Lag Synchronisation in the Human Brain: Evidence from 17,722 Healthy Subjects EEG Analyses

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1 40 Lag Synchronisation in the Human Brain: Evidence from 17,722 Healthy Subjects EEG Analyses Oldrich Vysata*, Jaromir Kukal, Martin Valis, Ladislav Pazdera, Jakub Hort ll, Ales Prochazka** ABSTRACT The lag synchronisation of two different chaotic oscillators is a phenomenon that occurs when the signal from a lower frequency system is delayed with respect to a higher frequency system. The interaction among the multiple brain oscillators might produce lag synchronisation. In addition, phase differences between EEG channels might also reflect this time delay phenomenon. It has been suggested that the lag-synchronisation of chaotic oscillators depends on the direction of the delay differences between characteristic frequencies. The purpose of this study was to determine whether the direction of the phase difference between two electroencephalography (EEG) channels depends on the source of the characteristic frequency. The dependence of the phase shift on the mean frequency between two channels were examined in a group of 17,722 healthy truck drivers. The mean phase difference between two EEG channels was estimated using the Hilbert transform and compared with the difference in the characteristic frequency. The number of EEG segments with a phase delay from the electrode with a lower frequency to the electrode with a higher frequency was significantly higher than that moving in the opposite direction. The most significant direction of the phase delay was occipito-frontal. These results support the hypothesis that lag synchronisation occurs in the human brain as a result of phase differences that lead to time delays in the transfer of information from one part of the brain to another. However, this mechanism does not explain the dependence of phase differences on the frequencies between the electrodes. This work provides an alternative explanation for the phase shift between oscillations in different parts of the brain by the theory of nonlinear dynamical systems. Key Words: at least five keywords, separated by comma DOI Number: /nq NeuroQuantology 2014; 1: Introduction 1 The human electroencephalogram might represent the most complex set of signals in nature. Each scalp electrode detects the electrical activity of approximately 10 billion cortical neurons that are organised in columns. A common approach for the interpretation and spatial analysis is to assume that the cortex is composed of a mosaic of quasi-autonomous areas. Each area transmits a signal to one or Corresponding author: Vysata Oldrich Address: Please see end of article. Phone: , Fax: vysatao@gmail.com Received: Sept 15, 2013; Revised: Feb 5, 2014; Accepted: Feb 9, 2014 more other areas in a network, and this signal might appear in the scalp electroencephalography (EEG), where it spatially and temporally overlaps with other signals through volume conduction. The synchronisation of cerebral activity is an important physiological mechanism for the functional integration of different brain regions. The synchronisation of the EEG can be quantified in a linear fashion, such as coherence, wavelet coherence or non-linear mutual information ('mutual information'), phase synchronisation and generalised synchronisation. Coherence is a major problem that affects common reference and solid leadership, and several approaches have been proposed to manage these effects. One

2 approach involves the reconstruction of a suitable source space (Lehmann et al., 2006). Nolte and co-workers (2004) argued that the imaginary part of coherence is a measure of correlation between signals, which cannot be influenced through a common source. Stam and colleagues (2007) proposed a new measure of synchronisation, called phase lag index, based on the assumption that the volume conduction from one source or the strong influence of active reference cannot explain the phase shift between the two signals. Indeed, Hilbert transform is used to calculate the instantaneous phase and estimate the phase shift between the two EEG signals, and index asymmetry phase differences are determined from the time series of phase differences using the 'signum function'. Phase relationships are regarded as variable that determine spatiotemporal ordering between cortical components. The relative phase has been demonstrated to change abruptly at state transitions. György Buzsáki (2006) provided support for the idea that EEG activity results from multiple weakly connected networks of chaotic oscillators in metastable states. Interactions among neural network oscillators might produce non-linear phenomena, such as lag synchronisation (Chen et al., 2007). Lag synchronisation might occur between mutually connected chaotic oscillators with different characteristic frequencies (Taherion et al., 1999). In this phenomenon, the signal from a lower frequency system is delayed with respect to that from a higher frequency system (Rosenblum et al., 1996; Rosenblum et al., 1997). Lag synchronisation is a special case of generalised synchronisation. Lag-synchronised systems in uncoupled states are structurally different, with different characteristic frequencies; therefore, the frequencies of these systems are adjusted before phase synchronisation, and continue, with increased coupling, to a lag-synchronised state, i.e., these frequencies evolve through the same sequence of states but experience some time lag. Thus, the frequencies of lag-synchronised systems should be identical, and their instantaneous phase differences should be constant (or fluctuating but bounded). Another approach to managing coherence involves calculating the rational ratio (n:m) of the frequencies of these systems. As the most commonly used measure of synchronisation, coherence is not sensitive to generalised synchronisation (Stam et al., 2007). The purpose of this study was to determine whether the direction of the phase difference between two EEG channels depends on the source characteristic frequency. Because imaginary and phase coherence are more affected through displacement direction and the electrically active reference electrode than the estimated instantaneous phase Hilbert transform (Stam et al., 2007; Sweeney-Reed and Nasuto, 2007), we used this method. 2. Methods 2.1 Subjects In this retrospective population study, EEG data were obtained during the examination of 31,009 healthy truck drivers using 32 EEG machines. This large sample population reflects a new law concerning preventive neuropsychological and EEG exams for all professional drivers of vehicles over 3.5 T in the Czech Republic. The subjects were also subjected to neurological examinations. Individuals with potential brain damage were excluded (897 subjects). The exclusion criteria included alcoholism, drug abuse, and abnormal neurological and neuropsychological examinations. Another 12,390 EEG recordings were excluded due to high noise levels that could not be filtered or corrected. The remaining 17,722 subjects included 17,540 males and 182 females with a mean age of 43.2 years (SD=11.2). 2.2 EEG measurement All recordings were performed under similar conditions. The subjects were asked to be comfortable, and lie on the bed with closed eyes. Sleep was not permitted. The electrodes were placed according to the system of electrode placement, and the recordings were conducted using a 21-channel digital EEG machine (Alien), with a 22-bit AD conversion and a sampling frequency of 128 Hz. The filter settings were Hz. The frequencies were recorded for 15 minutes before artefact removal. 2.3 EEG preprocessing Linked ears were used as a physical reference. For the analysis the potential difference between each electrode and physical reference was used. Stored digitalised data (128 Hz) were zero-phase digitally filtered through a Hz bandpass FIR filter (100 coefficients, Hamming window) and a Hz bandstop filter. The analysis was referenced to united ear 41

3 electrodes, as this methodology is not sensitive to the influence of reference electrodes with non-zero activity (Stam et al., 2007). The analysis was initiated through automatic artefact recognition and removal. Automatic artefact recognition, based on a regularised LD classifier, was used to remove 91% artefacts, and blinking and extraocular and muscle movements and electrode artefacts were automatically removed. Subsequently, an offline manual artefact expert removed preprocessed data, including less frequent and less automatically identifiable artefacts, such as EKG and stepping artefacts. Moreover, all the other artefacts, such as frequencies with short duration and low amplitude, which escaped automatic detection, were corrected. For each entry, a 4-second waking EEG was selected for further processing. 2.4 Statistics Phase shift and mean characteristic frequency for each channel and segment were evaluated. The phase shift was estimated by Hilbert transform (Oppenheim and Schafer, 1998; Yi- Wen Liu, 2012) of 2-seconds EEG segments (256 samples). Differences in the average instant phase between two channels were compared with the differences in their characteristic frequencies. Characteristic frequency of the EEG curve was estimated through return or Poincaré maps: T R = N T i=1 i N where T1, T2,..., T N are distances between N consecutive maxima, i.e., return times. The desired frequency was = 2 / TR. Every electrode pair was characterized in k -th segment by fk, k. The electrode pair relationship was examined using statistical sample of size m comprising fk, k for all segments from all patients. All electrode pairs (171) were investigated. Let q represent probability that the frequency shift f has the same sign as phase shift, i.e., q = prob( f > 0). Under the assumption of independence, we tested the hypothesis H : = 0 0 q, using a standard two-tailed sign test at p=0.01. The number of segments with a phase lag from a slower to a faster channel was compared with the number of segments with a reverse order using a two-tailed sign test for all channels pairs. According to the zero hypothesis, the number of those pairs should be the same. The direction of lag synchronisation between two channels might be different in the different segments (directional prevalence). According to the zero hypothesis, the number of segments with opposite directions should be the same. The number of segments with lag synchronisation in one direction was compared with the number of segments in the opposite direction using a two-tailed sign test. In both cases, Bonferroni correction was performed for all 171 pairs of channels. 2.5 Coherence Coherence function (Sanei, 2013) has been used to find similarities between individual EEG channels. Denoting signal segments of separate channels by { x( i )} N i=1 and { y( i )} N i=1 with their length N it is possible to evaluate coherence function by relation C xy 2 Pxy( f ) ( f ) = P ( f ) P ( f ) xx yy 42 (1) Where P xx(ƒ) and P yy(ƒ) stand for the power spectral density of individual signals and P xy(ƒ) represents their cross spectral density. Each pair of channels has been processed by this function and the average frequency content in the given frequency range evaluated to find channels with the highest correspondence. 3. Results In the 17,722 normal low-artefact EEG recordings, 3,052,86 two-second electrode pairs were observed among all electrodes with coherence >0.3. Among these pairs, 1,360,738 segments showed positive phase-shift, and the remaining segment showed negative phase-shift from channels with higher to lower average frequencies (p<10 20 ). Therefore, we can reject the null hypothesis. These findings are consistent with the lag synchronisation hypothesis (Stam et al., 2007). The highest probability of lag synchronisation occurred between the frontal and parieto-occipital regions (Table-1, Figure-1). While lag synchronisation might change directions between EEG channels, the prevailing direction was followed. The highest probability of the coincident direction of lag synchronisation showed a similar distribution as lag synchronisation, with a uniform occipitofrontal direction (Table-2, Figure 2-3).

43 Figure 1. Electrode pairs with lag synchronisation probabilities greater than 0.70. This parameter corresponds to the phase lag index >0.7 (Stam et al., 2007). Figure-3.

4 43 Figure 1. Electrode pairs with lag synchronisation probabilities greater than This parameter corresponds to the phase lag index >0.7 (Stam et al., 2007). Figure-3. Electrode pairs with directional prevalence of lag synchronisation greater than Table 1. Electrode pairs with lag synchronization probability greater then 0.7. Electrode pair Lag synchronization probability P3-Fp Pz-Fp P4-Fp O1-Fp O2-Fp P3-Fp Pz-Fp P4-Fp O1-Fp O2-Fp Figure-2. Electrode pairs with directional prevalence of lag synchronisation greater than The lower-frequency EEG signal has a phase delay with respect to the higher-frequency signal. Table 2. Electrode pairs with directional prevalence of lag synchronization greater then Electrode pair Directional prevalence Characteristic frequency Phase angle (in radians) P3-Fp Pz-Fp P4-Fp O1-Fp O2-Fp P3-Fp Pz-Fp P4-Fp O1-Fp O2-Fp P3-F Pz-F P4-F O1-F O2-F P3-F Pz-F P4-F O1-F O2-F

5 4. Discussion The average phase and frequency differences in EEG segments were studied. The results suggested that the positive phase shifts correlate with the differences in the characteristic frequencies. Although, in theory, lag-synchronised oscillators have the same characteristic frequencies, some segments might undergo synchronisation (Baier et al., 2000). These segments might involve nonsynchronised signals with different frequencies. Our findings support the hypothesis concerning the occurrence of lag synchronisation in the brain. The existence of non-zero-lag phase synchronisation was observed in neurons (Roelfsema et al., 1997) and intracranial recordings (Tallon-Boundry et al., 2001). Nonlinear interactions between chaotic oscillators in the brain might explain phase delays between EEG channels. Rosenblum (Rosenblum et al., 1996; 1997) described the lag synchronisation of chaotic oscillators with close frequencies. Even different frequency oscillations, such as alpha and beta, can be lag-synchronised, assuming these frequencies are in a rational ratio. The aim of this study was to determine the dependence of the directions of lag synchronisation on the differences between the characteristic frequencies of the two EEG signals. Traffic delays in the transfer of information between different parts of the brain with typical frequencies might be a random coincidence. However, we observed a statistically significant relationship between lag synchronisation and differences in the frequency characteristics when the lag phase of the characteristic frequency was slower due to the faster characteristic frequencies. This idea is better explained through the phase-lag synchronisation of different chaotic oscillators. The most significant lag synchronisation was observed in the longitudinal direction, as fronto-occipital brain pathways connect regions with different characteristic frequencies, while in the transversal direction corresponding areas are connected in both hemispheres with similar characteristic frequencies. The prevailing direction of lag-synchronisation (phase lag from a lower to a higher characteristic frequency) occurred from the occipital region (with a slower alpha rhythm) to the frontal region (with faster beta rhythm). The existence of this type of synchronisation in EEG is theoretically interesting. Thatcher et al. (2005) observed a significant relationship phase-lag synchronisation in frontal EEG channels for intelligence. Stam et al. (2007) observed a significant reduction in the 'phase lag index' in patients with Alzheimer's disease. While the synchronisation of EEG signals with zero phase delay is primarily attributed to the influence of volume conduction and active reference, phaselag synchronisation reflects the "true" synchronisation between locations. About Authors *Vysata Oldrich, Charles University, Faculty of Medicine in Hradec Kralove, Dept. of Neurology, Sokolska 581, Hradec Kralove. Jaromir Kukal, Department of Computing and Control Engineering, Institute of Chemical Technology, Prague. Martin Valis, Charles University, Faculty of Medicine in Hradec Kralove, Dept. of Neurology, Sokolska 581, Hradec Kralove. Ladislav Pazdera, Neurocenter caregroup, Rychnov nad Kneznou. ll Jakub Hort, Memory Disorders Clinic, Department of Neurology, Charles University in Prague, 2nd Faculty of Medicine and University Hospital Motol, Prague, International Clinical Research Centre, St. Annes University Hospital, Brno, Brno. **Ales Prochazka, Department of Computing and Control Engineering, Institute of Chem-ical Technology, Prague. 44

6 References Baier G, Leder R, Parmananda P. Human electroencephalogram induces transient coherence in excitable spatiotemporal chaos. Phys Rev Lett 2000; 84:4501. Buzsáki G. Rhythms of the Brain, New York: Oxford University Press, Chen Y, Chen XX, Gu SS. Lag synchronization of structurally nonequivalent chaotic systems with time delays. Nonlinear Anal 2007; 66: Lehmann D, Faber PL, Gianotti LRR, Kochi K, Pascual- Marqui RD. Coherence and phase locking in the scalp EEG and between LORETA model sources, and microstates as putative mechanisms of brain temporospatial functional organization. J Physiol 2006; 99: Nolte G, Wheaton OBL, Mari Z, Vorbach S, Hallett M. Identifying true brain interaction from EEG data using the imaginary part of coherency. Clin Neurophysiol 2004; 115: Oppenheim AV, and Schafer RW. Discrete-Time Signal Processing, 2nd ed., Prentice-Hall, Roelfsema PR, Engel AK, Konig P, Singer W. Visuomotor integration is associated with zero time-lag synchronization among cortical areas. Nature 1997; 385: Rosenblum MG, Pikovsky AS, Kurths J. From Phase to Lag Synchronization in Coupled Chaotic Oscillators. Phys Rev Lett 1997; 78: Rosenblum MG, Pikovsky AS, Kurths J. Phase synchronization of chaotic oscillators. Phys Rev Lett 1996; 76: Sanei S, Adaptive Processing of Brain Signals. John Wiley & Sons, Stam CJ, Nolte G, Daffertshofer A. Phase Lag Index: Assessment of Functional Connectivity From Multi Channel EEG and MEG With Diminished Bias From Common Sources. Hum Brain Mapp 2007; 28: Stam CJ, van Cappellen van Walsum AM, Pijnenburg Yolande AL, Berendse HW, de Munck JC, Scheltens P. Generalized Synchronization of MEG Recordings in Alzheimer's Disease: Evidence for Involvement of the Gamma Band. J Clin Neurophysiol 2002;19: Sweeney-Reed CM and Nasuto SJ. A novel approach to the detection of synchronisation in EEG based on empirical mode decomposition. J Comput Neurosci 2007; 23: Taherion S, Lai YC. Observability of lag synchronization of coupled chaotic oscillators. Phys Rev E 1999; 59: Tallon-Baudry C, Betrand O, Fischer C. Oscillatory synchrony between human extrastriate areas during visual shortterm memory maintenance. J Neurosci 2001; 21:1-5. Yi-Wen Liu. Hilbert Transform and Applications, Fourier Transform Applications, Dr Salih Salih (Ed.),

Effects of Light Stimulus Frequency on Phase Characteristics of Brain Waves

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