Principles from multidimensional NMR spectroscopy, and in particular solid-state NMR, have recently been transferred to the field of diffusion MRI, offering non-invasive characterization of heterogeneous anisotropic materials, such as the human brain, at an unprecedented level of detail. Here we revisit the basic physics of solid-state NMR and diffusion MRI to pinpoint the origin of the somewhat unexpected analogy between the two fields, and provide an overview of current diffusion MRI acquisition protocols and data analysis methods to quantify the composition of heterogeneous materials in terms of diffusion tensor distributions with size, shape, and orientation dimensions. While the most advanced methods allow estimation of the complete multidimensional distributions, simpler methods focus on various projections onto lower-dimensional spaces as well as determination of means and variances rather than actual distributions. Even the less advanced methods provide simple and intuitive scalar parameters that are directly related to microstructural features that can be observed in optical microscopy images, e.g. average cell eccentricity, variance of cell density, and orientational order - properties that are inextricably entangled in conventional diffusion MRI. Key to disentangling all these microstructural features is MRI signal acquisition combining isotropic and directional dimensions, just as in the field of multidimensional solid-state NMR from which most of the ideas for the new methods are derived.
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