1. What is Brain dynamics? Jaeseung Jeong, Ph.D Department of Bio and Brain Engineering, Program of Brain and Cognitive Engineering, KAIST

3. 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.

4. Electroencephalography (EEG) or brain waves

6. 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.

7. 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.

8. Brain oscillations consist of slow oscillation, fast oscillation, and its interactions.

9. EEG waves with specific frequency bands are associated with brain functions.

10. 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)

11. 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.

12. 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!

13. 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.

14. 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.

15. 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.

16. 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.

17. 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.

18. 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.

19. 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.

20. 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.

21. 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.

22. 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.

23. 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.

24. 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.

26. 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.

28. 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.

30. Interactions between fast and slow rhythms

31. 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].

32. Theta-gamma oscillations

34. What is the role for theta-gamma coupling?

37. Delta-gamma coupling and risk-taking behaviors Lee and Jeong (2012)

39. Why are brain oscillations so complex?

40. 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.

41. Complexity during different sleep stages

42. Approximate Entropy in AD/HD patients

43. 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)

44. 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.

45. The effect of alcohol on the EEG complexity measured by Approximate entropy

46. 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. Complex systems: complex is not random!

47. 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

48. 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.

49. Synchronization

53. Several sources of complexity in EEG

54. 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.

55. 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).

56. 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.

57. 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.

58. 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.

59. 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).

61. 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.

62. 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.

66. 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.

67. Is EEG deterministic or stochastic? 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. 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)

68. Detecting determinism in independent components of the EEG using ICA

70. [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). Why is determinism important?

71. 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.

72. 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.

73. AD/HD: Attention-Deficit/Hyperactivity disorder 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. 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. Dynamical nonstationarity

75. 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

76. Physics  Biology Theory driven: –first principles Reductionism: –simplify the world Qualitative understanding: –mathematics 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