The tensor distribution function

A. D. Leow, S. Zhu, L. Zhan, McMahon, K., De Zubicaray, G.I., Meredith, M., M. J. Wright, A. W. Toga and P. M. Thompson (2009) The tensor distribution function. Magnetic Resonance in Medicine, 61 1: 205-214. doi:10.1002/mrm.21852


Author A. D. Leow
S. Zhu
L. Zhan
McMahon, K.
De Zubicaray, G.I.
Meredith, M.
M. J. Wright
A. W. Toga
P. M. Thompson
Title The tensor distribution function
Journal name Magnetic Resonance in Medicine   Check publisher's open access policy
ISSN 0740-3194
1522-2594
Publication date 2009-01-01
Year available 2008
Sub-type Article (original research)
DOI 10.1002/mrm.21852
Open Access Status DOI
Volume 61
Issue 1
Start page 205
End page 214
Total pages 10
Place of publication Baltimore, Md., U. S. A.
Publisher John Wiley & Sons
Language eng
Subject C1
0903 Biomedical Engineering
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. (C) 2008 Wiley-Liss, Inc.
Formatted 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.
© 2008 Wiley-Liss, Inc.
Keyword Diffusion MRI
Diffusion tensor imaging
High angular resolution diffusion imaging
Q-Index Code C1
Q-Index Status Confirmed Code
Grant ID U54 RR021813-05
R01 EB007813
R01 HD050735
Institutional Status UQ
Additional Notes Published Online: 18 Dec 2008

Document type: Journal Article
Sub-type: Article (original research)
Collections: 2009 Higher Education Research Data Collection
Centre for Advanced Imaging Publications
 
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Created: Sat, 13 Jun 2009, 03:15:53 EST by Siona Saplos on behalf of Office of Sponsored Research