad and overlapping spectra of these materials. Therefore, signal deconvolution and prediction are great challenges for their ssNMR analysis. We examined signal deconvolution methods using a short-time Fourier transform (STFT) and a non-negative tensor/matrix factorization (NTF, NMF), and methods for predicting NMR signals and physical properties using generative topographic mapping regression (GTMR). We demonstrated the applications for macromolecular samples involved in cellulose degradation, plastics, and microalgae such as Euglena gracilis. During cellulose degradation, ¹³C cross-polarization (CP)-magic angle spinning spectra were separated into signals of cellulose, proteins, and lipids by STFT and NTF. GTMR accurately predicted cellulose degradation for catabolic products such as acetate and CO₂. Using these methods, the ¹H anisotropic spectrum of poly-ε-caprolactone was separated into the signals of crystalline and amorphous solids. Forward prediction and inverse prediction of GTMR were used to compute STFT-processed NMR signals from the physical properties of polylactic acid. These signal deconvolution and prediction methods for ssNMR spectra of macromolecules can resolve the problem of overlapping spectra and support macromolecular characterization and material design.

Broadband adiabatic inversion experiments for the measurement of longitudinal relaxation time constants

Accurate measurements of longitudinal relaxation time constants (T₁) in solid-state nuclear magnetic resonance (SSNMR) experiments are important for the study of molecular-level structure and dynamics. Such measurements are often made under magic-angle spinning conditions; however, there are numerous instances where they must be made on stationary samples, which often give rise to broad powder patterns arising from large anisotropic NMR interactions. In this work, we explore the use of wideband uniform-rate smooth-truncation pulses for the measurement of T₁ constants. Two experiments are introduced: (i) BRAIN-CPT1, a modification of the BRAIN-CP (BRoadband Adiabatic-INversion-Cross Polarization) sequence, for broadband CP-based T₁ measurements and (ii) WCPMG-IR, a modification of the WURST-CPMG sequence, for direct-excitation (DE) inversion-recovery experiments. A series of T₁ constants are measured for spin-1/2 and quadrupolar nuclei with broad powder patterns, such as ¹¹⁹Sn (I = 1/2), ³⁵Cl (I = 3/2), ²H (I = 1), and ¹⁹⁵Pt (I = 1/2). High signal-to-noise spectra with uniform patterns can be obtained due to signal enhancements from T₂ ^eff-weighted echo trains, and in favorable cases, BRAIN-CPT1 allows for the rapid measurement of T₁ in comparison to DE experiments. Protocols for spectral acquisition, processing, and analysis of relaxation data are discussed. In most cases, relaxation behavior can be modeled with either monoexponential or biexponential functions based upon measurements of integrated powder pattern intensity; however, it is also demonstrated that one must interpret such T₁ values with caution, as demonstrated by measurements of T₁ anisotropy in ¹¹⁹Sn, ²H, and ¹⁹⁵Pt NMR spectra.

Signal Deconvolution and Noise Factor Analysis Based on a Combination of Time-Frequency Analysis and Probabilistic Sparse Matrix Factorization

Nuclear magnetic resonance (NMR) spectroscopy is commonly used to characterize molecular complexity because it produces informative atomic-resolution data on the chemical structure and molecular mobility of samples non-invasively by means of various acquisition parameters and pulse programs. However, analyzing the accumulated NMR data of mixtures is challenging due to noise and signal overlap. Therefore, data-cleansing steps, such as quality checking, noise reduction, and signal deconvolution, are important processes before spectrum analysis. Here, we have developed an NMR measurement informatics tool for data cleansing that combines short-time Fourier transform (STFT; a time-frequency analytical method) and probabilistic sparse matrix factorization (PSMF) for signal deconvolution and noise factor analysis. Our tool can be applied to the original free induction decay (FID) signals of a one-dimensional NMR spectrum. We show that the signal deconvolution method reduces the noise of FID signals, increasing the signal-to-noise ratio (SNR) about tenfold, and its application to diffusion-edited spectra allows signals of macromolecules and unsuppressed small molecules to be separated by the length of the T₂* relaxation time. Noise factor analysis of NMR datasets identified correlations between SNR and acquisition parameters, identifying major experimental factors that can lower SNR.