Standard Model of Diffusion in White Matter: The SMI Toolbox

MATLAB software for robust standard-model parameter estimation from diffusion MRI data

We are sharing a robust implementation of parameter estimation for the standard model of diffusion in white matter along with example datasets. The toolbox can be used to analyze diffusion MRI images and extract information about various structures present in a voxel of white matter, such as axons, extra-axonal space, and cerebrospinal fluid.

The standard model is a unifying framework of white matter diffusion models, most of which are described by the same underlying physics (NMR Biomed. 2019;32[4]:e3998. doi: 10.1002/nbm.3998). In such a framework, most diffusion models can be understood as special cases of the standard model (Neuroimage. 2018;174:518-538. doi: 10.1016/j.neuroimage.2018.03.006).

White matter voxels contain signal contributions from many fiber bundles. Each bundle comprises distinct structures, which are different water compartments, such as axons, extra-axonal space, and cerebrospinal fluid. In the standard-model framework, axons are modeled as impermeable zero-radius cylinders (so-called sticks) arranged in locally coherent fascicles. The extra-axonal space of each fascicle is modeled with an axially symmetric diffusion tensor. Cerebrospinal fluid is an optional compartment modeled with an isotropic tensor. The bundle’s signal is the sum of the contributions from each compartment. Such multi-compartment bundles are distributed in a voxel according to an arbitrary fiber orientation distribution function. 

The SMI Toolbox supports:

  • Linear tensor encoding data only (i.e. single diffusion encoding) and equal echo time (TE) in all diffusion-weighted images.
  • Multiple tensor encodings and equal TE in all diffusion-weighted images.
  • Multiple tensor encodings and differing TE between all diffusion-weighted images (when multiple TE data are used, the SMI Toolbox returns axonal and extra-axonal T2 estimates).

For best results, we suggest preprocessing the diffusion-weighted data with the DESIGNER pipeline, which outputs a noise map that can be used as an input for the SMI Toolbox.

Examples of microstructure maps obtained with the standard model on a thirty-year-old normal volunteer. From left to right: axonal water fraction, intra-axonal diffusivity, parallel and perpendicular extra-axonal diffusivities, free water fraction, axonal T2 relaxation, extra-axonal T2 relaxation, and fiber dispersion.

Coelho S, Baete SH, Lemberskiy G, Ades-Aaron B, Barrol G, Veraart J, Novikov DS, Fieremans E.
Reproducibility of the Standard Model of diffusion in white matter on clinical MRI systems.
Neuroimage. 2022 May 8:119290. doi: 10.1016/j.neuroimage.2022.119290

Please cite this work if you are using the SMI Toolbox in your research.


Novikov DS, Veraart J, Jelescu IO, Fieremans E.
Rotationally-invariant mapping of scalar and orientational metrics of neuronal microstructure with diffusion MRI.
Neuroimage. 2018;174:518-538. doi: 10.1016/j.neuroimage.2018.03.006

Reisert M, Kellner E, Dhital B, Hennig J, Kiselev VG.
Disentangling micro from mesostructure by diffusion MRI: A Bayesian approach.
Neuroimage. 2017;147:964-975. doi: 10.1016/j.neuroimage.2016.09.058

Novikov D, Jelescu I, Veraart E, Fieremans E, Kiselev V, Reisert M, inventors; Albert Ludwigs Universitaet Freiburg, New York University, assignees.
System, method and computer-accessible medium for determining brain microstructure parameters from diffusion magnetic resonance imaging signal’s rotational invariants.
US Patent 2016/0343129 A1. July 23, 2019.

Get the Code

This resource is maintained on Github as Standard Model Imaging (SMI) Toolbox.

Example Data

Below, we provide three example datasets for easy testing of the SMI toolbox. All data were preprocessed with DESIGNER.

  • dataset_1 contains a 2-shell diffusion MRI protocol similar to the one in the UK biobank.
  • dataset_2 contains multiple b-value b-tensor shape combinations (all with the same echo time), similar to the one we proposed in the related publication cited above.
  • dataset_3 contains multiple combinations of b-values, b-tensor shapes, and echo times.

Note that all three datasets are provided in nifti format. We used Jimmy Shen’s Tools for NIfTI and ANALYZE image toolbox to handle the data in MATLAB but users may turn to other tools of their choice and modify the lines in the example code.

Get the Data

The data available on this page are provided free of charge and comes without any warranty. CAI²R and NYU Grossman School of Medicine do not take any liability for problems or damage of any kind resulting from the use of the files provided. Operation of the software is solely at the user’s own risk. The software developments provided are not medical products and must not be used for making diagnostic decisions.

The software is provided for non-commercial, academic use only. Usage or distribution of the software for commercial purpose is prohibited. All rights belong to the author (Santiago Coelho) and NYU Grossman School of Medicine. If you use the software for academic work, please give credit to the author in publications and cite the related publications.

Please spell out your affiliation (e.g. "New York University" rather than "NYU").


Questions about this resource may be directed to Santiago Coelho, PhD, or raised as issues on Github.