Table 1.
Configuration of hardware, imaging protocols and gradient waveforms.
Configurations A-C used 20-channel receive head/neck coil arrays. Configuration D used a 32-channel transmit/receive head coil array. The maximal gradient waveform amplitude and slew rate allowed by the hardware (Gmax and Smax) and the maximum that was used for STE and LTE are stated along with imaging and waveform timing parameters.
Fig 1.
Schematic spin-echo sequence with echo planar imaging readout and diffusion-encoding gradient waveforms that yield linear (red line) and spherical b-tensor encoding (black lines). Note that the STE waveform is asymmetric around the refocusing pulse [20] and that it must therefore be designed to compensate for errors caused by concomitant fields [40]. The LTE waveform is bipolar to match the effective diffusion times for STE and LTE [41]. Note that crusher gradients (dotted lines) are not engaged when the diffusion encoding acts as a crusher.
Fig 2.
DIVIDE parameter maps in transversal and coronal slices for configurations A-D. The image quality generally improves with higher field strength and gradient amplitude. Most notably there is a discernably higher level of noise for configuration A. Configuration D generally exhibited higher MKA, a pronounced geometrical distortion at the anterior part of the brain, and more pronounced ghosting artifacts, as compared with the other configurations. Furthermore, large regions of negative MKI were observed only for configuration D.
Fig 3.
SNR maps at b = 2 ms/μm2 in three transversal slices for configurations A-D and SNR distributions in the brain parenchyma at b = 0.1 and 2 ms/μm2 (histograms). White outlines show the outer perimeter within which SNR > 3, and the red outlines show regions where SNR < 3. At high b-values, images from all systems exhibited low SNR in the ventricles due to the high diffusivity of CSF. Configuration A shows low SNR in the central and inferior parts of the brain. Configuration C exhibited the highest SNR across all b-values, but also a posterior rim of low SNR caused by poor fat suppression (red arrows). Configuration D generally exhibited high SNR in the peripheral regions; in the lower parts of the brain, it exhibited a heterogeneous SNR. It also exhibited an irregular perimeter in the inferior part of the brain, which was likely caused by local field heterogeneity in proximity to the ear canal and poor RF homogeneity, both commonly associated to dMRI at ultra-high field strengths [58].
Table 2.
Quality and repeatability parameters for configurations A-D.
Q3 and Q6 are the fraction of tissue where SNR is above 3 and 6 at b = 2 ms/μm2. The voxel-wise parameter difference between acquisition 1 and 2 (ΔX) is reported as the average ± one standard deviation. The lowest and highest SNR was observed for configurations A and C, respectively, and parameter precision follows the same pattern. Neither the signal attenuation nor DIVIDE parameters had a relevant bias compared to their standard deviation. Furthermore, MKI consistently exhibits a larger standard deviation compared to MKA.
Fig 4.
Simulation of DIVIDE parameter accuracy and precision in three model tissues.
Markers show the mean parameter value, and the whiskers show one standard deviation across 104 independent realizations of noise. The dashed horizontal lines show the parameter values that are estimated for a noise-free signal; deviation from the line indicates parameter bias caused by noise. As expected, precision and accuracy both improve with increasing SNR. The estimation of MD and μFA appear to be the most accurate and precise, although the μFA shows a deterioration of accuracy and precision when its true value is low (panel II) [19]. Both MKA and MKI suffer a positive bias when SNR in the b = 0 image is approximately 20 or less. Interestingly, MKA is always more precise and accurate than MKI, indicating that it is generally less sensitive to noise. The simulations show that signal noise can cause negative values for both MKI and MKA, which is especially likely when the true values are close to zero. Finally, in the case where MKI = 0 (panel III), signal noise did not cause a strong positive bias in MKI for SNR levels that match configuration C (where the majority of voxels have SNR > 20 at b = 0.1 ms/μm2, Fig 3). This suggests that signal noise alone is not likely to explain the positive MKI that is observed throughout the brain parenchyma.
Fig 5.
DIVIDE parameters and SNR maps for configurations A* and C*. The parameter maps from configuration A* are markedly less noisy than at the original resolution shown in Fig 2. For configuration C*, the resolution was increased, while maintaining high SNR in the superior and peripheral parts of the brain, although inferior and central parts showed regions where SNR was below 3 and may therefore suffer from non-negligible signal bias.
Fig 6.
Parameter maps from repeated acquisitions and analysis of repeatability for configurations A-D. The voxel-wise difference (Diff.) between the first and second acquisition (Acq. 1 and 2) is color coded in red-green. The normalized powder-averaged signal at b = 2 ms/μm2 (A(L) and A(S)) is given in percent, and the MD is given in units of μm2/ms. The difference maps show the largest differences in tissue interfaces where small misregistration between the first and second acquisition causes large parameter discrepancy. Bland-Altman plots show the distributions of voxel-wise differences in tissue where μFA < 0.7 and MD < 1.5 μm2/ms. Solid and dashed lines show the average and two standard deviations of the distributions. All configurations showed negligible bias in repeatability of signal and DIVIDE parameters, and a configuration-dependent parameter precision. Note that the estimated precision pertains to the per-voxel parameter uncertainty; analyzing the average over multiple voxels is expected to markedly improve the precision.