Symmetric diffeomorphic registration of fibre orientation distributions

Registration of diffusion-weighted images is an important step in comparing white matter fibre bundles across subjects, or in the same subject at different time points. Using diffusion-weighted imaging, Spherical Deconvolution enables multiple fibre populations within a voxel to be resolved by computing the fibre orientation distribution (FOD). In this paper, we present a novel method that employs FODs for the registration of diffusion-weighted images. Registration was performed by optimising a symmetric diffeomorphic non-linear transformation model, using image metrics based on the mean squared difference, and cross-correlation of the FOD spherical harmonic coefficients. The proposed method was validated by recovering known displacement fields using FODs represented with maximum harmonic degrees (l(max)) of 2, 4 and 6. Results demonstrate a benefit in using FODs at l(max)=4 compared to l(max)=2. However, a decrease in registration accuracy was observed when l(max)=6 was used; this was likely caused by noise in higher harmonic degrees. We compared our proposed method to fractional anisotropy driven registration using an identical code base and parameters. FOD registration was observed to perform significantly better than FA in all experiments. The cross-correlation metric performed significantly better than the mean squared difference. Finally, we demonstrated the utility of this method by computing an unbiased group average FOD template that was used for probabilistic fibre tractography. This work suggests that using crossing fibre information aids in the alignment of white matter and could therefore benefit several methods for investigating population differences in white matter, including voxel based analysis, tensor based morphometry, atlas based segmentation and labelling, and group average fibre tractography.