Phase Synchronization Index Research Articles

Interactive sonification of synchronisation of motoric behaviour in social active listening to music with mobile devices

This paper evaluates three different interactive sonifications of dyadic coordinated human rhythmic activity. An index of phase synchronisation of gestures was chosen as coordination metric. The sonifications are implemented as three prototype applications exploiting mobile devices: Sync’n’Moog, Sync’n’Move, and Sync’n’Mood. Sync’n’Moog sonifies the phase synchronisation index by acting directly on the audio signal and applying a nonlinear time-varying filtering technique. Sync’n’Move intervenes on the multi-track music content by making the single instruments emerge and hide. Sync’n’Mood manipulates the affective features of the music performance. The three sonifications were also tested against a condition without sonification.

Noninvasive Epileptic Seizure Localization from Stochastic Behavior of Short Duration Interictal High Density Scalp EEG Data

The stochastic behavior of the phase synchronization index (SI) in different EEG bands was examined for noninvasive localization of the epileptogenic areas from the short duration (30-60s), seizure-free and spike-free high density (256 channel) scalp EEG data. We also examined the cross-frequency and cross-electrode coupling in different EEG bands. EEG data of four subjects was used. The seizure areas were localized with subdural recordings with an 8×8 grid electrode array. It was found that the stochastic behavior of the SI in low gamma band (30-50Hz) was higher in epileptogenic areas. The beta (12-30Hz) band also showed similar tendencies. The stochastic behavior in theta (3-7Hz) band was depressed in the seizure area while it was widespread in large areas over the scalp in the alpha (7-12Hz) band. The stochastic behavior of the cross-frequency and cross-electrode couplings in theta-gamma, alpha-gamma and beta-gamma bands were decreased in the seizure areas for all four subjects. These findings suggest that it is possible to localize the epileptogenic areas from the short duration seizure-free and spike-free high density scalp EEG data.

SYNCHRONIZATION BEHAVIOR IN DISCRETE SYSTEMS

This work explores the synchronization behavior in discrete systems with both discrete time and discrete state. In order to describe the self-driven function of the node’s state, a state transfer matrix is introduced. Three typical network structures (random network, small-world network and scale-free network) are numerically studied in order to investigate the impact of network structure. Simulation results show that, according to the phase synchronization index, the coupling strength is divided into four regions: the increasing region, the maximum region, the decreasing region and the oscillation region. Moreover, the size of the oscillation region seems to be changeless, independent of the network structure and a parameter describing the number of total node’s states.

An improved index of phase-synchronization for electrophysiological data in the presence of volume-conduction, noise and sample-size bias

Phase-synchronization is a manifestation of interaction between neuronal groups measurable from LFP, EEG or MEG signals, however, volume conduction can cause the coherence and the phase locking value to spuriously increase. It has been shown that the imaginary component of the coherency (ImC) cannot be spuriously increased by volume-conduction of independent sources. Recently, it was proposed that the phase lag index (PLI), which estimates to what extent the phase leads and lags between signals from two sensors are nonequiprobable, improves on the ImC. Compared to ImC, PLI has the advantage of being less influenced by phase delays. However, sensitivity to volume-conduction and noise, and capacity to detect changes in phase-synchronization, is hindered by the discontinuity of the PLI, as small perturbations turn phase lags into leads and vice versa. To solve this problem, we introduce a related index, namely the weighted phase lag index (WPLI). Differently from PLI, in WPLI the contribution of the observed phase leads and lags is weighted by the magnitude of the imaginary component of the cross-spectrum. We demonstrate two advantages of the WPLI over the PLI, in terms of reduced sensitivity to additional, uncorrelated noise sources and increased statistical power to detect changes in phase-synchronization. Another factor that can affect phase-synchronization indices is sample-size bias. We show that, when directly estimated, both PLI and the magnitude of the ImC have typically positively biased estimators. To solve this problem, we develop an unbiased estimator of the squared PLI, and a debiased estimator of the squared WPLI.

Phase synchronisation of the three leg joints in quiet human stance

Quiet human stance is a dynamic multi-segment phenomenon. In literature, coupled ankle and hip actions are in the focus and examinations are usually restricted to frequency contributions below 4 Hz. Very few studies point to the knee playing an active role, and just one study gives evidence of higher frequency contributions. In order to investigate the dynamic coupling of all three leg joints in more depth, we revisited an experimental data set on quiet human stance. Since phase synchronisation is a strong indicator of non-linear coupling behind, we used the phase synchronisation index (PSI) to quantify the degree of leg joint coupling as a function of frequency. One main result is that we did not find any synchronisation between ankle and hip across the whole frequency range examined up to 8 Hz. In contrast, there is significant synchronisation between ankle and knee at a couple of frequencies between 1.25 Hz and 8 Hz when looking at the kinematics. Their joint torques rather synchronise below 2 Hz. There is also synchronisation between knee and hip kinematics above 6 Hz, however, only significant at one frequency bin in our data set. From this, we would infer that the multiple mechanical degrees of freedom contributing to quiet human stance should be chosen according to, thus map, physiology. Thereby, the knee is indispensable and bi-articular muscles play a central role in organising quiet human stance. Examining the non-stationarity of phase synchronisations will probably advance the understanding of self-organisation of quiet human stance.

Multivariate Empirical Mode Decomposition for Quantifying Multivariate Phase Synchronization

Quantifying the phase synchrony between signals is important in many different applications, including the study of the chaotic oscillators in physics and the modeling of the joint dynamics between channels of brain activity recorded by electroencephalogram (EEG). Current measures of phase synchrony rely on either the wavelet transform or the Hilbert transform of the signals and suffer from constraints such as the limit on time-frequency resolution in the wavelet analysis and the prefiltering requirement in Hilbert transform. Furthermore, the current phase synchrony measures are limited to quantifying bivariate relationships and do not reveal any information about multivariate synchronization patterns, which are important for understanding the underlying oscillatory networks. In this paper, we address these two issues by employing the recently introduced multivariate empirical mode decomposition (MEMD) for quantifying multivariate phase synchrony. First, an MEMD-based bivariate phase synchrony measure is defined for a more robust description of time-varying phase synchrony across frequencies. Second, the proposed bivariate phase synchronization index is used to quantify multivariate synchronization within a network of oscillators using measures of multiple correlation and complexity. Finally, the proposed measures are applied to both simulated networks of chaotic oscillators and real EEG data.

Respiration drives phase synchronization between blood pressure and RR interval following loss of cardiovagal baroreflex during vasovagal syncope

Loss of the cardiovagal baroreflex (CVB), thoracic hypovolemia, and hyperpnea contribute to the nonlinear time-dependent hemodynamic instability of vasovagal syncope. We used a nonlinear phase synchronization index (PhSI) to describe the extent of coupling between cardiorespiratory parameters, systolic blood pressure (SBP) or arterial pressure (AP), RR interval (RR), and ventilation, and a directional index (DI) measuring the direction of coupling. We also examined phase differences directly. We hypothesized that AP-RR interval PhSI would be normal during early upright tilt, indicating intact CVB, but would progressively decrease as faint approached and CVB failed. Continuous measurements of AP, RR interval, respiratory plethysomography, and end-tidal CO2 were recorded supine and during 70-degree head-up tilt in 15 control subjects and 15 fainters. Data were evaluated during five distinct times: baseline, early tilt, late tilt, faint, and recovery. During late tilt to faint, fainters exhibited a biphasic change in SBP-RR interval PhSI. Initially in fainters during late tilt, SBP-RR interval PhSI decreased (fainters, from 0.65±0.04 to 0.24±0.03 vs. control subjects, from 0.51±0.03 to 0.48±0.03; P<0.01) but then increased at the time of faint (fainters=0.80±0.03 vs. control subjects=0.42±0.04; P<0.001) coinciding with a change in phase difference from positive to negative. Starting in late tilt and continuing through faint, fainters exhibited increasing phase coupling between respiration and AP PhSI (fainters=0.54±0.06 vs. control subjects=0.27±0.03; P<0.001) and between respiration and RR interval (fainters=0.54±0.05 vs. control subjects=0.37±0.04; P<0.01). DI indicated respiratory driven AP (fainters=0.84±0.04 vs. control subjects=0.39±0.09; P<0.01) and RR interval (fainters=0.73±0.10 vs. control subjects=0.23±0.11; P<0.001) in fainters. The initial drop in the SBP-RR interval PhSI and directional change of phase difference at late tilt indicates loss of cardiovagal baroreflex. The subsequent increase in SBP-RR interval PhSI is due to a respiratory synchronization and drive on both AP and RR interval. Cardiovagal baroreflex is lost before syncope and supplanted by respiratory reflexes, producing hypotension and bradycardia.

Time-variant analysis of phase couplings and amplitude–frequency dependencies of and between frequency components of EEG burst patterns in full-term newborns

Objective Burst activity of the ‘trace alternant’ ( TA) EEG pattern in the quiet sleep of full-term newborns is investigated to explore the timing and the time-variant coupling characteristics of and between a burst’s oscillatory components. The working hypothesis is that signal properties provide information about the neuronal initiation processes of the burst, and about the coupling and interrelation dynamics between cortical low-frequency oscillations and high-frequency spindles in thalamic structures which substantially contribute to the burst pattern. Methods For time-variant phase-locking index ( PLI), phase-synchronization index ( PSI), quadratic phase coupling ( QPC) measures, and amplitude–frequency dependency analyses the Gabor and the Hilbert transformation, both implemented as fast Fourier transformation-based approaches, were used. Additionally, models of mutually coupled Duffing oscillators were adapted to the burst data derived from the neonates (‘measured bursts’), and the corresponding ‘modeled burst’ simulations were analyzed in comparison to the measured bursts. Results A strong phase-locking of the high-frequency oscillations and synchronization between low- and high-frequency oscillatory activity at burst onset can be observed. The QPC courses and the amplitude of all oscillations rise slightly before or at the burst onset and reach their maximum within the following 1–3 s after onset. Additionally, correlative envelope–envelope and envelope–frequency couplings within and between the burst oscillations can be demonstrated. All theses time-variant signal properties can be simulated by the model. Conclusions The amplitude-independent phase measures point to a phase stabilization of high-frequency oscillatory activity which occurs before the initiation of the low-frequency oscillation. This finding points to a trigger process in which the thalamus is initially involved. After burst onset the cortical low-frequency oscillation modulates the high-frequency oscillatory activities, where modulation and additional coupling effects can be explained by three mutually coupled oscillators. Significance The model-based analysis strategy offers an up-to-date methodological guideline and sets a new standard of analysis for the investigation of EEG patterns and event-related potentials.

On the Stability of the n:m Phase Synchronization Index

Synchronization analysis of multitrial EEG or (magneto encephalogram) MEG signals is an excellent approach to detect functional connectivity between different neuronal oscillators. In our current research, the n:m phase synchronization index (n:m PSI ) is of special interest. We prove the existence of stable and unstable synchronies dependent upon the analysis frequencies and show that they lie closely together in the frequency domain. Thus, a plot of the time-frequency plane of the n:m PSI automatically violates the sampling theorem and accordingly, the method cannot be considered as a black box. A frequency-tiling approach is presented that can detect robust synchronies while ignoring the unstable ones. The improved synchrony detection is evaluated in numerical experiments on using both simulated and real-life data. It can be demonstrated that the transient synchronization events between MEG oscillations in distant frequency ranges can be detected and that compactly textured EEG synchronization patterns can be reliably characterized.

Nonlinear phase synchronization changes between SBP and R‐R interval precede syncope in the young

Nonlinear phase synchronization (PhS) between systolic BP (SBP) and R‐R interval (R‐R) can measure cardiovagal baroreflex. We hypothesized that desynchronization (loss of baroreflex) occurs prior to fainting. 15 fainters (F) and 15 control subjects (C) aged 15–25 underwent 70° head‐up tilt. Hilbert transform followed by bandpass filter (0.005–0.5 Hz) was applied to SBP and R‐R, and phase difference [ΔΦ(t)=(Φ(t)SBP − Φ(t)R‐R)] used to calculate the nonlinear PhS index: PhSI = √(&lt;cos(ΔΦ(t))&gt;2 + &lt;sin(ΔΦ(t))&gt;2). PhSI baseline values were not different between groups. During early tilt, PhSI increased for F and C (F: .22± .04 to .81±.03; C: .23±.04 to .74±.02) followed by a steep decline in F(from .50±.04 to .17±.03), which was absent in C (from .55±0.04 to .37±.05). Directional analysis indicated a small dependence of SBP on R‐R. Approximately 3 min prior to faint, PhSI increased in F (from .17±.03 to .61±.03) that was associated with directional dependence of R‐R on SBP. Wavelet analysis showed coupling and entrainment at the respiratory frequency. Loss of PhS in simple faint is consistent with cardiovagal baroreflex failure.

Fluctuation of gamma-band phase synchronization within the auditory cortex in schizophrenia

To study the phase stability of the 40Hz auditory steady-state response (ASSR) in Sz, and in addition, to investigate inter-hemispheric phase synchronization using ipsilateral and contralateral hemisphere gamma band ASSRs. Whole head magnetoencephalography (MEG) was used to detect ASSR from both hemispheres in Sz patients and their control counterparts. Source localization, spatial and temporal filtering were performed to infer gamma band activity from the neural generators of the ASSR. The response gamma band phase stability relative to a reference signal was quantified using the phase synchronization index (PSI). Results indicated reduced phase synchronization of the ASSR and the stimulus reference signal in Sz patients compared to control subjects, in addition to reduced inter-hemispheric phase synchronization between contralateral and ipsilateral hemispheric responses in Sz patients. Greater intra and inter hemispheric fluctuations of ASSR gamma band phase synchronization in Sz add to previous studies suggesting timing deficiencies within neural populations, possibly caused by impairments of neural network parameters. This study provides experimental support that may aid in understanding the dynamics of neural phase synchrony caused by modifications of underlying neurotransmitter systems, as reflected in disease states such as schizophrenia.

Detecting synchronization in coupled stochastic ecosystem networks

Instantaneous phase difference, synchronization index and mutual information are considered in order to detect phase transitions, collective behaviours and synchronization phenomena that emerge for different levels of diffusive and reactive activity in stochastic networks. The network under investigation is a spatial 2D lattice which serves as a substrate for Lotka–Volterra dynamics with 3rd order nonlinearities. Kinetic Monte Carlo simulations demonstrate that the system spontaneously organizes into a number of asynchronous local oscillators, when only nearest neighbour interactions are considered. In contrast, the oscillators can be correlated, phase synchronized and completely synchronized when introducing different interactivity rules (diffusive or reactive) for nearby and distant species. The quantitative measures of synchronization show that long distance diffusion coupling induces phase synchronization after a well defined transition point, while long distance reaction coupling induces smeared phase synchronization.

Increased phase synchronization and decreased cerebral autoregulation during fainting in the young

Vasovagal syncope may be due to a transient cerebral hypoperfusion that accompanies frequency entrainment between arterial pressure (AP) and cerebral blood flow velocity (CBFV). We hypothesized that cerebral autoregulation fails during fainting; a phase synchronization index (PhSI) between AP and CBFV was used as a nonlinear, nonstationary, time-dependent measurement of cerebral autoregulation. Twelve healthy control subjects and twelve subjects with a history of vasovagal syncope underwent 10-min tilt table testing with the continuous measurement of AP, CBFV, heart rate (HR), end-tidal CO2 (ETCO2), and respiratory frequency. Time intervals were defined to compare physiologically equivalent periods in fainters and control subjects. A PhSI value of 0 corresponds to an absence of phase synchronization and efficient cerebral autoregulation, whereas a PhSI value of 1 corresponds to complete phase synchronization and inefficient cerebral autoregulation. During supine baseline conditions, both control and syncope groups demonstrated similar oscillatory changes in phase, with mean PhSI values of 0.58+/-0.04 and 0.54+/-0.02, respectively. Throughout tilt, control subjects demonstrated similar PhSI values compared with supine conditions. Approximately 2 min before fainting, syncopal subjects demonstrated a sharp decrease in PhSI (0.23+/-0.06), representing efficient cerebral autoregulation. Immediately after this period, PhSI increased sharply, suggesting inefficient cerebral autoregulation, and remained elevated at the time of faint (0.92+/-0.02) and during the early recovery period (0.79+/-0.04) immediately after the return to the supine position. Our data demonstrate rapid, biphasic changes in cerebral autoregulation, which are temporally related to vasovagal syncope. Thus, a sudden period of highly efficient cerebral autoregulation precedes the virtual loss of autoregulation, which continued during and after the faint.

Estimation of Effective and Functional Cortical Connectivity From Neuroelectric and Hemodynamic Recordings

In this paper, different linear and nonlinear methodologies for the estimation of cortical connectivity from neuroelectric and hemodynamic measurements are reviewed and applied on common data set in order to highlight similarities and differences in the results. Different effective and functional connectivity methods were applied to motor and cognitive data sets, including structural equation modeling (SEM), directed transfer function (DTF), partial directed coherence (PDC), and direct directed transfer function (dDTF). Comparisons were made between the results in order to understand if, for a same dataset, effective and functional connectivity estimators can return the same cortical connectivity patterns. An application of a nonlinear method [phase synchronization index (PSI)] to similar executed and imagined movements was also reviewed. Connectivity patterns estimated with the use of the neuroelectric information and of the information from the multimodal integration of neuroelectric and hemodynamic data were also compared. Results suggests that the estimation of the cortical connectivity patterns performed with the linear methods (SEM, DTF, PDC, dDTF) or with the nonlinear method (PSI) on movement related potentials returned similar cortical networks. Differences in cortical connectivity were noted between the patterns estimated with the use of multimodal integration and those estimated by using only the neuroelectric data.

Small-World Network Models of Intercellular Coupling Predict Enhanced Synchronization in the Suprachiasmatic Nucleus

The suprachiasmatic nucleus (SCN) of the hypothalamus is a multioscillator system that drives daily rhythms in mammalian behavior and physiology. Based on recent data implicating vasoactive intestinal polypeptide (VIP) as the key intercellular synchronizing agent, we developed a multicellular SCN model to investigate the effects of cellular heterogeneity and intercellular connectivity on circadian behavior. A 2-dimensional grid was populated with 400 model cells that were heterogeneous with respect to their uncoupled rhythmic behavior (intrinsic and damped pacemakers with a range of oscillation periods) and VIP release characteristics (VIP producers and nonproducers). We constructed small-world network architectures in which local connections between VIP producing cells and their 4 nearest neighbors were augmented with random connections, resulting in long-range coupling across the grid. With only 10% of the total possible connections, the small-world network model was able to produce similar phase synchronization indices as a mean-field model with VIP producing cells connected to all other cells. Partial removal of random connections decreased the synchrony among neurons, the amplitude of VIP and cAMP response element binding protein oscillations, the mean period of intrinsic periods across the population, and the percentage of oscillating cells. These results indicate that small-world connectivity provides the optimal compromise between the number of connections and control of circadian amplitude and synchrony. This model predicts that small decreases in long-range VIP connections in the SCN could have dramatic effects on period and amplitude of daily rhythms, features commonly described with aging.

EEG phase synchronization in patients with paranoid schizophrenia

Recent findings suggest that specific deficits in neural synchrony and binding may underlie cognitive disturbances in schizophrenia and that key aspects of schizophrenia pathology involve discoordination and disconnection of distributed processes in multiple cortical areas associated with cognitive deficits. In the present study we aimed to investigate the underlying cortical mechanism of disturbed frontal-temporal-central-parietal connectivity in schizophrenia by examination of the synchronization patterns using wavelet phase synchronization index and coherence between all defined couples of 8 EEG signals recorded at different cortical sites in its relationship to positive and negative symptoms of schizophrenia. 31 adult schizophrenic outpatients with diagnosis of paranoid schizophrenia (mean age 27.4) were assessed in the study. The obtained results present the first quantitative evidence indicating direct relationship between wavelet phase synchronization and coherence in pairs of EEG signals recorded from frontal, temporal, central and parietal brain areas and positive and negative symptoms of schizophrenia. The performed analysis demonstrates that the level of phase synchronization and coherence in some pairs of EEG signals is inversely related to positive symptoms, negative symptoms and general psychopathology in temporal scales (frequency ranges) given by wavelet frequencies (WFs) equal to or higher than 7.56 Hz, and positively related to negative symptoms in wavelet frequencies equal to or lower than 5.35 Hz. This finding suggests that higher and lower frequencies may play a specific role in binding and connectivity and may be related to decreased or increased synchrony with specific manifestation in cognitive deficits of schizophrenia.

Effects of levetiracetam vs topiramate and placebo on visually evoked phase synchronization changes of alpha rhythm in migraine

Objective Recent theories about migraine pathogenesis have outlined an abnormal central processing of sensory signals, also suggested by an abnormal pattern of EEG hyper-synchronization under visual stimulation. The aim of the present study was to test the efficacy of topiramate and levetiracetam vs placebo in a double blind project observing the effects of the three treatments on the EEG synchronization in the alpha band under sustained flash stimulation. Methods Forty-five migraine without aura outpatients (MO) were selected and randomly assigned to 100 mg topiramate, 1000 mg levetiracetam or placebo treatment. In addition, 24 non-migraine healthy controls were submitted to EEG analysis. The EEG was recorded by 19 channels: flash stimuli with a luminosity of 0.2 J were delivered, in a frequency range from 3 to 30 Hz. We evaluated the phase synchronization index, that we previously applied in migraine, after EEG signals filtering in the alpha band. Our approach was based on the Hilbert transform. Results Both levetiracetam and topiramate significantly decreased migraine frequency, compared with placebo. MO patients displayed increased alpha-band phase synchronization as an effect of stimulus frequency; on the other hand the stimuli had an overall desynchronizing effect on control subjects. The phase synchronization index separates the two stages, before and after the treatment, only for levetiracetam, at stimulus frequencies of 9, 18, 24 and 27 Hz. Conclusions An abnormal alpha band synchronization under visual stimuli was confirmed in migraine; this phenomenon was reversed by levetiracetam preventive treatment. Significance These results confirmed in humans the inhibiting action of levetiracetam on neuronal hyper-synchronization.

Loss of coherence in a population of diffusively coupled oscillators

The authors investigate the relationship between the natural frequency distribution of diffusively coupled chemical oscillators and their entrainment by pacemakers. The system consists of micrometer-sized catalyst beads which are coupled to their neighbors by diffusion of the activator/inhibitor species through the catalyst-free Belousov-Zhabotinsky (BZ) reaction solution. The frequency distribution is measured as a function of the beads' number of neighbors. With the maximum number of neighbors, either target waves or disordered patterns are observed in the reaction domain and there is a shift to higher frequencies than those observed in the natural frequency distribution. The loss of coherence between neighbor oscillators is quantified by a decrease in the phase synchronization index. The experimental results are reproduced in simulations which demonstrate that the decrease in the degree of synchronization is correlated with the appearance of a small fraction of permanently excited beads in BZ populations of high mean frequency and/or large width.

Partial Phase Synchronization for Multivariate Synchronizing Systems

Graphical models applying partial coherence to multivariate time series are a powerful tool to distinguish direct and indirect interdependencies in multivariate linear systems. We carry over the concept of graphical models and partialization analysis to phase signals of nonlinear synchronizing systems. This procedure leads to the partial phase synchronization index which generalizes a bivariate phase synchronization index to the multivariate case and reveals the coupling structure in multivariate synchronizing systems by differentiating direct and indirect interactions. This ensures that no false positive conclusions are drawn concerning the interaction structure in multivariate synchronizing systems. By application to the paradigmatic model of a coupled chaotic Roessler system, the power of the partial phase synchronization index is demonstrated.

COHERENT RESONANCE AND PHASE LOCKING IN NOISE-DRIVEN EXCITABLE SYSTEMS

The dynamical responses of an excitable FitzHugh–Nagumo (FHN) system under the drive of an external noise are studied. Noise can induce a sequence of firings. The n:m coherent resonance of the FHN oscillator with an intrinsic natural frequency is shown. This effect is discussed by resorting to the phase dynamics of a spike train and the phase synchronization index γnm.