1. Introduction: Brain Dynamics Jaeseung Jeong, Ph.D Department of Bio and Brain Engineering, KAIST

2. Complex spatiotemporal dynamics in the Brain

4. Several sources of complexity in EEG

5. EEG recordings

6. Complex rhythms and oscillations in the brain

7. Chaos in the Brain

8. Stam, 2005

9. Phase space and attractor

11. Nonlinear dynamical analysis attractor Jeong, 2002

12. How to quantify dynamical states of physiological systems Physiological system States Physiological Time series Embedding procedure (delay coordinates) 1-dimensional time series  multi-dimensional dynamical systems Attractor in phase space Dynamical measures (L1, D2) A deterministic (chaotic) system Topologically equivalent

13. C(r)  r D2 D2 algorithm Nonlinear measure: correlation dimension (D2)

14. Correlation integral attractor Scaling region

15. Nonlinear measures: The first positive Lyapunov exponent

16. Surrogate data method This method detects nonlinear determinism. Surrogate data are linear stochastic time series that have the same power spectra as the raw time series. They are randomized to destroy any deterministic nonlinear structure that may be present. Statistical differences of nonlinear measures between the raw data and their surrogate data imply the presence of nonlinear determinism in the original data.

17. Bursting as an information carrier of temporal spiking patterns of nigral dopamine neurons (a) Dopamine neurons in substantia nigra Substantia nigra, a region of the basal ganglia that is rich in dopamine-containing neurons, is thought to be etiologies of Parkinson’s disease, Schizophrenia, Tourette's syndrome etc.

18. Electrophysiology of DA neurons in substantia nigra Irregular and complex single spiking and bursting states in vivo The presence of nonlinear deterministic structure in ISI firing patterns (Hoffman et al. Biophysical J, 1995) Deterministic structure of ISI data produced by nigral DA neurons reflects interactions with forebrain structures (Hoffman et al. Synapse 2000)

19. Surrogate data method for neuronal activity Histogram D2s of ISI data of DA neurons D2s of surrogate ISI data Embedding dim. vs. D2

20. Nonlinear determinism of bursting DA neurons D2s of ISI data of DA neuronsD2s of ISI surrogate data HistogramEmbedding dim. vs. D2

21. Why is brain dynamics important?

22. 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)

23. [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] Dynamics of the Brain suggests that EEGs reflecting thoughts and emotion are able to be utilized in the brain-computer interface (BCI). Why is brain dynamics important?

24. The origin of brain complex dynamics: 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.