Efficient 3D Low-Discrepancy k -Space Sampling Using Highly Adaptable Seiffert Spirals

Electric potential energy optimized 3D radial sampling trajectories for MRI

A novel method for creating "golden" 3D center-out radial MRI sampling trajectories was developed and analyzed. This method, called ELECTRO (ELECTRic potential energy Optimized), uses repulsive forces to minimize electric potential energy. An objective function [Formula: see text], the electric potential energies of all subsets of consecutive readouts in a 3D radial trajectory, and its reduced form were minimized using a multi-stage optimization strategy. A metric called normalized mean nearest neighbor angular distance (NMNA) was proposed for describing distributions of points on a sphere. ELECTRO and other relevant golden trajectories were compared in silico using NMNA and point spread function analysis. Consecutive readouts from an ELECTRO trajectory were well spread out, with consistent NMNA values across sphere sizes (σNMNA = 0.005) and between regions on the sphere (NMNA ≈ 1.49). Conversely, the supergolden trajectory had poor consistency in NMNA values (σNMNA = 0.090) and clustering (NMNA = 1.28 at the pole with 40,000 readouts) that lead to artifact in the point spread function. Multi-stage optimization was faster than single-stage and obtained lower values of [Formula: see text] (e.g., 0.87 vs. 0.91, for a sphere size of 40). In conclusion, ELECTRO trajectories are more golden than other 3D center-out radial trajectories, making them a suitable candidate for dynamic 3D MR imaging.

Efficient 3D cone trajectory design for improved combined angiographic and perfusion imaging using arterial spin labeling

PURPOSE

To improve the spatial resolution and repeatability of a non-contrast MRI technique for simultaneous time resolved 3D angiography and perfusion imaging by developing an efficient 3D cone trajectory design.

METHODS

A novel parameterized 3D cone trajectory design incorporating the 3D golden angle was integrated into 4D combined angiography and perfusion using radial imaging and arterial spin labeling (CAPRIA) to achieve higher spatial resolution and sampling efficiency for both dynamic angiography and perfusion imaging with flexible spatiotemporal resolution. Numerical simulations and physical phantom scanning were used to optimize the cone design. Eight healthy volunteers were scanned to compare the original radial trajectory in 4D CAPRIA with our newly designed cone trajectory. A locally low rank reconstruction method was used to leverage the complementary k-space sampling across time.

RESULTS

The improved sampling in the periphery of k-space obtained with the optimized 3D cone trajectory resulted in improved spatial resolution compared with the radial trajectory in phantom scans. Improved vessel sharpness and perfusion visualization were also achieved in vivo. Less dephasing was observed in the angiograms because of the short TE of our cone trajectory and the improved k-space sampling efficiency also resulted in higher repeatability compared to the original radial approach.

CONCLUSION

The proposed 3D cone trajectory combined with 3D golden angle ordering resulted in improved spatial resolution and image quality for both angiography and perfusion imaging and could potentially benefit other applications that require an efficient sampling scheme with flexible spatial and temporal resolution.

Reducing clustering of readouts in non-Cartesian cine magnetic resonance imaging

BACKGROUND

Non-Cartesian magnetic resonance imaging trajectories at golden angle increments have the advantage of allowing motion correction and gating using intermediate real-time reconstructions. However, when the acquired data are cardiac binned for cine imaging, trajectories can cluster together at certain heart rates (HR) causing image artifacts. Here, we demonstrate an approach to reduce clustering by inserting additional angular increments within the trajectory, and optimizing them while still allowing for intermediate reconstructions.

METHODS

Three acquisition models were simulated under constant and variable HR: golden angle (Mtrd), random additional angles (Mrnd), and optimized additional angles (Mopt). The standard deviations of trajectory angular differences (STAD) were compared through their interquartile ranges (IQR) and the Kolmogorov-Smirnov test (significance level: p = 0.05). Agreement between an image reconstructed with uniform sampling and images from Mtrd, Mrnd, and Mopt was analyzed using the structural similarity index measure (SSIM). Mtrd and Mopt were compared in three adults at high, low, and no HR variability.

RESULTS

STADs from Mtrd were significantly different (p < 0.05) from Mopt and Mrnd. STAD (IQR × 10-2 rad) showed that Mopt (0.5) and Mrnd (0.5) reduced clustering relative to Mtrd (1.9) at constant HR. For variable HR, Mopt (0.5) and Mrnd (0.5) outperformed Mtrd (0.9). The SSIM (IQR) showed that Mopt (0.011) produced the best image quality, followed by Mrnd (0.014), and Mtrd (0.030). Mopt outperformed Mtrd at reduced HR variability in in-vivo studies. At high HR variability, both models performed well.

CONCLUSION

This approach reduces clustering in k-space and improves image quality.

Three-dimensional sector-wise golden angle-improved k-space uniformity after electrocardiogram binning

PURPOSE

To develop and evaluate a 3D sector-wise golden-angle (3D-SWIG) profile ordering scheme for cardiovascular MR cine imaging that maintains high k-space uniformity after electrocardiogram (ECG) binning.

METHOD

Cardiovascular MR (CMR) was performed at 1.5 T. A balanced SSFP pulse sequence was implemented with a novel 3D-SWIG radial ordering, where k-space was divided into wedges, and each wedge was acquired in a separate heartbeat. The high uniformity of k-space coverage after physiological binning can be used to perform functional imaging using a very short acquisition. The 3D-SWIG was compared with two commonly used 3D radial trajectories for CMR (i.e., double golden angle and spiral phyllotaxis) in numerical simulations. Free-breathing 3D-SWIG and conventional breath-held 2D cine were compared in patients (n = 17) referred clinically for CMR. Quantitative comparison was performed based on left ventricular segmentation.

RESULTS

Numerical simulations showed that 3D-SWIG both required smaller steps between successive readouts and achieved better k-space sampling uniformity after binning than either the double golden angle or spiral phyllotaxis trajectories. In vivo evaluation showed that measurements of left ventricular ejection fraction calculated from a 48 heart-beat free-breathing 3D-SWIG acquisition were highly reproducible and agreed with breath-held 2D-Cartesian cine (mean ± SD difference of -3.1 ± 3.5% points).

CONCLUSIONS

The 3D-SWIG acquisition offers a simple solution for highly improved k-space uniformity after physiological binning. The feasibility of the 3D-SWIG method is demonstrated in this study through whole-heart cine imaging during free breathing with an acquisition time of less than 1 min.

3D MR fingerprinting using Seiffert spirals

PURPOSE

Seiffert spirals were recently explored as an efficient way to traverse 3D k-space compared to traditional 3D techniques. Several studies have shown the ability of 3D MR fingerprinting (MRF) techniques to acquire T₁ and T₂ relaxation maps in a short period of time. However, these sequences do not sample across a large region of 3D k-space every TR, especially in the way that Seiffert trajectories can.

METHODS

A 3D MRF sequence was designed using 8 Seiffert spirals rotated in 3D k-space, with flip angle modulation for T₁ and T₂ sensitivity. The sequence was compared to an MRF sequence using a 2D spiral rotated in 3D k-space using the tiny golden angle acquisition with similar resolution/readout duration. Both sequences were evaluated using simulations, phantom validation, and in vivo imaging.

RESULTS

In all experiments, the Seiffert spiral MRF sequence performed similar to if not better than the multi-axis 2D spiral MRF sequence. Strong intraclass correlation coefficients (> 0.9) were found between conventional and MRF sequences in phantoms, whereas the in vivo results showed slightly less aliasing artifact with the Seiffert trajectory.

CONCLUSION

In this study, Seiffert spirals were used within the MRF framework to acquire high-resolution T₁ and T₂ relaxation time maps in less than 2.5 min. The reduced aliasing artifacts seen with the Seiffert sequence suggests that sampling over 3D k-space evenly each TR can improve quantification or shorten scan times.

Tiny golden angle stack-of-stars (tygaSoS) free-breathing functional lung imaging

PURPOSE

MRI of the lung parenchyma is still challenging due to cardiac and respiratory motion, and the low proton density and short T₂*. Clinical feasible MRI methods for functional lung assessment are of great interest. It was the objective of this study to evaluate the potential of combining the ultra-short echo-time stack-of-stars approach with tiny golden angle (tyGASoS) profile ordering for self-gated free-breathing lung imaging.

METHODS

Free-breathing tyGASoS data were acquired in 10 healthy volunteers (3 smoker (S), 7 non-smoker (NS)). Images in different respiratory phases were reconstructed applying an image-based self-gating technique. Resulting image quality and sharpness, and parenchyma visibility were qualitatively scored by three blinded independent reader, and the signal-to-noise ratio (SNR), proton fraction (f_P) and fractional ventilation (FV) quantified.

RESULT

The imaging protocol was well tolerated by all volunteers. Image quality was sufficient for subsequent quantitative analysis in all cases with good to excellent inter-reader reliability. Between expiration (EX) and inspiration (IN) significant differences (p < 0.001) were observed in SNR (EX: 3.73 ± 0.89, IN: 3.14 ± 0.74) and f_P (EX: 0.27 ± 0.09, IN: 0.25 ± 0.08). A significant (p < 0.05) higher f_P (EX/IN: 0.22 ± 0.07/0.21 ± 0.07 (NS), 0.33 ± 0.07/0.30 ± 0.06 (S)) was observed in the smoker group. No significant FV differences resulted between S and NS.

CONCLUSION

The study proves the feasibility of free-breathing tyGASoS for multiphase lung imaging. Changes in f_P may indicate an initial response in the smoker group and as such proves the sensitivity of the proposed technique. A major limitation in FV quantification rises from the large inter-subject variability of breathing patterns and amplitudes, requiring further consideration.