Zifei Liang^{1} and Jiangyang Zhang^{1}

Diffusion MRI based fiber orientation distribution (FOD) estimates are widely used to examine structural connectivity in the brain. For group comparison using nonlinear spatial normalization, FOD needs to be adjusted based on the estimated degree of rotation and scaling at each voxel. We compared the current method implemented in Mrtrix for spatial normalization of FODs with an image-based method. The results suggest that the method in Mrtrix is accurate for rotation but generates potential bias in FOD peak amplitude and orientation when large anisotropic scaling is present. This knowledge is important for studies to use spatially normalized FOD maps.

We selected 9 subject data from the HCP dataset to compare the two FOD mapping methods with rotation (5, 15, and 30 degrees), scaling (1.1, 1.5, and 2 times along the left-right axis), and nonlinear image mapping. To remove the effects of interpolation, nearest neighbor interpolation was used in all experiments. Fractional anisotropy (FA) and mean DWI from the original data were used to generate a mapping between subject and template data. The template was selected from one of the HCP datasets. We then use the mapping to transform all DWI data to the template space. We calculated the Jacobian matrix at each voxel from the mapping and used it as a linear approximation of image deformation. Instead of using the Jacobian matrix to reorient FODs as in MRtrix [5], we used it to reorient diffusion gradient table as.

v'_{i}=Tv_{i} Eq.
1

Where v_{i} is the ¡ th gradient corresponding to the ¡ th diffusion encoding vector, T is the Jacobian
matrix, and v'_{i} is the output diffusion encoding vector. We then
performed FOD fitting with transformed diffusion weighted imaging and adjusted
gradient table voxel by voxel.

For the experiments with rotation and scaling, we estimated the ground truth FODs based on the degree of rotation and scaling. For nonlinear image mapping, we compared the differences in FOD peak direction and amplitude between FOD data generated from the two methods.

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Fig. 1 How rotation and scaling affect FODs reconstructed
using MRtrix and image-based method. A: the
original FA image and zoomed FODs near the splenium of the corpus callosum. B: Reconstructed FODs after rotation (30 degrees) and scaling (2 times along the x
axis) using MRtrix and image-based methods. The two methods produced similar
results for rotation. For scaling, the image-based results showed better
approximation to the original results than the MRtrix results.

Fig. 2 Quantitative
evaluation of difference between MRtrix and image-based results in terms of FOD
peak orientation and amplitude under varying degrees of rotation (5, 15, and 30
degrees) and scaling (1.1, 1.5, and 2.0 along the X axis).

Fig. 3 Uniform gradient vector fields compared
to non-uniform gradient vector fields and reconstructed FODs using MRtrix and
image-based method for non-linear deformation. The FODs from the image-based
method better approximate the orientation of the template FODs than the MRtrix
results.

Fig. 4 Maps
of differences in FOD peak amplitude (A) and orientation (B) between MRtrix and
image-based results after nonlinear spatial normalization. The differences
between MRtrix and image-based results are shown in selected regions (C).
Comparisons to Jacobian map and angular resolution map suggest that the
differences are potentially due to large anisotropic scaling.