Advertisement

Dynamic Regression for Partial Correlation and Causality Analysis of Functional Brain Networks

  • Lipeng NingEmail author
  • Yogesh Rathi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10433)

Abstract

We propose a general dynamic regression framework for partial correlation and causality analysis of functional brain networks. Using the optimal prediction theory, we present the solution of the dynamic regression problem by minimizing the entropy of the associated stochastic process. We also provide the relation between the solutions and the linear dependence models of Geweke and Granger and derive novel expressions for computing partial correlation and causality using an optimal prediction filter with minimum error variance. We use the proposed dynamic framework to study the intrinsic partial correlation and causality between seven different brain networks using resting state functional MRI (rsfMRI) data from the Human Connectome Project (HCP) and compare our results with those obtained from standard correlation and causality measures. The results show that our optimal prediction filter explains a significant portion of the variance in the rsfMRI data at low frequencies, unlike standard partial correlation analysis.

Notes

Acknowledgements

This work has been supported by NIH grants: R01MH097979 (PI: Rathi), R01MH074794 (PI: Westin), P41EB015902 (PI: Kikinis).

Supplementary material

455905_1_En_42_MOESM1_ESM.pdf (71 kb)
Supplementary material 1 (pdf 71 KB)

References

  1. 1.
    Akaike, H.: A new look at the statistical model identification. IEEE Trans. Autom. Control 19(6), 716–723 (1974)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Baccalá, L., Sameshima, K.: Partial directed coherence: a new concept in neural structural determination. Biol. Cybern. 84, 463–474 (2001)CrossRefGoogle Scholar
  3. 3.
    Barnett, L., Seth, A.K.: Behaviour of granger causality under filtering: theoretical invariance and practical application. J. Neurosci. Methods 201(2), 404–419 (2011)CrossRefGoogle Scholar
  4. 4.
    Colclough, G., Woolrich, W., Tewarie, P., Brookes, M., Quinn, A., Smith, S.M.: How reliable are MEG resting-state connectivity metrics? NeuroImage 138, 284–293 (2016)CrossRefGoogle Scholar
  5. 5.
    Deshpande, G., LaConte, S., James, G., Peltier, S., Hu, X.: Multivariate granger causality analysis of fMRI data. Hum. Brain Mapp. 30, 1361–1373 (2009)CrossRefGoogle Scholar
  6. 6.
    Geweke, J.: Measurement of linear dependence and feedback between multiple time series. J. Am. Stat. Assoc. 77, 304–13 (1982)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Granger, C.: Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37, 424–438 (1969)CrossRefGoogle Scholar
  8. 8.
    Jiang, X., Ning, L., Georgiou, T.: Distance and riemannian metrics for multivariate spectral densities. IEEE Trans. Autom. Control 57(7), 1723–1735 (2012)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Liu, P., Zhang, Y., Zhou, G., Yuan, K., Qin, W., Zhuo, L., Liang, J., Chen, P., Dai, J., Liu, Y., Tian, J.: Partial correlation investigation on the default mode network involved in acupuncture: an fMRI study. Neurosci. Lett. 462(3), 183–187 (2009)CrossRefGoogle Scholar
  10. 10.
    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, 228–237 (2006)CrossRefGoogle Scholar
  11. 11.
    Masani, P.: Recent trends in multivariable prediction theory. In: Krishnaiah (ed.) Multivariate Analysis. Academic Press, Cambridge (1966)Google Scholar
  12. 12.
    Papoulis, A., Pillai, S.: Probability, Random Variables, and Stochastic Processes. McGraw-Hill, New York (2002)Google Scholar
  13. 13.
    Pinsker, M.: Information and Information Stability of Random Variables and Processes. Holden-Day, San Francisco (1964)zbMATHGoogle Scholar
  14. 14.
    Ryali, S., Chen, T., Supekar, K., Menon, V.: Estimation of functional connectivity in fMRI data using stability selection-based sparse partial correlation with elastic net penalty. NeuroImage 59(4), 3852–3861 (2012)CrossRefGoogle Scholar
  15. 15.
    Van Dijk, K., Hedden, T., Venkataraman, A., Evans, K., Lazar, S., Buckner, R.: Intrinsic functional connectivity as a tool for human connectomics: theory, properties, and optimization. J. Neurophysiol. 103(1), 297–321 (2010)CrossRefGoogle Scholar
  16. 16.
    Van Essen, D.C., Smith, S.M., Barch, D.M., Behrens, T.E., Yacoub, E., Ugurbil, K.: The WU-Minn human connectome project: an overview. Neuroimage 80, 62–79 (2013)CrossRefGoogle Scholar
  17. 17.
    Wiener, N., Masani, P.: The prediction theory of multivariate stochastic processes. Part I Acta Math. 98, 111–150 (1957)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Yeo, B.T., Krienen, F.M., Sepulcre, J., Sabuncu, M.R., Lashkari, D., Hollinshead, M., Roffman, J.L., Smoller, J.W., Zöllei, L., Polimeni, J.R., Fischl, B., Liu, H., Buckner, R.: The organization of the human cerebral cortex estimated by intrinsic functional connectivity. J. Neurophysiol. 106, 1125–1165 (2011)CrossRefGoogle Scholar
  19. 19.
    Yuan, M., Lin, Y.: Model selection and estimation in the gaussian graphical model. Biometrika 94(1), 19–35 (2007)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Brigham and Women’s Hospital, Harvard Medical SchoolBostonUSA

Personalised recommendations