On the Riemannian rationale for diffusion tensor imaging

One of the approaches in the analysis of brain diffusion MRI data is to consider white matter as a Riemannian manifold, with a metric given by the inverse of the diffusion tensor. Such a metric is used for white matter tractography and connectivity analysis. Although this choice of metric is heuristically justified it has not been derived from first principles. We propose a modification of the metric tensor motivated by the underlying mathematics of diffusion