High-Resolution Reconstruction for Multidimensional Laplace NMR

A genetic optimisation and iterative reconstruction framework for sparse multi-dimensional diffusion-relaxation correlation MRI

Multi-dimensional diffusion-relaxation correlation (DRC) magnetic resonance imaging (MRI) techniques have recently been developed to investigate tissue microstructures. Sub-voxel tissue heterogeneity is resolved from the local correlation distributions of relaxation time and molecular diffusivity. However, the implementation of these techniques considerably increases the total acquisition time, and simply reducing the scan time may be at the expense of detailed structural resolution. To overcome these limitations, an optimised framework was proposed for acquiring microstructural maps of the human brain on a clinically feasible timescale. First, the acquisition parameters of the multi-dimensional DRC MRI method were sparsely optimised using a genetic algorithm with a fitness function according to the spectral resolution of the correlation map, hardware requirements, and total scan time. Next, the acquired DRC MRI data were processed using a proposed numerical algorithm based on the dynamic inverse Laplace transform (ILT). Prior knowledge from one-dimensional data was then utilised in the iterative procedure to improve the spectral resolution. Finally, the proposed framework was validated using Monte Carlo simulations and experimental data acquired from healthy participants on an MRI scanner. The results demonstrated that the suggested approach is feasible for offering high-resolution DRC maps that correspond to distinct microstructures with a limited amount of optimised acquisition data from two-dimensional DRC sampling space. By significantly reducing scan time while retaining structural resolution, this approach may enable multi-dimensional DRC MRI to be more widely used for quantitative evaluation in biological and medical settings.

SCREENES: Enhancing non-uniform sampling reconstruction for symmetrical NMR spectroscopy

BACKGROUND

Symmetrical NMR spectroscopy, such as Total Correlation Spectroscopy (TOCSY) and other homonuclear spectroscopy, displays symmetry in chemical shift but are generally not symmetrical in terms of intensity, which constitutes a pivotal branch of multidimensional NMR spectroscopy and offers a robust tool for elucidating the structures and dynamics of complex samples, particularly in the context of biological macromolecules. Non-Uniform Sampling (NUS) stands as a critical technique for accelerating multidimensional NMR experiments. However, symmetrical NMR spectroscopy inherently presents dynamic peak intensities, where cross peaks tend to be substantially weaker compared to diagonal peaks. Recovering these weaker cross peaks from NUS data poses a significant challenge, often resulting in compromised data quality.

RESULTS

We enhance the reconstruction quality of NUS symmetrical NMR spectroscopy based on the assumption that the asymmetry in intensity is mild. Regarding the sampling schedule, we employ the symmetrical sampling structure integrated with Poisson sampling schedule to enhance the efficiency of data acquisition. In term of the reconstruction algorithm, we propose the new method by incorporating hard and soft symmetrical constraints into our recently developed L1-norm-based Compressed Sensing (CS) method known as Sparse Complex-valued REconstruction Enabled by Newton method (SCREEN). Additionally, we propose a two-step reconstruction strategy that separately addresses diagonal and cross peaks. In this two-step strategy, cross peaks are effectively reconstructed by excluding the stronger diagonal peaks. Extensive experimental results validate the effectiveness of our proposed methodology.

SIGNIFICANCE

This method enhances the overall quality of the reconstructed NUS symmetrical NMR spectra, especially in terms of cross peaks, thereby enriching the interpretation of spectral information. Furthermore, it boosts the robustness towards regularization parameters, facilitating a user-friendly experience.

Smooth deconvolution of low-field NMR signals

BACKGROUND

Low resolution nuclear magnetic resonance (LR-NMR) is a common technique to identify the constituents of complex materials (such as food and biological samples). The output of LR-NMR experiments is a relaxation signal which can be modelled as a type of convolution of an unknown density of relaxation times with decaying exponential functions, plus random Gaussian noise. The challenge is to estimate that density, a severely ill-posed problem. A complication is that non-negativity constraints need to be imposed in order to obtain valid results.

SIGNIFICANCE AND NOVELTY

We present a smooth deconvolution model for solution of the inverse estimation problem in LR-NMR relaxometry experiments. We model the logarithm of the relaxation time density as a smooth function using (adaptive) P-splines while matching the expected residual magnetisations with the observed ones. The roughness penalty removes the singularity of the deconvolution problem, and the estimated density is positive by design (since we model its logarithm). The model is non-linear, but it can be linearized easily. The penalty has to be tuned for each given sample. We describe an efficient EM-type algorithm to optimize the smoothing parameter(s).

RESULTS

We analyze a set of food samples (potato tubers). The relaxation spectra extracted using our method are similar to the ones described in the previous experiments but present sharper peaks. Using penalized signal regression we are able to accurately predict dry matter content of the samples using the estimated spectra as covariates.

GRIN-toolbox: A versatile and light toolbox for NMR inversion

NMR technique serves as a powerful analytical tool with diverse applications in fields such as chemistry, biology, and material science. However, the effectiveness of NMR heavily relies on data post-processing which is often modeled as regularized inverse problem. Recently, we proposed the Generally Regularized INversion (GRIN) algorithm and demonstrated its effectiveness in NMR data processing. GRIN has been integrated as a friendly graphic user interface-based toolbox which was not detailed in the original paper. In this paper, to make GRIN more practically accessible to NMR practitioners, we focus on introducing the usage of GRIN-Toolbox with processing examples and the corresponding processing graphic interfaces, and the user manual is attached as Supplementary Material. GRIN-Toolbox is versatile and lightweight, where various kinds of data processing tasks can be completed with one click, including but not limited to diffusion-ordered spectroscopy processing, magnetic resonance imaging under-sampling reconstruction, Laplace (diffusion or relaxation) NMR inversion, spectrum denoising, etc. In addition, GRIN-Toolbox could be extended to more applications with user-designed inversion models and freely available at https://github.com/EricLin1993/GRIN.

Radiofrequency coil design for improving human liver fat quantification in a portable single-side magnetic resonance system

Earlier diagnosis of nonalcoholic fatty liver disease (NAFLD) is important to prevent progression of the disease. Recently, a low-cost portable magnetic resonance (MR) system was developed as a point-of-care screening tool for in vivo liver fat quantification. However, subcutaneous fat may confound the liver fat quantification, particularly in the NAFLD population. In this work, we propose a novel radiofrequency (RF) coil design composed of a set of "saturation" coils sandwiching a main coil to improve human liver fat quantification. By comparison with conventional MR imaging, we demonstrate the capability and effectiveness of the novel RF coil design in phantom experiments as well as in vivo liver scans. In the phantom experiment, the saturation coil reduced the error in the measured proton density fat fraction (PDFF) results from 28.9% to 4.0%, and in the in vivo experiment, it reduced the discrepancy in the PDFF results from 13.2% to 4.0%. The novel coil design, together with the adapted Carr-Purcell-Meiboom-Gill-based sequence, improves the practicability and robustness of the portable single-side MR system.

A Pure Shift-Based Nuclear Magnetic Resonance Method for In-Phase Three-Dimensional Diffusion-Ordered Spectroscopy

Diffusion-ordered nuclear magnetic resonance spectroscopy (DOSY) plays a vital role in mixture studies. However, its applications to complex mixture samples are generally limited by spectral congestion along the chemical shift domain caused by extensive J coupling networks and abundant compounds. Herein, we develop the in-phase multidimensional DOSY strategy for complex mixture analyses by simultaneously revealing molecular self-diffusion behaviors and multiplet structures with optimal spectral resolution. As a proof of concept, two pure shift-based three-dimensional (3D) DOSY protocols are proposed to record high-resolution 3D spectroscopic view with separated mixture components and their resolved multiplet coupling structures, thus suitable for analyzing complex mixtures that contain abundant compounds and complicated molecular structures, even under adverse magnetic field conditions. Therefore, this study shows a promising tool for component analyses and multiplet structure studies on practical mixture samples.

Neural Network Method for Diffusion-Ordered NMR Spectroscopy

Diffusion-ordered NMR spectroscopy (DOSY) presents an essential tool for the analysis of compound mixtures by revealing intrinsic diffusion behaviors of the mixed components. For the interpretation of the diffusion information, intrinsically designed algorithms for a DOSY spectrum reconstruction are required. The estimated diffusion coefficients are desired to have consistency for all the spectral signals from the same molecule and good separation of signals from different molecules. For this purpose, we propose a novel method that adopts a coordinated multiexponential fitting to ensure the consistency of diffusion coefficients and apply a sparse constraint to enhance the robustness. A lightweight neural network is applied as an optimizer to solve this highly nonlinear and nonconvex optimization problem. The proposed method provides estimated diffusion coefficients with excellent distinguishment between species and outperforms the state-of-the-art reconstruction algorithms, such as the Laplacian inversion and the multivariate fitting methods.

Interactions between PAMAM-NH2 and 6-Mercaptopurine: Qualitative and Quantitative NMR studies

Despite being used as an anti-leukemic drug, the poor solubility of 6-mercaptopurine (6-MP) limits its use in topical and parenteral applications. Dendrimers are commonly used as drug carriers to improve their solubility in aqueous solution. In this work, the interactions between 6-MP and the amine-terminated poly(amidoamine) dendrimers (PAMAM-NH₂ ) were investigated by various NMR technology. The chemical shift titrations disclosed that the 6-MP interacted with the surface of PAMAM-NH₂ mainly through electrostatics. The determination of diffusion coefficient and relaxation measurements further confirmed the presence of interactions in 6-MP/PAMAM-NH₂ complexes. In addition, the encapsulation of 6-MP within the cavity of PAMAM-NH₂ was revealed through nuclear Overhauser effect spectroscopy and Saturation Transfer Double Difference analysis. Finally, the binding strength (H-8 is 100% and H-2 is 70%) of 6-MP to PAMAM-NH₂ was quantitatively expressed using epitope maps. This study provides a systematic methodology for qualitative and quantitative studies of the interactions between dendrimers and drug molecules in general.

A General Reconstruction Method for Multidimensional Sparse Sampling Nuclear Magnetic Resonance Spectroscopy

Multidimensional NMR spectroscopy provides a powerful tool for structure elucidation and dynamic analysis of complex samples, particularly for biological macromolecules. Multidimensional sparse sampling effectively accelerates NMR experiments while an efficient reconstruction method is generally required for unraveling spectra. Various reconstruction methods were proposed for pure Fourier NMR (only involving chemical shifts and J couplings detection). However, reconstruction concerned with Laplace-related NMR (i.e., involving relaxation or diffusion detection) is more challenging due to its ill-posed property. The existing Laplace-related NMR sparse sampling reconstruction methods suffer from poor resolution and possible artifacts in the resulting spectra owing to the pitfalls of the optimization algorithms. Herein, we propose a general approach for fast high-resolution reconstruction of multidimensional sparse sampling NMR, including pure Fourier, mixed Fourier-Laplace, and pure Laplace NMR, benefiting from the comprehensive sparse constraint and effective optimization algorithm and thus showing the promising prospects of multidimensional NMR.