Anomalous Diffusion Tensor Imaging

Introduction The observation of non-monoexponential decay of diffusion-weighted MR signals with b-value has been widely reported [1]. Using the theory of anomalous diffusion, several groups have derived a stretched-exponential form for this signal decay (e.g. [2][3]) which parameterises the signal in terms of a distributed diffusivity α (measuring the overall rate of diffusion) and an anomalous exponent γ which is a measure of the complexity of the environment and controls the degree of deviation of the signal from mono-exponential decay. Studies based on fitting the stretched-exponential form [2][3] have reported contrast between tissue types in images weighted by both parameters. In this study we extend the formalism of [3] to include directional anisotropy. The resulting technique, anomalous diffusion tensor imaging (aDTI), provides a tensor-based description of both parameters in the stretched-exponential form. This technique estimates a distributed diffusivity tensor, Α, and an anomalous exponent tensor, Γ, in each image voxel. As both tensors are symmetric and positive definite the same analysis methods may be applied as those routinely used in regular diffusion tensor imaging [4]. In particular, we examine the eigenvalues, Trace and FA of the tensors describing the distributed diffusivity and anomalous exponent as well as their principal eigenvector orientations. We find that both tensors provide estimates of principal fibre directions that are sufficient for tractographical reconstruction of the corpus callosum in a healthy subject.