Nonlinear dynamical analysis of the EEG in Psychiatric disorders

Jaeseung Jeong, Ph.D

Department of Bio and Brain EngineeringKAIST,

Daejeon, South Korea

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

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).

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?• 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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• 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

average D2 values

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Detecting determinism in independent components of the EEG using ICA

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[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?

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.

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.

J Jeong, JC Gore, BS Peterson. Mutual information analysis of the EEG in patients with Alzheimer's disease. Clin Neurophysiol (2001)

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.

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

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) 

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

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).

• 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

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).

• 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).

Controversial about seizure prediction I

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.

• 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).

Controversial about seizure prediction I

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

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.

EEG characteristics of seizures

• 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.

Controversial about seizure prediction II

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., 1997).

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.

EEG time series recorded from a patient with AD

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EEG dynamics in patients with Alzheimer’s disease

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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Resting EEG: normal vs. TS 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 dynamics.

• 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 at the level of the hippocampi showing no significant atrophy, but FDG-PET SPM indicates posterior cingulate hypometabolism

Coronal MRI slices perpendicular to the long axis of the hippocampus showing a smaller hippocampus in an MCI patient.

(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 Neurobiology

• 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