Diffusion MRI is an excellent method for detecting subtle microscopic changes of the living human brain, but often fails to assign the experimental observations to specific structural properties such as cell density, size, shape, or orientation. When attempting to solve this problem, we have chosen to disregard essentially all previous work in the field of diffusion MRI, and instead translate data acquisition and processing schemes from multidimensional solid-state NMR spectroscopy [1, 2]. Key elements of our approach are q-vector trajectories and correlations between isotropic and directional diffusion encoding. By approximating the water displacement probability as a sum of anisotropic Gaussians, the voxel composition can be reported as a diffusion tensor distribution where each component of the distribution corresponds to a distinct tissue environment. Our new methods yield estimates of the complete diffusion tensor distribution or well-defined statistical properties thereof, such as the mean and variance of isotropic diffusivities, mean-square anisotropy, and orientational order parameter, which derive from analogous parameters in solid-state NMR and can be related to the structural properties of the tissue. This presentation will give an overview of the new methods, including basic physical principles, pulse sequences, and data processing, as well as examples of applications in soft matter systems from lipid membranes to living brains.
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 Topgaard D. Multidimensional diffusion MRI. J Magn Reson 2017;275:98-113. https://dx.doi.org/10.1016/j.jmr.2016.12.007