A GRAPPA algorithm for arbitrary 2D/3D non-Cartesian sampling trajectories with rapid calibration

Self-calibrated through-time spiral GRAPPA for real-time, free-breathing evaluation of left ventricular function

PURPOSE

Through-time spiral GRAPPA is a real-time imaging technique that enables ungated, free-breathing evaluation of the left ventricle. However, it requires a separate fully-sampled calibration scan to calculate GRAPPA weights. A self-calibrated through-time spiral GRAPPA method is proposed that uses a specially designed spiral trajectory with interleaved arm ordering such that consecutive undersampled frames can be merged to form calibration data, eliminating the separate fully-sampled acquisition.

THEORY AND METHODS

The proposed method considers the time needed to acquire data at all points in a GRAPPA calibration kernel when using interleaved arm ordering. Using this metric, simulations were performed to design a spiral trajectory for self-calibrated GRAPPA. Data were acquired in healthy volunteers using the proposed method and a comparison electrocardiogram-gated and breath-held cine scan. Left ventricular functional values and image quality are compared.

RESULTS

A 12-arm spiral trajectory was designed with a temporal resolution of 32.72 ms/cardiac phase with an acceleration factor of 3. Functional values calculated using the proposed method and the gold-standard method were not statistically significantly different (paired t-test, p < 0.05). Image quality ratings were lower for the proposed method, with statistically significantly different ratings (Wilcoxon signed rank test, p < 0.05) for two of five image quality aspects rated (level of artifact, blood-myocardium contrast).

CONCLUSIONS

A self-calibrated through-time spiral GRAPPA reconstruction can enable ungated, free-breathing evaluation of the left ventricle in 71 s. Functional values are equivalent to a gold-standard cine technique, although some aspects of image quality may be inferior due to the real-time nature of the data collection.

Iterative static field map estimation for off-resonance correction in non-Cartesian susceptibility weighted imaging

Purpose

Patient‐induced inhomogeneities in the magnetic field cause distortions and blurring during acquisitions with long readouts such as in susceptibility‐weighted imaging (SWI). Most correction methods require collecting an additional ΔB0 field map to remove these artifacts.

Theory

The static ΔB0 field map can be approximated with an acceptable error directly from a single echo acquisition in SWI. The main component of the observed phase is linearly related to ΔB0 and the echo time (TE), and the relative impact of non‐ ΔB0 terms becomes insignificant with TE >20 ms at 3 T for a well‐tuned system.

Methods

The main step is to combine and unfold the multi‐channel phase maps wrapped many times, and several competing algorithms are compared for this purpose. Four in vivo brain data sets collected using the recently proposed 3D spreading projection algorithm for rapid k‐space sampling (SPARKLING) readouts are used to assess the proposed method.

Results

The estimated 3D field maps generated with a 0.6 mm isotropic spatial resolution provide overall similar off‐resonance corrections compared to reference corrections based on an external ΔB0 acquisitions, and even improved for 2 of 4 individuals. Although a small estimation error is expected, no aftermath was observed in the proposed corrections, whereas degradations were observed in the references.

Conclusion

A static ΔB0 field map estimation method was proposed to take advantage of acquisitions with long echo times, and outperformed the reference technique based on an external field map. The difference can be attributed to an inherent robustness to mismatches between volumes and external ΔB0 maps, and diverse other sources investigated.

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Improved Image Quality for Static BLADE Magnetic Resonance Imaging Using the Total-Variation Regularized Least Absolute Deviation Solver

In order to improve the image quality of BLADE magnetic resonance imaging (MRI) using the index tensor solvers and to evaluate MRI image quality in a clinical setting, we implemented BLADE MRI reconstructions using two tensor solvers (the least-squares solver and the L1 total-variation regularized least absolute deviation (L1TV-LAD) solver) on a graphics processing unit (GPU). The BLADE raw data were prospectively acquired and presented in random order before being assessed by two independent radiologists. Evaluation scores were examined for consistency and then by repeated measures analysis of variance (ANOVA) to identify the superior algorithm. The simulation showed the structural similarity index (SSIM) of various tensor solvers ranged between 0.995 and 0.999. Inter-reader reliability was high (Intraclass correlation coefficient (ICC) = 0.845, 95% confidence interval: 0.817, 0.87). The image score of L1TV-LAD was significantly higher than that of vendor-provided image and the least-squares method. The image score of the least-squares method was significantly lower than that of the vendor-provided image. No significance was identified in L1TV-LAD with a regularization strength of λ= 0.4–1.0. The L1TV-LAD with a regularization strength of λ= 0.4–0.7 was found consistently better than least-squares and vendor-provided reconstruction in BLADE MRI with a SENSitivity Encoding (SENSE) factor of 2. This warrants further development of the integrated computing system with the scanner.

k-Space Domain Parallel Transmit Pulse Design

PURPOSE

To accelerate the design of (under- or oversampled) multidimensional parallel transmission pulses.

METHODS

A k-space domain parallel transmission pulse design algorithm was proposed that produces a sparse matrix relating a complex-valued target excitation pattern to the pulses that produce it, and can be finely parallelized. The algorithm was applied in simulations to the design of 3D SPINS pulses for inner volume excitation in the brain at 7 Tesla. It was characterized in terms of the dependence of computation time, excitation error, and required memory on algorithm parameters, and it was compared to an iterative spatial domain pulse design method in terms of computation time, excitation error, Gibbs ringing, and ability to compensate off-resonance.

RESULTS

The proposed algorithm achieved approximately 80% faster pulse design compared to the spatial domain method with the same number of parallel threads, with the tradeoff of increased excitation error and RMS RF amplitude. It reduced the memory required to store the design matrix by 99% compared to a full matrix solution. Even with a coarse design grid, the algorithm produced patterns that were free of Gibbs ringing. It was similarly sensitive to k-space undersampling as the spatial domain method, and was similarly capable of compensating for off-resonance.

CONCLUSIONS

The proposed k-space domain algorithm accelerates and finely parallelizes parallel transmission pulse design, with a modest tradeoff of excitation error and RMS RF amplitude.

Three-dimensional Yarnball k-space acquisition for accelerated MRI

PURPOSE

To introduce an efficient sampling technique named Yarnball, which may serve as a direct alternative to 3D Cones.

METHODS

Yarnball evolves through 3D k-space with increasing loop size, and the differential equations defining this flexible trajectory are presented in detail. The sampling efficiencies of Yarnball and 3D Cones were compared through point spread function analysis and simulated imaging (which highlights undersampling in the absence of other scanning effects). The feasibility of Yarnball implementation was demonstrated for fully sampled T₁ -weighted images of the human head at 3 T.

RESULTS

The mostly large 3D loops of the Yarnball trajectory facilitate rapid sampling under peripheral nerve stimulation constraint, an advantage that increases with readout duration (T_RO ). Point spread function analysis yielded 89% (T_RO = 2 ms) and 77% (T_RO = 10 ms) of Yarnball voxels with magnitude less than 0.01% of the point spread function peak. For 3D Cones, these values were only 52% and 29%. The 3D-Cones technique required 1.4 times (T_RO = 2 ms) and 1.8 times (T_RO = 10 ms) more trajectories than Yarnball to produce simulated images of a sphere free from undersampling artifact. For a prolate spheroidal (head-like) object, 1.75 times and 2.6 times more trajectories were required for 3D Cones. Yarnball produced 0.72 mm (1/2k_max ) isotropic T₁ -weighted human brain images free from undersampling artifact in only 98 seconds at 3 T.

CONCLUSION

Yarnball demonstrated greater k-space sampling efficiency than directly comparable 3D Cones, and may have value wherever 3D Cones has been considered. Yarnball may also have value in the context of rapid T₁ -weighted brain imaging.

Silent myelin-weighted magnetic resonance imaging

Background: Inhomogeneous Magnetization Transfer (ihMT) is an emerging, uniquely myelin-specific magnetic resonance imaging (MRI) contrast. Current ihMT acquisitions utilise fast Gradient Echo sequences which are among the most acoustically noisy MRI sequences, reducing patient comfort during acquisition. We sought to address this by modifying a near silent MRI sequence to include ihMT contrast.

Methods: A Magnetization Transfer preparation module was incorporated into a radial Zero Echo-Time sequence. Repeatability of the ihMT ratio and inverse ihMT ratio were assessed in a cohort of healthy subjects. We also investigated how head orientation affects ihMT across subjects, as a previous study in a single subject suggests this as a potential confound.

Results: We demonstrated that ihMT ratios comparable to existing, acoustically loud, implementations could be obtained with the silent sequence. We observed a small but significant effect of head orientation on inverse ihMTR.

Conclusions: Silent ihMT imaging is a comparable alternative to conventional, noisy, alternatives. For all future ihMT studies we recommend careful positioning of the subject within the scanner.

Silent myelin-weighted magnetic resonance imaging

Background: Inhomogeneous Magnetization Transfer (ihMT) is an emerging, uniquely myelin-specific magnetic resonance imaging (MRI) contrast. Current ihMT acquisitions utilise fast Gradient Echo sequences which are among the most acoustically noisy MRI sequences, reducing patient comfort during acquisition. We sought to address this by modifying a near silent MRI sequence to include ihMT contrast. Methods: A Magnetization Transfer preparation module was incorporated into a radial Zero Echo-Time sequence. Repeatability of the ihMT ratio and inverse ihMT ratio were assessed in a cohort of healthy subjects. We also investigated how head orientation affects ihMT across subjects, as a previous study in a single subject suggests this as a potential confound. Results: We demonstrated that ihMT ratios comparable to existing, acoustically loud, implementations could be obtained with the silent sequence. We observed a small but significant effect of head orientation on inverse ihMTR. Conclusions: Silent ihMT imaging is a comparable alternative to conventional, noisy, alternatives. For all future ihMT studies we recommend careful positioning of the subject within the scanner.

Self-calibrated interpolation of non-Cartesian data with GRAPPA in parallel imaging

PURPOSE

To develop a non-Cartesian k-space reconstruction method using self-calibrated region-specific interpolation kernels for highly accelerated acquisitions.

METHODS

In conventional non-Cartesian GRAPPA with through-time GRAPPA (TT-GRAPPA), the use of region-specific interpolation kernels has demonstrated improved reconstruction quality in dynamic imaging for highly accelerated acquisitions. However, TT-GRAPPA requires the acquisition of a large number of separate calibration scans. To reduce the overall imaging time, we propose Self-calibrated Interpolation of Non-Cartesian data with GRAPPA (SING) to self-calibrate region-specific interpolation kernels from dynamic undersampled measurements. The SING method synthesizes calibration data to adapt to the distinct shape of each region-specific interpolation kernel geometry, and uses a novel local k-space regularization through an extension of TT-GRAPPA. This calibration approach is used to reconstruct non-Cartesian images at high acceleration rates while mitigating noise amplification. The reconstruction quality of SING is compared with conjugate-gradient SENSE and TT-GRAPPA in numerical phantoms and in vivo cine data sets.

RESULTS

In both numerical phantom and in vivo cine data sets, SING offers visually and quantitatively similar reconstruction quality to TT-GRAPPA, and provides improved reconstruction quality over conjugate-gradient SENSE. Furthermore, temporal fidelity in SING and TT-GRAPPA is similar for the same acceleration rates. G-factor evaluation over the heart shows that SING and TT-GRAPPA provide similar noise amplification at moderate and high rates.

CONCLUSION

The proposed SING reconstruction enables significant improvement of acquisition efficiency for calibration data, while matching the reconstruction performance of TT-GRAPPA.