Magnetic resonance methods include modeling magnetic resonance signals obtained from specimens at low and high q-values to obtain parameters associated with specimen structure and orientation. In evaluation of brain white matter specimens, diffusion within axons can be modeled based on hindered diffusion parallel to an axis of the axon and restricted diffusion perpendicular to the axis. Diffusion exterior to axons can be modeled as hindered diffusion with differing diffusivities parallel to and perpendicular to the axis. Based on extracted parameters and associated model functions, specimen properties such as intra and extra-axonal principal diffusivities and the corresponding principal directions can be estimated.