Fast conjugate phase image reconstruction based on a Chebyshev approximation to correct for B0 field inhomogeneity and concomitant gradients

Low-field MRI: A report on the 2022 ISMRM workshop

In March 2022, the first ISMRM Workshop on Low-Field MRI was held virtually. The goals of this workshop were to discuss recent low field MRI technology including hardware and software developments, novel methodology, new contrast mechanisms, as well as the clinical translation and dissemination of these systems. The virtual Workshop was attended by 368 registrants from 24 countries, and included 34 invited talks, 100 abstract presentations, 2 panel discussions, and 2 live scanner demonstrations. Here, we report on the scientific content of the Workshop and identify the key themes that emerged. The subject matter of the Workshop reflected the ongoing developments of low-field MRI as an accessible imaging modality that may expand the usage of MRI through cost reduction, portability, and ease of installation. Many talks in this Workshop addressed the use of computational power, efficient acquisitions, and contemporary hardware to overcome the SNR limitations associated with low field strength. Participants discussed the selection of appropriate clinical applications that leverage the unique capabilities of low-field MRI within traditional radiology practices, other point-of-care settings, and the broader community. The notion of "image quality" versus "information content" was also discussed, as images from low-field portable systems that are purpose-built for clinical decision-making may not replicate the current standard of clinical imaging. Speakers also described technical challenges and infrastructure challenges related to portability and widespread dissemination, and speculated about future directions for the field to improve the technology and establish clinical value.

Concomitant magnetic-field compensation for 2D spiral-ring turbo spin-echo imaging at 0.55T and 1.5T

PURPOSE

To develop 2D turbo spin-echo (TSE) imaging using annular spiral rings (abbreviated "SPRING-RIO TSE") with compensation of concomitant gradient fields and B0 inhomogeneity at both 0.55T and 1.5T for fast T2 -weighted imaging.

METHODS

Strategies of gradient waveform modifications were implemented in SPRING-RIO TSE for compensation of self-squared concomitant gradient terms at the TE and across echo spacings, along with reconstruction-based corrections to simultaneously compensate for the residual concomitant gradient and B0 field induced phase accruals along the readout. The signal pathway disturbance caused by time-varying and spatially dependent concomitant fields was simulated, and echo-to-echo phase variations before and after sequence-based compensation were compared. Images from SPRING-RIO TSE with no compensation, with compensation, and Cartesian TSE were also compared via phantom and in vivo acquisitions.

RESULTS

Simulation showed how concomitant fields affected the signal evolution with no compensation, and both simulation and phantom studies demonstrated the performance of the proposed sequence modifications, as well as the readout off-resonance corrections. Volunteer data showed that after full correction, the SPRING-RIO TSE sequence achieved high image quality with improved SNR efficiency (15%-20% increase), and reduced RF SAR (˜50% reduction), compared to the standard Cartesian TSE, presenting potential benefits, especially in regaining SNR at low-field (0.55T).

CONCLUSION

Implementation of SPRING-RIO TSE with concomitant field compensation was tested at 0.55T and 1.5T. The compensation principles can be extended to correct for other trajectory types that are time-varying along the echo train and temporally asymmetric in TSE-based imaging.

Concomitant field compensation of spiral turbo spin-echo at 0.55 T

OBJECTIVE

Diagnostic-quality neuroimaging methods are vital for widespread clinical adoption of low field MRI. Spiral imaging is an efficient acquisition method that can mitigate the reduced signal-to-noise ratio at lower field strengths. As concomitant field artifacts are worse at lower field, we propose a generalizable quadratic gradient-field nulling as an echo-to-echo compensation and apply it to spiral TSE at 0.55 T.

MATERIALS AND METHODS

A spiral in-out TSE acquisition was developed with a compensation for concomitant field variation between spiral interleaves, by adding bipolar gradients around each readout to minimize phase differences at each refocusing pulse. Simulations were performed to characterize concomitant field compensation approaches. We demonstrate our proposed compensation method in phantoms and (n = 8) healthy volunteers at 0.55 T.

RESULTS

Spiral read-outs with integrated spoiling demonstrated strong concomitant field artifacts but were mitigated using the echo-to-echo compensation. Simulations predicted a decrease of concomitant field phase RMSE between echoes of 42% using the proposed compensation. Spiral TSE improved SNR by 17.2 ± 2.3% compared to reference Cartesian acquisition.

DISCUSSION

We demonstrated a generalizable approach to mitigate concomitant field artifacts for spiral TSE acquisitions via the addition of quadratic-nulling gradients, which can potentially improve neuroimaging at low-field through increased acquisition efficiency.

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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SPRING-RIO TSE: 2D T2 -Weighted Turbo Spin-Echo brain imaging using SPiral RINGs with retraced in/out trajectories

PURPOSE

To develop a new approach to 2D turbo spin -echo (TSE) imaging using annular spiral rings with a retraced in/out trajectory, dubbed "SPRING-RIO TSE", for fast T₂ -weighted brain imaging at 3T.

METHODS

A long spiral trajectory was split into annular segmentations that were then incorporated into a 2D TSE acquisition module to fully exploit the sampling efficiency of spiral rings. A retraced in/out trajectory strategy coupled with spiral-ring TSE was introduced to increase SNR, mitigate T₂ -decay induced artifacts, and self-correct moderate off-resonance while maintaining the target TE and causing no scan time penalty. Model-based k-space estimation and semiautomatic off-resonance correction algorithms were implemented to minimize effects of k-space trajectory infidelity and B₀ inhomogeneity, respectively. The resulting SPRING-RIO TSE method was compared to the original spiral-ring (abbreviated "SPRING") TSE and Cartesian TSE using simulations, and phantom and in vivo acquisitions.

RESULTS

Simulation and phantom studies demonstrated the performance of the proposed SPRING-RIO TSE pulses sequence, as well as that of trajectory correction and off-resonance correction. Volunteer data showed that the proposed method achieves high-quality 2D T₂ -weighted brain imaging with a higher scan efficiency (0:45 min/14 slices versus 1:31 min/14 slices), improved image contrast, and reduced specific absorption rate compared to conventional 2D Cartesian TSE.

CONCLUSION

2D T₂ -weighted brain imaging using spiral-ring TSE was implemented and tested, providing several potential advantages over conventional 2D Cartesian TSE imaging.

Velocity vector reconstruction for real-time phase-contrast MRI with radial Maxwell correction

PURPOSE

To develop an auto-calibrated image reconstruction for highly accelerated multi-directional phase-contrast (PC) MRI that compensates for (1) reconstruction instabilities occurring for phase differences near ± π and (2) phase errors by concomitant magnetic fields that differ for individual radial spokes.

THEORY AND METHODS

A model-based image reconstruction for real-time PC MRI based on nonlinear inversion is extended to multi-directional flow by exploiting multiple flow-encodings for the estimation of velocity vectors. An initial smoothing constraint during iterative optimization is introduced to resolve the ambiguity of the solution space by penalizing phase wraps. Maxwell terms are considered as part of the signal model on a line-by-line basis to address phase errors by concomitant magnetic fields. The reconstruction methods are evaluated using simulated data and cross-sectional imaging of a rotating-disc, as well as in vivo for the aortic arch and cervical spinal canal at 3T.

RESULTS

Real-time three-directional velocity mapping in the aortic arch is achieved at 1.8 × 1.8 × 6 mm³ spatial and 60 ms temporal resolution. Artificial phase wraps are avoided in all cases using the smoothness constraint. Inter-spoke differences of concomitant magnetic fields are effectively compensated for by the model-based image reconstruction with integrated radial Maxwell correction.

CONCLUSION

Velocity vector reconstructions based on nonlinear inversion allow for high degrees of radial data undersampling paving the way for multi-directional PC MRI in real time. Whether a spoke-wise treatment of Maxwell terms is required or a computationally cheaper frame-wise approach depends on the individual application.

Real-time dynamic vocal tract imaging using an accelerated spiral GRE sequence and low rank plus sparse reconstruction

PURPOSE

To develop a real-time dynamic vocal tract imaging method using an accelerated spiral GRE sequence and low rank plus sparse reconstruction.

METHODS

Spiral k-space sampling has high data acquisition efficiency and thus is suited for real-time dynamic imaging; further acceleration can be achieved by undersampling k-space and using a model-based reconstruction. Low rank plus sparse reconstruction is a promising method with fast computation and increased robustness to global signal changes and bulk motion, as the images are decomposed into low rank and sparse terms representing different dynamic components. However, the combination with spiral scanning has not been well studied. In this study an accelerated spiral GRE sequence was developed with an optimized low rank plus sparse reconstruction and compared with L1-SPIRiT and XD-GRASP methods. The off-resonance was also corrected using a Chebyshev approximation method to reduce blurring on a frame-by-frame basis.

RESULTS

The low rank plus sparse reconstruction method is sensitive to the weights of the low rank and sparse terms. The optimized reconstruction showed advantages over other methods with reduced aliasing and improved SNR. With the proposed method, spatial resolution of 1.3*1.3 mm² with 150 mm field-of-view (FOV) and temporal resolution of 30 frames-per-second (fps) was achieved with good image quality. Blurring was reduced using the Chebyshev approximation method.

CONCLUSION

This work studies low rank plus sparse reconstruction using the spiral trajectory and demonstrates a new method for dynamic vocal tract imaging which can benefit studies of speech disorders.

Correcting image blur in spiral, retraced in/out (RIO) acquisitions using a maximized energy objective

PURPOSE

Images acquired with spiral k-space trajectories can suffer from off-resonance image blur. Previous work showed that averaging 2 images acquired with a retraced, in/out (RIO) trajectory self-corrects image blur so long as off-resonant spins accrue less than 1 half-cycle of relative phase over the readout. Practical scenarios frequently exceed this threshold. Here, we derive and characterize a more-robust off-resonance image blur correction method for RIO acquisitions.

METHODS

Phantom and human volunteer data were acquired using a RIO trajectory with readout durations ranging from 4 to 60 ms. The resulting images were deblurred using 3 candidate methods: conventional linear correction of the component images; semiautomatic deblurring of the component images using an established minimized phase objective function; and semiautomatic deblurring of the average of the component images using a maximized energy objective function, derived below. Deblurring errors were estimated relative to images acquired with 4 ms readouts.

RESULTS

All 3 methods converged to similar solutions in cases where less than 2 and 4 cycles of phase accrued over the readout in in vivo and phantom images, respectively (<13 ms readout at 3T). Above this threshold, the linear and minimized phase methods introduced several errors. The maximized energy function provided accurate deblurring so long as less than 6 and 10 cycles of phase accrued over the readout in in vivo and phantom images, respectively (<34 ms readout at 3T).

CONCLUSION

The maximized energy objective function can accurately deblur RIO acquisitions over a wide spectrum of off resonance frequencies.

High resolution in-vivo DT-CMR using an interleaved variable density spiral STEAM sequence

PURPOSE

Diffusion tensor cardiovascular magnetic resonance (DT-CMR) has a limited spatial resolution. The purpose of this study was to demonstrate high-resolution DT-CMR using a segmented variable density spiral sequence with correction for motion, off-resonance, and T2*-related blurring.

METHODS

A single-shot stimulated echo acquisition mode (STEAM) echo-planar-imaging (EPI) DT-CMR sequence at 2.8 × 2.8 × 8 mm³ and 1.8 × 1.8 × 8 mm³ was compared to a single-shot spiral at 2.8 × 2.8 × 8 mm³ and an interleaved spiral sequence at 1.8 × 1.8 × 8 mm³ resolution in 10 healthy volunteers at peak systole and diastasis. Motion-induced phase was corrected using the densely sampled central k-space data of the spirals. STEAM field maps and T2* measures were obtained using a pair of stimulated echoes each with a double spiral readout, the first used to correct the motion-induced phase of the second.

RESULTS

The high-resolution spiral sequence produced similar DT-CMR results and quality measures to the standard-resolution sequence in both cardiac phases. Residual differences in fractional anisotropy and helix angle gradient between the resolutions could be attributed to spatial resolution and/or signal-to-noise ratio. Data quality increased after both motion-induced phase correction and off-resonance correction, and sharpness increased after T2* correction. The high-resolution EPI sequence failed to provide sufficient data quality for DT-CMR reconstruction.

CONCLUSION

In this study, an in vivo DT-CMR acquisition at 1.8 × 1.8 mm² in-plane resolution was demonstrated using a segmented spiral STEAM sequence. Motion-induced phase and off-resonance corrections are essential for high-resolution spiral DT-CMR. Segmented variable density spiral STEAM was found to be the optimal method for acquiring high-resolution DT-CMR data.

A spiral-based volumetric acquisition for MR temperature imaging

PURPOSE

To develop a rapid pulse sequence for volumetric MR thermometry.

METHODS

Simulations were carried out to assess temperature deviation, focal spot distortion/blurring, and focal spot shift across a range of readout durations and maximum temperatures for Cartesian, spiral-out, and retraced spiral-in/out (RIO) trajectories. The RIO trajectory was applied for stack-of-spirals 3D imaging on a real-time imaging platform and preliminary evaluation was carried out compared to a standard 2D sequence in vivo using a swine brain model, comparing maximum and mean temperatures measured between the two methods, as well as the temporal standard deviation measured by the two methods.

RESULTS

In simulations, low-bandwidth Cartesian trajectories showed substantial shift of the focal spot, whereas both spiral trajectories showed no shift while maintaining focal spot geometry. In vivo, the 3D sequence achieved real-time 4D monitoring of thermometry, with an update time of 2.9-3.3 s.

CONCLUSION

Spiral imaging, and RIO imaging in particular, is an effective way to speed up volumetric MR thermometry. Magn Reson Med 79:3122-3127, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Assessment of velopharyngeal function with dual-planar high-resolution real-time spiral dynamic MRI

PURPOSE

To develop a real-time dynamic MRI method for comprehensive evaluation of velum movement during speech.

METHODS

Dynamic MRI has been used to study velopharyngeal insufficiency (VPI) by imaging the movement of the velum during speech, because it can provide good anatomic details with no exposed radiation. To be able to comprehensively evaluate dynamic velum movement, a real-time spiral non-balanced SSFP sequence was developed with simultaneous dual-planar coverage and improved spatial and temporal resolution using a combination of parallel imaging and spatial and temporal compressed sensing to achieve 6 × acceleration. New off-resonance correction and post-processing methods were also developed to reduce blurring and slice crosstalk.

RESULTS

The method demonstrated good image quality for visualizing dynamic velum movement with reduced blurring and improved image homogeneity. Spatial resolution of 1.2*1.2 mm² with 150 mm FOV and temporal resolution of 20 frames-per-second with simultaneous dual-planar coverage was achieved.

CONCLUSIONS

This work describes a new technique for studying speech disorders using dual-planar accelerated spiral dynamic MRI.

Adenosine stress cardiovascular magnetic resonance with variable-density spiral pulse sequences accurately detects coronary artery disease: initial clinical evaluation

BACKGROUND

Adenosine stress cardiovascular magnetic resonance perfusion imaging can be limited by motion-induced dark-rim artifacts, which may be mistaken for true perfusion abnormalities. A high-resolution variable-density spiral pulse sequence with a novel density compensation strategy has been shown to reduce dark-rim artifacts in first-pass perfusion imaging. We aimed to assess the clinical performance of adenosine stress cardiovascular magnetic resonance using this new perfusion sequence to detect obstructive coronary artery disease.

METHODS AND RESULTS

Cardiovascular magnetic resonance perfusion imaging was performed during adenosine stress (140 μg/kg per minute) and at rest on a Siemens 1.5-T Avanto scanner in 41 subjects with chest pain scheduled for coronary angiography. Perfusion images were acquired during injection of 0.1 mmol/kg Gadolinium-diethylenetriaminepentacetate at 3 short-axis locations using a saturation recovery interleaved variable-density spiral pulse sequence. Significant stenosis was defined as >50% by quantitative coronary angiography. Two blinded reviewers evaluated the perfusion images for the presence of adenosine-induced perfusion abnormalities and assessed image quality using a 5-point scale (1 [poor] to 5 [excellent]). The prevalence of obstructive coronary artery disease by quantitative coronary angiography was 68%. The average sensitivity, specificity, and accuracy were 89%, 85%, and 88%, respectively, with a positive predictive value and negative predictive value of 93% and 79%, respectively. The average image quality score was 4.4±0.7, with only 1 study with more than mild dark-rim artifacts. There was good inter-reader reliability with a κ statistic of 0.67.

CONCLUSIONS

Spiral adenosine stress cardiovascular magnetic resonance results in high diagnostic accuracy for the detection of obstructive coronary artery disease with excellent image quality and minimal dark-rim artifacts.

Noncontrast peripheral MRA with spiral echo train imaging

PURPOSE

To develop a spin echo train sequence with spiral readout gradients with improved artery-vein contrast for noncontrast angiography.

THEORY

Venous T2 becomes shorter as the echo spacing is increased in echo train sequences, improving contrast. Spiral acquisitions, due to their data collection efficiency, facilitate long echo spacings without increasing scan times.

METHODS

Bloch equation simulations were performed to determine optimal sequence parameters, and the sequence was applied in five volunteers. In two volunteers, the sequence was performed with a range of echo times and echo spacings to compare with the theoretical contrast behavior. A Cartesian version of the sequence was used to compare contrast appearance with the spiral sequence. Additionally, spiral parallel imaging was optionally used to improve image resolution.

RESULTS

In vivo, artery-vein contrast properties followed the general shape predicted by simulations, and good results were obtained in all stations. Compared with a Cartesian implementation, the spiral sequence had superior artery-vein contrast, better spatial resolution (1.2 mm(2) versus 1.5 mm(2) ), and was acquired in less time (1.4 min versus 7.5 min).

CONCLUSION

The spiral spin echo train sequence can be used for flow-independent angiography to generate three-dimensional angiograms of the periphery quickly and without the use of contrast agents.

A simple acquisition strategy to avoid off-resonance blurring in spiral imaging with redundant spiral-in/out k-space trajectories

PURPOSE

The major hurdle to widespread adoption of spiral trajectories has been their poor off-resonance performance. Here we present a self-correcting spiral k-space trajectory that avoids much of the well-known spiral blurring during data acquisition.

THEORY AND METHODS

In comparison with a traditional spiral-out trajectory, the spiral-in/out trajectory has improved off-resonance performance. By combining two spiral-in/out acquisitions, one rotated 180° in k-space compared with the other, multishot spiral-in/out artifacts are eliminated. A phantom was scanned with the center frequency manually tuned 20, 40, 80, and 160 Hz off-resonance with both a spiral-out gradient echo sequence and the redundant spiral-in/out sequence. The phantom was also imaged in an oblique orientation in order to demonstrate improved concomitant gradient field performance of the sequence. Additionally, the trajectory was incorporated into a spiral turbo spin echo sequence for brain imaging.

RESULTS

Phantom studies with manually tuned off-resonance agree well with theoretical calculations, showing that moderate off-resonance is well-corrected by this acquisition scheme. Blur due to concomitant fields is reduced, and good results are obtained in vivo.

CONCLUSION

The redundant spiral-in/out trajectory results in less image blur for a given readout length than a traditional spiral-out scan, reducing the need for complex off-resonance correction algorithms.

High-resolution quantitative sodium imaging at 9.4 Tesla

PURPOSE

Investigation of the feasibility to perform high-resolution quantitative sodium imaging at 9.4 Tesla (T).

METHODS

A proton patch antenna was combined with a sodium birdcage coil to provide a proton signal without compromising the efficiency of the X-nucleus coil. Sodium density weighted images with a nominal resolution of 1 × 1 × 5 mm(3) were acquired within 30 min with an ultrashort echo time sequence. The methods used for signal calibration as well as for B0, B1, and off-resonance correction were verified on a phantom and five healthy volunteers.

RESULTS

An actual voxel volume of roughly 40 μL could be achieved at 9.4T, while maintaining an acceptable signal-to-noise ratio (8 for brain tissue and 35 for cerebrospinal fluid). The measured mean sodium concentrations for gray and white matter were 36 ± 2 and 31 ± 1 mmol/L of wet tissue, which are comparable to values previously reported in the literature.

CONCLUSION

The reduction of partial volume effects is essential for accurate measurement of the sodium concentration in the human brain. Ultrahigh field imaging is a viable tool to achieve this goal due to its increased sensitivity.

Nonrigid autofocus motion correction for coronary MR angiography with a 3D cones trajectory

PURPOSE

To implement a nonrigid autofocus motion correction technique to improve respiratory motion correction of free-breathing whole-heart coronary magnetic resonance angiography acquisitions using an image-navigated 3D cones sequence.

METHODS

2D image navigators acquired every heartbeat are used to measure superior-inferior, anterior-posterior, and right-left translation of the heart during a free-breathing coronary magnetic resonance angiography scan using a 3D cones readout trajectory. Various tidal respiratory motion patterns are modeled by independently scaling the three measured displacement trajectories. These scaled motion trajectories are used for 3D translational compensation of the acquired data, and a bank of motion-compensated images is reconstructed. From this bank, a gradient entropy focusing metric is used to generate a nonrigid motion-corrected image on a pixel-by-pixel basis. The performance of the autofocus motion correction technique is compared with rigid-body translational correction and no correction in phantom, volunteer, and patient studies.

RESULTS

Nonrigid autofocus motion correction yields improved image quality compared to rigid-body-corrected images and uncorrected images. Quantitative vessel sharpness measurements indicate superiority of the proposed technique in 14 out of 15 coronary segments from three patient and two volunteer studies.

CONCLUSION

The proposed technique corrects nonrigid motion artifacts in free-breathing 3D cones acquisitions, improving image quality compared to rigid-body motion correction.

Three-dimensional late gadolinium-enhanced MR imaging of the left atrium: a comparison of spiral versus Cartesian k-space trajectories

PURPOSE

To investigate the feasibility of high-resolution late gadolinium enhancement (LGE) imaging using a three-dimensional (3D) stack of spirals k-space trajectory for the detection of left atrial (LA) ablation lesions. LGE imaging inherently suffers from low SNR, so that improvements in spatial resolution and imaging time are challenging. The spiral trajectory offers greater acquisition efficiency, and this is used for increased spatial resolution.

MATERIALS AND METHODS

Nine healthy subjects and 10 pre/post pulmonary vein isolation patients underwent an MRI examination. A Cartesian 3D inversion-recovery gradient-echo sequence was performed followed by a 3D inversion-recovery gradient-echo with a spiral trajectory. Image quality, fat suppression and sharpness were graded by expert cardiologists.

RESULTS

No statistical significance was determined for SNR or image quality between the Cartesian and spiral images; however, fat suppression was significantly improved with the spiral approach (P = 0.002). The enhancement in the Cartesian scan was found to have significantly higher CNR (P = 0.02).

CONCLUSION

The feasibility of spiral LGE in the left atrium has been demonstrated. Similar image quality and sharpness were observed with both acquisitions. This spiral sequence has sub-millimeter spatial resolution improved fat suppression and maintains a comparable level of SNR compared with the Cartesian scan.

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.

The effect of concomitant gradient fields on diffusion tensor imaging

Concomitant gradient fields are transverse magnetic field components that are necessarily present to satisfy Maxwell's equations when magnetic field gradients are utilized in magnetic resonance imaging. They can have deleterious effects that are more prominent at lower static fields and/or higher gradient strengths. In diffusion tensor imaging schemes that employ large gradients that are not symmetric about a refocusing radiofrequency pulse (unlike Stejskal-Tanner, which is symmetric), concomitant fields may cause phase accrual that could corrupt the diffusion measurement. Theory predicting the error from this dephasing is described and experimentally validated for both Reese twice-refocused and split gradient single spin-echo diffusion gradient schemes. Bias in apparent diffusion coefficient values was experimentally found to worsen with distance from isocenter and with increasing duration of gradient asymmetry in both a phantom and in the brain. The amount of error from concomitant gradient fields depends on many variables, including the diffusion gradient pattern, pulse sequence timing, maximum effective gradient amplitude, static magnetic field strength, voxel size, slice distance from isocenter, and partial Fourier fraction. A prospective correction scheme that can reduce concomitant gradient errors is proposed and verified for diffusion imaging.

Application of the fractional Fourier transform to image reconstruction in MRI

The classic paradigm for MRI requires a homogeneous B(0) field in combination with linear encoding gradients. Distortions are produced when the B(0) is not homogeneous, and several postprocessing techniques have been developed to correct them. Field homogeneity is difficult to achieve, particularly for short-bore magnets and higher B(0) fields. Nonlinear magnetic components can also arise from concomitant fields, particularly in low-field imaging, or intentionally used for nonlinear encoding. In any of these situations, the second-order component is key, because it constitutes the first step to approximate higher-order fields. We propose to use the fractional Fourier transform for analyzing and reconstructing the object's magnetization under the presence of quadratic fields. The fractional fourier transform provides a precise theoretical framework for this. We show how it can be used for reconstruction and for gaining a better understanding of the quadratic field-induced distortions, including examples of reconstruction for simulated and in vivo data. The obtained images have improved quality compared with standard Fourier reconstructions. The fractional fourier transform opens a new paradigm for understanding the MR signal generated by an object under a quadratic main field or nonlinear encoding.

Fast concomitant gradient field and field inhomogeneity correction for spiral cardiac imaging

Non-Cartesian imaging provides many advantages in terms of flexibility, functionality, and speed. However, a major drawback to these imaging methods is off-resonance distortion artifacts. These artifacts manifest as blurring in spiral imaging. Common techniques that remove the off-resonance field inhomogeneity distortion effects are not sufficient, because the high order concomitant gradient fields are nontrivial for common imaging conditions, such as imaging 5 cm off isocenter in an 1.5 T scanner. Previous correction algorithms are either slow or do not take into account the known effects of concomitant gradient fields along with the field inhomogeneities. To ease the correction, the distortion effects are modeled as a non-stationary convolution problem. In this work, two fast and accurate postgridding algorithms are presented and analyzed. These methods account for both the concomitant field effects and the field inhomogeneities. One algorithm operates in the frequency domain and the other in the spatial domain. To take advantage of their speed and accuracy, the algorithms are applied to a real-time cardiac study and a high-resolution cardiac study. Both of the presented algorithms provide for a practical solution to the off-resonance problem in spiral imaging.

Optimization of spiral-based pulse sequences for first-pass myocardial perfusion imaging

Although spiral trajectories have multiple attractive features such as their isotropic resolution, acquisition efficiency, and robustness to motion, there has been limited application of these techniques to first-pass perfusion imaging because of potential off-resonance and inconsistent data artifacts. Spiral trajectories may also be less sensitive to dark-rim artifacts that are caused, at least in part, by cardiac motion. By careful consideration of the spiral trajectory readout duration, flip angle strategy, and image reconstruction strategy, spiral artifacts can be abated to create high-quality first-pass myocardial perfusion images with high signal-to-noise ratio. The goal of this article was to design interleaved spiral pulse sequences for first-pass myocardial perfusion imaging and to evaluate them clinically for image quality and the presence of dark-rim, blurring, and dropout artifacts.

Spiral demystified

Spiral acquisition schemes offer unique advantages such as flow compensation, efficient k-space sampling and robustness against motion that make this option a viable choice among other non-Cartesian sampling schemes. For this reason, the main applications of spiral imaging lie in dynamic magnetic resonance imaging such as cardiac imaging and functional brain imaging. However, these advantages are counterbalanced by practical difficulties that render spiral imaging quite challenging. Firstly, the design of gradient waveforms and its hardware requires specific attention. Secondly, the reconstruction of such data is no longer straightforward because k-space samples are no longer aligned on a Cartesian grid. Thirdly, to take advantage of parallel imaging techniques, the common generalized autocalibrating partially parallel acquisitions (GRAPPA) or sensitivity encoding (SENSE) algorithms need to be extended. Finally, and most notably, spiral images are prone to particular artifacts such as blurring due to gradient deviations and off-resonance effects caused by B(0) inhomogeneity and concomitant gradient fields. In this article, various difficulties that spiral imaging brings along, and the solutions, which have been developed and proposed in literature, will be reviewed in detail.