Quantifying the brain's sheet structure with normalized convolution
Tax, Chantal M.W.; Westin, Carl Fredrik; Dela Haije, Tom; Fuster, Andrea; Viergever, Max A.; Calabrese, Evan; Florack, Luc; Leemans, Alexander
(2017) Medical Image Analysis, volume 39, pp. 162 - 177
(Article)
Abstract
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
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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.
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Keywords: Radiological and Ultrasound Technology, Radiology Nuclear Medicine and imaging, Computer Vision and Pattern Recognition, Health Informatics, Computer Graphics and Computer-Aided Design, Journal Article
ISSN: 1361-8415
Publisher: Elsevier
Note: Funding Information: The authors thank many colleagues in the field for useful discussions. C.T. is supported by a grant (No. 612.001.104) from the Physical Sciences division of the Netherlands Organization for Scientific Research (NWO), and is grateful to dr. ir. Marina van Damme and University Fund Eindhoven for financial support. The research of A.L. is supported by VIDI Grant 639.072.411 from NWO. T.D. gratefully acknowledges NWO (No 617.001.202) for financial support. The authors acknowledge the NIH grants R01MH074794, P41EB015902, P41EB015898. The work of A.F. is part of the research programme of the Foundation for Fundamental Research on Matter (FOM), which is financially supported by the Netherlands Organisation for Scientific Research (NWO). Data were provided by the Duke Center of In Vivo Microscopy, and NIH/NIBIB National Biomedical Technology Resource Center (P41 EB015897) with additional funding from NIH/1S10 ODOD010683-01. Data were provided in part by the Human Connectome Project, WU?Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research; and by the McDonnell Center for Systems Neuroscience at Washington University. Data collection and sharing for this project was provided in part by the MGH?USC Human Connectome Project (HCP; Principal Investigators: Bruce Rosen, M.D., Ph.D., Arthur W. Toga, Ph.D., Van J. Wedeen, MD). HCP funding was provided by the National Institute of Dental and Craniofacial Research (NIDCR), the National Institute of Mental Health (NIMH), and the National Institute of Neurological Disorders and Stroke (NINDS). HCP data are disseminated by the Laboratory of Neuro Imaging at the University of California, Los Angeles. Publisher Copyright: © 2017 Elsevier B.V.
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