nonlinear time series analysis on eeg. review x v x v
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Nonlinear Time Series Analysis on EEG
Nonlinear Time Series Analysis on EEG
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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
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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
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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 .
),(.
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2 ) i t e r a t e d m a p
)1(1 nnn xrxx
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v
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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)
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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
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NrC
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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)
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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
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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
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Data ProcessData Process
•Time delay
•Embedded dimension
Delay Reconstruction
Raw data
Correlation Dimension
N
jiji XX
NrC
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(a)
(b)
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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.
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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