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2019 | OriginalPaper | Buchkapitel

Brain Connectivity Measures via Direct Sub-Finslerian Front Propagation on the 5D Sphere Bundle of Positions and Directions

verfasst von : Jorg Portegies, Stephan Meesters, Pauly Ossenblok, Andrea Fuster, Luc Florack, Remco Duits

Erschienen in: Computational Diffusion MRI

Verlag: Springer International Publishing

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Abstract

We propose a novel connectivity measure between brain regions using diffusion-weighted MRI. This connectivity measure is based on optimal sub-Finslerian geodesic front propagation on the 5D base manifold of (3D) positions and (2D) directions, the so-called sphere bundle. The advantage over spatial front propagations is that it prevents leakage at omnipresent crossings. Our optimal fronts on the sphere bundle are geodesically equidistant w.r.t. an asymmetric Finsler metric, and can be computed with existing anisotropic fast-marching methods. Comparisons to ground truth connectivities provided by the ISBI-HARDI challenge reveal promising results, both quantitatively and qualitatively. We also apply the connectivity measures to real data from the Human Connectome Project.

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Fußnoten
1
‘Quasi’ pertains to its asymmetrical nature.
 
Literatur
1.
Zurück zum Zitat Barron, D.S., Tandon, N., Lancaster, J.L., Fox, P.T.: Thalamic structural connectivity in medial temporal lobe epilepsy. Epilepsia 55(6), e50–5 (2014)CrossRef Barron, D.S., Tandon, N., Lancaster, J.L., Fox, P.T.: Thalamic structural connectivity in medial temporal lobe epilepsy. Epilepsia 55(6), e50–5 (2014)CrossRef
2.
Zurück zum Zitat Bekkers, E., Duits, R., Mashtakov, A., Sanguinetti, G.: A PDE approach to data-driven sub-riemannian geodesics in SE(2). SIAM J. Imaging Sci. 8(4), 2740–2770 (2015)MathSciNetCrossRef Bekkers, E., Duits, R., Mashtakov, A., Sanguinetti, G.: A PDE approach to data-driven sub-riemannian geodesics in SE(2). SIAM J. Imaging Sci. 8(4), 2740–2770 (2015)MathSciNetCrossRef
3.
Zurück zum Zitat Chen, D.: New minimal paths models for tubular structure extraction and image segmentation. Ph.D. thesis, Université Paris Dauphine (2016) Chen, D.: New minimal paths models for tubular structure extraction and image segmentation. Ph.D. thesis, Université Paris Dauphine (2016)
4.
Zurück zum Zitat Daducci, A., Caruyer, E., Descoteaux, M., Thiran, J.P.: HARDI reconstruction challenge 2013. In: IEEE International of Symposium on Biomedical Imaging (2013) Daducci, A., Caruyer, E., Descoteaux, M., Thiran, J.P.: HARDI reconstruction challenge 2013. In: IEEE International of Symposium on Biomedical Imaging (2013)
5.
Zurück zum Zitat Dela Haije, T.C.J., Duits, R., Tax, C.M.W.: Sharpening fibers in diffusion weighted MRI via erosion. In: Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data, pp. 97–126. Springer (2014) Dela Haije, T.C.J., Duits, R., Tax, C.M.W.: Sharpening fibers in diffusion weighted MRI via erosion. In: Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data, pp. 97–126. Springer (2014)
6.
Zurück zum Zitat Descoteaux, M., Deriche, R., Knosche, T.R., Anwander, A.: Deterministic and probabilistic tractography based on complex fibre orientation distributions. IEEE Trans. Med. Imaging 28(2), 269–286 (2009)CrossRef Descoteaux, M., Deriche, R., Knosche, T.R., Anwander, A.: Deterministic and probabilistic tractography based on complex fibre orientation distributions. IEEE Trans. Med. Imaging 28(2), 269–286 (2009)CrossRef
7.
Zurück zum Zitat Desikan, R.S., Segonne, F., et al.: An automated labeling system for subdividing the human cerebral cortex on MRI scans into gyral based regions of interest. Neuroimage 31(3), 968–980 (2006)CrossRef Desikan, R.S., Segonne, F., et al.: An automated labeling system for subdividing the human cerebral cortex on MRI scans into gyral based regions of interest. Neuroimage 31(3), 968–980 (2006)CrossRef
8.
Zurück zum Zitat Duits, R., Franken, E.M.: Left-invariant diffusions on the space of positions and orientations and their application to crossing-preserving smoothing of HARDI images. Int. J. Comput. Vis. (IJCV) 92, 231–264 (2011)MathSciNetCrossRef Duits, R., Franken, E.M.: Left-invariant diffusions on the space of positions and orientations and their application to crossing-preserving smoothing of HARDI images. Int. J. Comput. Vis. (IJCV) 92, 231–264 (2011)MathSciNetCrossRef
9.
Zurück zum Zitat Duits, R., Meesters, S.P.L., Mirebeau, J.M., Portegies, J.M.: Optimal paths for variants of the 2D and 3D reeds-shepp car with applications in image analysis, JMIV S.I. Differ. Geom. Orientat. Anal. 60(6), 818–846 (2018) Duits, R., Meesters, S.P.L., Mirebeau, J.M., Portegies, J.M.: Optimal paths for variants of the 2D and 3D reeds-shepp car with applications in image analysis, JMIV S.I. Differ. Geom. Orientat. Anal. 60(6), 818–846 (2018)
10.
Zurück zum Zitat Fisher, R., Salanova, V., et al.: Electrical stimulation of the anterior nucleus of thalamus for treatment of refractory epilepsy. Epilepsia 51(5), 899–908 (2010)CrossRef Fisher, R., Salanova, V., et al.: Electrical stimulation of the anterior nucleus of thalamus for treatment of refractory epilepsy. Epilepsia 51(5), 899–908 (2010)CrossRef
11.
Zurück zum Zitat Fletcher, P., Joshi, S.: Riemannian geometry for the statistical analysis of diffusion tensor data. Signal Process. 87(2), 250–262 (2007)CrossRef Fletcher, P., Joshi, S.: Riemannian geometry for the statistical analysis of diffusion tensor data. Signal Process. 87(2), 250–262 (2007)CrossRef
12.
Zurück zum Zitat Fuster, A., Dela Haije, T., Tristán-Vega, A., Plantinga, B., Westin, C.F., Florack, L.: Adjugate diffusion tensors for geodesic tractography in white matter. J. Math. Imaging Vis. 54(1), 1–14 (2016)MathSciNetCrossRef Fuster, A., Dela Haije, T., Tristán-Vega, A., Plantinga, B., Westin, C.F., Florack, L.: Adjugate diffusion tensors for geodesic tractography in white matter. J. Math. Imaging Vis. 54(1), 1–14 (2016)MathSciNetCrossRef
13.
Zurück zum Zitat Glasser, M.F., Sotiropoulos, S.N., Wilson, J.A., Coalson, T.S., Fischl, B., Andersson, J.L., Xu, J., Jbabdi, S., Webster, M., Polimeni, J.R., Van Essen, D.C., Jenkinson, M.: The minimal preprocessing pipelines for the human connectome project. Neuroimage 80, 105–124 (2013)CrossRef Glasser, M.F., Sotiropoulos, S.N., Wilson, J.A., Coalson, T.S., Fischl, B., Andersson, J.L., Xu, J., Jbabdi, S., Webster, M., Polimeni, J.R., Van Essen, D.C., Jenkinson, M.: The minimal preprocessing pipelines for the human connectome project. Neuroimage 80, 105–124 (2013)CrossRef
14.
Zurück zum Zitat Gologorsky, Y., Alterman, R.: Chapter 3—cerebral-deep. In: Arle, J.E., Shils, J.L. (eds.) Essential Neuromodulation, pp. 47–72. Academic Press, San Diego (2011)CrossRef Gologorsky, Y., Alterman, R.: Chapter 3—cerebral-deep. In: Arle, J.E., Shils, J.L. (eds.) Essential Neuromodulation, pp. 47–72. Academic Press, San Diego (2011)CrossRef
15.
Zurück zum Zitat Granziera, C., Hadjikhani, N., Arzy, S., Seeck, M., Meuli, R., Krueger, G.: In-vivo magnetic resonance imaging of the structural core of the papez circuit in humans. Neuroreport 22(5), 227–31 (2011)CrossRef Granziera, C., Hadjikhani, N., Arzy, S., Seeck, M., Meuli, R., Krueger, G.: In-vivo magnetic resonance imaging of the structural core of the papez circuit in humans. Neuroreport 22(5), 227–31 (2011)CrossRef
16.
Zurück zum Zitat Hodaie, M., Cordella, R., Lozano, A.M., Wennberg, R., Dostrovsky, J.O.: Bursting activity of neurons in the human ATN. Brain Res. 1115(1), 1–8 (2006)CrossRef Hodaie, M., Cordella, R., Lozano, A.M., Wennberg, R., Dostrovsky, J.O.: Bursting activity of neurons in the human ATN. Brain Res. 1115(1), 1–8 (2006)CrossRef
17.
Zurück zum Zitat Jakab, A., Blanc, R., Berényi, E.L., Székely, G.: Generation of individualized thalamus target maps by using statistical shape models and thalamocortical tractography. Am. J. Neuroradiol. 33(11), 2110–2116 (2012)CrossRef Jakab, A., Blanc, R., Berényi, E.L., Székely, G.: Generation of individualized thalamus target maps by using statistical shape models and thalamocortical tractography. Am. J. Neuroradiol. 33(11), 2110–2116 (2012)CrossRef
18.
Zurück zum Zitat Jankowski, M.M., Ronnqvist, K.C., Tsanov, l., O’Mara, S.M.: The anterior thalamus provides a subcortical circuit supporting memory and spatial navigation. Front. Syst. Neurosci. 7, 45 (2013) Jankowski, M.M., Ronnqvist, K.C., Tsanov, l., O’Mara, S.M.: The anterior thalamus provides a subcortical circuit supporting memory and spatial navigation. Front. Syst. Neurosci. 7, 45 (2013)
19.
Zurück zum Zitat Jbabdi, S., Bellec, P., Toro, R., Daunizeau, J., Pélégrini-Issac, M., Benali, H.: Accurate anisotropic fast marching for diffusion-based geodesic tractography. Int. J. Biomed. Imaging 2008 (2008)CrossRef Jbabdi, S., Bellec, P., Toro, R., Daunizeau, J., Pélégrini-Issac, M., Benali, H.: Accurate anisotropic fast marching for diffusion-based geodesic tractography. Int. J. Biomed. Imaging 2008 (2008)CrossRef
20.
Zurück zum Zitat Jenkinson, M., Beckmann, C.F., Behrens, T.E.J., Woolrich, M.W., Smith, S.M.: FSL. Neuroimage 62(2), 782–790 (2012)CrossRef Jenkinson, M., Beckmann, C.F., Behrens, T.E.J., Woolrich, M.W., Smith, S.M.: FSL. Neuroimage 62(2), 782–790 (2012)CrossRef
21.
Zurück zum Zitat Jeurissen, B., Tournier, J.D., Dhollander, T., Connelly, A., Sijbers, J.: Multi-tissue constrained spherical deconvolution for improved analysis of multi-shell diffusion MRI data. Neuroimage 103(0), 411–426 (2014)CrossRef Jeurissen, B., Tournier, J.D., Dhollander, T., Connelly, A., Sijbers, J.: Multi-tissue constrained spherical deconvolution for improved analysis of multi-shell diffusion MRI data. Neuroimage 103(0), 411–426 (2014)CrossRef
22.
Zurück zum Zitat Kerrigan, J.F., Litt, B., Fisher, R.S., Cranstoun, S., French, J.A., Blum, D.E., Dichter, M., Shetter, A., Baltuch, G., Jaggi, J., Krone, S., Brodie, M., Rise, M., Graves, N.: Electrical stimulation of the anterior nucleus of the thalamus for the treatment of intractable epilepsy. Epilepsia 45(4), 346–354 (2004)CrossRef Kerrigan, J.F., Litt, B., Fisher, R.S., Cranstoun, S., French, J.A., Blum, D.E., Dichter, M., Shetter, A., Baltuch, G., Jaggi, J., Krone, S., Brodie, M., Rise, M., Graves, N.: Electrical stimulation of the anterior nucleus of the thalamus for the treatment of intractable epilepsy. Epilepsia 45(4), 346–354 (2004)CrossRef
23.
Zurück zum Zitat Krauth, A., Blanc, R., Poveda, A., Jeanmonod, D., Morel, A., Székely, G.: A mean three-dimensional atlas of the human thalamus: generation from multiple histological data. Neuroimage 49(3), 2053–2062 (2010)CrossRef Krauth, A., Blanc, R., Poveda, A., Jeanmonod, D., Morel, A., Székely, G.: A mean three-dimensional atlas of the human thalamus: generation from multiple histological data. Neuroimage 49(3), 2053–2062 (2010)CrossRef
24.
Zurück zum Zitat Melonakos, J., Mohan, V., Niethammer, M., Smith, K., Kubicki, M., Tannenbaum, A.: Finsler tractography for white matter connectivity analysis of the cingulum bundle. Med. Image Comput. Comput. Assist. Interv. 10(01), 36–43 (2007) Melonakos, J., Mohan, V., Niethammer, M., Smith, K., Kubicki, M., Tannenbaum, A.: Finsler tractography for white matter connectivity analysis of the cingulum bundle. Med. Image Comput. Comput. Assist. Interv. 10(01), 36–43 (2007)
25.
Zurück zum Zitat Melonakos, J., Pichon, E., Angenent, S., Tannenbaum, A.: Finsler active contours. IEEE Trans. Pattern Anal. Mach. Intell. 30(3), 412–423 (2008)CrossRef Melonakos, J., Pichon, E., Angenent, S., Tannenbaum, A.: Finsler active contours. IEEE Trans. Pattern Anal. Mach. Intell. 30(3), 412–423 (2008)CrossRef
26.
Zurück zum Zitat Mirebeau, J.: Anisotropic fast-marching on cartesian grids using lattice basis reduction. SIAM J. Numer. Anal. 52(4), 1573–1599 (2014)MathSciNetCrossRef Mirebeau, J.: Anisotropic fast-marching on cartesian grids using lattice basis reduction. SIAM J. Numer. Anal. 52(4), 1573–1599 (2014)MathSciNetCrossRef
27.
28.
Zurück zum Zitat MomayyezSiahkal, P., Siddiqi, K.: 3D stochastic completion fields for mapping connectivity in diffusion MRI. IEEE Trans. Pattern Anal. Mach. Intell. 35(4), 983–995 (2013)CrossRef MomayyezSiahkal, P., Siddiqi, K.: 3D stochastic completion fields for mapping connectivity in diffusion MRI. IEEE Trans. Pattern Anal. Mach. Intell. 35(4), 983–995 (2013)CrossRef
29.
Zurück zum Zitat Niemann, K., Mennicken, V.R., Jeanmonod, D., Morel, A.: The morel stereotactic atlas of the human thalamus: atlas-to-MR registration of internally consistent canonical model. Neuroimage 12(6), 601–616 (2000)CrossRef Niemann, K., Mennicken, V.R., Jeanmonod, D., Morel, A.: The morel stereotactic atlas of the human thalamus: atlas-to-MR registration of internally consistent canonical model. Neuroimage 12(6), 601–616 (2000)CrossRef
30.
Zurück zum Zitat 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, pp. 459–466. Springer, Berlin (2002)CrossRef 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, pp. 459–466. Springer, Berlin (2002)CrossRef
31.
Zurück zum Zitat Péchaud, M., Descoteaux, M., Keriven, R.: Brain connectivity using geodesics in HARDI. Med. Image Comput. Comput. Assist. Interv. 12(2), 482–489 (2009) Péchaud, M., Descoteaux, M., Keriven, R.: Brain connectivity using geodesics in HARDI. Med. Image Comput. Comput. Assist. Interv. 12(2), 482–489 (2009)
32.
Zurück zum Zitat Portegies, J.M., Fick, R.H.J., Sanguinetti, G.R., Meesters, S.P.L., Girard, G., Duits, R.: Improving fiber alignment in HARDI by combining contextual PDE flow with constrained spherical deconvolution. PLoS One 10(10) (2015)CrossRef Portegies, J.M., Fick, R.H.J., Sanguinetti, G.R., Meesters, S.P.L., Girard, G., Duits, R.: Improving fiber alignment in HARDI by combining contextual PDE flow with constrained spherical deconvolution. PLoS One 10(10) (2015)CrossRef
33.
Zurück zum Zitat Portegies, J.: PDEs on the Lie Group SE(3) and their applications in diffusion-weighted MRI. Ph.D. thesis, Department of Mathematics and Computer Science, TU/e (2018) Portegies, J.: PDEs on the Lie Group SE(3) and their applications in diffusion-weighted MRI. Ph.D. thesis, Department of Mathematics and Computer Science, TU/e (2018)
34.
Zurück zum Zitat Prckovska, V., Rodrigues, P., Duits, R., Vilanova, A., ter Haar Romeny, B.: Extrapolating fiber crossings from DTI data. Can we infer similar fiber crossings as in HARDI? In: CDMRI 2010. vol. 1, pp. 26–37. Springer, Beijing (2010) Prckovska, V., Rodrigues, P., Duits, R., Vilanova, A., ter Haar Romeny, B.: Extrapolating fiber crossings from DTI data. Can we infer similar fiber crossings as in HARDI? In: CDMRI 2010. vol. 1, pp. 26–37. Springer, Beijing (2010)
35.
Zurück zum Zitat Reisert, M., Skibbe, H.: Fiber continuity based spherical deconvolution in spherical harmonic domain. In: Mori, K.e.a. (ed.) MICCAI, pp. 493–500. Springer (2013) Reisert, M., Skibbe, H.: Fiber continuity based spherical deconvolution in spherical harmonic domain. In: Mori, K.e.a. (ed.) MICCAI, pp. 493–500. Springer (2013)
36.
Zurück zum Zitat Sanguinetti, G., Bekkers, E., Duits, R., Janssen, M.H.J., Mashtakov, A., Mirebeau, J.M.: Sub-Riemannian Fast Marching in SE(2). Springer (2015) Sanguinetti, G., Bekkers, E., Duits, R., Janssen, M.H.J., Mashtakov, A., Mirebeau, J.M.: Sub-Riemannian Fast Marching in SE(2). Springer (2015)
37.
Zurück zum Zitat Sepasian, N., ten Thije Boonkkamp, J.H.M., ter Haar Romeny, B.M., Vilanova, A.: Multivalued geodesic ray-tracing for computing brain connections using diffusion tensor imaging. SIAM-JIS 5(2), 483–504 (2012)MathSciNetMATH Sepasian, N., ten Thije Boonkkamp, J.H.M., ter Haar Romeny, B.M., Vilanova, A.: Multivalued geodesic ray-tracing for computing brain connections using diffusion tensor imaging. SIAM-JIS 5(2), 483–504 (2012)MathSciNetMATH
38.
Zurück zum Zitat Shah, A., Jhawar, S.S., Goel, A.: Analysis of the anatomy of the Papez circuit and adjoining limbic system by fiber dissection techniques. J. Clin. Neurosci. 19(2), 289–98 (2012)CrossRef Shah, A., Jhawar, S.S., Goel, A.: Analysis of the anatomy of the Papez circuit and adjoining limbic system by fiber dissection techniques. J. Clin. Neurosci. 19(2), 289–98 (2012)CrossRef
39.
Zurück zum Zitat Tax, C.M.W., Duits, R., Vilanova, A., ter Haar Romeny, B.M., Hofman, P., Wagner, L., Leemans, A., Ossenblok, P.: Evaluating contextual processing in diffusion MRI: application to optic radiation reconstruction for epilepsy surgery. PLoS One 9(7), 1–19 (2014)CrossRef Tax, C.M.W., Duits, R., Vilanova, A., ter Haar Romeny, B.M., Hofman, P., Wagner, L., Leemans, A., Ossenblok, P.: Evaluating contextual processing in diffusion MRI: application to optic radiation reconstruction for epilepsy surgery. PLoS One 9(7), 1–19 (2014)CrossRef
40.
Zurück zum Zitat Tournier, J.D., Calamante, F., Connelly, A.: MRtrix: diffusion tractography in crossing fiber regions. Int. J. Imaging Syst. Technol. 22(1), 53–66 (2012)CrossRef Tournier, J.D., Calamante, F., Connelly, A.: MRtrix: diffusion tractography in crossing fiber regions. Int. J. Imaging Syst. Technol. 22(1), 53–66 (2012)CrossRef
41.
Zurück zum Zitat Tournier, J.D., Yeh, C.H., Calamante, F., Cho, K.H., Connelly, A., Lin, C.P.: Resolving crossing fibres using constrained spherical deconvolution: validation using diffusion-weighted imaging phantom data. NeuroImage 42(2), 617–625 (2008)CrossRef Tournier, J.D., Yeh, C.H., Calamante, F., Cho, K.H., Connelly, A., Lin, C.P.: Resolving crossing fibres using constrained spherical deconvolution: validation using diffusion-weighted imaging phantom data. NeuroImage 42(2), 617–625 (2008)CrossRef
42.
Zurück zum Zitat Van Essen, D.C., Smith, S.M., Barch, D.M., Behrens, T.E.J., Yacoub, E., Ugurbil, K.: The WU-Minn human connectome project. NeuroImage 80, 62–79 (2013)CrossRef Van Essen, D.C., Smith, S.M., Barch, D.M., Behrens, T.E.J., Yacoub, E., Ugurbil, K.: The WU-Minn human connectome project. NeuroImage 80, 62–79 (2013)CrossRef
43.
Zurück zum Zitat Vogt, T., Lellmann, J.: Measure-valued variational models with applications to diffusion-weighted imaging. J. Math. Imaging Vis. (2018) Vogt, T., Lellmann, J.: Measure-valued variational models with applications to diffusion-weighted imaging. J. Math. Imaging Vis. (2018)
Metadaten
Titel
Brain Connectivity Measures via Direct Sub-Finslerian Front Propagation on the 5D Sphere Bundle of Positions and Directions
verfasst von
Jorg Portegies
Stephan Meesters
Pauly Ossenblok
Andrea Fuster
Luc Florack
Remco Duits
Copyright-Jahr
2019
DOI
https://doi.org/10.1007/978-3-030-05831-9_24