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Keywords
(12)
Density Functional
Distribution Function
Eigenvalues
Orientation Distribution Function
Partial Differential Equation
Probability Density
Volume Fraction
High Angular Resolution Diffusion Imaging
kullback leibler
Q Ball Imaging
Symmetric Positive Definite
White Matter
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Analysis of Fiber Reconstruction Accuracy in High Angular Resolution Diffusion Images (HARDI)
Analysis of Fiber Reconstruction Accuracy in High Angular Resolution Diffusion Images (HARDI),10.1016/S10538119(09)701417,Neuroimage,L. Zhan,A. D. L
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Analysis of Fiber Reconstruction Accuracy in High Angular Resolution Diffusion Images (HARDI)
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L. Zhan
,
A. D. Leow
,
S. Zhu
,
M. C. Chiang
,
M. Barysheva
,
A. W. Toga
,
K. L. McMahon
,
G. I. de Zubicaray
,
M. J. Wright
,
P. M. Thompson
Introduction:
High angular resolution diffusion imaging
(HARDI) is a powerful extension of MRI that maps the directional diffusion of water in the brain. With more diffusion gradients and directions, fiber directions may be tracked with greater angular precision, fiber crossings can be resolved, and anisotropy measures can be derived from the full fiber orientation density function. To better reconstruct HARDI, we recently introduced the tensor
distribution function
(TDF), which models multidirectional diffusion as a probabilistic mixture of all
symmetric positive definite
tensors (1). The TDF overcomes limitations of several HARDI reconstruction methods (e.g., qball imaging, DOT, PAS) which restrict all component fibers in a voxel to have the same anisotropy profile. The TDF models the HARDI signal more flexibly, as a unitmass
probability density
on the 6D manifold of
symmetric positive definite
tensors, yielding a TDF, or continuous mixture of tensors, at each point in the brain. From the TDF, one can derive analytic formulae for the
orientation distribution function
(ODF), tensor orientation density (TOD), and their corresponding anisotropy measures. Because this model can accurately resolve sharp signal peaks in angular space where fibers cross, we studied how many gradients are required in practice to compute accurate orientation density functions, as more gradients require longer scanning times. In simulated twofiber systems with varying Rician noise, we assessed how many diffusion sensitized gradients were sufficient for (1) accurately resolving the diffusion profile, and (2) measuring the exponential isotropy (EI), a TDFderived measure of fiber integrity that exploits the full multidirectional HARDI signal. Methods: We created various models of twofiber systems, crossing at 90 degrees with equal volume fractions and
eigenvalues
typical for
white matter
(1). Data were sampled at 94 points evenly distributed on the hemisphere using a
Partial Differential Equation
(PDE) based on electrostatic repulsion (2). Rician noise with different amplitudes (SNR=5, 15, 25) was added. Several angular sampling schemes, with between 6 to 94 directions, were subsampled from the original 94 angular points to maximize the total angular energy (3). Using these optimized subsets of angular points, we subsampled the original HARDI94 data, and assessed how accurately the diffusion profile could be reconstructed, using the KullbackLeibler (KL) divergence to measure the reconstruction accuracy of the ODF derived from the subsampled schemes.
Journal:
Neuroimage
, vol. 47, pp. S52S52, 2009
DOI:
10.1016/S10538119(09)701417
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