2 H transmit-receive NMR probes for magnetic field monitoring in MRI: 2 H Transmit-Receive NMR Probes for MFM Applications

A correction algorithm for improved magnetic field monitoring with distal field probes

PURPOSE

A significant source of artifacts in MRI are field fluctuations. Field monitoring is a new technology that allows measurement of field dynamics during a scan via "field probes," which can be used to improve image reconstruction. Ideally, probes are located within the volume where gradients produce nominally linear field patterns. However, in some situations probes must be located far from isocenter where rapid field variation can arise, leading to erroneous field-monitoring characterizations and images. This work aimed to develop an algorithm that improves the robustness of field dynamics in these situations.

METHODS

The algorithm is split into three components. Component 1 calculates field dynamics one spatial order at a time, whereas the second implements a weighted least squares solution based on probe distance. Component 3 then calculates phase residuals and removes the residual phase for distant probes before recalculation. Two volunteers and a phantom were scanned on a 7T MRI using diffusion-weighted sequences, and field monitoring was performed. Image reconstructions were informed with field dynamics calculated conventionally, and with the correction algorithm, after which in vivo images were compared qualitatively and phantom image error was quantitatively assessed.

RESULTS

The algorithm was able to correct corrupted field dynamics, resulting in image-quality improvements. Significant artifact reduction was observed when correcting higher-order fits. Stepwise fitting provided the most correction benefit, which was marginally improved when adding the other correction strategies.

CONCLUSION

The proposed algorithm can mitigate effects of phase errors in field monitoring, providing improved characterization of field dynamics.

Direct comparison of gradient Fidelity and acoustic noise of the same MRI system at 3 T and 0.75 T

PURPOSE

To analyze the difference between gradient fidelity and acoustic noise of the same MRI scanner operated at product field strength (3 T) and lower field strength (0.75 T).

METHODS

Gradient modulation transfer functions (GMTFs) were measured using a four-slice 2D phase-encoded chirp-based sequence on the same scanner operated at 3 T and, following ramp-down, at 0.75 T with identical gradient specifications (40 mT/m, 200 T/m/s). Calibrated audio measurements were performed at both field strengths to correlate audio spectra with GMTFs.

RESULTS

While eddy currents were independent of field strength, mechanical resonances were substantially decreased at lower field, resulting in a reduction of GMTF distortions by up to 95% (88% on average) at the mechanical resonances of the gradient system. Audio spectra amplitudes were reduced by up to 87% when comparing 0.75 T versus 3 T.

CONCLUSION

Lower static fields lead to reduced Lorentz forces on the gradient coil and, in turn, to reduced mechanical resonances, thereby improving gradient fidelity. Simultaneously, the reduction of acoustic noise may help to improve patient comfort.

MaxGIRF: Image reconstruction incorporating concomitant field and gradient impulse response function effects

Purpose

To develop and evaluate an improved strategy for compensating concomitant field effects in non‐Cartesian MRI at the time of image reconstruction.

Theory

We present a higher‐order reconstruction method, denoted as MaxGIRF, for non‐Cartesian imaging that simultaneously corrects off‐resonance, concomitant fields, and trajectory errors without requiring specialized hardware. Gradient impulse response functions are used to predict actual gradient waveforms, which are in turn used to estimate the spatiotemporally varying concomitant fields based on analytic expressions. The result, in combination with a reference field map, is an encoding matrix that incorporates a correction for all three effects.

Methods

The MaxGIRF reconstruction is applied to noiseless phantom simulations, spiral gradient‐echo imaging of an International Society for Magnetic Resonance in Medicine/National Institute of Standards and Technology phantom, and axial and sagittal multislice spiral spin‐echo imaging of a healthy volunteer at 0.55 T. The MaxGIRF reconstruction was compared against previously established concomitant field‐compensation and image‐correction methods. Reconstructed images are evaluated qualitatively and quantitatively using normalized RMS error. Finally, a low‐rank approximation of MaxGIRF is used to reduce computational burden. The accuracy of the low‐rank approximation is studied as a function of minimum rank.

Results

The MaxGIRF reconstruction successfully mitigated blurring artifacts both in phantoms and in vivo and was effective in regions where concomitant fields counteract static off‐resonance, superior to the comparator method. A minimum rank of 8 and 30 for axial and sagittal scans, respectively, gave less than 2% error compared with the full‐rank reconstruction.

Conclusions

The MaxGIRF reconstruction simultaneously corrects off‐resonance, trajectory errors, and concomitant field effects. The impact of this method is greatest when imaging with longer readouts and/or at lower field strength.

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Integration of an RF coil and commercial field camera for ultrahigh-field MRI

PURPOSE

To develop an RF coil with an integrated commercial field camera for ultrahigh field (7T) neuroimaging. The RF coil would operate within a head-only gradient coil and be subject to the corresponding design constraints. The RF coil can thereafter be used for subject-specific correction of k-space trajectories-notably in gradient-sensitive sequences such as single-shot spiral imaging.

METHODS

The transmit and receive performance was evaluated before and after the integration of field probes, whereas field probes were evaluated when in an optimal configuration external to the coil and after their integration. Diffusion-weighted EPI and single-shot spiral acquisitions were employed to evaluate the efficacy of correcting higher order field perturbations and the consequent effect on image quality.

RESULTS

Field probes had a negligible effect on RF-coil performance, including the transmit efficiency, transmit uniformity, and mean SNR over the brain. Modest reductions in field-probe signal lifetimes were observed, caused primarily by nonidealities in the gradient and shim fields of the head-only gradient coil at the probe positions. The field-monitoring system could correct up to second-order field perturbations in single-shot spiral imaging.

CONCLUSION

The integrated RF coil and field camera was capable of concurrent-field monitoring within a 7T head-only scanner and facilitated the subsequent correction of k-space trajectories during spiral imaging.

Control of a wireless sensor using the pulse sequence for prospective motion correction in brain MRI

PURPOSE

To synchronize and pass information between a wireless motion-tracking device and a pulse sequence and show how this can be used to implement customizable navigator interleaving schemes that are part of the pulse sequence design.

METHODS

The device tracks motion by sampling the voltages induced in 3 orthogonal pickup coils by the changing gradient fields. These coils were modified to also detect RF-transmit events using a 3D RF-detection circuit. The device could then detect and decode a set RF signatures while ignoring excitations in the parent pulse sequence. A set of unique RF signatures were then paired with a collection of navigators and used to trigger readouts on the wireless device synchronous to the pulse sequence execution. Navigator interleaving schemes were then demonstrated in 3D RF-spoiled gradient echo, T₁ -FLAIR (fluid-attenuated inversion recovery) PROPELLER (periodically rotated overlapping parallel lines with enhanced reconstruction), and T₂ -FLAIR PROPELLER pulse sequences.

RESULTS

Excitations in the parent pulse sequences were successfully rejected and the RF signatures successfully decoded. For the 3D gradient echo sequence, distortions were removed by interleaving flipped polarity navigators and taking the difference between consecutive readouts. The impact on scan duration was reduced by 54% by breaking up the navigators into smaller parts. Successful motion correction was performed using the PROPELLER pulse sequences in 3 Tesla and 1.5 Tesla MRI scanners without modifications to the device hardware or software.

CONCLUSION

The proposed RF signature-based triggering scheme enables complex interactions between the pulse sequence and a wireless device. Thus, enabling prospective motion correction that is repeatable, versatile, and minimally invasive with respect to hardware setup.

A single-chip integrated transceiver for high field NMR magnetometry

We present the design and performance of a broad-band single-chip integrated transceiver specifically conceived for nuclear magnetic resonance magnetometry. The single-chip transceiver is realized using a standard silicon complementary metal-oxide-semiconductor integrated circuit technology. A radio-frequency (RF) transmit amplifier, a transmit/receive switch, a low noise RF receive amplifier, a quadrature (IQ)-mixer, and two intermediate frequency amplifiers are integrated on a single silicon chip of 1.8 mm². The advantages and problematic aspects with respect to conventional discrete electronic approaches are discussed. We show the results of magnetic field measurements performed at 1.4 and 7.05 T, using solid and liquid samples having volumes from 40 μl down to 100 pl. Particular attention is devoted to the comparison of the experimentally measured magnetic field standard deviation with respect to the Cramer-Rao lower bound value. With a sample of distilled water (T₁ ≅ T₂ ≅ 3 s, T₂ ^*≅ 20 ms) having a volume of 40 μl, a standard deviation of 2.5 nT at 7.05 T (i.e., 0.5 ppb) in 1 s of averaging time is achieved, with a projected Cramer-Rao lower bond of 8 pT (i.e., 1.1 ppt).

Constrained optimization for position calibration of an NMR field camera

PURPOSE

Knowledge of the positions of field probes in an NMR field camera is necessary for monitoring the B₀ field. The typical method of estimating these positions is by switching the gradients with known strengths and calculating the positions using the phases of the FIDs. We investigated improving the accuracy of estimating the probe positions and analyzed the effect of inaccurate estimations on field monitoring.

METHODS

The field probe positions were estimated by 1) assuming ideal gradient fields, 2) using measured gradient fields (including nonlinearities), and 3) using measured gradient fields with relative position constraints. The fields measured with the NMR field camera were compared to fields acquired using a dual-echo gradient recalled echo B₀ mapping sequence. Comparisons were done for shim fields from second- to fourth-order shim terms.

RESULTS

The position estimation was the most accurate when relative position constraints were used in conjunction with measured (nonlinear) gradient fields. The effect of more accurate position estimates was seen when compared to fields measured using a B₀ mapping sequence (up to 10%-15% more accurate for some shim fields). The models acquired from the field camera are sensitive to noise due to the low number of spatial sample points.

CONCLUSION

Position estimation of field probes in an NMR camera can be improved using relative position constraints and nonlinear gradient fields. Magn Reson Med 80:380-390, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Decoupled dynamic magnetic field measurements improves diffusion-weighted magnetic resonance images

Field probes are miniature receiver coils with localized NMR-active samples inside. They are useful in monitoring magnetic field. This information can be used to improve magnetic resonance image quality. While field probes are coupled to each other marginally in most applications, this coupling can cause incorrect resonance frequency estimates and image reconstruction errors. Here, we propose a method to reduce the coupling between field probes in order to improve the accuracy of magnetic field estimation. An asymmetric sensitivity matrix describing the coupling between channels of field probes and NMR active droplets within field probes was empirically measured. Localized signal originating from each probe was derived from the product of the inverse of the sensitivity matrix and the coupled probe measurements. This method was used to estimate maps of dynamic magnetic fields in diffusion weighted MRI. The estimated fields using decoupled probe measurement led to images more robust to eddy currents caused by diffusion sensitivity gradients along different directions.

gr-MRI: A software package for magnetic resonance imaging using software defined radios

The goal of this work is to develop software that enables the rapid implementation of custom MRI spectrometers using commercially-available software defined radios (SDRs). The developed gr-MRI software package comprises a set of Python scripts, flowgraphs, and signal generation and recording blocks for GNU Radio, an open-source SDR software package that is widely used in communications research. gr-MRI implements basic event sequencing functionality, and tools for system calibrations, multi-radio synchronization, and MR signal processing and image reconstruction. It includes four pulse sequences: a single-pulse sequence to record free induction signals, a gradient-recalled echo imaging sequence, a spin echo imaging sequence, and an inversion recovery spin echo imaging sequence. The sequences were used to perform phantom imaging scans with a 0.5Tesla tabletop MRI scanner and two commercially-available SDRs. One SDR was used for RF excitation and reception, and the other for gradient pulse generation. The total SDR hardware cost was approximately $2000. The frequency of radio desynchronization events and the frequency with which the software recovered from those events was also measured, and the SDR's ability to generate frequency-swept RF waveforms was validated and compared to the scanner's commercial spectrometer. The spin echo images geometrically matched those acquired using the commercial spectrometer, with no unexpected distortions. Desynchronization events were more likely to occur at the very beginning of an imaging scan, but were nearly eliminated if the user invoked the sequence for a short period before beginning data recording. The SDR produced a 500kHz bandwidth frequency-swept pulse with high fidelity, while the commercial spectrometer produced a waveform with large frequency spike errors. In conclusion, the developed gr-MRI software can be used to develop high-fidelity, low-cost custom MRI spectrometers using commercially-available SDRs.

Concurrent recording of RF pulses and gradient fields - comprehensive field monitoring for MRI

Reconstruction of MRI data is based on exact knowledge of all magnetic field dynamics, since the interplay of RF and gradient pulses generates the signal, defines the contrast and forms the basis of resolution in spatial and spectral dimensions. Deviations caused by various sources, such as system imperfections, delays, eddy currents, drifts or externally induced fields, can therefore critically limit the accuracy of MRI examinations. This is true especially at ultra-high fields, because many error terms scale with the main field strength, and higher available SNR renders even smaller errors relevant. Higher baseline field also often requires higher acquisition bandwidths and faster signal encoding, increasing hardware demands and the severity of many types of hardware imperfection. To address field imperfections comprehensively, in this work we propose to expand the concept of magnetic field monitoring to also encompass the recording of RF fields. In this way, all dynamic magnetic fields relevant for spin evolution are covered, including low- to audio-frequency magnetic fields as produced by main magnets, gradients and shim systems, as well as RF pulses generated with single- and multiple-channel transmission systems. The proposed approach permits field measurements concurrently with actual MRI procedures on a strict common time base. The combined measurement is achieved with an array of miniaturized field probes that measure low- to audio-frequency fields via (19) F NMR and simultaneously pick up RF pulses in the MRI system's (1) H transmit band. Field recordings can form the basis of system calibration, retrospective correction of imaging data or closed-loop feedback correction, all of which hold potential to render MRI more robust and relax hardware requirements. The proposed approach is demonstrated for a range of imaging methods performed on a 7 T human MRI system, including accelerated multiple-channel RF pulses. Copyright © 2015 John Wiley & Sons, Ltd.

Continuous Magnetic Field Monitoring Using Rapid Re-Excitation of NMR Probe Sets

MRI relies on static and spatially varying dynamic magnetic fields of high accuracy. NMR field probes permit the direct observation of spatiotemporal field dynamics for diverse purposes such as data correction, field control, sequence validation, and hardware characterization. However, due to probe signal decay and dephasing existing field cameras are limited in terms of readout duration and the extent of k -space that can be covered. The present work aims to overcome these limitations by the transition to short-lived NMR probes and rapid re-excitation. The proposed approach uses probes with T 2 so short that thermal relaxation dominates signal decay even in the presence of strongest gradients. They are integrated with transmit, receive and sequencing electronics that permit high-rate re-excitation with optional probe alternation as well as complementary RF pulse recording. The system is demonstrated by monitoring of sample MRI sequences with long readouts and large gradient moments. It is compared with the conventional long-lived probe concept and characterized in terms of net sensitivity and sources of systematic error. Continuous k -space trajectory mapping is demonstrated and validated by trajectory-based image reconstruction.

3D high spectral and spatial resolution imaging of ex vivo mouse brain

PURPOSE

Widely used MRI methods show brain morphology both in vivo and ex vivo at very high resolution. Many of these methods (e.g., T2*-weighted imaging, phase-sensitive imaging, or susceptibility-weighted imaging) are sensitive to local magnetic susceptibility gradients produced by subtle variations in tissue composition. However, the spectral resolution of commonly used methods is limited to maintain reasonable run-time combined with very high spatial resolution. Here, the authors report on data acquisition at increased spectral resolution, with 3-dimensional high spectral and spatial resolution MRI, in order to analyze subtle variations in water proton resonance frequency and lineshape that reflect local anatomy. The resulting information compliments previous studies based on T2* and resonance frequency.

METHODS

The proton free induction decay was sampled at high resolution and Fourier transformed to produce a high-resolution water spectrum for each image voxel in a 3D volume. Data were acquired using a multigradient echo pulse sequence (i.e., echo-planar spectroscopic imaging) with a spatial resolution of 50 × 50 × 70 μm(3) and spectral resolution of 3.5 Hz. Data were analyzed in the spectral domain, and images were produced from the various Fourier components of the water resonance. This allowed precise measurement of local variations in water resonance frequency and lineshape, at the expense of significantly increased run time (16-24 h).

RESULTS

High contrast T2*-weighted images were produced from the peak of the water resonance (peak height image), revealing a high degree of anatomical detail, specifically in the hippocampus and cerebellum. In images produced from Fourier components of the water resonance at -7.0 Hz from the peak, the contrast between deep white matter tracts and the surrounding tissue is the reverse of the contrast in water peak height images. This indicates the presence of a shoulder in the water resonance that is not present at +7.0 Hz and may be specific to white matter anatomy. Moreover, a frequency shift of 6.76 ± 0.55 Hz was measured between the molecular and granular layers of the cerebellum. This shift is demonstrated in corresponding spectra; water peaks from voxels in the molecular and granular layers are consistently 2 bins apart (7.0 Hz, as dictated by the spectral resolution) from one another.

CONCLUSIONS

High spectral and spatial resolution MR imaging has the potential to accurately measure the changes in the water resonance in small voxels. This information can guide optimization and interpretation of more commonly used, more rapid imaging methods that depend on image contrast produced by local susceptibility gradients. In addition, with improved sampling methods, high spectral and spatial resolution data could be acquired in reasonable run times, and used for in vivo scans to increase sensitivity to variations in local susceptibility.

Single-shot imaging with higher-dimensional encoding using magnetic field monitoring and concomitant field correction

PURPOSE

PatLoc (Parallel Imaging Technique using Localized Gradients) accelerates imaging and introduces a resolution variation across the field-of-view. Higher-dimensional encoding employs more spatial encoding magnetic fields (SEMs) than the corresponding image dimensionality requires, e.g. by applying two quadratic and two linear spatial encoding magnetic fields to reconstruct a 2D image. Images acquired with higher-dimensional single-shot trajectories can exhibit strong artifacts and geometric distortions. In this work, the source of these artifacts is analyzed and a reliable correction strategy is derived.

METHODS

A dynamic field camera was built for encoding field calibration. Concomitant fields of linear and nonlinear spatial encoding magnetic fields were analyzed. A combined basis consisting of spherical harmonics and concomitant terms was proposed and used for encoding field calibration and image reconstruction.

RESULTS

A good agreement between the analytical solution for the concomitant fields and the magnetic field simulations of the custom-built PatLoc SEM coil was observed. Substantial image quality improvements were obtained using a dynamic field camera for encoding field calibration combined with the proposed combined basis.

CONCLUSION

The importance of trajectory calibration for single-shot higher-dimensional encoding is demonstrated using the combined basis including spherical harmonics and concomitant terms, which treats the concomitant fields as an integral part of the encoding.

A low-cost, mechanically simple apparatus for measuring eddy current-induced magnetic fields in MRI

The fidelity of gradient waveforms in MRI pulse sequences is essential to the acquisition of images and spectra with minimal distortion artefacts. Gradient waveforms can become nonideal when eddy currents are created in nearby conducting structures; however, the resultant magnetic fields can be characterised and compensated for by measuring the spatial and temporal field response following a gradient impulse. This can be accomplished using a grid of radiofrequency (RF) coils. The RF coils must adhere to strict performance requirements: they must achieve a high sensitivity and signal-to-noise ratio (SNR), have minimal susceptibility field gradients between the sample and surrounding material interfaces and be highly decoupled from each other. In this study, an apparatus is presented that accomplishes these tasks with a low-cost, mechanically simple solution. The coil system consists of six transmit/receive RF coils immersed in a high-molarity saline solution. The sensitivity and SNR following an excitation pulse are sufficiently high to allow accurate phase measurements during free-induction decays; the intrinsic susceptibility matching of the materials, because of the unique design of the coil system, results in sufficiently narrow spectral line widths (mean of 19 Hz), and adjacent RF coils are highly decoupled (mean S12 of -47 dB). The temporal and spatial distributions of eddy currents following a gradient pulse are measured to validate the efficacy of the design, and the resultant amplitudes and time constants required for zeroth- and first-order compensation are provided.

Fast higher-order MR image reconstruction using singular-vector separation

Medical resonance imaging (MRI) conventionally relies on spatially linear gradient fields for image encoding. However, in practice various sources of nonlinear fields can perturb the encoding process and give rise to artifacts unless they are suitably addressed at the reconstruction level. Accounting for field perturbations that are neither linear in space nor constant over time, i.e., dynamic higher-order fields, is particularly challenging. It was previously shown to be feasible with conjugate-gradient iteration. However, so far this approach has been relatively slow due to the need to carry out explicit matrix-vector multiplications in each cycle. In this work, it is proposed to accelerate higher-order reconstruction by expanding the encoding matrix such that fast Fourier transform can be employed for more efficient matrix-vector computation. The underlying principle is to represent the perturbing terms as sums of separable functions of space and time. Compact representations with this property are found by singular-vector analysis of the perturbing matrix. Guidelines for balancing the accuracy and speed of the resulting algorithm are derived by error propagation analysis. The proposed technique is demonstrated for the case of higher-order field perturbations due to eddy currents caused by diffusion weighting. In this example, image reconstruction was accelerated by two orders of magnitude.

Analysis and correction of background velocity offsets in phase-contrast flow measurements using magnetic field monitoring

The value of phase-contrast magnetic resonance imaging for quantifying tissue motion and blood flow has been long recognized. However, the sensitivity of the method to system imperfections can lead to inaccuracies limiting its clinical acceptance. A key source of error relates to eddy current-induced phase fluctuations, which can offset the measured object velocity significantly. A higher-order dynamic field camera was used to study the spatiotemporal evolution of background phases in cine phase-contrast measurements. It is demonstrated that eddy current-induced offsets in phase-difference data are present up to the second spatial order. Oscillatory temporal behaviors of offsets in the kHz range suggest mechanical resonances of the MR system to be non-negligible in phase-contrast imaging. By careful selection of the echo time, their impact can be significantly reduced. When applying field monitoring data for correcting eddy current and mechanically induced velocity offsets, errors decrease to less than 0.5% of the maximum velocity for various sequence settings proving the robustness of the correction approach. In vivo feasibility is demonstrated for aortic and pulmonary flow measurements in five healthy subjects. Using field monitoring data, mean error in stroke volume was reduced from 10% to below 3%.