Interpolation of Orientation Distribution Functions (ODFs) in High Angular Resolution Diffusion Imaging

Diffusion tensor magnetic resonance imaging (DTMRI) is a non-invasive method for investigating the brain white matter structure. It can be used to evaluate fiber bundles in the brain but in the regions with crossing fibers, it fails. To resolve this problem, high angular resolution diffusion imaging (HARDI) with a large number of diffusion encoding directions is used and for reconstruction, the Q-ball method is applied. In this method, orientation distribution function (ODF) of fibers can be calculated. Mathematical models play a crucial role in the field of ODF. For instance, in registering Q-ball images for applications like group analysis or atlas construction, one needs to interpolate ODFs. To this end, principal diffusion directions (PDDs) of each ODF are needed. In this paper, PDDs are defined as vectors that connect the corresponding local maxima of ODF values. Then, ODFs are interpolated using PDDs.We find the principal direction of ODF of the dataset to be interpolated and then rotate it to lie in the direction of the reference dataset. Now that ODFs are parallel, we apply linear interpolation to generate interpolated data. The proposed method is evaluated and compared with previous protocols. Experimental results show that the proposed interpolation algorithm preserves the principal direction of fiber tracts without producing any deviations in the tracts.  It is shown that changes in the entropy of the interpolated ODFs are almost linear and the bloating effect (blurring of the principal directions) can be removed.