Advertisement

Three Testing Perspectives on Connectome Data

  • Alessandra Cabassi
  • Alessandro Casa
  • Matteo FontanaEmail author
  • Massimiliano Russo
  • Alessio Farcomeni
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 257)

Abstract

Guided by an application in the analysis of Magnetic Resonance Imaging (MRI) scans from the neuroimaging realm, we provide some perspectives on statistical techniques that are able to address issues commonly encountered when dealing with Magnetic Resonance images. The first section of the chapter is devoted to a boostrap-based inferential tool to test for correlation between anatomy and functional activity. The second provides a Bayesian framework to improve estimation of fiber counts from Diffusion Tensor Imaging (DTI) scans. The third one introduces an object-oriented framework to explore and perform testing over network-valued data.

Keywords

Hypothesis testing Permutation tests Object oriented data analysis Bootstrap inference Bayesian statistics Graphical lasso 

Notes

Acknowledgements

The authors are very grateful to Greg Kiar and Eric Bridgeford from NeuroData at Johns Hopkins University, who graciously pre-processed the raw DTI and R-fMRI imaging data available at http://fcon_1000.projects.nitrc.org/indi/CoRR/html/nki_1.html, using the pipelines ndmg and C-PAC. Moreover, the authors would like to thank the organizing committee of StartUp Research for the splendid management of such a beautiful event. Alessandra Cabassi and Matteo Fontana wish to thank Dr. Davide Pigoli and Prof. Piercesare Secchi for the fruitful discussions.

References

  1. 1.
    Agosta, F., Sala, S., Valsasina, P., Meani, A., Canu, E., Magnani, G., Cappa, S.F., Scola, E., Quatto, P., Horsfield, M.A., Falini, A., Comi, G., Filippi, M.: Brain network connectivity assessed using graph theory in frontotemporal dementia. Neurology 81(2), 134–143 (2013)CrossRefGoogle Scholar
  2. 2.
    Arden, R., Chavez, R.S., Grazioplene, R., Jung, R.E.: Neuroimaging creativity: a psychometric view. Behav. Brain Res. 214(2), 143–156 (2010)CrossRefGoogle Scholar
  3. 3.
    Arsigny, V., Fillard, P., Pennec, X., Ayache, N.: Log Euclidean metrics for fast and simple calculus on diffusion tensors. Magn. Reson. Med. 56(2), 411–421 (2006)CrossRefGoogle Scholar
  4. 4.
    Belilovsky, E., Varoquaux, G., Blaschko, M. B.: Testing for differences in Gaussian graphical models: applications to brain connectivity. In: Advances in Neural Information Processing Systems, pp. 595–60 (2016)Google Scholar
  5. 5.
    Bonilha, L., Gleichgerrcht, E., Fridriksson, J., Rorden, C., Breedlove, J.L., Nesland, T., Paulus, W., Helms, G., Focke, N.K.: Reproducibility of the structural brain connectome derived from diffusion tensor imaging. PloS one 10(9), e0135247 (2015)CrossRefGoogle Scholar
  6. 6.
    Bullmore, E., Sporns, O.: Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10(3), 186–198 (2009)CrossRefGoogle Scholar
  7. 7.
    Cabassi, A., Pigoli, D., Secchi, P., Carter, P.A.: Permutation tests for the equality of covariance operators of functional data with applications to evolutionary biology. Electron. J. Stat. 11(2), 3815–3840 (2017).  https://doi.org/10.1214/17-EJS1347MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    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
  9. 9.
    Dryden, I.L., Koloydenko, A., Zhou, D.: Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging. Ann. Appl. Stat. 3(3), 1102–1123 (2009)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Durante, D., Dunson, D.B.: Bayesian inference and testing of group differences in brain networks. Bayesian Anal. 13(1), 29–58 (2018)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Fornito, A., Zalesky, A., Breakspear, M.: Graph analysis of the human connectome: promise, progress, and pitfalls. Neuroimage 80, 426–444 (2013)CrossRefGoogle Scholar
  12. 12.
    Fréchet, M.: Les éléments aléatoires de nature quelconque dans un espace distancié. Ann. l’Institut Henri Poincaré 10(3), 215–310 (1948)Google Scholar
  13. 13.
    Friedman, J., Hastie, T., Tibshirani, R: Sparse inverse covariance estimation with the graphical lasso. Biostatistics 9(3), 432–441 (2008)CrossRefGoogle Scholar
  14. 14.
    Friston, K.J.: Functional and effective connectivity in neuroimaging: a synthesis. Hum. Brain Mapp. 2(1–2), 56–78 (1994)CrossRefGoogle Scholar
  15. 15.
    Ginestet, C.E., Li, J., Balachandran, P., Rosenberg, S., Kolaczyk, E.D.: Hypothesis testing for network data in functional neuroimaging. Ann. Appl. Stat. 11(2), 725–750 (2017)MathSciNetCrossRefGoogle Scholar
  16. 16.
    GSell, M.G., Taylor, J., Tibshirani, R.: Adaptive testing for the graphical lasso. arXiv preprint (2013). arXiv:1307.4765
  17. 17.
    Honey, C., Sporns, O., Cammoun, L., Gigandet, X., Thiran, J.P., Meuli, R., Hagmann, P.: Predicting human resting-state functional connectivity from structural connectivity. Proc. Natl. Acad. Sci. 106(6), 2035–2040 (2009)CrossRefGoogle Scholar
  18. 18.
    Jones, D.K., Knösche, T.R., Turner, R.: White matter integrity, fiber count, and other fallacies: the do’s and don’ts of diffusion MRI. Neuroimage 73, 239–254 (2013)CrossRefGoogle Scholar
  19. 19.
    Lee, S., Chugh, P.E., Shen, H., Eberle, R., Dittmer, D.P.: Poisson factor models with applications to non-normalized microrna profiling. Bioinformatics 29(9), 1105–1111 (2013)CrossRefGoogle Scholar
  20. 20.
    Marron, J.S., Alonso, A.M.: Overview of object oriented data analysis. Biometrical J. 56, 732–753 (2014)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Meinshausen, N., Bühlmann, P.: High-dimensional graphs and variable selection with the lasso. Ann. Stat. 34(3), 1436–1462 (2006)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Mémoli, F.: The Gromov-Wasserstein distance: a brief overview. Axioms 3(3), 335–341 (2014)CrossRefGoogle Scholar
  23. 23.
    Mémoli, F.: Gromov-Wasserstein distances and the metric approach to object matching. Found. Comput. Math. 11(4), 417–487 (2011)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Pigoli, D., Aston, J.A., Dryden, I.L., Secchi, P.: Distances and inference for covariance operators. Biometrika 101(2), 409–422 (2014)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Rubinov, M., Sporns, O: Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52(3), 1059–1069 (2010)CrossRefGoogle Scholar
  26. 26.
    Rykhlevskaia, E., Gratton, G., Fabiani, M: Combining structural and functional neuroimaging data for studying brain connectivity: a review. Psychophysiology 45(2), 173–187 (2008)CrossRefGoogle Scholar
  27. 27.
    Scott, J.G., Kelly, R.C., Smith, M.A., Zhou, P., Kass, R.E.: False discovery rate regression: an application to neural synchrony detection in primary visual cortex. J. Am. Stat. Assoc. 110(510), 459471 (2015)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Simpson, S.L., Hayasaka, S., Laurienti, P.J.: Exponential random graph modeling for complex brain networks. PloS one 6(5), e20039 (2011)CrossRefGoogle Scholar
  29. 29.
    Simpson, S.L., Bowman, F.D., Laurienti, P.J.: Analyzing complex functional brain networks: fusing statistics and network science to understand the brain. Stat. Surv. 7, 1 (2013)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Stam, C.J.: Modern network science of neurological disorders. Nat. Rev. Neurosci. 15(10), 683–695 (2014)CrossRefGoogle Scholar
  31. 31.
    Stippich, C.: Clinical Functional MRI: Presurgical Functional Neuroimaging. Springer, Heidelberg (2015)Google Scholar
  32. 32.
    Stan Development Team. RStan: the R interface to Stan. R package version 2.17.2 (2017). http://mc-stan.org/
  33. 33.
    Wang, H., Marron, J.S.: Object oriented data analysis: sets of trees. Ann. Stat. 35(5), 1849–1873 (2007)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Zalesky, A., Fornito, A., Bullmore, E.T.: Network-based statistic: identifying differences in brain networks. Neuroimage 53(4), 1197–1207 (2010)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Alessandra Cabassi
    • 1
  • Alessandro Casa
    • 2
  • Matteo Fontana
    • 3
  • Massimiliano Russo
    • 2
  • Alessio Farcomeni
    • 4
  1. 1.MRC Biostatistics Unit, School of Clinical MedicineUniversity of CambridgeCambridgeUK
  2. 2.Department of Statistical SciencesUniversity of PadovaPaduaItaly
  3. 3.Department of Management, Economics and Industrial Engineering, DIGPolitecnico di MilanoMilanoItaly
  4. 4.Department of Public Health and Infectious DiseasesSapienza University of RomeRomeItaly

Personalised recommendations