title: Multi-Dimensional Dynamics of Human Electromagnetic Brain Activity.
abstract: Magnetoencephalography (MEG) and electroencephalography (EEG) are invaluable neuroscientific tools for unveiling human neural dynamics in three dimensions (space, time, and frequency), which are associated with a wide variety of perceptions, cognition, and actions. MEG/EEG also provides different categories of neuronal indices including activity magnitude, connectivity, and network properties along the three dimensions. In the last 20 years, interest has increased in inter-regional connectivity and complex network properties assessed by various sophisticated scientific analyses. We herein review the definition, computation, short history, and pros and cons of connectivity and complex network (graph-theory) analyses applied to MEG/EEG signals. We briefly describe recent developments in source reconstruction algorithms essential for source-space connectivity and network analyses. Furthermore, we discuss a relatively novel approach used in MEG/EEG studies to examine the complex dynamics represented by human brain activity. The correct and effective use of these neuronal metrics provides a new insight into the multi-dimensional dynamics of the neural representations of various functions in the complex human brain.
authors.affiliation: Department of Integrative Physiology, National Institute for Physiological Sciences Okazaki, Japan.
authors.forename: Tetsuo
authors.initials: T
authors.lastname: Kida
authors.affiliation: Department of Integrative Physiology, National Institute for Physiological Sciences Okazaki, Japan.
authors.forename: Emi
authors.initials: E
authors.lastname: Tanaka
authors.affiliation: Department of Integrative Physiology, National Institute for Physiological Sciences Okazaki, Japan.
authors.forename: Ryusuke
authors.initials: R
authors.lastname: Kakigi
keywords: complex systems; graph theory; inter-regional connectivity; neuronal avalanche; non-linear dynamical system; self-organized criticality
references.citation: Exp Brain Res. 1991;84(3):505-16
references.pmid: 1864322
references.citation: Science. 1968 Aug 23;161(3843):784-6
references.pmid: 5663803
references.citation: Hum Brain Mapp. 2008 Jul;29(7):770-7
references.pmid: 18454457
references.citation: Neuroimage. 2011 Jan 1;54(1):253-63
references.pmid: 20643211
references.citation: J Neurosci. 2013 Jul 3;33(27):11212-20
references.pmid: 23825424
references.citation: PLoS One. 2013 Nov 04;8(11):e79023
references.pmid: 24223876
references.citation: Neurosci Lett. 2004 Jan 23;355(1-2):25-8
references.pmid: 14729226
references.citation: Nat Neurosci. 2000 Mar;3(3):277-83
references.pmid: 10700261
references.citation: J Neurophysiol. 1968 Jan;31(1):14-27
references.pmid: 4966614
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Jun;69(6 Pt 2):066138
references.pmid: 15244698
references.citation: Neuroimage. 2013 Feb 1;66:500-7
references.pmid: 23108269
references.citation: Biol Cybern. 1991;65(3):203-10
references.pmid: 1912013
references.citation: Neurosci Biobehav Rev. 2014 Jul;44:76-93
references.pmid: 22917915
references.citation: Neuroimage. 2007 Jul 1;36(3):645-60
references.pmid: 17466539
references.citation: Nature. 1998 Jun 4;393(6684):440-2
references.pmid: 9623998
references.citation: Proc Natl Acad Sci U S A. 2008 Dec 9;105(49):19514-9
references.pmid: 19033466
references.citation: PLoS One. 2007 Jul 04;2(7):e597
references.pmid: 17611629
references.citation: Psychometrika. 1949 Jun;14(2):95-116
references.pmid: 18152948
references.citation: Brain. 2009 Jan;132(Pt 1):213-24
references.pmid: 18952674
references.citation: Neuroimage. 2013 Oct 15;80:53-61
references.pmid: 23528922
references.citation: Science. 1972 Feb 11;175(4022):664-6
references.pmid: 5009769
references.citation: Neuroimage. 2008 Aug 15;42(2):649-62
references.pmid: 18565765
references.citation: J Comput Neurosci. 2011 Feb;30(1):45-67
references.pmid: 20706781
references.citation: Hum Brain Mapp. 2008 Jul;29(7):802-9
references.pmid: 18438885
references.citation: Hum Brain Mapp. 2008 Feb;29(2):193-206
references.pmid: 17390316
references.citation: J Cereb Blood Flow Metab. 1993 Jan;13(1):5-14
references.pmid: 8417010
references.citation: Science. 1995 May 12;268(5212):889-93
references.pmid: 7754376
references.citation: Front Hum Neurosci. 2015 May 12;9:255
references.pmid: 26029079
references.citation: PLoS One. 2013;8(3):e59204
references.pmid: 23544057
references.citation: Annu Int Conf IEEE Eng Med Biol Soc. 2010;2010:1714-7
references.pmid: 21096404
references.citation: Trends Cogn Sci. 2004 May;8(5):204-10
references.pmid: 15120678
references.citation: Clin Neurophysiol. 2005 Apr;116(4):920-32
references.pmid: 15792902
references.citation: Neuron. 2014 Jan 8;81(1):195-206
references.pmid: 24333055
references.citation: Proc Natl Acad Sci U S A. 2010 Mar 30;107(13):6040-5
references.pmid: 20304792
references.citation: Psychometrika. 1966 Dec;31(4):581-603
references.pmid: 5232444
references.citation: Neuroimage. 2006 May 15;31(1):209-27
references.pmid: 16413209
references.citation: Phys Rev Lett. 2003 Feb 28;90(8):088101
references.pmid: 12633462
references.citation: Neuroimage. 2003 Sep;20(1):186-201
references.pmid: 14527580
references.citation: Nature. 2005 Jun 9;435(7043):814-8
references.pmid: 15944704
references.citation: J Neurosci Methods. 2014 Mar 30;225:71-80
references.pmid: 24472530
references.citation: Cereb Cortex. 1999 Jul-Aug;9(5):415-30
references.pmid: 10450888
references.citation: J Neurophysiol. 2011 Dec;106(6):2888-95
references.pmid: 21880941
references.citation: Neuroimage. 2006 Mar;30(1):245-53
references.pmid: 16253520
references.citation: Neuroimage. 2012 Mar;60(1):305-23
references.pmid: 22209808
references.citation: Annu Int Conf IEEE Eng Med Biol Soc. 2013;2013:4414-7
references.pmid: 24110712
references.citation: Exp Neurol. 1963 Aug;8:155-81
references.pmid: 20191690
references.citation: Phys Rev Lett. 2000 Jul 10;85(2):461-4
references.pmid: 10991308
references.citation: Nat Neurosci. 2009 Jan;12(1):85-91
references.pmid: 19098905
references.citation: Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1996 Dec;54(6):6708-6724
references.pmid: 9965897
references.citation: Neuroimage. 2015 Mar;108:364-76
references.pmid: 25562823
references.citation: Science. 1990 Jun 22;248(4962):1556-9
references.pmid: 2360050
references.citation: Neuroimage. 2014 Oct 1;99:451-60
references.pmid: 24862079
references.citation: Neuroimage. 2011 Apr 15;55(4):1548-65
references.pmid: 21276857
references.citation: Neuron. 2004 Mar 4;41(5):809-23
references.pmid: 15003179
references.citation: Neuroimage. 2006 Jul 1;31(3):1051-60
references.pmid: 16545966
references.citation: Electroencephalogr Clin Neurophysiol. 1998 Jan;106(1):87-91
references.pmid: 9680169
references.citation: Brain Topogr. 1989 Fall-Winter;2(1-2):63-72
references.pmid: 2641476
references.citation: Neuroimage. 1999 Aug;10(2):173-80
references.pmid: 10417249
references.citation: Exp Brain Res. 1991;87(3):641-8
references.pmid: 1783032
references.citation: Neuroimage. 2014 Feb 15;87:427-43
references.pmid: 24055554
references.citation: J Neurophysiol. 2008 Apr;99(4):2012-20
references.pmid: 18234981
references.citation: Annu Int Conf IEEE Eng Med Biol Soc. 2009;2009:65-8
references.pmid: 19965115
references.citation: Curr Biol. 2015 Jun 15;25(12):1649-53
references.pmid: 26028433
references.citation: Electroencephalogr Clin Neurophysiol. 1994 Nov;91(5):337-45
references.pmid: 7525230
references.citation: Science. 1969 May 16;164(3881):828-30
references.pmid: 5767782
references.citation: Clin Neurophysiol. 2004 Oct;115(10):2292-307
references.pmid: 15351371
references.citation: Front Neuroinform. 2014 Feb 14;8:9
references.pmid: 24592235
references.citation: Proc Natl Acad Sci U S A. 2013 Feb 26;110(9):3585-90
references.pmid: 23401536
references.citation: Cell. 2014 May 8;157(4):773-5
references.pmid: 24813604
references.citation: J Neurosci. 1997 May 1;17(9):3178-84
references.pmid: 9096152
references.citation: Cereb Cortex. 1996 May-Jun;6(3):354-61
references.pmid: 8670663
references.citation: Neuroimage. 2002 Jul;16(3 Pt 1):638-50
references.pmid: 12169249
references.citation: J Physiol. 1968 Mar;195(1):215-43
references.pmid: 4966457
references.citation: Brain Topogr. 2010 Sep;23(3):227-32
references.pmid: 20640882
references.citation: Science. 1982 Jun 18;216(4552):1339-40
references.pmid: 7079770
references.citation: Phys Rev Lett. 2012 Jun 1;108(22):228703
references.pmid: 23003665
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Mar;77(3 Pt 2):036104
references.pmid: 18517458
references.citation: Nature. 1972 Dec 15;240(5381):414-6
references.pmid: 4564321
references.citation: Neuroimage. 2003 Aug;19(4):1273-302
references.pmid: 12948688
references.citation: Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1996 Aug;54(2):2115-2117
references.pmid: 9965293
references.citation: Neuroimage. 2005 Mar;25(1):141-58
references.pmid: 15734351
references.citation: Cereb Cortex. 2003 Apr;13(4):422-33
references.pmid: 12631571
references.citation: PLoS Biol. 2008 Jul 1;6(7):e159
references.pmid: 18597554
references.citation: Phys Rev Lett. 2008 Jun 13;100(23):234101
references.pmid: 18643502
references.citation: Proc Natl Acad Sci U S A. 2006 Jun 6;103(23):8577-82
references.pmid: 16723398
references.citation: Psychophysiology. 2010 Sep;47(5):799-808
references.pmid: 20210875
references.citation: Neuroimage. 2014 Jan 1;84:585-604
references.pmid: 24055704
references.citation: Nat Rev Neurosci. 2009 Mar;10(3):186-98
references.pmid: 19190637
references.citation: Hum Brain Mapp. 2014 Jan;35(1):213-26
references.pmid: 22965769
references.citation: J Neurosci Methods. 2008 Sep 30;174(2):292-300
references.pmid: 18703089
references.citation: Exp Brain Res. 2008 Oct;190(4):389-400
references.pmid: 18604526
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Nov;90(5-1):052714
references.pmid: 25493823
references.citation: Nature. 2005 Jun 23;435(7045):1102-7
references.pmid: 15973409
references.citation: Curr Biol. 2015 May 18;25(10):1368-74
references.pmid: 25936551
references.citation: Neuron. 2008 Nov 26;60(4):709-19
references.pmid: 19038226
references.citation: PLoS One. 2008 Apr 30;3(4):e0002051
references.pmid: 18446219
references.citation: Hum Brain Mapp. 2000 Oct;11(2):77-92
references.pmid: 11061335
references.citation: Proc Natl Acad Sci U S A. 2009 Sep 15;106(37):15921-6
references.pmid: 19717463
references.citation: Brain Topogr. 2004 Summer;16(4):233-8
references.pmid: 15379219
references.citation: Neuroimage. 2005 May 15;26(1):91-8
references.pmid: 15862209
references.citation: Neuroimage. 2004 Oct;23(2):473-82
references.pmid: 15488397
references.citation: IEEE Trans Biomed Eng. 2011 Nov;58(11):3121-9
references.pmid: 21824842
references.citation: Neuroimage. 2012 Mar;60(1):476-88
references.pmid: 22178298
references.citation: J Neurosci. 1996 Aug 15;16(16):5205-15
references.pmid: 8756449
references.citation: PLoS Comput Biol. 2005 Sep;1(4):e42
references.pmid: 16201007
references.citation: Med Biol Eng Comput. 1996 May;34(3):232-8
references.pmid: 8762831
references.citation: Brain Res. 1999 May 29;830(1):43-55
references.pmid: 10350559
references.citation: Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1995 Feb;51(2):980-994
references.pmid: 9962737
references.citation: Neuroimage. 2004;23 Suppl 1:S234-49
references.pmid: 15501094
references.citation: J Neurophysiol. 2014 Apr;111(7):1455-65
references.pmid: 24431400
references.citation: PLoS Comput Biol. 2009 Mar;5(3):e1000314
references.pmid: 19300473
references.citation: Front Hum Neurosci. 2013 Nov 08;7:754
references.pmid: 24265613
references.citation: J Neurosci. 1997 Jun 1;17(11):4302-11
references.pmid: 9151747
references.citation: Neuroimage. 2015 Oct 1;119:221-8
references.pmid: 26123380
references.citation: J Neurosci. 2013 Apr 17;33(16):7079-90
references.pmid: 23595765
references.citation: Neuroimage. 2003 May;19(1):156-62
references.pmid: 12781735
references.citation: Front Hum Neurosci. 2013 Dec 02;7:784
references.pmid: 24348359
references.citation: Conf Proc IEEE Eng Med Biol Soc. 2006;2006:3666-9
references.pmid: 17945788
references.citation: Neuroimage. 2015 Mar;108:460-75
references.pmid: 25585017
references.citation: J Neurosci. 2011 Sep 14;31(37):13128-36
references.pmid: 21917796
references.citation: Science. 1999 Oct 15;286(5439):509-12
references.pmid: 10521342
references.citation: PLoS Biol. 2004 Jun;2(6):e176
references.pmid: 15208723
references.citation: PLoS Biol. 2005 Mar;3(3):e79
references.pmid: 15736981
references.citation: Phys Rev Lett. 1996 Mar 11;76(11):1804-1807
references.pmid: 10060525
references.citation: Neuroimage. 2010 Sep;52(3):1059-69
references.pmid: 19819337
references.citation: Electroencephalogr Clin Neurophysiol. 1975 Apr;38(4):415-22
references.pmid: 46821
references.citation: J Neurosci. 2001 Feb 15;21(4):1370-7
references.pmid: 11160408
references.citation: Front Hum Neurosci. 2013 Aug 05;7:429
references.pmid: 23935576
references.citation: Neuroimage. 2007 Jan 1;34(1):264-73
references.pmid: 17049275
references.citation: Arq Neuropsiquiatr. 2005 Dec;63(4):977-83
references.pmid: 16400416
references.citation: Neurosci Lett. 2000 Jun 23;287(2):93-6
references.pmid: 10854720
references.citation: Neuropsychologia. 2000;38(1):11-21
references.pmid: 10617288
references.citation: Neuroreport. 2000 May 15;11(7):1509-14
references.pmid: 10841367
references.citation: Neuroreport. 1997 Nov 10;8(16):3537-40
references.pmid: 9427322
references.citation: Magn Reson Med. 1992 Jun;25(2):390-7
references.pmid: 1614324
references.citation: Neuron. 2008 Jun 12;58(5):802-13
references.pmid: 18549790
references.citation: Brain Stimul. 2009 Apr;2(2):58-80
references.pmid: 20633405
references.citation: Proc Natl Acad Sci U S A. 2006 Dec 19;103(51):19518-23
references.pmid: 17159150
references.citation: Hum Brain Mapp. 2012 Aug;33(8):1914-28
references.pmid: 21769991
references.citation: Philos Trans R Soc Lond B Biol Sci. 2015 May 19;370(1668):
references.pmid: 25823867
references.citation: J Neurosci. 2010 Mar 24;30(12):4295-305
references.pmid: 20335465
references.citation: Eur J Neurosci. 2004 Apr;19(7):1950-62
references.pmid: 15078569
references.citation: Neuron. 2011 Nov 17;72(4):665-78
references.pmid: 22099467
references.citation: Science. 1994 May 20;264(5162):1102-5
references.pmid: 8178168
references.citation: PLoS One. 2015 Jun 22;10(6):e0128485
references.pmid: 26098628
references.citation: Brain Connect. 2011;1(1):13-36
references.pmid: 22432952
references.citation: Hum Brain Mapp. 2008 Jul;29(7):791-801
references.pmid: 18465788
references.citation: Med Biol Eng Comput. 1994 Jan;32(1):35-42
references.pmid: 8182960
references.citation: Science. 1989 Oct 27;246(4929):486-8
references.pmid: 2814476
references.citation: Proc Natl Acad Sci U S A. 2001 Jan 16;98(2):694-9
references.pmid: 11209067
references.citation: Proc Natl Acad Sci U S A. 2015 Oct 6;112(40):12522-7
references.pmid: 26371305
references.citation: Phys Rev Lett. 2008 Mar 21;100(11):118703
references.pmid: 18517839
references.citation: Neuroscientist. 2013 Feb;19(1):88-100
references.pmid: 22627091
references.citation: Prog Neurobiol. 2000 Aug;61(5):495-523
references.pmid: 10748321
references.citation: Proc Natl Acad Sci U S A. 1990 Dec;87(24):9868-72
references.pmid: 2124706
references.citation: Neuroimage. 2006 Sep;32(3):1335-44
references.pmid: 16815039
references.citation: Neuroimage. 2010 Jan 1;49(1):641-55
references.pmid: 19596072
references.citation: Neuroimage. 2015 Sep;118:193-8
references.pmid: 26080311
references.citation: Nat Neurosci. 2012 Jun;15(6):884-90
references.pmid: 22561454
references.citation: Phys Rev Lett. 1987 Jul 27;59(4):381-384
references.pmid: 10035754
references.citation: Brain. 1991 Dec;114 ( Pt 6):2465-503
references.pmid: 1782527
references.citation: Hum Brain Mapp. 1994;1(3):210-20
references.pmid: 24578041
references.citation: Proc Natl Acad Sci U S A. 2008 May 27;105(21):7576-81
references.pmid: 18499802
references.citation: IEEE Trans Biomed Eng. 1989 Jan;36(1):4-14
references.pmid: 2646211
references.citation: Neuroimage. 2012 Jun;61(2):371-85
references.pmid: 22227136
references.citation: Exp Neurol. 1961 Jun;3:501-24
references.pmid: 13681481
references.citation: Biol Cybern. 2001 Jun;84(6):463-74
references.pmid: 11417058
references.citation: J Neurophysiol. 2010 Dec;104(6):3312-22
references.pmid: 20631221
references.citation: Neuroimage. 2015 Oct 15;120:362-70
references.pmid: 26187453
references.citation: Electroencephalogr Clin Neurophysiol. 1988 Jun;69(6):581-4
references.pmid: 2453336
references.citation: Science. 2006 Feb 3;311(5761):670-4
references.pmid: 16456083
references.citation: Science. 2001 Sep 28;293(5539):2470-3
references.pmid: 11577239
references.citation: J Comput Neurosci. 2011 Feb;30(1):85-107
references.pmid: 20799057
references.citation: Front Hum Neurosci. 2015 Feb 04;9:20
references.pmid: 25698955
references.citation: Neuroimage. 2014 Jan 15;85 Pt 2:853-72
references.pmid: 24007803
references.citation: IEEE Trans Biomed Eng. 2001 Jul;48(7):760-71
references.pmid: 11442288
references.citation: Nat Neurosci. 2008 Sep;11(9):1100-8
references.pmid: 19160509
references.citation: Hum Brain Mapp. 1999;8(4):194-208
references.pmid: 10619414
references.citation: Front Hum Neurosci. 2010 Nov 22;4:209
references.pmid: 21151369
references.citation: Nat Rev Neurosci. 2014 Oct;15(10):683-95
references.pmid: 25186238
references.citation: Proc Natl Acad Sci U S A. 2011 Oct 4;108(40):16783-8
references.pmid: 21930901
references.citation: IEEE Trans Biomed Eng. 2002 Sep;49(9):975-87
references.pmid: 12214887
references.citation: Neuroimage. 2015 Jul 1;114:398-413
references.pmid: 25828884
references.citation: Brain. 2012 Mar;135(Pt 3):922-34
references.pmid: 22366801
references.citation: J Neurophysiol. 2011 Aug;106(2):554-63
references.pmid: 21562190
references.citation: Neuron. 2007 Oct 25;56(2):366-83
references.pmid: 17964252
references.citation: Neuroimage. 2015 Feb 1;106:144-53
references.pmid: 25463464
references.citation: Neuroimage. 2004 Oct;23(2):582-95
references.pmid: 15488408
references.citation: PLoS One. 2015 Jun 02;10(6):e0128787
references.pmid: 26035750
references.citation: J Neurophysiol. 1980 Jan;43(1):118-36
references.pmid: 7351547
references.citation: Neuroimage. 2012 Aug 1;62(1):530-41
references.pmid: 22569064
references.citation: Front Hum Neurosci. 2014 Jul 16;8:510
references.pmid: 25076883
references.citation: Neuroimage. 2014 Feb 15;87:444-64
references.pmid: 24055702
references.citation: Neuroimage. 2015 Feb 15;107:219-228
references.pmid: 25512038
references.citation: Neuroimage. 2015 Jan 15;105:380-94
references.pmid: 25462688
references.citation: Cereb Cortex. 2007 Jan;17(1):92-9
references.pmid: 16452642
references.citation: J Neurophysiol. 1981 Aug;46(2):369-84
references.pmid: 6267219
references.citation: PLoS One. 2013 Jul 09;8(7):e68192
references.pmid: 23874535
references.citation: Front Hum Neurosci. 2013 Jul 15;7:365
references.pmid: 23874285
references.citation: Neuroimage. 2013 Feb 15;67:203-12
references.pmid: 23165323
references.citation: Neuroimage. 2008 Jun;41(2):437-47
references.pmid: 18396062
references.citation: J Neurosci. 2003 Dec 3;23(35):11167-77
references.pmid: 14657176
references.citation: Science. 2002 Oct 25;298(5594):824-7
references.pmid: 12399590
references.citation: J Neurosci. 2010 May 19;30(20):7078-87
references.pmid: 20484650
references.citation: J Neurosci Methods. 2003 Apr 15;124(2):113-28
references.pmid: 12706841
references.citation: Neuroscience. 2011 Feb 23;175:169-77
references.pmid: 21130847
references.citation: Hum Brain Mapp. 2012 Dec;33(12):2856-72
references.pmid: 21928311
references.citation: Neuroimage. 2015 Oct 1;119:44-53
references.pmid: 26095089
references.citation: Biol Cybern. 1989;61(5):347-59
references.pmid: 2790066
references.citation: Phys Med Biol. 1987 Jan;32(1):11-22
references.pmid: 3823129
references.citation: Phys Rev Lett. 2001 Nov 5;87(19):198701
references.pmid: 11690461
references.citation: J Neurosci. 2012 Jan 18;32(3):1061-72
references.pmid: 22262904
references.citation: J Neurosci. 2012 Oct 24;32(43):14915-20
references.pmid: 23100414
references.citation: Neuron. 2011 Feb 10;69(3):572-83
references.pmid: 21315266
references.citation: Neuroimage. 2015 Apr 15;110:60-77
references.pmid: 25638756
references.citation: Hum Brain Mapp. 2007 Nov;28(11):1178-93
references.pmid: 17266107
references.citation: Neuroimage. 2004 Mar;21(3):1155-66
references.pmid: 15006682
references.citation: Prog Biophys Mol Biol. 2011 Mar;105(1-2):80-97
references.pmid: 21115029