Higher rank tensors in diffusion MRI

Abstract

In this work we review how the diffusivity profiles obtained from diffusion MRI can be expressed in terms of Cartesian tensors of ranks higher than 2. When the rank of the tensor being used is 2, one recovers traditional diffusion tensor imaging (DTI). Therefore our approach can be seen as a generalization of DTI. The properties of generalized diffusion tensors are discussed. The shortcomings of DTI experienced in the presence of orientational heterogeneity may cause inaccurate anisotropy values and incorrect fiber orientations. Employment of higher rank tensors is helpful in overcoming these difficulties.