Manuel Stich^{1}, Tobias Wech^{1}, Anne Slawig^{1}, Ralf Ringler^{2}, Andrew Dewdney ^{3}, Andreas Greiser^{3}, Gudrun Ruyters^{3}, Thorsten Bley^{1}, and Herbert Köstler^{1}

The gradient impulse response function (GIRF) completely characterizes the gradient system as a linear and time-invariant (LTI) system, and has recently been used to correct for distorted k-space trajectories in image reconstruction. We now report on the implementation of a GIRF-based pre-emphasis, which is resulting in gradient waveforms already matching the desired k-space trajectory and rendering post-corrections obsolete. The method was successfully tested in a sequence with modulated phase-encoding gradients, as for example used in Wave-CAIPI.

K-space trajectories are frequently impaired by eddy currents, readout timing and amplifier errors and other system imperfections. The gradient impulse response function (GIRF) has been used to describe the distorted k-space trajectory for image reconstruction [1]. Purpose of this work was to use the GIRF to determine the pre-emphasis for an undistorted gradient output and intended k-space trajectory. As an example, a sequence with phase-encoding gradient modulation as it is used for Wave-CAIPI [2] was corrected.

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[2] Bilgic B. et. al. Wave CAIPI for Highly Accelerated 3D Imaging. MRM. 2015;73:2152-2162.

[3] Hinks R.S., Xiang Q-S., Henkelman R.M. Ghost Phase Cancellation with Phase-encoding Gradient Modulation. MRM. 1993;3:777-785.

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[5] Campbell-Washburn AE. et. al. Real-time distortion correction of spiral and echo planar images using the gradient system impulse response function. MRM. 2016;75:2278-2285.

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[8] Liebig P., Heidemann R.M., Porter D.A. Echo-planar imaging on a true zig-zag trajectory. ESMRMB Congress 2015. S.100.

Fig. 1. Gradient echo sequence with phase-encoding
gradient modulation. The applied gradient causes an oscillating shift in
k-space for the phase-encoding direction during a single readout. (A) depicts
the initially intended gradient waveform, i.e. the nominal gradient output. (B)
shows the resulting waveform using a GIRF-based correction of the waveform in
1A in post-processing, i.e the GIRF trajectory prediction. This waveform
was not applied in any measurement; it was used for a corrected reconstruction
of the data acquired using the input waveform of 1A. (C) shows the gradient waveform after
applying the GIRF-based pre-emphasis.

Fig. 2. Magnitude of the
GIRF measured in y-direction while playing out triangular input-pulses in the
same direction (GIRF_{yy}).

Fig. 3. A (Nominal
gradient output): (i) Image reconstructed using the initially intended
gradient waveform and the corresponding k-space-trajectory. Ghosting artifacts
are highlighted by red arrows. (ii) Intensity profile in frequency-encoding
direction (dashed line) shows the ghosting artifacts (red
rectangle). B (GIRF trajectory prediction): (i) Image reconstructed
using a GIRF-based trajectory correction in post-processing. (ii) Intensity
profile in frequency-encoding direction (dashed line). C (GIRF pre-emphasis): (i) Image reconstructed using the nominal
k-space trajectory (see Fig. 1A) and a GIRF-based pre-emphasis for the oscillating
gradient (see Fig. 1C). (ii) Intensity profile in frequency-encoding direction
(dashed line).

Fig. 4. A (Nominal
gradient output): (i) In-vivo head image reconstructed using the initially
intended gradient waveform and the corresponding k-space-trajectory. Ghosting
artifacts are highlighted by red arrows. (ii) Intensity profile in
frequency-encoding direction (dashed line) also shows the ghosting artifacts (red rectangle). B (GIRF pre-emphasis): (i) Image reconstructed
using the nominal k-space trajectory (see Fig. 1A) and a GIRF-based
pre-emphasis for the oscillating gradient (see Fig. 1C). (ii) Intensity profile
in frequency-encoding direction (dashed line) does not show ghosting artifacts.