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Interactive Visualization of Volumetric White Matter Connectivity in DT-MRI Using a Parallel-Hardware Hamilton-Jacobi Solver
November/December 2007 (vol. 13 no. 6)
pp. 1480-1487
In this paper we present a method to compute and visualize volumetric white matter connectivity in diffusion tensor magnetic resonance imaging (DT-MRI) using a Hamilton-Jacobi (H-J) solver on the GPU (Graphics Processing Unit). Paths through the volume are assigned costs that are lower if they are consistent with the preferred diffusion directions. The proposed method finds a set of voxels in the DTI volume that contain paths between two regions whose costs are within a threshold of the optimal path. The result is a volumetric optimal path analysis, which is driven by clinical and scientific questions relating to the connectivity between various known anatomical regions of the brain. To solve the minimal path problem quickly, we introduce a novel numerical algorithm for solving H-J equations, which we call the Fast Iterative Method (FIM). This algorithm is well-adapted to parallel architectures, and we present a GPU-based implementation, which runs roughly 50-100 times faster than traditional CPU-based solvers for anisotropic H-J equations. The proposed system allows users to freely change the endpoints of interesting pathways and to visualize the optimal volumetric path between them at an interactive rate. We demonstrate the proposed method on some synthetic and real DT-MRI datasets and compare the performance with existing methods.

[1] SCIRun: A scientific computing problem solving environment, Scientific Computing and Imaging institute (SCI), 2002. http://software.sci.utah.eduscirun.html.
[2] NVIDIA CUDA programming guide, 2007. .
[3] P. J. Basser, S. Pajevic, C. Pierpaoli, J. Duda, and A. Aldroubi, In-vivo fiber tractography using DT-MRI data. Magnetic Resonance in Medicine, 44: 625–632, 2000.
[4] T. Behrens, M. Woolrich, M. Jenkinson, H. Johansen-Berg, R. Nunes, S. Clare, P. Matthews, J. Brady, and S. Smith, Characterization and propagation of uncertainty in diffusion-weighted MR imaging. Magnetic Resonance in Medicine, 50: 1077–1088, 2003.
[5] B. Fischl, A. van der Kouwe, C. Destrieux, E. Halgren, F. Sgonne, D. H. Salat, E. Busa, L. J. Seidman, J. Goldstein, D. Kennedy, V. Caviness, N. Makris, B. Rosen, and A. M. Dale, Automatically parcellating the human cerebral cortex. Cerebral Cortex, 14 (1): 11–22, 2004.
[6] P. T. Fletcher, R. Tao, W.-K. Jeong, and R. T. Whitaker, A volumetric approach to quantifying region-to-region white matter connectivity in Difusion Tensor MRI. In Information Processing in Medical Imaging 2007 Conference Proceedings (to appear), 2007.
[7] K. E. Hoff III, J. Keyser, M. Lin, D. Manocha, and T. Culver, Fast computation of generalized Voronoi diagrams using graphics hardware. In SIGGRAPH 1999 Conference Proceedings, pages 277–286, 1999.
[8] M. Jackowski, C. Y. Kao, M. Qiu, R. T. Constable, and L. H. Staib, Estimation of anatomical connectivity by anisotropic front propagation and diffusion tensor imaging. In MICCAI, pages 663–667, 2004.
[9] W.-K. Jeong and R. T. Whitaker, A fast iterative method for a class of Hamilton-Jacobi equations on parallel systems. Technical Report UUCS-07-010, University of Utah, 2007. .
[10] C. Kao, S. Osher, and J. Qian, Lax-friedrichs sweeping scheme for static Hamilton-Jacobi equations. Journal of Computational Physics, 196 (1): 367–391, 2004.
[11] C. Kao, S. Osher, and Y. Tsai, Fast sweeping methods for static Hamilton-Jacobi equations. Technical report, Department of Mathematics, University of California, Los Angeles, 2002.
[12] G. Kindlmann, Superquadric tensor glyphs. In Proceedings of IEEE TVCG/EG Symposium on Visualization 2004, pages 147–154, May 2004.
[13] M. A. Koch, D. G. Norris, and H.-G. M. , An investigation of functional and anatomical connectivity using magnetic resonance imaging. NeuroImage, 16: 241–250, 2002.
[14] M. Lazar and A. L. Alexander, Bootstrap white matter tractography (BOOT-TRAC). NeuroImage, 24: 524–532, 2005.
[15] A. Lefohn, J. Kniss, C. Hansen, and R. Whitaker, Interactive deformation and visualization of level set surfaces using graphics hardware. In IEEE Visualization 2003 Conference Proceedings, pages 75–82, 2003.
[16] L. O'Donnell, S. Haker, and C.-F. Westin, New approaches to estimation of white matter connectivity in diffusion tensor MRI: elliptic PDEs and geodesics in a tensor-warped space. In MICCAI, pages 459–466, 2002.
[17] J. D. Owens, D. Luebke, N. Govindaraju, M. Harris, J. Krüger, A. E. Lefohn, and T. J. Purcell, A survey of general-purpose computation on graphics hardware. Computer Graphics Forum, 26 (1): 80–113, March 2007.
[18] G. Parker, C. Wheeler-Kingshott, and G. Barker, Estimating distributed anatomical connectivity using fast marching methods and diffusion tensor imaging. Transactions on Medical Imaging, 21: 505–512, 2002.
[19] G. J. M. Parker, H. A. Haroon, and C. A. M. Wheeler-Kingshott, A framework for a streamline-based probabilistic index of connectivity (PICo) using a structural interpretation of MRI diffusion measurements. Journal of Magnetic Resonance Imaging, 18: 242–254, 2003.
[20] E. Pichon, C.-F. Westin, and A. Tannenbaum, A Hamilton-Jacobi-Bellman approach to high angular resolution diffusion tractography. In MICCAI, pages 180–187, 2005.
[21] L. C. Polymenakos, D. P. Bertsekas, and J. N. Tsitsiklis, Implementation of efficient algorithms for globally optimal trajectories. IEEE Trans. Automatic Control, 43 (2): 278–283, 1998.
[22] F. Qin, Y. Luo, K. Olsen, W. Cai, and G. Schuster, Finite-difference solution of the eikonal equation along expanding wavefronts. Geophysics, 57 (3): 478–487, 1992.
[23] E. Rouy and A. Tourin, A viscosity solutions approach to shape-from-shading. SIAM Journal of Numerical Analysis, 29: 867–884, 1992.
[24] J. Sethian, A fast marching level set method for monotonically advancing fronts. In Proc. Natl. Acad. Sci., volume 93, pages 1591–1595, February 1996.
[25] J. Sethian, Fast marching methods. SIAM Review, 41 (2): 199–235, 1999.
[26] J. A. Sethian and A. Vladimirsky, Ordered upwind methods for static Hamilton-Jacobi equations: Theory and algorithms. SIAM Journal of Numerical Analysis, 41 (1): 325–363, 2003.
[27] C. Sigg, R. Peikert, and M. Gross, Signed distance transform using graphics hardware. In IEEE Visualization 2003 Conference Proceedings, pages 83–90, 2003.
[28] A. Sud, M. A. Otaduy, and D. Manocha, Difi: Fast 3d distance field computation using graphics hardware. Computer Graphics Forum, 23 (3): 557–566, 2004.
[29] Y.-H. R. Tsai, L.-T. Cheng, S. Osher, and H.-K. Zhao, Fast sweeping algorithms for a class of Hamilton-Jacobi equations. SIAM Journal of Numerical Analysis, 41 (2): 659–672, 2003.
[30] H. Zhao, A fast sweeping method for eikonal equations. Mathematics of Computation, 74: 603–627, 2004.

Index Terms:
Diffusion tensor visualization, graphics hardware, interactivity.
Won-Ki Jeong, P. Thomas Fletcher, Ran Tao, Ross Whitaker, "Interactive Visualization of Volumetric White Matter Connectivity in DT-MRI Using a Parallel-Hardware Hamilton-Jacobi Solver," IEEE Transactions on Visualization and Computer Graphics, vol. 13, no. 6, pp. 1480-1487, Nov.-Dec. 2007, doi:10.1109/TVCG.2007.70571
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