Abstract
Low-rank higher-order tensor approximation has been used successfully to extract discrete directions for tractography from continuous fiber orientation density functions (fODFs). However, while it accounts for fiber crossings, it has so far ignored fanning, which has led to incomplete reconstructions. In this work, we integrate an anisotropic model of fanning based on the Bingham distribution into a recently proposed tractography method that performs low-rank approximation with an Unscented Kalman Filter. Our technical contributions include an initialization scheme for the new parameters, which is based on the Hessian of the low-rank approximation, pre-integration of the required convolution integrals to reduce the computational effort, and representation of the required 3D rotations with quaternions. Results on 12 subjects from the Human Connectome Project confirm that, in almost all considered tracts, our extended model significantly increases completeness of the reconstruction, at acceptable excess and additional computational cost. Its results are also more accurate than those from a simpler, isotropic fanning model that is based on Watson distributions.
Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 422414649. Data were provided by the Human Connectome Project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research; and by the McDonnell Center for Systems Neuroscience at Washington University.
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References
Ankele, M., Lim, L.H., Groeschel, S., Schultz, T.: Versatile, robust, and efficient tractography with constrained higher-order tensor fODFs. Int. J. Comput. Assisted Radiol. Surg. 12(8), 1257–1270 (2017). https://doi.org/10.1007/s11548-017-1593-6
Bernal-Polo, P., Martínez-Barberá, H.: Kalman filtering for attitude estimation with quaternions and concepts from manifold theory. Sensors 19(1), 149 (2019). https://doi.org/10.3390/s19010149
Bingham, C.: An antipodally symmetric distribution on the sphere. Ann. Stat. 2(6), 1201–1225 (1974). https://doi.org/10.1214/aos/1176342874
Chen, Z., et al.: Corticospinal tract modeling for neurosurgical planning by tracking through regions of peritumoral edema and crossing fibers using two-tensor unscented Kalman filter tractography. Int. J. Comput. Assisted Radiol. Surg. 11(8), 1475–1486 (2016). https://doi.org/10.1007/s11548-015-1344-5
Cheng, G., Salehian, H., Forder, J.R., Vemuri, B.C.: Tractography from HARDI using an intrinsic unscented Kalman filter. IEEE Trans. Med. Imaging 34(1), 298–305 (2015). https://doi.org/10.1109/TMI.2014.2355138
Dalamagkas, K., et al.: Individual variations of the human corticospinal tract and its hand-related motor fibers using diffusion MRI tractography. Brain Imaging Behav. 14, 696–714 (2020). https://doi.org/10.1007/s11682-018-0006-y
Dell’Acqua, F., Tournier, J.D.: Modelling white matter with spherical deconvolution: how and why? NMR Biomed. 32(4) (2018). https://doi.org/10.1002/nbm.3945
Friedman, M.: The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J. Am. Stat. Assoc. 32(200), 675–701 (1937). https://doi.org/10.1080/01621459.1937.10503522
Grün, J., Gröschel, S., Schultz, T.: Spatially regularized low-rank tensor approximation for accurate and fast tractography. NeuroImage 271 (2023). https://doi.org/10.1016/j.neuroimage.2023.120004
Huttenlocher, D., Klanderman, G., Rucklidge, W.: Comparing images using the Hausdorff distance. IEEE Trans. Pattern Anal. Mach. Intell. 15(9), 850–863 (1993). https://doi.org/10.1109/34.232073
Jeurissen, B., Descoteaux, M., Mori, S., Leemans, A.: Diffusion MRI fiber tractography of the brain. NMR Biomed. 32(4), e3785 (2019). https://doi.org/10.1002/nbm.3785
Julier, S., Uhlmann, J.: Unscented filtering and nonlinear estimation. Proc. IEEE 92(3), 401–422 (2004). https://doi.org/10.1109/JPROC.2003.823141
Kaden, E., Knösche, T.R., Anwander, A.: Parametric spherical deconvolution: inferring anatomical connectivity using diffusion MR imaging. Neuroimage 37(2), 474–488 (2007). https://doi.org/10.1016/j.neuroimage.2007.05.012
Kraft, E.: A quaternion-based unscented Kalman filter for orientation tracking. In: Proceedings of the Sixth International Conference of Information Fusion, vol. 1, pp. 47–54 (2003). https://doi.org/10.1109/ICIF.2003.177425
Maier-Hein, K., et al.: The challenge of map** the human connectome based on diffusion tractography. Nat. Commun. 8, 1349 (2017). https://doi.org/10.1038/s41467-017-01285-x
Malcolm, J., Shenton, M., Rathi, Y.: Filtered multitensor tractography. IEEE Trans. Med. Imaging 29, 1664–1675 (2010). https://doi.org/10.1109/TMI.2010.2048121
Malcolm, J.G., Michailovich, O., Bouix, S., Westin, C.F., Shenton, M.E., Rathi, Y.: A filtered approach to neural tractography using the Watson directional function. Med. Image Anal. 14(1), 58–69 (2010). https://doi.org/10.1016/j.media.2009.10.003
Riffert, T.W., Schreiber, J., Anwander, A., Knösche, T.R.: Beyond fractional anisotropy: extraction of bundle-specific structural metrics from crossing fiber models. Neuroimage 100, 176–191 (2014). https://doi.org/10.1016/j.neuroimage.2014.06.015
Schultz, T., Kindlmann, G.: A maximum enhancing higher-order tensor glyph. Comput. Graph. Forum 29(3), 1143–1152 (2010). https://doi.org/10.1111/j.1467-8659.2009.01675.x
Schultz, T., Seidel, H.P.: Estimating crossing fibers: a tensor decomposition approach. IEEE Trans. Vis. Comput. Graph. 14(6), 1635–1642 (2008). https://doi.org/10.1109/TVCG.2008.128
Sotiropoulos, S.N., Behrens, T.E., Jbabdi, S.: Ball and rackets: inferring fiber fanning from diffusion-weighted MRI. Neuroimage 60(2), 1412–1425 (2012). https://doi.org/10.1016/j.neuroimage.2012.01.056
Tournier, J.D., Calamante, F., Connelly, A.: Robust determination of the fibre orientation distribution in diffusion MRI: non-negativity constrained super-resolved spherical deconvolution. Neuroimage 35(4), 1459–1472 (2007). https://doi.org/10.1016/j.neuroimage.2007.02.016
Van Essen, D.C., Smith, S.M., Barch, D.M., Behrens, T.E., Yacoub, E., Ugurbil, K.: The WU-Minn human connectome project: an overview. Neuroimage 80, 62–79 (2013). https://doi.org/10.1016/j.neuroimage.2013.05.041
Wakana, S., et al.: Reproducibility of quantitative tractography methods applied to cerebral white matter. Neuroimage 36, 630–644 (2007). https://doi.org/10.1016/j.neuroimage.2007.02.049
Wasserthal, J., Neher, P., Maier-Hein, K.H.: TractSeg - fast and accurate white matter tract segmentation. Neuroimage 183, 239–253 (2018). https://doi.org/10.1016/j.neuroimage.2018.07.070
Wiener, T.F.: Theoretical analysis of gimballess inertial reference equipment using delta-modulated instruments. Ph.D. thesis, Massachusetts Institute of Technology (1962)
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Gruen, J., Sieg, J., Schultz, T. (2023). Anisotropic Fanning Aware Low-Rank Tensor Approximation Based Tractography. In: Karaman, M., Mito, R., Powell, E., Rheault, F., Winzeck, S. (eds) Computational Diffusion MRI. CDMRI 2023. Lecture Notes in Computer Science, vol 14328. Springer, Cham. https://doi.org/10.1007/978-3-031-47292-3_13
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