Jürgen Rahmer^{1}, Ingo Schmale^{1}, Peter Mazurkewitz^{1}, and Peter Börnert^{1}

^{1}Philips Research, Hamburg, Germany

Spiral sequences sample data during gradient variation and are therefore susceptible to dynamic field deviations caused by eddy currents, timing inaccuracies, or gradient amplifier non-linearities. Linear effects can be corrected using a gradient impulse response function for trajectory calculation. Non-linear effects require a measurement-based approach, e.g. measurement of the gradient fields during imaging using a field camera or an induction-based field measurement. To avoid the need for additional hardware, we propose a hybrid method that combines current measurements using the amplifier-internal current sensors with correction based on the current-to-gradient impulse response function. The approach improves trajectory accuracy in spiral imaging.

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Gradient
chain and two different characterization approaches. The chain consists of
waveform pre-emphasis for eddy current compensation (ECC), gradient amplifier,
and gradient coils. The conventional GIRF characterization considers the whole
chain as a linear system (lower path). To compensate for gradient amplifier
non-linearities, the amplifier output current is measured and the response from
current to spins is determined for characterization of the remaining chain
(upper path, “CGIRF”). “GMTF” stands for gradient modulation transfer function.

Measured output currents of the
gradient amplifiers during application of the spiral imaging sequence in the xy
plane. (a) Current traces on y channel for all 12 spiral interleaves. (b) Currents
on x and y channel for one spiral interleave.

Figure 3: Comparison between full GMTF (a) and
CGMTF (b) in the frequency range relevant for spiral imaging. (a) Above about
1.8 kHz, the full GMTF contains oscillations resulting from amplifier
non-linearities acting on the chirp waveform. (b) The current-to-gradient
transfer function is smooth, except for mechanical resonance peaks between 0.6
and 1.7 kHz.

Differences between spiral
trajectories determined using different approaches. (a) k space trajectory
using the model-based approach implemented in the standard software. (b) Zoom
into center of k-space (upper graph) and difference with model-based trajectory
for trajectory calculated using the GIRF approach. (c) Zoom into center of
k-space (upper graph) and difference with model-based trajectory for trajectory
calculated using the CGIRF approach that is based on measured currents.

Comparison
of reconstruction results for (a) standard model-based trajectory, (b) GIRF-corrected
trajectory, and (c) current-based trajectory with CGIRF correction,
respectively. The GIRF correction already shows an improvement with respect to
the standard reconstruction, but the trajectory based on measured currents
convolved with the CGIRF delivers the lowest signal level outside the phantom
(see insets).