# Rotationally-invariant mapping of scalar and orientational metrics of neuronal microstructure with diffusion MRI

arXiv: https://arxiv.org/abs/1609.09144 · HTML: https://mlsanity.com/paper/1609.09144/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Sep 2016.

## Built on by (most cited first, 8 of 8)

- [Inverting brain grey matter models with likelihood-free inference: a tool for trustable cytoarchitecture measurements](https://mlsanity.com/paper/2111.08693/) (2021)
- [Parameter estimation for WMTI-Watson model of white matter using encoder-decoder recurrent neural network](https://mlsanity.com/paper/2203.00595/) (2022)
- [Implicit neural representations for accurate estimation of the standard model of white matter](https://mlsanity.com/paper/2506.15762/) (2025)
- [Cellular EXchange Imaging (CEXI): Evaluation of a diffusion model including water exchange in cells using numerical phantoms of permeable spheres](https://mlsanity.com/paper/2303.16112/) (2023)
- [DeepMpMRI: Tensor-decomposition Regularized Learning for Fast and High-Fidelity Multi-Parametric Microstructural MR Imaging](https://mlsanity.com/paper/2405.03159/) (2024)
- [Single-Shell NODDI Using Dictionary Learner Estimated Isotropic Volume Fraction](https://mlsanity.com/paper/2102.02772/) (2021)
- [μGUIDE: a framework for quantitative imaging via generalized uncertainty-driven inference using deep learning](https://mlsanity.com/paper/2312.17293/) (2023)
- [Scattering approach to diffusion quantifies axonal damage in brain injury](https://mlsanity.com/paper/2501.18167/) (2025)

## Abstract (arXiv)

We develop a general analytical and numerical framework for estimating intra- and extra-neurite water fractions and diffusion coefficients, as well as neurite orientational dispersion, in each imaging voxel. By employing a set of rotational invariants and their expansion in the powers of diffusion weighting, we analytically uncover the nontrivial topology of the parameter estimation landscape, showing that multiple branches of parameters describe the measurement almost equally well, with only one of them corresponding to the biophysical reality. A comprehensive acquisition shows that the branch choice varies across the brain. Our framework reveals hidden degeneracies in MRI parameter estimation for neuronal tissue, provides microstructural and orientational maps in the whole brain without constraints or priors, and connects modern biophysical modeling with clinical MRI.