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. 2018 Feb 13;8:2930. doi: 10.1038/s41598-018-19475-y

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© The Author(s) 2018

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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(a) An example of signal surfaces for three different distributions of diffusion tensors calculated from Eqn. 10 over a range of b-values and ellipticity angles χ. MD is the mean diffusivity of the underlying diffusion tensor. The lowest plane highlighted with green lines is a single isotropic domain resulting in a mono-exponential attenuation and no χ-modulation. The curved middle plane highlighted with solid red lines over different b and solid blue lines over different χ was generated from an ensemble of uniformly oriented anisotropic tensors. The top plane highlighted with dashed black lines comes from a distribution of isotropic diffusivities and shows no χ-modulation as expected for isotropic compartments. The three planes share the same mean diffusivity indicated by their common initial slope. (b) The ratio E_χ=45/E_χ=0 for D_T – D_L varied to realize different tensor geometries from oblate to prolate with varying μFA. The ratio, corresponding to the depth of the modulation, clearly depends on μFA and tensor geometry.