M. Okan Irfanoglu^{1}, Alan Seth Barnett^{1}, Neda Sadeghi^{1}, and Carlo Pierpaoli^{1}

Gradient nonlinearities in MRI cause spatially-varying b-values and diffusion gradient directions. In this work, we analyze whether these nonlinearities have a significant impact on data reproducibility and accuracy for brain studies. Our results indicate that not only FA and TR values have an increasing bias away from the isocenter of the magnet, but also differences in subject positioning and head orientation combined with nonlinearities have a significant effect on reproducibility. The effects were also observed in principal eigenvector directions computed with the tensor model.

Six subjects were scanned with the same protocol on five different days on a Philips Achieva 3T MRI system. Diffusion weighted images (DWIs) were acquired with typical parameters of clinical acquisitions (single-shot spin-echo, 10 volumes with low b-values, and 32 volumes with a b-value of 1100s/mm^{2}, 32-channel coil, sense factor=2). This acquisition scheme was repeated for both AP and PA phase encoding directions, and a T2-weighted turbo spin-echo image was also acquired with 1.7mm isotropic resolution to enable robust EPI distortion correction.

** 1) Data processing with gradient nonlinearity correction:** We computed GNL fields from measurements on a PVP solution

** 2) Analysis:** For each scan, diffusion tensors were estimated using nonlinear regression once with a spatially constant B-matrix (uncorrected) and once with the corresponding voxelwise B-matrices (corrected). Fractional anisotropy (FA), Trace (TR) (equivalent to 3 times the mean diffusivity) and the principal eigenvector (e

Figure 1 shows maps for the uncorrected and corrected diffusion metrics in a representative subject. As expected effects of nonlinearities were more pronounced in regions farther from the isocenter of the magnet. For TR errors were up to 8% and for FA up to 3%.

Figure 2 shows (1-p_values) maps obtained from an unpaired *t*-test on corrected vs. non corrected TR values for each subject. These maps essentially show in each voxel the likelihood of finding spurious statistically significant differences in longitudinal scans because of gradient nonlinearities. Not surprisingly, the likelihood of finding these spurious differences increases farther from the magnet isocenter. Interestingly, there is a halo-like band of lower probability in different locations for each subject. These bands reflect the effect of variability in repositioning subjects in repeated scans and originate from a relatively large variance in voxelwise B-matrices. Figure 3 displays the average of all maps warped into population atlas space. Averaging across a population
reduces the effects of single subject repositioning; therefore the
population averaged maps more closely resemble the actual nonlinearity
fields and the low probability bands are no longer detectable.

Figure 4 displays the maps for FA *t*-tests. Bands of varying probability are not observable for FA. One should not expect the same pattern for both TR and FA, because FA is also affected by the off-diagonal elements of B-matrices and not only its trace. Figure 5 displays the regions where e_{1} was more coherent among scans in orange and less coherent in blue after correction. Coherency is generally improved at different levels but this improvement becomes apparent near brain periphery.

Our results indicated that gradient nonlinearities combined with differences in subject positioning can have a significant impact not only on the accuracy of diffusion MRI metrics, but also on their reproducibility. The statistical manifestations of these effects have a non-obvious spatial pattern, particularly for longitudinal scans. In general effects are more pronounced at the periphery of the brain, impairing one's ability to asses subtle cortical and sub-cortical diffusivity changes, as it is needed for example in TBI research. Gradient nonlinearities were also shown to alter the reproducibility of the directional information in sub-cortical white matter regions with potential implications for tractography and connectivity analyses.

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** Figure 2.** Maps obtained from