Orthogonal invariant sets of the diffusion tensor and the development of a curvilinear set suitable for low-anisotropy tissues

Damion, Robin A.; Radjenovic, Aleksandra; Ingham, Eileen; Jin, Zhongmin; Ries, Michael E.

Abstract

We develop a curvilinear invariant set of the diffusion tensor which may be applied to Diffusion Tensor Imaging measurements on tissues and porous media. This new set is an alternative to the more common invariants such as fractional anisotropy and the diffusion mode. The alternative invariant set possesses a different structure to the other known invariant sets; the second and third members of the curvilinear set measure the degree of orthotropy and oblateness/prolateness, respectively. The proposed advantage of these invariants is that they may work well in situations of low diffusion anisotropy and isotropy, as is often observed in tissues such as cartilage. We also explore the other orthogonal invariant sets in terms of their geometry in relation to eigenvalue space; a cylindrical set, a spherical set (including fractional anisotropy and the mode), and a log-Euclidean set. These three sets have a common structure. The first invariant measures the magnitude of the diffusion, the second and third invariants capture aspects of the anisotropy; the magnitude of the anisotropy and the shape of the diffusion ellipsoid (the manner in which the anisotropy is realised). We also show a simple method to prove the orthogonality of the invariants within a set. © 2013 Damion et al.

Citation

Damion, R. A., Radjenovic, A., Ingham, E., Jin, Z., & Ries, M. E. (2013). Orthogonal invariant sets of the diffusion tensor and the development of a curvilinear set suitable for low-anisotropy tissues. PLoS ONE, 8(11), Article e78798. https://doi.org/10.1371/journal.pone.0078798

• Journal Article Type: Article
• Acceptance Date: Sep 24, 2013
• Online Publication Date: Nov 11, 2013
• Publication Date: Nov 11, 2013
• Deposit Date: Dec 5, 2022
• Publicly Available Date: Dec 5, 2022
• Journal: PLoS ONE
• Electronic ISSN: 1932-6203
• Publisher: Public Library of Science
• Peer Reviewed: Peer Reviewed
• Volume: 8
• Issue: 11
• Article Number: e78798
• DOI: https://doi.org/10.1371/journal.pone.0078798
• Public URL: https://nottingham-repository.worktribe.com/output/14321125
• Publisher URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0078798