Low-cost, pseudo-Halbach dipole magnets for NMR

Spatiotemporal encoding MRI in a portable low-field system

PURPOSE

Demonstrate the potential of spatiotemporal encoding (SPEN) MRI to deliver largely undistorted 2D, 3D, and diffusion weighted images on a 110 mT portable system.

METHODS

SPEN's quadratic phase modulation was used to subsample the low-bandwidth dimension of echo planar acquisitions, delivering alias-free images with an enhanced immunity to image distortions in a laboratory-built, low-field, portable MRI system lacking multiple receivers.

RESULTS

Healthy brain images with different SPEN time-bandwidth products and subsampling factors were collected. These compared favorably to EPI acquisitions including topup corrections. Robust 3D and diffusion weighted SPEN images of diagnostic value were demonstrated, with 2.5 mm isotropic resolutions achieved in 3 min scans. This performance took advantage of the low specific absorption rate and relative long TEs associated with low-field MRI.

CONCLUSION

SPEN MRI provides a robust and advantageous fast acquisition approach to obtain faithful 3D images and DWI data in low-cost, portable, low-field systems without parallel acceleration.

NMRduino: A modular, open-source, low-field magnetic resonance platform

The NMRduino is a compact, cost-effective, sub-MHz NMR spectrometer that utilizes readily available open-source hardware and software components. One of its aims is to simplify the processes of instrument setup and data acquisition control to make experimental NMR spectroscopy accessible to a broader audience. In this introductory paper, the key features and potential applications of NMRduino are described to highlight its versatility both for research and education.

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.

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.

Image distortion correction for MRI in low field permanent magnet systems with strong B0 inhomogeneity and gradient field nonlinearities

Objective

To correct for image distortions produced by standard Fourier reconstruction techniques on low field permanent magnet MRI systems with strong \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{0}$$\end{document}B0 inhomogeneity and gradient field nonlinearities.

Materials and methods

Conventional image distortion correction algorithms require accurate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta B}_{0}$$\end{document}ΔB0 maps which are not possible to acquire directly when the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{0}$$\end{document}B0 inhomogeneities also produce significant image distortions. Here we use a readout gradient time-shift in a TSE sequence to encode the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{0}$$\end{document}B0 field inhomogeneities in the k-space signals. Using a non-shifted and a shifted acquisition as input, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {B}_{0}$$\end{document}ΔB0 maps and images were reconstructed in an iterative manner. In each iteration, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {B}_{0}$$\end{document}ΔB0 maps were reconstructed from the phase difference using Tikhonov regularization, while images were reconstructed using either conjugate phase reconstruction (CPR) or model-based (MB) image reconstruction, taking the reconstructed field map into account. MB reconstructions were, furthermore, combined with compressed sensing (CS) to show the flexibility of this approach towards undersampling. These methods were compared to the standard fast Fourier transform (FFT) image reconstruction approach in simulations and measurements. Distortions due to gradient nonlinearities were corrected in CPR and MB using simulated gradient maps.

Results

Simulation results show that for moderate field inhomogeneities and gradient nonlinearities, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {B}_{0}$$\end{document}ΔB0 maps and images reconstructed using iterative CPR result in comparable quality to that for iterative MB reconstructions. However, for stronger inhomogeneities, iterative MB reconstruction outperforms iterative CPR in terms of signal intensity correction. Combining MB with CS, similar image and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {B}_{0}$$\end{document}ΔB0 map quality can be obtained without a scan time penalty. These findings were confirmed by experimental results.

Discussion

In case of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{0}$$\end{document}B0 inhomogeneities in the order of kHz, iterative MB reconstructions can help to improve both image quality and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {B}_{0}$$\end{document}ΔB0 map estimation.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10334-021-00907-2.

Zero-Field NMR J-Spectroscopy of Organophosphorus Compounds

Organophosphorus compounds are a wide and diverse class of chemicals playing a crucial role in living organisms. This aspect has been often investigated using nuclear magnetic resonance (NMR), which provides information about molecular structure and function. In this paper, we report the results of theoretical and experimental studies on basic organophosphorus compounds using zero-field NMR, where spin dynamics are investigated in the absence of a magnetic field with the dominant heteronuclear J-coupling. We demonstrate that the zero-field NMR enables distinguishing the chemicals owing to their unique electronic environment even though their spin systems have the same alphabetic designation. Such information can be obtained just in a single measurement, while amplitudes and widths of observed low-field NMR resonances enable the study of processes affecting spin dynamics. An excellent agreement between simulations and measurements of the spectra, particularly in the largest frequency J-couplings range ever reported in zero-field NMR, is demonstrated.

Topochemical Engineering of Cellulose-Carboxymethyl Cellulose Beads: A Low-Field NMR Relaxometry Study

The demand for more ecological, highly engineered hydrogel beads is driven by a multitude of applications such as enzyme immobilization, tissue engineering and superabsorbent materials. Despite great interest in hydrogel fabrication and utilization, the interaction of hydrogels with water is not fully understood. In this work, NMR relaxometry experiments were performed to study bead-water interactions, by probing the changes in bead morphology and surface energy resulting from the incorporation of carboxymethyl cellulose (CMC) into a cellulose matrix. The results show that CMC improves the swelling capacity of the beads, from 1.99 to 17.49, for pure cellulose beads and beads prepared with 30% CMC, respectively. Changes in water mobility and interaction energy were evaluated by NMR relaxometry. Our findings indicate a 2-fold effect arising from the CMC incorporation: bead/water interactions were enhanced by the addition of CMC, with minor additions having a greater effect on the surface energy parameter. At the same time, bead swelling was recorded, leading to a reduction in surface-bound water, enhancing water mobility inside the hydrogels. These findings suggest that topochemical engineering by adjusting the carboxymethyl cellulose content allows the tuning of water mobility and porosity in hybrid beads and potentially opens up new areas of application for this biomaterial.

Accounting for material imperfections in the design and optimization of low cost Halbach magnets

We demonstrate an experimental method for the improvement of the magnetic field homogeneity in Halbach magnets by taking magnet material imperfection into account. This method relies on the determination of the magnetization magnitude only for individual magnet blocks based on nuclear magnetic resonance field measurements in a simplified system, which, in our case, consists of four blocks. Then, a set of configurations with highest homogeneities can be found from simplified field map simulations of all possible configurations or by applying sophisticated optimum search algorithms if the number of blocks is large. Finally, the residual effect of angular magnetization deviations can be reduced by the experimental selection of the best configuration from the set found on the simulation step. This selection strategy is based on the conclusions made from statistical analysis of simulated field maps. By applying the described method to our eight-element magnet, we experimentally achieved tenfold field homogeneity improvement. Thus, in the best configuration, we obtained an average value of the magnetic field of 598.0 mT and a half-width of 226.9 ppm for a sample with a diameter of 4 mm and a height of 10 mm. These parameters along with the compact magnet size (40 × 40 × 102 mm³) and weight (0.6 kg) provide reasonable magnet quality compared with analogous systems having more complex magnet arrangements and significantly higher costs.

In vivo 3D brain and extremity MRI at 50 mT using a permanent magnet Halbach array

Purpose

To design a low‐cost, portable permanent magnet‐based MRI system capable of obtaining in vivo MR images within a reasonable scan time.

Methods

A discretized Halbach permanent magnet array with a clear bore diameter of 27 cm was designed for operation at 50 mT. Custom‐built gradient coils, RF coil, gradient amplifiers, and RF amplifier were integrated and tested on both phantoms and in vivo.

Results

Phantom results showed that the gradient nonlinearity in the y‐direction and z‐direction was less than 5% over a 15‐cm FOV and did not need correcting. For the x‐direction, it was significantly greater, but could be partially corrected in postprocessing. Three‐dimensional in vivo scans of the brain of a healthy volunteer using a turbo spin‐echo sequence were acquired at a spatial resolution of 4 × 4 × 4 mm in a time of about 2 minutes. The T₁‐weighted and T₂‐weighted scans showed a good degree of tissue contrast. In addition, in vivo scans of the knee of a healthy volunteer were acquired at a spatial resolution of about 3 × 2 × 2 mm within 12 minutes to show the applicability of the system to extremity imaging.

Conclusion

This work has shown that it is possible to construct a low‐field MRI unit with hardware components costing less than 10 000 Euros, which is able to acquire human images in vivo within a reasonable data‐acquisition time. The system has a high degree of portability with magnet weight of approximately 75 kg, gradient and RF amplifiers each 15 kg, gradient coils 10 kg, and spectrometer 5 kg.

Design and implementation of a J-coupled spectrometer for multidimensional structure and relaxation detection at low magnetic fields

In recent years, it has been realized that low and ultra-low field (mT-nT magnetic field range) nuclear magnetic resonance spectroscopy can be used for molecular structural analysis. However, spectra are often hindered by lengthy acquisition times or require large sample volumes and high concentrations. Here, we report a low field (50 μT) instrument that employs a linear actuator to shuttle samples between a 1 T prepolarization field and a solenoid detector in a laboratory setting. The current experimental setup is benchmarked using water and ¹³C-methanol with a single scan detection limit of 2 × 10²⁰ spins (3 µl, 55M H₂O) and detection limit of 2.9 × 10¹⁹ (200 µl, 617 mM ¹³C-methanol) spins with signal averaging. The system has a dynamic range of >3 orders of magnitude. Investigations of room-temperature relaxation dynamics of ¹³C-methanol show that sample dilution can be used in lieu of sample heating to acquire spectra with linewidths comparable to high-temperature spectra. These results indicate that the T₁ and T₂ mechanisms are governed by both the proton exchange rate and the dissolved oxygen in the sample. Finally, a 2D correlation spectroscopy experiment is reported, performed in the strong coupling regime that resolves the multiple resonances associated with the heteronuclear J-coupling. The spectrum was collected using 10 times less sample and in less than half the time from previous reports in the strong coupling limit.

Design and implementation of a low-cost, tabletop MRI scanner for education and research prototyping

While access to a laboratory MRI system is ideal for teaching MR physics as well as many aspects of signal processing, providing multiple MRI scanners can be prohibitively expensive for educational settings. To address this need, we developed a small, low-cost, open-interface tabletop MRI scanner for academic use. We constructed and tested 20 of these scanners for parallel use by teams of 2-3 students in a teaching laboratory. With simplification and down-scaling to a 1 cm FOV, fully-functional scanners were achieved within a budget of $10,000 USD each. The design was successful for teaching MR principles and basic signal processing skills and serves as an accessible testbed for more advanced MR research projects. Customizable GUIs, pulse sequences, and reconstruction code accessible to the students facilitated tailoring the scanner to the needs of laboratory exercise. The scanners have been used by >800 students in 6 different courses and all designs, schematics, sequences, GUIs, and reconstruction code is open-source.

Scalar relaxation of NMR transitions at ultralow magnetic field

Nuclear magnetic resonance signals for ¹H in simple chlorinated, brominated and deuterated liquids were detected at field strengths between 1 nT and a few μT to investigate the influence of scalar relaxation of the second kind (SR2K). SR2K describes the acceleration in magnetization decay rate for a spin-1/2 nucleus that is scalar coupled to a fast-relaxing quadrupolar nucleus. In agreement with simple theoretical models, the experimental data show that couplings to nuclei with small, nonzero quadrupole moments (²H) give rise to higher transverse relaxation rates at ultralow field than rapidly relaxing quadrupolar nuclei (Cl and Br). This behavior is opposite to the case normally encountered in high-field NMR, and demonstrates that certain nuclei in the spin system may be "weakly coupled" or even decoupled when the applied magnetic field is zero. The results show that the capability for precision determination of NMR frequencies and molecular structural information depends strongly on the composition and topology of the nuclear spin system.

NMR relaxation in porous materials at zero and ultralow magnetic fields

NMR detection in the ultralow-field regime (below 10 μT) was used to measure the nuclear spin relaxation rates of liquids imbibed into silica pellets with mean pore diameters in the 10-50 nm range. Heptane, formic acid and acetic acid were studied and relaxation rate data were compared with a conventional field-cycling NMR technique. Detection of ¹H-¹³C spin coupling NMR signals at zero field (∼0.1 nT) allowed spectroscopic identification of molecules inside the porous material and unambiguous measurements of the chemistry-specific relaxation rates in liquid mixtures. In the case of molecules that contain ¹H and ¹³C, spin-singlet state relaxation can provide additional information about the dynamics. Applications and future improvements to the methodology are discussed.

An ultra-compact low temperature scanning probe microscope for magnetic fields above 30 T

We present the design of a highly compact high field scanning probe microscope (HF-SPM) for operation at cryogenic temperatures in an extremely high magnetic field, provided by a water-cooled Bitter magnet able to reach 38 T. The HF-SPM is 14 mm in diameter: an Attocube nano-positioner controls the coarse approach of a piezoresistive atomic force microscopy cantilever to a scanned sample. The Bitter magnet constitutes an extreme environment for scanning probe microscopy (SPM) due to the high level of vibrational noise; the Bitter magnet noise at frequencies up to 300 kHz is characterized, and noise mitigation methods are described. The performance of the HF-SPM is demonstrated by topographic imaging and noise measurements at up to 30 T. Additionally, the use of the SPM as a three-dimensional dilatometer for magnetostriction measurements is demonstrated via measurements on a magnetically frustrated spinel sample.

Simple and low-cost tabletop NMR system for chemical-shift-resolution spectra measurements

We have been working on developing a low-cost tabletop NMR system. We reported that a field homogeneity as high as 50 ppm was achieved with a simple NMR magnet by employing two facing ferrite magnets with iron disks in between (Chonlathep et al., 2017). In this paper, we report two improvements added to our previous system: (1) an FPGA based signal processing unit to improve the S/N ratio and (2) a simple shimming mechanism to improve the field homogeneity. We obtained as high as 1 ppm field homogeneity in the best case. The signals from hydrogen nuclear spins in a methyl and carboxy group in acetic acid were resolved in NMR spectra.

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.