Slide 1 EEG
:
:



Significant
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Structural connectivity
( ): () .
. .
( ) ( ) .
(DTI) .
Brain-Connectivity * / 47
Functional connectivity
: .
.
( )
.
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Effective connectivity
: . .
.
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Significant
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EEG () EEG .
(Volume conduction effect) (Field spread) .
EEG Cross talk ( ) .
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EEG ( ) . ()
A: .
B: MEG
C: ( )
EEG\MEG

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(ECoG)
ill-posed ( )
( )
(Handbook of brain connectivity)

EEG (Common Reference Electrode) .
... EEG . ( )
(Active common reference electrode) ( ) EEG . ()
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EEG\MEG

EEG Task . ( )
.
(Average common reference) 64 .
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Significant
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(Coherence)
EEG\MEG .
.
x(t) y(t) : Coherency
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(Coherence)
Coherency ( ) [0,1] : Coherence
f . 0 1 f .
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(Coherence) MVAR
X(t)=[x1(t)…xk(t)] MVAR Coherence Coherence .
Coherence xi(t) xj(t)
S(f): X(t)
H(f):
Brain-Connectivity * / 47
MVAR
. (Multiple coherence) xi(t) .
Mii(f) S(f) i i .
Gi2(f) [0,1] . 1 xi(t) .
.
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Partial coherence MVAR
Coherence .
:
(Partial coherence function)
(Florin PHD thesis)
Partial coherence MVAR
(Partial functions) .
.
(PC) xi(t) xj(t) f .
Mij(f) S(f) i j . Cij2(f) Coherence [0,1] xi(t) xj(t) .
Brain-Connectivity * / 47
EEG
Δ=
(Kus et al. 2004)
(Kus et al. 2004)

3 EEG
: Coherence
: Partial Coherence
: Multiple Coherence
: 0 25
: 0 1
(Kus et al. 2004)
PC
(Kus et al. 2004)

3 EEG
Coherence
(Sleep stage 2)
: Coherence
: Partial Coherence
: Multiple Coherence
: 0 30
: 0 1
(Kaminski et al. 1997)

TASK .
EEG\MEG .
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:
(Mean Phase Coherence)

.
MPC .
MPC 0 1 . 1 0
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(Mutual Information)
x y :
x y MI x=y MI Shannon x .
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(Mutual Information)
MI(x,y) x y .
MI(x,y) x y . .
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Significant
Brain-Connectivity * / 47
Wiener
.
Wiener 1956 (Causality) (Predictability) .
Wiener X(t) Y(t) Y(t) X(t) .
1969 Granger Wiener (AR) .
Brain-Connectivity * / 47
Granger causality
var(ε(t))<var(ε’(t)) Y(t) X(t) Granger causality .
Granger causality : GY→X .
Granger .
causality Granger k : Xm X1 Xm Xm X1 ( Granger causality ) .
Brain-Connectivity * / 47

Granger causality EEG
(Kus et al. 2004)
(Kus et al. 2004)

MVAR: (DC)
MVAR (Direct causality) :
(Aij)m ( Am) xi(t) xj(t) . i j .
Brain-Connectivity * / 47
MVAR: (DTF)
DTF
Hij(f) : i j H(f) xi(t) xj(t) f
DTF DTF :
DTF [0,1] . 1 f i j 0 f j i .
Brain-Connectivity * / 47

DTF EEG
(Kus et al. 2004)
(Kus et al. 2004)

MVAR: (ffDTF)
DTF ( ) .
DTF DTF . DTF .
DTF (ffDTF) :
( ffDTF) .
Brain-Connectivity * / 47
DTF
DTF j i DTF j i .
.
DTF (dDTF) (PDC) .
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MVAR: (dDTF)
dDTF (direct Directed Transfer Function) () (Cascade) .
dDTF ffDTF (PC) :
dDTF ffDTF PC . j i j i .
Brain-Connectivity * / 47
dDTF EEG
(Kus et al. 2004)
(Kus et al. 2004)
MVAR: (PDC)
PDC 0 1 j i .
Aij(f): i j A(f)
aj(f): j A(f)
PDC .
Brain-Connectivity * / 47

PDC DTF
PDC j i j . DTF j i i .
PDC A(f) . PDC DTF PDC DTF
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PDC EEG
(Kus et al. 2004)
(Kus et al. 2004)



Significant
Brain-Connectivity * / 47
(TE)
(Partial Mutual Information) .
I(X,Y|Z): X Y Z .
Brain-Connectivity * / 47

: (TE)
Wiener Y X X Y X .
(Transfer Entropy) :
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Significant
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Significant
( ) Surrogate .
Surrogate .
. [0,2π] . .
.
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Significant
Surrogate .
Significant .
Surrogate Significant .
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