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Shape Analysis of White Matter Tracts via the Laplace-Beltrami Spectrum

  • Lindsey KitchellEmail author
  • Daniel Bullock
  • Soichi Hayashi
  • Franco Pestilli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11167)

Abstract

Diffusion-weighted magnetic resonance imaging (dMRI) allows for non-invasive, detailed examination of the white matter structures of the brain. White matter tract specific measures based on either the diffusion tensor model (e.g. FA, ADC, and MD) or tractography (e.g. volume, streamline count or density) are often compared between groups of subjects to localize differences within the white matter. Less commonly examined is the shape of the individual white matter tracts. In this paper, we propose to use the Laplace-Beltrami (LB) spectrum as a descriptor of the shape of white matter tracts. We provide an open, automated pipeline for the computation of the LB spectrum on segmented white matter tracts and demonstrate its efficacy through machine learning classification experiments. We show that the LB spectrum allows for distinguishing subjects diagnosed with bipolar disorder from age and sex matched healthy controls, with classification accuracy reaching 95%. We further demonstrate that the results cannot be explained by traditional measures, such as tract volume, streamline count, or mean and total length. The results indicate that there is valuable information in the anatomical shape of the human white matter tracts.

Keywords

Shape analysis White matter Laplace beltrami spectrum 

Notes

Acknowledgements

This research was supported by NSF IIS-1636893, NSF BCS-1734853, NIH NIMH ULTTR001108, and a Microsoft Research Award, the Indiana University Areas of Emergent Research initiative “Learning: Brains, Machines, Children”, the Pervasive Technology Institute and the Research Technologies Division of University Information Technology Services at Indiana University. The authors thank Yu Wang and Justin Solomon who provided insight and expertise on the Laplace-Beltrami operator.

References

  1. 1.
    Styner, M., et al.: Statistical shape analysis of neuroanatomical structures based on medial models. Med. Image Anal. 7(3), 207–220 (2003)CrossRefGoogle Scholar
  2. 2.
    Styner, M., et al.: Framework for the statistical shape analysis of brain structures using SPHARM-PDM. Insight J. 1071, 242 (2006)Google Scholar
  3. 3.
    Ashburner, J., Friston, K.J.: Voxel-based morphometry—the methods. Neuroimage 11(6), 805–821 (2000)CrossRefGoogle Scholar
  4. 4.
    Niethammer, M., et al.: Global medical shape analysis using the laplace-beltrami spectrum. In: Ayache, N., Ourselin, S., Maeder, A. (eds.) MICCAI 2007. LNCS, vol. 4791, pp. 850–857. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-75757-3_103CrossRefGoogle Scholar
  5. 5.
    Corouge, I., Gouttard, S., Gerig, G.: A statistical shape model of individual fiber tracts extracted from diffusion tensor MRI. In: Barillot, C., Haynor, D.R., Hellier, P. (eds.) MICCAI 2004. LNCS, vol. 3217, pp. 671–679. Springer, Heidelberg (2004).  https://doi.org/10.1007/978-3-540-30136-3_82CrossRefGoogle Scholar
  6. 6.
    O’Donnell, L.J., et al.: Tract-based morphometry for white matter group analysis. Neuroimage 45(3), 832–844 (2009)CrossRefGoogle Scholar
  7. 7.
    Glozman, T., et al.: Framework for shape analysis of white matter fiber bundles. Neuroimage 167, 466–477 (2018)CrossRefGoogle Scholar
  8. 8.
    Durrleman, S., et al.: Registration, atlas estimation and variability analysis of white matter fiber bundles modeled as currents. Neuroimage 55(3), 1073–1090 (2011)CrossRefGoogle Scholar
  9. 9.
    Reuter, M., et al.: Laplace-Beltrami spectra as ‘Shape-DNA’ of surfaces and solids. Comput. Aided Des. 38(4), 342–366 (2006)CrossRefGoogle Scholar
  10. 10.
    Shi, Y., Morra, J.H., Thompson, P.M., Toga, A.W.: Inverse-consistent surface mapping with Laplace-Beltrami eigen-features. In: Prince, J.L., Pham, D.L., Myers, K.J. (eds.) IPMI 2009. LNCS, vol. 5636, pp. 467–478. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-3-642-02498-6_39CrossRefGoogle Scholar
  11. 11.
    Wachinger, C., Golland, P., Kremen, W., Fischl, B., Reuter, M., Initiative, A.D.N.: BrainPrint: a discriminative characterization of brain morphology. NeuroImage 109, 232–248 (2015)CrossRefGoogle Scholar
  12. 12.
    Wachinger, C., et al.: Whole-brain analysis reveals increased neuroanatomical asymmetries in dementia for hippocampus and amygdala. Brain 139(12), 3253–3266 (2016)CrossRefGoogle Scholar
  13. 13.
    Shishegar, R., et al.: Hippocampal shape analysis in epilepsy using Laplace-Beltrami spectrum. In: 2011 19th Iranian Conference on Electrical Engineering (ICEE). IEEE (2011)Google Scholar
  14. 14.
    Poldrack, R.A., et al.: A phenome-wide examination of neural and cognitive function. Sci. Data 3, 160110 (2016).  https://doi.org/10.1038/sdata.2016.110CrossRefGoogle Scholar
  15. 15.
    Fields, R.D.: White matter in learning, cognition and psychiatric disorders. Trends Neurosci. 31(7), 361–370 (2008)CrossRefGoogle Scholar
  16. 16.
    Fischl, B.: FreeSurfer. NeuroImage 62, 774–781 (2012)CrossRefGoogle Scholar
  17. 17.
    Takemura, H., Caiafa, C.F., Wandell, B.A., Pestilli, F.: Ensemble tractography. PLoS Comput. Biol. 12(2), e1004692 (2016)CrossRefGoogle Scholar
  18. 18.
    Caiafa, C.F., Pestilli, F.: Multidimensional encoding of brain connectomes. Sci. Rep. 7(1), 11491 (2017)CrossRefGoogle Scholar
  19. 19.
    Pestilli, F., Yeatman, J.D., Rokem, A., Kay, K.N., Wandell, B.A.: Evaluation and statistical inference for human connectomes. Nat. Methods 11(10), 1058 (2014)CrossRefGoogle Scholar
  20. 20.
    Tournier, J.D., Calamante, F., Connelly, A.: MRtrix: diffusion tractography in crossing fiber regions. Int. J. Imaging Syst. Technol. 22(1), 53–66 (2012)CrossRefGoogle Scholar
  21. 21.
    Yeatman, J.D., Dougherty, R.F., Myall, N.J., Wandell, B.A., Feldman, H.M.: Tract profiles of white matter properties: automating fiber-tract quantification. PLoS One 7(11), e49790 (2012)CrossRefGoogle Scholar
  22. 22.
    Taubin, G., Zhang, T., Golub, G.: Optimal surface smoothing as filter design. In: Buxton, B., Cipolla, R. (eds.) ECCV 1996. LNCS, vol. 1064, pp. 283–292. Springer, Heidelberg (1996).  https://doi.org/10.1007/BFb0015544CrossRefGoogle Scholar
  23. 23.
    Jacobson, A., et al.: gptoolbox: geometry processing toolbox (2016). http://github.com/alecjacobson/gptoolbox
  24. 24.
    Pedregosa, F., et al.: Scikit-learn: machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011)MathSciNetzbMATHGoogle Scholar
  25. 25.
    Dietterich, Thomas G.: Ensemble methods in machine learning. In: Kittler, J., Roli, F. (eds.) MCS 2000. LNCS, vol. 1857, pp. 1–15. Springer, Heidelberg (2000).  https://doi.org/10.1007/3-540-45014-9_1CrossRefGoogle Scholar
  26. 26.
    Sun, Z.Y., et al.: Shape analysis of the cingulum, uncinate and arcuate fasciculi in patients with bipolar disorder. J. Psychiatry Neurosci.: JPN 42(1), 27 (2017)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Lindsey Kitchell
    • 1
    Email author
  • Daniel Bullock
    • 1
  • Soichi Hayashi
    • 1
  • Franco Pestilli
    • 1
  1. 1.Indiana UniversityBloomingtonUSA

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