Nonlinear Time Series Analysis on EEG

Nonlinear Time Series Analysis on EEG

Middle Age

Reductionism

1666 Isacc Newton Calculus F=ma

1700s Classical mechanics

1870s Ludwig Boltzmann Entropy

1890s Henri Poincare 3 bodies planetary motions nightmare of chaos

ReviewReview

1920- 1960

nonlinear oscillator radio, radar, laser complex behavior

1963 Lorenz Stranger attractor Sensitive to initial condition

1970s Ruelle&Takens turbulence and chaso

Robert May chaos in logistic map

Feigenbaun universality

Mandelbort fractal

Russell soliton – self organization

1985s A Babloyantz Nonlinear brain

N o n l i n e a r d y n a m i c s a n d p h a s e p o r t r a i t

1 ) d i f f e r e n t i a l E q .

),(.

yxfx

),(.

yxgy

2 ) i t e r a t e d m a p

)1(1 nnn xrxx

x

v

x

v

Takens’s delay embedding theorem (1981)

scalar time series scalar time series

Ni xxx ,...,,...,1

m-dimensional vectorsm-dimensional vectors

)1(2 ,...,,, miiiii xxxxt

• Time Lag: Mutual information (A. M. Fraser, Physical Review A 33, 1134)

• Embedded dimension: m False nearest neighbor method (M. B. Kennel, Physical Review A 45, 3403)

Quantitative value on dynamical complexityP. Grassberger’s Correlation dimension (D2)

Quantitative value on dynamical complexityP. Grassberger’s Correlation dimension (D2)

ln

ln2

CD

•S. H. O.: D2 = 1

•Lorenz attractor: D2 = 2.05

N

jiji XX

NrC

12

)(1

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2D

Chaotic Dynamics in Brain ActivityA. Babloyantz (1985)

Chaotic Dynamics in Brain ActivityA. Babloyantz (1985)

• Differentiated D2 in SWS stages

(a) awake (b) stage2 sleep(c) stage4 sleep (d,e) REM

(a)

(b)

(c)

(d)

Strange Attractors in Intracranial StructureJ. Roschke and E. Basar

Strange Attractors in Intracranial StructureJ. Roschke and E. Basar

•Differentiated D2 in functionally independent brain structures

DGEA>DRF>DHI

Experimental protocolExperimental protocol

•Male Sprague Dawley rats (250~350g)

•The EEG signals were recorded in the somatosenseroy cortex (bragma –1, ML -3) with a 1x16 (16 channels) Michigan probe

•The sampling rates of recording were 6KHz and 250Hz in a data acquisition system based on PC system (TDT Inc. USA)

•Each epoch of 8s time series data (among a total of 200s recording period) was used for data analysis

•The data analysis program was based on the “Nonlinear Time Series Analysis” sub programs (in C language) written by Rainer Hegger et. al.

150um

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EEG raw dataEEG raw data

Data ProcessData Process

•Time delay

•Embedded dimension

Delay Reconstruction

Raw data

Correlation Dimension

N

jiji XX

NrC

12

)(1

)(

2Dr

(a)

(b)

ResultsResults

• The EEG data of 16 channels can be classified into 5 types with different phase portraits and D2.

• After anatomical mapping, cortical layer IV (channel 5,6) showed the higher D2. This may imply more complex neuronal activity on layer IV.

• D2 decreased with increasing different Halothane anesthesia concentration.

Principle of Neural Science

•Stellate neurons are the principle target of thalamocortical axons.

•The axons of Stellate neurons project and terminate on the apical dendrites of pyramidal cells who somas lie in layers II, III, and V.

Schematic cortical circuitSchematic cortical circuit