Distortion correction of Golden Angle radial images with GIRF-predicted k-space trajectories using the gradient waveform history
Adrienne E Campbell-Washburn1, Robert J Lederman1, Anthony Z Faranesh1, and Michael S Hansen1

1Cardiovascular and Pulmonary Branch, Division of Intramural Research, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, MD, United States

Synopsis

Balanced SSFP Golden Angle radial imaging uses a rapidly varying gradient scheme and thus is susceptible to image distortion caused by gradient delays and eddy currents. We propose that storing a history of the gradient waveforms in each axis can enable us to better predict our true k-space coordinates during sampling. We use the gradient system impulse response function to predict k-space coordinates and demonstrate reduced image distortion (shading and streaking) in a phantom and in vivo when utilizing the gradient waveform history. This method will be useful for dynamic and real-time imaging with Golden Angle balanced SSFP imaging schemes.

Purpose

Golden Angle radial sampling, where each successive radial arm is rotated by 111.246°, is appealing for dynamic imaging because it has reduced sensitivity to motion and provides uniform k-space coverage for any arbitrary number of consecutive projections [1]. A balanced steady state free precession (bSSFP) sequence with Golden Angle profile ordering often results in image artifacts caused by gradient delays and varying eddy currents during the rapidly switching gradient scheme [2]. In recent work, the gradient system impulse response function (GIRF) has been characterized and used to predict true k-space trajectories during spiral and EPI imaging to reduce image distortion [3, 4]. Here, we propose to store a history of the time-varying gradient waveforms during a Golden Angle acquisition scheme and apply the GIRF calibration to predict true k-space coordinates during sampling in order to reduce image artifacts.

Methods

Fully sampled Golden Angle radial bSSFP imaging was performed at 1.5T (Aera, Siemens Healthcare, Erlangen, Germany). The GIRF was calibrated for each gradient axis (GIRF bandwidth = 100 kHz and resolution = 26 Hz) [4] and convolved with the nominal x, y and z gradient waveforms in order predict the true gradient waveforms for arbitrary slice orientation. Images were reconstructed in MATLAB (R2013a, Mathworks, Natick, MA) with a nonuniform FFT. Three images were compared: 1) assuming nominal gradient waveforms for perfect radial projections, 2) using the GIRF-predicted k-space trajectories treating each radial profile independently (including the prephasing and readout gradients) and 3) using the GIRF-predicted k-space trajectories informed by the entire gradient waveform history up to and including the current profile. Phantom imaging and in vivo imaging of a swine heart were performed using the following parameters: TE/TR = 1.47/2.94 ms, 201 radial projections, FOV = 300mm, flip angle = 45°, matrix = 128 x 128, slice thickness = 5 mm, bandwidth = 1000 Hz/Px. Animal experiments were approved by the institutional animal care and use committee according to contemporary NIH guidelines.

Results

The improvement in image artifact was visible in both an axial phantom image (Figure 1) and an oblique short axis image of the swine heart (Figure 2). Images reconstructed using the nominal radial trajectories displayed significant image streaking and shading (Figure 1A, 2A). Images were improved by applying GIRF prediction to calculate k-space trajectories from each radial profile independently, but some residual image artifact remained (Figure 1B, 2B). Using the entire gradient waveform history to inform k-space trajectory prediction produced the best quality images, with negligible remaining artifact (Figure 1C, 2C). The images shown here were in transition to steady state, creating worst-case scenario artifacts. Figure 3 shows the trajectories through the center of k-space for the final 6 radial projections, where the nominal trajectories assume perfect central alignment of the radial profiles and the GIRF-predicted trajectories depict a mismatch at the k-space center caused by both gradient delays and eddy currents.

Discussion

Using the GIRF calibration for a retrospective trajectory prediction can simultaneously correct distortions from both eddy currents and gradient delays, and can be applied as a standard step during real-time image reconstruction [4], which could improve the clinical applicability of radial imaging. In the future, this method will be implemented in real-time using a buffer of the gradient history and we will apply this distortion correction during MRI-guided interventions where multiple slice orientations are interleaved, thus amplifying the eddy current artifacts. Further studies will assess the duration of waveform history required for sufficient artifact correction. Our preliminary data suggests that the ability to store a gradient waveform history allows a better prediction of the sampled k-space locations with the gradient system impulse response function.

Acknowledgements

This work was supported by the NHLBI Division of Intramural Research (Z01-HL006039, Z01-HL005062)

References

[1] Winkelmann S et al, An optimal radial profile order based on the Golden Ratio for time-resolved MRI. IEEE Trans Med Imaging (2007) 26:68–76. [2] Wundrak S et al, A Small Surrogate for the Golden Angle in Time-Resolved Radial MRI Based on Generalized Fibonacci Sequences. IEEE Trans Med Imaging (2015) 34:1262-9. [3] Vannesjo S et al, Gradient System Characterization by Impulse Response Measurements with a Dynamic Field Camera. MRM (2013) 69:583–593. [4] Campbell-Washburn A et al, Real-Time distortion correction of spiral and echo planar images using the gradient system impulse response function. MRM (2015) doi: 10.1002/mrm.25788

Figures

Figure 1: Golden Angle radial bSSFP images of a phantom reconstructed according to nominal k-space trajectories (A), GIRF-predicted k-space trajectories from each TR independently (B), and GIRF-predicted k-space trajectories incorporating gradient waveform history (C).

Figure 2: Golden Angle radial bSSFP images of a swine heart reconstructed according to nominal k-space trajectories (A), GIRF-predicted k-space trajectories from each TR independently (B), and GIRF-predicted k-space trajectories incorporating gradient waveform history (C). Arrowheads in (B) indicate residual image shading, whereas negligible image artifact remains in (C).

Figure 3: Trajectories through the center of k-space during the final 6 projections of an image. Nominal trajectories (black) assume perfect projections through the k-space center, whereas GIRF-predicted trajectories from the waveform history (red) more accurately reflect misalignment caused by gradient waveform distortion.



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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