Neural interactions occur on different levels and scales. It is of particular importance to understand how they are distributed among different neuroanatomical and physiological relevant brain regions. We investigated neural cross-frequency couplings between different brain regions according to the Desikan–Killiany brain parcellation. The adaptive dynamic Bayesian inference method was applied to EEG measurements of healthy resting subjects in order to reconstruct the coupling functions. It was found that even after averaging over all subjects, the mean coupling function showed a characteristic waveform, confirming the direct influence of the delta-phase on the alpha-phase dynamics in certain brain regions and that the shape of the coupling function changes for different regions. While the averaged coupling function within a region was of similar form, the region-averaged coupling function was averaged out, which implies that there is a common dependence within separate regions across the subjects. It was also found that for certain regions the influence of delta on alpha oscillations is more pronounced and that oscillations that influence other are more evenly distributed across brain regions than the influenced oscillations. When presenting the information on brain lobes, it was shown that the influence of delta emanating from the brain as a whole is greatest on the alpha oscillations of the cingulate frontal lobe, and at the same time the influence of delta from the cingulate parietal brain lobe is greatest on the alpha oscillations of the whole brain.

1.
H.-J.
Park
and
K.
Friston
, “
Structural and functional brain networks: From connections to cognition
,”
Science
342
,
1238411
(
2013
).
2.
K.
Lehnertz
,
G.
Ansmann
,
S.
Bialonski
,
H.
Dickten
,
C.
Geier
, and
S.
Porz
, “
Evolving networks in the human epileptic brain
,”
Physica D
267
,
7
15
(
2014
).
3.
L. R.
Chai
,
A. N.
Khambhati
,
R.
Ciric
,
T. M.
Moore
,
R. C.
Gur
,
R. E.
Gur
,
T. D.
Satterthwaite
, and
D. S.
Bassett
, “
Evolution of brain network dynamics in neurodevelopment
,”
Network Neurosci.
1
,
14
30
(
2017
).
4.
D.
Rudrauf
,
A.
Douiri
,
C.
Kovach
,
J. P.
Lachaux
,
D.
Cosmelli
,
M.
Chavez
,
C.
Adam
,
B.
Renault
,
J.
Martinerie
, and
M. L.
Van Quyen
, “
Frequency flows and the time-frequency dynamics of multivariate phase synchronization in brain signals
,”
NeuroImage
31
,
209
227
(
2006
).
5.
Q.
Li
,
T.
Peron
,
T.
Stankovski
, and
P.
Ji
, “
Effects of structural modifications on cluster synchronization patterns
,”
Nonlinear Dyn.
108
,
3529
3541
(
2022
).
6.
P.
Sauseng
,
W.
Klimesch
,
W. R.
Gruber
, and
N.
Birbaumer
, “
Cross-frequency phase synchronization: A brain mechanism of memory matching and attention
,”
NeuroImage
40
,
308
317
(
2008
).
7.
X.
Suo
,
D.
Lei
,
K.
Li
,
F.
Chen
,
F.
Li
,
L.
Li
,
X.
Huang
,
S.
Lui
,
L.
Li
,
G. J.
Kemp
, and
Q.
Gong
, “
Disrupted brain network topology in pediatric posttraumatic stress disorder: A resting-state fMRI study
,”
Hum. Brain Mapp.
36
,
3677
3686
(
2015
).
8.
K. T.
Olde Dubbelink
,
A.
Hillebrand
,
D.
Stoffers
,
J. B.
Deijen
,
J. W.
Twisk
,
C. J.
Stam
, and
H. W.
Berendse
, “
Disrupted brain network topology in Parkinson’s disease: A longitudinal magnetoencephalography study
,”
Brain
137
,
197
207
(
2014
).
9.
R. S.
Desikan
,
F.
Ségonne
,
B.
Fischl
,
B. T.
Quinn
,
B. C.
Dickerson
,
D.
Blacker
,
R. L.
Buckner
,
A. M.
Dale
,
R. P.
Maguire
,
B. T.
Hyman
,
M. S.
Albert
, and
R. J.
Killiany
, “
An automated labeling system for subdividing the human cerebral cortex on MRI scans into gyral based regions of interest
,”
NeuroImage
31
,
968
980
(
2006
).
10.
L.
Fan
,
H.
Li
,
J.
Zhuo
,
Y.
Zhang
,
J.
Wang
,
L.
Chen
,
Z.
Yang
,
C.
Chu
,
S.
Xie
,
A. R.
Laird
et al., “
The human Brainnetome Atlas: A new brain atlas based on connectional architecture
,”
Cereb. Cortex
26
,
3508
3526
(
2016
).
11.
M. F.
Glasser
,
T. S.
Coalson
,
E. C.
Robinson
,
C. D.
Hacker
,
J.
Harwell
,
E.
Yacoub
,
K.
Ugurbil
,
J.
Andersson
,
C. F.
Beckmann
,
M.
Jenkinson
,
S. M.
Smith
, and
D. C.
Van Essen
, “
A multi-modal parcellation of human cerebral cortex
,”
Nature
536
,
171
178
(
2016
).
12.
R. T.
Canolty
,
E.
Edwards
,
S. S.
Dalal
,
M.
Soltani
,
S. S.
Nagarajan
,
H. E.
Kirsch
,
M. S.
Berger
,
N. M.
Barbaro
, and
R. T.
Knight
, “
High gamma power is phase-locked to theta oscillations in human neocortex
,”
Science
313
,
1626
1628
(
2006
).
13.
O.
Jensen
and
L. L.
Colgin
, “
Cross-frequency coupling between neuronal oscillations
,”
Trends Cognit. Sci.
11
,
267
269
(
2007
).
14.
J. M.
Palva
,
S.
Palva
, and
K.
Kaila
, “
Phase synchrony among neuronal oscillations in the human cortex
,”
J. Neurosci.
25
,
3962
3972
(
2005
).
15.
V.
Jirsa
and
V.
Müller
, “
Cross-frequency coupling in real and virtual brain networks
,”
Frontiers Comput. Neurosci.
7
,
78
(
2013
).
16.
P.
Sorrentino
,
M.
Ambrosanio
,
R.
Rucco
,
J.
Cabral
,
L. L.
Gollo
,
M.
Breakspear
, and
F.
Baselice
, “
Detection of cross-frequency coupling between brain areas: An extension of phase linearity measurement
,”
Front. Neurosci.
16
,
846623
(
2022
).
17.
M. K.
Delimayanti
,
B.
Purnama
,
N. G.
Nguyen
,
M. R.
Faisal
,
K. R.
Mahmudah
,
F.
Indriani
,
M.
Kubo
, and
K.
Satou
, “
Classification of brainwaves for sleep stages by high-dimensional FFT features from EEG signals
,”
Appl. Sci.
10
,
1797
(
2020
).
18.
M.
Gorgoni
,
S.
Scarpelli
,
F.
Reda
, and
L.
De Gennaro
, “
Sleep EEG oscillations in neurodevelopmental disorders without intellectual disabilities
,”
Sleep Med. Rev.
49
,
101224
(
2020
).
19.
J. M.
Krueger
,
M. G.
Frank
,
J. P.
Wisor
, and
S.
Roy
, “
Sleep function: Toward elucidating an enigma
,”
Sleep Med. Rev.
28
,
46
54
(
2016
).
20.
A.
Bashan
,
R. P.
Bartsch
,
J. W.
Kantelhardt
,
S.
Havlin
, and
P. C.
Ivanov
, “
Network physiology reveals relations between network topology and physiological function
,”
Nat. Commun.
3
,
702
(
2012
).
21.
T.
Penzel
,
M.
Hirshkowitz
,
J.
Harsh
,
R. D.
Chervin
,
N.
Butkov
,
M.
Kryger
,
B.
Malow
,
M. V.
Vitiello
,
M. H.
Silber
,
C. A.
Kushida
, and
A. L.
Chesson
, “
Digital analysis and technical specifications
,”
J. Clin. Sleep Med.
3
,
109
120
(
2007
).
22.
S.
Palva
and
J. M.
Palva
, “
New vistas for α-frequency band oscillations
,”
Trends Neurosci.
30
,
150
158
(
2007
).
23.
C. L.
Ehlers
and
D. J.
Kupfer
, “
Effects of age on delta and REM sleep parameters
,”
Electroencephalogr. Clin. Neurophysiol.
72
,
118
125
(
1989
).
24.
M. S.
Keshavan
,
C. F.
Reynolds
,
J. M.
Miewald
,
D. M.
Montrose
,
J. A.
Sweeney
,
R. C.
Vasko
, and
D. J.
Kupfer
, “
Delta sleep deficits in schizophrenia: Evidence from automated analyses of sleep data
,”
Arch. Gen. Psychiatry
55
,
443
448
(
1998
).
25.
R. M.
Benca
,
W. H.
Obermeyer
,
C. L.
Larson
,
B.
Yun
,
I.
Dolski
,
K. D.
Kleist
,
S. M.
Weber
, and
R. J.
Davidson
, “
EEG alpha power and alpha power asymmetry in sleep and wakefulness
,”
Psychophysiology
36
,
430
436
(
1999
).
26.
W.
Scheuler
,
D.
Stinshoff
, and
S.
Kubicki
, “
The alpha-sleep pattern
,”
Neuropsychobiology
10
,
183
189
(
1983
).
27.
P.
Hauri
and
D. R.
Hawkins
, “
Alpha-delta sleep
,”
Electroencephalogr. Clin. Neurophysiol.
34
,
233
237
(
1973
).
28.
S.
Vijayan
,
E. B.
Klerman
,
G. K.
Adler
, and
N. J.
Kopell
, “
Thalamic mechanisms underlying alpha-delta sleep with implications for fibromyalgia
,”
J. Neurophysiol.
114
,
1923
1930
(
2015
).
29.
T.
Stankovski
,
S.
Petkoski
,
J.
Raeder
,
A. F.
Smith
,
P. V. E.
McClintock
, and
A.
Stefanovska
, “
Alterations in the coupling functions between cortical and cardio-respiratory oscillations due to anaesthesia with propofol and sevoflurane
,”
Philos. Trans. R. Soc., A
374
,
20150186
(
2016
).
30.
T.
Stankovski
,
V.
Ticcinelli
,
P. V. E.
McClintock
, and
A.
Stefanovska
, “
Neural cross-frequency coupling functions
,”
Front. Syst. Neurosci.
11
,
33
(
2017
).
31.
J. R.
Isler
,
P. G.
Grieve
,
D.
Czernochowski
,
R. I.
Stark
, and
D.
Friedman
, “
Cross-frequency phase coupling of brain rhythms during the orienting response
,”
Brain Res.
1232
,
163
172
(
2008
).
32.
D.
Manasova
and
T.
Stankovski
, “
Neural cross-frequency coupling functions in sleep
,”
Neuroscience
523
,
20
30
(
2023
).
33.
Y.
Kuramoto
,
Chemical Oscillations, Waves, and Turbulence
(
Springer-Verlag
,
Berlin
,
1984
).
34.
V. N.
Smelyanskiy
,
D. G.
Luchinsky
,
A.
Stefanovska
, and
P. V. E.
McClintock
, “
Inference of a nonlinear stochastic model of the cardiorespiratory interaction
,”
Phys. Rev. Lett.
94
,
098101
(
2005
).
35.
T.
Stankovski
,
A.
Duggento
,
P. V. E.
McClintock
, and
A.
Stefanovska
, “
Inference of time-evolving coupled dynamical systems in the presence of noise
,”
Phys. Rev. Lett.
109
,
024101
(
2012
).
36.
D.
Lukarski
,
M.
Ginovska
,
H.
Spasevska
, and
T.
Stankovski
, “
Time window determination for inference of time-varying dynamics: Application to cardiorespiratory interaction
,”
Front. Physiol.
11
,
341
(
2020
).
37.
K. J.
Friston
, “
Functional and effective connectivity: A review
,”
Brain. Connect.
1
,
13
36
(
2011
).
38.
T.
Stankovski
,
T.
Pereira
,
P. V. E.
McClintock
, and
A.
Stefanovska
, “
Coupling functions: Universal insights into dynamical interaction mechanisms
,”
Rev. Mod. Phys.
89
,
045001
(
2017
).
39.
I. Z.
Kiss
,
C. G.
Rusin
,
H.
Kori
, and
J. L.
Hudson
, “
Engineering complex dynamical structures: Sequential patterns and desynchronization
,”
Science
316
,
1886
1889
(
2007
).
40.
W.
Moon
and
J. S.
Wettlaufer
, “
Coupling functions in climate
,”
Philos. Trans. R. Soc., A
377
,
20190006
(
2019
).
41.
T.
Stankovski
,
P. V. E.
McClintock
, and
A.
Stefanovska
, “
Coupling functions enable secure communications
,”
Phys. Rev. X
4
,
011026
(
2014
).
42.
B.
Kralemann
,
L.
Cimponeriu
,
M.
Rosenblum
,
A.
Pikovsky
, and
R.
Mrowka
, “
Phase dynamics of coupled oscillators reconstructed from data
,”
Phys. Rev. E
77
,
066205
(
2008
).
43.
S.
Ranganathan
,
V.
Spaiser
,
R. P.
Mann
, and
D. J. T.
Sumpter
, “
Bayesian dynamical systems modelling in the social sciences
,”
PLoS One
9
,
e86468
(
2014
).
44.
B.
Kralemann
,
M.
Frühwirth
,
A.
Pikovsky
,
M.
Rosenblum
,
T.
Kenner
,
J.
Schaefer
, and
M.
Moser
, “
In vivo cardiac phase response curve elucidates human respiratory heart rate variability
,”
Nat. Commun.
4
,
2418
(
2013
).
45.
D.
Lukarski
,
D.
Stavrov
, and
T.
Stankovski
, “
Variability of cardiorespiratory interactions under different breathing patterns
,”
Biomed. Signal Process. Control
71
,
103152
(
2022
).
46.
T.
Stankovski
, “Coupling functions in neuroscience,” in Physics of Biological Oscillators (Springer, 2021), pp. 175–189.
47.
C.
Bick
,
M.
Goodfellow
,
C. R.
Laing
, and
E. A.
Martens
, “
Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: A review
,”
J. Math. Neurosci.
10
,
9
(
2020
).
48.
A.
Yeldesbay
,
G. R.
Fink
, and
S.
Daun
, “
Reconstruction of effective connectivity in the case of asymmetric phase distributions
,”
J. Neurosci. Methods
317
,
94
(
2019
).
49.
K.
Suzuki
,
T.
Aoyagi
, and
K.
Kitano
, “
Bayesian estimation of phase dynamics based on partially sampled spikes generated by realistic model neurons
,”
Front. Comput. Neurosci.
11
,
116
(
2018
).
50.
A.
Jafarian
,
P.
Zeidman
,
V.
Litvak
, and
K.
Friston
, “
Structure learning in coupled dynamical systems and dynamic causal modelling
,”
Philos. Trans. R. Soc., A
377
,
20190048
(
2019
).
51.
H.
Su
,
C.
Huo
,
B.
Wang
,
W.
Li
,
G.
Xu
,
Q.
Liu
, and
Z.
Li
, “
Alterations in the coupling functions between cerebral oxyhaemoglobin and arterial blood pressure signals in post-stroke subjects
,”
PLoS One
13
,
e0195936
(
2018
).
52.
C. N.
Takembo
,
A.
Mvogo
,
H. P. E.
Fouda
, and
T. C.
Kofané
, “
Effect of electromagnetic radiation on the dynamics of spatiotemporal patterns in memristor-based neuronal network
,”
Nonlinear Dyn.
95
,
1067
1078
(
2018
).
53.
A.
Gruszecka
,
M. K.
Nuckowska
,
M.
Waskow
,
J.
Kot
,
P. J.
Winklewski
,
W.
Guminski
,
A. F.
Frydrychowski
,
J.
Wtorek
,
A.
Bujnowski
,
P.
Lass
,
T.
Stankovski
, and
M.
Gruszecki
, “
Coupling between blood pressure and subarachnoid space width oscillations during slow breathing
,”
Entropy
23
,
113
(
2021
).
54.
H.
Nakao
,
T.
Yanagita
, and
Y.
Kawamura
, “
Phase-reduction approach to synchronization of spatiotemporal rhythms in reaction-diffusion systems
,”
Phys. Rev. X
4
,
021032
(
2014
).
55.
F. A.
Rodrigues
,
T. K. D.
M. Peron
,
P.
Ji
, and
J.
Kurths
, “
The Kuramoto model in complex networks
,”
Phys. Rep.
610
,
1
98
(
2016
).
56.
A.
Duggento
,
T.
Stankovski
,
P. V. E.
McClintock
, and
A.
Stefanovska
, “
Dynamical Bayesian inference of time-evolving interactions: From a pair of coupled oscillators to networks of oscillators
,”
Phys. Rev. E
86
,
061126
(
2012
).
57.
T.
Stankovski
,
A.
Duggento
,
P. V. E.
McClintock
, and
A.
Stefanovska
, “
A tutorial on time-evolving dynamical Bayesian inference
,”
Eur. Phys. J.: Spec. Top.
223
,
2685
2703
(
2014
).
58.
M.
Schirner
,
A. R.
McIntosh
,
V.
Jirsa
,
G.
Deco
, and
P.
Ritter
, “
Inferring multi-scale neural mechanisms with brain network modelling
,”
eLife
7
,
e28927
(
2018
).
59.
I.
Daubechies
,
Ten Lectures on Wavelets
(
SIAM
,
1992
).
60.
G.
Kaiser
,
A Friendly Guide to Wavelets
(
Birkhäuser
,
Boston
,
1994
).
61.
A.
Stefanovska
,
M.
Bračič
, and
H. D.
Kvernmo
, “
Wavelet analysis of oscillations in the peripheral blood circulation measured by laser Doppler technique
,”
IEEE Trans. Bio. Med. Eng.
46
,
1230
1239
(
1999
).
62.
G.
Buzsáki
and
A.
Draguhn
, “
Neuronal oscillations in cortical networks
,”
Science
304
,
1926
1929
(
2004
).
63.
T.
Schreiber
and
A.
Schmitz
, “
Surrogate time series
,”
Physica D
142
,
346
382
(
2000
).
64.
G.
Lancaster
,
D.
Iatsenko
,
A.
Pidde
,
V.
Ticcinelli
, and
A.
Stefanovska
, “
Surrogate data for hypothesis testing of physical systems
,”
Phys. Rep.
748
,
1
60
(
2018
).
65.
T.
Stankovski
,
V.
Ticcinelli
,
P. V. E.
McClintock
, and
A.
Stefanovska
, “
Coupling functions in networks of oscillators
,”
New J. Phys.
17
,
035002
(
2015
).
66.
D.
Iatsenko
,
A.
Bernjak
,
T.
Stankovski
,
Y.
Shiogai
,
P. J.
Owen-Lynch
,
P. B. M.
Clarkson
,
P. V. E.
McClintock
, and
A.
Stefanovska
, “
Evolution of cardio-respiratory interactions with age
,”
Philos. Trans. R. Soc., A
371
,
20110622
(
2013
).
67.
F.
Battiston
,
G.
Cencetti
,
I.
Iacopini
,
V.
Letora
,
M.
Lucas
,
A.
Patania
,
J.
Young
, and
G.
Petri
, “
Networks beyond pairwise interactions: Structure and dynamics
,”
Phys. Rep.
874
,
1
92
(
2020
).
68.
P.
Sorrentino
,
S.
Petkoski
,
M.
Sparaco
,
E. T.
Lopez
,
R.
Rucco
,
E.
Signoriello
,
F.
Baselice
,
S.
Bonavita
,
M.
Pirozzi
,
M.
Quarantelli
,
G.
Sorrentino
, and
V.
Jirsa
, “
Whole-brain propagation delays in multiple sclerosis, a combined tractography–magnetoencephalography study
,”
J. Neurosci.
42
,
8807
(
2022
).
69.
J.-D.
Lemaréchal
,
M.
Jedynak
,
L.
Trebaul
,
A.
Boyer
,
F.
Tadel
,
M.
Bhattacharjee
,
P.
Deman
,
V.
Tuyisenge
,
L.
Ayoubian
,
E.
Hugues
et al., “
A brain atlas of axonal and synaptic delays based on modelling of cortico-cortical evoked potentials
,”
Brain
145
,
1653
(
2021
).
70.
S.
Petkoski
and
V. K.
Jirsa
, “
Transmission time delays organize the brain network synchronization
,”
Philos. Trans. R. Soc., A
377
,
20180132
(
2019
).
71.
P.
Fries
, “
Rhythms for cognition: Communication through coherence
,”
Neuron
88
,
220
235
(
2015
).
72.
S.
Petkoski
and
V. K.
Jirsa
, “
Normalizing the brain connectome for communication through synchronization
,”
Network Neurosci.
6
,
722
744
(
2022
).
73.
M.
Mancini
,
A.
Karakuzu
,
J.
Cohen-Adad
,
M.
Cercignani
,
T. E.
Nichols
, and
N.
Stikov
, “
An interactive meta-analysis of MRI biomarkers of myelin
,”
eLife
9
,
e61523
(
2020
).
74.
A. L.
Foundas
,
C. M.
Leonard
,
R. L.
Gilmore
,
E. B.
Fennell
, and
K. M.
Heilman
, “
Pars triangularis asymmetry and language dominance
,”
Proc. Natl. Acad. Sci. U.S.A.
93
,
719
722
(
1996
).
75.
J.
Mai
and
G.
Paxinos
,
The Human Nervous System
(
Elsevier Science
,
2011
).
76.
P.
Johns
, Clinical Neuroscience: An Illustrated Colour Text, An Illustrated Colour Text Series (Churchill Livingstone/Elsevier, 2014).
77.
I.
Deschamps
,
S. R.
Baum
, and
V. L.
Gracco
, “
On the role of the supramarginal gyrus in phonological processing and verbal working memory: Evidence from rTMS studies
,”
Neuropsychologia
53
,
39
46
(
2014
).
78.
J.
Leinweber
,
S.
Heim
,
F.
Altenbach
,
A.
Chatterjee
,
U.
Habel
, and
K.
Sass
, “
Deeper insights into semantic relations: An fMRI study of part-whole and functional associations
,”
Brain Lang.
129C
,
30
42
(
2014
).
79.
L.
Ma
,
S.
Narayana
,
D.
Robin
,
P.
Fox
, and
J.
Xiong
, “
Changes occur in resting state network of motor system during 4 weeks of motor skill learning
,”
NeuroImage
58
,
226
33
(
2011
).
80.
A.
Assmus
,
J.
Marshall
,
A.
Ritzl
,
J.
Noth
,
K.
Zilles
, and
G.
Fink
, “
Left inferior parietal cortex integrates time and space during collision judgments
,”
NeuroImage
20(Suppl 1)
,
S82
S88
(
2003
).
81.
Y.
Zhao
,
Z.
Zhen
,
X.
Liu
,
Y.
Song
, and
J.
Liu
, “
The neural network for face recognition: Insights from an fMRI study on developmental prosopagnosia
,”
NeuroImage
169
,
151
161
(
2018
).
82.
K.
Katanoda
,
K.
Yoshikawa
, and
M.
Sugishita
, “
Neural substrates for the recognition of newly learned faces: A functional MRI study
,”
Neuropsychologia
38
,
1616
1625
(
2000
).
83.
V.
Axelrod
and
G.
Yovel
, “
Successful decoding of famous faces in the fusiform face area
,”
PLoS One
10
,
e0117126
(
2015
).
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