Nonlinear dynamical analysis of the EEG in Psychiatric disorders

1. Nonlinear dynamical analysis of the EEG in Psychiatric disorders Jaeseung Jeong, Ph.D Department of Bio and Brain Engineering KAIST, Daejeon, South Korea

2. Why are brain oscillations so complex?

3. 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.

4. Complexity during different sleep stages

5. Approximate Entropy in AD/HD patients

6. 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)

7. 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.

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

9. 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.

10. 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).

11. 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.

12. 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.

13. 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.

14. 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).

15. 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.

16. 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.

17. (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.

21. EEG recordings

22. Several sources of complexity in EEG

23. 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.

24. Several limitations on Nonlinear Dynamical Aanalysis 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 low-dimensional attractor (Osborne and Provenzale, 1989).

25. 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.

26. 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)

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

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

29. [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?

30. 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.

31. 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.

32. 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.

34. 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.

35. 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)

36. 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.

37. 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.

38. 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).

39. Nonlinear coupling among cortical areas

40. 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 time-varying 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)

41. 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

42. 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.

43. 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).

44. 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).

45. 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) Epilepsy as a dynamical disorder

46. 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)

47. 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).

48. 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).

49. 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.

50. 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).