Single-sided mobile NMR with a Halbach magnet

Scanning ex situ solid-state magnetic resonance imaging on polymeric films using a static magnetic field gradient by an electromagnet

A new technique for ex situ solid-state nuclear magnetic resonance imaging of polymeric films has been developed. This method uses the static magnetic field gradient generated by a water-cooled copper electromagnet. The imaging process involves scanning the sample in the plane of the film under a static magnetic field gradient. Two-dimensional (2D) 19F MRI measurements are attempted, where the fast Fourier transform (FFT) spectra of the second half of a Hahn echo peak is used for the depth (X-axis) direction, and the sample film is mechanically moved for the Y-axis, which is in-plane with respect to the film surface and normal to the inter-magnetic-pole line (Z-axis). The sample is a poly(tetrafluoroethylene) [PTFE] film with carved stripes on its surface. Furthermore, three-dimensional (3D) measurements of the film surface and thickness orientations were also performed for an analogous PTFE film. For 2D profiling on the film surface, 2D sample-moving was used. For depth profiling, FFT spectrum analysis was undertaken for each voxel situated at a specific (Y, Z) coordinate within the film. As a result, a 3D image of the sample and its corresponding geometry were obtained, although the scanning area was restricted to a part of the sample. Finally, numerical simulations of the spatial distribution of the static magnetic field were performed to confirm the validity of the present method.

Theoretical foundation for designing multilayer Halbach array magnets for benchtop NMR and MRI

Multilayer Halbach array magnets support portable NMR and MRI, but optimizing their design to maximize performance and minimize the use of expensive magnet materials is challenging. This is partly because our theoretical understanding of such arrays is incomplete and computationally intensive. Here we provide a theoretical description of the magnetic field distribution and we demonstrate that inhomogeneity is greatest along the z axis in multilayer Halbach array magnets. This allows the configuration of the multilayer Halbach array magnets to be optimized in a way that takes into account homogeneity, magnet volume, and magnetic flux density. At the same time, our description simplifies the design of multilayer array magnets, while accommodating the possibility of different outer radii, lengths for each layer array, or the presence of separation between the rings. We validated the theoretical description in simulations of a three-layer Halbach array magnet, then with a prototype three-layer 1-T Halbach array magnet. After adjusting the position of magnet blocks in the neighboring rings, we achieved homogeneity of 220 ppm for a standard 5 mm NMR tube while the inner diameter of the magnet is 20 mm. Our work provides a theoretical foundation for designing multilayer Halbach array magnets to maximize homogeneity and minimize the use of magnet materials.

Deep neural-network based optimization for the design of a multi-element surface magnet for MRI applications

We present a combination of a CNN-based encoder with an analytical forward map for solving inverse problems. We call it an encoder-analytic (EA) hybrid model. It does not require a dedicated training dataset and can train itself from the connected forward map in a direct learning fashion. A separate regularization term is not required either, since the forward map also acts as a regularizer. As it is not a generalization model it does not suffer from overfitting. We further show that the model can be customized to either find a specific target solution or one that follows a given heuristic. As an example, we apply this approach to the design of a multi-element surface magnet for low-field magnetic resonance imaging (MRI). We further show that the EA model can outperform the benchmark genetic algorithm model currently used for magnet design in MRI, obtaining almost 10 times better results.

A single-sided magnet for deep-depth fat quantification

Early detection of fatty-liver disease is important before further aggravations of the disease, such as cirrhosis, can develop. In this study, we developed a low-cost, movable single-sided magnet for in vivo liver fat quantification. A gradient field of 73.5 G/cm and a field strength of 0.0725 T were obtained by structurally optimizing the concave U-shaped magnet, on which the region of interest (ROI) was a curved shape about 0.4 mm thick, 8 cm above the surface of the radiofrequency (RF) coil. We constructed a prototype nuclear magnetic-resonance (NMR) relaxometry system based on this optimized magnet. Subsequent phantom experiments demonstrated the effectiveness of the single-sided magnet in evaluating different proton density fat fraction (PDFF) phantoms. As expected, the results of the six phantoms showed good positive correlation between PDFF and the fitted fat amplitude, which suggested that single-sided NMR relaxometry could be used to quantify liver fat in vivo.

Magnetostatic reciprocity for MR magnet design

Electromagnetic reciprocity has long been a staple in magnetic resonance (MR) radio-frequency development, offering geometrical insights and a figure of merit for various resonator designs. In a similar manner, we use magnetostatic reciprocity to compute manufacturable solutions of complex magnet geometries, by establishing a quantitative metric for the placement and subsequent orientation of discrete pieces of permanent magnetic material. Based on magnetostatic theory and non-linear finite element modelling (FEM) simulations, it is shown how assembled permanent magnet setups perform in the embodiment of a variety of designs and how magnetostatic reciprocity is leveraged in the presence of difficulties associated with self-interactions, to fulfil various design objectives, including self-assembled micro-magnets, adjustable magnetic arrays, and an unbounded magnetic field intensity in a small volume, despite realistic saturation field strengths.

Characterization of Structural Bone Properties through Portable Single-Sided NMR Devices: State of the Art and Future Perspectives

Nuclear Magnetic Resonance (NMR) is a well-suited methodology to study bone composition and structural properties. This is because the NMR parameters, such as the T2 relaxation time, are sensitive to the chemical and physical environment of the 1H nuclei. Although magnetic resonance imaging (MRI) allows bone structure assessment in vivo, its cost limits the suitability of conventional MRI for routine bone screening. With difficulty accessing clinically suitable exams, the diagnosis of bone diseases, such as osteoporosis, and the associated fracture risk estimation is based on the assessment of bone mineral density (BMD), obtained by the dual-energy X-ray absorptiometry (DXA). However, integrating the information about the structure of the bone with the bone mineral density has been shown to improve fracture risk estimation related to osteoporosis. Portable NMR, based on low-field single-sided NMR devices, is a promising and appealing approach to assess NMR properties of biological tissues with the aim of medical applications. Since these scanners detect the signal from a sensitive volume external to the magnet, they can be used to perform NMR measurement without the need to fit a sample inside a bore of a magnet, allowing, in principle, in vivo application. Techniques based on NMR single-sided devices have the potential to provide a high impact on the clinical routine because of low purchasing and running costs and low maintenance of such scanners. In this review, the development of new methodologies to investigate structural properties of trabecular bone exploiting single-sided NMR devices is reviewed, and current limitations and future perspectives are discussed.

EPR Everywhere

This review is inspired by the contributions from the University of Denver group to low-field EPR, in honor of Professor Gareth Eaton's 80th birthday. The goal is to capture the spirit of innovation behind the body of work, especially as it pertains to development of new EPR techniques. The spirit of the DU EPR laboratory is one that never sought to limit what an EPR experiment could be, or how it could be applied. The most well-known example of this is the development and recent commercialization of rapid-scan EPR. Both of the Eatons have made it a point to remain knowledgeable on the newest developments in electronics and instrument design. To that end, our review touches on the use of miniaturized electronics and applications of single-board spectrometers based on software-defined radio (SDR) implementations and single-chip voltage-controlled oscillator (VCO) arrays. We also highlight several non-traditional approaches to the EPR experiment such as an EPR spectrometer with a "wand" form factor for analysis of the OxyChip, the EPR-MOUSE which enables non-destructive in situ analysis of many non-conforming samples, and interferometric EPR and frequency swept EPR as alternatives to classical high Q resonant structures.

Table-top nuclear magnetic resonance system for high-pressure studies with in situ laser heating

High pressure Nuclear Magnetic Resonance (NMR) is known to reveal the behavior of matter under extreme conditions. However, until now, significant maintenance demands, space requirements, and high costs of superconducting magnets render its application unfeasible for regular modern high pressure laboratories. Here, we present a table-top NMR system based on permanent Halbach magnet arrays with a diameter of 25 cm and height of 4 cm. At the highest field of 1013 mT, ¹H-NMR spectra of ice VII have been recorded at 25 GPa and ambient temperature. The table-top NMR system can be used together with double sided laser heating setups. Feasibility of high-pressure high-temperature NMR was demonstrated by collecting ¹H-NMR spectra of H₂O at 25 GPa and 1063(50) K. The change in the signal intensity in a laser-heated NMR diamond anvil cell has been found to yield a convenient way for temperature measurements.

Low-Field, Benchtop NMR Spectroscopy as a Potential Tool for Point-of-Care Diagnostics of Metabolic Conditions: Validation, Protocols and Computational Models

Novel sensing technologies for liquid biopsies offer promising prospects for the early detection of metabolic conditions through omics techniques. Indeed, high-field nuclear magnetic resonance (NMR) facilities are routinely used for metabolomics investigations on a range of biofluids in order to rapidly recognise unusual metabolic patterns in patients suffering from a range of diseases. However, these techniques are restricted by the prohibitively large size and cost of such facilities, suggesting a possible role for smaller, low-field NMR instruments in biofluid analysis. Herein we describe selected biomolecule validation on a low-field benchtop NMR spectrometer (60 MHz), and present an associated protocol for the analysis of biofluids on compact NMR instruments. We successfully detect common markers of diabetic control at low-to-medium concentrations through optimised experiments, including α-glucose (≤2.8 mmol/L) and acetone (25 µmol/L), and additionally in readily accessible biofluids, particularly human urine. We present a combined protocol for the analysis of these biofluids with low-field NMR spectrometers for metabolomics applications, and offer a perspective on the future of this technique appealing to ‘point-of-care’ applications.

A low-cost home-built NMR using Halbach magnet

The objective of this work is to develop a low-cost compact desktop NMR system based on Halbach magnets with the advantages of small size and ability to generate relatively high field strength. Considering the cost of manufacturing and assembling the magnetic blocks, the system utilized a 3-layer Halbach magnet and a wedge-shaped mechanical structure, which was designed for magnet rapid assembling. The comparison between simulation and calculation results of the initial magnetic field strength distribution showed that design theory and practice were in accordance. The initial homogeneity was 576 ppm in a square with a length of 5 mm. After passive shimming with two magnetic blocks and steel pieces, the uniformity reached 120 ppm in the same area. We developed and tested a compact single board spectrometer with digital modulation and demodulation in order to enhance the system mobility and improve the SNR. A self-made probe was used to carry out experiments with the spectrometer, and the spectral width at half-height reached 20 ppm in a cylinder with a diameter of 1.5 mm and a length of 1 mm. Compact structure and low cost of the system will facilitate and extend the application of desktop NMR system.

Design and experimental validation of Unilateral Linear Halbach magnet arrays for single-sided magnetic resonance

Single-sided NMR has the potential for broad utility and has found applications in healthcare, materials analysis, food quality assurance, and the oil and gas industry. These sensors require a remote, strong, uniform magnetic field to perform high sensitivity measurements. We demonstrate a new permanent magnet geometry, the Unilateral Linear Halbach, that combines design principles from "sweet-spot" and linear Halbach magnets to achieve this goal through more efficient use of magnetic flux. We perform sensitivity analysis using numerical simulations to produce a framework for Unilateral Linear Halbach design and assess tradeoffs between design parameters. Additionally, the use of hundreds of small, discrete magnets within the assembly allows for a tunable design, improved robustness to variability in magnetization strength, and increased safety during construction. Experimental validation using a prototype magnet shows close agreement with the simulated magnetic field. The Unilateral Linear Halbach magnet increases the sensitivity, portability, and versatility of single-sided NMR.

Topology optimization based design of unilateral NMR for generating a remote homogeneous field

This paper presents a topology optimization based design method for the design of unilateral nuclear magnetic resonance (NMR), with which a remote homogeneous field can be obtained. The topology optimization is actualized by seeking out the optimal layout of ferromagnetic materials within a given design domain. The design objective is defined as generating a sensitive magnetic field with optimal homogeneity and maximal field strength within a required region of interest (ROI). The sensitivity of the objective function with respect to the design variables is derived and the method for solving the optimization problem is presented. A design example is provided to illustrate the utility of the design method, specifically the ability to improve the quality of the magnetic field over the required ROI by determining the optimal structural topology for the ferromagnetic poles. Both in simulations and experiments, the sensitive region of the magnetic field achieves about 2 times larger than that of the reference design, validating validates the feasibility of the design method.

High-resolution NMR spectroscopy in inhomogeneous fields

High-resolution NMR spectroscopy, providing information on chemical shifts, J coupling constants, multiplet patterns, and relative peak areas, is a mainstream tool for analysis of molecular structures, conformations, compositions, and dynamics. Generally, a homogeneous magnetic field is a prerequisite for obtaining high-resolution NMR information. Magnetic field inhomogeneity, whether from non-ideal experimental conditions or from intrinsic magnetic susceptibility discontinuities in samples, represents a hurdle for applications of high-resolution NMR. Numerous techniques have been proposed for measuring high-resolution NMR spectra free from the influence of inhomogeneous magnetic fields. Besides developments and improvements in NMR instrumentation, various types of experimental approaches have been established for recovering NMR information in inhomogeneous magnetic fields. Three main types are systematically described in this review. In addition, other high-resolution NMR approaches or data processing methods are also briefly described. All high-resolution NMR approaches covered in this review have individual advantages and disadvantages in practical applications, and no one technique is applicable to all practical circumstances. Hence, they are complementary for high-resolution NMR applications in inhomogeneous fields. The underlying mechanisms of these approaches are presented, together with analyses of their applicability and efficiency.

Low-gradient single-sided NMR sensor for one-shot profiling of human skin

This paper describes a shimming approach useful to reduce the gradient strength of the magnetic field generated by single-sided sensors simultaneously maximizing its uniformity along the lateral directions of the magnet. In this way, the thickness of the excited sensitive volume can be increased without compromising the depth resolution of the sensor. By implementing this method on a standard U-shaped magnet, the gradient strength was reduced one order of magnitude. In the presence of a gradient of about 2 T/m, slices of 2mm could be profiled with a resolution that ranges from 25 μm at the center of the slice to 50 μm at the borders. This sensor is of particular advantage for applications, where the scanning range is of the order of the excited slice. In those cases, the full profile is measured in a single excitation experiment, eliminating the need for repositioning the excited slice across the depth range to complete the profile as occurs with standard high gradient sensors. Besides simplifying the experimental setup, the possibility to move from a point-by-point measurement to the simultaneous acquisition of the full profile led to the shortening of the experimental time. A further advantage of performing the experiment under a smaller static gradient is a reduction of the diffusion attenuation affecting the signal decay measured with a CPMG sequence, making it possible to measure the T(2) of samples with high diffusivity (comparable to the water diffusivity). The performance of the sensor in terms of resolution and sensitivity is first evaluated and compared with conventional singled-sided sensors of higher gradient strength using phantoms of known geometry and relaxation times. Then, the device is used to profile the structure of human skin in vivo. To understand the contrast between the different skin layers, the distribution of relaxation times T(2) and diffusion coefficients is spatially resolved along the depth direction.

A unilateral magnet with an extended constant magnetic field gradient

Unilateral magnetic resonance (UMR) has become, in different research areas, a powerful tool to interrogate samples of arbitrary size. Numerous designs have been suggested in the literature to produce the desired magnetic field distributions, including designs which feature constant magnetic field gradients suitable for diffusion and profiling experiments. This work presents a new approach which features extended constant magnetic field gradients with a three magnet array. Constant gradients of more than 3cm extent can be achieved in a very simple, compact and safe design. Diffusion measurements from different positions over the magnet are presented in addition to practical applications for reservoir core plug characterization. The idea of a solenoid as a probe for specific measurements in UMR is introduced. Simple profiling experiments are also presented.

Magnetic resonance in porous media: recent progress

Recent years have seen significant progress in the NMR study of porous media from natural and industrial sources and of cultural significance such as paintings. This paper provides a brief outline of the recent technical development of NMR in this area. These advances are relevant for broad NMR applications in material characterization.

Operating nanoliter scale NMR microcoils in a 1 tesla field

Microcoil probes enclosing sample volumes of 1.2, 3.3, 7.0, and 81 nanoliters are constructed as nuclear magnetic resonance (NMR) detectors for operation in a 1 tesla permanent magnet. The probes for the three smallest volumes utilize a novel auxiliary tuning inductor for which the design criteria are given. The signal-to-noise ratio (SNR) and line width of water samples are measured. Based on the measured DC resistance of the microcoils, together with the calculated radio frequency (RF) resistance of the tuning inductor, the SNR is calculated and shown to agree with the measured values. The details of the calculations indicate that the auxiliary inductor does not degrade the NMR probe performance. The diameter of the wire used to construct the microcoils is shown to affect the signal line widths.

A compact permanent magnet array with a remote homogeneous field

We present the design and construction of a single sided magnet array generating a homogeneous field in a remote volume. The compact array measures 11.5 cm by 10 cm by 6 cm and weights approximately 5 kg. It produces a B(0) field with a 'sweet spot' at a point 1cm above its surface, where its first and second spatial derivatives are approximately zero. Unlike other sweet spot magnets of this general type, our array has B(0) oriented parallel to its surface. This allows an ordinary surface coil to be used for unilateral measurements, giving the potential for dramatic SNR improvement.