Polish theoretical studies on oscillations and cognition

Włodzimierz Klonowski

Polish theoretical studies on oscillations and cognition

• Centre of Theor. Physics PAS - Prof. M.Kus, K.Zyczkowski - quantum chaos, synchronization in chaotic systems, quantum brain

• I.Biocybernetics & Biomed.Eng. PAS - Prof.W.Klonowski- nonlinear analysis of biosignals (EEG) - deterministic chaos and fractal theory

• Jagiellonian University, Cracow - Prof. M.Ogorzałek- chaos-based signal processing, analysis and optimization of neural system

• Nencki Institute PAS, Warsaw - Dr. D.Wójcik- evoked potentials, spatiotemporal chaotic systems (Prof.A.Wrobel’s team)

• Nicolaus Copernicus Univ. Torun - Prof. W.Duch- computational cognitive neuroscience, informational dynamics,

• Polish scientists working abroad

(in Germany, Japan, Singapore, USA)

Linear vs Nonlinear Methods3N’s Problem -

Biosignals are: Noisy, Non-stationary, Non-linear

Living system are highly nonlinear and operate far from thermodynamic equilibrium, while linear methods, like FFT or wavelet transform, work properly only for stationary signals.

So why Medical Doctors when analyzing e.g. EEG use linear methods like FFT? I think that it is so because of long, much too long, post-paper-tape tradition.

Nonlinear methods that assess signal complexity may be used for EEG (and other biosignals) analysis no matter if the signal itself is chaotic, deterministic, or stochastic, also when it is nonstationary and noisy.

Difficulties in replication“It should be noted that difficulties sometimes

experienced in attempts to independently replicate certain frequency-specific non-thermal effects are actually to be expected. For in consequence of the highly non-linear, non-equilibrium nature of living systems, even the slightest differences in the physiological state of the biosystems used, and in the conditions obtaining in a particular experiment can, in consequence of deterministic chaos, assume singular importance”.

European Parliament, Directorate General for Research, Division Industry, Research and Energy, Scientific and Technological Options Assessment (STOA), Working document for the STOA Panel PE 297.574/Fin.St. Luxembourg, March 2001, p. 14

Brain and Chaos“Future research sponsored by the EC,

should incorporate the following recommendations: (…) That systematic investigation be made of the influence of different kinds of pulsing (of real phones) on the human EEG, and ideally on the MEG, and of whether any observed changes in power spectra are correlated with changes in the level of deterministic chaos”.

European Parliament, Directorate General for Research, Division Industry, Research and Energy, Scientific and Technological Options Assessment (STOA), Working document for the STOA Panel PE 297.574/Fin.St. Luxembourg, March 2001, pp. 23-24

Daniel Wojcik

Nencki Institute of Experimental Biology PAS, Warsaw

Classification of evoked potentials recorded from behaving animals

Applications of wavelets and PCA in data-based classification of attentional states of behaving animals

EXAMPLE - RAT R49

EFFICIENCY OF CLASSIFICATIONS: WAVELETS: 81%PCA (1-50): 64%PCA (7-18): 68%DIFFERENCE OF MEANS (1-50): 85%DIFFERENCE OF MEANS (7-18): 68% PART OF CROSS-VALIDATION: WAVELETS vs PCA (1-50): 75%WAVELETS vs MEANS (1-50): 92%PCA (1-50) vs MEANS (1-50): 72%

Field fluctuations in spatiotemporal chaotic systems

Transport in quantum random walks

We study transport in Quantum MultiBaker Maps (QMBs). Depending on the details of quantization the QMB is either translationally invariant and has ballistic transport, or disordered and exhibits localization. In both cases semiclassical limit is the same 1-D random walk (diffusive). The detailed nature of this transition in the first case is understood; disordered case is under study.

Time dependence of mean square displacement in QMBs for “h=1/64”. Numerical results for regular and disordered cases. Regular case shows transition from diffusion to ballistic motion; diffusion in disordered case lasts longer and is followed by localisation.

regular

disordered

time

msd

References

• Classification problems:– Wróbel A., Kublik E. i Musiał P. “Gating of the sensory activity within barrel

cortex of the awake rat” Exp. Brain Res. 123 (1998) 117-123

– Wypych M., Kublik E., Wojdyłło P. i Wróbel A. “Sorting functional classes of evoked potentials by wavelets” Neuroinformatics, 3 (2003) 193-202

– Jakuczun, W., Kublik E., Wójcik, D. i Wróbel A. “Classifying Evoked Potentials With Local Classifiers”, in preparation (2005)

• Local Lyapunov exponents in CGLE– Garnier, N. and Wójcik, D. “Spatiotemporal chaos: the microscopic

perspective”, submitted (2005)

• Quantum multibaker maps– Wójcik, D. and Dorfman, J. R. "Quantum multibaker maps: extreme

quantum regime" Phys. Rev. E 66 (2002) 036110

– Wójcik, D. and Dorfman, J. R. "Diffusive-ballistic crossover in 1D quantum walks" Phys. Rev. Lett. 90 (2003) 230602

– Wójcik, D. and Dorfman, J. R. "Crossover from diffusive to ballistic transport in periodic quantum maps" Physica D 187 (2004) 223-243

Włodzimierz Klonowski

Head, Lab. of Biosignal Analysis FundamentalsHead, Lab. of Biosignal Analysis Fundamentals

Institute of Biocybernetics and Biomedical Engineering (IBIB PAN),Institute of Biocybernetics and Biomedical Engineering (IBIB PAN),

Polish Academy of Sciences, WarsawPolish Academy of Sciences, Warsaw

wklon@hrabia.ibib.waw.pl ; ; http://www.ibib.waw.pl/~lbaf

Group Leader, GBAF-SENSATION (Group of Biosignal Analysis Fundamentals)

Medical Research Center (CMDiK PAN), Polish Academy of Sciences, Warsaw gbaf@cmdik.pan.pl; http://www.cmdik.pan.pl/~gbaf/

METHODS

We develop such new methods, based on nonlinear and symbolic dynamics. One method is based on Higuchi’s fractal dimension of the time series (signal). Another is a new symbolic method applied to signal’s derivative that measures total contribution of slow waves with frequencies smaller than certain value, e.g. 8 Hz.

The methods do not require preliminary embedding of the data in a phase space; it is also important that they may be applied to non-stationary time series since EEG-signals show serious non-stationarity.

Sleep-EEG data that we analyze are registered in the Dept. of Psychiatry, Medical University of Warsaw (Head Prof. W.Szelenberger), using commercially available data acquisition system made in Poland by P.I.M. ELMIKO, Warsaw.

Automatic Sleep Stager FRAST ™

The model works well for drowsiness monitoringbecause Df certainly decreases from wakefullness

to stage 1 – it maybe a false alarm but it’s o.k.

Fractal dimension of different sleep stages for 15 healthy persons0 - wake5 - REM

1,2,3,4 - stages 1,2,3,4, respectively

1,0

1,2

1,4

1,6

1,8

2,0

0 1 2 3 4 5 6

stage

Df

0 - wake

5 -

Monitoring of the depth of anesthesia - fractal dimension of EEG is like BIS

Influence of EMFs – cellular phones basal - phone at place but not in use; con - in use with a special screening device; sin - in use, without the screening device

1 in 5-6 healthy persons shows sensitivity to EMFs of cellulars

Multi-channel symbolic analysisof sleep-EEG (healthy person)

Symbolic Method - adult, severe ictal activity

More reddish colour means more slow waves

Quasi-periodicity of whole-night sleep(symbolic dynamics)

0 100 200 300 400 500 -20

0

20

40

60

80

100

120

140

S 8x0

t[min]

Diagram of the number of counts of the symbol „zero” (binary sequence 8x0, [00000000])

in binary encoded derivative of the whole-night EEG-signal (CDS on the electrode C3);

black – a healthy person, blue (lower) – a person with insomnia.

‘EPILEPTIC SEIZURES’ IN ECONOMIC ORGANISM(Physica A, 342 (2004) 701-707)

Summary of results Unlike ‘classical’ linear methods, the

nonlinear methods that we developed assess different aspects of what is called signal’s complexity. EEG-signal complexity depends on the state of brain and so it changes due to different brain pathologies, e.g. epileptic seizures, as well as to physiological shifts, e.g. due to the stage of sleep.

The same methods should be useful also in neurofeedback.

ReferencesKlonowski, W., Olejarczyk E. and Stepien R. (2004). Complexity of Polysomnogram

Signals. WSEAS Transactions on Computers, Issue 5, vol. 3, 1290-1294.

Olejarczyk E. (2003). Analysis of EEG signals using fractal dimension. PhD Thesis, IBBE PAS, Warsaw, Supervisor: Prof. W.Klonowski.

Klonowski, W., Olejarczyk E. and Stepien R. (2003). New Methods of Nonlinear and Symbolic Dynamics in Sleep EEG-Signal Analysis, In: Modelling and Control in Biomedical Systems 2003 (Feng D.D. and Carson E.R., Eds.), pp. 241-244 IFAC Publications, Elsevier, Oxford.

Klonowski, W. (2002). Nonlinear Dynamics – From Micro- to Macro-Cosmos. In: Attractors, Signals, and Synergetics. (W.Klonowski, Ed.). Frontiers on Nonlinear Dynamics. Vol. 1, 11-15. Pabst Science Publishers, Lengerich, Berlin.

Klonowski, W. (2002). Chaotic dynamics applied to signal complexity in phase space and in time domain. Chaos, Solitons and Fractals, 14, 1379-1387.

Klonowski, W., Olejarczyk E. and R Stepien R. (2002). Complexity of EEG-signal in Time Domain – Possible Biomedical Application. In: Experimental Chaos, AIP Conference Proceedings (Boccaletti, S., B.J. Gluckman, J. Kurths, L.M. Pecora and M.L. Spano, Eds.), Vol. 622, pp. 155-160,, Melville, New York.

Klonowski, W., Olejarczyk E. and Stepien R. (2001). Nonlinear dynamics. From conformons to human brain. Technology and Health Care  9, 87-89; also http://www.ibib.waw.pl/~lbaf