Cited by 277Advanced Neuroimaging Techniques and ApplicationsAdvanced MRI Techniques and ApplicationsTensor decomposition and applications

Orthogonal tensor invariants and the analysis of diffusion tensor magnetic resonance images

Ennis, Daniel B., Kindlmann, Gordon·2006·Magnetic Resonance in Medicine

Abstract

This paper outlines the mathematical development and application of two analytically orthogonal tensor invariants sets. Diffusion tensors can be mathematically decomposed into shape and orientation information, determined by the eigenvalues and eigenvectors, respectively. The developments herein orthogonally decompose the tensor shape using a set of three orthogonal invariants that characterize the magnitude of isotropy, the magnitude of anisotropy, and the mode of anisotropy. The mode of anisotropy is useful for resolving whether a region of anisotropy is linear anisotropic, orthotropic, or planar anisotropic. Both tensor trace and fractional anisotropy are members of an orthogonal invariant set, but they do not belong to the same set. It is proven that tensor trace and fractional anisotropy are not mutually orthogonal measures of the diffusive process. The results are applied to the analysis and visualization of diffusion tensor magnetic resonance images of the brain in a healthy volunteer. The theoretical developments provide a method for generating scalar maps of the diffusion tensor data, including novel fractional anisotropy maps that are color encoded for the mode of anisotropy and directionally encoded colormaps of only linearly anisotropic structures, rather than of high fractional anisotropy structures.

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Crossref · 10.1002/mrm.20741

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Authors
Ennis, D. B., & Kindlmann, G.
Affiliations
  • Stanford University (US)
  • Harvard University (US)
Corresponding author
Ennis, Daniel B.
Venue
Magnetic Resonance in Medicine
Publisher
Wiley
Published
2005-12-09
Volume
55
Issue
1
Pages
136-146
ISSN
  • 0740-3194 (ISSN-L)
  • 1522-2594
OpenAlex
W2106841463
Cited by
276
References
15
Citations by year
2026: 11 · 2025: 8 · 2024: 10 · 2023: 13 · 2022: 8 · 2021: 17 · 2020: 13 · 2019: 12 · 2018: 15 · 2017: 11 · 2016: 19 · 2015: 23 · 2014: 26 · 2013: 22 · 2012: 20
FWCI
3.83
Type
journal article
Language
en
Open access
closed
Locations
  • Magnetic Resonance in Medicine (publishedVersion)
  • PubMed (publishedVersion)
Funders
  • National Cancer Institute (T32CA09695, T32CA009695)
  • National Institute of Biomedical Imaging and Bioengineering (T32EB002177)
Topics
  • Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced Neuroimaging Techniques and Applications
  • Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced MRI Techniques and Applications
  • Physical Sciences › Mathematics › Computational Mathematics › Tensor decomposition and applications
Keywords
diffusion tensor imaging, tensor invariants, anisotropy, fractional anisotropy, linear anisotropy, orthotropic anisotropy, easy-plane anisotropy
MeSH terms
Brain Mapping, Humans, Image Processing, Computer-Assisted, Linear Models, Anisotropy, Diffusion Magnetic Resonance Imaging

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