Download 7. nonlinear EEG - Brain Dynamics Laboratory

Nonlinear dynamical analysis
of the EEG in Psychiatric disorders
Jaeseung Jeong, Ph.D
Department of Bio and Brain Engineering
KAIST,
Daejeon, South Korea
Why are brain oscillations so
complex?
EEG Complexity and emotion
• Longitudinal variation of global
entropy (K) and scores to mood
assessment scale for each subject.
• Entropy evolution is represented
with open circles, and corresponds
to the left ordinate axis scale.
• Depressive mood modulation is
depicted with black squares and
corresponds to the right ordinate
axis scale.
• Days of recording are given in
abscissa. Depressed patients : Mrs.
G., Mss. S. and Mrs. R.
Complexity during different sleep stages
Approximate Entropy in AD/HD patients
This EEG time series shows the transition between interictal
and ictal brain dynamics. The attractor corresponding to the
inter ictal state is high dimensional and reflects a low level of
synchronization in the underlying neuronal networks, whereas
the attractor reconstructed from the ictal part on the right shows
a clearly recognizable structure. (Stam, 2003)
One possible answer for why seizures occur is that:
Seizures have to occur to reset (recover) some
abnormal connections among different areas in the
brain. Seizures serve as a dynamical resetting mechanism.
The effect of alcohol on the EEG complexity
measured by Approximate entropy
Measures of Complexity
• Most extant complexity measures can be grouped into two main
categories:
• Members of the first category (algorithmic information content
and logical depth) all capture the randomness, information
content or description length of a system or process, with
random processes possessing the highest complexity since they
most resist compression.
Measures of Complexity
• The second category (including statistical complexity, physical
complexity and neural complexity) conceptualizes complexity
as distinct from randomness.
• Here, complex systems are those that possess a high amount of
structure or information, often across multiple temporal and
spatial scales. Within this category of measures, highly complex
systems are positioned somewhere between systems that are
highly ordered (regular) or highly disordered (random).
A schematic diagram of the shape of such measures. It should be
emphasized again that a generally accepted quantitative
expression linking complexity and disorder does not currently
exist.
Complex Networks
• A key insight is that network topology, the graph structure of
the interactions, places important constraints on the system's
dynamics, by directing information flow, creating patterns of
coherence between components, and by shaping the emergence
of macroscopic system states.
• Complexity is highly sensitive to changes in network topology.
Changes in connection patterns or strengths may thus serve as
modulators of complexity.
• The link between network structure and dynamics represents
one of the most promising areas of complexity research in the
near future.
Why complexity?
• Why does complexity exist in the first place, especially among
biological systems? A definitive answer to this question
remains elusive.
• One perspective is based on the evolutionary demands
biological systems face. The evolutionary success of biological
structures and organisms depends on their ability to capture
information about the environment, be it molecular or
ecological.
• Biological complexity may then emerge as a result of
evolutionary pressure on the effective encoding of structured
relationships which support differential survival.
Why complexity?
• Another clue may be found in the emerging link between
complexity and network structure.
• Complexity appears very prominently in systems that combine
segregated and heterogeneous components with large-scale
integration.
• Such systems become more complex as they more efficiently
integrate more information, that is, as they become more
capable to accommodate both the existence of specialized
components that generate information and the existence of
structured interactions that bind these components into a
coherent whole.
• Thus reconciling parts and wholes, complexity may be a
necessary manifestation of a fundamental dialectic in nature
(Scholapedia).
Functional segregation and integration
• While the evidence for regional specialization in the brain is
overwhelming, it is clear that the information conveyed by
the activity of specialized groups of neurons must be
functionally integrated in order to guide adaptive behavior
• Like functional specialization, functional integration occurs
at multiple spatial and temporal scales.
• The rapid integration of information within the
thalamocortical system does not occur in a particular
location but rather in terms of a unified neural process.
How does the brain ‘bind' together the
attributes of objects to construct a unified
conscious scene?
• Neurons can integrate frequently co-occurring constellations of
features by convergent connectivity. However, convergence is
unlikely to be the predominant mechanism for integration.
• First, no single (‘master') brain area has been identified, the
activity of which represents entire perceptual or mental states.
• Second, the vast number of possible perceptual stimuli
occurring in ever changing contexts greatly exceeds the number
of available neuronal groups (or even single neurons), thus
causing a combinatorial explosion.
• Third, convergence does not allow for dynamic (‘on-the-fly')
conjunctions in response to novel, previously unencountered
stimuli.
• (A) Connections between groups are arranged such that groups with similar
response selectivity are preferentially connected, are arranged
anisotropically along the axis of their orientation selectivity, and connection
density falls off with distance. This produces spike patterns with significant
correlations between some groups and not others, as well as a temporally
varying EEG that reflects a mixture of synchronization and
desynchronization. Segregation and integration are balanced and
complexity is high. (B) Connection density is reduced. No statistically
significant correlations exist, and a flat EEG results. (C) Connections are of
the same overall density as in (A), but are spread out uniformly and
randomly over the network. The system is fully integrated but functional
specialization is lost, and complexity is low.
EEG recordings
Several sources of complexity in EEG
Fundamental assumptions of
Nonlinear dynamical analysis
• EEG signals are generated by nonlinear deterministic processes
with nonlinear coupling interactions between neuronal populations.
• Nonlinear deterministic systems may show a sensitive dependence
on initial conditions, implying that different states of a system,
being arbitrarily close initially, can become exponentially
separated in sufficiently long times. This behavior is called
deterministic chaos.
• These systems behave very irregular and complex, similar to
stochastic systems.
• Given the highly nonlinear nature of neuronal interactions at
multiple levels of spatial scales, it is quite natural to apply
nonlinear methods to the EEG.
Several limitations
on Nonlinear Dynamical Aanalysis
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The proper computations and interpretations of the nonlinear
measures involves several pitfalls.
The computation of the nonlinear measures can be biased by
autocorrelation effects in the time series. This can be avoided by
discarding vector pairs with time indices less than the
autocorrelation time (Theiler, 1986).
Insufficient length of the time series can bias the nonlinear
measures estimate (Eckman and Ruelle, 1992).
The computation of the nonlinear measures can be influenced by
noise (Möller et al., 1989).
[Examples] Colored, filtered noise can give rise to linear scaling
regions of the plot and saturation with increasing embedding
dimensions, spuriously suggesting the existence of a lowdimensional attractor (Osborne and Provenzale, 1989).
Several limitations
on Nonlinear Dynamical Aanalysis
• The fundamental assumption of NDA that the EEG generates by a
deterministic process is still disputable.
• The absolute values of nonlinear measures depend sensitively on
algorithms used or parameters in the algorithms, such as the
embedding dimension, the time delay, the number of data point, the
cut-off noise level.
• Given that nonlinear measures like the D2 or L1 reflect nonlinear
dynamics of the attractor in the phase space reconstructed from the
EEG, the physiological implications of the changes in these
measures in pathological brain states are not clear.
• Nonlinear dynamics of the EEG is possibly influenced by many
physiological factors including age, sex intelligence as well as by
the severity of the disease.
Is EEG deterministic or stochastic?
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• If the time series are generated
from deterministic systems
that are governed by nonlinear
ordinary differential equations,
then nearby points on the
phase space behave similarly
under time evolution.
• These smoothness properties
imply determinism.
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Tim e D e lay
• Jeong et al. Tests for low dimensional determinism in EEG. Physical Review E
(1999).
• Jeong et al. Detecting determinism in a short sample of stationary EEG. IEEE
Transactions on Biomedical Engineering (2002)
• Jeong et al. Detecting determinism in short time series, with an application to the
analysis of a stationary EEG recording. Biological Cybernetics (2002)
Detecting determinism in independent
components of the EEG using ICA
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Detecting determinism in independent
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Why is determinism important?
[1] Whether a time series is deterministic or not decides our
approach to investigate the time series. Thus determinism test
provides us with appropriate tools for analyzing EEG signals.
[2] Determinism in the EEG (or electrocorticogram) suggests that
EEGs reflecting thoughts and emotion are able to be utilized in the
brain-computer interface (BCI).
Three general ways
to overcome these limitations
(i) Still compute classic measures, but refrain from an interpretation
in terms of dimensions or deterministic chaos, and consider them as
tentative indices of different brain states.
(ii) Check the validity of the results with surrogate data
(iii) Use novel nonlinear measures which attempt to characterize
some of the structure of the reconstructed trajectories without making
strong assumptions about the nature of the underlying dynamics.
[Examples]
Nonlinear forecasting; Unstable periodic orbits; Mutual dimension etc.
The importance of dynamical
stationarity
• Time series generated from nonlinear dynamical systems
exhibit nonstationary (i.e. time-dependent) based on
statistical measures (weak statistics) including the mean
and variance, despite that the parameters in the dynamical
process all remain constant.
• It indicates that the statistical stationarity of the time series
does not imply its dynamical stationarity.
• Given that the EEG is possibly generated by the dynamical,
cognitive process of the brain, the dynamical
nonstationarity of the EEG can reflect on the state transition
of the brain.
Dynamical nonstationarity
AD/HD: Attention-Deficit/Hyperactivity disorder
Definition of the Dynamical stationarity:
For two consecutive windows of a non stationary dynamical
system time series, there should be change in dynamic from
passage of one windows to another one.
Correspondence with cognitive science (for a pretreated data):
Cognitive tasks (rest, image recognition, games…) = Brain Dynamical State
Change in cognitive States (Attention, Brain Functions …) = Nonstat. Detection
Main Hypothesis:
Since ADHD could have shorter characteristic time for attention, we could
expect same order behavior inside a Cognitive State, which could be found
analyzing the time criterion in loss of Dynamical Nonstationarity.
Measures of nonlinear interdependency
• The brain can be conceived as a complex network of coupled and
interacting subsystems. Higher brain functions depend upon
effective processing and integration of information in this network.
This raises the question how functional interactions between
different brain areas take place, and how such interactions may be
changed in different types of pathology.
Mutual information of the EEG
•The MI between measurement xi generated from system X and
measurement yj generated from system Y is the amount of
information that measurement xi provides about yj.
J Jeong, JC Gore, BS Peterson. Mutual information analysis of the EEG
in patients with Alzheimer's disease. Clin Neurophysiol (2001)
Recent MI studies on the EEG
• Schlogl A, Neuper C, Pfurtscheller G. Estimating the mutual
information of an EEG-based Brain-Computer Interface.
Biomed Tech. 2002;47(1-2):3-8.
Na et al., EEG in schizophrenic patients: mutual information
analysis. Clin Neurophysiol. 2002;113(12):1954-60.
Huang L, Yu P, Ju F, Cheng J. Prediction of response to
incision using the mutual information of
electroencephalograms during anaesthesia. Med Eng Phys.
2003;25(4):321-7.
Phase synchronization in chaotic systems
• Coupled chaotic oscillators can display phase synchronization even
when their amplitudes remain uncorrelated (Rosenblum et al., 1996).
Phase synchronization is characterized by a non uniform distribution
of the phase difference between two time series. It may be more
suitable to track nonstationary and nonlinear dynamics.
Phase synchronization
• ‘Synchronization of chaos refers to a process, wherein two (or
many) systems (either equivalent or nonequivalent) adjust a given
property of their motion to a common behavior due to a coupling or
to a forcing (periodical or noisy)’ (Boccaletti et al., 2002).
Nonlinear coupling among cortical areas
Phase synchronization and interdependence
Definition of synchronization: two or many subsystems sharing specific
common frequencies
Broader notion: two or many subsystems adjust some of their timevarying properties to a common behavior due to coupling or common
external forcing
Jansen et al., Phase synchronization of the ongoing EEG and
auditory EP generation. Clin Neurophysiol. 2003;114(1):79-85.
Le Van Quyen et al., Nonlinear interdependencies of EEG signals
in human intracranially recorded temporal lobe seizures. Brain Res.
(1998)
Breakspear and Terry. Detection and description of non-linear
interdependence in normal multichannel human EEG data. Clin
Neurophysiol (2002)
Generalized Synchronization
• Generalized synchronization exists between two interacting systems
if the state of the response system Y is a function of the state of the
driver system X: Y=F(X). Cross prediction is the extent to which
prediction of X is improved by knowledge about Y, which allows the
detection of driver and response systems.
• The nonlinear interdependence is not a pure measure of coupling but
is also affected by the complexity or degrees of freedom of the
interacting systems
Nonlinear analysis of the sleep EEG
• In many of these studies it was suggested that sleep EEG reflects
low-dimensional chaotic dynamics (Cerf et al., 1996, Fell et al.,
1993, Kobayashi et al., 1999, Kobayashi et al., 2001, Niestroj et al.,
1995, Pradhan et al., 1995, Pradhan and Sadasivan, 1996, Röschke,
1992, Röschke and Aldenhoff, 1991 and Röschke et al., 1993).
• The general pattern that emerges from these studies is that deeper
sleep stages are almost always associated with a ‘lower complexity’
as exemplified by lower dimensions and lower values for the
largest Lyapunov exponent.
• This type of finding has suggested the possible usefulness of
nonlinear EEG analysis to obtain automatic hypnograms.
Nonlinear analysis of the sleep EEG
• An analysis of an all night sleep recording found an evidence for
weak nonlinear structure but not low-dimensional chaos
(Achermann et al., 1994 and Achermann et al., 1994; Fell et al.
(1996a) using the nonlinear cross prediction (NLCP) to search for
nonlinear structure in sleep EEGs of adults and infants.
• sleep EEG of young infants showed nonlinear structure mostly
during quiet sleep (Ferri et al., 2003).
• The nonlinear measures were better in discriminating between
stages I and II, whereas the spectral measures were superior in
separating stage II and slow wave sleep: Nonlinear structure may be
most outspoken in stage II.
• nonlinear and asymmetric coupling during slow wave sleep in
infants (Pereda et al., 2003).
Nonlinear EEG analysis of Coma and anesthesia
• Matousek et al. (1995) studied the correlation dimension (based
upon a spatial embedding) in a small group of 14 healthy subjects
aged from 1.5 to 61 years. They found an increase of the
dimension during drowsiness as compared to the awake state.
• The usefulness of nonlinear EEG analysis as a tool to monitor
anesthetic depth was suggested (Watt and Hameroff, 1988).
• The correlation dimension correlated with the estimated level of
sevoflurane in the brain (Widman et al., 2000; Van den Broek,
2003).
Epilepsy as a dynamical disorder
• A dynamical brain disorder
• Spatial synchronization of brain electrical / magnetic
activity
• Brain fails to function as a multi-task multi-processing
machine
• Hallmarks of epilepsy:
- Interictal spikes
- Epileptic seizures
(detectable from electroencephalograms – EEGs)
EEGs in Epileptic seizures
• there is now fairly strong evidence that seizures reflect strongly
nonliner brain dynamics (Andrzejak et al., 2001b, Casdagli et al.,
1997, Ferri et al., 2001, Pijn et al., 1991, Pijn et al., 1997 and Van der
Heyden et al., 1996).
• Epileptic seizures are also characterized by nonlinear
interdependencies between EEG channels.
• Other studies have investigated the nature of interictal brain
dynamics in patients with epilepsy. In intracranial recordings, the
epileptogenic area is characterized by a loss of complexity as
determined with a modified correlation dimension (Lehnertz and
Elger, 1995).
• A time dependent Lyapunov exponent calculated from interictal
MEG recordings could also be used to localize the epileptic focus
(Kowalik et al., 2001)
The importance of seizure prediction
• The importance of seizure prediction can easily be appreciated: if a
reliable and robust measure can indicate an oncoming seizure
twenty or more minutes before it actually starts, the patient can be
warned and appropriate treatment can be installed.
• Ultimately a closed loop system involving the patient, a seizure
prediction device and automatic administration of drugs could be
envisaged (Peters et al., 2001).
Controversial about seizure prediction I
• In 1998, within a few months time, two papers were published that,
in restrospect, can be said to have started the field of seizure
prediction. The first paper showed that the dimensional complexity
loss L, previously used by the same authors to identify
epileptogenic areas in interictal recordings, dropped to lower
levels up to 20 min before the actual start of the seizure (Elger and
Lehnertz, 1998 and Lehnertz and Elger, 1998).
• The second paper was published in Nature Medicine by a French
group and showed that intracranially recorded seizures could be
anticipated 2–6 minutes in 17 out of 19 cases (Martinerie et al.,
1998).
• Schiff spoke about ‘forecasting brainstorms’ in an editorial
comment on this paper (Schiff, 1998).
One possible answer for why seizures occur is that:
Seizures have to occur to reset (recover) some
abnormal connections among different areas in
the brain. Seizures serve as a dynamical resetting
mechanism.
Controversial about seizure prediction I
• It was shown that seizure prediction was also possible with
surface EEG recordings (Le van Quyen et al., 2001b). This
was a significant observation, since the first two studies both
involved high quality intracranial recordings.
• Next, it was shown that seizure anticipation also worked for
extra temporal seizures (Navarro et al., 2002).
• This early phase was characterized by great enthusiasm and a
hope for clinical applications (Lehnertz et al., 2000).
Changes in D2 of epileptic patients
Le Van Quyen M et al., Nonlinear interdependencies
of EEG signals in human intracranially recorded
temporal lobe seizures. Brain Res. 792(1):24-40 (1998).
EEG characteristics of seizures
Traditional view: interictal  ictal  postictal
• Seizures’ occurrences are random
• Random occurrence of interictal spikes
• The transition from an interictal to ictal state is very
abrupt (seconds)
• Ictal activity may spread from the epileptogenic focus
to other normal brain areas after seizure’s onset
EEG characteristics of seizures
Emerging view:
interictal  preictal  ictal  postictal
• Seizures or spikes are NOT random events
• Existence of a preictal state
• The transition from the interictal to preictal to ictal
state is progressive (minutes to hours)
• Preictal and ictal spatio-temporal entrainment of the
epileptogenic focus with normal brain sites
• Seizures reset: postictal disentrainment of the
epileptogenic focus from normal brain sites.
Controversial about seizure prediction II
• Aschenbrenner-Scheibe et al. (2003). These authors showed that
with an acceptable false positive rate the sensitivity of the method
was not very high.
• The results of Martinerie et al. were also critically re-examined.
McSharry et al. suggested that the measure used by Martinerie et
al. was sensitive to signal amplitudes and that the good results
might also have been obtained with a linear method (McSharry et
al., 2003).
• Another group attempted to replicate the results of Le van Quyen
et al. in predicting seizures from surface EEG recordings (De
Clercq et al., 2003). These authors could not replicate the results in
their own group.
Online real-time seizure prediction
General features of EEGs in AD
• The hallmark of EEG abnormalities in AD patients is slowing of the
rhythms and a decrease in coherence among different brain regions:
A major promising candidate is the cholinergic deficit. AD is thought
to be a syndrome of neocortical disconnection, in which profound
cognitive losses arise from the disrupted structural and functional
integrity of long cortico-cortical tracts
Correlation dimension analysis
of the EEG in AD patients
• The D2 reflects the number of independent variables that are
necessary to describe the dynamics of the system, and is
considered to be a reflection of the complexity of the cortical
dynamics underlying EEG recordings.
• Thus, reduced D2 values of the EEG in AD patients indicate that
brains injured by AD exhibit a decrease in the complexity of brain
electrical activity (Woyshville and Calabrese (1994) Besthorn et al
., 1995 and Jeong et al., 1998, Stam et al., 1995 and Yagyu et al., 1
997).
EEG dynamics in patients with Alzheimer’s disease
EEG time series recorded from a patient with AD
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EEG amplitude (mV)
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Non-linear dynamical analysis of the EEG in Alzheimer's disease
with optimal embedding dimension.
Jeong et al. (1998) Electroencephalogr Clin Neurophysiol
AD patients have significantly lower nonlinear complex measures
than those for age-approximated healthy controls, suggesting that
brains afflicted by Alzheimer's disease show less chaotic
behaviors than those of normal healthy brains.
Pathophysiological implications of the
decreased EEG complexity in AD
• A decrease in dynamic complexity of the EEG in AD patients might
arise from neuronal death, deficiency of neurotransmitters like
acetylcholine, and/or loss of connectivity of local neuronal
networks.
• The reduction of the dimensionality in AD is possibly an expression
of the inactivation of previously active networks. Also, a loss of
dynamical brain responsivity to stimuli might be responsible for the
decrease in the EEG complexity of AD patients.
• AD patients do not have D2 differences between in eyes-open and
eyes-close conditions, whereas normal subjects have prominently
increased eyes-open D2 values compared with eyes-closed D2
values, suggesting a loss of dynamical brain responsivity to external
stimuli in AD patients.
Nonlinear measures
as a diagnostic indicator of AD
• Pritchard et al (1994) assessed the classification accuracy of the
EEG using nonlinear measures and a neural-net classification
procedure in addition to linear methods.
• The combination of linear and nonlinear analyses improves the
classification accuracy of the AD/control status of subjects up to
92%.
• Besthorn et al. (1997) reported that the D2 correctly classified AD
and normal subjects with an accuracy of 70%.
• Good correlations are found between nonlinear measures and the
severity of the disease, a slowing of EEG rhythms, and
neuropsychological performance.
• Furthermore, the global entropy can quantify EEG changes induced
by drugs, suggesting a possibility that nonlinear measures is
capable of quantifying the effect of drugs on the course of the
disease.
Nonlinear dynamical analysis of the EEG in patients
with Alzheimer's disease and vascular dementia.
Jeong et al., J Clin Neurophysiol (2001)
VaD patients have relatively increased values of nonlinear measures
compared with AD patients, and have an uneven distribution of D2
values over the regions than AD patients and healthy subjects.
Controversial on EEG complexity
in Schizophrenia
• The majority of these studies focused upon the question whether
schizophrenia is characterized by a loss of dynamical complexity
or rather by an abnormal increase of complexity, reflecting a
‘loosening of neural networks’.
• Many and especially more recent studies have found a lower
complexity in terms of a lower correlation dimension or lower
Lyapunov exponent (Jeong et al., 1998, Kim et al., 2000, Kotini
and Anninos, 2002, Lee et al., 2001 and Rockstroh et al., 1997).
• However, increases in dimension and Lyapunov exponent have
also been reported in the older studies (Elbert et al., 1992,
Koukkou et al., 1993 and Saito et al., 1998).
Decreased complexity of cortical dynamics
in Schizophrenic patients
• Jaeseung Jeong, Dai-Jin Kim, Jeong-Ho Chae, Soo Yong Kim,
et al. Nonlinear analysis of the EEG of Schizophrenics with
optimal embedding dimension. Medical Engineering and
Physics (1998).
• Dai-Jin Kim, Jaeseung Jeong, Jeong-Ho Chae, et al. The
estimation of the first positive Lyapunov exponent of the EEG
in patients with Schizophrenia. Psychiatry Research (2000).
• Jeong-Ho Chae, Jaeseung Jeong, Dai-Jin Kim, et al. The effect
of antipsychotic medications on nonlinear dynamics of the
EEG in schizophrenic patients. Clinical Neurophysiology
(2003)
• Jaeseung Jeong, Dai-Jin Kim, Soo Yong Kim, Jeong-Ho Chae, et
al. Effect of total sleep deprivation on the dimensional complexity
of the waking EEG. Sleep (2001)
• Jeong-Ho Chae, Jaeseung Jeong, Bradley S. Peterson, Dai-Jin Kim,
Seung-Hyun Jin, et al. Dimensional complexity of the EEG in
patients with Posttraumatic stress disorder. Psychiatry Research:
neuroimaging (2003)
• Dai-jin Kim, Jaeseung Jeong, Kook Jin Ahn, Kwang-Soo Kim,
Jeong-Ho Chae, et al. Complexity change in the EEG in alcohol
dependents during alcohol cue exposure. Alcoholism: Clinical &
Experimental Research (2003)
• Dai-Jin Kim, Won Kim, Su-Jung Yoon, Yong-Ku Kim, Jaeseung
Jeong, Effects of alcohol hangover on cytokine production in
healthy subjects. Alcohol (2003)
Nonlinear dynamics of the EEG
during photic and auditory stimulation
• Jaeseung Jeong, Moo Kwang Joung and Soo Yong Kim.
Quantification of emotion by nonlinear analysis of the chaotic
dynamics of EEGs during perception of 1/f music. Biological
Cybernetics (1998)
• Seung Hyun Jin, Jaeseung Jeong, Dong-Gyu Jeong, Dai-Jin Kim
et al. Nonlinear dynamics of the EEG separated by Independent
Component Analysis after sound and light stimulation. Biological
Cybernetics (2002)
• Jaeseung Jeong, Sangbaek Han, Bradley S. Peterson, and Soo
Yong Kim, "The effect of photic and auditory stimulation on
nonlinear dynamics of the human electroencephalogram," Clinical
Neurophysiology (in press)
Information flow during Tic suppression
of Tourette’s syndrome patients
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T4
Resting EEG: normal vs. TS
T3
T4
TS: Normal vs. Tic suppression
The effect of alcohol on the EEG complexity
measured by Approximate entropy
Perspectives
• For the last thirty years, progress in the field of nonlinear
dynamics has increased our understanding of complex systems dy
namics.
• This framework can become a valuable tool in scientific fields
such as neuroscience and psychiatry where objects possess natural
time dependency (i.e. dynamical properties) and non-linear
characteristics.
• Relative estimates of nonlinear measures can reliably characterize
different states of normal and pathologic brain function.
• Nonlinear dynamical analysis provides valuable information for
developing mathematical models of the systems.
Multimodal approach for psychiatric disorders
• For example, the combination of EEG and PET variables results in
approximately 90% of overall correct classification with a
specificity of 100% (Jelic et al., 1999).
• EEG and MRI measurements of the hippocampus obtain the
highest scores of abnormalities in patients with probable AD
( Jonkman, 1997).
• Furthermore, CT- and MRI-based measurements of hippocampal
atrophy provide a useful early marker of AD ( Scheltens, 1999).
• These neuroimaging techniques can offer not only supplementary
information for diagnosis of AD, but also an opportunity to
explore structural, functional, and biochemical changes in the
brain leading to new insights into the pathogenesis of AD.
Coronal MRI slices perpendicular to the long axis of the hippocampus
showing a smaller hippocampus in an MCI patient.
Coronal MRI at the level of the hippocampi showing no significant
atrophy, but FDG-PET SPM indicates posterior cingulate
hypometabolism
(Nestor et al., 2004)
Decreased EEG synchronization in MCI
Koenig et al. (2005)
Stam et al. (2003)
Brain Dynamics
• Experiments:
– Microscopic (multi electrode)
– Macroscopic (EEG or MEG)
• Mathematical modeling:
– From spiking neuron to large scaled networks
• Comparison with experiments
• Modification of model
• System behavior: senses, learning and memory, motor behavior
Dynamics
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• Theory driven:
– first principles
• Reductionism:
– simplify the world
• Qualitative understanding:
– mathematics
Neurobiology
• Empirical and descriptive:
– phenomena
• Systems level:
– details of the system
• Quantitative understanding:
– measurements
• Paradigm Shift
– Complex: real systems
– Synthesis: whole-istic
– System biology using mathematical models
– Universality among the diversity: biology