Technical Note
Tensor Deflection (TEND) Tractography With
Adaptive Subvoxel Stepping
Ming-Chung Chou, BS,
1,2
Ming-Long Wu, PhD,
1
Cheng-Yu Chen, MD,
2
Chao-Ying Wang, BS,
1,2
Teng-Yi Huang, PhD,
3
Yi-Jui Liu, PhD,
4
Chun-Jung Juan, MD,
2
and Hsiao-Wen Chung, PhD
1,2
*
Purpose: To develop an adaptive subvoxel stepping
scheme, as an adjunct to tensor deflection (TEND) tractog-
raphy, that automatically adjusts the stepping size by con-
sidering the tensor linearity to properly trace fiber bundles
in regions with different degrees of tensor anisotropy.
Materials and Methods: A theoretical investigation of the
TEND algorithm was performed to assess the degree of
deflection of the propagation vector toward the major eig-
envector. Mathematically generated phantoms (one with
curved fibers and the other with crossing fibers) at wide
ranges of signal-to-noise ratio (SNR), and human brain
images obtained in vivo were used to test the performance
of the adaptive stepping algorithm.
Results: The degree of deflection was found to be inversely
related to the stepping size. A small stepping size was ad-
vantageous for tracing single curved fiber bundles, whereas
a large stepping size was beneficial for passing through
fiber crossing regions. The performance of the adaptive
stepping algorithm was superior to fixed stepping in both
situations, leading to an approximately 0.17 voxel of devi-
ation in curved fibers and a nearly 100% successful track-
ing rate in crossing fibers at typical SNR. Human brain
images demonstrated similar results.
Conclusion: The adaptive stepping algorithm is a helpful
adjunct to TEND tractography.
Key Words: diffusion tensor imaging; TEND tractography;
adaptive stepping size; linear coefficient; tensor deflection
J. Magn. Reson. Imaging 2006;24:451– 458.
© 2006 Wiley-Liss, Inc.
MAGNETIC RESONANCE DIFFUSION TENSOR IMAG-
ING (MR-DTI) can uniquely reveal orientational infor-
mation concerning tissue microstructure by measuring
the three-dimensional distribution of water diffusion in
vivo (1). In tissues such as white matter in the brain, the
direction of fastest diffusion is believed to coincide with
the orientation of the neural fiber tract (2). The connec-
tivity of different brain regions can further be estimated
by reconstructing the three-dimensional continuous fi-
ber tracts in the DT field, which is potentially helpful for
clinical assessment of disease-related structural
changes in the brain (3).
A number of recently proposed fiber-tracking algo-
rithms, such as streamline tracking (5), fiber assign-
ment by continuous tracking (FACT) (6), and EZ-tracing
(7), reconstruct the connectivity maps using in vivo
data obtained from DTI (4). The algorithms mentioned
above use the major eigenvector as the sole information
to determine the tract direction. An alternative algo-
rithm termed tensor deflection (TEND) (8) uses the en-
tire tensor to determine the direction of fiber tract prop-
agation. Since the TEND algorithm determines fiber
tract direction by considering the entire tensor rather
than the single major eigenvector, it is potentially a
more comprehensive approach, especially in regions
where the two larger eigenvalues of the DT are close to
each other in value (9).
In TEND tractography, the choice of stepping size
may have deterministic effects on the degree of deflec-
tion (8,10). As will become clear in a later section, a
small stepping size in TEND results in high deflection,
which has the advantage of being able to trace highly
curved fiber bundles in regions that show linear-
shaped anisotropic tensors (a property typical of single
unidirectional fiber tracts). In contrast, a large stepping
size leads to less deflection, which is unfavorable for
single curved fibers but good for tracing fibers in less
anisotropic regions that show planar- or spherical-
1
Department of Electrical Engineering, National Taiwan University,
Taipei, Taiwan, R.O.C.
2
Department of Radiology, Tri-Service General Hospital, Taipei, Tai-
wan, R.O.C.
3
Department of Electrical Engineering, National Taiwan University of
Science and Technology, Taipei, Taiwan, R.O.C.
4
Department and Graduate Institute of Automatic Control Engineering,
Feng-Chia University, Taichung, Taiwan, R.O.C.
Contract grant sponsor: National Science Council; Contract grant num-
ber: NSC93–2213-E-002–135.
*Address reprint requests to: H.-W.C., Department of Electrical Engi-
neering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road,
Taipei, Taiwan 10764, R.O.C. E-mail: chung@cc.ee.ntu.edu.tw
Received August 9, 2005; Accepted April 27, 2006.
DOI 10.1002/jmri.20652
Published online 19 June 2006 in Wiley InterScience (www.interscience.
wiley.com).
JOURNAL OF MAGNETIC RESONANCE IMAGING 24:451– 458 (2006)
© 2006 Wiley-Liss, Inc. 451