title: The temporal structures and functional significance of scale-free brain activity.
abstract: Scale-free dynamics, with a power spectrum following P proportional to f(-beta), are an intrinsic feature of many complex processes in nature. In neural systems, scale-free activity is often neglected in electrophysiological research. Here, we investigate scale-free dynamics in human brain and show that it contains extensive nested frequencies, with the phase of lower frequencies modulating the amplitude of higher frequencies in an upward progression across the frequency spectrum. The functional significance of scale-free brain activity is indicated by task performance modulation and regional variation, with beta being larger in default network and visual cortex and smaller in hippocampus and cerebellum. The precise patterns of nested frequencies in the brain differ from other scale-free dynamics in nature, such as earth seismic waves and stock market fluctuations, suggesting system-specific generative mechanisms. Our findings reveal robust temporal structures and behavioral significance of scale-free brain activity and should motivate future study on its physiological mechanisms and cognitive implications.
authors.affiliation: Department of Radiology, Washington University School of Medicine, 4525 Scott Avenue, St. Louis, MO 63110, USA. biyu.jade.he@gmail.com
authors.forename: Biyu J
authors.initials: BJ
authors.lastname: He
authors.forename: John M
authors.initials: JM
authors.lastname: Zempel
authors.forename: Abraham Z
authors.initials: AZ
authors.lastname: Snyder
authors.forename: Marcus E
authors.initials: ME
authors.lastname: Raichle
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D001921:Brain / Q000502:physiology*; D001931:Brain Mapping; D004567:Electrodes, Implanted; D004569:Electroencephalography; D006801:Humans; D008279:Magnetic Resonance Imaging; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology; D009474:Neurons / Q000502:physiology*; D012815:Signal Processing, Computer-Assisted; D009435:Synaptic Transmission / Q000502:physiology
references.citation: Psychon Bull Rev. 2004 Aug;11(4):579-615
references.pmid: 15581115
references.citation: J Neurophysiol. 2005 Sep;94(3):1904-11
references.pmid: 15901760
references.citation: Vision Res. 2003 Nov;43(24):2527-37
references.pmid: 13129540
references.citation: Neuron. 2008 May 8;58(3):429-41
references.pmid: 18466752
references.citation: Proc Natl Acad Sci U S A. 1991 Apr 15;88(8):3507-9
references.pmid: 11607178
references.citation: J Neurosci. 2001 Feb 15;21(4):1370-7
references.pmid: 11160408
references.citation: Hum Brain Mapp. 2004 Jun;22(2):97-109
references.pmid: 15108297
references.citation: Psychol Rev. 2001 Jan;108(1):33-56
references.pmid: 11212631
references.citation: Proc Natl Acad Sci U S A. 2004 Apr 6;101(14):5053-7
references.pmid: 15044698
references.citation: Proc Natl Acad Sci U S A. 2008 Dec 23;105(51):20517-22
references.pmid: 19074268
references.citation: J Neurosci. 2003 May 15;23(10):4251-60
references.pmid: 12764113
references.citation: Int J Psychophysiol. 2008 Mar;67(3):252-61
references.pmid: 17669531
references.citation: Curr Biol. 2008 Mar 11;18(5):375-80
references.pmid: 18328702
references.citation: Prog Brain Res. 1994;102:405-26
references.pmid: 7800830
references.citation: Philos Trans R Soc Lond B Biol Sci. 2002 Aug 29;357(1424):1003-37
references.pmid: 12217171
references.citation: PLoS Comput Biol. 2009 Dec;5(12):e1000609
references.pmid: 20019800
references.citation: J Neurosci. 1997 Aug 1;17(15):5666-77
references.pmid: 9221766
references.citation: Cogn Neurodyn. 2009 Mar;3(1):97-103
references.pmid: 19003455
references.citation: Neuroscience. 2003;121(1):233-52
references.pmid: 12946714
references.citation: Brain Res. 1988 Jan-Mar;472(1):57-75
references.pmid: 3342336
references.citation: Nature. 1964 Jul 25;203:380-4
references.pmid: 14197376
references.citation: Front Hum Neurosci. 2009 Dec 23;3:61
references.pmid: 20076775
references.citation: Neuron. 2007 Sep 6;55(5):809-23
references.pmid: 17785187
references.citation: Trends Neurosci. 2009 Jan;32(1):9-18
references.pmid: 19012975
references.citation: Neuron. 2007 Oct 4;56(1):171-84
references.pmid: 17920023
references.citation: J Neurophysiol. 1992 Jun;67(6):1464-74
references.pmid: 1629758
references.citation: Trends Neurosci. 2008 Aug;31(8):428-34
references.pmid: 18603311
references.citation: J Neurosci. 2009 Mar 11;29(10):3132-7
references.pmid: 19279250
references.citation: J Neurophysiol. 2005 Jul;94(1):479-90
references.pmid: 15703230
references.citation: BMC Neurosci. 2003 Aug 28;4:18
references.pmid: 12946281
references.citation: Neuron. 2009 Sep 24;63(6):865-78
references.pmid: 19778514
references.citation: Physiol Rev. 1990 Jan;70(1):1-41
references.pmid: 2404287
references.citation: Cereb Cortex. 2003 Apr;13(4):422-33
references.pmid: 12631571
references.citation: J Appl Physiol (1985). 1991 Sep;71(3):1143-50
references.pmid: 1757311
references.citation: Biophys J. 1999 Feb;76(2):691-708
references.pmid: 9929474
references.citation: Front Med Biol Eng. 1991;3(2):135-7
references.pmid: 1911468
references.citation: Science. 2009 Jul 24;325(5939):412-3
references.pmid: 19628854
references.citation: J Neurosci. 2006 Aug 2;26(31):8148-59
references.pmid: 16885228
references.citation: Cognition. 1999 Jan 1;69(3):B17-24
references.pmid: 10193053
references.citation: Phys Rev Lett. 2005 Jan 14;94(1):018102
references.pmid: 15698136
references.citation: Nat Rev Neurosci. 2009 Mar;10(3):186-98
references.pmid: 19190637
references.citation: J Neurosci. 2009 Oct 28;29(43):13613-20
references.pmid: 19864573
references.citation: Psychon Bull Rev. 2001 Mar;8(1):162-7
references.pmid: 11340862
references.citation: PLoS One. 2009;4(2):e4338
references.pmid: 19190760
references.citation: Nat Rev Neurosci. 2008 Apr;9(4):292-303
references.pmid: 18319728
references.citation: Proc Natl Acad Sci U S A. 2009 Sep 15;106(37):15921-6
references.pmid: 19717463
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Sep;76(3 Pt 1):031114
references.pmid: 17930206
references.citation: Neuroimage. 2004 Apr;21(4):1232-41
references.pmid: 15050551
references.citation: J Neurosci Methods. 2008 May 30;170(2):352-7
references.pmid: 18328571
references.citation: J Neurosci. 2008 May 28;28(22):5696-709
references.pmid: 18509031
references.citation: Trends Neurosci. 2010 Mar;33(3):111-20
references.pmid: 20045201
references.citation: J Neurosci. 1995 Jan;15(1 Pt 1):47-60
references.pmid: 7823151
references.citation: Nature. 1993 Nov 11;366(6451):153-6
references.pmid: 8232553
references.citation: Neuroimage. 2008 Nov 15;43(3):528-39
references.pmid: 18786642
references.citation: Neuroscience. 2007 May 25;146(3):1400-12
references.pmid: 17418496
references.citation: Phys Rev Lett. 2006 Jan 20;96(2):028107
references.pmid: 16486652
references.citation: Hum Brain Mapp. 2001 Feb;12(2):61-78
references.pmid: 11169871
references.citation: Proc Natl Acad Sci U S A. 2003 Nov 11;100(23):13638-43
references.pmid: 14595013
references.citation: Trends Cogn Sci. 2009 Jun;13(6):239-45
references.pmid: 19428286
references.citation: Science. 2009 May 22;324(5930):1084-7
references.pmid: 19461004
references.citation: Neurosci Res. 2004 Feb;48(2):203-10
references.pmid: 14741395
references.citation: Proc Natl Acad Sci U S A. 2008 Oct 14;105(41):16039-44
references.pmid: 18843113
references.citation: Neuron. 2009 May 14;62(3):426-40
references.pmid: 19447097
references.citation: Phys Rev Lett. 1987 Jul 27;59(4):381-384
references.pmid: 10035754
references.citation: Nature. 1997 Jan 16;385(6613):207-10
references.pmid: 9000068
references.citation: PLoS One. 2007 May 16;2(5):e443
references.pmid: 17505542
references.citation: Nature. 2009 Jun 4;459(7247):663-7
references.pmid: 19396156
references.citation: Pflugers Arch Gesamte Physiol Menschen Tiere. 1965 May 10;284:1-17
references.pmid: 14341490
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jan;71(1 Pt 2):016133
references.pmid: 15697684
references.citation: J Neurosci. 2008 Aug 13;28(33):8268-72
references.pmid: 18701689
references.citation: Science. 2006 Sep 15;313(5793):1626-8
references.pmid: 16973878
references.citation: Science. 2009 Jul 24;325(5939):408
references.pmid: 19628851
references.citation: Nat Rev Neurosci. 2007 Sep;8(9):700-11
references.pmid: 17704812
references.citation: Trends Neurosci. 2007 Mar;30(3):101-10
references.pmid: 17275102
references.citation: J Neurosci. 2008 Aug 6;28(32):7968-78
references.pmid: 18685022
references.citation: Psychophysiology. 1991 Nov;28(6):648-55
references.pmid: 1816592
references.citation: J Evol Biol. 2009 Aug;22(8):1563-85
references.pmid: 19538344
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Oct;74(4 Pt 2):045101
references.pmid: 17155118
references.citation: Trends Cogn Sci. 2007 Jul;11(7):267-9
references.pmid: 17548233
references.citation: Trends Cogn Sci. 2009 Jul;13(7):302-9
references.pmid: 19535283
references.citation: Neuroimage. 1997 Apr;5(3):179-97
references.pmid: 9345548
references.citation: Proc Natl Acad Sci U S A. 1995 Dec 5;92(25):11568-72
references.pmid: 8524805
references.citation: Biol Rev Camb Philos Soc. 2001 May;76(2):161-209
references.pmid: 11396846
references.citation: Biol Cybern. 1989;60(3):161-9
references.pmid: 2923921
references.citation: Science. 2008 Apr 4;320(5872):110-3
references.pmid: 18388295