Abstract
Partial differential equations have been successfully used for fibre tractography and for mapping connectivity indices in the brain. However, the current implementation of methods which require 3D orientation to be tracked can suffer from serious shortcomings when invariance to 3D rotation is desired. In this paper we focus on the 3D stochastic completion field and introduce a new methodology to solve the underlying PDE in a manner that achieves rotation invariance. The key idea is to use spherical harmonics to solve the Fokker-Planck equation representing the evolution of the probability density function of a 3D directional random walk. We validate the new approach by presenting improved connectivity indices on synthetic data, on the MICCAI 2009 Fibre Cup phantom and on a biological phantom comprised of two rat spinal chords in a crossing configuration.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alexander, D.C., Barker, G.J., Arridge, S.R.: Detection and modeling of non-gaussian apparent diffusion coefficient profiles in human brain data. Mag. Reson. in Med. 48, 331–340 (2002)
Batchelor, P.G., Hill, D.L.G., Calamante, F., Atkinson, D.: Study of connectivity in the brain using the full diffusion tensor from MRI. In: Insana, M.F., Leahy, R.M. (eds.) IPMI 2001. LNCS, vol. 2082, pp. 121–133. Springer, Heidelberg (2001)
Berman, J.I., Chung, S., Mukherjee, P., Hess, C.P., Han, E.T., Henrya, R.G.: Probabilistic streamline Q-ball tractography using the residual bootstrap. NeuroImage 39, 215–222 (2008)
Campbell, J.S.W., Siddiqi, K., Rymar, V.V., Sadikot, A.F., Pike, G.B.: Flow-based fiber tracking with diffusion tensor and Q-ball data: validation and comparison to principal diffusion direction techniques. NeuroImage 27, 725–736 (2005)
Descoteaux, M., Angelino, E., Fitzgibbons, S., Deriche, R.: Regularized, fast, and robust analytical Q-ball imaging. Mag. Reson. in Med. 58, 497–510 (2007)
Fletcher, P.T., Tao, R., Jeong, W.-K., Whitaker, R.T.: A volumetric approach to quantifying region-to-region white matter connectivity in diffusion tensor MRI. In: Karssemeijer, N., Lelieveldt, B. (eds.) IPMI 2007. LNCS, vol. 4584, pp. 346–358. Springer, Heidelberg (2007)
Fornberg, B., Merrill, D.: Comparison of finite difference and pseudo-spectral methods for convective flow over a sphere. Geoph. Res. Letters 24, 3245–3248 (1997)
Hageman, N.S., Toga, A.W., Narr, K.L., Shattuck, D.W.: A diffusion tensor imaging tractography algorithm based on Navier-Stokes fluid mechanics. IEEE Transactions on Medical Imaging 28(3), 348–360 (2009)
MomayyezSiahkal, P., Siddiqi, K.: Probabilistic anatomical connectivity using completion fields. In: Jiang, T., Navab, N., Pluim, J.P.W., Viergever, M.A. (eds.) MICCAI 2010. LNCS, vol. 6361, pp. 566–573. Springer, Heidelberg (2010)
O’Donnell, L., Haker, S., Westin, C.-F.: New approaches to estimation of white matter connectivity in diffusion tensor MRI: Elliptic pDEs and geodesics in a tensor-warped space. In: Dohi, T., Kikinis, R. (eds.) MICCAI 2002. LNCS, vol. 2488, pp. 459–466. Springer, Heidelberg (2002)
Pichon, E., Westin, C.-F., Tannenbaum, A.R.: A hamilton-jacobi-bellman approach to high angular resolution diffusion tractography. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3749, pp. 180–187. Springer, Heidelberg (2005)
Poupon, C., Rieul, B., Kezele, I., Perrin, M., Poupon, F., Mangin, J.: New diffusion phantoms dedicated to the study and validation of high-angular-resolution diffusion imaging (HARDI) models. Mag. Reson. in Med. 60, 1276–1283 (2008)
Tournier, J.D., Yeh, C., Calamante, F., Cho, H., Connelly, A., Lin, P.: Resolving crossing fibres using constrained spherical deconvolution: validation using diffusion-weighted imaging phantom data. NeuroImage 41, 617–625 (2008)
Williams, L.R., Jacobs, D.W.: Stochastic completion fields: A neural model of illusory contour shape and salience. Neural Computation 9, 837–858 (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
MomayyezSiahkal, P., Siddiqi, K. (2011). Rotation Invariant Completion Fields for Mapping Diffusion MRI Connectivity. In: Székely, G., Hahn, H.K. (eds) Information Processing in Medical Imaging. IPMI 2011. Lecture Notes in Computer Science, vol 6801. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22092-0_58
Download citation
DOI: https://doi.org/10.1007/978-3-642-22092-0_58
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22091-3
Online ISBN: 978-3-642-22092-0
eBook Packages: Computer ScienceComputer Science (R0)