Multidimensional RF pulse design with consideration of concomitant field effects.

PURPOSE: To develop a small-tip multidimensional RF pulse design procedure that incorporates linear time-invariant gradient imperfections and concomitant field effects. This could be particularly important for contemporary low-field MRI systems with high-performance gradients. THEORY AND METHODS: We developed an extension of the small-tip excitation k-space formalism, where concomitant fields were approximated as a Bloch-Siegert shift in the rotating frame. This was evaluated using realistic simulations of 2D selective excitation at various field strengths (0.2T, 0.55T, 1.5T, 3T, and 7T) with single and parallel transmit. Simulated excitation profiles from the original and extended k-space formalisms were compared. Experimental validations were performed at 0.55T with a single-channel transmit. RESULTS: The extended formalism provides improved 2D excitation profiles in all scenarios simulated, compared against the original formalism. The proposed method corrects the concomitant field effects on 2D selective excitations for B0 > 0.2T when the magnitude of the B0 is far larger than that of nonrotating concomitant fields. Simulation and phantom experiments at 0.55T match well for both original and proposed methods, with the proposed method providing sharper and more accurate excitation profiles at off-isocenter distances up to 15 cm. The impact of the proposed method is greatest in scenarios where concomitant fields are substantial, such as low field strengths and off-isocenter. CONCLUSION: Concomitant fields can be modeled as a Bloch-Siegert shift in the rotating frame during multidimensional RF pulse design, resulting in improved excitation profiles with sharp edges. This is important to consider for off-isocenter excitations and imaging at low field strengths with strong gradients.

On the correction of spiral trajectories on a preclinical MRI scanner with a high-performance gradient insert.

This study aimed to examine different trajectory correction methods for spiral imaging on a preclinical scanner with high-performance gradients with respect to image quality in a phantom and in vivo. The gold standard method of measuring the trajectories in a separate experiment is compared to an isotropic delay-correction, a correction using the gradient system transfer function (GSTF), and a combination of the two. Three different spiral trajectories, with 96, 16, and three interleaves, are considered. The best image quality is consistently achieved when determining the trajectory in a separate phantom measurement. However, especially for the spiral with 96 interleaves, the other correction methods lead to almost comparable results. Remaining imperfections in the corrected gradient waveforms and trajectories are attributed to asymmetrically occurring undulations in the actual, generated gradients, suggesting that the underlying assumption of linearity is violated. In conclusion, images of sufficient quality can be acquired on preclinical small-animal scanners using spiral k-space trajectories without the need to carry out separate trajectory measurements each time. Depending on the trajectory, a simple isotropic delay-correction or a GSTF-based correction can provide images of similar quality.

Trajectory correction enables free-running chemical shift encoded imaging for accurate cardiac proton-density fat fraction quantification at 3T.

BACKGROUND: Metabolic diseases can negatively alter epicardial fat accumulation and composition, which can be probed using quantitative cardiac chemical shift encoded (CSE) cardiovascular magnetic resonance (CMR) by mapping proton-density fat fraction (PDFF). To obtain motion-resolved high-resolution PDFF maps, we proposed a free-running cardiac CSE-CMR framework at 3T. To employ faster bipolar readout gradients, a correction for gradient imperfections was added using the gradient impulse response function (GIRF) and evaluated on intermediate images and PDFF quantification. METHODS: Ten minutes free-running cardiac 3D radial CSE-CMR acquisitions were compared in vitro and in vivo at 3T. Monopolar and bipolar readout gradient schemes provided 8 echoes (TE1/ΔTE = 1.16/1.96 ms) and 13 echoes (TE1/ΔTE = 1.12/1.07 ms), respectively. Bipolar-gradient free-running cardiac fat and water images and PDFF maps were reconstructed with or without GIRF correction. PDFF values were evaluated in silico, in vitro on a fat/water phantom, and in vivo in 10 healthy volunteers and 3 diabetic patients. RESULTS: In monopolar mode, fat-water swaps were demonstrated in silico and confirmed in vitro. Using bipolar readout gradients, PDFF quantification was reliable and accurate with GIRF correction with a mean bias of 0.03% in silico and 0.36% in vitro while it suffered from artifacts without correction, leading to a PDFF bias of 4.9% in vitro and swaps in vivo. Using bipolar readout gradients, in vivo PDFF of epicardial adipose tissue was significantly lower compared to subcutaneous fat (80.4 ± 7.1% vs 92.5 ± 4.3%, P < 0.0001). CONCLUSIONS: Aiming for an accurate PDFF quantification, high-resolution free-running cardiac CSE-MRI imaging proved to benefit from bipolar echoes with k-space trajectory correction at 3T. This free-breathing acquisition framework enables to investigate epicardial adipose tissue PDFF in metabolic diseases.

Fast measurement of the gradient system transfer function at 7 T.

PURPOSE: In this work, a new method to determine the gradient system transfer function (GSTF) with high frequency resolution and high SNR is presented, using fast and simple phantom measurements. The GSTF is an effective instrument for hardware characterization and calibration, which can be used to correct for gradient distortions, or enhance gradient fidelity. METHODS: The thin-slice approach for phantom-based measurements of the GSTF is expanded by adding excitations that are shifted after the application of the probing gradient, to capture long-lasting field fluctuations with high SNR. A physics-informed regularization procedure is implemented to derive high-quality transfer functions from a small number of measurements. The resulting GSTFs are evaluated by means of gradient time-course estimation and pre-emphasis of a trapezoidal test gradient on a 7T scanner. RESULTS: The GSTFs determined with the proposed method capture sharp mechanical resonances with a high level of detail. The measured trapezoidal gradient progressions are authentically reproduced by the GSTF estimations on all three axes. The GSTF-based pre-emphasis considerably improves the gradient fidelity in the plateau phase of the test gradient and almost completely eliminates lingering field oscillations. CONCLUSION: The presented approach allows fast and simple characterization of gradient field fluctuations caused by long-living eddy current and vibration effects, which become more pronounced at ultrahigh field strengths.

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.

Thermal variation in gradient response: measurement and modeling.

PURPOSE: Many aspects and imperfections of gradient dynamics in MRI have been successfully captured by linear time-invariant (LTI) models. Changes in gradient behavior due to heating, however, violate time invariance. The goal of this work is to study such changes at the level of transfer functions and model them by thermal extension of the LTI framework. METHODS: To study the impact of gradient heating on transfer functions, a clinical MR system was heated using a range of high-amplitude DC and AC waveforms, each followed by measuring transfer functions in rapid succession while the system cooled down. Simultaneously, gradient temperature was monitored with an array of temperature sensors positioned according to initial infrared recordings of the gradient tube. The relation between temperatures and transfer functions is cast into local and global linear models. The models are analysed in terms of self-consistency, conditioning, and prediction performance. RESULTS: Pronounced thermal effects are observed in the time resolved transfer functions, largely attributable to in-coil eddy currents and mechanical resonances. Thermal modeling is found to capture these effects well. The keys to good model performance are well-placed temperature sensors and suitable training data. CONCLUSION: Heating changes gradient response, violating time invariance. The utility of LTI modeling can nevertheless be recovered by a linear thermal extension, relying on temperature sensing and adequate one-time training.

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.

Non-Cartesian k-space trajectory calculation based on concurrent reading of the gradient amplifiers' output currents.

PURPOSE: Non-Cartesian imaging sequences involve sampling during rapid variation of the encoding field gradients. The quality of the reconstructed images often suffers from insufficient knowledge of the exact dynamics of the actual fields applied during sampling. METHODS: We propose determination of the accurate field dynamics by measuring the currents at the gradient amplifier outputs using the amplifiers' internal sensors concurrently with imaging. The actual dynamic field evolution is then determined by convolution with the measured current-to-field impulse response function of the gradient coil. Integration of the gradient field evolution allows derivation of the k-space trajectory for reconstruction. RESULTS: The current-based approach is investigated in spiral and ultrashort TE phantom imaging. In comparison with the model-based product reconstruction as well as a correction approach based on the conventional input waveform-to-field impulse response function, it provides slightly improved image quality. The improvement is ascribed to a better representation of eddy current and amplifier nonlinearity effects. CONCLUSION: Trajectory calculation based on measured amplifier output currents offers a robust, purely measurement-based alternative to conventional model-based approaches. The implementation can mitigate gradient amplifier imperfections with no or little additional hardware effort.

The temperature dependence of gradient system response characteristics.

PURPOSE: The gradient system transfer function (GSTF) characterizes the frequency transfer behavior of a dynamic gradient system and can be used to correct non-Cartesian k-space trajectories. This study analyzes the impact of the gradient coil temperature of a 3T scanner on the GSTF. METHODS: GSTF self- and B0 -cross-terms were acquired for a 3T Siemens scanner (Siemens Healthcare, Erlangen, Germany) using a phantom-based measurement technique. The GSTF terms were measured for various temperature states up to 45°C. The gradient coil temperatures were measured continuously utilizing 12 temperature sensors which are integrated by the vendor. Different modeling approaches were applied and compared. RESULTS: The self-terms depend linearly on temperature, whereas the B0 -cross-term does not. Effects induced by thermal variation are negligible for the phase response. The self-terms are best represented by a linear model including the three gradient coil sensors that showed the maximum temperature dependence for the three axes. The use of time derivatives of the temperature did not lead to an improvement of the model. The B0 -cross-terms can be modeled by a convolution model which considers coil-specific heat transportation. CONCLUSION: The temperature dependency of the GSTF was analyzed for a 3T Siemens scanner. The self- and B0 -cross-terms can be modeled using a linear and convolution modeling approach based on the three main temperature sensor elements.

Time optimal control-based RF pulse design under gradient imperfections.

PURPOSE: This study incorporates a gradient system imperfection model into an optimal control framework for radio frequency (RF) pulse design. THEORY AND METHODS: The joint design of minimum-time RF and slice selective gradient shapes is posed as an optimal control problem. Hardware limitations such as maximal amplitudes for RF and slice selective gradient or its slew rate are included as hard constraints to assure practical applicability of the optimized waveforms. In order to guarantee the performance of the optimized waveform with possible gradient system disturbances such as limited system bandwidth and eddy currents, a measured gradient impulse response function (GIRF) for a specific system is integrated into the optimization. RESULTS: The method generates optimized RF and pre-distorted slice selective gradient shapes for refocusing that are able to fully compensate the modeled imperfections of the gradient system under investigation. The results nearly regenerate the optimal results of an idealized gradient system. The numerical Bloch simulations are validated by phantom and in-vivo experiments on 2 3T scanners. CONCLUSIONS: The presented design approach demonstrates the successful correction of gradient system imperfections within an optimal control framework for RF pulse design.

Rapid acquisition of the 3D MRI gradient impulse response function using a simple phantom measurement.

PURPOSE: To provide a simple tool for rapid measurement of the 3D gradient modulation transfer function (GMTF) of clinical MRI systems using a phantom. Knowledge of the transfer function is useful for gradient chain characterization, system calibration, and improvement of image reconstruction results. METHODS: Starting from the well-established thin slice method used for phantom-based measurement of the 1D GMTF, we add phase encoding to partition the thin slices into voxels that act as localized field probes. From the signal phase evolution measured at the 3D voxel positions, the GMTF can be derived for cross and higher order spatial terms represented by spherical harmonics up to 3rd order. RESULTS: Using spherical phantoms, 16 GMTFs representing all terms up to 3rd order harmonics can be determined in a scan time of <2 min. A large voxel volume of >1 mL yields high SNR, enabling signal acquisition using the system's body coil. The method is applied for improving system calibration and for characterizing the effect of additional hardware in the bore. CONCLUSION: The presented method seems well-suited for rapid measurement of the GMTF of a clinical system, as it delivers high-quality results in a short scan time.

Gradient waveform pre-emphasis based on the gradient system transfer function.

PURPOSE: The gradient system transfer function (GSTF) has been used to describe the distorted k-space trajectory for image reconstruction. The purpose of this work was to use the GSTF to determine the pre-emphasis for an undistorted gradient output and intended k-space trajectory. METHODS: The GSTF of the MR system was determined using only standard MR hardware without special equipment such as field probes or a field camera. The GSTF was used for trajectory prediction in image reconstruction and for a gradient waveform pre-emphasis. As test sequences, a gradient-echo sequence with phase-encoding gradient modulation and a gradient-echo sequence with a spiral read-out trajectory were implemented and subsequently applied on a structural phantom and in vivo head measurements. RESULTS: Image artifacts were successfully suppressed by applying the GSTF-based pre-emphasis. Equivalent results are achieved with images acquired using GSTF-based post-correction of the trajectory as a part of image reconstruction. In contrast, the pre-emphasis approach allows reconstruction using the initially intended trajectory. CONCLUSION: The artifact suppression shown for two sequences demonstrates that the GSTF can serve for a novel pre-emphasis. A pre-emphasis based on the GSTF information can be applied to any arbitrary sequence type.

VERSE-guided parallel RF excitations using dynamic field correction.

In parallel RF pulse design, peak RF magnitudes and specific absorption rate levels are critical concerns in the hardware and safety limits. The variable rate selective excitation (VERSE) method is an efficient technique to limit the peak RF power by applying a local-only RF and gradient waveform reshaping while retaining the on-resonance profile. The accuracy of the excitation performed by the VERSEd RF and gradient waveforms strictly depends on the performance of the employed hardware. Any deviation from the nominal gradient fields as a result of frequency dependent system imperfections violates the VERSE condition similarly to off-resonance effects, leading to significant excitation errors and the RF pulse not converging to the targeted peak RF power. Moreover, for iterative VERSE-guided RF pulse design (i.e. reVERSE), the k-space trajectory actually changes at every iteration, which is assumed to be constant. In this work, we show both theoretically and experimentally the effect of gradient system imperfections on iteratively VERSEd parallel RF excitations. In order to improve the excitation accuracy besides limiting the RF power below certain thresholds, we propose to integrate gradient field monitoring or gradient impulse response function (GIRF) estimations of the actual gradient fields into the RF pulse design problem. A third-order dynamic field camera comprising a set of NMR field sensors and GIRFs was used to measure or estimate the actual gradient waveforms that are involved in the VERSE algorithm respectively. The deviating and variable k-space is counteracted at each iteration of the VERSE-guided iterative RF pulse design. The proposed approaches are demonstrated for accelerated multiple-channel spatially selective RF pulses, and highly improved experimental performance was achieved at both 3 T and 7 T.

Real-time distortion correction of spiral and echo planar images using the gradient system impulse response function.

PURPOSE: MRI-guided interventions demand high frame rate imaging, making fast imaging techniques such as spiral imaging and echo planar imaging (EPI) appealing. In this study, we implemented a real-time distortion correction framework to enable the use of these fast acquisitions for interventional MRI. METHODS: Distortions caused by gradient waveform inaccuracies were corrected using the gradient impulse response function (GIRF), which was measured by standard equipment and saved as a calibration file on the host computer. This file was used at runtime to calculate the predicted k-space trajectories for image reconstruction. Additionally, the off-resonance reconstruction frequency was modified in real time to interactively deblur spiral images. RESULTS: Real-time distortion correction for arbitrary image orientations was achieved in phantoms and healthy human volunteers. The GIRF-predicted k-space trajectories matched measured k-space trajectories closely for spiral imaging. Spiral and EPI image distortion was visibly improved using the GIRF-predicted trajectories. The GIRF calibration file showed no systematic drift in 4 months and was demonstrated to correct distortions after 30 min of continuous scanning despite gradient heating. Interactive off-resonance reconstruction was used to sharpen anatomical boundaries during continuous imaging. CONCLUSIONS: This real-time distortion correction framework will enable the use of these high frame rate imaging methods for MRI-guided interventions. Magn Reson Med 75:2278-2285, 2016. © 2015 Wiley Periodicals, Inc.

Field camera versus phantom-based measurement of the gradient system transfer function (GSTF) with dwell time compensation.

PURPOSE: The gradient system transfer function (GSTF) can be used to describe the dynamic gradient system and applied for trajectory correction in non-Cartesian MRI. This study compares the field camera and the phantom-based methods to measure the GSTF and implements a compensation for the difference in measurement dwell time. METHODS: The self-term GSTFs of a MR system were determined with two approaches: 1) using a dynamic field camera and 2) using a spherical phantom-based measurement with standard MR hardware. The phantom-based GSTF was convolved with a box function to compensate for the dwell time dependence of the measurement. The field camera and phantom-based GSTFs were used for trajectory prediction during retrospective image reconstruction of 3D wave-CAIPI phantom images. RESULTS: Differences in the GSTF magnitude response were observed between the two measurement methods. For the wave-CAIPI sequence, this led to deviations in the GSTF predicted trajectories of 4% compared to measured trajectories, and residual distortions in the reconstructed phantom images generated with the phantom-based GSTF. Following dwell-time compensation, deviations in the GSTF magnitudes, GSTF-predicted trajectories, and resulting image artifacts were eliminated (< 0.5% deviation in trajectories). CONCLUSION: With dwell time compensation, both the field camera and the phantom-based GSTF self-terms show negligible deviations and lead to strong artifact reduction when they are used for trajectory correction in image reconstruction.