1. 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

2. 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.

3. 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: 1/10 5 - 1/10 4

4. measurement channels

5. mental states and associated rhythms considered as events of the brain rhythms δθαβγ frequency Hz mental state 0.5-4 1.5-4.0 sleep 4-8 4-7 mental arithmetic 8-13 8-16 eyes closed at rest 13-35 18-30 eyes opened at mental activity 35-100 36-64 perception, a circuit of cortex and brain stem

6. estimate a dynamical system of the intensity variations of brain magnetism and its rhythms difficult to estimate because of unknown system from which data was measured possible to estimate because we have the RBF network system into which the information of data is taken as the synaptic coefficients measurement data

7. 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

8. the alpha rhythm embedded in a state space 2.5ms 2.5sec m=3 τ=15ms

9. correlation dimension of alpha rhythm 2.5msec 1-1000point, ch81 GP, Judd system’s dynamical dimension is necessary for the RBF network analysis

10. … x2x2 xNxN …… x1x1 C1C1 CNCN C2C2 ∑ λ1λ1 λ2λ2 λNλN Radial Basis Function Network x2x2 xNxN …… x1x1 C1C1 CNCN C2C2 ∑ λ1λ1 λ2λ2 λNλN x2x2 xNxN …… x1x1 C1C1 CNCN C2C2 ∑ λ1λ1 λ2λ2 λNλN x2x2 xNxN …… x1x1 C1C1 CNCN C2C2 ∑ λ1λ1 λ2λ2 λNλN x x 2 x x 3 x x N+1 …

11. solve the network function from real data

12. a short term map function estimated from data alpha rhythm: 2 ～ 3 wave lengths and 20 ～ 30 wave lengths x 1 = ( 1, 7, 13, 19 ) → x 2 = ( 20 ) x 100 =( 100, 106, 112,118 ) → x 101 = ( 119 ) c j = x j, j=1,…,100 initial value x 101 = ( 101, 107, 113, 119 ) ←real data free run x 101 =( 120 ), x 102, ……. 200 steps by the solution function {120,121,....,319} at the parameter b = 1000,..,b = 10000,.. for solution prediction sampling rate: 2.5ms

13. measured predicted x t+2τ =35 fT x t+3τ =135 fT b=10000 short term used for the solution of the function prediction reproduction evaluate from the function for short term

14. correlation coefficient real and the predicted b=1000 10000 7000 4000 a short term

15. 22,103ch x 1 = ( 1, 2, 3, 4 ) → x 2 = ( 5 ) x 100 =( 100, 101, 102,103 ) → x 101 = ( 104 ) c j = x j, j=1,…,100 initial vectors x 1, x 51, x 76, x 101 sampling rate: 25ms for solution a long term evaluate from the estimated function free run EX. initial vector x 76 : reproduction, prediction

16. real data free run reproduction prediction correlation coefficient

17. Henon map

18. real data time alpha rhythm

19. k=100 k=50 k=80 k=1 the map function of the Henon solved by RFB network

20. 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 2.5s 100ms 1.0 0.31 250ms Hurst exponent, sine, by D kimoto 1.0 0 short term and long term prediction of alpha rhythm alpha rhythm The function of the alpha rhythm fluctuates along passage of time.

21. opened closed KS-entropy 103 1020304050 0 500 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

22. frequency spectrum of another subject mm, 22 healthy male eyes closed at rest eyes opened at mental arithmetic eyes opened at rest 30ch 94ch frontal occipital

23. 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 frontal occipital frontal occipital frontal occipital Vectors at time

24. 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

25. frontal occipital difference vectors at 61 positions t 2 - t 1 =2.5ms difference vectors : ecr eoma eor

26. 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