Abstract
The purpose of this paper is to measure the variability of a population of white matter fiber bundles without imposing unrealistic geometrical priors. In this respect, modeling fiber bundles as currents seems particularly relevant, as it gives a metric between bundles which relies neither on point nor on fiber correspondences and which is robust to fiber interruption. First, this metric is included in a diffeomorphic registration scheme which consistently aligns sets of fiber bundles. In particular, we show that aligning directly fiber bundles may solve the aperture problem which appears when fiber mappings are constrained by tensors only. Second, the measure of variability of a population of fiber bundles is based on a statistical model which considers every bundle as a random diffeomorphic deformation of a common template plus a random non-diffeomorphic perturbation. Thus, the variability is decomposed into a geometrical part and a “texture” part. Our results on real data show that both parts may contain interesting anatomical features.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Durrleman, S., Pennec, X., Trouvé, A., Thompson, P., Ayache, N.: Inferring brain variability from diffeomorphic deformations of currents: an integrative approach. Medical Image Analysis 12(5), 626–637 (2008)
Fillard, P., Arsigny, V., Pennec, X., Hayashi, K., Thompson, P., Ayache, N.: Measuring brain variability by extrapolating sparse tensor fields measured on sulcal lines. NeuroImage 34(2), 639–650 (2007)
Vaillant, M., Miller, M., Younes, L., Trouvé, A.: Statistics on diffeomorphisms via tangent space representations. NeuroImage 23, 161–169 (2004)
Durrleman, S., Pennec, X., Trouvé, A., Ayache, N.: A forward model to build unbiased atlases from curves and surfaces. In: Proc. of MFCA 2008 (2008)
Goodlett, C., Fletcher, P., Gilmore, J., Gerig, G.: Group statistics of DTI fiber bundles using spatial functions of tensor measures. In: Metaxas, D., Axel, L., Fichtinger, G., Székely, G. (eds.) MICCAI 2008, Part II. LNCS, vol. 5242, pp. 1068–1075. Springer, Heidelberg (2008)
Smith, S., Jenkinson, M., Johansen-Berg, H., Rueckert, D., Nichols, T., Mackay, C., Watkins, K., Ciccarelli, O., Cader, M., Matthews, P., Behrens, T.: Tract-based spatial statistics: Voxelwise analysis of multi-subject diffusion data. NeuroImage 31, 1487–1505 (2006)
Zhang, H., Yushkevich, P.A., Rueckert, D., Gee, J.C.: Unbiased white matter atlas construction using diffusion tensor images. In: Ayache, N., Ourselin, S., Maeder, A. (eds.) MICCAI 2007, Part II. LNCS, vol. 4792, pp. 211–218. Springer, Heidelberg (2007)
Yeo, B., Vercauteren, T., Fillard, P., Pennec, X., Golland, P., Ayache, N., Clatz, O.: DTI registration with exact finite-strain differential. In: ISBI 2008, pp. 700–703 (2008)
Corouge, I., Fletcher, P., Joshi, S., Gouttard, S., Gerig, G.: Fiber tract-oriented statistics for quantitative diffusion tensor MRI analysis. Medical Image Analysis (10), 786–798 (2006)
Ziyan, U., Sabuncu, M.R., O’Donnell, L.J., Westin, C.-F.: Nonlinear Registration of Diffusion MR Images Based on Fiber Bundles. In: Ayache, N., Ourselin, S., Maeder, A. (eds.) MICCAI 2007, Part I. LNCS, vol. 4791, pp. 351–358. Springer, Heidelberg (2007)
Batchelor, P.G., Calamante, F., Tournier, J.D., Atkinson, D., Hill, D.L.G., Connelly, A.: Quantification of the shape of fiber tracts. MRM 55(4), 894–903 (2006)
Vaillant, M., Glaunès, J.: Surface matching via currents. In: Christensen, G.E., Sonka, M. (eds.) IPMI 2005. LNCS, vol. 3565, pp. 381–392. Springer, Heidelberg (2005)
Durrleman, S., Pennec, X., Trouvé, A., Ayache, N.: Sparse approximation of currents for statistics on curves and surfaces. In: Metaxas, D., Axel, L., Fichtinger, G., Székely, G. (eds.) MICCAI 2008, Part II. LNCS, vol. 5242, pp. 390–398. Springer, Heidelberg (2008)
Saitoh, S.: Theory of Reproducing Kernels and Its Applications. Pitman Research Notes in Mathematics Series, vol. 189. Wiley, Chichester (1988)
Miller, M.I., Trouvé, A., Younes, L.: On the metrics and Euler-Lagrange equations of computational anatomy. Annual Review of Biomed. Eng. 4, 375–405 (2002)
Allassonnière, S., Amit, Y., Trouvé, A.: Towards a coherent statistical framework for dense deformable template estimation. J. Roy. Stat. Soc. B 69(1), 3–29 (2007)
Fillard, P., Arsigny, V., Pennec, X., Ayache, N.: Clinical DT-MRI estimation, smoothing and fiber tracking with log-Euclidean metrics. IEEE Trans. on Medical Imaging 26(11), 1472–1482 (2007)
Vercauteren, T., Pennec, X., Malis, E., Perchant, A., Ayache, N.: Insight into efficient image registration techniques and the demons algorithm. In: Karssemeijer, N., Lelieveldt, B. (eds.) IPMI 2007. LNCS, vol. 4584, pp. 495–506. Springer, Heidelberg (2007)
Maddah, M., Wells, W.M., Warfield, S.K., Westin, C.F., Grimson, W.E.L.: Probabilistic clustering and quantitative analysis of white matter fiber tracts. In: Karssemeijer, N., Lelieveldt, B. (eds.) IPMI 2007. LNCS, vol. 4584, pp. 372–383. Springer, Heidelberg (2007)
El Kouby, V., Cointepas, Y., Poupon, C., Rivière, D., Golestani, N., Pallier, C., Poline, J.B., Bihan, D.L., Mangin, J.F.: MR diffusion-based inference of a fiber bundle model from a population of subjects. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3749, pp. 196–204. Springer, Heidelberg (2005)
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
Durrleman, S., Fillard, P., Pennec, X., Trouvé, A., Ayache, N. (2009). A Statistical Model of White Matter Fiber Bundles Based on Currents. 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_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-02498-6_10
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)