NonCartesian MR image reconstruction with integrated gradient nonlinearity correction

Analysis of blurring due to short T2 decay at different resolutions in 23Na MRI

The nuclear magnetic resonance signal from sodium (23Na) nuclei demonstrates a fast bi-exponential T2 decay in biological tissues (T2,short = 0.5-5 ms and T2,long = 10-30 ms). Hence, blurring observed in sodium images acquired with center-out sequences is generally assumed to be dominated by signal attenuation at higher k-space frequencies. Most of the studies in the field primarily focus on the impact of readout duration on blurring but neglect the impact of resolution. In this paper, we examine the blurring effect of short T2 on images at different resolutions. A series of simulations, as well as phantom and in vivo scans were performed at varying resolutions and readout durations in order to evaluate progressive changes in image quality. We demonstrate that, given a fixed readout duration, T2 decay produces distinct blurring effects at different resolutions. Therefore, in addition to voxel size-dependent partial volume effects, the choice of resolution adds additional T2-dependent blurring.

Distortion-corrected image reconstruction with deep learning on an MRI-Linac

PURPOSE

MRI is increasingly utilized for image-guided radiotherapy due to its outstanding soft-tissue contrast and lack of ionizing radiation. However, geometric distortions caused by gradient nonlinearities (GNLs) limit anatomical accuracy, potentially compromising the quality of tumor treatments. In addition, slow MR acquisition and reconstruction limit the potential for effective image guidance. Here, we demonstrate a deep learning-based method that rapidly reconstructs distortion-corrected images from raw k-space data for MR-guided radiotherapy applications.

METHODS

We leverage recent advances in interpretable unrolling networks to develop a Distortion-Corrected Reconstruction Network (DCReconNet) that applies convolutional neural networks (CNNs) to learn effective regularizations and nonuniform fast Fourier transforms for GNL-encoding. DCReconNet was trained on a public MR brain dataset from 11 healthy volunteers for fully sampled and accelerated techniques, including parallel imaging (PI) and compressed sensing (CS). The performance of DCReconNet was tested on phantom, brain, pelvis, and lung images acquired on a 1.0T MRI-Linac. The DCReconNet, CS-, PI-and UNet-based reconstructed image quality was measured by structural similarity (SSIM) and RMS error (RMSE) for numerical comparisons. The computation time and residual distortion for each method were also reported.

RESULTS

Imaging results demonstrated that DCReconNet better preserves image structures compared to CS- and PI-based reconstruction methods. DCReconNet resulted in the highest SSIM (0.95 median value) and lowest RMSE (<0.04) on simulated brain images with four times acceleration. DCReconNet is over 10-times faster than iterative, regularized reconstruction methods.

CONCLUSIONS

DCReconNet provides fast and geometrically accurate image reconstruction and has the potential for MRI-guided radiotherapy applications.

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.

Characterisation of a split gradient coil design induced systemic imaging artefact on 0.35 T MR-linac systems

Objective. The aim of this work was to highlight and characterize a systemic 'star-like' artefact inherent to the low field 0.35 T MRIdian MR-linac system, a magnetic resonance guided radiotherapy device. This artefact is induced by the original split gradients coils design. This design causes a surjection of the intensity gradient inZ(or head-feet) direction. This artefact appears on every sequence with phase encoding in the head-feet direction.Approach. Basic gradient echo sequence and clinical mandatory bSSFP sequence were used. Three setups using manufacturer provided QA phantoms were designed: two including the linearity control grid used for the characterisation and a third including two homogeneity control spheres dedicated to the artefact management in a more clinical like situation. The presence of the artefact was checked in four different MRidian sites. The tested parameters based on the literature were: phase encoding orientation, slab selectivity, excitation bandwidth (BW_RF), acceleration factor (R) and phase/slab oversampling (PO/SO).Main results. The position of this artefact is constant and reproducible over the tested MRIdian sites. The typical singularity saturated dot or star is visible even with the 3D slab-selection enabled. A management is proposed by decreasing the BW_RF, theRin head-feet direction and increasing the PO/SO. The oversampling can be optimized using a formula to anticipate the location of artefact in the field of view.Significance. The star-like artefact has been well characterised. A manageable solution comes at the cost of acquisition time. Observed in clinical cases, the artefact may degrade the images used for the RT planning and repositioning during the treatment unless corrected.

ReUINet: A fast GNL distortion correction approach on a 1.0 T MRI-Linac scanner

PURPOSE

The hybrid system combining a magnetic resonance imaging (MRI) scanner with a linear accelerator (Linac) has become increasingly desirable for tumor treatment because of excellent soft tissue contrast and nonionizing radiation. However, image distortions caused by gradient nonlinearity (GNL) can have detrimental impacts on real-time radiotherapy using MRI-Linac systems, where accurate geometric information of tumors is essential.

METHODS

In this work, we proposed a deep convolutional neural network-based method to efficiently recover undistorted images (ReUINet) for real-time image guidance. The ReUINet, based on the encoder-decoder structure, was created to learn the relationship between the undistorted images and distorted images. The ReUINet was pretrained and tested on a publically available brain MR image dataset acquired from 23 volunteers. Then, transfer learning was adopted to implement the pretrained model (i.e., network with optimal weights) on the experimental three-dimensional (3D) grid phantom and in-vivo pelvis image datasets acquired from the 1.0 T Australian MRI-Linac system.

RESULTS

Evaluations on the phantom (768 slices) and pelvis data (88 slices) showed that the ReUINet achieved improvement over 15 times and 45 times on computational efficiency in comparison with standard interpolation and GNL-encoding methods, respectively. Moreover, qualitative and quantitative results demonstrated that the ReUINet provided better correction results than the standard interpolation method, and comparable performance compared to the GNL-encoding approach.

CONCLUSIONS

Validated by simulation and experimental results, the proposed ReUINet showed promise in obtaining accurate MR images for the implementation of real-time MRI-guided radiotherapy.

Empirical field mapping for gradient nonlinearity correction of multi-site diffusion weighted MRI

BACKGROUND

Achieving inter-site / inter-scanner reproducibility of diffusion weighted magnetic resonance imaging (DW-MRI) metrics has been challenging given differences in acquisition protocols, analysis models, and hardware factors.

PURPOSE

Magnetic field gradients impart scanner-dependent spatial variations in the applied diffusion weighting that can be corrected if the gradient nonlinearities are known. However, retrieving manufacturer nonlinearity specifications is not well supported and may introduce errors in interpretation of units or coordinate systems. We propose an empirical approach to mapping the gradient nonlinearities with sequences that are supported across the major scanner vendors.

STUDY TYPE

Prospective observational study.

SUBJECTS

A spherical isotropic diffusion phantom, and a single human control volunteer.

FIELD STRENGTH/SEQUENCE

3 T (two scanners). Stejskal-Tanner spin echo sequence with b-values of 1000, 2000 s/mm² with 12, 32, and 384 diffusion gradient directions per shell.

ASSESSMENT

We compare the proposed correction with the prior approach using manufacturer specifications against typical diffusion pre-processing pipelines (i.e., ignoring spatial gradient nonlinearities). In phantom data, we evaluate metrics against the ground truth. In human and phantom data, we evaluate reproducibility across scans, sessions, and hardware.

STATISTICAL TESTS

Wilcoxon rank-sum test between uncorrected and corrected data.

RESULTS

In phantom data, our correction method reduces variation in mean diffusivity across sessions over uncorrected data (p < 0.05). In human data, we show that this method can also reduce variation in mean diffusivity across scanners (p < 0.05).

CONCLUSION

Our method is relatively simple, fast, and can be applied retroactively. We advocate incorporating voxel-specific b-value and b-vector maps should be incorporated in DW-MRI harmonization preprocessing pipelines to improve quantitative accuracy of measured diffusion parameters.

Optimization of MRI Gradient Coils With Explicit Peripheral Nerve Stimulation Constraints

Peripheral Nerve Stimulation (PNS) limits the acquisition rate of Magnetic Resonance Imaging data for fast sequences employing powerful gradient systems. The PNS characteristics are currently assessed after the coil design phase in experimental stimulation studies using constructed coil prototypes. This makes it difficult to find design modifications that can reduce PNS. Here, we demonstrate a direct approach for incorporation of PNS effects into the coil optimization process. Knowledge about the interactions between the applied magnetic fields and peripheral nerves allows the optimizer to identify coil solutions that minimize PNS while satisfying the traditional engineering constraints. We compare the simulated thresholds of PNS-optimized body and head gradients to conventional designs, and find an up to 2-fold reduction in PNS propensity with moderate penalties in coil inductance and field linearity, potentially doubling the image encoding performance that can be safely used in humans. The same framework may be useful in designing and operating magneto- and electro-stimulation devices.

Partial fourier shells trajectory for non-cartesian MRI

Non-Cartesian MRI acquisition has demonstrated various advantages in many clinical applications. The shells trajectory is a 3D non-Cartesian MRI acquisition technique that samples the k-space using a series of concentric shells to achieve efficient 3D isotropic acquisition. Partial Fourier acquisition is an acceleration technique that is widely used in Cartesian MRI. It exploits the conjugate symmetry of k-space measurement to reduce the number of k-space samples compared to full-k-space acquisition, without loss of spatial resolution. For a Cartesian MRI acquisition, the direction of partial Fourier acceleration is aligned either with the phase encoded or frequency encoded direction. In those cases, the underlying image matrix can be reconstructed from the undersampled k-space data using a non-iterative, homodyne reconstruction framework. However, designing a non-Cartesian acquisition trajectory that is compatible with non-iterative homodyne reconstruction is not nearly as straightforward as in the Cartesian case. One reason is the non-iterative homodyne reconstruction requires (slightly over) half of the k-space to be fully sampled. Since the direction of partial Fourier acceleration varies throughout the acquisition in the non-Cartesian trajectory, directly applying the same partial Fourier acquisition pattern (as in Cartesian acquisitions) to a non-Cartesian trajectory does not necessarily yield a continuous, physically-achievable trajectory. In this work, we develop an asymmetric shells trajectory with fully-automated trajectory and gradient waveform design to achieve partial Fourier acquisition for the shells trajectory. We then demonstrate a non-iterative image reconstruction framework for the proposed trajectory. Phantom and in vivo brain scans based on spoiled gradient echo (SPGR) shells and magnetization-prepared shells (MP-shells) were performed to test the proposed trajectory design and reconstruction method. Our phantom and in vivo results demonstrate that the proposed partial Fourier shells trajectory maintains the desirable image contrast and high sampling efficiency from the fully sampled shells, while further reducing data acquisition time.

Rapid compressed sensing reconstruction of 3D non-Cartesian MRI

PURPOSE

Conventional non-Cartesian compressed sensing requires multiple nonuniform Fourier transforms every iteration, which is computationally expensive. Accordingly, time-consuming reconstructions have slowed the adoption of undersampled 3D non-Cartesian acquisitions into clinical protocols. In this work we investigate several approaches to minimize reconstruction times without sacrificing accuracy.

METHODS

The reconstruction problem can be reformatted to exploit the Toeplitz structure of matrices that are evaluated every iteration, but it requires larger oversampling than what is strictly required by nonuniform Fourier transforms. Accordingly, we investigate relative speeds of the two approaches for various nonuniform Fourier transform kernel sizes and oversampling for both GPU and CPU implementations. Second, we introduce a method to minimize matrix sizes by estimating the image support. Finally, density compensation weights have been used as a preconditioning matrix to improve convergence, but this increases noise. We propose a more general approach to preconditioning that allows a trade-off between accuracy and convergence speed.

RESULTS

When using a GPU, the Toeplitz approach was faster for all practical parameters. Second, it was found that properly accounting for image support can prevent aliasing errors with minimal impact on reconstruction time. Third, the proposed preconditioning scheme improved convergence rates by an order of magnitude with negligible impact on noise.

CONCLUSION

With the proposed methods, 3D non-Cartesian compressed sensing with clinically relevant reconstruction times (<2 min) is feasible using practical computer resources. Magn Reson Med 79:2685-2692, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Magnetization-prepared shells trajectory with automated gradient waveform design

PURPOSE

To develop a fully automated trajectory and gradient waveform design for the non-Cartesian shells acquisition, and to develop a magnetization-prepared (MP) shells acquisition to achieve an efficient three-dimensional acquisition with improved gray-to-white brain matter contrast.

METHODS

After reviewing the shells k-space trajectory, a novel, fully automated trajectory design is developed that allows for gradient waveforms to be automatically generated for specified acquisition parameters. Designs for two types of shells are introduced, including fully sampled and undersampled/accelerated shells. Using those designs, an MP-Shells acquisition is developed by adjusting the acquisition order of shells interleaves to synchronize the center of k-space sampling with the peak of desired gray-to-white matter contrast. The feasibility of the proposed design and MP-Shells is demonstrated using simulation, phantom, and volunteer subject experiments, and the performance of MP-Shells is compared with a clinical Cartesian magnetization-prepared rapid gradient echo acquisition.

RESULTS

Initial experiments show that MP-Shells produces excellent image quality with higher data acquisition efficiency and improved gray-to-white matter contrast-to-noise ratio (by 36%) compared with the conventional Cartesian magnetization-prepared rapid gradient echo acquisition.

CONCLUSION

We demonstrated the feasibility of a three-dimensional MP-Shells acquisition and an automated trajectory design to achieve an efficient acquisition with improved gray-to-white matter contrast. Magn Reson Med 79:2024-2035, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

B0 concomitant field compensation for MRI systems employing asymmetric transverse gradient coils

PURPOSE

Imaging gradients result in the generation of concomitant fields, or Maxwell fields, which are of increasing importance at higher gradient amplitudes. These time-varying fields cause additional phase accumulation, which must be compensated for to avoid image artifacts. In the case of gradient systems employing symmetric design, the concomitant fields are well described with second-order spatial variation. Gradient systems employing asymmetric design additionally generate concomitant fields with global (zeroth-order or B₀ ) and linear (first-order) spatial dependence.

METHODS

This work demonstrates a general solution to eliminate the zeroth-order concomitant field by applying the correct B₀ frequency shift in real time to counteract the concomitant fields. Results are demonstrated for phase contrast, spiral, echo-planar imaging (EPI), and fast spin-echo imaging.

RESULTS

A global phase offset is reduced in the phase-contrast exam, and blurring is virtually eliminated in spiral images. The bulk image shift in the phase-encode direction is compensated for in EPI, whereas signal loss, ghosting, and blurring are corrected in the fast-spin echo images.

CONCLUSION

A user-transparent method to compensate the zeroth-order concomitant field term by center frequency shifting is proposed and implemented. This solution allows all the existing pulse sequences-both product and research-to be retained without any modifications. Magn Reson Med 79:1538-1544, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Gradient nonlinearity calibration and correction for a compact, asymmetric magnetic resonance imaging gradient system

Due to engineering limitations, the spatial encoding gradient fields in conventional magnetic resonance imaging cannot be perfectly linear and always contain higher-order, nonlinear components. If ignored during image reconstruction, gradient nonlinearity (GNL) manifests as image geometric distortion. Given an estimate of the GNL field, this distortion can be corrected to a degree proportional to the accuracy of the field estimate. The GNL of a gradient system is typically characterized using a spherical harmonic polynomial model with model coefficients obtained from electromagnetic simulation. Conventional whole-body gradient systems are symmetric in design; typically, only odd-order terms up to the 5th-order are required for GNL modeling. Recently, a high-performance, asymmetric gradient system was developed, which exhibits more complex GNL that requires higher-order terms including both odd- and even-orders for accurate modeling. This work characterizes the GNL of this system using an iterative calibration method and a fiducial phantom used in ADNI (Alzheimer's Disease Neuroimaging Initiative). The phantom was scanned at different locations inside the 26 cm diameter-spherical-volume of this gradient, and the positions of fiducials in the phantom were estimated. An iterative calibration procedure was utilized to identify the model coefficients that minimize the mean-squared-error between the true fiducial positions and the positions estimated from images corrected using these coefficients. To examine the effect of higher-order and even-order terms, this calibration was performed using spherical harmonic polynomial of different orders up to the 10th-order including even- and odd-order terms, or odd-order only. The results showed that the model coefficients of this gradient can be successfully estimated. The residual root-mean-squared-error after correction using up to the 10th-order coefficients was reduced to 0.36 mm, yielding spatial accuracy comparable to conventional whole-body gradients. The even-order terms were necessary for accurate GNL modeling. In addition, the calibrated coefficients improved image geometric accuracy compared with the simulation-based coefficients.

Image-based gradient non-linearity characterization to determine higher-order spherical harmonic coefficients for improved spatial position accuracy in magnetic resonance imaging

PURPOSE

Spatial position accuracy in magnetic resonance imaging (MRI) is an important concern for a variety of applications, including radiation therapy planning, surgical planning, and longitudinal studies of morphologic changes to study neurodegenerative diseases. Spatial accuracy is strongly influenced by gradient linearity. This work presents a method for characterizing the gradient non-linearity fields on a per-system basis, and using this information to provide improved and higher-order (9th vs. 5th) spherical harmonic coefficients for better spatial accuracy in MRI.

METHODS

A large fiducial phantom containing 5229 water-filled spheres in a grid pattern is scanned with the MR system, and the positions all the fiducials are measured and compared to the corresponding ground truth fiducial positions as reported from a computed tomography (CT) scan of the object. Systematic errors from off-resonance (i.e., B0) effects are minimized with the use of increased receiver bandwidth (±125kHz) and two acquisitions with reversed readout gradient polarity. The spherical harmonic coefficients are estimated using an iterative process, and can be subsequently used to correct for gradient non-linearity. Test-retest stability was assessed with five repeated measurements on a single scanner, and cross-scanner variation on four different, identically-configured 3T wide-bore systems.

RESULTS

A decrease in the root-mean-square error (RMSE) over a 50cm diameter spherical volume from 1.80mm to 0.77mm is reported here in the case of replacing the vendor's standard 5th order spherical harmonic coefficients with custom fitted 9th order coefficients, and from 1.5mm to 1mm by extending custom fitted 5th order correction to the 9th order. Minimum RMSE varied between scanners, but was stable with repeated measurements in the same scanner.

CONCLUSIONS

The results suggest that the proposed methods may be used on a per-system basis to more accurately calibrate MR gradient non-linearity coefficients when compared to vendor standard corrections.

Gradient pre-emphasis to counteract first-order concomitant fields on asymmetric MRI gradient systems

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.