Martin Berzl^{1,2}, Antoine Pfeil^{1}, Craig Meyer^{3}, Adrienne Campbell-Washburn^{4}, Gregor Körzdörfer^{1}, Mathias Nittka^{1}, Andreas Maier^{2}, and Josef Pfeuffer^{1}

The purpose of this study is to evaluate different spiral trajectory prediction models - isotropic, Tan-Meyer and GIRF - to mitigate image artifacts for spiral MRI and improve accuracy of quantitative T1/T2 values for MR Fingerprinting. GIRF scan parameters were optimized to allow a total measurement time of only six minutes for a one-time calibration. GIRF similarly provided excellent results for vastly different trajectory types, varying in max. slew rate, gradient amplitude and number of interleaves, and showed some advantages against Tan-Meyer for trajectory designs with high k-space center slew rate, both for qualitative and quantitative results.

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3. Campbell-Washburn A, Xue H, Lederman R, et al. Real-Time Distortion Correction of Spiral and Echo Planar Images Using the Gradient System Impulse Response Function. Magnetic Resonance in Medicine. 2016;75:2278-2285.

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5. Vannesjo J, Graedel N, Kapser L, et al. Image Reconstruction Using a Gradient Impulse Response Model for Trajectory Prediction. Magnetic Resonance in Medicine. 2016;76:45-58.

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7. Meyer C, Zhao L, Lustig M, et al: Dual-density and parallel spiral ASL for motion artifact reduction. Proceedings ISMRM 2011;3986.

8. Robison R, Pipe J: Linear Gradient System Characterization Using a Rapid Thin-slice Measurement. Proceedings ISMRM 2016;4283.

9. Jiang Y, Ma D, Seiberlich N, et al. MR fingerprinting using fast imaging with steady state precession (FISP) with spiral readout. Magnetic Resonance in Medicine. 2015;74(6):1621-1631.

Different trajectory designs with readout
axis (blue), phase axis (red) and their envelope (orange) using a) the
Hargreaves algorithm (Traj-H); b) the Meyer algorithm (Traj-M). Note the
modification in the Meyer design by ramping the slew rate at k-space center,
whereas the Hargreaves design starts at maximum design slew rate.

Residual error of different models
compared to the measured trajectory (isotropic correction, Tan-Meyer model,
GIRF model) for a) Traj-H and b) Traj-M (first interleave). Tan-Meyer and GIRF
model have a significantly lower residual error compared to the isotropic model
which only corrects linear delays and no eddy currents. The
Tan-Meyer model cannot adequately describe the steep gradient demanded by the Traj-H trajectory’s slew at k-space center. The GIRF model achieves lower
residuals overall.

Normalized mean absolute error (NMAE) in
k-space for different trajectory types and models (transversal orientation) for
a) readout axis (physical x-axis) and b) phase axis (physical y-axis). The
normalization basis is the isotropic MAE. Both, Tan-Meyer and GIRF model obtain
very low NMAE values, whereas the GIRF values are slightly smaller for all
trajectory types.

Comparison of Traj-H spiral images reconstructed
using the isotropic, Tan-Meyer and GIRF model. Difference images are relative
to the image reconstructed with the measured trajectory. A spatial object
scaling artifact (edges) is clearly visible in the isotropic delay model caused
by uncorrected eddy currents. The Tan-Meyer and GIRF model corrects for this as
well as for a rotation artifact. Small image intensity deviations were
additionally corrected by the GIRF model (intensity scaling in difference
images is multiplied by a factor of 3).

Quantitative MR Fingerprinting results
from the spheres of a NIST phantom. Relative deviations of quantitative T1/T2
values for different models (isotropic, Tan-Meyer, GIRF) compared to the
measured trajectory. Quantitative values for the Traj-H (left) and the Traj-M
trajectory (right). T1 and T2 values differ for the isotropic and Tan-Meyer
model from the measured trajectory values (more distinct for T2), whereas the GIRF
values are within error limits. Tan-Meyer model yielded only small improvements
compared to isotropic delay. However, the values with the Traj-M trajectory
(right column) are already very close to the values with the measured
trajectory.