Abstract
We describe a technique to simultaneously estimate a local neural fiber model and trace out its path. Existing techniques estimate the local fiber orientation at each voxel independently so there is no running knowledge of confidence in the estimated fiber model. We formulate fiber tracking as recursive estimation: at each step of tracing the fiber, the current estimate is guided by the previous. To do this we model the signal as a mixture of Gaussian tensors and perform tractography within a filter framework. Starting from a seed point, each fiber is traced to its termination using an unscented Kalman filter to simultaneously fit the local model and propagate in the most consistent direction. Despite the presence of noise and uncertainty, this provides a causal estimate of the local structure at each point along the fiber. Synthetic experiments demonstrate that this approach reduces signal reconstruction error and significantly improves the angular resolution at crossings and branchings. In vivo experiments confirm the ability to trace out fibers in areas known to contain such crossing and branching while providing inherent path regularization.
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Basser, P., Jones, D.: Diffusion-tensor MRI: theory, experimental design and data analysis - A technical review. NMR in Biomedicine 25, 456–467 (2002)
Behrens, T., Woolrich, M., Jenkinson, M., Johansen-Berg, H., Nunes, R., Clare, S., Matthews, P., Brady, J., Smith, S.: Characterization and propagation of uncertainty in diffusion-weighted MR imaging. Magnetic Resonance in Medicine 50, 1077–1088 (2003)
Alexander, D., Barker, G., Arridge, S.: Detection and modeling of non-Gaussian apparent diffusion coefficient profiles in human brain data. Magnetic Resonance in Medicine 48, 331–340 (2002)
Frank, L.: Characterization of anisotropy in high angular resolution diffusion-weighted MRI. Magnetic Resonance in Medicine 47, 1083–1099 (2002)
Alexander, A., Hasan, K., Tsuruda, J., Parker, D.: Analysis of partial volume effects in diffusion-tensor MRI. Magnetic Resonance in Medicine 45, 770–780 (2001)
Tuch, D., Reese, T., Wiegell, M., Makris, N., Belliveau, J., Wedeen, V.: High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity. Magnetic Resonance in Medicine 48, 577–582 (2002)
Kreher, B., Schneider, J., Mader, I., Martin, E., Hennig, J., Il’yasov, K.: Multitensor approach for analysis and tracking of complex fiber configurations. Magnetic Resonance in Medicine 54, 1216–1225 (2005)
Peled, S., Friman, O., Jolesz, F., Westin, C.F.: Geometrically constrained two-tensor model for crossing tracts in DWI. Magnetic Resonance in Medicine 24(9), 1263–1270 (2006)
Hlawitschka, M., Scheuermann, G.: HOT-lines: Tracking lines in higher order tensor fields. In: Visualization, pp. 27–34 (2005)
McGraw, T., Vemuri, B., Yezierski, B., Mareci, T.: Von Mises-Fisher mixture model of the diffusion ODF. In: Int. Symp. on Biomedical Imaging, pp. 65–68 (2006)
Kaden, E., Knøsche, T., Anwander, A.: Parametric spherical deconvolution: Inferring anatomical connectivity using diffusion MR imaging. NeuroImage 37, 474–488 (2007)
Rathi, Y., Michailovich, O., Shenton, M., Bouix, S.: Directional functions for orientation distribution estimation. Medical Image Analysis (in press, 2009)
Özarslan, E., Shepherd, T., Vemuri, B., Blackband, S., Mareci, T.: Resolution of complex tissue microarchitecture using the diffusion orientation transform. NeuroImage 31(3) (2006)
Tuch, D.: Q-ball imaging. Magnetic Resonance in Medicine 52, 1358–1372 (2004)
Anderson, A.: Measurement of fiber orientation distributions using high angular resolution diffusion imaging. Magnetic Resonance in Medicine 54(5), 1194–1206 (2005)
Hess, C., Mukherjee, P., Han, E., Xu, D., Vigneron, D.: Q-ball reconstruction of multimodal fiber orientations using the spherical harmonic basis. Magnetic Resonance in Medicine 56, 104–117 (2006)
Descoteaux, M., Angelino, E., Fitzgibbons, S., Deriche, R.: Regularized, fast, and robust analytical Q-ball imaging. Magnetic Resonance in Medicine 58, 497–510 (2007)
Michailovich, O., Rathi, Y.: On approximation of orientation distributions by means of spherical ridgelets. In: Int. Symp. on Biomedical Imaging, pp. 939–942 (2008)
Poupon, C., Roche, A., Dubois, J., Mangin, J.F., Poupon, F.: Real-time MR diffusion tensor and Q-ball imaging using Kalman filtering. Medical Image Analysis 12(5), 527–534 (2008)
Jian, B., Vemuri, B.: A unified computational framework for deconvolution to reconstruct multiple fibers from diffusion weighted MRI. Trans. on Medical Imaging 26(11), 1464–1471 (2007)
Jansons, K., Alexander, D.: Persistent angular structure: New insights from diffusion MRI data. Inverse Problems 19, 1031–1046 (2003)
Tournier, J.D., Calamante, F., Gadian, D., Connelly, A.: Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution. NeuroImage 23, 1176–1185 (2004)
Kumar, R., Barmpoutis, A., Vemuri, B., Carney, P., Mareci, T.: Multi-fiber reconstruction from DW-MRI using a continuous mixture of von Mises-Fisher distributions. In: Mathematical Methods in Biomedical Image Analysis (MMBIA), pp. 1–8 (2008)
Alexander, D.: Multiple-fiber reconstruction algorithms for diffusion MRI. Annals of the New York Academy of Sciences 1046 (2005)
Descoteaux, M., Deriche, R., Anwander, A.: Deterministic and probabilistic Q-ball tractography: from diffusion to sharp fiber distributions. Technical Report 6273, INRIA (2007)
Basser, P., Pajevic, S., Pierpaoli, C., Duda, J., Aldroubi, A.: In vivo fiber tractography using DT-MRI data. Magnetic Resonance in Medicine 44, 625–632 (2000)
Hagmann, P., Reese, T., Tseng, W.Y., Meuli, R., Thiran, J.P., Wedeen, V.: Diffusion spectrum imaging tractography in complex cerebral white matter: An investigation of the centrum semiovale. In: Int. Symp. on Magnetic Resonance in Medicine (ISMRM), p. 623 (2004)
Guo, W., Zeng, Q., Chen, Y., Liu, Y.: Using multiple tensor deflection to reconstruct white matter fiber traces with branching. In: Int. Symp. on Biomedical Imaging, pp. 69–72 (2006)
Qazi, A., Radmanesh, A., O’Donnell, L., Kindlmann, G., Peled, S., Whalen, S., Westin, C.F., Golby, A.: Resolving crossings in the corticospinal tract by two-tensor streamline tractography: Method and clinical assessment using fMRI. NeuroImage (2008)
Gössl, C., Fahrmeir, L., Putz, B., Auer, L., Auer, D.: Fiber tracking from DTI using linear state space models: Detectability of the pyramidal tract. NeuroImage 16, 378–388 (2002)
Björnemo, M., Brun, A., Kikinis, R., Westin, C.F.: Regularized stochastic white matter tractography using diffusion tensor MRI. In: Dohi, T., Kikinis, R. (eds.) MICCAI 2002. LNCS, vol. 2488, pp. 435–442. Springer, Heidelberg (2002)
Zhang, F., Goodlett, C., Hancock, E., Gerig, G.: Probabilistic fiber tracking using particle filtering. In: Ayache, N., Ourselin, S., Maeder, A. (eds.) MICCAI 2007, Part II. LNCS, vol. 4792, pp. 144–152. Springer, Heidelberg (2007)
Zhukov, L., Barr, A.: Oriented tensor reconstruction: Tracing neural pathways from diffusion tensor MRI. In: Visualization, pp. 387–394 (2002)
Parker, G., Alexander, D.: Probabilistic Monte Carlo based mapping of cerebral connections utilizing whole-brain crossing fiber information. In: Taylor, C.J., Noble, J.A. (eds.) IPMI 2003. LNCS, vol. 2732, pp. 684–696. Springer, Heidelberg (2003)
Campbell, J.W., Siddiqi, K., Rymar, V., Sadikot, A., Pike, G.: Flow-based fiber tracking with diffusion tensor and Q-ball data: Validation and comparison to principal diffusion direction techniques. NeuroImage 27(4), 725–736 (2005)
Hosey, T., Williams, G., Ansorge, R.: Inference of multiple fiber orientations in high angular resolution diffusion imaging. Magnetic Resonance in Medicine 54, 1480–1489 (2005)
Behrens, T., Johansen-Berg, H., Jbabdi, S., Rushworth, M., Woolrich, M.: Probabilistic diffusion tractography with multiple fibre orientations: What can we gain? NeuroImage 34, 144–155 (2007)
Zhan, W., Yang, Y.: How accurately can the diffusion profiles indicate multiple fiber orientations? A study on general fiber crossings in diffusion MRI. J. of Magnetic Resonance 183, 193–202 (2006)
Seunarine, K., Cook, P., Hall, M., Embleton, K., Parker, G., Alexander, D.: Exploiting peak anisotropy for tracking through complex structures. In: Mathematical Methods in Biomedical Image Analysis (MMBIA), pp. 1–8 (2007)
Bloy, L., Verma, R.: On computing the underlying fiber directions from the diffusion orientation distribution function. In: Metaxas, D., Axel, L., Fichtinger, G., Székely, G. (eds.) MICCAI 2008, Part I. LNCS, vol. 5241, pp. 1–8. Springer, Heidelberg (2008)
Schultz, T., Seidel, H.: Estimating crossing fibers: A tensor decomposition approach. Trans. on Visualization and Computer Graphics 14(6), 1635–1642 (2008)
Ramirez-Manzanares, A., Cook, P., Gee, J.: A comparison of methods for recovering intra-voxel white matter fiber architecture from clinical diffusion imaging scans. In: Metaxas, D., Axel, L., Fichtinger, G., Székely, G. (eds.) MICCAI 2008, Part I. LNCS, vol. 5241, pp. 305–312. Springer, Heidelberg (2008)
Friman, O., Farnebäck, G., Westin, C.F.: A Bayesian approach for stochastic white matter tractography. Trans. on Medical Imaging 25(8), 965–978 (2006)
Parker, G., Alexander, D.: Probabilistic anatomical connectivity derived from the microscopic persistent angular structure of cerebral tissue. Phil. Trans. R. Soc. B 360, 893–902 (2005)
Julier, S., Uhlmann, J.: Unscented filtering and nonlinear estimation. IEEE 92(3), 401–422 (2004)
van der Merwe, R., Wan, E.: Sigma-point Kalman filters for probabilistic inference in dynamic state-space models. In: Workshop on Advances in Machine Learning (2003)
Mallat, S., Zhang, Z.: Matching pursuits with time-frequency dictionaries. Trans. on Signal Processing 41, 3397–3415 (1993)
Anwander, A., Descoteaux, M., Deriche, R.: Probabilistic Q-Ball tractography solves crossings of the callosal fibers. In: Human Brain Mapping, p. 342 (2007)
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Malcolm, J.G., Shenton, M.E., Rathi, Y. (2009). Neural Tractography Using an Unscented Kalman Filter. In: Prince, J.L., Pham, D.L., Myers, K.J. (eds) Information Processing in Medical Imaging. IPMI 2009. Lecture Notes in Computer Science, vol 5636. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02498-6_11
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DOI: https://doi.org/10.1007/978-3-642-02498-6_11
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