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Cited by 101Advanced Neuroimaging Techniques and ApplicationsAdvanced MRI Techniques and ApplicationsNMR spectroscopy and applications

The tensor distribution function

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Leow, A. D., Zhu, S., Zhan, L., McMahon, K., de Zubicaray, G. I., Meredith, M., Wright, M. J., Toga, A. W. +1 more·2009·Magnetic Resonance in Medicine
DOI 10.1002/mrm.21852PMC PMC2770429
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Abstract

Diffusion weighted magnetic resonance imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion‐sensitized gradients along a minimum of six directions, second‐order tensors (represented by three‐by‐three positive definite matrices) can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g., crossing fiber tracts. Recently, a number of high‐angular resolution schemes with more than six gradient directions have been employed to address this issue. In this article, we introduce the tensor distribution function (TDF), a probability function defined on the space of symmetric positive definite matrices. Using the calculus of variations, we solve the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function. Moreover, a tensor orientation distribution function (TOD) may also be derived from the TDF, allowing for the estimation of principal fiber directions and their corresponding eigenvalues. Magn Reson Med 61:205–214, 2009. © 2008 Wiley‐Liss, Inc.

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Authors
Leow, A. D., Zhu, S., Zhan, L., McMahon, K., de Zubicaray, G. I., Meredith, M., Wright, M. J., Toga, A. W., & Thompson, P. M.
Affiliations
  • University of California, Los Angeles (US)
  • The University of Queensland (AU)
  • QIMR Berghofer Medical Research Institute (AU)
Corresponding author
Leow, A. D.
ORCID
Venue
Magnetic Resonance in Medicine
Publisher
Wiley
Published
2008-12-18
Volume
61
Issue
1
Pages
205-214
ISSN
  • 0740-3194 (ISSN-L)
  • 1522-2594
DOI
10.1002/mrm.21852
PMC
PMC2770429
OpenAlex
W2103536416
Cited by
101
References
3
Citations by year
2025: 7 · 2024: 6 · 2023: 1 · 2022: 1 · 2021: 8 · 2020: 5 · 2019: 4 · 2018: 3 · 2017: 6 · 2016: 4 · 2015: 3 · 2014: 9 · 2013: 4 · 2012: 7
FWCI
8.22
Type
journal article
Language
en
Open access
Licence
onlinelibrary.wiley.com/termsAndConditions#vor (vor)
Locations
  • Magnetic Resonance in Medicine (publishedVersion)
  • PubMed (publishedVersion)
  • PubMed Central (acceptedVersion)
Funders
  • National Institutes of Health
  • National Institute of Biomedical Imaging and Bioengineering (R01EB008281, R01EB007813)
  • National Center for Research Resources (U54RR021813, U54 RR02183)
  • Eunice Kennedy Shriver National Institute of Child Health and Human Development (R01HD050735)
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 › Physics and Astronomy › Nuclear and High Energy Physics › NMR spectroscopy and applications
Keywords
diffusion-weighted imaging, white matter microstructure, crossing fibers, orientation distribution function, symmetric positive definite matrices, calculus of variations, high angular resolution diffusion imaging
MeSH terms
Algorithms, Brain, Computer Simulation, Data Interpretation, Statistical, Humans, Image Enhancement, Image Interpretation, Computer-Assisted, Models, Neurological, Nerve Fibers, Myelinated, Sensitivity and Specificity, Reproducibility of Results, Models, Statistical, Statistical Distributions, Imaging, Three-Dimensional, Diffusion Magnetic Resonance Imaging

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