Preliminary Exploration of T1ρ and T2 Mapping in Porcine Articular Cartilage Using Very-low-field Magnetic Resonance Imaging.

OBJECTIVE: The high prevalence of osteoarthritis emphasizes the need for a cost-effective and accessible method for its early diagnosis. Recently, the portability and affordability of very-low-field (VLF) magnetic resonance imaging (MRI, 10-100 mT) have caused it to gain popularity. Nevertheless, there is insufficient evidence to quantify early degenerative changes in cartilage using VLF MRI. This study assessed the potential of T1ρ and T2 mapping for detecting degenerative changes in porcine cartilage specimens using a 50 mT MRI scanner. METHODS: T2- and T1ρ-weighted images were acquired using a 50 mT MRI scanner with 2D spin-echo and triple-refocused T1ρ preparation sequences. MRI scans of porcine cartilage were also acquired using a 3 T MRI scanner for comparison. A mono-exponential algorithm was applied to fit a series of T2- and T1ρ-weighted images. T2 values for CuSO4·5H2O solutions measured via Carr-Purcell-Meiboom-Gill (CPMG) and spin-echo sequences were compared to verify the algorithm's reliability. The nonparametric Kruskal-Wallis statistical test was used to compare T2 and T1ρ values. Experimental repeatability was assessed using the root-mean-square of the coefficient of variation (rmsCV). RESULTS: T2 values of the CuSO4·5H2O solutions obtained using the spin-echo sequence showed differences within 2.3% of those obtained using the CPMG sequence, indicating the algorithm's reliability. The T1ρ values for varying concentrations of agarose gel solutions were higher than the T2 values. Furthermore, 50 mT and 3 T MRI results showed that both the T1ρ and T2 values were significantly higher for porcine cartilage degraded for 6 h vs intact cartilage, with p-values of 0.006 and 0.01, respectively. Our experimental results showed good reproducibility (rmsCV < 8%). CONCLUSION: We demonstrated the feasibility of quantitative cartilage imaging via T2 and T1ρ mapping at 50 mT MRI for the first time.

Optimal bi-planar gradient coil configurations for diamond nitrogen-vacancy based diffusion-weighted NMR experiments.

INTRODUCTION: Diffusion weighting in optically detected magnetic resonance experiments involving diamond nitrogen-vacancy (NV) centers can provide valuable microstructural information. Bi-planar gradient coils employed for diffusion weighting afford excellent spatial access, essential for integrating the NV-NMR components. Nevertheless, owing to the polar tilt of roughly [Formula: see text] of the diamond NV center, the primary magnetic field direction must be taken into account accordingly. METHODS: To determine the most effective bi-planar gradient coil configurations, we conducted an investigation into the impact of various factors, including the square side length, surface separation, and surface orientation. This was accomplished by generating over 500 bi-planar surface configurations using automated methods. RESULTS: We successfully generated and evaluated coil layouts in terms of sensitivity and field accuracy. Interestingly, inclined bi-planar orientations close to the NV-NMR setup's requirement, showed higher sensitivity for the transverse gradient channels than horizontal or vertical orientations. We fabricated a suitable solution as a three-channel bi-planar double-layered PCB system and experimentally validated the sensitivities at [Formula: see text] and [Formula: see text] for the transverse [Formula: see text] and [Formula: see text] gradients, and [Formula: see text] for the [Formula: see text] gradient. DISCUSSION: We found that the chosen relative bi-planar tilt of [Formula: see text] represents a reasonable compromise in terms of overall performance and allows for easier coil implementation with a straight, horizontal alignment within the overall experimental setup.

Imaging local diffusion in microstructures using NV-based pulsed field gradient NMR.

Understanding diffusion in microstructures plays a crucial role in many scientific fields, including neuroscience, medicine, or energy research. While magnetic resonance (MR) methods are the gold standard for diffusion measurements, spatial encoding in MR imaging has limitations. Here, we introduce nitrogen-vacancy (NV) center-based nuclear MR (NMR) spectroscopy as a powerful tool to probe diffusion within microscopic sample volumes. We have developed an experimental scheme that combines pulsed gradient spin echo (PGSE) with optically detected NV-NMR spectroscopy, allowing local quantification of molecular diffusion and flow. We demonstrate correlated optical imaging with spatially resolved PGSE NV-NMR experiments probing anisotropic water diffusion within an individual model microstructure. Our optically detected PGSE NV-NMR technique opens up prospects for extending the current capabilities of investigating diffusion processes with the future potential of probing single cells, tissue microstructures, or ion mobility in thin film materials for battery applications.

RF-induced heating of interventional devices at 23.66 MHz.

OBJECTIVE: Low-field MRI systems are expected to cause less RF heating in conventional interventional devices due to lower Larmor frequency. We systematically evaluate RF-induced heating of commonly used intravascular devices at the Larmor frequency of a 0.55 T system (23.66 MHz) with a focus on the effect of patient size, target organ, and device position on maximum temperature rise. MATERIALS AND METHODS: To assess RF-induced heating, high-resolution measurements of the electric field, temperature, and transfer function were combined. Realistic device trajectories were derived from vascular models to evaluate the variation of the temperature increase as a function of the device trajectory. At a low-field RF test bench, the effects of patient size and positioning, target organ (liver and heart) and body coil type were measured for six commonly used interventional devices (two guidewires, two catheters, an applicator and a biopsy needle). RESULTS: Electric field mapping shows that the hotspots are not necessarily localized at the device tip. Of all procedures, the liver catheterizations showed the lowest heating, and a modification of the transmit body coil could further reduce the temperature increase. For common commercial needles no significant heating was measured at the needle tip. Comparable local SAR values were found in the temperature measurements and the TF-based calculations. CONCLUSION: At low fields, interventions with shorter insertion lengths such as hepatic catheterizations result in less RF-induced heating than coronary interventions. The maximum temperature increase depends on body coil design.

Advancements in Gradient System Performance for Clinical and Research MRI.

In magnetic resonance imaging (MRI), spatial field gradients are applied along each axis to encode the location of the nuclear spin in the frequency domain. During recent years, the development of new gradient technologies has been focused on the generation of stronger and faster gradient fields for imaging with higher spatial and temporal resolution. This benefits imaging methods, such as brain diffusion and functional MRI, and enables human imaging at ultra-high field MRI. In addition to improving gradient performance, new technologies have been presented to minimize peripheral nerve stimulation and gradient-related acoustic noise, both generated by the rapid switching of strong gradient fields. This review will provide a general background on the gradient system and update on the state-of-the-art gradient technology. EVIDENCE LEVEL: 5 TECHNICAL EFFICACY: Stage 1.

CoilGen: Open-source MR coil layout generator.

PURPOSE: An automated algorithm for generating realizable MR gradient and shim coil layouts based on the boundary element method is presented here. The overall goal is to reduce postprocessing effort and thus enable for rapid prototyping of new coil designs. For a given surface mesh and target field, the algorithm generates a connected, non-overlapping wire path. METHODS: The proposed algorithm consists of several steps: Stream function optimization, two-dimensional surface projection, potential discretization, topological contour sorting, opening and interconnecting contours, and finally adding non-overlapping return paths. Several technical parameters such as current strength, inductance and field accuracy are assessed for quality control. RESULTS: The proposed method is successfully demonstrated in four different examples. All exemplary results demonstrate high accuracy with regard to reaching the respective target field. The optimal discretization for a given stream function is found by generating multiple layouts while varying the input parameter values. CONCLUSION: The presented algorithm allows for a rapid generation of interconnected coil layouts with high flexibility and low discretization error. This enables to reduce the overall post-processing effort. The source code of this work is publicly available ( https://github.com/Philipp-MR/CoilGen).

Design of a high-performance non-linear gradient coil for diffusion weighted MRI of the breast.

Diffusion-weighted imaging (DWI) in the female breast is a magnetic resonance imaging (MRI) technique that complements clinical routine protocols, and that might provide an independent diagnostic value for specific clinical tasks in breast imaging. To further improve specificity of DWI in the breast, stronger and faster diffusion weighting is advantageous. Here, a dedicated gradient coil is designed, targeted at diffusion weighting in the female breast, with the peak gradient magnitude exceeding that of the current clinical MR scanners by an order of a magnitude. Design of application-tailored gradient coils in MRI has recently attracted increased attention. With the target application in mind, the gradient coil is designed on an irregularly shaped semi-open current-carrying surface. Due to the coil former closely fitting the non-spherical target region, non-linear encoding fields become particularly advantageous for achieving locally exceptionally high gradient strengths. As breast tissue has a predominantly isotropic cellular microstructure, the direction of the diffusion-weighting gradient may be allowed to vary within the target volume. However, due to the quadratic dependency of the b-factor on the gradient strength, variation of the gradient magnitude should be carefully controlled. To achieve the above design goals the corresponding multi-objective optimization problem is reformulated as a constrained optimization, allowing for flexible and precise control of the coil properties. A novel constraint is proposed, limiting gradient magnitude variation within every slice while allowing for variations in both the direction of the gradient within the slice and the magnitude across the slices. These innovations enable the design of a unilateral coil for diffusion weighting in the female breast with local gradient strengths exceeding 1 T/m with highly homogeneous diffusion weighting for imaging in the coronal slice orientation.

Design of a shim coil array matched to the human brain anatomy.

PURPOSE: The purpose of this study is to introduce a novel design method of a shim coil array specifically optimized for whole brain shimming and to compare the performance of the resulting coils to conventional spherical harmonic shimming. METHODS: The proposed design approach is based on the stream function method and singular value decomposition. Eighty-four field maps from 12 volunteers measured in seven different head positions were used during the design process. The cross validation technique was applied to find an optimal number of coil elements in the array. Additional 42 field maps from 6 further volunteers were used for an independent validation. A bootstrapping technique was used to estimate the required population size to achieve a stable coil design. RESULTS: Shimming using 12 and 24 coil elements outperforms fourth- and fifth-order spherical harmonic shimming for all measured field maps, respectively. Coil elements show novel coil layouts compared to the conventional spherical harmonic coils and existing multi-coils. Both leave-one-out and independent validation demonstrate the generalization ability of the designed arrays. The bootstrapping analysis predicts that field maps from approximately 140 subjects need to be acquired to arrive at a stable design. CONCLUSIONS: The results demonstrate the validity of the proposed method to design a shim coil array matched to the human brain anatomy, which naturally satisfies the laws of electrodynamics. The design method may also be applied to develop new shim coil arrays matched to other human organs.

Switching Circuit Optimization for Matrix Gradient Coils.

Matrix gradient coils with up to 84 coil elements were recently introduced for magnetic resonance imaging. Ideally, each element is driven by a dedicated amplifier, which may be technically and financially infeasible. Instead, several elements can be connected in series (called a "cluster") and driven by a single amplifier. In previous works, a set of clusters, called a "configuration," was sought to approximate a target field shape. Because a magnetic resonance pulse sequence requires several distinct field shapes, a mechanism to switch between configurations is needed. This can be achieved by a hypothetical switching circuit connecting all terminals of all elements with each other and with the amplifiers. For a predefined set of configurations, a switching circuit can be designed to require only a limited amount of switches. Here we introduce an algorithm to minimize the number of switches without affecting the ability of the configurations to accurately create the desired fields. The problem is modeled using graph theory and split into 2 sequential combinatorial optimization problems that are solved using simulated annealing. For the investigated cases, the results show that compared to unoptimized switching circuits, the reduction of switches in optimized circuits ranges from 8% to up to 44% (average of 31%). This substantial reduction is achieved without impeding circuit functionality. This study shows how technical effort associated with implementation and operation of a matrix gradient coil is related to different hardware setups and how to reduce this effort.

Clinical Potential of a New Approach to MRI Acceleration.

Fast ROtary Nonlinear Spatial ACquisition (FRONSAC) was recently introduced as a new strategy that applies nonlinear gradients as a small perturbation to improve image quality in highly undersampled MRI. In addition to experimentally showing the previously simulated improvement to image quality, this work introduces the insight that Cartesian-FRONSAC retains many desirable features of Cartesian imaging. Cartesian-FRONSAC preserves the existing linear gradient waveforms of the Cartesian sequence while adding oscillating nonlinear gradient waveforms. Experiments show that performance is essentially identical to Cartesian imaging in terms of (1) resilience to experimental imperfections, like timing errors or off-resonance spins, (2) accommodating scan geometry changes without the need for recalibration or additional field mapping, (3) contrast generation, as in turbo spin echo. Despite these similarities to Cartesian imaging, which provides poor parallel imaging performance, Cartesian-FRONSAC consistently shows reduced undersampling artifacts and better response to advanced reconstruction techniques. A final experiment shows that hardware requirements are also flexible. Cartesian-FRONSAC improves accelerated imaging while retaining the robustness and flexibility critical to real clinical use.

Optimization of Coil Element Configurations for a Matrix Gradient Coil.

Recently, matrix gradient coils (also termed multi-coils or multi-coil arrays) were introduced for imaging and B0 shimming with 24, 48, and even 84 coil elements. However, in imaging applications, providing one amplifier per coil element is not always feasible due to high cost and technical complexity. In this simulation study, we show that an 84-channel matrix gradient coil (head insert for brain imaging) is able to create a wide variety of field shapes even if the number of amplifiers is reduced. An optimization algorithm was implemented that obtains groups of coil elements, such that a desired target field can be created by driving each group with an amplifier. This limits the number of amplifiers to the number of coil element groups. Simulated annealing is used due to the NP-hard combinatorial nature of the given problem. A spherical harmonic basis set up to the full third order within a sphere of 20-cm diameter in the center of the coil was investigated as target fields. We show that the median normalized least squares error for all target fields is below approximately 5% for 12 or more amplifiers. At the same time, the dissipated power stays within reasonable limits. With a relatively small set of amplifiers, switches can be used to sequentially generate spherical harmonics up to third order. The costs associated with a matrix gradient coil can be lowered, which increases the practical utility of matrix gradient coils.

Development and implementation of an 84-channel matrix gradient coil.

PURPOSE: Design, implement, integrate, and characterize a customized coil system that allows for generating spatial encoding magnetic fields (SEMs) in a highly-flexible fashion. METHODS: A gradient coil with a high number of individual elements was designed. Dimensions of the coil were chosen to mimic a whole-body gradient system, scaled down to a head insert. Mechanical shape and wire layout of each element were optimized to increase the local gradient strength while minimizing eddy current effects and simultaneously considering manufacturing constraints. RESULTS: Resulting wire layout and mechanical design is presented. A prototype matrix gradient coil with 12 × 7 = 84 elements consisting of two element types was realized and characterized. Measured eddy currents are <1% of the original field. The coil is shown to be capable of creating nonlinear, and linear SEMs. In a DSV of 0.22 m gradient strengths between 24 mT∕m and 78 mT∕m could be realized locally with maximum currents of 150 A. Initial proof-of-concept imaging experiments using linear and nonlinear encoding fields are demonstrated. CONCLUSION: A shielded matrix gradient coil setup capable of generating encoding fields in a highly-flexible manner was designed and implemented. The presented setup is expected to serve as a basis for validating novel imaging techniques that rely on nonlinear spatial encoding fields. Magn Reson Med 79:1181-1191, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Design of a shielded coil element of a matrix gradient coil.

The increasing interest in spatial encoding with non-linear magnetic fields has intensified the need for coils that generates such fields. Matrix coils consisting of multiple coil elements appear to offer a high flexibility in generating customized encoding fields and are particularly promising for localized high resolution imaging applications. However, coil elements of existing matrix coils were primarily designed and constructed for better shimming and therefore are not expected to achieve an optimal performance for local spatial encoding. Moreover, eddy current properties of such coil elements were not fully explored. In this work, an optimization problem is formulated based on the requirement of local non-linear encoding and eddy current reduction that results in novel designs of coil elements for an actively-shielded matrix gradient coil. Two metrics are proposed to assess the performance of different coil element designs. The results are analyzed to reveal new insights into coil element design.

Pulseq: A rapid and hardware-independent pulse sequence prototyping framework.

PURPOSE: Implementing new magnetic resonance experiments, or sequences, often involves extensive programming on vendor-specific platforms, which can be time consuming and costly. This situation is exacerbated when research sequences need to be implemented on several platforms simultaneously, for example, at different field strengths. This work presents an alternative programming environment that is hardware-independent, open-source, and promotes rapid sequence prototyping. METHODS: A novel file format is described to efficiently store the hardware events and timing information required for an MR pulse sequence. Platform-dependent interpreter modules convert the file to appropriate instructions to run the sequence on MR hardware. Sequences can be designed in high-level languages, such as MATLAB, or with a graphical interface. Spin physics simulation tools are incorporated into the framework, allowing for comparison between real and virtual experiments. RESULTS: Minimal effort is required to implement relatively advanced sequences using the tools provided. Sequences are executed on three different MR platforms, demonstrating the flexibility of the approach. CONCLUSION: A high-level, flexible and hardware-independent approach to sequence programming is ideal for the rapid development of new sequences. The framework is currently not suitable for large patient studies or routine scanning although this would be possible with deeper integration into existing workflows. Magn Reson Med 77:1544-1552, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Trajectory optimization based on the signal-to-noise ratio for spatial encoding with nonlinear encoding fields.

PURPOSE: Multiple nonlinear gradient fields offer many potential benefits for spatial encoding including reduced acquisition time, fewer artefacts and region-specific imaging, although designing a suitable trajectory for such a setup is difficult. This work aims to optimize encoding trajectories for multiple nonlinear gradient fields based on the image signal-to-noise ratio. THEORY AND METHODS: Image signal-to-noise ratio is directly linked to the covariance of the reconstructed pixels, which can be calculated recursively for each projection of the trajectory under a Bayesian formulation. An evolutionary algorithm is used to find the higher-dimensional projections that minimize the pixel covariance, incorporating receive coil profiles, intravoxel dephasing, and reconstruction regularization. The resulting trajectories are tested through simulations and experiments. RESULTS: The optimized trajectories produce images with higher resolution and fewer artefacts compared with traditional approaches, particularly for high undersampling. However, higher-dimensional projection experiments strongly depend on accurate hardware and calibration. CONCLUSION: Computer-based optimization provides an efficient means to explore the large trajectory space created by the use of multiple nonlinear encoding fields. The optimization framework, as presented here, is necessary to fully exploit the advantages of nonlinear fields. Magn Reson Med 76:104-117, 2016. © 2015 Wiley Periodicals, Inc.

Performance evaluation of matrix gradient coils.

OBJECTIVE: In this paper, we present a new performance measure of a matrix coil (also known as multi-coil) from the perspective of efficient, local, non-linear encoding without explicitly considering target encoding fields. MATERIALS AND METHODS: An optimization problem based on a joint optimization for the non-linear encoding fields is formulated. Based on the derived objective function, a figure of merit of a matrix coil is defined, which is a generalization of a previously known resistive figure of merit for traditional gradient coils. RESULTS: A cylindrical matrix coil design with a high number of elements is used to illustrate the proposed performance measure. The results are analyzed to reveal novel features of matrix coil designs, which allowed us to optimize coil parameters, such as number of coil elements. A comparison to a scaled, existing multi-coil is also provided to demonstrate the use of the proposed performance parameter. CONCLUSIONS: The assessment of a matrix gradient coil profits from using a single performance parameter that takes the local encoding performance of the coil into account in relation to the dissipated power.

Monoplanar gradient system for imaging with nonlinear gradients.

OBJECT: In this paper we present a monoplanar gradient system capable of imaging a volume comparable with that covered by linear gradient systems. Such a system has been designed and implemented. MATERIALS AND METHODS: Building such a system was made possible by relaxing the constraint of global linearity and replacing it with a requirement for local orthogonality. A framework was derived for optimization of local orthogonality within the physical boundaries and geometric constraints. Spatial encoding of magnetic fields was optimized for their local orthogonality over a large field of view. RESULTS: A coil design consisting of straight wire segments was optimized, implemented, and integrated into a 3T human scanner to show the feasibility of this approach. Initial MR images are shown and further applications of the derived optimization method and the nonlinear planar gradient system are discussed. CONCLUSION: Encoding fields generated by the prototype encoding system were shown to be locally orthogonal and able to encode a cylindrical volume sufficient for some abdomen imaging applications for humans.

Stages: sub-Fourier dynamic shim updating using nonlinear magnetic field phase preparation.

Heterogeneity of the static magnetic field in magnetic resonance imaging may cause image artifacts and degradation in image quality. The field heterogeneity can be reduced by dynamically adjusting shim fields or dynamic shim updating, in which magnetic field homogeneity is optimized for each tomographic slice to improve image quality. A limitation of this approach is that a new magnetic field can be applied only once for each slice, otherwise image quality would improve somewhere to its detriment elsewhere in the slice. The motivation of this work is to overcome this limitation and develop a technique using nonlinear magnetic fields to dynamically shim the static magnetic field within a single Fourier-encoded volume or slice, called sub-Fourier dynamic shim updating. However, the nonlinear magnetic fields are not used as shim fields; instead, they impart a strong spatial dependence to the acquired MR signal by nonlinear phase preparation, which may be exploited to locally improve magnetic field homogeneity during acquisition. A theoretical description of the method is detailed, simulations and a proof-of-principle experiment are performed using a magnet coil with a known field geometry. The method is shown to remove artifacts associated with magnetic field homogeneity in balanced steady-state free-precession pulse sequences. We anticipate that this method will be useful to improve the quality of magnetic resonance images by removing deleterious artifacts associated with a heterogeneous static magnetic field.

Excitation and geometrically matched local encoding of curved slices.

In this work, the concept of excitation and geometrically matched local in-plane encoding of curved slices (ExLoc) is introduced. ExLoc is based on a set of locally near-orthogonal spatial encoding magnetic fields, thus maintaining a local rectangular shape of the individual voxels and avoiding potential problems arising due to highly irregular voxel shapes. Unlike existing methods for exciting curved slices based on multidimensional radiofrequency-pulses, excitation and geometrically matched local encoding of curved slices does not require long duration or computationally expensive radiofrequency-pulses. As each encoding field consists of a superposition of potentially arbitrary (spatially linear or nonlinear) magnetic field components, the resulting field shape can be adapted with high flexibility to the specific region of interest. For extended nonplanar structures, this results in improved relevant volume coverage for fewer excited slices and thus increased efficiency. In addition to the mathematical description for the generation of dedicated encoding fields and data reconstruction, a verification of the ExLoc concept in phantom experiments and examples for in vivo curved single and multislice imaging are presented.