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This chapter considers alternating current (AC) conductor losses and skin effect in the context of both strip conductors and then round conductors, and focuses on proximity effect. Skin effect is a phenomenon in which current density becomes concentrated at the outside of a conductor rather than being uniformly distributed. Skin effect is associated with AC currents and becomes increasingly pronounced as frequency increases. Proximity effect is a loss mechanism in which a time‐varying field from nearby conductors induces eddy currents in a given conductor. The chapter aims to demonstrate why the two loss mechanisms may be treated separately. It also considers the calculation of the proximity‐effect loss for an entire winding, and these losses for particular cases, including rotating machinery and a UI‐core inductor. The chapter concludes by considering the ac conductor losses in rotating electric machinery and in a UI‐core inductor.

This chapter focuses on calculating magnetic material losses and characterizing magnetic materials, especially with regard to loss. First, eddy current loss and then hysteresis loss is considered, and behavioral models to predict these losses is set forth. Next, experimental procedures to characterize the material anhysteretic B–H characteristic and losses are discussed. The chapter considers a variety of empirical or behavioral approaches to modeling core loss. Then, it addresses the problem of experimentally obtaining loss coefficients for empirical core loss models, such as the modified Steinmetz equation model. The chapter considers time‐domain models for modeling hysteresis. An alternate approach to the time‐domain modeling of magnetic behavior is the Jiles–Atherton model. This approach is very attractive in that it represents hysteresis with a first‐order ordinary differential equation.

PURPOSE: The purpose of this study was to identify the cause of severe image artifacts that occurred during gantry rotation in a 0.35 T MRI-Linac by comparing measurements of eddy currents, center frequency, and field inhomogeneities made with the gantry in motion and stationary. METHODS: Gradient and B(0) eddy currents were calculated from the free induction decays (FIDs) resulting from selective excitation at a temporal resolution of 200 ms/measurement. B(0) eddy currents were also calculated from FIDs acquired with nonselective excitation at a temporal resolution of 100 ms/measurement. Center frequencies and B(0) inhomogeneities were measured by acquiring FIDs with a repetition time (TR) of 290 ms. Cartesian and radial 2D true fast imaging with steady-state precession (TrueFISP) pulse sequences used in real-time MRI-guided radiation therapy (MR-IGRT) were acquired. To assess artifact severity, the normalized root mean square error (nRMSE) was calculated between a reference MRI (static gantry) and MRIs acquired during gantry rotation for each serial acquisition. Image artifacts were qualitatively graded as nominal, minor, or severe. Measurements were conducted while the gantry was rotated through its entire range for both clockwise and counterclockwise. Measurements during gantry rotation were compared to measurements with a stationary gantry (every 30°). RESULTS: Severe image artifacts were observed 22–35% of the time while the gantry was rotating. Short time constant eddy currents were not affected by gantry rotation. The peak to peak center frequency and FWHM rose by factors of 13.2–14.5 and 1.1–1.6, respectively, for the rotating versus stationary gantry. The magnitude of the center frequency offset and field inhomogeneities depended on the direction of the gantry rotation. CONCLUSIONS: Image artifacts during gantry rotation were primarily caused by center frequency variations and field inhomogeneities. Therefore, dynamic B(0) compensation techniques should be able to reduce artifacts during gantry rotation.

PURPOSE The purpose of this study was to measure gantry angle-related eddy currents in a 0.35-T MRI-Linac and determine if B0 (zeroth order) eddy currents are the primary cause of gantry angle-dependent imaging isocenter shifts vs other potential causes like B0 inhomogeneities and gradient (first order) eddy currents. For conventional Cartesian acquisitions, B0 eddy currents can cause imaging isocenter shifts along both phase encode and readout directions. Gradient eddy currents can cause spatial distortion along both the phase encode and readout directions. Center frequency offsets can cause imaging isocenter shifts along the readout direction that vary with readout gradient polarity. METHODS MRI-related eddy currents and imaging isocenter shifts were measured on a 0.35-T MRI-Linac at gantry angles from 0° to 330° in increments of 30° . All measurements were made after gradient shimming and center frequency tuning at each planned gantry angle. Eddy current and field homogeneity measurements were conducted using a 24-cm diameter spherical phantom. Gradient and B0 eddy currents were calculated from the free induction decays (FIDs) resulting from selective excitation of slices located ±5 cm from isocenter. B0 eddy currents were also calculated from FIDs acquired with nonselective excitation and compared with B0 eddy current values derived using selective excitation. B0 inhomogeneities and center frequency offsets were measured by acquiring FIDs with nonselective excitation. Imaging isocenter shifts were measured using a 33x33x10.5 cm3 uniformity linearity (grid) phantom and a 3D true fast imaging with steady-state precession (TrueFISP) sequence used in MRI-guided radiation therapy. Eddy currents were compared to vendor specifications and correlated with the imaging isocenter shifts. Measurements were conducted before and after the MRI-Linac's waveguide was replaced with an updated design to reduce eddy currents. RESULTS B0 eddy currents were highly correlated (r = 0.986, P <

The rotor eddy current loss of high‐speed permanent magnet motor has an important influence on the temperature distribution of permanent magnet. In traditional method, the unbalanced distribution of eddy current in permanent magnet is ignored, and the eddy current loss is applied to the calculation of temperature field in the form of average heat density, which makes a certain error in the calculation of the temperature field in permanent magnet motors. This study proposes the 50 kW and 30,000 rpm high‐speed permanent magnet prototype and an eddy current loss segmentation model of permanent magnet. The unbalanced distribution of eddy current in permanent magnet is considered in this model, and the permanent magnet is divided into different regions. According to the eddy current loss segmentation model, the eddy current losses in different regions are obtained, then the heat density in different regions of permanent magnet is applied to the calculation of temperature field in the motor. The application of the proposed model is simple and convenient, and makes temperature simulation results closer to the actual situation. At the same time, in order to verify the accuracy of the model, the temperature calculation results using the proposed model are compared with the traditional method, and both the results are verified by relevant experiments.

Purpose The aim of the study was to investigate whether incorrectly compensated eddy currents are the source of persistent X-nuclear spectroscopy and imaging artifacts, as well as methods to correct this. Methods Pulse-acquire spectra were collected for 1 H and X-nuclei (23 Na or 31 P) using the minimum TR permitted on a 3T clinical MRI system. Data were collected in 3 orientations (axial, sagittal, and coronal) with the spoiler gradient at the end of the TR applied along the slice direction for each. Modifications to system calibration files to tailor eddy current compensation for each X-nucleus were developed and applied, and data were compared with and without these corrections for: slice-selective MRS (for 23 Na and 31 P), 2D spiral trajectories (for 13 C), and 3D cones trajectories (for 23 Na). Results Line-shape distortions characteristic of eddy currents were demonstrated for X-nuclei, which were not seen for 1 H. The severity of these correlated with the amplitude of the eddy current frequency compensation term applied by the system along the axis of the applied spoiler gradient. A proposed correction to eddy current compensation, taking account of the gyromagnetic ratio, was shown to dramatically reduce these distortions. The same correction was also shown to improve data quality of non-Cartesian imaging (2D spiral and 3D cones trajectories). Conclusion A simple adaptation of the default compensation for eddy currents was shown to eliminate a range of artifacts detected on X-nuclear spectroscopy and imaging.

PURPOSE: To describe and implement a strategy for dynamic slice-by-slice and multiband B0 shimming using spherical harmonic shims in the human brain at 7T. THEORY: For thin axial slices, spherical harmonic shims can be divided into pairs of shims (z-degenerate and non-z-degenerate) that are spatially degenerate, such that only ½ of the shims (non-z-degenerate) are required for single slice optimizations. However, when combined, the pairs of shims can be used to simultaneously generate the same in-plane symmetries but with different amplitudes as a function of their z location. This enables multiband shimming equivalent to that achievable by single slice-by-slice optimization. METHODS: All data were acquired at 7T using a spherical harmonic shim insert enabling shimming up through 4th order with two additional 5th order shims (1st-4th+). Dynamic shim updating was achieved using a 10A shim power supply with 2 ms ramps and constrained optimizations to minimize eddy currents. RESULTS: In groups of eight subjects, we demonstrated that: 1) dynamic updating using 1st-4th+ order shims reduced the SD of the B0 field over the whole brain from 32.4 ± 2.6 and 24.9 ± 2 Hz with 1st-2nd and 1st-4th+ static global shimming to 15.1 ± 1.7 Hz; 2) near equivalent performance was achieved when dynamically updating only the non-z-degenerate shims (14.3 ± 1.5 Hz), or when a using multiband shim factor of 2, MBs = 2, and all shims (14.4 ± 2.0 Hz). CONCLUSION: High order spherical harmonics provide substantial improvements over static global shimming and enable dynamic multiband shimming with near equivalent performance to that of dynamic slice-by-slice shimming. This reduces distortion in echo planar imaging.

Purpose The impact of gradient imperfections on UTE images and UTE image-derived bone water quantification was investigated at 3 T field strength. Methods The effects of simple gradient time delays and eddy currents on UTE images, as well as the effects of gradient error corrections, were studied with simulation and phantom experiments. The k-space trajectory was mapped with a 2D sequence with phase encoding on both spatial axes by measuring the phase of the signal in small time increments during ramp-up of the read gradient. In vivo 3D UTE images were reconstructed with and without gradient error compensation to determine the bias in bone water quantification. Finally, imaging was performed on 2 equally configured Siemens TIM Trio systems (Siemens Medical Solutions, Erlangen, Germany) to investigate the impact of such gradient imperfections on inter-scanner measurement bias. Results Compared to values derived from UTE images with full gradient error compensation, total bone water was found to deviate substantially with no (up to 17%) or partial (delay-only) compensation (up to 10.8%). Bound water, obtained with inversion recovery-prepared UTE, was somewhat less susceptible to gradient errors (up to 2.2% for both correction strategies). Inter-scanner comparison indicated a statistically significant bias between measurements from the 2 MR systems for both total and bound water, which either vanished or was substantially reduced following gradient error correction. Conclusion Gradient imperfections impose spatially dependent artifacts on UTE images, which compromise not only bone water quantification accuracy but also inter-scanner measurement agreement if left uncompensated.

Purpose To propose an explicit Balanced steady-state free precession (bSSFP) signal model that predicts eddy current-induced steady-state disruptions and to provide a prospective, practical, and general eddy current compensation method. Theory and methods Gradient impulse response functions (GIRF) were used to simulate trajectory-specific eddy current-induced phase errors at the end of a repetition block. These phase errors were included in bloch simulations to establish a bSSFP signal model to predict steady-state disruptions and their corresponding image artifacts. The signal model was embedded in the MR system and used to compensate the phase errors by prospectively modifying the phase cycling scheme of the RF pulse. The signal model and eddy current compensation method were validated in phantom and in vivo experiments. In addition, the signal model was used to analyze pre-existing eddy current mitigation methods, such as 2D tiny golden angle radial and 3D paired phase encoded Cartesian acquisitions. Results The signal model predicted eddy current-induced image artifacts, with the zeroth-order GIRF being the primary factor to predict the steady-state disruption. Prospective RF phase cycling schemes were automatically computed online and considerably reduced eddy current-induced image artifacts. The signal model provides a direct relationship for the smoothness of k-space trajectories, which explains the effectiveness of phase encode pairing and tiny golden angle trajectory. Conclusions The proposed signal model can accurately predict eddy current-induced steady-state disruptions for bSSFP imaging. The signal model can be used to derive the eddy current-induced phase errors required for trajectory-specific RF phase cycling schemes, which considerably reduce eddy current-induced image artifacts.

Purpose To perform direct, selective MRI of short-T2 tissues using zero echo time (ZTE) imaging with weighted echo subtraction (WSUB). Methods Radial imaging was performed at 7T, acquiring both ZTE and gradient echo (GRE) signals created by bipolar gradients. Long-T2 suppression was achieved by weighted subtraction of ZTE and GRE images. Special attention was given to imperfections of gradient dynamics, to which radial GRE imaging is particularly susceptible. To compensate for gradient errors, matching of gradient history was combined with data correction based on trajectory measurement. The proposed approach was first validated in phantom experiments and then demonstrated in musculoskeletal (MSK) imaging. Results Trajectory analysis and phantom imaging demonstrated that gradient imperfections were successfully addressed. Gradient history matching enabled consistency between antiparallel projections as required for deriving zeroth-order eddy current dynamics. Trajectory measurement provided individual echo times per projection that showed considerable variation between gradient directions. In in vivo imaging of knee, ankle, and tibia, the proposed approach enabled high-resolution 3D depiction of bone, tendons, and ligaments. Distinct contrast of these structures indicates excellent selectivity of long-T2 suppression. Clarity of depiction also confirmed sufficient SNR of short-T2 tissues, achieved by high baseline sensitivity at 7T combined with high SNR efficiency of ZTE acquisition. Conclusion Weighted subtraction of ZTE and GRE data reconciles robust long-T2 suppression with fastest k-space coverage and high SNR efficiency. This approach enables high-resolution imaging with excellent selectivity to short-T2 tissues, which are of major interest in MSK and neuroimaging applications.

Purpose To overcome existing challenges in dynamic B0 shimming by implementing a shim optimization algorithm which limits shim current amplitudes and their temporal variation through the application of constraints and regularization terms. Theory and methods Spherical harmonic dynamic B0 shimming is complicated by eddy currents, ill-posed optimizations, and the need for strong power supplies. Based on the fact that eddy current amplitudes are proportional to the magnitude of the shim current changes, and assuming a smoothness of the B0 inhomogeneity variation in the slice direction, a novel algorithm was implemented to reduce eddy current generation by limiting interslice shim current changes. Shim degeneracy issues and resulting high current amplitudes are additionally addressed by penalizing high solution norms. Applicability of the proposed algorithm was validated in simulations and in phantom and in vivo measurements. Results High-order dynamic shimming simulations and measurements have shown that absolute shim current amplitudes and their temporal variation can be substantially reduced with negligible loss in achievable B0 homogeneity. Whereas conventional dynamic shim updating optimizations improve the B0 homogeneity, on average, by a factor of 2.1 over second-order static solutions, our proposed routine reached a factor of 2.0, while simultaneously providing a 14-fold reduction of the average maximum shim current changes. Conclusions The proposed algorithm substantially reduces the shim amplitudes and their temporal variation, while only marginally affecting the achievable B0 homogeneity. As a result, it has the potential to mitigate the remaining challenges in dynamic B0 shimming and help in making its application more readily available.

Strain : the journal of the British Society for Strain Measurement 12387 (2021). doi:10.1111/str.12387, Published by Wiley- Blackwell, Oxford [u.a.]

Cutting of electrical steel sheets typically deteriorates the permeability and increases the iron loss close to the cutting edges. We estimated iron losses in the cross‐section of electrical steel sheets by numerically solving the 1‐D and 2‐D eddy‐current distributions while accounting for static magnetic behaviour with a hysteresis model. The magnetization curves in the cross‐section are defined using a continuous local material model, making them dependent on the distance from the cut edge by a degradation profile. Damaged and undamaged hysteresis loops were identified by measurements of different wide strips of M400‐50A steel sheets. The eddy‐current distributions were solved when the strips of different widths were excited with sinusoidal average flux densities at different frequencies. It was found that the cutting degradation also affects the eddy‐current loss particularly around 1.0 T. The exact shape of the degradation profile was found to be less significant while the increase of excess losses is significant for the overall loss estimation. acceptedVersion

PURPOSE Velocity-selective saturation (VSS) pulse trains provide a viable alternative to the spatially selective methods for measuring cerebral blood volume (CBV) by reducing the sensitivity to arterial transit time. This study is to compare the Fourier-transform-based velocity-selective saturation (FT-VSS) pulse trains with the conventional flow-dephasing VSS techniques for CBV quantification. METHODS The proposed FT-VSS label and control modules were compared with VSS pulse trains utilizing double refocused hyperbolic tangent (DRHT) and 8-segment B1-insensitive rotation (BIR-8). This was done using both numerical simulations and phantom studies to evaluate their sensitivities to gradient imperfections such as eddy currents. DRHT, BIR-8, and FT-VSS prepared CBV mapping was further compared for velocity-encoding gradients along 3 orthogonal directions in healthy subjects at 3T. RESULTS The phantom studies exhibited more consistent immunity to gradient imperfections for the utilized FT-VSS pulse trains. Compared to DRHT and BIR-8, FT-VSS delivered more robust CBV results across the 3 VS encoding directions with significantly reduced artifacts along the superior-inferior direction and improved temporal signal-to-noise ratio (SNR) values. Average CBV values obtained from FT-VSS based sequences were 5.3 mL/100 g for gray matter and 2.3 mL/100 g for white matter, comparable to literature expectations. CONCLUSION Absolute CBV quantification utilizing advanced FT-VSS pulse trains had several advantages over the existing approaches using flow-dephasing VSS modules. A greater immunity to gradient imperfections and the concurrent tissue background suppression of FT-VSS pulse trains enabled more robust CBV measurements and higher SNR than the conventional VSS pulse trains.

Purpose B0 eddy currents are a subtle but important source of artifacts in spiral MRI. This study illustrates the importance of addressing these artifacts and presents a system response-based eddy current correction strategy using B0 eddy current phase measurements on a phantom. Methods B0 and linear eddy current system response measurements were estimated from phantom-based measurement and used to predict residual eddy current effects in spiral acquisitions. The measurements were evaluated across multiple systems and gradient sets. The corresponding eddy current corrections were studied in both axial spiral-in/out TSE and sagittal spiral-out MPRAGE volunteer data. Results Correction of B0 eddy currents using the proposed method mitigated blurriness in the axial spiral-in/out images and artifacts in the sagittal spiral-out images. The system response measurement was found to yield repeatable results over time with some variation in the B0 eddy current responses measured between different systems. Conclusions The proposed eddy current correction framework was effective in mitigating the effects of residual B0 and linear eddy currents. Any spiral acquisition should take residual eddy currents into account. This is particularly important in spiral-in/out acquisitions.

Extensive research papers of three-dimensional computational techniques are widely used for the investigation of human brain pathophysiology. Eddy current analyzing could provide an indication of conductivity change within a biological body. A significant obstacle to current trend analyses is the development of a numerically stable and efficiency-finite element scheme that performs well at low frequency and does not require a large number of degrees of freedom. Here, a custom finite element method (FEM) solver based on edge elements is proposed using the weakly coupled theory, which separates the solution into two steps. First, the background field (the magnetic vector potential on each edge) is calculated and stored. Then, the electric scalar potential on each node is obtained by FEM based on Galerkin formulations. Consequently, the electric field and eddy current distribution in the object can be obtained. This solver is more efficient than typical commercial solvers since it reduces the vector eddy current equation to a scalar one, and reduces the meshing domain to just the eddy current region. It can therefore tackle complex eddy current calculations for models with much larger numbers of elements, such as those encountered in eddy current computation in biological tissues. An example is presented with a realistic human brain mesh of 2 million elements. In addition, with this solver, the equivalent magnetic field induced from the excitation coil is applied, and therefore there is no need to mesh the excitation coil. In combination, these significantly increase the efficiency of the solver. Bioelectromagnetics. 39:604-616, 2018. © 2018 Wiley Periodicals, Inc.

PURPOSE Sensitivity to imperfections of image-encoding gradient fields may significantly impair widespread use of radial MR data acquisition. Such imperfections can cause individual echo shifts for each spoke acquired in the k-space and may produce severe image artifacts. Therefore, fast and robust methods to quantify and correct for those echo shifts are required. THEORY AND METHODS Echo shifts can be induced by inhomogeneities of the static magnetic field (δnB ) and by imbalances of the imaging gradients (δnG ) mainly caused by eddy currents. However, mismatch between data acquisition and gradient switching may additionally play a role. From the position of the echo maxima of 2 opposing spokes, δnG and δnB can be determined and corrected by adapting the read-dephasing gradient accordantly. This approach was implemented on MR-systems of different field strengths, gradient systems, and vendors, and the dependencies of echo shift and acquisition parameters were analyzed. Data sets of phantoms and of mice under in vivo conditions were obtained using RF-spoiled 2D radial-FLASH. RESULTS The presented method allowed for echo-shift detection and correction of

PURPOSE Uneven flow distribution in patients with Fontan circulation is suspected to lead to complications. 4D flow MRI offers evaluation using time-resolved pathlines; however, the potential error is not well understood. The aim of this study was to systematically assess variability in flow distribution caused by well-known sources of error. METHODS 4D flow MRI was acquired in 14 patients with Fontan circulation. Flow distribution was quantified by the % of caval venous flow pathlines reaching the left and right pulmonary arteries. Impact of data acquisition and data processing uncertainties were investigated by (1) probabilistic 4D blood flow tracking at varying noise levels, (2) down-sampling to mimic acquisition at different spatial resolutions, (3) pathline calculation with and without eddy current correction, and (4) varied segmentation of the Fontan geometry to mimic analysis errors. RESULTS Averaged among the cohort, uncertainties accounted for flow distribution errors from noise ≤3.2%, low spatial resolution ≤2.3% to 3.8%, eddy currents ≤6.4%, and inaccurate segmentation ≤3.9% to 9.1% (dilation and erosion, respectively). In a worst-case scenario (maximum additive errors for all 4 sources), flow distribution errors were as high as 22.5%. CONCLUSION Inaccuracies related to postprocessing (segmentation, eddy currents) resulted in the largest potential error (≤15.5% combined) whereas errors related to data acquisition (noise, low spatial resolution) had a lower impact (≤5.5%-7.0% combined). Whereas it is unlikely that these errors will be additive or affect the identification of severe asymmetry, these results illustrate the importance of eddy current correction and accurate segmentation to minimize Fontan flow distribution errors.

We introduce a novel design for millimeter wave electromagnetic structures within magic angle spinning (MAS) rotors. In this demonstration, a copper coating is vacuum deposited onto the outside surface of a sapphire rotor at a thickness of 50 nm. This thickness is sufficient to reflect 197-GHz microwaves, yet not too thick as to interfere with radiofrequency fields at 300 MHz or prevent sample spinning due to eddy currents. Electromagnetic simulations of an idealized rotor geometry show a microwave quality factor of 148. MAS experiments with sample rotation frequencies of ωr /2π = 5.4 kHz demonstrate that the drag force due to eddy currents within the copper does not prevent sample spinning. Spectra of sodium acetate show resolved 13 C J-couplings of 60 Hz and no appreciable broadening between coated and uncoated sapphire rotors, demonstrating that the copper coating does not prevent shimming and high-resolution nuclear magnetic resonance spectroscopy. Additionally, 13 C Rabi nutation curves of ω1 /2π = 103 kHz for both coated and uncoated rotors indicate no detrimental impact of the copper coating on radio frequency coupling of the nuclear spins to the sample coil. We present this metal coated rotor as a first step towards an MAS resonator. MAS resonators are expected to have a significant impact on developments in electron decoupling, pulsed dynamic nuclear polarization (DNP), room temperature DNP, DNP with low-power microwave sources, and electron paramagnetic resonance detection.

PURPOSE To combine the metabolite-cycling technique with diffusion-weighted H-MR spectroscopy and to use the inherent water reference for compensation of motion-related signal loss for improved estimation of metabolite apparent diffusion coefficients (ADCs). METHODS Diffusion-weighted spectra of water and metabolites were acquired simultaneously using metabolite-cycling at 3 T. The water information was used for signal correction of phase, frequency, and eddy currents, as well as for compensation of motion-induced signal loss. ADCs were estimated by 2D simultaneous fitting. The quality of ADC restoration was investigated in vitro. Subsequently, the new approach was applied in 13 subjects for enhanced metabolite ADC estimation in gray matter. RESULTS Metabolite-cycled diffusion H-MRS is suitable to measure metabolite and water ADCs simultaneously. The water reference facilitates signal amplitude restoration, compensating for motion-related artefacts. 2D fitting stabilizes the fitting procedure and allows the estimation of ADCs even for low signal-to-noise metabolites. Use of the motion-compensation scheme leads to estimation of smaller ADCs for virtually all metabolites (44% smaller ADC on average), to a reduction of fitting uncertainties for metabolite ADCs in individual subjects and reduced variance over the cohort (45% smaller SD on average). CONCLUSION Using the simultaneously acquired water signal as internal reference allows not only for compensation of phase and frequency fluctuations but also for signal amplitude restoration, and thus improved metabolite ADC estimation. Combination with 2D simultaneous fitting promises access to the diffusion properties even for low signal-to-noise metabolites. The combination of both techniques increases the specificity and sensitivity of estimated metabolite ADC values in the cohort.

The issue of justifying the eddy current approximation of Maxwell's equations is re-considered in the time-dependent setting. Convergence of the solution operators is shown in the sense of strong operator limits., keywords and phrases: electrodynamics, eddy current problem, evolutionary equations, material laws

PURPOSE To investigate frequency-offset effects in edited magnetic resonance spectroscopy (MRS) experiments arising from B0 eddy currents. MATERIALS AND METHODS Macromolecule-suppressed (MM-suppressed) γ-aminobutyric acid (GABA)-edited experiments were performed at 3T. Saturation-offset series of MEGA-PRESS experiments were performed in phantoms, in order to investigate different aspects of the relationship between the effective editing frequencies and eddy currents associated with gradient pulses in the sequence. Difference integrals were quantified for each series, and the offset dependence of the integrals was analyzed to quantify the difference in frequency (Δf) between the actual vs. nominal expected saturation frequency. RESULTS Saturation-offset N-acetyl-aspartate-phantom experiments show that Δf varied with voxel orientation, ranging from 10.4 Hz (unrotated) to 6.4 Hz (45° rotation about the caudal-cranial axis) and 0.4 Hz (45° rotation about left-right axis), indicating that gradient-related B0 eddy currents vary with crusher-gradient orientation. Fixing the crusher-gradient coordinate-frame substantially reduced the orientation dependence of Δf (to ∼2 Hz). Water-suppression crusher gradients also introduced a frequency offset, with Δf = 0.6 Hz ("excitation" water suppression), compared to 10.2 Hz (no water suppression). In vivo spectra showed a negative edited "GABA" signal, suggesting Δf on the order of 10 Hz; with fixed crusher-gradient coordinate-frame, the expected positive edited "GABA" signal was observed. CONCLUSION Eddy currents associated with pulsed field gradients may have a considerable impact on highly frequency-selective spectral-editing experiments, such as MM-suppressed GABA editing at 3T. Careful selection of crusher gradient orientation may ameliorate these effects. LEVEL OF EVIDENCE 2 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2018;47:673-681.

Purpose To investigate the effect of the asymmetric gradient concomitant fields (CF) with zeroth and first-order spatial dependence on fast/turbo spin-echo acquisitions, and to demonstrate the effectiveness of their real-time compensation. Methods After briefly reviewing the CF produced by asymmetric gradients, the effects of the additional zeroth and first-order CFs on these systems are investigated using extended-phase graph simulations. Phantom and in vivo experiments are performed to corroborate the simulation. Experiments are performed before and after the real-time compensations using frequency tracking and gradient pre-emphasis to demonstrate their effectiveness in correcting the additional CFs. The interaction between the CFs and prescan-based correction to compensate for eddy currents is also investigated. Results It is demonstrated that, unlike the second-order CFs on conventional gradients, the additional zeroth/first-order CFs on asymmetric gradients cause substantial signal loss and dark banding in fast spin-echo acquisitions within a typical brain-scan field of view. They can confound the prescan correction for eddy currents and degrade image quality. Performing real-time compensation successfully eliminates the artifacts. Conclusions We demonstrate that the zeroth/first-order CFs specific to asymmetric gradients can cause substantial artifacts, including signal loss and dark bands for brain imaging. These effects can be corrected using real-time compensation. Magn Reson Med, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

Purpose Magnetic resonance–compatible medical devices operate within the MR environment while benefitting from the superior anatomic information of MRI. Avoiding electromagnetic interference between such instrumentation and the MR system is crucial. In this work, various shielding configurations for positron emission tomography (PET) detectors were studied and analyzed regarding radiofrequency (RF) shielding effectiveness and gradient-induced eddy current performances. However, the results of this work apply to shielding considerations for any MR-compatible devices. Methods Six shielding enclosure configurations with various thicknesses, patterns, and materials were designed: solid and segmented copper, phosphor bronze mesh (PBM), and carbon fiber composite (CFC). A series of tests was performed on RF shielding effectiveness and the gradient-induced eddy current. Results For the shielding effectiveness, the solid copper with various thickness and PBM configurations yield significantly better shielding effectiveness (>15 dB) compared with CFC and segmented configurations. For the gradient-induced eddy current performance, the solid copper shielding configurations with different thicknesses showed significantly worse results, up to a factor of 3.89 dB, compared with the segmented copper, PBM, and the CFC configurations. Conclusions We evaluated the RF shielding effectiveness and the gradient-induced eddy current artifacts of several shielding designs, and only the PBM showed positive outcomes for both aspects. Magn Reson Med 79:1745–1752, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Purpose To investigate the acoustic radiation due to eddy current-cryostat interactions and perform a qualitative analysis on noise reduction methods. Methods In order to evaluate the sound pressure level (SPL) of the eddy current induced warm bore wall vibration, a Finite Element (FE) model was created to simulate the noises from both the warm bore wall vibration and the gradient coil assembly. For the SPL reduction of the warm bore wall vibration, we first improved the active shielding of the gradient coil, thus reducing the eddy current on the warm bore wall. A damping treatment was then applied to the warm bore wall to control the acoustic radiation. Results Initial simulations show that the SPL of the warm bore wall is higher than that of the gradient assembly with typical design shielding ratios at many frequencies. Subsequent simulation results of eddy current control and damping treatment application show that the average SPL reduction of the warm bore wall can be as high as 9.6 dB, and even higher in some frequency bands. Conclusions Combining eddy current control and suggested damping scheme, the noise level in a MRI system can be effectively reduced. This article is protected by copyright. All rights reserved.

Purpose To design and evaluate eddy current–nulled convex optimized diffusion encoding (EN-CODE) gradient waveforms for efficient diffusion tensor imaging (DTI) that is free of eddy current–induced image distortions. Methods The EN-CODE framework was used to generate diffusion-encoding waveforms that are eddy current–compensated. The EN-CODE DTI waveform was compared with the existing eddy current–nulled twice refocused spin echo (TRSE) sequence as well as monopolar (MONO) and non–eddy current–compensated CODE in terms of echo time (TE) and image distortions. Comparisons were made in simulations, phantom experiments, and neuro imaging in 10 healthy volunteers. Results The EN-CODE sequence achieved eddy current compensation with a significantly shorter TE than TRSE (78 versus 96 ms) and a slightly shorter TE than MONO (78 versus 80 ms). Intravoxel signal variance was lower in phantoms with EN-CODE than with MONO (13.6 ± 11.6 versus 37.4 ± 25.8) and not different from TRSE (15.1 ± 11.6), indicating good robustness to eddy current–induced image distortions. Mean fractional anisotropy values in brain edges were also significantly lower with EN-CODE than with MONO (0.16 ± 0.01 versus 0.24 ± 0.02, P

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

To calculate the distribution of the magnetic field and eddy current density on the surface of an aluminium plate, a method that couples the face-smoothed finite element method (FS-FEM) to the boundary element method (BEM) is proposed in this study. This method combines the advantages of the FS-FEM and BEM, which can rapidly and accurately calculate the distributions of vertical magnetic field and eddy current field on the surface of an aluminium plate. The structural parameters and material properties of the coil and aluminium plate are considered. An accurate three-dimensional calculation model is established. Then, the vertical magnetic field and eddy current field distributions are calculated in this study. In the case of the same grid density, compared with the finite element–boundary element coupling algorithm, the simulation results show that the FS-FEM and the boundary element coupling method have obvious advantage in improving the calculation accuracy. The maximum relative error between the calculated results and measured results is only 4%. The proposed method in this study is available for reference to the transient open-domain eddy current field analysis.

This paper deals with the synthesis of an RL Cauer ladder network to homogenize multiturn windings in time-domain finite element (FE) computations. In frequency domain, the macroscopic model of eddy currents in the winding can be described by frequency-dependent complex impedance and reluctivity for skin and proximity effects respectively. To represent those in time domain, two RL Cauer networks are synthesized to match each, with the accuracy depending on the order of the network to be appended. The proposed method yields an improved accuracy as compared with the previous work in which the topology of the ladder network was not well chosen. The results are validated by means of a 2-D axisymmetric inductor with a nonlinear gapped core., SCOPUS: ar.j, info:eu-repo/semantics/published

Thermal ablation using alternating electromagnetic fields is a promising method to treat tissues including tumors. With this approach, an electromagnetic field is generated around an induction coil, which is supplied with high frequency current from a power source. Any electrically conducting object, which is placed in the electromagnetic field, is then heated due to eddy currents. Basic principles underlying this novel thermotherapy needle system are internal induction and resistance heating. This presents a new design of a standard gauge 18 percutaneous trans-hepatic cholangiography needle module combined with a compact power source. Three needle modules containing coils of different lengths were used to locally heat up different volumes of tissues in in vitro experiments on pig livers. Temperature on the inside surface of the needle was controlled and monitored through a K-type thermocouple. By using this needle module system, no two-section or ferromagnetic nanoparticle-coated needles were required; the system worked well with the SUS-304 stainless-steel needle. Successful results were demonstrated in the in vitro experiments on pig livers with different heating lengths of 10, 20, and 30 mm needles. With low power sources, needles could be heated up to a high temperature. The novel design of the needle module incorporated with a high frequency power source was thus shown to be a promising technology for tissue ablation. Bioelectromagnetics. 2016;9999:XX–XX. © 2016 Wiley Periodicals, Inc.

Induction welding of metals and thermoplastic fiber reinforced polymer composites is a promising technology for the joining of hybrid components. It uses the possibility to induce eddy currents into a metal in order to melt the polymer of the adjacent composite. By applying pressure onto both parts, for example with a consolidation roller, the polymer adheres to the metal and a bond is generated. However, the relatively low process speed, caused by a slow cooling of the components, prevents a wide use of this method so far. Therefore, this study examines the influence of an active component cooling on the process speed and the resulting effects on the joining strength.

This paper investigates the physical properties of 99.91% pure copper produced by Additive Manufacturing via selective electron beam melting (SEBM). Eddy current measurements and laser flash analyses are used to determine the electrical and the thermal conductivity. Electrical and thermal conductivity follow the Wiedemann-Franz law. The correlation of conductivities and porosity shows that 99.95 % dense components with nearly optimal conductivities (σ = 55.82 MS m–1 and λ = 400.1 W m–1 K–1) can be fabricated with SEBM. The small deviation from the theoretical maximum of copper (59.7 MS m–1) can be explained by the characteristics of the raw material and chemical impurities.

Purpose To develop single and double acquisition methods to compensate for artifacts from eddy currents and transient oscillations in balanced steady-state free precession (bSSFP) with centric phase-encoding (PE) order for magnetization-prepared bSSFP imaging. Theory and Methods A single and four different double acquisition methods were developed and evaluated with Bloch equation simulations, phantom/in vivo experiments, and quantitative analyses. For the single acquisition method, multiple PE groups, each of which was composed of N linearly changing PE lines, were ordered in a pseudocentric manner for optimal contrast and minimal signal fluctuations. Double acquisition methods used complex averaging of two images that had opposite artifact patterns from different acquisition orders or from different numbers of dummy scans. Results Simulation results showed high sensitivity of eddy-current and transient-oscillation artifacts to off-resonance frequency and PE schemes. The artifacts were reduced with the PE-grouping with N values from 3 to 8, similar to or better than the conventional pairing scheme of N = 2. The proposed double acquisition methods removed the remaining artifacts significantly. The proposed methods conserved detailed structures in magnetization transfer imaging well, compared with the conventional methods. Conclusion The proposed single and double acquisition methods can be useful for artifact-free magnetization-prepared bSSFP imaging with desired contrast and minimized dummy scans. Magn Reson Med 78:254–263, 2017. © 2016 International Society for Magnetic Resonance in Medicine

Purpose To develop a gradient pre-emphasis scheme that prospectively counteracts the effects of the first-order concomitant fields for any arbitrary gradient waveform played on asymmetric gradient systems, and to demonstrate the effectiveness of this approach using a real-time implementation on a compact gradient system. Methods After reviewing the first-order concomitant fields that are present on asymmetric gradients, we developed a generalized gradient pre-emphasis model assuming arbitrary gradient waveforms to counteract their effects. A numerically straightforward, easily implemented approximate solution to this pre-emphasis problem was derived that was compatible with the current hardware infrastructure of conventional MRI scanners for eddy current compensation. The proposed method was implemented on the gradient driver subsystem, and its real-time use was tested using a series of phantom and in vivo data acquired from two-dimensional Cartesian phase-difference, echo-planar imaging, and spiral acquisitions. Results The phantom and in vivo results demonstrated that unless accounted for, first-order concomitant fields introduce considerable phase estimation error into the measured data and result in images with spatially dependent blurring/distortion. The resulting artifacts were effectively prevented using the proposed gradient pre-emphasis. Conclusion We have developed an efficient and effective gradient pre-emphasis framework to counteract the effects of first-order concomitant fields of asymmetric gradient systems. Magn Reson Med 77:2250–2262, 2017. © 2016 International Society for Magnetic Resonance in Medicine

Purpose To develop a new Nyquist ghost and geometric distortion correction method in echo planar imaging (EPI) using parallel imaging. Methods Two frames of EPI data are acquired with normal and phase-labeled sequence. The phase label is applied by modifying the PE prephase gradient to shift the central echo by one echo spacing. GRAPPA weights are trained from both frames and used to reconstruct images from positive or negative echoes in each frame to remove Nyquist ghost. Geometric distortion is then corrected by the B0 field map generated from the phase difference between positive and negative echo images. Phantom and in vivo experiments at 7 Tesla (T) and 3T were performed to evaluate the proposed method. Results Nyquist ghost was greatly reduced in all images even under oblique imaging and poor eddy current conditions, yielding significant improvements over the existing reference scan and image entropy minimization based methods. Image geometries were fully restored after distortion correction. Phantom results indicated that the signal-to-noise ratio efficiency was largely preserved while fMRI results showed no apparent degradation of temporal resolution. Conclusion The proposed method provides robust correction of both Nyquist ghost and geometric distortion in EPI, and it is particularly suitable for dynamic EPI applications. Magn Reson Med 77:1749-1761, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

The magnetic field gradient waveform monitor (MFGM) technique permits characterization of the temporal evolution of magnetic field gradients in magnetic resonance (MR) instruments (MRIs). Knowledge of the gradient waveform performance permits the development of further techniques, such as gradient waveform pre-equalization, that correct and optimize gradient waveform distortions due to eddy currents induced during the application of switched magnetic fields and other system limitations. The accuracy of the MFGM technique is important since the overall uncertainty of the gradient waveform measurement will propagate into an uncertainty in corrected gradient waveforms impacting the precision of the resulting MR/MRI measurements. The accuracy of MFGM is investigated through a treatment of the noise present in a MRI. A noisy receiver model provides the basis for characterization of the noise and permits examination of the overall impact of noise on the phase accumulated in a pure-phase encoded MR signal. Ultimately, a relationship between the signal-to-noise ratio of a measurement and the corresponding MFGM uncertainty is developed. The theoretical development is supported through simulation in conjunction with experimental results. The propagation of uncertainties to gradient waveform pre-equalization is also discussed.

The combination of a hard subsurface layer and a ductile component core is advantageous for many applications. Steels are often heat treated to create such a hardened subsurface, which is both time- and energy-consuming. It is of great advantage to create a hardened subsurface directly within the machining process, as the production line of most components includes such a process to produce the desired geometric dimensions and surface quality. To achieve a martensitic subsurface layer within the machining process, cryogenic, external turning using a metastable AISI304 austenitic steel is used herein. Herein eddy current testing and the analysis of higher harmonics are used for the detection of the ferromagnetic, martensitic phase in the parent austenite. A good correlation is found between the martensite content and the amplitude of the signals measured. Therefore, eddy current testing is considered as a suitable real-time, nondestructive testing method, which forms the basis for the generation of a tailored, deformation-induced martensitic subsurface layer during external turning.

A detailed research of mechanisms causing the rotation of dust structures formed in striations of the glow discharge in longitudinal magnetic field is presented. Literary data speak about sign-variable dependence of angular velocity of dust structure on the magnetic field. The first done experiment proves that ion drag force is the reason of rotation with the negative projection of angular velocity on magnetic induction in small magnetic fields. The method of a variation of an ion flux in mixes of gases was used for the research. In the second experiment the gas rotation arising because of eddy electron current in the magnetic field was revealed by the method of probing of the discharge by dust particles. Estimates show that a prevalence of the mechanism of rotation of dust structures and correspondingly the direction of rotation depends both on discharge conditions and on the size of dust particles. (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)