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Geometry of the cumulant series in diffusion MRI

Coelho, Santiago ; Chen, Jenny ; Szczepankiewicz, Filip LU orcid ; Fieremans, Els and Novikov, Dmitry S. (2026) In Nature Communications 17(1).
Abstract

Water diffusion gives rise to micron-scale sensitivity of diffusion MRI (dMRI) to cellular-level tissue structure. Precision medicine and quantitative imaging depend on uncovering the information content of dMRI and establishing its parsimonious hardware-independent fingerprint. Based on the rotational SO(3) symmetry, we study the geometry of the dMRI signal and the topology of its acquisition, identify irreducible components and a full set of invariants for the cumulant tensors, and relate them to tissue properties. Including all kurtosis invariants improves multiple sclerosis classification in a cohort of 1189 subjects. We design the shortest acquisitions based on icosahedral vertices to determine the most used invariants in only 1–2... (More)

Water diffusion gives rise to micron-scale sensitivity of diffusion MRI (dMRI) to cellular-level tissue structure. Precision medicine and quantitative imaging depend on uncovering the information content of dMRI and establishing its parsimonious hardware-independent fingerprint. Based on the rotational SO(3) symmetry, we study the geometry of the dMRI signal and the topology of its acquisition, identify irreducible components and a full set of invariants for the cumulant tensors, and relate them to tissue properties. Including all kurtosis invariants improves multiple sclerosis classification in a cohort of 1189 subjects. We design the shortest acquisitions based on icosahedral vertices to determine the most used invariants in only 1–2 minutes for whole brain. Representing dMRI via scalar invariant maps with definite symmetries will underpin machine learning classifiers of pathology, development, and aging, while fast protocols will enable translation of advanced dMRI into clinic.

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author
; ; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Nature Communications
volume
17
issue
1
article number
4220
publisher
Nature Publishing Group
external identifiers
  • scopus:105038603920
  • pmid:42108286
ISSN
2041-1723
DOI
10.1038/s41467-026-70018-w
language
English
LU publication?
yes
additional info
Publisher Copyright: © The Author(s) 2026.
id
1151a51d-3483-44b6-90de-1d3810152795
date added to LUP
2026-07-15 12:35:06
date last changed
2026-09-09 16:41:55
@article{1151a51d-3483-44b6-90de-1d3810152795,
  abstract     = {{<p>Water diffusion gives rise to micron-scale sensitivity of diffusion MRI (dMRI) to cellular-level tissue structure. Precision medicine and quantitative imaging depend on uncovering the information content of dMRI and establishing its parsimonious hardware-independent fingerprint. Based on the rotational SO(3) symmetry, we study the geometry of the dMRI signal and the topology of its acquisition, identify irreducible components and a full set of invariants for the cumulant tensors, and relate them to tissue properties. Including all kurtosis invariants improves multiple sclerosis classification in a cohort of 1189 subjects. We design the shortest acquisitions based on icosahedral vertices to determine the most used invariants in only 1–2 minutes for whole brain. Representing dMRI via scalar invariant maps with definite symmetries will underpin machine learning classifiers of pathology, development, and aging, while fast protocols will enable translation of advanced dMRI into clinic.</p>}},
  author       = {{Coelho, Santiago and Chen, Jenny and Szczepankiewicz, Filip and Fieremans, Els and Novikov, Dmitry S.}},
  issn         = {{2041-1723}},
  language     = {{eng}},
  number       = {{1}},
  publisher    = {{Nature Publishing Group}},
  series       = {{Nature Communications}},
  title        = {{Geometry of the cumulant series in diffusion MRI}},
  url          = {{http://dx.doi.org/10.1038/s41467-026-70018-w}},
  doi          = {{10.1038/s41467-026-70018-w}},
  volume       = {{17}},
  year         = {{2026}},
}