Local White Matter Geometry Indices from Diffusion Tensor Gradients

We introduce a framework for computing geometrical properties of white matter fibres directly from diffusion tensor fields. The key idea is to isolate the portion of the gradient of the tensor field corresponding to local variation in tensor orientation, and to project it onto a coordinate frame of tensor eigenvectors. The resulting eigenframe-centered representation makes it possible to define scalar geometrical measures that describe the underlying white matter fibres, directly from the diffusion tensor field and its gradient, without requiring prior tractography. We define two new scalar measures of (1) fibre dispersion and (2) fibre curving, and we demonstrate them on synthetic and in-vivo datasets. Finally, we illustrate their applicability in a group study on schizophrenia.