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