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Evaluating Structural Symmetry of Weighted Brain Networks via Graph Matching

  • Chenhui Hu
  • Georges El Fakhri
  • Quanzheng Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8674)

Abstract

We study the symmetry of weighted brain networks to understand the roles of individual brain areas and the redundancy of the brain connectivity. We quantify the structural symmetry of every node pair in the network by isomorphism of the residual graphs of those nodes. The efficacy of the symmetry measure is evaluated on both simulated networks and real data sets. In the resting state fMRI (rs-fMRI) data, we discover that subjects with inattentive type of Attention Deficit Hyperactivity Disorder (ADHD) demonstrate a higher level of network symmetry in contrast to the typically development group, consistent with former findings. Moreover, by comparing the average functional networks of normal subjects during resting state and activation, we obtain a higher symmetry level in the rs-fMRI network when applying median thresholds to the networks. But the symmetry levels of the networks are almost the same when larger thresholds are used, which may imply the invariance of the prominent network symmetry for ordinary people.

Keywords

network symmetry weighted brain networks graph matching ADHD rs-fMRI coactivation network 

References

  1. 1.
    Mitra, N.J., Pauly, M., Wand, M., Ceylan, D.: Symmetry in 3D Geometry: Extraction and Applications. In: Computer Graphics Forum (2013)Google Scholar
  2. 2.
  3. 3.
    Marjorie, M.: Asymmetries of the Skull and Handedness: Phrenology Revisited. Journal of the Neurological Sciences 32, 243–253 (1977)CrossRefGoogle Scholar
  4. 4.
    Aboitiz, F., Scheibel, A.B., Fisher, R.S., Zaidel, E.: Individual Differences in Brain Asymmetries and Fiber Composition in the Human Corpus Callosum. Brain Research 598, 154–161 (1992)CrossRefGoogle Scholar
  5. 5.
    Seger, C.A., Poldrack, R.A., Prabhakaran, V., Zhao, M., Glover, G.H., Gabrieli, J.D.: Hemispheric Asymmetries and Individual Differences in Visual Concept Learning as Measured by FMRI. Neuropsychologia 38, 1316–1324 (2000)CrossRefGoogle Scholar
  6. 6.
    Park, H.J., Friston, K.: Structural and Functional Brain Networks: from Connections to Cognition. Science 342, 1238411 (2013)CrossRefGoogle Scholar
  7. 7.
    Zalesky, A., Fornito, A., Bullmore, E.T.: Network-based Statistic: Identifying Differences in Brain Networks. Neuroimage 53, 1197–1207 (2010)CrossRefGoogle Scholar
  8. 8.
    Sporns, O., Kötter, R.: Motifs in Brain Networks. PLoS Biology 2, e369 (2004)Google Scholar
  9. 9.
    Umeyama, S.: An Eigendecomposition Approach to Weighted Graph Matching Problems. IEEE Trans. on Pattern Analysis and Machine Intelligence 10, 695–703 (1988)CrossRefzbMATHGoogle Scholar
  10. 10.
    Shaw, P., Lalonde, F., Lepage, C., Rabin, C., Eckstrand, K., Sharp, W., Greenstein, D., Evans, A., Giedd, J.N., Rapoport, J.: Development of Cortical Asymmetry in Typically Developing Children and Its Disruption in Attention-Deficit/Hyperactivity Disorder. Archives of General Psychiatry 66, 888 (2009)CrossRefGoogle Scholar
  11. 11.
    Jesse, A.B., Rudie, J.D., Bandrowski, A., Horn, J.D.V., Bookheimer, S.Y.: The UCLA Multimodal Connectivity Database: A Web-based Platform for Brain Connectivity Matrix Sharing and Analysis. Frontiers in Neuroinformatics 6 (2012)Google Scholar
  12. 12.
    Fair, D.A., Nigg, J.T., Iyer, S., Bathula, D., Mills, K.L., Dosenbach, N.U., Schlaggar, B.L., et al.: Distinct Neural Signatures Detected for ADHD Subtypes After Controlling for Micro-movements in Resting State Functional Connectivity MRI Data. Frontiers in Systems Neuroscience 6 (2012)Google Scholar
  13. 13.
    Crossley, N.A., Mechelli, A., Vértes, P.E., Winton-Brown, T.T., Patel, A.X., Ginestet, C.E., McGuire, P., Bullmore, E.T.: Cognitive Relevance of the Community Structure of the Human Brain Functional Coactivation Network. Proceedings of the National Academy of Sciences 110, 11583–11588 (2013)CrossRefGoogle Scholar
  14. 14.
    Kolaczyk, E.D.: Statistical Analysis of Network Data: Methods and Models. Springer, New York (2009)CrossRefGoogle Scholar
  15. 15.
    Southwell, R.: Finding Symmetries in Graphs. Master Thesis, Univ. of York (2006)Google Scholar
  16. 16.
    Godsil, C.D., Royle, G.: Algebraic Graph Theory, vol. 8. Springer, New York (2001)CrossRefzbMATHGoogle Scholar
  17. 17.
    Foggia, P., Sansone, C., Vento, M.: A Performance Comparison of Five Algorithms for Graph Isomorphism. In: Proc. of the 3rd IAPR TC-15 Workshop on Graph-based Representations in Pattern Recognition, pp. 188–199 (2001)Google Scholar
  18. 18.
    Pilgrim, R.A.: Munkres’ Assignment Algorithm: Modified for Rectangular Matrices, Course notes, Murray State UniversityGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Chenhui Hu
    • 1
    • 2
  • Georges El Fakhri
    • 1
  • Quanzheng Li
    • 1
  1. 1.Center for Advanced Medical Imaging Science, NMMI, RadiologyMassachusetts General HospitalBostonUSA
  2. 2.School of Engineering and Applied SciencesHarvard UniversityCambridgeUSA

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