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Quantifying the Brain's Sheet Structure with Normalized Convolution

Institution:
1Image Sciences Institute, University Medical Center Utrecht, Utrecht, Netherlands. Electronic address: taxc@cardiff.ac.uk.
2Laboratory for Mathematical Imaging, Brigham and Women’s Hospital, Harvard Medical School, Boston, MA, USA.
Publisher:
Elsevier Science
Publication Date:
Apr-2017
Journal:
Med Image Anal
Volume Number:
39
Pages:
162-77
Citation:
Med Image Anal. 2017 Apr 4;39:162-77.
PubMed ID:
28511065
Appears in Collections:
NAC, LMI, NCIGT, SPL
Sponsors:
P41 EB015902/EB/NIBIB NIH HHS/United States
P41 EB015898/EB/NIBIB NIH HHS/United States
U01 MH093765/MH/NIMH NIH HHS/United States
R01 MH074794/MH/NIMH NIH HHS/United States
Generated Citation:
Tax C.M.W., Westin C-F., Dela Haije T., Fuster A., Viergever M.A., Calabrese E., Florack L., Leemans A. Quantifying the Brain's Sheet Structure with Normalized Convolution. Med Image Anal. 2017 Apr 4;39:162-77. PMID: 28511065.
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The hypothesis that brain pathways form 2D sheet-like structures layered in 3D as "pages of a book" has been a topic of debate in the recent literature. This hypothesis was mainly supported by a qualitative evaluation of "path neighborhoods" reconstructed with diffusion MRI (dMRI) tractography. Notwithstanding the potentially important implications of the sheet structure hypothesis for our understanding of brain structure and development, it is still considered controversial by many for lack of quantitative analysis. A means to quantify sheet structure is therefore necessary to reliably investigate its occurrence in the brain. Previous work has proposed the Lie bracket as a quantitative indicator of sheet structure, which could be computed by reconstructing path neighborhoods from the peak orientations of dMRI orientation density functions. Robust estimation of the Lie bracket, however, is challenging due to high noise levels and missing peak orientations. We propose a novel method to estimate the Lie bracket that does not involve the reconstruction of path neighborhoods with tractography. This method requires the computation of derivatives of the fiber peak orientations, for which we adopt an approach called normalized convolution. With simulations and experimental data we show that the new approach is more robust with respect to missing peaks and noise. We also demonstrate that the method is able to quantify to what extent sheet structure is supported for dMRI data of different species, acquired with different scanners, diffusion weightings, dMRI sampling schemes, and spatial resolutions. The proposed method can also be used with directional data derived from other techniques than dMRI, which will facilitate further validation of the existence of sheet structure.