eeg-data assimilation for the resting human brain•the kuramoto model (km) driven by the neural...
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EEG-data assimilation for the resting human brain
Takumi Sase (Research Scientist)
Keiichi Kitajo(Unit Leader)
Rhythm-based Brain Information Processing Unit
RIKEN BSI-TOYOTA Collaboration Center
RIKEN Brain Science Institute
Overview
Introduction Motivation
Research Strategy1st stage
2nd stage 3rd stage
Conclusions
Results
Our previous work
What is EEG:
Keywords: Resting state, Metastability
Micro- to Macro-dynamics in the brain
Vareta et al., Nat. Rev. Neurosci., 2001
micro
macroH
iera
rch
ical le
ve
l
Introduction
LFPs
iEEG
EEG
Single units
EEG LFPs
Spontaneous macro-dynamics
https://en.wikipedia.org/wiki/Resting_state_fMRI
Lehmann, Scholarpedia, 2009
Lee et al., PLOS ONE, 2012
clustering
Introduction
Koenig et al., NeuroImage, 2002
clustering
Mathematical view of spontaneous brain
No fluctuation Driven by fluctuations
Torus
Limit cycle
Chaos
Fixed point
Tsuda, 2016
Introduction
Note: Tsuda is proposing chaotic itinerancy as a possible mechanism of spontaneous brain activity.
Metastable states
Spontaneous and evoked brain dynamics
Luczak et al., Neuron, 2009
Spontaneous
Introduction
Evoked
Execute a task
Tsuda, 2016
Our previous studySase & Kitajo, in preparationMotivation
Pote
ntia
l ene
rgy
Pote
ntia
l energ
y
Our previous studyMotivation Sase & Kitajo, in preparation
Pote
ntia
l energ
y
Pote
ntial energ
y
Tra
nsitio
ns
am
on
g 3
tori
Metastable state0 100 200 300 400 500 600 700 800
Time (s)
This study crosses over 3 stageshttps://en.wikipedia.org/wiki/Kuramoto_model
Lehmann, Scholarpedia, 2009
))()(sin()(
))()(sin(1
tθtψtKrω
tθtθN
Kω
dt
dθ
ii
N
j
ijii
N
j
tθtψ
tψ
j
Ntr
trtEEG
1
)(i)(i
)(i
e1
)e(where
,)e(Re)(
Freeston et al., Front. Neurosci., 2014
Jansen & Rit, Biol. Cybern., 1995
Drive!
Phases ofNeural mass model (NMM)
Drive!
1st
2nd
3rd
Research Strategy
NMM can produce alpha wave (8-12 Hz)
Jansen & Rit, Biol. Cybern., 1995 Grimbert & Faugeras, Neural Comput., 2006
Disturbance
1st stage
Results:1st stage
Drive!
Freeston et al., 2014 https://en.wikipedia.org/wiki
/Kuramoto_model
Master EEG
Slave EEG
Var = 3.92
Var = 0.0412
Var = 8.17
Var = 0.962
Grimbert & Faugeras,
2006
Grimbert & Faugeras,
2006
Disturbance Disturbance
<
<
Results:
R = 0.603 (P < 0.001)
Phases Drive!
2nd stage
PLF
K
https://en.wikipedia.org/wiki
/Kuramoto_modelLehmann, 2009
Functional connectivity
Master EEG phase
Slave EEG phase
Connection of previous study to DA3rd stage
2-tori driven by fluctuations
Limit cycles driven by fluctuations
10 Hz
0.3 HzE
EG
EE
G
Po
we
rP
ow
er
Frequency (Hz)
Frequency (Hz)
Setting for DA3rd stage
)(
1
));();(sin(sN
j
ijijiji βstθstθJω
dt
dθ
)(
1
);(i);(i
);(i
e)(
1)e;(where
,)e;(Re);(
sN
j
stθstψ
stψ
j
sNstr
strstEEG
jiijiijiijii βββJJJ ,0,,0
N(s):
s: update index
2 3 4 50
Constraints
{Jij}
&
{βij}
s=s+1 s=s+1:s=0
Results: Drive!
3rd stage
{Jij}
{βij}
N(s)=2
N(s)=50
https://en.wikipedia.org/wiki
/Kuramoto_modelLehmann, 2009
Master EEG
Slave EEG
EE
Gs
EE
Gs
EE
Gs
EE
Gs
Results:3rd stage
Time (s)
https://en.wikipedia.org/wiki/Kuramoto_modelS
imula
ted E
EG
Sim
ula
ted E
EG
Sim
ula
ted E
EG
Sim
ula
ted E
EG
Sim
ula
ted E
EG
Discussion3rd stage
Chaotic attractor
……
Summary
• The Kuramoto model (KM) driven by the Neural mass model (NMM)suggests that the KM, considering mesoscopic oscillators underlyingEEG differently from the NMM, considering only macroscopicelements, may be suitable for DA study.
• The KM driven by the phase of EEG suggests that the estimatedcoupling strength, K, clearly reflects functional connectivity on EEGdynamics.
• The KM driven by EEG suggests that metastable dynamics, revealedfrom our previous study, may be ideally phase chaos, which cannotbe observed from the human brain.
Conclusions
Future workConclusions
Vareta et al., Nat. Rev. Neurosci., 2001
https://en.wikipedia.org/wiki/Kuramoto_model
…
Individual 1
…
Individual 2
{Jij(1)} {Jij
(2)}
Jij
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