predictability of consciousness states studied with human brain magnetism
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Predictability of Consciousness States Studied with
Human Brain Magnetism
Noboru Tanizuka *1 Mostafizur R. Khan*1,3 Teruhisa Hochin*2
*1 Graduate School of Science, Osaka Prefecture University, Osaka *2 Graduate School of Sci. and Techn., Kyoto Inst. of Technology, Kyoto *3 (at present ) Summit System Service, Inc., Osaka
5th Int. Conf. on Unsolved Problems on Noise and Fluctuations in Physics, Biology and High Technology École Normale Supérieure de Lyon, Lyon, 2008.6.2-6
motive for study
• complex and active dynamics of the electric current in the neural networks of the cerebral cortex seems to reflect the state of consciousness (a kind of data processing in the brain)
• the activity of the neural current can be measured with magnetoencephalogram (MEG) at a high spatiotemporal resolving power
• is a consciousness state able to be given in a quantitative way by the analysis of the spatiotemporal data of neural current activity?
ex. a state of mind identified through a quantitative agent?
• at a first stage, we started to do experiments under simple consciousness states and do the analysis of the measurement data.
MEG (magnetoencephalogram)
122 channels
61 positions over scalp
Resolving power
space: 5mm, time: 1ms measurement: fT noise level: 2fT
(Geomagn.: 30μT)
Neuromag-122TM, 4-D Neuroimaging Ltd, Finland Planer-differential type coil
AIST, Osaka
Magnetic shield room: 1/105 - 1/104
measurement channels
mental states and associated rhythms considered as events of the brain
rhythms δ θ α β γfrequency
Hzmental
state
0.5-41.5-4.0
sleep
4-8 4-7
mental arithmetic
8-13 8-16eyes
closed at rest
13-3518-30eyes
opened at
mental activity
35-10036-64
perception,a circuit of cortex and brain stem
estimate a dynamical system of the intensity variations of brain magnetism and its rhythms
),(,),2(),1( tyyy
)))1((,),(),(()( mtytytytx
))(()1( txftx
DD RRf : difficult to estimate because of unknown system from which data was measured
RRf D:possible to estimate because we have the RBF network system into which the information of data is taken as the synaptic coefficients
measurement data
10 20 30 40 50
0
500
1000
1500
2000
2500 s.r. 2.5 ms, 4000 points
subject: yi. 22, ecr-103ch
frequency spectrum of the magnetism variations measured at an occipital channel at under eyes closed at rest of a healthy young male
alpha rhythm
at first, a simple system was tested
the alpha rhythm embedded in a state space 2.5ms 2.5sec m=3 τ=15ms
correlation dimension of alpha rhythm
2 4 6 8 10m
2
3
4
5
6
rmC
2.5msec 1-1000point, ch81
GP, Judd
system’s dynamical dimension is necessary for the RBF network analysis
RxRxxfx im
iii 11
…
x2
xN
… …x1 C1
CN
C2
∑λ1
λ2
λN
Radial Basis Function Network
x2
xN
… …x1 C1
CN
C2
∑λ1
λ2
λN
x2
xN
… …x1 C1
CN
C2
∑λ1
λ2
λN
x2
xN
… …x1 C1
CN
C2
∑λ1
λ2
λN
x2
x3
xN+1
… )1(,.....,, miiii
yyyx
mii yx 1
N
jjiji cxxf
1
solve the network function from real data
)exp()( 2 brr
TN ),,,( 21
Niixjc 1)()(
|)()(|),,,( 21
jcixrxxxz
ij
TNiii
NNN
N
rr
rrP
1
111
λPz
zP 1
a short term
N
jjt jctxtxfx
11 )()(ˆor)(ˆ
map function estimated from data
alpha rhythm: 2~ 3 wave lengths and 20~ 30 wave lengths
)ms15(6,100,4 Nm
x1= (1, 7, 13, 19) → x2 = (20)
x100=(100, 106, 112,118) → x101 = (119) cj = xj , j=1,…,100
initial value x101= (101, 107, 113, 119) ←real data free run x101=(120), x102, ……. 200 steps by the solution function {120,121,....,319} at the parameter b = 1000,..,b = 10000,..
for solution
prediction
20 40 60 80 100
-150
-100
-50
50
100
150
sampling rate: 2.5ms
measuredpredicted
xt+2τ=35 fT xt+3τ=135 fT b=10000
)(ˆ1 txfxt
short term used for the solution of the function
prediction reproduction
evaluate from the function for short termf̂
correlation coefficientreal and the predicted
b=1000
10000
70004000
a short term
1
-200-100
0100
200
t-200
-100
0
100
200
t 1
-400-200
0200
t 4
-200-100
0100
200
t
0 20 40 60 80 100Step
-200
-100
0
100
200
Tf
1
)ms25(1,100,4 Nm
x1= (1, 2, 3, 4) → x2 = (5) x100=(100, 101, 102,103) → x101 = (104) cj = xj , j=1,…,100
initial vectors x1, x51, x76, x101
sampling rate: 25ms
for solution
a long term
evaluate from the estimated function
)(ˆ1 txfxt
free run
)101(),76(),51(),1( xxxx
,)101(ˆ,,)77(ˆ,)76(ˆ1027877 xfxxfxxfx
EX. initial vector x76:
reproduction, prediction
0 20 40 60 80 100step
20
40
60
80
100
tnecrep
0 20 40 60 80 100step
20
40
60
80
100
tnecrep
0 20 40 60 80 100step
20
40
60
80
100
tnecrep
0 20 40 60 80 100step
20
40
60
80
100
tnecrep
0 20 40 60 80 100step
-200
-100
0
100
200
Tfmc
0 20 40 60 80 100step
-200
-100
0
100
200
Tfmc
0 20 40 60 80 100step
-200
-100
0
100
200
Tfmc
0 20 40 60 80 100step
-200
-100
0
100
200
Tfmc
)1(x
)51(x
)76(x
)101(x
real datafree run
repr
oduc
tion
pred
ictio
n
correlation coefficient
-1
0
1x t -1
0
1
xt1-2
-1
0
1
xt2-1
0
1x t
0 20 40 60 80 100steps
20
40
60
80
100
tnecrep
0 20 40 60 80 100steps
20
40
60
80
100
tnecrep
0 20 40 60 80 100steps
20
40
60
80
100tnecrep
0 20 40 60 80 100steps
20
40
60
80
100
tnecrep
0 20 40 60 80 100steps
-1
-0.5
0
0.5
1
0 20 40 60 80 100steps
-1
-0.5
0
0.5
1
0 20 40 60 80 100steps
-1
-0.5
0
0.5
1
0 20 40 60 80 100steps
-1
-0.5
0
0.5
1
)1(x
)1051(x
)1076(x
)1101(x
40)2(,90)1(:)(30)1(211)2( 2 .y.yny.ny.ny
1optimum)(1000
2
bm
Henon map
)(ˆ1 txfxt
50
-200-100
0
100
200 -200
-100
0
100
200
-400-200
0
200
-200-100
0
100
200
38
-200-100
0100
200
t-200
-100
0
100
200
t1-600-400-200
0200
t 4
-200-100
0100
200
t
25
-200-100
0100
200
t-200
-100
0
100
200
t 1
-500
0
500t 4
-200-100
0100
200
t
1
-200-100
0100
200
t-200
-100
0
100
200
t 1
-400-200
0200
t 4
-200-100
0100
200
t
real data
time
alpha rhythm
1
-1
0
1N -1
0
1
NLag
-2-10
1
N2Lag
-1
0
1N
50
-1
0
1N -1
0
1
NLag
-2-101
N2Lag
-1
0
1N
80
-1
0
1N -1
0
1
NLag
-2-101
N2Lag
-1
0
1N
100
-1
0
1N -1
0
1
NLag
-2-101
N2Lag
-1
0
1N
k=100k=50 k=80k=1
the map function of the Henon solved by RFB network
ktxfxt ),(ˆ1
},,,,,,,,,{ 1071061051041031025432,1 yyyyyyyyyyy1k 2k 100,,3 k ktxfxt ),(ˆ
1
the map function for every data window k, stepped by 50ms
data window
Hurst exponent, alpha rhythm, YI-ecr 103ch, 2.5s, by D kimoto
2.5s100ms
1.0
0.31
250ms
Hurst exponent, sine, by D kimoto
1.00
short term and long term prediction of alpha rhythm
alpha rhythm
The function of the alpha rhythm fluctuates along passage of time.
-50
0
50
100
N
-50
0
50
100NLag
-50
0
50
100
N2Lag
-50
0
50
100
N
-50
0
50
100NLag
-200
0
200N
-200
0
200NLag
-200
0
200
N2Lag
-200
0
200N
-200
0
200NLag
openedclosed
KS-entropy
103
10 20 30 40 500
50
100
150
200
250
300
350
10 20 30 40 500
500
1000
1500
2000
2500
eyes closed 0-10sec eyes opened 0-10sec
103ch, 0-2.5s
comparison of the rhythms appearing at different mental states of subject yi
eyes closed eyes opened
frequency spectrum of another subject mm, 22 healthy male
100 200 300 400 5000
20
40
60
80
100
100 200 300 400 5000
20
40
60
80
100
100 200 300 400 5000
100
200
300
400
500
100 200 300 400 5000
100
200
300
400
500
100 200 300 400 5000
20
40
60
80
100 200 300 400 5000
50
100
150
200
250
300
eyes closed at rest eyes opened at mental arithmetic eyes opened at rest
30ch
94ch
frontal
occipital
magnetic vectors at 61 positions over scalp under different consciousness states
Subject mm 22, healthy male
eyes crosed at rest eyes opened at mental arithmetic eyes opened at rest
5 10 15 20 25
-15
-10
-5
0
5
10
15
5 10 15 20 25
-15
-10
-5
0
5
10
15
5 10 15 20 25
-15
-10
-5
0
5
10
15
frontal
occipital
frontal
occipital
frontal
occipital
61
11 1:
pptVtVectors at time
ms50
2.5ms ms,5.2
61
1 ttpptV
The vectors varying along time passage
eyes closed at rest eyes opened at mental arithmetic
different dynamical patterns of the magnetic vectors under different consciousness states
5 10 15 20 25
-15
-10
-5
0
5
10
15
5 10 15 20 25
-15
-10
-5
0
5
10
15
5 10 15 20 25
-15
-10
-5
0
5
10
15
frontal
occipital
difference vectors at 61 positions t2 - t1=2.5ms
61
112
ppt
pt VVdifference vectors :
ecr eoma eor
conclusion• alpha rhythm as a most remarkable activity in a
resting state: possible to predict for the short term, impossible for the long term
• a network (function) generating the alpha rhythm is fluctuating with the passage of time
• the pattern of the magnetic vectors is evidently different for the different consciousness state
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