Improving Relative Anisotropy Measurement using Directional Correlation of Eigenvectors

Introduction The relative anisotropy (RA) exhibits a great contrast between brain white and gray matters [1]. However, RA is susceptible to the influence of noise [2, 3]. Although the proposed inter-voxel indices reduce noise influence on measured diffusion anisotropy [3], the partial volume effect originating from the inter-voxel operation adds uncertainty to the estimated anisotropy depending on tissues of interest. To improve the accuracy of relative anisotropy determination without the unwanted partial volume effect, a newly proposed approach, i.e., intra-voxel directional-correlation weighted relative anisotropy (DRA), is examined. Tensor inner products will be performed on the individual voxels between the two identically acquired DTIs, without the local average of neighboring voxels, in combination with the calculation of RA. The effect of noise is reduced with such operation since random noise is not directionally correlated between repeated scans. In order to demonstrate the ability of the intravoxel DRA to reduce the partial volume effect, an inter-voxel DRA, taking the diffusion tensor inner product weighted average of neighboring voxels, will also be examined. The noise influence of intra-voxel DRA will be compared with RA and inter-voxel DRA in different brain regions in vivo. Theorem The derivation of intra-voxel DRA is achieved by repeating the DTI data acquisition on the same subject under examination. The intravoxel DRA can be defined as