Robust Methods for Detecting Spontaneous Activations in fMRI Data

  • Francesca GasperoniEmail author
  • Alessandra Luati
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 257)


Functional magnetic resonance imaging (fMRI) is a technique for measuring brain activity. The outcomes of fMRI measurements are complex data that can be interpreted as multivariate time series, recorded at different brain locations, usually across subjects. The literature has been mainly concerned with task-based fMRI analysis, which focuses on the response to controlled exogenous stimuli. Nevertheless, resting state fMRI (RfMRI) analysis, dealing with spontaneous brain activity, is considered the key to understand the neuronal organisation of the brain. The aim of this paper is to identify spontaneous neural activations and to estimate the brain response function in RfMRI data, called Hemodynamic Response Function (HRF). To this purpose, we apply an existing method based on a normality assumption for the data generating process and we consider a novel, more general method, based on robust filtering. Finally, we compare the neural activations and HRF estimates for two specific patients.


BOLD signal Heavy tails HRF estimation Resting state Robust filtering Spatial dependence 



We thank two anonymous referees for their insightful comments and Federico Crescenzi, Michele Peruzzi and Alexios Polymeropoulos for constructive discussions at the Certosa di Pontignano, Bologna and Milano during the initial stages of the current work. We would like to thank Antonio Canale, Daniele Durante, Lucia Paci and Bruno Scarpa for bringing us together and providing us with the challenging dataset analysed in the paper. These data are provided by 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, using the pipelines ndmg and C-PAC. We would also like to thank all the participants of the StartUp Research event held at the Certosa di Pontignano on June 25-27, 2017, for the stimulating and nice discussions.


  1. 1.
    Aston, J., Kirsch, C.: Evaluating stationarity via change-point alternatives with applications to fMRI data. Ann. Appl. Statist. 6(4), 1906–1948 (2012)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Biswal, B., Zerrin Yetkin, F., Haughton, V.M., Hyde, J.S.: Functional connectivity in the motor cortex of resting human brain using echo-planar MRI. Magn. Reson. Med. 34(4), 537–541 (1995)CrossRefGoogle Scholar
  3. 3.
    Biswal, B.: Toward discovery science of human brain function. PNAS 107(10), 4734–4739 (2010)CrossRefGoogle Scholar
  4. 4.
    Blasques, F., Koopman, S.J., Lucas, A., Schaumburg, J.: Spillover dynamics for systemic risk measurement using spatial financial time series models. J. Econom. 195(2), 211–223 (2016)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Bullmore, E., Fadili, J., Breakspear, M., Salvador, R., Suckling, J., Brammer, M.: Wavelets and statistical analysis of functional magnetic resonance images of the human brain. Statist. Methods Med. Res. 12(5), 375–399 (2003)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Castruccio, S., Ombao, H., Genton, M. G.: A scalable multi-resolution spatio-temporal model for brain activation and connectivity in fMRI data. Biometrics (2018)Google Scholar
  7. 7.
    Catania, L., Billé, A.G.: Dynamic spatial autoregressive models with autoregressive and heteroskedastic disturbances. J. Appl. Econom. (2017)Google Scholar
  8. 8.
    Choi, S.S., Cha, S.H., Tappert, C.C.: A survey of binary similarity and distance measures. J. Syst. Cybern. Inf. 8, 43–48 (2010)Google Scholar
  9. 9.
    Creal, D., Koopman, S., Lucas, A.: A dynamic multivariate heavy-tailed model for the time-varying volatility and correlations. J. Bus. Econom. Statist. 29, 552–563 (2011)MathSciNetCrossRefGoogle Scholar
  10. 10.
    D’Esposito, M., Deouell, L., Gazzaley, A.: Alterations in the bold fMRI signal with ageing and disease: a challenge for neuro imaging. Nature Rev. Neurosci. (4), 863–872 (2003)CrossRefGoogle Scholar
  11. 11.
    Dice, L.R.: Measures of the amount of ecologic association between species. Ecology 26(3), 297–302 (1945)CrossRefGoogle Scholar
  12. 12.
    Fox, M.D., Raichle, M.E.: Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging. Nature Rev. Neurosci. 8(9), 700 (2007)CrossRefGoogle Scholar
  13. 13.
    Fox, M.D., Snyder, A.Z., Vincent, J.L., Corbetta, M., Van Essen, D.C., Raichle, M.E.: The human brain is intrinsically organized into dynamic, anticorrelated functional networks. Proc. Natl. Acad. Sci. U. S. A. 102(27), 9673–9678 (2005)CrossRefGoogle Scholar
  14. 14.
    Friston, K.J., Fletcher, P., Josephs, O., Holmes, A.P., Rugg, M., Turner, R.: Event-related fMRI: characterizing differential responses. Neuroimage 7(1), 30–40 (1998)CrossRefGoogle Scholar
  15. 15.
    Friston, K.J., Holmes, A.P., Worsley, K.J., Poline, J.P., Frith, C.D., Frackowiak, R.S.: Statistical parametric maps in functional imaging: a general linear approach. Huma. Brain Mapp. 2(4), 189–210 (1994)CrossRefGoogle Scholar
  16. 16.
    Glover, G.H.: Deconvolution of impulse response in event-related BOLD fMRI. Neuroimage 9(4), 416–429 (1999)CrossRefGoogle Scholar
  17. 17.
    Handwerker, D.A., Ollinger, J.M., D’Esposito, M.: Variation of BOLD hemodynamic responses across subjects and brain regions and their effects on statistical analyses. Neuroimage 21(4), 1639–1651 (2004)CrossRefGoogle Scholar
  18. 18.
    Harvey, A., Luati, A.: Filtering with heavy tails. J. Am. Statist. Assoc. 109(507), 1112–1122 (2014)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Harvey, A.C.: Dynamic Models for Volatility and Heavy Tails: With Applications to Financial and Economic Time Series. Cambridge University Press (2013)Google Scholar
  20. 20.
    Henson, R., Friston, K.: Convolution models for fMRI. Statistical parametric mapping: the analysis of functional brain images, pp. 178–192 (2007)CrossRefGoogle Scholar
  21. 21.
    Kruggel, F., von Cramon, D.Y.: Temporal properties of the hemodynamic response in functional MRI. Hum. Brain Mapp. 8(4), 259–271 (1999)CrossRefGoogle Scholar
  22. 22.
    Lange, N., Zeger, S.L.: Non-linear fourier time series analysis for human brain mapping by functional magnetic resonance imaging. J. Royal Statist. Soc. Ser. C (Appl. Statist.) 46(1), 1–29 (1997)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Lindquist, M.A.: The statistical analysis of fMRI data. Statist. Sci. 23(4), 439–464 (2008)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Lund, T.E.: Non-white noise in fMRI: Does modelling have an impact? Neuroimage 29(4), 1639–1651 (2006)MathSciNetGoogle Scholar
  25. 25.
    Poldrack, R.A., Mumford, J.A., Nichols, T.E.: Handbook of Functional MRI data Analysis. Cambridge University Press (2011)Google Scholar
  26. 26.
    Woolrich, M.W., Ripley, B.D., Brady, M., Smith, S.M.: Temporal autocorrelation in univariate linear modeling of fMRI data. Neuroimage 14(6), 1370–1386 (2001)CrossRefGoogle Scholar
  27. 27.
    Worsley, K.J., Liao, C., Aston, J., Petre, V., Duncan, G., Morales, F., Evans, A.: A general statistical analysis for fMRI data. Neuroimage 15(1), 1–15 (2002)CrossRefGoogle Scholar
  28. 28.
    Worsley, K.: Detecting activation in fMRI data. Statist. Methods Med. Res. 12(5), 401–418 (2003)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Wu, G.R., Liao, W., Stramaglia, S., Ding, J.R., Chen, H., Marinazzo, D.: A blind deconvolution approach to recover effective connectivity brain networks from resting state fMRI data. Med. Image Anal. 17(3), 365–374 (2013)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.MOX, Department of MathematicsPolitecnico di MilanoMilanItaly
  2. 2.Department of StatisticsUniversity of BolognaBolognaItaly

Personalised recommendations