Scale-free and multifractal time dynamics of fmri signals during rest and task

Frontiers in Physiology

Volumn 3 JUN, Issue , 2012, Pages

  Ciuciu, P ^a   Varoquaux, G ^a,b   Abry, P ^c   Sadaghiani, S ^d   Kleinschmidt, A ^a  

^a NeuroSpin   (France)

^b INRIA SACLAY   (France)

^c UNIVERSITÉ DE LYON   (France)

^d UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Brain dynamics; Fmri; Multifractality; Rest; Scale invariance; Self similarity; Task; Wavelet leader

Indexed keywords

EID: 84866402527     PISSN: None     EISSN: 1664042X     Source Type: Journal    
DOI: 10.3389/fphys.2012.00186     Document Type: Article

References (77)

1. Abry, P., Baraniuk, R., Flandrin, P., Riedi, R., and Veitch, D. (2002). Multiscale network traffic analysis, modeling, and inference using wavelets, multifractals, and cascades. IEEE Signal Process. Mag. 3, 28-46.
2. Abry, P., Gonçalvès, P., and Flandrin, P. (1995). Wavelets, Spectrum Estimation and 1/f Processes, Chap. 103. Springer-Verlag, NY: Wavelets and Statistics, Lecture Notes in Statistics.
3. Abry, P., Veitch, D., and Flandrin, P. (1998). Long-range dependence: revisiting aggregation with wavelets. J. Time Ser. Anal. 19, 253-266.
4. Achard, S., Salvador, R., Whitcher, B., Suckling, J., and Bullmore, E. (2006). A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs. J. Neurosci. 26, 63-72.
5. Arneodo, A., Audit, B., Decoster, N., Muzy, J.-F., and Vaillant, C. (2002). "Wavelet-based multifractal formalism: applications to dna sequences, satellite images of the cloud structure and stock market data," in The Science of Disasters, eds A. Bunde, J. Kropp, and H. J. Schellnhuber (Springer), 27-102.
6. Bacry, E., Delour, J., and Muzy, J. (2001). Multifractal random walk. Phys. Rev. EStat. Nonlin. Soft Matter Phys. 64, 026103.
7. Bak, P., and Paczuski, M. (1995). Complexity, contingency, and critical-ity. Proc. Natl. Acad. Sci. U.S.A. 92, 6689-6696.
8. Barral, J., and Mandelbrot, B. (2002). Multifractal products of cylindrical pulses. Probab. Theor. Relat. Fields 124,409-430
9. Beckmann, C., and Smith, S. (2004). Probabilistic independent component analysis for functional magnetic resonance imaging. IEEE Trans. Med. Imaging 23, 137-152.
10. Biswal, B., Zerrin Yetkin, F., Haughton, V., and Hyde, J. (1995). Functional connectivity in the motor cortex of resting human brain using echo-planar MRI. Magn. Reson. Med. 34, 537-541.
11. Britz, J., Van De Ville, D., and Michel, C. M. (2010). BOLD correlates of EEG topography reveal rapid resting-state network dynamics. Neuroimage 52, 1162-1170.
12. Bullmore, E., Long, C., Suckling, J., Fadili, J., Calvert, G., Zelaya, F., Carpenter, T., and Brammer, M. (2001). Colored noise and computational inference in neurophysio-logical (fMRI) time series analysis: resampling methods in time and wavelet domains. Hum. Brain Mapp. 12, 61-78.
13. Bullmore, E., and Sporns, O. (2009). Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10, 186-198.
14. Bullock, T., Mcclune, M., and Enright, J. (2003). Are the electroencephalograms mainly rhythmic? Assessment of periodicity in wide-band time series. Neuroscience 121, 233-252.
15. Buxton, R. B., Uludag, K., Dubowitz, D. J., and Liu, T. T. (2004). Modeling the hemodynamic response to brain activation. 23(SUPPL 1), S220-S233.
16. Buxton, R. B., Wong, E. C., and Frank, L. R. (1998). Dynamics of blood flow and oxygenation changes during brain activation: the balloon model. Magn. Reson. Med. 39, 855-864.
17. Buzsáki, G. (2006). RhythmsoftheBrain. New York: Oxford University Press.
18. Calhoun, V. D., Adali, T., Pearlson, G. D., and Pekar, J. J. (2001). A method for making group inferences from functional MRI data using independent component analysis. Hum. Brain Mapp. 14, 140-151.
19. Chaari, L., Forbes, F., Vincent, T., Dojat, M., and Ciuciu, P. (2011a). "Vari-ational solution to the joint detection estimation of brain activity in fMRI," in 14th MICCAI'11, LNCS 6892 (Part II) (Toronto: Springer Verlag), 260-268.
20. Chaari, L., Pesquet, J.-C., Benazza-Benyahia, A.,and Ciuciu, P. (2011b). A wavelet-based regularized reconstruction algorithm for SENSE parallel MRI with applications to neuroimaging. Med. Image Anal. 15, 185-201.
21. Chainais, P., Riedi, R., and Abry P. (2005). On non scale invariant infinitely divisible cascades. IEEE Trans. Inform. Theor. 51, 1063-1083.
22. Chialvo, D. R. (2004). Critical brain networks. Physica A 340, 756-765.
23. Chialvo, D. R. (2010). Emergent complex neural dynamics. Nat. Phys. 6, 744-750.
24. Ciuciu, P., Abry, P., Rabrait, C., and Wendt, H. (2008). Log Wavelet Leaders Cumulant Based Multifrac-tal Analysis of EVI fMRI Time Series: Evidence of Scaling in Ongoing and Evoked Brain Activity. IEEE J. Sel. Top. Signal Process. 2, 929-943.
25. Ciuciu, P., Sockeel, S., Vincent, T., and Idier, J. (2009). "Modelling the neurovascular habituation effect on fMRI time series," in Proceedings of the 34th IEEE International Conference on Acoustic, Speech and Signal Processing, (Taipei: IEEE Conference Publications), 433-436.
26. Cole, D. M., Smith, S. M., and Beckmann, C. F. (2010). Advances and pitfalls in the analysis and interpretation of resting-state FMRI data. Front. Syst. Neurosci. 4:8. doi:10.3389/fnsys.2010.00008
27. Cordes, D., Haughton, V., Arfanakis, K., Carew, J., Turski, P., Moritz, C., Quigley, M., and Meyerand, M. (2001). Frequencies contributing to functional connectivity in the cerebral cortex in "resting-state" data. AJNR Am. J. Neuroradiol. 22, 1326-1333.
28. Dale, A.M. (1999). Optimal experimental design for event-related fMRI. Hum. Brain Mapp. 8, 109-114.
29. Damoiseaux, J. S., Rombouts, S. A., Barkhof, F., Scheltens, P., Stam, C. J., Smith, S. M., and Beckmann, C. F. (2006). Consistent resting-state networks across healthy subjects. Proc. Natl. Acad. Sci. U.S.A. 103, 13848-13853.
30. Daubechies, I., Roussos, E., Takerkart, S., Benharrosh, M., Golden, C., D'Ardenne, K., Richter, W., Cohen, J. D., and Haxby, J. (2009). Independent component analysis for brain fmri does not select for independence. Proc. Natl. Acad. Sci. U.S.A. 106,10415-10422.
31. Dehaene-Lambertz, G., Dehaene, S., Anton, J.-L., Campagne, A., Ciuciu, P., Dehaene, G. P., Denghien, I., Jobert, A., Le Bihan, D., Sig-man, M., Pallier, C., and Poline, J.-B. (2006). Functional segregation of cortical language areas by sentence repetition. Hum. Brain Mapp. 27, 360-371.
32. Eguiluz, V M., Chialvo, D. R., Cecchi, G. A., Baliki, M., and Apkarian, A. V (2005). Scale-free brain functional networks. Phys. Rev. Lett. 94, 1-4.
33. Eke, A., Herman, P., Kocsis, L., and Kozak, L. R. (2002). Fractal characterization of complexity in temporal physiological signals. Physiol. Meas. 23, R1-R38.
34. Fadili, J., and Bullmore, E. (2002). Wavelet-generalized least squares: a new BLU estimator of linear regression models with 1/f errors. Neu-roimage 15, 217-232.
35. Fox, M. D., Snyder, A. Z., Vincent, J. L., and Raichle, M. E. (2007). Intrinsic fluctuations within cortical systems account for intertrial variability in human evoked brain responses. Proc. Natl. Acad. Sci. U.S.A. 56, 171-184.
36. Friston, K., Holmes, A. P., Worlsey, K., Poline, J.-B., Frith, C., and Frackowiak, R. (1995). Statistical parametric maps in functional neuroimaging: a general linear approach. Hum. Brain Mapp. 2, 189-210.
37. Glover, G. H. (1999). Deconvolu-tion of impulse response in event-related BOLD fMRI. Neuroimage 9, 416-429.
38. Greicius, M., Krasnow, B., Reiss, A., and Menon, V. (2003). Functional connectivity in the resting brain: a network analysis of the default mode hypothesis. Proc. Natl. Acad. Sci. U.S.A. 100, 253-258.
39. He, B. (2011). Scale-free properties of the functional magnetic resonance imaging signal during rest and task. J. Neurosci. 31, 13786-13795.
40. He, B., Zempel, J., Snyder, A., and Raichle, M. (2010). The temporal structures and functional significance of scale-free brain activity. Neuron 66, 353-369.
41. Hebiri, M., and Van de Geer, S. (2011). The smooth-lasso and other 1 + 2-penalized methods. Electron. J. Stat. 5, 1184-1226.
42. Holden, J. G., Choi, I., Amazeen, P. G., and Van Orden, G. (2011). Fractal 1/f dynamics suggest entanglement of measurement and human performance. J. Exp. Psychol. Hum. Percept. Perform. 37, 935-948.
43. Kiviniemi, V., Kantola, J., Jauhiainen, J., Hyvärinen, A., and Tervonen, O. (2003). Independent component analysis of nondeterministic fMRI signal sources. Neuroimage 19, 253-260.
44. Laufs, H., Krakow, K., Sterzer, P., Eger, E., Beyerle, A., Salek-Haddadi, A., and Kleinschmidt, A. (2003). Electroen-cephalographic signatures of atten-tional and cognitive default modes in spontaneous brain activity fluctuations at rest. Proc. Natl. Acad. Sci. U.S.A. 100, 11053-11058.
45. Leopold, D., Murayama, Y., and Logo-thetis, N. (2003). Very slow activity fluctuations in monkey visual cortex: implications for functional brain imaging. Cereb. Cortex 13, 422-433.
46. Linkenkaer-Hansen, K., Nikouline, V., Palva, J., and Ilmoniemi, R. (2001). Long-range temporal correlations and scaling behavior in human brain oscillations. J. Neurosci. 21, 1370-1377.
47. Liu, H.-L., and Gao, J.-H. (2000). An investigation of the impulse functions for the nonlinear BOLD response in functional MRI. Magn. Reson. Imaging 18, 11053-11058.
48. Makni, S., Ciuciu, P., Idier, J., and Poline, J.-B. (2005). Joint detection-estimation of brain activity in functional MRI: a multichannel decon-volution solution. IEEE Trans. Signal Process. 53, 3488-3502.
49. Makni, S., Idier, J., Vincent, T., Thirion, B., Dehaene-Lambertz, G., and Ciuciu, P. (2008). A fully Bayesian approach to the parcel-based detection-estimation of brain activity in fMRI. Neuroimage 41, 941-969.
50. Mallat, S. (2009). A Wavelet Tour of Signal Processing: The Sparse Way. Burlington, MA: Academic Press.
51. Mandelbrot, B., and Van Ness, J. (1968). Fractional Brownian motion, fractional noises and applications. SIAM Rev. Soc. Ind. Appl. Math. 10, 422-437.
52. Mantini, D., Perrucci, M. G., Del Gratta, C., Romani, G. L., and Corbetta, M. (2007). Electrophysiological signatures of resting state networks in the human brain. Proc. Natl. Acad. Sci. U.S.A. 104, 13170-13175.
53. Maxim, V., Sendur, L., Fadili, J., Suckling, J., Gould, R., Howard, R., and Bullmore, E. (2005). Fractional Gaussian noise, functional MRI and Alzheimer's disease. Neuroimage 25, 141-158.
54. McKeown, M., Makeig, S., Brown, G., Jung, T., Kindermann, S., Bell, A., and Sejnowski, T. (1998). Analysis of fMRI data by blind separation into independent spatial components. Hum. Brain Mapp. 6, 160-188.
55. Musso, F., Brinkmeyer, J., Mobascher, A., Warbrick, T., and Winterer, G. (2010). Spontaneous brain activity and EEG microstates. A novel EEG/fMRI analysis approach to explore resting-state networks. Neuroimage 52,1149-1161.
56. Rabrait, C., Ciuciu, P., Ribès, A., Poupon, C., Leroux, P., Lebon, V., Dehaene-Lambertz, G., Le Bihan, D., and Lethimonnier, F. (2008). High temporal resolution functional MRI using parallel echo volume imaging. J. Magn. Reson. Imaging 27, 744-753.
57. Rosen, B. R., Buckner, R. L., and Dale, A. M. (1998). Event-related functional MRI: past, present and future. Proc. Natl. Acad. Sci. U.S.A. 95, 773-780.
58. Sadaghiani, S., Hesselmann, G., and Kleinschmidt, A. (2009). Distributed and antagonistic contributions of ongoing activity fluctuations to auditory stimulus detection. J. Neurosci. 29, 13410-13417.
59. Samorodnitsky, G., and Taqqu, M. (1994). Stable Non-Gaussian Random Processes. New York: Chapman and Hall.
60. Seitz, A., Kim, R., Van Wassenhove, V., and Shams, L. (2007). Simultaneous and independent acquisition of multisensory and unisen-sory associations. Perception 36, 1445-1453.
61. Shimizu, Y., Barth, M., Windischberger, C., Moser, E.,andThurner, S. (2004). Wavelet-based multifractal analysis of fMRI time series. Neuroimage 22, 1195-1202.
62. Smith, S. M., Fox, P. T., Miller, K. L., Glahn, D. C., Fox, P. M., Mackay, C. E., Filippini, N., Watkins, K. E., Toro, R., Laird, A. R., and Beckmann, C. F. (2009). Correspondence of the brain's functional architecture during activation and rest. Proc. Natl. Acad. Sci. U.S.A. 106, 13040.
63. Smith, S. M., Miller, K. L., Moeller, S., Xu, J., Auerbach, E. J., Woolrich, M. W., Beckmann, C. F., Jenkin-son, M., Andersson, J., Glasser, M. F., Van Essen, D. C., Feinberg, D. A., Yacoub, E. S.,andUgurbil, K. (2012). Temporally-independent functional modes of spontaneous brain activity. Proc. Natl. Acad. Sci. U.S.A. 109, 3131-3136.
64. Stam, C. J., and De Bruin, E. A. (2004). Scale-free dynamics of global functional connectivity in the human brain. Hum. Brain Mapp. 22, 97-109.
65. Thurner, S., Windischberger, C. Moser, E., Walla, P., and Barth, M. (2003). Scaling laws and persistence in human brain activity. Physica A 326, 511-521.
66. Van de Ville, D., Britz, J., and Michel, C. M. (2010). EEG microstate sequences in healthy humans at rest reveal scale-free dynamics. Proc. Natl. Acad. Sci U.S.A. 107, 18179-18184.
67. Varoquaux, G., Gramfort, A., Pedregosa, E, Michel, V., and Thirion, B. (2011). Multi-subject dictionary learning to segment an atlas of brain spontaneous activity. Inf. Process. Med. Imaging 22, 562-573.
68. Varoquaux, G., Keller, M., Poline, J., Ciuciu, P., and Thirion, B. (2010a). "ICA-based sparse features recovery from fMRI datasets," in Proceedings of the 7th IEEE International Symposium on Biomedical Imaging, Rotterdam, 1177-1180.
69. Varoquaux, G., Sadaghiani, S., Pinel, P., Kleinschmidt, A., Poline, J.-B., and Thirion, B. (2010b). A group model for stable multi-subject ICA on fMRI datasets. Neuroimage 51, 288-299.
70. Veitch, D., and Abry, P. (2001). A statistical test for the time constancy of scaling exponents. IEEE Trans. Signal Process. 49, 2325-2334.
71. Vincent, T., Risser, L., and Ciuciu, P. (2010). Spatially adaptive mixture modeling for analysis of within-subject fMRI time series. IEEE Trans. Med. Imaging 29, 1059-1074.
72. Wendt, H., Abry, P., and Jaffard, S. (2007). Bootstrap for empirical mul-tifractal analysis. IEEE Signal Process. Mag. 24, 38-48.
73. Wink, A.-M., Bullmore, E., Barnes, A., Bernard, F., and Suckling, J. (2008). Monofractal and multi-fractal dynamics of low frequency endogenous brain oscillations in functional MRI. Hum. Brain Mapp. 29, 791-801.
74. Yuan, H., Zotev, V., Phillips, R., Drevets, W. C., and Bodurka, J. (2012). Spatiotemporal dynamics of the brain at rest - exploring EEG microstates as electrophysio-logical signatures of BOLD resting state networks. Neuroimage 60, 2062-2072.
75. Zarahn, E., Aguirre, G. K., and D'Esposito, M. (1997). Empirical analysis of BOLD fMRI statistics. I. Spatially unsmoothed data collected under null-hypothesis conditions. Neuroimage 5, 179-197.
76. Zemanová, L., Zhou, C., and Kurths, J. (2006). Structural and functional clusters of complex brain networks. Physica D 224, 202-212.
77. Zilber, N., Ciuciu, P., Abry, P., and Van Wassenhove, V. (2012). "Modulation of scale-free properties of brain activity in MEG," in Proceedings of the 9th IEEE International Symposium on Biomedical Imaging, Barcelona, 1531-1534.