Maxwell‐compensated design of asymmetric gradient waveforms for tensor‐valued diffusion encoding

Abstract

Purpose Diffusion encoding with asymmetric gradient waveforms is appealing because the asymmetry provides superior efficiency. However, concomitant gradients may cause a residual gradient moment at the end of the waveform, which can cause significant signal error and image artifacts. The purpose of this study was to develop an asymmetric waveform designs for tensor‐valued diffusion encoding that is not sensitive to concomitant gradients. Methods The “Maxwell index” was proposed as a scalar invariant to capture the effect of concomitant gradients. Optimization of “Maxwell‐compensated” waveforms was performed in which this index was constrained. Resulting waveforms were compared to waveforms from literature, in terms of the measured and predicted impact of concomitant gradients, by numerical analysis as well as experiments in a phantom and in a healthy human brain. Results Maxwell‐compensated waveforms with Maxwell indices below 100 (mT/m)2 ms showed negligible signal bias in both numerical analysis and experiments. By contrast, several waveforms from literature showed gross signal bias under the same conditions, leading to a signal bias that was large enough to markedly affect parameter maps. Experimental results were accurately predicted by theory. Conclusion Constraining the Maxwell index in the optimization of asymmetric gradient waveforms yields efficient diffusion encoding that negates the effects of concomitant fields while enabling arbitrary shapes of the b‐tensor. This waveform design is especially useful in combination with strong gradients, long encoding times, thick slices, simultaneous multi‐slice acquisition, and large FOVs.

Searching for the neurite density with diffusion MRI: Challenges for biophysical modeling

“…No systematic effects of diffusion time were observed, which is in line with multiple studies showing negligible time dependence in living brain tissue for clinically relevant diffusion times, both in humans (Clark, Hedehus, & Moseley, ; Clark & Le Bihan, ; Nilsson et al, ) and animals (Niendorf, Dijkhuizen, Norris, van Lookeren Campagne, & Nicolay, ; Ronen, Moeller, Ugurbil, & Kim, ). Second, the waveforms used for groups B and C were not optimized for negligible concomitant fields, which may induce a positive bias in microscopic anisotropy (Szczepankiewicz & Nilsson, ). From assessing the data for characteristic gross signal errors, however, we do not believe that the effect was large for the waveforms used in this study.…”

“…From assessing the data for characteristic gross signal errors, however, we do not believe that the effect was large for the waveforms used in this study. Furthermore, such bias should have no systematic impact on the intercortical comparisons performed with the group B ROIs; and the group C data was only extracted from relatively deep parts of the brain (the corona radiata) where the effects of concomitant fields should be small (Szczepankiewicz & Nilsson, ). Third, due to the SNR penalty from studying deep gray matter while using small voxels, we acquired multi‐echo data for a maximum b ‐value of 0.5 ms/μm 2 .…”

In vivo demonstration of microscopic anisotropy in the human kidney using multidimensional diffusion MRI

“…Several limitations must be addressed in future research. First, the waveforms used here are not compensated with respect to concomitant fields that may cause a hyper‐attenuation of the STE and potentially yield overestimation of the LTE‐STE difference signal as recently reported . Second, the contribution of flow on anisotropy measures has not been investigated in this work.…”

“…See results for all subjects in Supporting Information Table S2 respect to concomitant fields that may cause a hyperattenuation of the STE and potentially yield overestimation of the LTE-STE difference signal as recently reported. 51 Second, the contribution of flow on anisotropy measures has not been investigated in this work. This would be required to disentangle fast pseudo-diffusion effects due to microscopic capillary and/or tubular flow from passive diffusion effects from which tissue microstructure properties can be estimated.…”

Eddy current nulled constrained optimization of isotropic diffusion encoding gradient waveforms

“…For acquisitions at moderate magnetic field strengths using strong gradients and large FOVs, the nonzero residual moment resulting from uncompensated concomitant fields may result in through‐plane dephasing, k‐space blurring, and k‐space shifting . The effect of concomitant fields can be reduced by minimizing the Maxwell Index as follows:…”