Water diffusion magnetic resonance imaging (dMRI) is a powerful tool for studying biological tissue microarchitectures in vivo. Recently, there has been increased effort to develop quantitative dMRI methods to probe both length scale and orientation information in diffusion media. Diffusion spectrum imaging (DSI) is one such approach that aims to resolve such information based on the three-dimensional diffusion propagator at each voxel. However, in practice, only the orientation component of the propagator function is preserved when deriving the orientation distribution function. Here, we demonstrate how a straightforward extension of the linear spherical deconvolution (SD) model can be used to probe tissue orientation structures over a range (or "spectrum") of length scales with minimal assumptions on the underlying microarchitecture. Using high b-value Cartesian q-space data on a rat brain tissue sample, we demonstrate how this "restriction spectrum imaging" (RSI) model allows for separating the volume fraction and orientation distribution of hindered and restricted diffusion, which we argue stems primarily from diffusion in the extraneurite and intraneurite water compartment, respectively. Moreover, we demonstrate how empirical RSI estimates of the neurite orientation distribution and volume fraction capture important additional structure not afforded by traditional DSI or fixed-scale SD-like reconstructions, particularly in gray matter. We conclude that incorporating length scale information in geometric models of diffusion offers promise for advancing state-of-the-art dMRI methods beyond white matter into gray matter structures while allowing more detailed quantitative characterization of water compartmentalization and histoarchitecture of healthy and diseased tissue.
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