Towards quantification of the brain's sheet structure : evaluation of the discrete Lie bracket

Recently, a debate in literature discussed the possibility of the cerebral pathways being organized in a grid structure of interwoven sheets. To prove or disprove this statement, a more quantitative evaluation is needed. In this work, we evaluate the capability of the discrete Lie bracket proposed in Wedeen (2012a) to quantify sheet structure as a function of noise and voxel size. On simulated vector fields, we show that this Lie bracket is indeed capable of distinguishing sheet structured from non-sheet structured vector fields within certain limits for noise and voxel size.