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What is Brain dynamics?
Jaeseung Jeong, Ph.D
Department of Bio and Brain Engineering,
Program of Brain and Cognitive Engineering,
KAIST
Brain oscillations
• The brain is constantly active, even during deep sleep. In the cerebral
cortex, this spontaneous activity (activity that is not obviously driven
by a sensory input or a motor command) often occurs as periodic, or
irregular, rhythmic discharges.
Electroencephalography (EEG) or brain waves
• Neuronal oscillations allow for temporal segmentation of neuronal spikes.
• Interdependent oscillators can integrate multiple layers of information.
• Neuronal oscillations are a natural mechanism for forming cell assemblies
since most brain oscillations are inhibition based, and inhibition can
segregate spike train messages.
• The cerebral cortex generates multitudes of oscillations at different
frequencies, but how the various rhythms interact with each other is not well
understood.
Neuronal Oscillations
• infra-slow: 0.02-0.1 Hz,
• slow: 0.1-15 Hz (during slow-wave sleep or anesthesia)
– Slow oscillation (0.2-1 Hz),
– Delta (1-4 Hz),
– Spindle (7-15Hz),
– Theta (generated in the limbic system)
• fast: 20-60 Hz,
• ultra-fast: 100-600 Hz.
Brain oscillations consist of slow oscillation,
fast oscillation, and its interactions.
EEG waves with specific frequency bands
are associated with brain functions.
The origin of oscillations
• Oscillatory activity is an emerging property of the brain network,
especially the thalamocortical system.
The various oscillatory rhythms generated in the thalamocortical
system are mediated by two types of mechanisms:
• Extrinsic or network mechanisms, which require the interaction of
excitatory and inhibitory neurons within a population. (e.g., spindles
depend on the interaction between thalamic relay and reticular
neurons as well as on their intrinsic properties).
• Intrinsic mechanisms, which depend on the interplay between
specific intrinsic currents. (e.g., thalamic delta oscillations from
thalamic relay cells, cortical slow oscillation depending on network
properties)
Infra-slow oscillation
• This type of oscillatory activity has a period within the range of tens
of seconds to a minute.
• Very little is known about the underlying mechanisms of these
oscillations but at least some of the factors responsible for their
generation could depend on non-neuronal dynamics. Infra-slow
activities likely have a cortical origin given that they can be
recorded from small regions of neocortex devoid of their inputs by
means of a surgical undercut.
• What is the functional role?
Indirect evidence suggests that infra-slow oscillations synchronize
faster activities, modulate cortical excitability.
Slow Oscillations
• The slow oscillation is characterized by periods of sustained
depolarization interweaved with periods of hyperpolarization and
silence at a rate of between once every 10 seconds to approximately
once per every 2 seconds (0.1 – 0.5 Hz or higher).
• The depolarized state is associated with low frequency neuronal
firing and is termed the UP state, while the hyperpolarized state is
referred to as the DOWN state.
• The frequent transitions between the UP and DOWN state can make
the membrane potential of the cortical neuron appear as a single
channel recording, even though the slow oscillation is generated by
the interaction of thousands of cells!
• Slow oscillation in vivo from cortex and its disruption by stimulation
of the brainstem.
• The top trace is an intracellular recording from a cortical pyramidal
cell during the slow oscillation.
• The bottom trace is the electrocorticogram (EcoG). Repetitive
stimulation of the brainstem results in activation of the EEG and
suppresses the "down" state of the slow oscillation.
Slow oscillations
• During slow-wave sleep and some types of anesthesia the dominant
activity pattern is slow oscillation, with frequency 0.3 - 1 Hz.
• The following observations point to an intracortical origin for this
rhythm:
a. It survives extensive thalamic lesions in vivo and exists in
cortical in vitro preparations.
b. It is absent in the thalamus of decorticated cats.
• The slow oscillation is generated in the cerebral cortex, since
removal of the thalamus does not block the slow oscillation and
isolation of slabs of cortex retain this activity.
• McCormick et al. demonstrated the slow oscillation in cortical slices
maintained in vitro.
UP and DOWN states
• During slow oscillation the entire cortical network alternates
between silent (Hyperpolarizing, or Down) and active
(Depolarizing, or Up) states, each lasting 0.2-1 sec.
• At EEG level, the slow oscillation appears as periodic alterations of
positive and negative waves (indicated by + and – signs in the
figure).
• During EEG depth-positivity, cortical neurons remain in
hyperpolarized, silent state.
• During EEG depth-negativity cortical neurons move to active states,
reveal barrages of synaptic events and fire action potentials.
Delta oscillations
• Field potential recordings from neocortex in human and animal
models during sleep reveal the presence of delta oscillations (1-4
Hz). The delta oscillation likely has two different components, one
of which originates in the neocortex and the other in the thalamus.
• Cortical delta activity. Both surgical removal of the thalamus and
recordings from neocortical slabs in chronic conditions result in the
significant enhancement of neocortical delta activity. One of the
hypotheses suggests that cortical delta could be driven by the
discharge of intrinsically bursting neurons.
• Thalamic delta (1-4 Hz) is a well known example of rhythmic
activity generated intrinsically by thalamic relay neurons as a result
of the interplay between their low-threshold Ca2+ current (IT) and
hyperpolarization activated cation current (Ih). As such, the delta
oscillation may be observed during deep sleep when thalamic relay
neurons are hyperpolarized sufficiently to deinactivate IT.
Properties of delta waves
• The amplitude of such activity increases and decreases without
changes in frequency.
• Synchrony between different thalamic relay neurons during delta
activity has not been found in decorticated cats. Thus, it is unlikely
that thalamic delta activity could play a leading role in the initiation
and maintenance of cortical delta rhythm. However, the presence of
a corticothalamic feedback in intact-cortex animals could
synchronize thalamic burst-firing at delta frequency and generate
field potentials.
Functional role of slow and delta oscillations
• Slow wave sleep may be essential for memory consolidation and
memory formation. It has been proposed that synaptic plasticity
associated with slow and delta oscillations could contribute to the
consolidation of memory traces acquired during wakefulness.
• Based on the analysis of multiple extracellular recordings of slow
oscillations during natural sleep, it was suggested that fast
oscillations during active states of slow-wave sleeps could reflect
‘recalled events experienced previously’; these events are
"imprinted" in the network via synchronized network events that
appear as slow-wave complexes in the EEG.
Beta oscillations
• Beta oscillation is the oscillation with frequency range above 12 Hz.
• Low amplitude beta with multiple and varying frequencies is often
associated with active, busy or anxious thinking and active
concentration.
• Rhythmic beta with a dominant set of frequencies is associated with
various pathologies and drug effects, especially benzodiazepines,
enhancing the effect of the neurotransmitter gamma-aminobutyric
acid (GABA) at the GABAA receptor.
Gamma oscillations
• Gamma oscillation is the rhythmic activity with the frequency
range approximately 26–100 Hz.
• Gamma rhythms may be involved in higher mental activity,
including perception, problem solving, fear, and consciousness.
The patterns and the dominant frequencies of thalamo-cortical
oscillations depend on the functional state of the brain
• The fast and ultra-fast activities may be present in various states
of vigilance and frequently coexist with slower rhythms (e.g., fast
gamma oscillations may be found during depolarized phases of
slow sleep oscillations).
• Spontaneous brain rhythms during different states of vigilance may
lead to increased responsiveness and plastic changes in the strength
of connections among neurons, thus affecting information flow in
the thalamocortical system.
Fast oscillations
• Fast oscillations could be divided on fast (beta and gamma) and
ultra-fast (>100 Hz, ripples).
• Fast oscillations have been implicated in cognitive processes. They
also occur in association with seizures.
• Ultrafast oscillations could be found during sharp waves and sleep.
The ripples are prominent in the onset of seizures.
Two major categories of fast oscillations
• (Homogeneous) Those which occur in a homogeneous collection of
neurons, all of the same type, for example CA1 pyramidal neurons.
• (Heterogeneous) Those which require synaptic interactions between
two or more populations of neurons, for example CA1 pyramidal
neurons together with fast-spiking CA1 interneurons.
Functional role of fast oscillations for
perception and behavior
• Cognitive functions like perception, attention, memory or language
are based on highly parallel and distributed information processing
by the brain.
• One of the major unresolved questions is how information can be
integrated and how coherent representational states can be
established in the distributed neuronal systems subserving these
functions. It has been suggested that this so-called 'binding problem'
may be solved in the temporal domain.
• The hypothesis is that synchronization of neuronal discharges can
serve for the integration of distributed neurons into cell assemblies
and that this process may underlie the selection of perceptually and
behaviourally relevant information.
Functional role of fast oscillations for
perception and behavior
• Moreover, it has been suggested that fast oscillations at
frequencies in the so-called gamma range (> 30 Hz) may help to
entrain spatially separate neurons into synchrony and thus may
indirectly promote the dynamic binding of neuronal populations.
• In accordance with these predictions, states characterized by
synchronized gamma activity have been shown to be associated
with functions like processing of coherent stimuli, perceptual
discrimination, focused attention, short-term memory, or
sensorimotor integration.
• Typically, the observed magnitude of gamma activity is positively
correlated with increased 'processing load' and thus with the level
of vigilance and attention, as well as with the difficulty or
integrative nature of the processing.
Interactions between fast and slow rhythms
Phase-amplitude coupling
• A well-studied mechanism is cross-frequency coupling. As
described first in the hippocampus, the phase of theta
oscillations biases the amplitude of the gamma waves [phase–
amplitude (P–A) coupling or “nested” oscillations].
Theta-gamma oscillations
What is the role for theta-gamma coupling?
Delta-gamma coupling and risk-taking behaviors
Lee and Jeong (2012)
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
Complex systems: complex is not random!
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nonlinear units
various interactions betweens units
network effects – More is different!
the presence of rich phenomena
Chaos, Fractal, Small-world effect,
Synchronization, Bursts, Intermittency
Life at the edge of chaos, scale-free behavior.
Chaos
• Butterfly effect (an MIT meteorologist, Edwards Lorenz )
[1] One meteorologist remarked that if the theory were correct,
one flap of a seagull's wings would be enough to alter the course of
the weather forever.
[2] Predictability: Does the Flap of a Butterfly’s Wings in Brazil set
off a Tornado in Texas?
• Chaos : sensitive dependence on initial conditions due to
nonlinearity in systems
Fractal
As a non-fractal object is
magnified, no new features are
revealed.
As a fractal object is magnified,
ever finer features are revealed.
A fractal object has features
over a broad range of sizes.
Self-similarity
The magnified piece of an
object is an exact copy of
the whole object.
Synchronization
Several sources of complexity in EEG
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
(from 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.
Does brain have dynamics?
• 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.
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.
Computational Neuroscience and
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
Physics

• Theory driven:
– first principles
• Reductionism:
– simplify the world
• Qualitative understanding:
– mathematics
Biology
• 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