We present a new model for fanning and bending white matter structures on a sub-voxel scale. We devise a parametric model of how the fibre orientation varies spatially over each sub-voxel in the voxel grid for both types of configuration. Fitting the model provides quantitative information about the degree of fanning or bending in each voxel. We demonstrate using data from a standard human brain diffusion MRI acquisition.
Preliminary work suggests that we can use the model to reconstruct fanning structures in real brain data and provide quantitative information about the fanning structure. Defining the structure more accurately allows more appropriate action to be taken by tractography algorithms, resulting in fewer false positive and false negative tracts. Further work will include an algorithm that uses fanning and bending models to the voxel measurements to classify voxels as either containing a fanning or bending structure. Such an algorithm will require knowledge from neighbouring voxels; if the set of sub-voxel orientations produced by fanning and bending models are the same, the spatial arrangement of the orientations will not affect the sum of the sub-voxel measurements.