Abstract
Multi-fiber reconstruction has attracted immense attention lately in the field of diffusion weighted MRI analysis. Several mathematical models have been proposed in literature but there is still scope for improvement. The key issues of importance in multi-fiber reconstruction are, fiber detection accuracy, robustness to noise and computational efficiency. To this end, we propose a novel mathematical model for representing the MR signal attenuation in the presence of multiple fibers at a single voxel and estimate the parameters of this model given the diffusion weighted MRI data. Our model for the diffusion MR signal consists of a continuous mixture of Hyperspherical von Mises-Fisher distributions. Being a continuous mixture, our model does not require the specification of the number of mixture components. We present a closed form expression for this continuous mixture that leads to a computationally efficient implementation. To validate our model we present extensive results on both synthetic and real data (human and rat brain) and demonstrate that even in presence of noise, our model clearly outperforms the state-of-the-art methods in fiber orientation estimation while maintaining a substantial computational advantage.
This research was in part supported by UF Alumni Fellowship to RK, NIH EB007082 to BCV and NIH EB004752 to PC and TM.
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.: Maximum entropy spherical deconvolution for diffusion MRI. In: Christensen, G.E., Sonka, M. (eds.) IPMI 2005. LNCS, vol. 3565, pp. 76–87. Springer, Heidelberg (2005)
Adam, W., Anderson, A.W.: Measurement of fiber orientation distributions using high angular resolution diffusion imaging. MRMÂ 54(5) (2005)
Assaf, Y., Freidlin, R.Z., Rohde, G.K., Basser, P.J.: New modeling and experimental framework to characterize hindered and restricted water diffusion in brain white matter. MRM (2004)
Barmpoutis, A., Jian, B., Vemuri, B.C., Shepherd, T.M.: Symmetric positive 4th order tensors and their estimation from diffusion weighted MRI. In: Karssemeijer, N., Lelieveldt, B. (eds.) IPMI 2007. LNCS, vol. 4584, pp. 308–319. Springer, Heidelberg (2007)
Barmpoutis, A., Vemuri, B.C., Forder, J.R.: Fast displacement probability profile approximation from hardi using 4th-order tensors. In: ISBI (2008)
Barmpoutis, A., Vemuri, B.C., Howland, D., Forder, J.R.: Extracting tractosemas from a displacement probability field for tractography in dw-MRI. In: Metaxas, D., Axel, L., Fichtinger, G., Székely, G. (eds.) MICCAI 2008, Part I. LNCS, vol. 5241, pp. 9–16. Springer, Heidelberg (2008)
Basser, P.J., Mattiello, J., Lebihan, D.: Estimation of the Effective Self-Diffusion Tensor from the NMR Spin Echo. J. Magn. Reson. BÂ 103 (1994)
Basser, P.J., Pajevic, S., Pierpaoli, C., Duda, J., Aldroubi, A.: In vivo fiber tractography using dt-MRI data. Magnetic Resonance in Medicine 44(4) (2000)
Bhalerao, A., Westin, C.-F.: Hyperspherical von mises fisher mixture (hvmf) modelling of high angular resolution diffusion MRI. In: Ayache, N., Ourselin, S., Maeder, A. (eds.) MICCAI 2007, Part I. LNCS, vol. 4791, pp. 236–243. Springer, Heidelberg (2007)
Descoteaux, M., Angelino, E., Fitzgibbons, S., Deriche, R.: Regularized, fast and robust analytical q-ball imaging. Magnetic Resonance in Medicine 58 (2007)
Shepherd, T.M., et al.: Structural insights from high-resolution diffusion tensor imaging and tractography of the isolated rat hippocampus. NeuroImage (2006)
Wedeen, V.J., et al.: Mapping complex tissue architecture with diffusion spectrum magnetic resonance imaging. MRMÂ 54(6) (2005)
Frank, L.R.: Characterization of anisotropy in high angular resolution diffusion-weighted MRI. MRMÂ 47(6) (2002)
Hess, C.P., Mukherjee, P., Han, E.T., Xu, D., Vigneron, D.B.: Q-ball reconstruction of multimodal fiber orientations using the spherical harmonic basis. MRM (2006)
Jian, B., Vemuri, B.C., Özarslan, E., Carney, P.R., Mareci, T.H.: A novel tensor distribution model for the diffusion weighted mr signal. NeuroImage (2007)
Knutsson, H.: Producing a continuous and distance preserving 5-d vector repesentation of 3-d orientation. In: IEEE Computer Society Workshop on Computer Architecture for Pattern Analysis and Image Database Management (1985)
Kumar, R., Barmpoutis, A., Vemuri, B.C., Carney, P.R., Mareci, T.H.: Multi-fiber reconstruction from dw-MRI using a continuous mixture of von mises-fisher distributions. MMBIA (2008)
Lawson, C., Hanson, R.J.: Solving Least Squares Problems. Prentice-Hall, Englewood Cliffs (1974)
Mardia, K.V., Jupp, P.: Directional Statistics, 2nd edn. John Wiley, New York (2000)
McGraw, T.E., Vemuri, B.C., Yezierski, R., Mareci, T.H.: Von Mises-Fisher mixture model of the diffusion ODF. In: ISBI (2006)
Özarslan, E., Shepherd, T.M., Vemuri, B.C., Blackband, S.J., Mareci, T.H.: Resolution of complex tissue microarchitecture using the diffusion orientation transform (DOT). NeuroImage 31, 1086–1103 (2006)
Özarslan, E., Mareci, T.H.: Generalized diffusion tensor imaging and analytical relationships between diffusion tensor imaging and high angular resolution diffusion imaging. MRM 50(5) (2003)
Söderman, O., Jönsson, B.: Restricted diffusion in cylindirical geometry. J. Magn. Reson. B 117(1) (1995)
Tournier, J.-D., Calamante, F., Gadian, D.G., Connelly, A.: Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution. NeuroImage (2004)
Tuch, D.S., Reese, T.G., Wiegell, M.R., Makris, N., Belliveau, J.W., Wedeen, V.J.: High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity. MRM (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kumar, R., Vemuri, B.C., Wang, F., Syeda-Mahmood, T., Carney, P.R., Mareci, T.H. (2009). Multi-fiber Reconstruction from DW-MRI Using a Continuous Mixture of Hyperspherical von Mises-Fisher Distributions. 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_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-02498-6_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02497-9
Online ISBN: 978-3-642-02498-6
eBook Packages: Computer ScienceComputer Science (R0)