A Study of Information Gain in High Angular Resolution Diffusion Imaging (HARDI)

Diffusion weighted magnetic resonance (MR) imaging is a powerful tool to investigate white matter microstructure, by mapping local 3D displacement profiles of water molecules in brain tissue. High- angular resolution diffusion imaging (HARDI) schemes have been em- ployed to resolve fiber crossing and more complex diffusion geometries. Most recently, the tensor distribution function (TDF) has been pro- posed as a novel technique for multi-tensor reconstruction by represent- ing the diffusion profile as a probabilistic mixture of tensors. Here, we propose a TDF-based framework for studying the amount of informa- tion in HARDI. To illustrate the proposed method, we compared a 94- direction HARDI scheme to its optimally sub-sampled schemes with 20, 40, 60 and 80 directions. We quantified the information gain when more gradient directions are used, as measured by the Shannon entropy of the recovered TDF. Our results showed an absence of significant gain beyond 60 directions, while anisotropy estimates of the recovered fibers stabilized with around 40 directions, suggesting asymptotic but clear advantages of HARDI over conventional DTI.