A novel tensor interpolation method is introduced that allows Diffusion Tensor Imaging (DTI) streamlining to overcome low-anisotropy regions and permits branching of trajectories using information gathered from the neighbourhood of low-anisotropy voxels met during the tracking. The interpolation method is performed in Log-Euclidean space and collects directional information in a spherical neighbourhood of the voxel in order to reconstruct a tensor with a higher linear diffusion coefficient than the original. The weight of the contribution of a certain neighbouring voxel is proportional to its linear diffusion coefficient and inversely proportional to a power of the spatial Euclidean distance between the two voxels. This inverse power law provides our method with robustness against noise. In order to resolve multiple fiber orientations, we divide the neighbourhood of a lowanisotropy voxel in sectors, and compute an interpolated tensor in each sector. The tracking then continues along the main eigenvector of the reconstructed tensors.
We test our method on artificial, phantom and brain data, and compare it with (a) standard streamline tracking, (b) the Tensorlines method, (c) streamline tracking after an interpolationmethod based on bilateral filtering, and (d) streamline tracking using moving least square regularisation. It is shown that the new method compares favourably with these methods in artificial datasets. The proposed approach gives the possibility to explore a DTI dataset to locate singularities as well as to enhance deterministic tractography techniques. In this way it allows to immediately obtain results more similar to those provided by more powerful but computationally much more demanding methods that are intrinsically able to solve crossing fibers, such as probabilistic tracking or high angular resolution diffusion imaging.
|Title of host publication||Visualization in Medicine and Life Sciences II|
|Editors||L. Linsen, B. Hamann, H. Hagen, H.C. Hege|
|Place of Publication||Berlin|
|Publication status||Published - 2012|
|Name||Mathematics and Visualization|