Non‐Cartesian k‐space trajectory calculation based on concurrent reading of the gradient amplifiers’ output currents

Abstract

Non-Cartesian imaging sequences involve sampling during rapid variation of the encoding field gradients. The quality of the reconstructed images often suffers from insufficient knowledge of the exact dynamics of the actual fields applied during sampling. Methods: We propose determination of the accurate field dynamics by measuring the currents at the gradient amplifier outputs using the amplifiers' internal sensors concurrently with imaging. The actual dynamic field evolution is then determined by convolution with the measured current-to-field impulse response function of the gradient coil. Integration of the gradient field evolution allows derivation of the k-space trajectory for reconstruction. Results: The current-based approach is investigated in spiral and ultrashort TE phantom imaging. In comparison with the model-based product reconstruction as well as a correction approach based on the conventional input waveform-to-field impulse response function, it provides slightly improved image quality. The improvement is ascribed to a better representation of eddy current and amplifier nonlinearity effects. Conclusion: Trajectory calculation based on measured amplifier output currents offers a robust, purely measurement-based alternative to conventional model-based approaches. The implementation can mitigate gradient amplifier imperfections with no or little additional hardware effort.

Fast measurement of the gradient system transfer function at 7 T

“…32 Nonlinearities of the gradient amplifiers could be circumvented by measuring their output currents and describing the system's transmission behavior by a current-to-field transfer function, which has been shown to fulfill the LTI criteria better than a traditional waveform-to-field transfer function. 31 Temperature effects have also been shown to confound GSTF-based gradient predictions. 21,33,34 However, we conducted all measurements on the same day and gave the scanner sufficient time (about 90 min) to reach thermal equilibrium between booting and the first measurement.…”

“…These deviations can be explained by nonlinear characteristics of the gradient amplifiers, 31 which might be exposed as a consequence to the different demands put on the amplifiers by using different gradient shapes (ie, triangles consisting only of a ramp‐up and a ramp‐down phase, on the one hand, and a trapezoid with relatively short ramp times and a relatively long plateau phase on the other). It has been reported before that the amplifiers can violate the LTI assumption for the entire gradient chain 31 . Limitations of the LTI model with respect to the applied gradient shape have also been observed at lower field strength 32 .…”

“…Limitations of the LTI model with respect to the applied gradient shape have also been observed at lower field strength 32 . Nonlinearities of the gradient amplifiers could be circumvented by measuring their output currents and describing the system's transmission behavior by a current‐to‐field transfer function, which has been shown to fulfill the LTI criteria better than a traditional waveform‐to‐field transfer function 31 . Temperature effects have also been shown to confound GSTF‐based gradient predictions 21,33,34 .…”

Advances in Spiral fMRI: A High-resolution Study with Single-shot Acquisition

“…If dynamic field effects constitute a significant artifact and noise source for spiral fMRI time series, in lieu of field monitoring, alternative correction methods comprise dynamic off-resonance updates or higher-order field navigators (Pfeuffer et al, 2002; Splitthoff and Zaitsev, 2009), as well as gradient response models that incorporate time-courses of gradient coil temperature (Dietrich et al, 2016b; Stich et al, 2020) or current measurements (Nussbaum et al, 2019; Rahmer et al, 2021).…”

Generating spiral gradient waveforms with a compact frequency spectrum

“…Likewise, there are many solutions to mitigate trajectory errors. Most adopt a linear, gradient impulse response function (GIRF) model for the gradient system, 14,15 while other methods account for the small nonlinearities that can be present in gradient hardware (primarily in gradient amplifiers) 16 . Some of this correction may involve precompensation of gradient waveforms (“inverting” the GIRF system response), while others use prediction or measurement of waveform degradation (or some combination of the two).…”