Deriving a Multi-subject Functional-Connectivity Atlas to Inform Connectome Estimation

  • Ronald Phlypo
  • Bertrand Thirion
  • Gaël Varoquaux
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8675)


The estimation of functional connectivity structure from functional neuroimaging data is an important step toward understanding the mechanisms of various brain diseases and building relevant biomarkers. Yet, such inferences have to deal with the low signal-to-noise ratio and the paucity of the data. With at our disposal a steadily growing volume of publicly available neuroimaging data, it is however possible to improve the estimation procedures involved in connectome mapping. In this work, we propose a novel learning scheme for functional connectivity based on sparse Gaussian graphical models that aims at minimizing the bias induced by the regularization used in the estimation, by carefully separating the estimation of the model support from the coefficients. Moreover, our strategy makes it possible to include new data with a limited computational cost. We illustrate the physiological relevance of the learned prior, that can be identified as a functional connectivity atlas, based on an experiment on 46 subjects of the Human Connectome Dataset.


functional connectivity sparse Gaussian graphical models 


  1. 1.
    Friston, K.J., Frith, C.D., Liddle, P.F., Frackowiak, R.S.J.: Functional connectivity: the principal-component analysis of large (PET) data sets. Journal of Cerebral Blood Flow and Metabolism 13, 5–14 (1993)CrossRefGoogle Scholar
  2. 2.
    Menon, V.: Developmental pathways to functional brain networks: emerging principles. Trends in Cognitive Sciences (2013)Google Scholar
  3. 3.
    Smith, S.M., Miller, K.L., Salimi-Khorshidi, G., Webster, M., Beckmann, C.F., Nichols, T.E., Ramsey, J.D., Woolrich, M.W.: Network modelling methods for fMRI. NeuroImage 54(2), 875–891 (2011)CrossRefGoogle Scholar
  4. 4.
    Hayasaka, S., Laurienti, P.J.: Comparison of characteristics between region-and voxel-based network analyses in resting-state fMRI data. NeuroImage 50(2), 499–508 (2010)CrossRefGoogle Scholar
  5. 5.
    Damoiseaux, J.S., Rombouts, S.A.R.B., Barkhof, F., Scheltens, P., Stam, C.J., Smith, S.M., Beckmann, C.F.: Consistent resting-state networks across healthy subjects. Proceedings of the National Academy of Sciences 103(37), 13848–13853 (2006)CrossRefGoogle Scholar
  6. 6.
    Smith, S.M., Miller, K.L., Moeller, S., Xu, J., Auerbach, E.J., Woolrich, M.W., Beckmann, C.F., Jenkinson, M., Andersson, J., Glasser, M.F., Van Essen, D.C., Feinberg, D.A., Yacoub, E.S., Ugurbil, K.: Temporally-independent functional modes of spontaneous brain activity. Proceedings of the National Academy of Sciences 109(8), 3131–3136 (2012)CrossRefGoogle Scholar
  7. 7.
    Marrelec, G., Krainik, A., Duffau, H., Pélégrini-Issac, M., Lehéricy, S., Doyon, J., Benali, H.: Partial correlation for functional brain interactivity investigation in functional MRI. NeuroImage 32(1), 228–237 (2006)CrossRefGoogle Scholar
  8. 8.
    Ma, S., Calhoun, V.D., Phlypo, R., Adalı, T.: Dynamic changes of spatial functional network connectivity in healthy individuals and schizophrenia patients using independent vector analysis. NeuroImage 90, 196–206 (2014)CrossRefGoogle Scholar
  9. 9.
    Rubinov, M., Sporns, O.: Complex network measures of brain connectivity: Uses and interpretations. NeuroImage 52(3), 1059–1069 (2010); Computational Models of the BrainGoogle Scholar
  10. 10.
    Ng, B., Varoquaux, G., Poline, J.B., Thirion, B.: A novel sparse graphical approach for multimodal brain connectivity inference. In: Ayache, N., Delingette, H., Golland, P., Mori, K. (eds.) MICCAI 2012, Part I. LNCS, vol. 7510, pp. 707–714. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  11. 11.
    Ng, B., Varoquaux, G., Poline, J.B., Thirion, B.: Implications of inconsistencies between fMRI and dMRI on multimodal connectivity estimation. In: Mori, K., Sakuma, I., Sato, Y., Barillot, C., Navab, N. (eds.) MICCAI 2013, Part III. LNCS, vol. 8151, pp. 652–659. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  12. 12.
    Wang, J.H., Zuo, X.N., Gohel, S., Milham, M.P., Biswal, B.B., He, Y.: Graph theoretical analysis of functional brain networks: Test-retest evaluation on short- and long-term resting-state functional MRI data. PLoS One 6(7), e21976 (2011)Google Scholar
  13. 13.
    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); Mapping the ConnectomeGoogle Scholar
  14. 14.
    Smith, S.M., Beckmann, C.F., Andersson, J., Auerbach, E.J., Bijsterbosch, J., Douaud, G., Duff, E., Feinberg, D.A., Griffanti, L., Harms, M.P., Kelly, M., Laumann, T., Miller, K.L., Moeller, S., Petersen, S., Power, J., Salimi-Khorshidi, G., Snyder, A.Z., Vu, A.T., Woolrich, M.W., Xu, J., Yacoub, E., Uǧurbil, K., Van Essen, D.C., Glasser, M.F.: Resting-state fMRI in the human connectome project. NeuroImage 80, 144–168 (2013); Mapping the Connectome Google Scholar
  15. 15.
    Behzadi, Y., Restom, K., Liau, J., Liu, T.T.: A component based noise correction method (CompCor) for BOLD and perfusion based fMRI. NeuroImage 37(1), 90–101 (2007)CrossRefGoogle Scholar
  16. 16.
    Desikan, R.S., Ségonne, F., Fischl, B., Quinn, B.T., Dickerson, B.C., Blacker, D., Buckner, R.L., Dale, A.M., Maguire, R.P., Hyman, B.T., Albert, M.S., Killiany, R.J.: 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)CrossRefGoogle Scholar
  17. 17.
    Deligianni, F., Varoquaux, G., Thirion, B., Sharp, D.J., Ledig, C., Leech, R., Rueckert, D.: A framework for inter-subject prediction of functional connectivity from structural networks. IEEE Transactions on Medical Imaging (August 2013)Google Scholar
  18. 18.
    Friedman, J., Hastie, T., Tibshirani, R.: Sparse inverse covariance estimation with the graphical lasso. Biostatistics 3, 432–441 (2008)CrossRefGoogle Scholar
  19. 19.
    Banerjee, O., El Ghaoui, L., d’Aspremont, A.: Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data. Journal of Machine Learning Research 9, 485–516 (2008)zbMATHGoogle Scholar
  20. 20.
    Lauritzen, S.L.: Graphical Models. Oxford Statistical Science, vol. 17. Clarendon Press (1996)Google Scholar
  21. 21.
    Mazumder, R., Hastie, T.: The graphical lasso: new insights and alternatives. Electronic Journal of Statistics 6, 2125–2149 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  22. 22.
    Meinshausen, N., Bühlmann, P.: Stability selection. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 72(4), 417–473 (2010)CrossRefMathSciNetGoogle Scholar
  23. 23.
    Rousseeuw, P.J.: Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics 20, 53–65 (1987)CrossRefzbMATHGoogle Scholar
  24. 24.
    Ng, B., Varoquaux, G., Poline, J.B., Thirion, B.: A novel sparse group Gaussian graphical model for functional connectivity estimation. In: Information Processing in Medical Imaging, Asilomar, États-Unis (June 2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Ronald Phlypo
    • 1
    • 2
  • Bertrand Thirion
    • 1
    • 2
  • Gaël Varoquaux
    • 1
    • 2
  1. 1.Parietal Team, Inria Saclay-Île-de-FranceSaclayFrance
  2. 2.CEA, DSV, I2BMGif-Sur-YvetteFrance

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