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Cellular Automata Tractography: Fast Geodesic Diffusion MR Tractography and Connectivity Based Segmentation on the GPU

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Abstract

Geodesic based tractography on diffusion magnetic resonance data is a method to devise long distance connectivities among the brain regions. In this study, cellular automata technique is applied to the geodesic tractography problem and the algorithm is implemented on a graphics processing unit. Cellular automaton based method is preferable to current techniques due to its parallel nature and ability to solve the connectivity based segmentation problem with the same computational complexity, which has important applications in neuroimaging. An application to prior-less tracking and connectivity based segmentation of corpus callosum fibers is presented as an example. A geodesic tractography based corpus callosum atlas is provided, which reveals high projections to the cortical language areas. The developed method not only allows fast computation especially for segmentation but also provides a powerful and intuitive framework, suitable to derive new algorithms to perform connectivity calculations and allowing novel applications.

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Notes

  1. Available at http://www.tractometer.org

  2. https://www.natbrainlab.co.uk

References

  • Avants, B.B., Epstein, C.L., Grossman, M., Gee, J.C. (2008). Symmetric diffeomorphic image registration with cross-correlation: evaluating automated labeling of elderly and neurodegenerative brain. Medical Image Analysis, 12(1), 26–41.

    CAS  PubMed  Google Scholar 

  • Basser, P.J., Pajevic, S., Pierpaoli, C., Duda, J., Aldroubi, A. (2000). In vivo fiber tractography using dt-mri data. Magnetic Resonance in Medicine, 44(4), 625–632.

    CAS  PubMed  Google Scholar 

  • Bastiani, M., Cottaar, M., Dikranian, K., Ghosh, A., Zhang, H., Alexander, D.C., Behrens, T.E., Jbabdi, S., Sotiropoulos, S.N. (2017). Improved tractography using asymmetric fibre orientation distributions. NeuroImage, 158, 205–218.

    PubMed  PubMed Central  Google Scholar 

  • Behrens, T.E., Johansen-Berg, H., Woolrich, M., Smith, S., Wheeler-Kingshott, C., Boulby, P., Barker, G., Sillery, E., Sheehan, K., Ciccarelli, O., et al. (2003a). Non-invasive mapping of connections between human thalamus and cortex using diffusion imaging. Nature Neuroscience, 6(7), 750.

    CAS  PubMed  Google Scholar 

  • Behrens, T.E., Woolrich, M.W., Jenkinson, M., Johansen-Berg, H., Nunes, R.G., Clare, S., Matthews, P.M., Brady, J.M., Smith, S.M. (2003b). Characterization and propagation of uncertainty in diffusion-weighted mr imaging. Magnetic Resonance in Medicine, 50(5), 1077–1088.

    CAS  PubMed  Google Scholar 

  • Booth, B.G., & Hamarneh, G. (2011). Exact integration of diffusion orientation distribution functions for graph-based diffusion mri analysis. In 2011 IEEE International Symposium on Biomedical Imaging: From Nano to Macro (pp. 935–938). IEEE.

  • Busato, F., & Bombieri, N. (2016). An efficient implementation of the bellman-ford algorithm for kepler gpu architectures. IEEE Transactions on Parallel and Distributed Systems, 27, 2222–2233.

    Google Scholar 

  • Calamante, F., & Chi, J.G. (2014). 7.0 Tesla MRI Brain White Matter Atlas. Berlin: Springer.

    Google Scholar 

  • Catani, M., & De Schotten, M.T. (2008). A diffusion tensor imaging tractography atlas for virtual in vivo dissections. Cortex, 44(8), 1105–1132.

    PubMed  Google Scholar 

  • Catani, M., Howard, R.J., Pajevic, S., Jones, D.K. (2002). Virtual in vivo interactive dissection of white matter fasciculi in the human brain. NeuroImage, 17(1), 77–94.

    PubMed  Google Scholar 

  • Christiaens, D., Reisert, M., Dhollander, T., Sunaert, S., Suetens, P., Maes, F. (2015). Global tractography of multi-shell diffusion-weighted imaging data using a multi-tissue model. NeuroImage, 123, 89–101.

    PubMed  Google Scholar 

  • Cieslak, M., Brennan, T., Meiring, W., Volz, L.J., Greene, C., Asturias, A., Suri, S., Grafton, S.T. (2018). Analytic tractography: a closed-form solution for estimating local white matter connectivity with diffusion mri. NeuroImage, 169, 473–484.

    PubMed  Google Scholar 

  • Conturo, T.E., Lori, N.F., Cull, T.S., Akbudak, E., Snyder, A.Z., Shimony, J.S., McKinstry, R.C., Burton, H., Raichle, M.E. (1999). Tracking neuronal fiber pathways in the living human brain. Proceedings of the National Academy of Sciences, 96(18), 10422–10427.

    CAS  Google Scholar 

  • Cote, M.A., Girard, G, Bore, A., Garyfallidis, E. , Houde, J.C., Descoteaux, M. (2013). Tractometer: Towards validation of tractography pipelines. Medical Image Analysis, 17(7), 844–857. special Issue on the 2012 Conference on Medical Image Computing and Computer Assisted Intervention.

    PubMed  Google Scholar 

  • Di Paola, M., Spalletta, G., Caltagirone, C. (2010). In vivo structural neuroanatomy of corpus callosum in alzheimer’s disease and mild cognitive impairment using different mri techniques: a review. Journal of Alzheimer’s disease, 20(1), 67–95.

    PubMed  Google Scholar 

  • Fawcett, T. (2006). An introduction to roc analysis. Pattern Recognition Letters, 27(8), 861–874. rOC Analysis in Pattern Recognition.

    Google Scholar 

  • Fillard, P., Descoteaux, M., Goh, A., Gouttard, S., Jeurissen, B., Malcolm, J., Ramirez-Manzanares, A., Reisert, M., Sakaie, K., Tensaouti, F., Yo, T., Mangin, J.F., Poupon, C. (2011). Quantitative evaluation of 10 tractography algorithms on a realistic diffusion mr phantom. NeuroImage, 56(1), 220–234.

    PubMed  Google Scholar 

  • Fonov, V., Evans, A., McKinstry, R., Almli, C., Collins, D. (2009). Unbiased nonlinear average age-appropriate brain templates from birth to adulthood. NeuroImage, 47, S102. organization for Human Brain Mapping 2009 Annual Meeting.

    Google Scholar 

  • Fuster, A., Dela Haije, T., Tristán-Vega, A, Plantinga, B., Westin, C.F., Florack, L. (2016). Adjugate diffusion tensors for geodesic tractography in white matter. Journal of Mathematical Imaging and Vision, 54(1), 1–14.

    Google Scholar 

  • Garyfallidis, E., Brett, M., Amirbekian, B., Rokem, A., Van Der Walt, S., Descoteaux, M., Nimmo-Smith, I. (2014). Dipy, a library for the analysis of diffusion mri data. Frontiers in Neuroinformatics, 8, 8.

    PubMed  PubMed Central  Google Scholar 

  • Gorgolewski, K., Burns, C., Madison, C., Clark, D., Halchenko, Y., Waskom, M., Ghosh, S. (2011). Nipype: a flexible, lightweight and extensible neuroimaging data processing framework in python. Frontiers in Neuroinformatics, 5, 13.

    PubMed  PubMed Central  Google Scholar 

  • Hae-Jeong, P., Jin, K.J., Seung-Koo, L., Ho, S.J., Jiwon, C., Ik, K.D., Doo, L.J. (2008). Corpus callosal connection mapping using cortical gray matter parcellation and dt-mri. Human Brain Mapping, 29 (5), 503–516.

    Google Scholar 

  • Hagberg, A.A., Schult, D.A., Swart, P.J. (2008). Exploring network structure, dynamics, and function using networkx. In Varoquaux, G., Vaught, T., Millman, J. (Eds.) Proceedings of the 7th Python in Science Conference, Pasadena, CA USA (pp. 11–15).

  • Hamamci, A., Kucuk, N., Karaman, K., Engin, K., Unal, G. (2012). Tumor-cut: segmentation of brain tumors on contrast enhanced mr images for radiosurgery applications. IEEE Transactions on Medical Imaging, 31(3), 790–804.

    PubMed  Google Scholar 

  • Harms, R., Fritz, F., Tobisch, A., Goebel, R., Roebroeck, A. (2017). Robust and fast nonlinear optimization of diffusion mri microstructure models. NeuroImage, 155, 82–96.

    CAS  PubMed  PubMed Central  Google Scholar 

  • Hernandez, M., Guerrero, G.D., Cecilia, J.M., Garcia, J.M., Inuggi, A., Jbabdi, S., Behrens, T.E.J., Sotiropoulos, S.N. (2013). Accelerating fibre orientation estimation from diffusion weighted magnetic resonance imaging using gpus. PLOS ONE, 8(4), 1–13.

    Google Scholar 

  • Hernandez-Fernandez, M., Reguly, I., Jbabdi, S., Giles, M., Smith, S., Sotiropoulos, S.N. (2019). Using gpus to accelerate computational diffusion mri: From microstructure estimation to tractography and connectomes. NeuroImage, 188, 598–615.

    PubMed  Google Scholar 

  • Hofer, S., & Frahm, J. (2006). Topography of the human corpus callosum revisited—comprehensive fiber tractography using diffusion tensor magnetic resonance imaging. NeuroImage, 32(3), 989–994.

    PubMed  Google Scholar 

  • Iturria-Medina, Y., Canales-Rodríguez, E., Melie-García, L., Valdés-Hernández, P., Martínez-Montes, E., Alemán-Gómez, Y., Sánchez-Bornot, J. (2007). Characterizing brain anatomical connections using diffusion weighted mri and graph theory. NeuroImage, 36(3), 645–660.

    CAS  PubMed  Google Scholar 

  • Jarbo, K., Verstynen, T., Schneider, W. (2012). In vivo quantification of global connectivity in the human corpus callosum. NeuroImage, 59(3), 1988–1996.

    PubMed  Google Scholar 

  • Jbabdi, S., Woolrich, M., Andersson, J., Behrens, T. (2007). A bayesian framework for global tractography. NeuroImage, 37(1), 116–129.

    CAS  PubMed  Google Scholar 

  • Jbabdi, S., Bellec, P., Toro, R., Daunizeau, J., Pélégrini-Issac, M., Benali, H. (2008). Accurate anisotropic fast marching for diffusion-based geodesic tractography. International Journal of Biomedical Imaging, 2008, 12.

    Google Scholar 

  • Kaneko, K. (1992). Overview of coupled map lattices. Chaos: an Interdisciplinary Journal of Nonlinear Science, 2(3), 279–282.

    Google Scholar 

  • Karayumak, S.C., Ozarslan, E., Unal, G. (2018). Asymmetric orientation distribution functions (aodfs) revealing intravoxel geometry in diffusion mri. Magnetic Resonance Imaging, 49, 145–158.

    Google Scholar 

  • Kasenburg, N., Liptrot, M., Reislev, N.L., Ørting, SN, Nielsen, M., Garde, E., Feragen, A. (2016). Training shortest-path tractography: Automatic learning of spatial priors. NeuroImage, 130(Supplement C), 63–76.

    PubMed  Google Scholar 

  • Kauffmann, C., & Piché, N. (2010). Seeded nd medical image segmentation by cellular automaton on gpu. International Journal of Computer Assisted Radiology and Surgery, 5(3), 251–262.

    PubMed  Google Scholar 

  • Li, M., Ratnanather, J.T., Miller, M.I., Mori, S. (2014). Knowledge-based automated reconstruction of human brain white matter tracts using a path-finding approach with dynamic programming. NeuroImage, 88, 271–281.

    PubMed  Google Scholar 

  • Maier-Hein, K.H., Neher, P.F., Houde, J.C., Cot, M.A., Garyfallidis, E., Zhong, J., Chamberland, M., Yeh, F.C., Lin, Y.C., Ji, Q., et al. (2017). The challenge of mapping the human connectome based on diffusion tractography. Nature Communications, 8(1), 1349.

    PubMed  PubMed Central  Google Scholar 

  • Mangin, J.F., Fillard, P., Cointepas, Y., Bihan, D.L., Frouin, V., Poupon, C. (2013). Toward global tractography. NeuroImage, 80(0), 290–296.

    PubMed  Google Scholar 

  • Mittmann, A., Comunello, E., von Wangenheim, A. (2008). Diffusion tensor fiber tracking on graphics processing units. Computerized Medical Imaging and Graphics, 32(7), 521–530.

    PubMed  Google Scholar 

  • Mojtaba, Z., Heidi, J., Steve, S., Olga, C., J TA, M.M.P. (2006). Functional anatomy of interhemispheric cortical connections in the human brain. Journal of Anatomy, 209(3), 311–320.

    Google Scholar 

  • Mori, S., Crain, B.J., Chacko, V.P., van Zijl, P.C. (1999). Three-dimensional tracking of axonal projections in the brain by magnetic resonance imaging. Annals of Neurology, 45(2), 265–9.

    CAS  PubMed  Google Scholar 

  • Oguz, I., Boucharin, A., Lu, W., Vachet, C., Budin, F., Shi, Y., Styner, M. (2012). A minimum cost approach to connectivity from orientation distribution functions via efficient multi-directional graph propagation. In Proceedings of CDMRI Workshop, MICCAI 2012 (pp. 210–221).

  • Ostrov, D.N., & Rucker, R. (1996). Continuous-valued cellular automata for nonlinear wave equations. Complex systems, 10(2), 91–120.

    Google Scholar 

  • Pannek, K., Mathias, J.L., Bigler, E.D., Brown, G., Taylor, J.D., Rose, S. (2010). An automated strategy for the delineation and parcellation of commissural pathways suitable for clinical populations utilising high angular resolution diffusion imaging tractography. NeuroImage, 50(3), 1044–1053.

    PubMed  Google Scholar 

  • Parker, G.J.M., Wheeler-Kingshott, C.A.M., Barker, G.J. (2002). Estimating distributed anatomical connectivity using fast marching methods and diffusion tensor imaging. IEEE Transactions on Medical Imaging, 21 (5), 505–512.

    PubMed  Google Scholar 

  • Peng, H., Orlichenko, A., Dawe, R.J., Agam, G., Zhang, S., Arfanakis, K. (2009). Development of a human brain diffusion tensor template. NeuroImage, 46(4), 967–980.

    PubMed  PubMed Central  Google Scholar 

  • Poupon, C., Mangin, J.F., Clark, C.A., Frouin, V., Régis, J, Le Bihan, D., Bloch, I. (2001). Towards inference of human brain connectivity from mr diffusion tensor data. Medical Image Analysis, 5(1), 1–15.

    CAS  PubMed  Google Scholar 

  • Poupon, C., Rieul, B., Kezele, I., Perrin, M., Poupon, F., Mangin, J.F. (2008). New diffusion phantoms dedicated to the study and validation of high-angular-resolution diffusion imaging (hardi) models. Magnetic Resonance in Medicine, 60(6), 1276–1283.

    PubMed  Google Scholar 

  • Ratnanather, J.T., Lal, R.M., An, M., Poynton, C.B., Li, M., Jiang, H., Oishi, K., Selemon, L.D., Mori, S., Miller, M.I. (2013). Cortico-cortical, cortico-striatal, and cortico-thalamic white matter fiber tracts generated in the macaque brain via dynamic programming. Brain Connectivity, 3(5), 475–490.

    PubMed  PubMed Central  Google Scholar 

  • Reisert, M., Mader, I., Anastasopoulos, C., Weigel, M., Schnell, S., Kiselev, V. (2011). Global fiber reconstruction becomes practical. NeuroImage, 54(2), 955–962.

    PubMed  Google Scholar 

  • Rex, D.E., Ma, J.Q., Toga, A.W. (2003). The loni pipeline processing environment. NeuroImage, 19(3), 1033–1048.

    PubMed  Google Scholar 

  • Schilling, K.G., Daducci, A., Maier-Hein, K., Poupon, C., Houde, J.C., Nath, V., Anderson, A.W., Landman, B.A., Descoteaux, M. (2019a). Challenges in diffusion mri tractography – lessons learned from international benchmark competitions. Magnetic Resonance Imaging, 57, 194–209.

    PubMed  Google Scholar 

  • Schilling, K.G., Nath, V., Hansen, C., Parvathaneni, P., Blaber, J., Gao, Y., Neher, P., Aydogan, D.B., Shi, Y., Ocampo-Pineda, M., Schiavi, S., Daducci, A., Girard, G., Barakovic, M., Rafael-Patino, J., Romascano, D., Rensonnet, G., Pizzolato, M., Bates, A., Fischi, E., Thiran, J.P., Canales-Rodríguez, E.J., Huang, C., Zhu, H., Zhong, L., Cabeen, R., Toga, A.W., Rheault, F., Theaud, G., Houde, J.C., Sidhu, J., Chamberland, M., Westin, C.F., Dyrby, T.B., Verma, R., Rathi, Y., Irfanoglu, M.O., Thomas, C., Pierpaoli, C., Descoteaux, M., Anderson, A.W., Landman, B.A. (2019b). Limits to anatomical accuracy of diffusion tractography using modern approaches. NeuroImage, 185, 1–11.

    PubMed  Google Scholar 

  • de Schotten, M.T., ffytche, D.H., Bizzi, A., Dell’Acqua, F., Allin, M., Walshe, M., Murray, R., Williams, S.C., Murphy, D.G., Catani, M. (2011). Atlasing location, asymmetry and inter-subject variability of white matter tracts in the human brain with mr diffusion tractography. NeuroImage, 54(1), 49–59.

    Google Scholar 

  • Schumacher, L.V., Reisert, M., Nitschke, K., Egger, K., Urbach, H., Hennig, J., Weiller, C., Kaller, C.P. (2018). Probing the reproducibility of quantitative estimates of structural connectivity derived from global tractography. NeuroImage, 175, 215–229.

    PubMed  Google Scholar 

  • Sotiropoulos, S.N., Bai, L., Morgan, P.S., Constantinescu, C.S., Tench, C.R. (2010). Brain tractography using q-ball imaging and graph theory: Improved connectivities through fibre crossings via a model-based approach. NeuroImage, 49(3), 2444–2456.

    PubMed  Google Scholar 

  • Sotiropoulos, SN, Jbabdi, S, Xu, J, Andersson, JL, Moeller, S, Auerbach, EJ, Glasser, MF, Hernandez, M, Sapiro, G, Jenkinson, M, Feinberg, DA, Yacoub, E, Lenglet, C, Essen, DCV, Ugurbil, K, Behrens, TE. (2013). Advances in diffusion mri acquisition and processing in the human connectome project. NeuroImage, 80, 125–143. mapping the Connectome.

    PubMed  PubMed Central  Google Scholar 

  • Staempfli, P., Jaermann, T., Crelier, G., Kollias, S., Valavanis, A., Boesiger, P. (2006). Resolving fiber crossing using advanced fast marching tractography based on diffusion tensor imaging. NeuroImage, 30(1), 110–120.

    CAS  PubMed  Google Scholar 

  • Tournier, J.D., Calamante, F., Gadian, D.G., Connelly, A. (2004). Direct estimation of the fiber orientation density function from diffusion-weighted mri data using spherical deconvolution. NeuroImage, 23(3), 1176–1185.

    PubMed  Google Scholar 

  • Tournier, J.D., Calamante, F., Connelly, A. (2007). Robust determination of the fibre orientation distribution in diffusion mri: Non-negativity constrained super-resolved spherical deconvolution. NeuroImage, 35(4), 1459–1472.

    PubMed  Google Scholar 

  • Tuch, D.S., Reese, T.G., Wiegell, M.R., Wedeen, V.J. (2003). Diffusion mri of complex neural architecture. Neuron, 40(5), 885–895.

    CAS  PubMed  Google Scholar 

  • Van Essen, DC, Smith, SM, Barch, DM, Behrens, TE, Yacoub, E, Ugurbil, K. (2013). The wu-minn human connectome project: an overview. NeuroImage, 80, 62–79. mapping the Connectome.

    PubMed  PubMed Central  Google Scholar 

  • Van Horn, J.D., & Toga, A.W. (2014). Human neuroimaging as a “big data” science. Brain Imaging and Behavior, 8(2), 323–331.

    PubMed  PubMed Central  Google Scholar 

  • Von Neumann, J, & Burks, AW. (1966). Theory of Self-Reproducing Automata. Urbana and London: University of Illinois Press.

    Google Scholar 

  • Wakana, S., Caprihan, A., Panzenboeck, M. M., Fallon, J.H., Perry, M., Gollub, R.L., Hua, K., Zhang, J., Jiang, H., Dubey, P., Blitz, A., van Zijl, P., Mori S. (2007). Reproducibility of quantitative tractography methods applied to cerebral white matter. Neuroimage, 36(3), 630–644.

    PubMed  PubMed Central  Google Scholar 

  • Weiner, M.W., Aisen, P.S., Jack, C.R., Jagust, W.J., Trojanowski, J.Q., Shaw, L., Saykin, A.J., Morris, J.C., Cairns, N., Beckett, L.A., Toga, A., Green, R., Walter, S., Soares, H., Snyder, P., Siemers, E., Potter, W., Cole, P.E., Schmidt, M. (2010). The alzheimer’s disease neuroimaging initiative: Progress report and future plans. Alzheimer’s and Dementia, 6(3), 202–211.e7.

    PubMed  Google Scholar 

  • Witelson, S.F. (1989). Hand and sex differences in the isthmus and genu of the human corpus callosum: a postmortem morphological study. Brain: A Journal of Neurology, 112(3), 799–835.

    Google Scholar 

  • Wolfram, S. (2002). A New Kind of Science Vol. 5. Champaign: Wolfram Media.

    Google Scholar 

  • Yi-Ping, C., Kuan-Hung, C., Chun-Hung, Y., Kun-Hsien, C., Jyh-Horng, C., Ching-Po, L. (2009). Probabilistic topography of human corpus callosum using cytoarchitectural parcellation and high angular resolution diffusion imaging tractography. Human Brain Mapping, 30(10), 3172–3187.

    Google Scholar 

  • Yoldemir, B., Acar, B., Firat, Z., Kilickesmez, O. (2012). Smt: a reliability based interactive dti tractography algorithm. IEEE Transactions on Medical Imaging, 31(10), 1929–1940.

    PubMed  Google Scholar 

  • Zalesky, A. (2008). Dt-mri fiber tracking: a shortest paths approach. IEEE Transactions on Medical Imaging, 27, 1458–71.

    PubMed  Google Scholar 

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Acknowledgements

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. The DTI atlas of corpus callosum was available online, provided by Natbrainlab (http://www.natbrainlab.com). The author thanks Umut Sarı for editing the text, Zeynep Fırat for helpful comments and Microsoft company for providing access to the Azure infrastructure.

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    Andac Hamamci

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This work was supported by the Scientific and Technological Research Council of Turkey (TUBITAK) (Project No: 116E407).

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Hamamci, A. Cellular Automata Tractography: Fast Geodesic Diffusion MR Tractography and Connectivity Based Segmentation on the GPU. Neuroinform 18, 25–41 (2020). https://doi.org/10.1007/s12021-019-09425-y

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