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Mean phase coherence as a measure for phase synchronization and its application to the EEG of epilepsy patients
Abstract
We apply the concept of phase synchronization of chaotic and/or noisy systems and the statistical distribution of the relative instantaneous phases to electroencephalograms (EEGs) recorded from patients with temporal lobe epilepsy. Using the mean phase coherence as a statistical measure for phase synchronization, we observe characteristic spatial and temporal shifts in synchronization that appear to be strongly related to pathological activity. In particular, we observe distinct differences in the degree of synchronization between recordings from seizure-free intervals and those before an impending seizure, indicating an altered state of brain dynamics prior to seizure activity.
... The two phase-based measures of synchronisation, that were used in this thesis are the Kuramoto order parameter [17] and mean phase coherence [45]. The next subsections describes the Kuramoto order parameter and the mean phase coherence in detail. ...
... The mean phase coherence R ij is a phase-based pairwise estimator for the strength of interaction [45] and, in this thesis, it is used as a measure of interaction between a pair of oscillators i and j. An interaction network of a system's dynamics can be constructed for certain range in time, with the interaction strength for all node pairs being estimated using mean phase coherence. ...
... Now to estimate the edge weights, we calculate the mean phase coherence [45] between a pair of oscillators (nodes). Since the mean phase coherence is a temporal average, so we need to take time windows and evolve the mean phase coherence with respect to time windows. ...
The main aim of this thesis was to estimate the importance of edges using centrality measures and to check the robustness of these edges in both structural and functional networks using a perturbation based approach. To do that, different network topologies were chosen that have been proved to mimic the real world systems. Perturbation experiments can be extended to complex dynamical systems consisting of well understood subsystems - the Kuramoto Oscillator. The underlying topology of the system’s interactions is defined using the network models. The properties of the system’s interactions understood using a network based approach can help to further comprehend the system’s dynamics.
... To remove the remaining artifacts (including eye blinking, eye movements, muscular activity, and cardiac artifacts) it was used independent component analysis (ICA). The number of computed independent components was the same as the number of EEG channels (i.e., 19). The identi ed components related to artifacts were eliminated, and the EEG was again reconstructed. ...
... The next step was to nd the existence and strength of connections between the activated brain areas (i.e., the areas identi ed in the previous step as being involved in the defensive reaction). In this sense, ve methods of functional connectivity were implemented: coherence (COH) 14,15 , imaginary part of coherence (iCOH) 14,16 , weighted phase lag index (wPLI) 17,18 , mean phase coherence (MPC) 19 , and direct transfer function (DTF) 20 . The connectivity methods iCOH and wPLIi overcome the problems of volume conduction and signal-to-noise ratio (SNR). ...
The study of brain activity under the appearance of an unexpected visual threat can give some insights into how the brain reacts to potential dangers, and how the consequent defensive response is originated. In this study, a virtual reality (VR) scene is used to present an unexpected threat aiming to invoke a defensive reaction, as well as non-threatening stimuli as control. The brain activity is measured along the pre and post stimuli conditions using electroencephalography (EEG). The goal is to identify how the information propagates between cortical regions once the threatening situation is presented. The functional connectivity study evidenced a flux of information from the left middle temporal gyrus to the premotor cortex, evidencing a defensive response induced by the sound involved in the stimulus. Additional connections involving diverse cortical areas as the left inferior frontal gyrus, the primary motor cortex, the prefrontal cortex, beside the premotor cortex may represent part of the information flux involved in action planning. Other activated cortical areas were the supplementary motor cortex, the right temporal gyrus, the associative visual cortex, and primary somatosensory cortex. Concluding, the immersive scenario provided by VR allowed to induce more natural defensive response, and consequently the identification of relevant brain activity.
... However, in the presence of noise, the phase of the oscillators can exhibit random jumps of ±2π , called phase slips, which can cause the phase difference, φ n,m , to compound errors, and lead to erroneous results. Therefore, instead of considering the natural phase in Equation 4, we consider the cyclic relative phase (Mormann et al., 2000;Rosenblum et al., 2001), ...
... /fncom. . of the oscillators, such that smaller values of | ϕ| correspond to a greater degree of synchrony. The second measure we use is the mean phase coherence, denoted R, which is defined as (Mormann et al., 2000;Rosenblum et al., 2001), ...
Synchronous dynamics play a pivotal role in various cognitive processes. Previous studies extensively investigate noise-induced synchrony in coupled neural oscillators, with a focus on scenarios featuring uniform noise and equal coupling strengths between neurons. However, real-world or experimental settings frequently exhibit heterogeneity, including deviations from uniformity in coupling and noise patterns. This study investigates noise-induced synchrony in a pair of coupled excitable neurons operating in a heterogeneous environment, where both noise intensity and coupling strength can vary independently. Each neuron is an excitable oscillator, represented by the normal form of Hopf bifurcation (HB). In the absence of stimulus, these neurons remain quiescent but can be triggered by perturbations, such as noise. Typically, noise and coupling exert opposing influences on neural dynamics, with noise diminishing coherence and coupling promoting synchrony. Our results illustrate the ability of asymmetric noise to induce synchronization in such coupled neural oscillators, with synchronization becoming increasingly pronounced as the system approaches the excitation threshold (i.e., HB). Additionally, we find that uneven coupling strengths and noise asymmetries are factors that can promote in-phase synchrony. Notably, we identify an optimal synchronization state when the absolute difference in coupling strengths is maximized, regardless of the specific coupling strengths chosen. Furthermore, we establish a robust relationship between coupling asymmetry and the noise intensity required to maximize synchronization. Specifically, when one oscillator (receiver neuron) receives a strong input from the other oscillator (source neuron) and the source neuron receives significantly weaker or no input from the receiver neuron, synchrony is maximized when the noise applied to the receiver neuron is much weaker than that applied to the source neuron. These findings reveal the significant connection between uneven coupling and asymmetric noise in coupled neuronal oscillators, shedding light on the enhanced propensity for in-phase synchronization in two-neuron motifs with one-way connections compared to those with two-way connections. This research contributes to a deeper understanding of the functional roles of network motifs that may serve within neuronal dynamics.
... The remaining artefact-free data were segmented in 4 seconds segments (epochs), plus 2 seconds of real data at each side as padding. Finally, MEG time series were filtered into delta (2-4Hz), theta (4-8Hz), alpha (8-12Hz), beta (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30) and gamma (30-45 Hz). ...
... This method has yielded reliable results for the estimation of resting-state functional connectivity (FC) [24]. FC between all 1202 nodes was assessed, for each participant and frequency band, by computing the phase locking value (PLV) [25], This metric was chosen for its proven high reliability across sessions, a key property of connectivity measures, guarantying repeatability and consistency of single-subject and group level results [26]. Lastly, we computed the nodal strength (also known as weighted global connectivity), which is defined as the sum of its FC with the rest of the nodes. ...
Background. Neurophysiological studies recognized that Autism Spectrum Disorder (ASD) is associated with altered patterns of over- and under-connectivity. However, few results are available about network organization in children with ASD in the early phases of development and the correlation with the severity of core autistic features.
Methods. The present study aimed at investigating the association between brain connectivity derived by MEG signals and severity of ASD traits measured with different diagnostic clinical scales, in a sample of 16 children with ASD aged 2 to 6 years.
Results. A significant correlation emerged between connectivity strength in cortical brain areas implicated in several resting state networks and the severity of communication anomalies, social interaction problems, social affect problems, and repetitive behaviors. Seed analysis revealed that this pattern of correlation was mainly caused by global rather than local effects.
Conclusions. The present results confirm that altered connectivity strength in several resting state networks is related to clinical features and may contribute to neurofunctional correlates of ASD. Future studies implementing the same method on a wider and stratified sample may further support functional connectivity as a possible biomarker of the condition.
... Konzentrieren sich die Werte dagegen auf dem Kreis, sind die Hirnregionen maximal gekoppelt; es liegt vollständige Phasensynchronisation vor. Eine Kenngröße, die die Breite dieser Verteilungen der Phasendifferenzen auf dem Einheitskreis bewertet, ist die mittlere Phasenkohärenz R (Mormann et al. 2000), die Werte zwischen 0 und 1 annimmt (0 im asynchronen und 1 im vollständig synchronen Fall). R ist ein Maß für die Stärke einer Interaktion. ...
... In verschiedenen Studien konnte jedoch gezeigt werden, dass nichtlineare EEG-Analysen zu einer Verbesserung der interiktualen Lokalisierung des epileptogenen Fokus beitragen können, was an dem folgenden Beispiel erläutert wird ): In der Mehrzahl der Fälle können stabile Ergebnisse bereits anhand nichtlinearer EEG-Analysen von ECoG-/SEEG-Registrierungen mit nur 2 h Dauer erzielt werden. Vergleichbar positive Ergebnisse ergaben sich auch mit anderen neu entwickelten nichtlinearen Kenngrößen Mormann et al. 2000;Prusseit und Lehnertz 2007; Staniek und Lehnertz 2008). ...
... Recently, Pedersen et al. compared SWPC with a more recently used technique for fMRI data, phase synchrony (Pedersen, Omidvarnia et al. 2018). PS measures the synchronization of neural activities based on the timing of their phase relationships (Lachaux, Rodriguez et al. 1999, Mormann, Lehnertz et al. 2000, Laird, Carew et al. 2001, Varela, Lachaux et al. 2001, Laird, Rogers et al. 2002, Deshmukh, Shivhare et al. 2004, Costa, Rognoni et al. 2006, Pockett, Bold et al. 2009, Fell and Axmacher 2011, Glerean, Salmi et al. 2012, Sun, Hong et al. 2012, Bolt, Nomi et al. 2018, Kumar, Reddy et al. 2018, Pedersen, Omidvarnia et al. 2018, Honari, Choe et al. 2020. PS is typically computed by estimating the phase of the signal and finding the phase difference. ...
Nitazoxanide has an anti-inflammatory effect, we clarified the ameliorative effect of nitazoxanide on asthmatic airway inflammation by conducting in vitro and in vivo experiments. In vitro, we assessed the effect of nitazoxanide on cytokine production by lipopolysaccharide-stimulated RAW 264.7 cells, as well as the diastolic effect of nitazoxanide on isolated rat airways. Nitazoxanide was found to have a diastolic effect on isolated tracheal spasms caused by spasmogenic substances, and to inhibit IL-6 and IL-1β production by RAW 264.7 cells. Meanwhile, nitazoxanide can inhibit the proliferation and migration of human bronchial smooth muscle cells (HBSMCs). In vivo, an ovalbumin (OVA)-induced asthma model was established in mice, and the airway resistance was measured by Whole Body Plethysmography (WBP) after inhalation of acetylcholine in mice, and the levels of IL-4, IL-6, IL-12, and IL-17 were detected in bronchoalveolar lavage fluid (BALF) of mice by ELISA and the inflammatory cells were counted. H&E staining was used to observe the changes in lung histopathology, and the expression of NFkB, MAPK, AMPK, and STAT3 in lung tissues was quantified using Western-blot. Nitazoxanide reduced inflammatory cell infiltration and goblet cell proliferation in the lungs of asthmatic mice. Moreover, the expression of IL-4, IL-5, and IL-6 in BALF was down-regulated in asthmatic mice. In addition, nitazoxanide could inhibit the expression of NFkB, MAPK, STAT 3 proteins and ascend the expression of AMPK in lung tissues. In conclusion, nitazoxanide could diastole airway smooth muscle and ameliorate OVA-induced airway inflammation in asthmatic mice via NFkB/MAPK and AMPK/STAT3 pathways.
... Recently, Pedersen et al. compared SWPC with a more recently used technique for fMRI data, phase synchrony (Pedersen, Omidvarnia et al. 2018). PS measures the synchronization of neural activities based on the timing of their phase relationships (Lachaux, Rodriguez et al. 1999, Mormann, Lehnertz et al. 2000, Laird, Carew et al. 2001, Varela, Lachaux et al. 2001, Laird, Rogers et al. 2002, Deshmukh, Shivhare et al. 2004, Costa, Rognoni et al. 2006, Pockett, Bold et al. 2009, Fell and Axmacher 2011, Glerean, Salmi et al. 2012, Sun, Hong et al. 2012, Bolt, Nomi et al. 2018, Kumar, Reddy et al. 2018, Pedersen, Omidvarnia et al. 2018, Honari, Choe et al. 2020. PS is typically computed by estimating the phase of the signal and finding the phase difference. ...
Time-resolved functional connectivity (trFC) assesses the time-resolved coupling between brain regions using functional magnetic resonance imaging (fMRI) data. This study aims to compare two techniques used to estimate trFC, to investigate their similarities and differences when applied to fMRI data. These techniques are the sliding window Pearson correlation (SWPC), an amplitude-based approach, and phase synchronization (PS), a phase-based technique.
To accomplish our objective, we used resting-state fMRI data from the Human Connectome Project (HCP) with 827 subjects (repetition time: 0.7s) and the Function Biomedical Informatics Research Network (fBIRN) with 311 subjects (repetition time: 2s), which included 151 schizophrenia patients and 160 controls.
Our simulations reveal distinct strengths in two connectivity methods: SWPC captures high-magnitude, low-frequency connectivity, while PS detects low-magnitude, high-frequency connectivity. Stronger correlations between SWPC and PS align with pronounced fMRI oscillations. For fMRI data, higher correlations between SWPC and PS occur with matched frequencies and smaller SWPC window sizes (~30s), but larger windows (~88s) sacrifice clinically relevant information. Both methods identify a schizophrenia-associated brain network state but show different patterns: SWPC highlights low anti-correlations between visual, subcortical, auditory, and sensory-motor networks, while PS shows reduced positive synchronization among these networks.
Our findings underscore the complementary nature of SWPC and PS, elucidating their respective strengths and limitations without implying the superiority of one over the other.
... Since the brain is a nonlinear dynamical system, phase-based connectivity measures provide a promising approach to quantify its interactions (Aydore et al., 2013). The most commonly used phase interaction measure is PLV, the magnitude of the mean phase difference between the two signals, with phase differences expressed as complex unit-length vectors (Mormann et al., 2000). The discrete-time PLV is defined as follows: ...
Electroencephalography (EEG) functional connectivity (FC) estimates are confounded by the volume conduction problem. This effect can be greatly reduced by applying FC measures insensitive to instantaneous, zero‐lag dependencies (corrected measures). However, numerous studies showed that FC measures sensitive to volume conduction (uncorrected measures) exhibit higher reliability and higher subject‐level identifiability. We tested how source reconstruction contributed to the reliability difference of EEG FC measures on a large (n = 201) resting‐state data set testing eight FC measures (including corrected and uncorrected measures). We showed that the high reliability of uncorrected FC measures in resting state partly stems from source reconstruction: idiosyncratic noise patterns define a baseline resting‐state functional network that explains a significant portion of the reliability of uncorrected FC measures. This effect remained valid for template head model‐based, as well as individual head model‐based source reconstruction. Based on our findings we made suggestions how to best use spatial leakage corrected and uncorrected FC measures depending on the main goals of the study.
... Furthermore, brain connectivity, whether within-or cross-region, plays a pivotal role in detecting pathological brain states across various neurological and psychiatric disorders, particularly those that impact distributed brain networks. For instance, it was shown that epileptic seizures manifest spatial and temporal changes in crosschannel phase synchronization [38]. Also, excessive phaseamplitude coupling (PAC) has been observed in patients with PD [39]. ...
Integrating smart algorithms on neural devices presents significant opportunities for various brain disorders. In this paper, we review the latest advancements in the development of three categories of intelligent neural prostheses featuring embedded signal processing on the implantable or wearable device. These include: 1) Neural interfaces for closed-loop symptom tracking and responsive stimulation; 2) Neural interfaces for emerging network-related conditions, such as psychiatric disorders; and 3) Intelligent BMI SoCs for movement recovery following paralysis.
... This approach allows one to assess the synchronization of local ensembles of neurons contributing to the signals measured at individual M/EEG sensors. The synchronization between pairs of neuron ensembles measured at pairs of M/EEG sensors can be quantified by the mean phase coherence 44 . The mean resultant length 45 , as well as its renormalized definition 46 , can be used to quantify the overall phase coherence of an extended network as measured by a multitude of M/EEG sensors. ...
We delve into the human brain's remarkable capacity for adaptability and sustained cognitive functioning, phenomena traditionally encompassed as executive functions or cognitive control. The neural underpinnings that enable the seamless navigation between transient thoughts without detracting from overarching goals form the core of our article. We discuss the concept of "metacontrol," which builds upon conventional cognitive control theories by proposing a dynamic balancing of processes depending on situational demands. We critically discuss the role of oscillatory processes in electrophysiological activity at different scales and the importance of desynchronization and partial phase synchronization in supporting adaptive behavior including neural noise accounts, transient dynamics, phase-based measures (coordination dynamics) and neural mass modelling. The cognitive processes focused and neurophysiological avenues outlined are integral to understanding diverse psychiatric disorders thereby contributing to a more nuanced comprehension of cognitive control and its neural bases in both health and disease.
... where ∆θ is the phase difference between two signals, also termed relative phase [18]. The more stable the ∆θ in the specific time window, the closer the R value is to 1 (R values are between 0 and 1). ...
We introduce a novel perspective in equal and multifrequency coupling derived from considering neuronal synchrony as a possible equivalence relation. The experimental results agree with the theoretical prediction that cross-frequency coupling results in a partition of the brain synchrony state space. We place these results in the framework of the integration and segregation of information in the processing of sensorimotor transformations by the brain cell circuits and propose that equal frequency (1:1) connectivity favours integration of information in the brain whereas cross-frequency coupling (n:m) favours segregation. These observations may provide an outlook about how to reconcile the need for stability in the brain's operations with the requirement for diversity of activity in order to process many sensorimotor transformations simultaneously.
... Tiesinga-Sejnowski synchrony S TS synchrony Golomb-Rinzel synchrony * (Golomb and Rinzel, 1993) S GR synchrony SPIKE-synchronization (Kreuz et al., 2015) S S synchrony Synőre indicator 2 (Kreuz et al., 2017) F S sequential structure Spike-Contrast (Ciba et al., 2018) S C synchrony Bivariate measures Mean Phase Coherence 3 (Mormann et al., 2000) MPC phase relationships Spike time tiling coefficient * (Cutts and Eglen, 2014) STTC synchrony Correlation index * (Wong et al., 1993) C i synchrony ISI-distance (Kreuz et al., 2007a) D ISI synchrony SPIKE-distance (Kreuz et al., 2011) D S synchrony Pairwise phase consistency (Vinck et al., 2010) PPC phase relationships Victor-Purpura distance * (Victor and Purpura, 1996) D VP őring pattern distance Normalized Victor-Purpura distance * (Kreiman et al., 2000) D VPN őring pattern distance Van Rossum distance * (Van Rossum, 2001) D vR őring pattern distance Normalized van Rossum distance * D vRn őring pattern distance LZ-distance (Christen et al., 2006) D LZ őring pattern similarity Schreiber correlation * (Schreiber et al., 2003) C S őring pattern similarity Kruskal correlation * (Kruskal et al., 2007) C K őring pattern similarity Hunter-Milton similarity * (Hunter and Milton, 2003) S HM őring pattern similarity Quian Quiroga event synchronization * (Quian Quiroga et al., 2002) S (Dorval, 2011) LCV ISI őring variability ISI CV2 (Holt et al., 1996) CV2 ISI őring variability Local variation (Shinomoto et al., 2003) Lv őring variability Revised local variation (Shinomoto et al., 2009) LvR őring variability Irregularity (Davies et al., 2006) IR őring variability Log ISI entropy (Bhumbra and Dyball, 2004) Ent őring variability Miura ISI irregularity (Miura et al., 2006) S M őring variability Spectral measures are listed in Table 3. 1 As indicated by the authors in the original publication. 2 Corresponding to the optimal ordering of neurons from leaders to followers. ...
Neuronal activity is organized in collective patterns that are critical for information coding, generation, and communication between brain areas. These patterns are often described in terms of synchrony, oscillations, and phase relationships. Many methods have been proposed for the quantification of these collective states of dynamic neuronal organization.
However, it is difficult to determine which method is best suited for which experimental setting and research question. This choice is further complicated by the fact that most methods are sensitive to a combination of synchrony, oscillations, and other factors; in addition, some of them display systematic biases that can complicate their interpretation. To address these challenges, we adopt a highly comparative approach, whereby spike trains are represented by a diverse library of measures. This enables unsupervised or supervised classification in the space of measures, or in that of spike trains. We compile a battery of 122 measures of synchrony, oscillations, and phase relationships, complemented with 9 measures of spiking intensity and variability. We first apply them to sets of synthetic spike trains with known statistical properties, and show that all measures are confounded by extraneous factors such as firing rate or population frequency, but to different extents. Then, we analyze spike trains recorded in different species---rat, mouse, and monkey---and brain areas---primary sensory cortices and hippocampus---and show that our highly comparative approach provides a high-dimensional quantification of collective network activity that can be leveraged for both unsupervised and supervised classification of firing patterns. Overall, the highly comparative approach provides a detailed description of the empirical properties of multineuron spike train analysis methods, including practical guidelines for their use in experimental settings, and advances our understanding of neuronal coordination and coding.
... Driven systems have had relevance in quite a few scientific fields such as medicine [1][2][3], physics [4,5], communication [6,7], mechanics [8], network [9,10], circuits [11] and engineering [12], among others. In fact, their behaviors can explain the phase transitions in ferromagnetic materials, the dynamics of which were studied using mean field coupling [13,14]. ...
When two systems are coupled, one can play the role of the driver, and the other can be the driven or response system. In this scenario, the driver system can behave as an external forcing. Thus, we study its interaction when a periodic forcing drives the driver system. In the analysis a new phenomenon shows up: when the driver system is forced by a periodic forcing, it can suffer a resonance and this resonance can be transmitted through the coupling mechanism to the driven system. Moreover, in some cases the enhanced oscillations amplitude can also interplay with a previous resonance already acting in the driven system dynamics.
... The selection of parameters such as filter cutoff frequency, order, etc. needs to be adjusted according to the characteristics of different EEG data. Mormann et al. (2000) filtered iEEG at 0.5-85 Hz with a bandpass filter. Savadkoohi et al. (2020) filtered scalp EEG from healthy subjects and iEEG from epileptic patients with 1-70 Hz bandpass filters. ...
At present, at least 30% of refractory epilepsy patients in the world cannot be effectively controlled and treated. The suddenness and unpredictability of seizures greatly affect the physical and mental health and even the life safety of patients, and the realization of early prediction of seizures and the adoption of interventions are of great significance to the improvement of patients’ quality of life. In this paper, we firstly introduce the design process of EEG-based seizure prediction methods, introduce several databases commonly used in the research, and summarize the commonly used methods in pre-processing, feature extraction, classification and identification, and post-processing. Then, based on scalp EEG and intracranial EEG respectively, we reviewed the current status of epileptic seizure prediction research from five commonly used feature analysis methods, and make a comprehensive evaluation of both. Finally, this paper describes the reasons why the current algorithms cannot be applied to the clinic, summarizes their limitations, and gives corresponding suggestions, aiming to provide improvement directions for subsequent research. In addition, deep learning algorithms have emerged in recent years, and this paper also compares the advantages and disadvantages of deep learning algorithms with traditional machine learning methods, in the hope of providing researchers with new technologies and new ideas and making significant breakthroughs in the field of epileptic seizure prediction.
... Our study investigated the effect of unilateral SD (a probable pathophysiological mechanism of migraine aura) on interhemispheric functional communication in freely behaving rats using local field potentials of the visual and motor cortex. Two methods were used to examine connectivity: mutual information function, computed using the method proposed in [1], and phase synchronization, calculated through the method [2], for four frequency bands: delta (1-4 Hz), theta (4-10 Hz), beta (10-25 Hz), and gamma (25-50 Hz). This was done by performing calculations on nonoverlapping twenty-second intervals. ...
Growing experimental and clinical evidence indicates the crucial role of network dysfunction in neurological disorders’ pathogenesis, including migraine, one of the most prevalent chronic brain diseases. Episodic headache attacks, frequently unilateral, accompanied by an aura, are associated with migraine. Migraine aura is a neurological condition characterized by the temporary development of unilateral sensory, motor, and/or speech disturbances. The symptoms are thought to indicate transient cerebral dysfunction in the cerebral cortex resulting from cortical spreading depolarization (SD), a wave of strong cellular depolarization that gradually spreads through the cortex at a rate of 3–5 mm/min. Electrophysiologically, the cortical SD wave is revealed by a high-amplitude slow negative shift in the extracellular potential and temporary suppression of the electrical activity of the cortex (EEG depression). The change in extracellular potential is associated with strong neuroglial depolarization and disruption of local ion homeostasis, which lasts for 1–2 min in healthy neuronal tissue. The SD results in a momentary suppression of the spontaneous electrical activity within the cortex, which is preceded by a brief excitation of the neurons. The neurological symptoms of the aura suggest a unilateral impairment of interhemispheric interactions during the early phase of a migraine attack. Our study investigated the effect of unilateral SD (a probable pathophysiological mechanism of migraine aura) on interhemispheric functional communication in freely behaving rats using local field potentials of the visual and motor cortex. Two methods were used to examine connectivity: mutual information function, computed using the method proposed in [1], and phase synchronization, calculated through the method [2], for four frequency bands: delta (1–4 Hz), theta (4–10 Hz), beta (10–25 Hz), and gamma (25–50 Hz). This was done by performing calculations on non-overlapping twenty-second intervals. Functional connectivity evolution was analyzed using local field potential records collected from homotopic points of the motor and visual cortex of two hemispheres in freely moving rats after inducing a single unilateral cortical SD in the somatosensory cortex. Cortical SD caused a significant wide-band decline (3–4 times) in interhemispheric functional connectivity in both the visual and motor cortex areas. Following the depolarization wave, the functional decoupling of the hemispheres began and progressively intensified, concluding by 5 min after the induction of the cortical SD wave. The network impairment displayed region- and frequency-specific features, with greater prominence observed in the visual cortex than in the motor cortex. The decline in functional connectivity was concurrent with abnormal animal behavior and aberrant activity in the ipsilateral cortex that appeared after the SD wave had ended. The study indicated that unilateral SD leads to a reversible decline in the functional interhemispheric connectivity in the awake animal cortex. Given the crucial role of synchronizing cortical oscillations for processing sensory information and integrating sensorimotor functions, the intracortical functional interactions disruption resulting from a unilateral SD wave, which we discovered in our present study, could contribute to the neuropathological mechanisms of migraine aura and sensory processing dysfunction during a migraine attack.
... Network links can be derived from bivariate statistical measures such as cross-correlation coefficients, mean phase coherence, mutual information, causal directionality, etc.; see, for instance, Refs. [37,38,43,70,71]. The matrix then provides an averaged pairwise influence of a given time series over others. ...
Natural and manmade complex systems are comprised of different elementary units, being either system components or diverse subsystems as in the case of networked systems. These units interact with each other in a possibly nonlinear way, which results in a complex dynamics that is generally dissipative and nonstationary. One of the challenges in the modeling of such systems is the identification of not only pairwise but, more importantly, higher-order interactions, together with their directions and strengths from measured multivariate time series. Here, we propose a novel data-driven approach for characterizing interactions of different orders. Our approach is based on solving a set of linear equations constructed from Kramers-Moyal coefficients derived from statistical moments of N-dimensional multivariate time series. We demonstrate the substantial potential for applications by a data-driven reconstruction of interactions in various multidimensional and networked dynamical systems.
... them are physics-biologically informed models, thus derived directly from fundamental mathematical descriptions of the dynamic behavior (such as the Hodgkin-Huxley, [11][12][13][14] the FitzHugh-Nagumo, 15,16 and phase-oscillators [17][18][19] ) and neural mass models, 20,21 the balloon model, 22 and Dynamic Causal Modeling (DCM) 23 (for a review of the various dynamic models, see also Ref. 7). On the other hand, there is the data-driven approach, exploiting a wide range of methods (see also Ref. 24) and extending from independent component analysis 25 to Granger causality-based models, [26][27][28][29][30][31][32][33] phasesynchronization, [34][35][36][37][38][39][40][41][42] and graph-based ones. [43][44][45][46][47] For an extended review of the various multiscale approaches, see the work of Siettos and Starke. ...
We propose a machine-learning approach to construct reduced-order models (ROMs) to predict the long-term out-of-sample dynamics of brain activity (and in general, high-dimensional time series), focusing mainly on task-dependent high-dimensional fMRI time series. Our approach is a three stage one. First, we exploit manifold learning and, in particular, diffusion maps (DMs) to discover a set of variables that parametrize the latent space on which the emergent high-dimensional fMRI time series evolve. Then, we construct ROMs on the embedded manifold via two techniques: Feedforward Neural Networks (FNNs) and the Koopman operator. Finally, for predicting the out-of-sample long-term dynamics of brain activity in the ambient fMRI space, we solve the pre-image problem, i.e., the construction of a map from the low-dimensional manifold to the original high-dimensional (ambient) space by coupling DMs with Geometric Harmonics (GH) when using FNNs and the Koopman modes per se. For our illustrations, we have assessed the performance of the two proposed schemes using two benchmark fMRI time series: (i) a simplistic five-dimensional model of stochastic discrete-time equations used just for a “transparent” illustration of the approach, thus knowing a priori what one expects to get, and (ii) a real fMRI dataset with recordings during a visuomotor task. We show that the proposed Koopman operator approach provides, for any practical purposes, equivalent results to the FNN-GH approach, thus bypassing the need to train a non-linear map and to use GH to extrapolate predictions in the ambient space; one can use instead the low-frequency truncation of the DMs function space of L2-integrable functions to predict the entire list of coordinate functions in the ambient space and to solve the pre-image problem.
... We quantified the degree of phase locking between signal pairs x(t j ) and y(t j ) consisting of N samples each taken at discrete times t j for j = 1, . . . , N using the mean phase coherence R [7]. To do so, we first computed the instantaneous phase using the Hilbert transform ϕ x (t j ) and ϕ y (t j ) and determine their relative phase difference ...
... 14 All the behavioral disorders that characterize psychiatric illness (unhealthy neural behaviors) are disturbances in brain functioning, 1 and abnormal levels of synchronization have been related to unhealthy neural behaviors, such as epilepsy and Parkinson's disease. 1,[15][16][17] The main goal of this study is to investigate the emergence of phase synchronization in a network of randomly connected neurons under the influence of a train of Poissonian spikes. Our primary objective is to understand the mechanisms underlying synchronization and how they are affected by the balance between external currents and coupling interactions. ...
This article investigates the emergence of phase synchronization in a network of randomly connected neurons by chemical synapses. The study uses the classic Hodgkin–Huxley model to simulate the neuronal dynamics under the action of a train of Poissonian spikes. In such a scenario, we observed the emergence of irregular spikes for a specific range of conductances and also that the phase synchronization of the neurons is reached when the external current is strong enough to induce spiking activity but without overcoming the coupling current. Conversely, if the external current assumes very high values, then an opposite effect is observed, i.e., the prevention of the network synchronization. We explain such behaviors considering different mechanisms involved in the system, such as incoherence, minimization of currents, and stochastic effects from the Poissonian spikes. Furthermore, we present some numerical simulations where the stimulation of only a fraction of neurons, for instance, can induce phase synchronization in the non-stimulated fraction of the network, besides cases in which for larger coupling values, it is possible to propagate the spiking activity in the network when considering stimulation over only one neuron.
... , the phase coherence coefficient [52] was estimated: ...
We propose for the first time a method for extracting the instantaneous phases of respiration from the signal of a photoplethysmogram (PPG). In addition to the instantaneous phases of respiration, this method allows for more accurately extracting the instantaneous frequencies of respiration from a PPG than other methods. The proposed method is based on a calculation of the element-wise product of the wavelet spectrum of a PPG and the sequence of intervals between the heartbeats extracted from a PPG, and a calculation of the skeleton of the resulting spectrum in the respiratory frequency range. It is shown that such an element-wise product makes it possible to extract the instantaneous phases and instantaneous frequencies of respiration more accurately than using the wavelet transform of a PPG signal or the sequence of the heartbeat intervals. The proposed method was verified by analyzing the signals from healthy subjects recorded during stress-inducing cognitive tasks. This method can be used in wearable devices for signal processing.
... The range of common behavior ranges from trajectories exhibiting complete agreement to phases being locked. Due to the seemingly random evolution and the broadband spectra that exhibit sensitive dependence on initial states, chaotic behavior can lead to beneficial effects in fields like secure communications [2], pattern recognition [3], brain activity analysis [4], and nonlinear system optimization [5]. Over the past few decades, research on chaos synchronization has gained significant attention and has been widely explored. ...
Compared to the synchronization of continuous-time chaotic systems which will usually satisfy the Lipschitz condition, rapid trajectory divergence is a key challenge in the synchronization of two high-dimensional discrete chaotic systems, for example two coupled map lattice systems. As a result, there is not yet a universal approach to the synchronization task in high-dimensional discrete chaotic systems. To overcome the challenge, hard constraints on the system states must be satisfied, which is defined as safety level III. We propose a safe reinforcement learning (RL) method with this high safety level. In this method, the RL agent’s policy is used to reach the goal of synchronization and a safety layer added directly on top of the policy is used to guarantee hard state constraints. The safety layer consists of a one-step predictor for the perturbed response system and an action correction formulation. The one-step predictor, based on a next generation reservoir computing, is used to identify whether the next state of the perturbed system is within the chaos domain, and if not, the action correction formula is activated to modify the corresponding perturbing force component to zero. According to the boundedness of chaotic systems, the state of the perturbed system will remain in the chaotic domain without diverging. We demonstrate that the proposed method succeeds in the task of synchronization without trajectory divergence through a numerical example with two coupled map lattice systems. We compare the performance in both cases with and without the safety layer to emphasize the significance of the safety layer and analyze the effect of hyper-parameters on the performance and stability of the algorithm.
... The corresponding measure can be the entropy of the distribution or the amplitude of its first Fourier mode. The latter is known as the phase locking value or synchronization index and is most popular because it has no parameters (Rodriguez et al., 1999;Mormann et al., 2000;. For the general case of n: m locking, where n, m are some positive integers, this measure is ...
We review an approach for reconstructing oscillatory networks’ undirected and directed connectivity from data. The technique relies on inferring the phase dynamics model. The central assumption is that we observe the outputs of all network nodes. We distinguish between two cases. In the first one, the observed signals represent smooth oscillations, while in the second one, the data are pulse-like and can be viewed as point processes. For the first case, we discuss estimating the true phase from a scalar signal, exploiting the protophase-to-phase transformation. With the phases at hand, pairwise and triplet synchronization indices can characterize the undirected connectivity. Next, we demonstrate how to infer the general form of the coupling functions for two or three oscillators and how to use these functions to quantify the directional links. We proceed with a different treatment of networks with more than three nodes. We discuss the difference between the structural and effective phase connectivity that emerges due to high-order terms in the coupling functions. For the second case of point-process data, we use the instants of spikes to infer the phase dynamics model in the Winfree form directly. This way, we obtain the network’s coupling matrix in the first approximation in the coupling strength.
... The IFG was defined as a region consisting of pars opercularis and pars triangularis and the TPJ was defined as a region consisting of the planum temporale of the superior temporal gyrus, angular gyrus, and supramarginal gyrus based on each participant's MRI (Fig. 1) using the Destrieux atlas (Destrieux et al., 2010). Functional connectivity between IFG and TPJ was assessed using the phase-locking value (PLV) method (Lachaux et al., 1999;Mormann et al., 2000). Based on the assumption that functionally integrated brain regions exhibit synchronous activity, PLV examines the consistency in the phase of signals originating from the two regions over time. ...
This study aimed to detect stressful hazard perception scenarios subjectively and objectively when using intelligent driving systems. We used electrooculography (EOG), electroencephalography (EEG), subjective ratings, and interviews to identify potential stressful hazard perceptions and record improvements in an intelligent navigation-guided pilot (NGP) system. Moreover, we analyzed electrophysiological data. Our study contributes to the use of engagement, concentration, and phase locking value connectivity based on EEG to support previous research methodologies using beta power, pupil size, fixation ratio, fixation duration, and subjective evaluations for investigating hazard perception. Our analyses showed that stressful hazard perception scenarios occurred mainly when encountering broken and solid lines, frequent lane changes, cars approaching suddenly, several cars driving in parallel, and the decision to change lanes but immediately pulling back upon using the NPG system. Our findings shed light on obtaining accurate results based on subjective and objective evaluations for developing intelligent driving systems.
The kidneys maintain fluid-electrolyte balance and excrete waste in the presence of constant fluctuations in plasma volume and systemic blood pressure. The kidneys perform these functions to control capillary perfusion and glomerular filtration by modulating the mechanisms of autoregulation. An effect of these modulations are spontaneous, natural fluctuations in nephron perfusion. Numerous other mechanisms can lead to fluctuations in perfusion and flow. The ability to monitor these spontaneous physiological fluctuations in vivo could facilitate the early detection of kidney disease. The goal of this work was to investigate the use of resting- state magnetic resonance imaging (rsMRI) to detect spontaneous physiological fluctuations in the kidney. We performed rsMRI of rat kidneys in vivo over 10 minutes, applying motion correction to resolve time series in each voxel. We observed spatially variable, spontaneous fluctuations in rsMRI signal between 0-0.3 Hz, in frequency bands also associated with autoregulatory mechanisms. We further applied rsMRI to investigate changes in these fluctuations in a rat model of diabetic nephropathy. Spectral analysis was performed on time series of rsMRI signal in kidney cortex and medulla. Power from spectra in specific frequency bands from kidney cortex correlated with severity of glomerular pathology caused by diabetic nephropathy. Finally, we investigated the feasibility of using rsMRI of the human kidney in two participants, observing the presence of similar, spatially variable fluctuations. This approach may enable a range of preclinical and clinical investigations of kidney function, and facilitate the development of new therapies to improve outcomes in patients with kidney disease.
Understanding and controlling neural network synchronization is crucial for neuroscience in revealing brain functions and addressing neurological disorders. This study explores the innovative use of dynamic learning of synchronization (DLS) technology to enhance synchronization within neuronal networks. Using the Hodgkin-Huxley model across various network topologies, including Erdos-R´enyi random graphs, small-world, and scale-free networks, it dynamically adjusts external electrical excitation to study its effects on network synchrony. To further demonstrate the universality of DLS technology, this study also validates the main results using larger-scale networks and the Izhikevich and FitzHugh-Nagumo models. The research quantifies the enhancement of synchrony through DLS, using root-mean-square error (RMSE) and synchronization factors as metrics. Findings show that DLS effectively boosts network synchrony by dynamically adjusting external excitation in response to node differences, significantly in both small-world and scale-free networks, irrespective of synaptic connections. Furthermore, DLS demonstrates potential for targeted synchronization enhancement in specific region of network. This paper highlights DLS technology’s effectiveness in modulating external excitation to improve complex neural network synchrony, providing new insights into neural synchronization and information transmission.
Neurophysiological studies recognized that Autism Spectrum Disorder (ASD) is associated with altered patterns of over- and under-connectivity. However, little is known about network organization in children with ASD in the early phases of development and its correlation with the severity of core autistic features.
The present study aimed at investigating the association between brain connectivity derived from MEG signals and severity of ASD traits measured with different diagnostic clinical scales, in a sample of 16 children with ASD aged 2 to 6 years.
A significant correlation emerged between connectivity strength in cortical brain areas implicated in several resting state networks (Default mode, Central executive, Salience, Visual and Sensorimotor) and the severity of communication anomalies, social interaction problems, social affect problems, and repetitive behaviors. Seed analysis revealed that this pattern of correlation was mainly caused by global rather than local effects.
The present evidence suggests that altered connectivity strength in several resting state networks is related to clinical features and may contribute to neurofunctional correlates of ASD. Future studies implementing the same method on a wider and stratified sample may further support functional connectivity as a possible biomarker of the condition.
The review is devoted to the application of methods of nonlinear dynamics to the analysis of dynamic changes in the patterns of physiological rhythms of the brain in the event of disorders associated with chronically elevated blood pressure and atrial fibrillation-type cardiac arrhythmias in the presence and absence of moderate cognitive impairment. The possibility of using these methods to identify markers of these disorders is shown. These markers are associated with the parameters of phase synchronization between rhythmic photostimuli and brain responses in the form of electroencephalographic patterns.
Developments in cognitive neuroscience have led to the emergence of hyperscanning, the simultaneous measurement of brain activity from multiple people. Hyperscanning is useful for investigating social cognition, including joint action, because of its ability to capture neural processes that occur within and between people as they coordinate actions toward a shared goal. Here, we provide a practical guide for researchers considering using hyperscanning to study joint action and seeking to avoid frequently raised concerns from hyperscanning skeptics. We focus specifically on EEG hyperscanning, which is widely available and optimally suited for capturing fine-grained temporal dynamics of action coordination. Our guidelines cover questions that are likely to arise when planning a hyperscanning project, ranging from whether hyperscanning is appropriate for answering one’s research questions to considerations for study design, dependent variable selection, data analysis, and visualization. By following clear guidelines that facilitate careful consideration of the theoretical implications of research design choices and other methodological decisions, joint action researchers can mitigate interpretability issues and maximize the benefits of hyperscanning paradigms.
When the scientific dataset evolves or is reused in workflows creating derived datasets, the integrity of the dataset with its metadata information, including provenance, needs to be securely preserved while providing assurances that they are not accidentally or maliciously altered during the process. Providing a secure method to efficiently share and verify the data as well as metadata is essential for the reuse of the scientific data. The National Science Foundation (NSF) funded Open Science Chain (OSC) utilizes consortium blockchain to provide a cyberinfrastructure solution to maintain integrity of the provenance metadata for published datasets and provides a way to perform independent verification of the dataset while promoting reuse and reproducibility. The NSF- and National Institutes of Health (NIH)-funded Neuroscience Gateway (NSG) provides a freely available web portal that allows neuroscience researchers to execute computational data analysis pipeline on high performance computing resources. Combined, the OSC and NSG platforms form an efficient, integrated framework to automatically and securely preserve and verify the integrity of the artifacts used in research workflows while using the NSG platform. This paper presents the results of the first study that integrates OSC–NSG frameworks to track the provenance of neurophysiological signal data analysis to study brain network dynamics using the Neuro-Integrative Connectivity tool, which is deployed in the NSG platform.
Database URL: https://www.opensciencechain.org.
Fundamental principles underlying computation in multi-scale brain networks illustrate how multiple brain areas and their coordinated activity give rise to complex cognitive functions. Whereas brain activity has been studied at the micro- to meso-scale to reveal the connections between the dynamical patterns and the behaviors, investigations of neural population dynamics are mainly limited to single-scale analysis. Our goal is to develop a cross-scale dynamical model for the collective activity of neuronal populations. Here we introduce a bio-inspired deep learning approach, termed NeuroBondGraph Network (NBGNet), to capture cross-scale dynamics that can infer and map the neural data from multiple scales. Our model not only exhibits more than an 11-fold improvement in reconstruction accuracy, but also predicts synchronous neural activity and preserves correlated low-dimensional latent dynamics. We also show that the NBGNet robustly predicts held-out data across a long time scale (2 weeks) without retraining. We further validate the effective connectivity defined from our model by demonstrating that neural connectivity during motor behaviour agrees with the established neuroanatomical hierarchy of motor control in the literature. The NBGNet approach opens the door to revealing a comprehensive understanding of brain computation, where network mechanisms of multi-scale activity are critical.
Experience and expression of Emotions have cultural influences. In behavioural experiments, Western and Eastern cultures are shown to have differences in emotional experience and expression. Western culture promotes the expression of emotional experience, whereas, in Eastern culture, emotional expressions are not very explicit and are sometimes restricted by social norms. However, there is limited evidence for this observation in terms of brain activity. In this study, we analyzed two different datasets, the DEAP data for the Western population and the DENS data for the Eastern population, focusing specifically on happy and sad emotions. We calculated functional connectivity among EEG electrodes using phase locking value and found that activity in the frontal electrodes is more pronounced in Eastern culture compared to Western culture. Meanwhile, activity in the centro-parietal electrodes is more dominant in Western culture. Activity in the frontal brain regions is high during emotion regulation. On the other hand, activity in the centro-parietal regions is more associated with sensori-motor activity.
The purpose of this work is to determine the possibility of detecting changes in the relationships between such physiological rhythms as the activity of neurons in the reticular formation of the medulla oblongata, fluctuations in the blood pressure and respiration in anesthetized rats before and during the development of a pathological state associated with painful colorectal distension. This stretch mimics the pain localized in the lower abdomen in patients with irritable bowel syndrome and it is accompanied by responses of the brain neurons, fluctuations in the blood pressure and respiration. The analysis of changes in the relationships of these rhythms consisted in identifying phase synchronization between the time series of the variability of neuronal activity intervals and the variability of blood pressure intervals at the respiratory rate before and during pain exposure. Methods. To solve this problem, the synchrosqueezed wavelet transform method was applied, which makes it possible to effectively calculate the instantaneous frequencies and phases of non-stationary signals. As indicators of synchronization, we used the values of the index and the duration of phase synchronization as a time interval during which the value of the synchronization index is close to 1. Results. It has been established that the pain effect provides an adjustment of the frequency of the neuronal activity variability and the occurrence of synchronization between this activity and the blood pressure variability at the respiratory rate or causes an adjustment of the frequency of the blood pressure variability and the occurrence of synchronization between the blood pressure variability and the respiratory rhythm. It was found that the pain effect increases the duration of phase synchronization between the variability of the blood pressure and the respiratory rhythm or reduces the duration of phase synchronization between the variability of neuronal activity and the respiratory rhythm. Conclusion. The effect of painful colorectal distension on changes in the parameters of phase synchronization between physiological rhythms in anesthetized rats was studied in detail.
In this paper, we propose a method for predicting epileptic seizures using a pre-trained model utilizing supervised contrastive learning and a hybrid model combining residual networks (ResNet) and long short-term memory (LSTM). The proposed training approach encompasses three key phases: pre-processing, pre-training as a pretext task, and training as a downstream task. In the pre-processing phase, the data is transformed into a spectrogram image using short time Fourier transform (STFT), which extracts both time and frequency information. This step compensates for the inherent complexity and irregularity of electroencephalography (EEG) data, which often hampers effective data analysis. During the pre-training phase, augmented data is generated from the original dataset using techniques such as band-stop filtering and temporal cutout. Subsequently, a ResNet model is pre-trained alongside a supervised contrastive loss model, learning the representation of the spectrogram image. In the training phase, a hybrid model is constructed by combining ResNet, initialized with weight values from the pre-trained model, and LSTM. This hybrid model extracts image features and time information to enhance prediction accuracy. The proposed method’s effectiveness is validated using datasets from CHB-MIT and Seoul National University Hospital (SNUH). The method’s generalization ability is confirmed through Leave-one-out cross-validation. From the experimental results measuring accuracy, sensitivity, and false positive rate (FPR), CHB-MIT was 91.90%, 89.64%, 0.058 and SNUH was 83.37%, 79.89%, and 0.131. The experimental results demonstrate that the proposed method outperforms the conventional methods.
Diagnostics and prognoses of brain disorders can be greatly aided by machine learning. To bring these tools into clinical routine, we argue that key challenges remain to be addressed by the community. To overcome the limitations of black-box approaches, we need to use interpretable models to overcome the shortcomings of validation and reproducible research practices. Extensive generalization studies are required. Many people die each year from brain diseases, which are the most prevalent. As the death toll continues to rise, it is estimated that it will reach 75 million by 2030. We cannot predict brain diseases with modern technology or an advanced healthcare system. In our paper, we use machine learning algorithms to implement the neurological disease prediction approach since such algorithms are a critical source of data prediction. MIT-BIH repository data comprising a variety of patients were used as the database. Based on the classifiers utilized, the findings have proven that the RDF produced the most accurate result with 96.32% accuracy.
We proposed mathematical models for the electrocardiogram and photoplethysmogram signals with functionality to preset the pattern of synchronization between the phases of the low-frequency oscillations, which are related to the sympathetic neuronal control of circulation. The simulated phase difference reproduced the statistical and spectral characteristics of the experimental data, including the alternating horizontal and sloped sections, corresponding to the intervals of synchronous and asynchronous behavior. Using the proposed model, we tested and tuned an algorithm for detection of the phase synchronization between the parts of the sympathetic control of circulation, improving both sensitivity and specificity of the algorithm.
Schizophrenia (SZ) is a prevalent mental disorder characterized by cognitive, emotional, and behavioral changes. Symptoms of SZ include hallucinations, illusions, delusions, lack of motivation, and difficulties in concentration. While the exact causes of SZ remain unproven, factors such as brain injuries, stress, and psychotropic drugs have been implicated in its development. SZ can be classified into different types, including paranoid, disorganized, catatonic, undifferentiated, and residual. Diagnosing SZ involves employing various tools, including clinical interviews, physical examinations, psychological evaluations, the Diagnostic and Statistical Manual of Mental Disorders (DSM), and neuroimaging techniques. Electroencephalography (EEG) recording is a significant functional neuroimaging modality that provides valuable insights into brain function during SZ. However, EEG signal analysis poses challenges for neurologists and scientists due to the presence of artifacts, long-term recordings, and the utilization of multiple channels. To address these challenges, researchers have introduced artificial intelligence (AI) techniques, encompassing conventional machine learning (ML) and deep learning (DL) methods, to aid in SZ diagnosis. This study reviews papers focused on SZ diagnosis utilizing EEG signals and AI methods. The introduction section provides a comprehensive explanation of SZ diagnosis methods and intervention techniques. Subsequently, review papers in this field are discussed, followed by an introduction to the AI methods employed for SZ diagnosis and a summary of relevant papers presented in tabular form. Additionally, this study reports on the most significant challenges encountered in SZ diagnosis, as identified through a review of papers in this field. Future directions to overcome these challenges are also addressed. The discussion section examines the specific details of each paper, culminating in the presentation of conclusions and findings.
Forebrain acetylcholine (ACh) signaling has been shown to drive attention and learning. Recent experimental evidence of spatially and temporally constrained cholinergic signaling has sparked interest to investigate how it facilitates stimulus-induced learning. We use biophysical excitatory-inhibitory (E-I) multi-module neural network models to show that external stimuli and ACh signaling can mediate spatially constrained synaptic potentiation patterns. The effects of ACh on neural excitability are simulated by varying the conductance of a muscarinic receptor-regulated hyperpolarizing slow K+ current (m-current). Each network module consists of an E-I network with local excitatory connectivity and global inhibitory connectivity. The modules are interconnected with plastic excitatory synaptic connections, that change via a spike-timing-dependent plasticity (STDP) rule. Our results indicate that spatially constrained ACh release influences the information flow represented by network dynamics resulting in selective reorganization of inter-module interactions. Moreover the information flow depends on the level of synchrony in the network. For highly synchronous networks, the more excitable module leads firing in the less excitable one resulting in strengthening of the outgoing connections from the former and weakening of its incoming synapses. For networks with more noisy firing patterns, activity in high ACh regions is prone to induce feedback firing of synchronous volleys and thus strengthening of the incoming synapses to the more excitable region and weakening of outgoing synapses. Overall, these results suggest that spatially and directionally specific plasticity patterns, as are presumed necessary for feature binding, can be mediated by spatially constrained ACh release.
Synergetics is a discipline concerned with the cooperation of individual parts of a system that produces spatial, temporal, or functional structures (see, e.g., Haken 1977, 1980 a, b). The macroscopic behavior of such a system can change dramatically when certain external parameters are varied. The classical physical example of a synergetic system is the laser, which exhibits quite a number of ordering effects. It was Haken (1977) and Başar (1983) who emphasized the similarity between the behavior of an excited neuronal population and that of a laser when it is pumped: The external stimulus pushes the spontaneous electric activity of the brain — which can be regarded as a set of weakly coupled oscillators — into the coherent state of a single harmonic oscillator, ringing with an intrinsic frequency, for a certain coherence time (“coherence length”), after which fluctuations set in again. Various brain structures were found to have different intrinsic frequencies (Başar 1983). The higher the entropy of the system, i.e., the more independently the individual neurons are firing, the higher is the “excitability” or “response susceptibility” of the neuronal population and vice versa: During a regular firing (state of low entropy), either maintained by stimulation or occurring spontaneously, the neuronal population is less or not at all responsive to a (second) stimulus.
The complex behaviour of cardiorespiratory dynamics is shown to be related to the interaction between several physiological oscillators. This study is based on electrocardiogram and respiratory flow data obtained from 3 different subjects during paced breathing at 10 different pacing cycle lengths ranging from 5 s to 12 s. Two different methods ideally suited for the analysis of synchronization pattern of coupled oscillators are applied: 1. Symbolic dynamics based on symbol coding adapted for the detection of respiratory modulation of cardiac parasympathetic activity discloses two regimes of different synchronization behaviour within the frequency area corresponding to the Arnold tongue of 1:1 frequency-locking between respiratory flow and respiratory heartbeat variation (respiratory sinus arrhythmia). 2. The analysis of the phase shift between respiratory flow and respiratory sinus arrhythmia indicates that synchronization is not a static but a dynamic phenomenon. The observed dependence of the phase shift on respiratory cycle length shows large inter-individual variation. These findings turn out to be further hints for the existence of an additional central oscillator in the frequency range of respiration interacting with the central respiratory oscillator driving mechanical respiration.
In periodically driven chaotic dynamical systems with a broad distribution of intrinsic time scales, perfect phase synchronization cannot be reached. Long segments of evolution during which the phase of a chaotic variable follows the phase of the driving force are interrupted by short segments of phase drift. We demonstrate that this drift is another short-lived synchronized state; its onset is caused by the passage near the long unstable periodic orbits whose frequencies are locked by external force in ratios different from 1:1.
We evaluate the capability of nonlinear time series analysis to extract features from brain electrical activity (EEG) predictive of epileptic seizures. Time-resolved analysis of the EEG recorded in 16 patients from within the seizure-generating area of the brain indicate marked changes in nonlinear characteristics for up to several minutes prior to seizures as compared to other states or recording sites. If interpreted as a loss of complexity in brain electrical activity these changes could reflect the hypothesized continuous increase of synchronization between pathologically discharging neurons and allow one to study seizure-generating mechanisms in humans.
A fundamental question about human memory is which brain structures are involved, and when, in transforming experiences into
memories. This experiment sought to identify neural correlates of memory formation with the use of intracerebral electrodes
implanted in the brains of patients with temporal lobe epilepsy. Event-related potentials (ERPs) were recorded directly from
the medial temporal lobe (MTL) as the patients studied single words. ERPs elicited by words subsequently recalled in a memory
test were contrasted with ERPs elicited by unrecalled words. Memory formation was associated with distinct but interrelated
ERP differences within the rhinal cortex and the hippocampus, which arose after about 300 and 500 milliseconds, respectively.
These findings suggest that declarative memory formation is dissociable into subprocesses and sequentially organized within
the MTL.
A prototype equation to the Lorenz model of turbulence contains just one (second-order) nonlinearity in one variable. The flow in state space allows for a “folded” Poincaré map (horseshoe map). Many more natural and artificial systems are governed by this type of equation.
We present the new effect of phase synchronization of weakly coupled self-sustained chaotic oscillators. To characterize this phenomenon, we use the analytic signal approach based on the Hilbert transform and partial Poincare maps. For coupled Rossler attractors, in the synchronous regime the phases are locked, while the amplitudes vary chaotically and are practically uncorrelated. Coupling a chaotic oscillator with a hyperchaotic one, we observe another new type of synchronization, where the frequencies are entrained, while the phase difference is unbounded. A relation between the phase synchronization and the properties of the Lyapunov spectrum is studied.
We use the concept of phase synchronization for the analysis of noisy nonstationary bivariate data. Phase synchronization is understood in a statistical sense as an existence of preferred values of the phase difference, and two techniques are proposed for a reliable detection of synchronous epochs. These methods are applied to magnetoencephalograms and records of muscle activity of a Parkinsonian patient. We reveal that the temporal evolution of the peripheral tremor rhythms directly reflects the time course of the synchronization of abnormal activity between cortical motor areas.
We use the concept of phase synchronization for the analysis of noisy nonstationary bivariate data. Phase synchronization is understood in a statistical sense as an existence of preferred values of the phase difference, and two techniques are proposed for a reliable detection of synchronous epochs. These methods are applied to magnetoencephalograms and records of muscle activity of a Parkinsonian patient. We reveal that the temporal evolution of the peripheral tremor rhythms directly reflects the time course of the synchronization of abnormal activity between cortical motor areas. [S0031-9007(98)07333-5].
Epileptic seizures are a principal brain dysfunction with important public health implications, as they affect 0.8% of humans. Many of these patients (20%) are resistant to treatment with drugs. The ability to anticipate the onset of seizures in such cases would permit clinical interventions. The view of chronic focal epilepsy now is that abnormally discharging neurons act as pacemakers to recruit and entrain other normal neurons by loss of inhibition and synchronization into a critical mass. Thus, preictal changes should be detectable during the stages of recruitment. Traditional signal analyses, such as the count of focal spike density, the frequency coherence or spectral analyses are not reliable predictors. Non-linear indicators may undergo consistent changes around seizure onset. Our objective was to follow the transition into seizure by reconstructing intracranial recordings in implanted patients as trajectories in a phase space and then introduce non-linear indicators to characterize them. These indicators take into account the extended spatio-temporal nature of the epileptic recruitment processes and the corresponding physiological events governed by short-term causalities in the time series. We demonstrate that in most cases (17 of 19), seizure onset could be anticipated well in advance (between 2-6 minutes beforehand), and that all subjects seemed to share a similar 'route' towards seizure.
An experimental observation of phase synchronization is presented for two unidirectionally coupled chaotic Rössler systems. We show that in this case phase synchronization is connected with generalized synchronization which occurs when the coupling strength exceeds a critical value.
A general approach for constructing chaotic synchronized dynamical systems is discussed that is based on a decomposition of given systems into active and passive parts. As a possible application the chapter considers an improved encoding method where the information signal is injected into the dynamical system of the transmitter. Furthermore, it highlights how to design in a systematic way high-dimensional synchronized systems that may be used for efficient hyperchaotic encoding of information. Synchronization of periodic signals is a well-known phenomenon in physics, engineering, and many other scientific disciplines.
Usually, diffusive coupling of nonlinear oscillators in one dynamical variable leads to synchronization of oscillators. We study a model of coupled neural oscillators in which simple diffusive coupling in voltage, counterintuitively, leads to dephasing of oscillators. We examine the general conditions under which dephasing through diffusive interaction will occur. We show that such systems with dephasing limit cycles lead to a new burstinglike behavior: oscillators switch between high and low oscillation amplitude. This occurs because the interaction is such that oscillators tend to synchronize for sufficiently small oscillation amplitude, while they tend to desynchronize once their oscillation amplitude has become large.
We present the new effect of phase synchronization of weakly coupled self-sustained chaotic oscillators. To characterize this phenomenon, we use the analytic signal approach based on the Hilbert transform and partial Poincaré maps. For coupled Rössler attractors, in the synchronous regime the phases are locked, while the amplitudes vary chaotically and are practically uncorrelated. Coupling a chaotic oscillator with a hyperchaotic one, we observe another new type of synchronization, where the frequencies are entrained, while the phase difference is unbounded. A relation between the phase synchronization and the properties of the Lyapunov spectrum is studied.
A fundamental question about human memory is which brain structures are involved, and when, in transforming experiences into memories. This experiment sought to identify neural correlates of memory formation with the use of intracerebral electrodes implanted in the brains of patients with temporal lobe epilepsy. Event-related potentials (ERPs) were recorded directly from the medial temporal lobe (MTL) as the patients studied single words. ERPs elicited by words subsequently recalled in a memory test were contrasted with ERPs elicited by unrecalled words. Memory formation was associated with distinct but interrelated ERP differences within the rhinal cortex and the hippocampus, which arose after about 300 and 500 milliseconds, respectively. These findings suggest that declarative memory formation is dissociable into subprocesses and sequentially organized within the MTL.
We describe a novel method of adaptively controlling epileptic seizure-like events in hippocampal brain slices using electric fields. Extracellular neuronal activity is continuously recorded during field application through differential extracellular recording techniques, and the applied electric field strength is continuously updated using a computer-controlled proportional feedback algorithm. This approach appears capable of sustained amelioration of seizure events in this preparation when used with negative feedback. Seizures can be induced or enhanced by using fields of opposite polarity through positive feedback. In negative feedback mode, such findings may offer a novel technology for seizure control. In positive feedback mode, adaptively applied electric fields may offer a more physiological means of neural modulation for prosthetic purposes than previously possible.
The onset of an epileptic seizure has become a matter of prime interest in the last two decades. For successful therapy it is of the greatest importance to understand how the different inhibitory mechanisms involved in the normally functioning brain are carried out, and how the devastating avalanche of the seizure activity may overrun wide areas of grey matter. This problem of how an attack may arise has been dealt with in several monographs, but from different points of view: on the one hand chiefly from the viewpoint of the clinical EEG (GAsTAuT et al. 1969), on the other hand from the viewpoint of experimental epilepsy, starting with the activities observed at the level of the nerve cell (JASPER et al. 1969). This volume has quite a different perspective. It contains the papers and discussions presented at a Symposium organized by the Austrian Academy of Sciences, the aim of which was to arrive at a better understanding of some of the electrical phenomena accompanying the epileptic seizure.
In this article, we restrict ourselves to an understanding of the synchronization phenomenon as an adjustment of rhythms of two weakly interacting self-sustained oscillators. We describe a unified approach to synchronization of noisy and chaotic systems and demonstrate that this approach can be used to address the inverse problem of identification of the presence of weak interaction between natural systems from bivariate data. In this way, we reveal the presence of weak interactions between the human cardiovascular and respiratory systems.
It is widely accepted that cardiac and respiratory rhythms in humans are unsynchronised. However, a newly developed data analysis technique allows any interaction that does occur in even weakly coupled complex systems to be observed. Using this technique, we found long periods of hidden cardiorespiratory synchronization, lasting up to 20 minutes, during spontaneous breathing at rest.
This second edition of Seizures and Epilepsy is completely revised, due to tremendous advances in the understanding of the fundamental neuronal mechanisms underlying epileptic phenomena, as well as current diagnosis and treatment, which have been heavily influenced over the past several decades by seminal neuroscientific developments, particularly the introduction of molecular neurobiology, genetics, and modern neuroimaging. This resource covers a broad range of both basic and clinical epileptology.
Methods for analysis of nonstationary EEGs, that is, EEGs whose patterns undergo changes with time (e.g., alpha blocking, paroxysmal slow waves, onset of drowsiness/sleep, but excluding spikes/sharp waves) are reviewed. The concepts of stationarity and nonstationarity, and general techniques for their evaluation, are discussed. Simpler methods for monitoring for nonstationarity include running determinations of average amplitude and average period or interval. Piecewise stationary analysis includes characterization, by spectra obtained by fast Fourier transform or by autoregressive modeling, of sections of EEGs preselected to be stationary. In Kalman filtering, the autoregressive model itself becomes time-varying. Segmentation of the EEG into stationary lengths can be carried out on a fixed-interval basis (i.e., of successive, e.g., 1-s intervals), with clustering (grouping) or classification according to the features (e.g., spectra) of each interval, and concatenation of adjacent similar intervals. Alternatively, in adaptive (variable-interval) segmentation, the EEG is continuously monitored automatically for any significant departure from stationarity, and segment boundaries are placed accordingly. A number of applications of the various methods are included, with examples of succinct summary displays. Problems and prospects are discussed.
Introduction Instantaneous phase of signals and systems Phase
synchronization of chaotic self-sustained oscillators Looking for
synchronization phenomena in real data Conclusions
We study synchronization transitions in a system of two coupled self-sustained chaotic oscillators. We demonstrate that with the increase of coupling strength the system first undergoes the transition to phase synchronization. With a further increase of coupling, a new synchronous regime is observed, where the states of two oscillators are nearly identical, but one system lags in time to the other. We describe this regime as a state with correlated amplitudes and a constant phase shift. These transitions are traced in the Lyapunov spectrum.
Experimental lesion studies in monkeys have demonstrated that the cortical areas surrounding the hippocampus, including the entorhinal, perirhinal and parahippocampal cortices play an important role in declarative memory (i.e. memory for facts and events). A series of neuroanatomical studies, motivated in part by the lesion studies, have shown that the macaque monkey entorhinal, perirhinal and parahippocampal cortices are polymodal association areas that each receive distinctive complements of cortical inputs. These areas also have extensive interconnections with other brain areas implicated in non-declarative forms of memory including the amygdala and striatum. This pattern of connections is consistent with the idea that the entorhinal, perirhinal and parahippocampal cortices may participate in a larger network of structures that integrates information across memory systems.
Epileptic seizures are defined as the clinical manifestation of excessive and hypersynchronous activity of neurons in the
cerebral cortex and represent one of the most frequent malfunctions of the human central nervous system. Therefore, the search
for precursors and predictors of a seizure is of utmost clinical relevance and may even guide us to a deeper understanding
of the seizure generating mechanisms. We extract chaos-indicators such as Lyapunov exponents and Kolmogorov entropies from
different types of electroencephalograms (EEGs). We concentrate on EEGs that originate from intracranially implanted electrodes
(semi-invasive and fully invasive recording techniques), which provides particularly “clean” signals in terms of noise-level
and stationarity. Among the analytical methods we tested up to now, we find that the spectral density of the local expansion
exponents is best suited to predict the onset of a forthcoming seizure. We also evaluate the time-evolution of the dissipation
in the EEGs: it exhibits strongly significant variations that clearly relate to the time relative to a seizure onset. We mainly
address ourselves to hidden properties in these signals, e.g., changes that indicate a seizure cannot be detected by a visual inspection. Further, we investigate interictal EEGs (i.e., far away from a seizure) in order to characterize their more general properties, such as the convergence of the reconstructed
quantities with respect to the number of phase space dimensions. Finally, we discuss our results within the general context
of complex dynamical systems.
Epileptic seizures are defined as the clinical manifestation of excessive and hypersynchronous activity of neurons in the cerebral cortex and represent one of the most frequent malfunctions of the human central nervous system. Therefore, the search for precursors and predictors of a seizure is of utmost clinical relevance and may even guide us to a deeper understanding of the seizure generating mechanisms. We extract chaos-indicators such as Lyapunov exponents and Kolmogorov entropies from different types of electroencephalograms (EEGs): this covers mainly intracranial EEGs (semi-invasive and invasive recording techniques), but also scalp-EEGs from the surface of the skin. Among the analytical methods we tested up to now, we find that the spectral density of the local expansion exponents is best suited to predict the onset of a forthcoming seizure. We also evaluate the time-evolution of the dissipation in these signals: it exhibits strongly significant variations that clearly relate to the time relative to a seizure onset. This article is mainly devoted to an assessment of these methods with respect to their sensitivity to EEG changes, e.g., prior to a seizure. Further, we investigate interictal EEGs (i.e., far away from a seizure) in order to characterize their more general properties, such as the convergence of the reconstructed quantities with respect to the number of phase space dimensions. Generally we use multichannel reconstruction, but we also present a comparison with the delay-embedding technique.
We extend the notion of phase locking to the case of chaotic oscillators. Different definitions of the phase are discussed. and the phase dynamics of a single self-sustanined chaotic oscillator subjected to external force is investigated. We describe regimes where the amplitude of the oscillator remains chaotic and the phase is synchronized by the external force. This effect is demonstrated for periodic and noisy driving. This phase synchronization is characterized via direct calculation of the phase, as well as by implicit indications, such as the resonant growth of the discrete component in the power spectrum and the appearance of a macroscopic average field in an ensemble of driven oscillators. The Rössler and the Lorenz systems are shown to provide examples of different phase coherence properties, with different response to the external force. A relation between the phase synchronization and the properties of the Lyapunov spectrum is discussed.
Invasive electroencephalographic (EEG) recordings from depth and subdural electrodes, performed in eight patients with temporal lobe epilepsy, are analyzed using a variety of nonlinear techniques. A surrogate data technique is used to find strong evidence for nonlinearities in epileptogenic regions of the brain. Most of these nonlinearities are characterized as “spiking” by a wavelet analysis. A small fraction of the nonlinearities are characterized as “recurrent” by a nonlinear prediction algorithm. Recurrent activity is found to occur in spatio-temporal patterns related to the location of the epileptogenic focus. Residual delay maps, used to characterize “lag-one nonlinearity”, are remarkably stationary for a given electrode, and exhibit striking variations among electrodes. The clinical and theoretical implications of these results are discussed.
We present a measure for characterizing statistical relationships between two time sequences. In contrast to commonly used measures like cross-correlations, coherence and mutual information, the proposed measure is non-symmetric and provides information about the direction of interdependence. It is closely related to recent attempts to detect generalized synchronization. However, we do not assume a strict functional relationship between the two time sequences and try to define the measure so as to be robust against noise, and to detect also weak interdependences. We apply our measure to intracranially recorded electroencephalograms of patients suffering from severe epilepsies.
Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.
A simple system representing cellular convection is solved numerically. All of the solutions are found to be unstable, and almost all of them are nonperiodic.
The feasibility of very-long-range weather prediction is examined in the light of these results.
Epileptiform activity requires that large aggregates of neurons act synchronously. The process of neuronal synchronization during seizure onset was studied in the human medial temporal lobe by measuring the coherence of EEG activity. Records were obtained from 10 consecutive patients with hippocampal depth electrodes being evaluated for possible resective surgery. Coherence and phase spectra were calculated from all possible pairs of contacts in the medial temporal lobe of seizure onset using the method of Gotman applied to successive 6.4 sec epochs. Signals derived from adjacent contacts within definable brain regions were coherent during both the preictal and ictal period. Transitions in the level of coherence were measured between contacts presumed to span the boundaries of these regions. Time delays were measured early in the development of the seizure discharge but were not sustained. These time delays spanned the borders of regions of differing coherence, especially in the posterior hippocampus, and were interpreted to represent a transient increase in the functional linkage between structural elements. We conclude that the process of neuronal entrainment during seizure onset involves a transient interaction between brain regions but the maintenance of this interaction is not required for sustained seizure activity.
Methods for analysis of nonstationary EEGs, that is, EEGs whose patterns undergo changes with time (e.g., alpha blocking, paroxysmal slow waves, onset of drowsiness/sleep, but excluding spikes/sharp waves) are reviewed. The concepts of stationarity and nonstationarity, and general techniques for their evaluation, are discussed. Simpler methods for monitoring for nonstationarity include running determinations of average amplitude and average period or interval. Piecewise stationary analysis includes characterization, by spectra obtained by fast Fourier transform or by autoregressive modeling, of sections of EEGs preselected to be stationary. In Kalman filtering, the autoregressive model itself becomes time-varying. Segmentation of the EEG into stationary lengths can be carried out on a fixed-interval basis (i.e., of successive, e.g., 1-s intervals), with clustering (grouping) or classification according to the features (e.g., spectra) of each interval, and concatenation of adjacent similar intervals. Alternatively, in adaptive (variable-interval) segmentation, the EEG is continuously monitored automatically for any significant departure from stationarity, and segment boundaries are placed accordingly. A number of applications of the various methods are included, with examples of succinct summary displays. Problems and prospects are discussed.
Neurons involved in the epileptic processes exhibit high frequency discharges scarcely modulated by physiological brain activity. This behaviour should be accompanied by a loss of complexity in the corresponding electrographic signal. From the theory of non-linear dynamics it is known that the correlation dimension allows a quantitative description of complexity in terms of the number of degrees of freedom. To test whether a relationship exists between spatio-temporal alterations of neuronal complexity and spatial extent and temporal dynamics of the epileptogenic area, a moving-window correlation dimension analysis was applied to intracranially recorded electrocorticograms of 20 patients with unilateral temporal lobe epilepsy. Dimension as a function of time was calculated for interictal activity (n = 98) and seizure activity including the pre- and postictal phase (n = 28) from recording locations within the epileptogenic area, in adjacent areas and in homologous contralateral sites. Pronounced changes of the dimension in time were found, gradually decreasing with increasing distance from the focal area. Extraction of a single value quantifying the dimension variance of interictal activity allowed the primary epileptogenic area to be laterized in exact agreement with the results of the presurgical work-up and the confirmation of the postoperative outcome, without the necessity of observing actual seizure activity.
An understanding of the principles governing the behavior of complex neuronal networks, in particular their capability of generating epileptic seizures implies the characterization of the conditions under which a transition from the interictal to the ictal state takes place. Signal analysis methods derived from the theory of nonlinear dynamics provide new tools to characterize the behavior of such networks, and are particularly relevant for the analysis of epileptiform activity.
We calculated the correlation dimension, tested for irreversibility, and made recurrence plots of EEG signals recorded intracranially both during interictal and ictal states in temporal lobe epilepsy patients who were surgical candidates.
Epileptic seizure activity often, but not always, emerges as a low-dimensional oscillation. In general, the seizure behaves as a nonstationary phenomenon during which both phases of low and high complexity may occur. Nevertheless a low dimension may be found mainly in the zone of ictal onset and nearby structures. Both the zone of ictal onset and the pattern of propagation of seizure activity in the brain could be identified using this type of analysis. Furthermore, the results obtained were in close agreement with visual inspection of the EEG records.
Application of these mathematical tools provides novel insights into the spatio-temporal dynamics of "epileptic brain states". In this way it may be of practical use in the localization of an epileptogenic region in the brain, and thus be of assistance in the presurgical evaluation of patients with localization-related epilepsy.
We examine the mutual coherence and phase dynamics of two solid-state lasers, generated adjacent to each other in a single Nd:YAG rod. The coupling of the lasers is varied by changing the separation of the pump beams. A model is formulated to interpret the experimental results, and theoretical predictions are obtained that are in excellent agreement with the measurements.
We investigate the synchronization of chaotic oscillations in coupled oscillator systems, both theoretically and in analog electronic circuits. Particular attention is paid to deriving and testing general conditions for the stability of synchronous chaotic behavior in cases where the coupled oscillator array possesses a shift-invariant symmetry. These cases include the well studied cases of nearest-neighbor diffusive coupling and all-to-all or global coupling. An approximate criterion is developed to predict the stability of synchronous chaotic oscillations in the strong coupling limit, when the oscillators are coupled through a single coordinate (scalar coupling). This stability criterion is illustrated numerically in a set of coupled Rössler-like oscillators. Synchronization experiments with coupled Rössler-like oscillator circuits are also carried out to demonstrate the applicability of the theory to real systems.
We report the observation of synchronization of the chaotic intensity fluctuations of two Nd:YAG lasers when one or both the lasers are driven chaotic by periodic modulation of their pump beams.
Chaotic synchronization involving a yttrium iron garnet film in ferromagnetic resonance at 1.2 GHz has been achieved through small perturbations. The perturbations were derived from the difference between the current system's chaotic signal and a prerecorded chaotic signal from the same attractor, and were applied continuously. A model of the system's dynamics predicts the observed synchronization.
Recent studies have shown that non-linear analysis of intracranial activities can detect a 'pre-ictal phase' preceding the epileptic seizure. Nevertheless, the dynamical nature of the underlying neuronal process and the spatial extension of this pre-ictal phase still remain unknown. In this paper, we address these aspects using a new non-linear measure of dynamic similarity between different parts of intracranial recordings of nine patients with medial temporal lobe epilepsy recorded during transitions to seizure. Our results confirm that non-linear changes in neuronal dynamics allow, in most cases (16 out of 17), a seizure anticipation several minutes in advance. Furthermore, we show that the spatial distribution of pre-ictal changes often involves an extended network projecting beyond the limits of the epileptogenic region. Finally, the pre-ictal phase could frequently (13 out of 17) be characterized with a marked shift toward slower frequencies in upper delta or theta frequency range.
The theory of deterministic chaos addresses simple deterministic dynamics in which nonlinearity gives rise to complex temporal behavior. Although biological neuronal networks such as the brain are highly complicated, a number of studies provide growing evidence that nonlinear time series analysis of brain electrical activity in patients with epilepsy is capable of providing potentially useful diagnostic information. In the present study, this analysis framework was extended by introducing a new measure xi, designed to discriminate between nonlinear deterministic and linear stochastic dynamics. For the evaluation of its discriminative power, xi was extracted from intracranial multi-channel EEGs recorded during the interictal state in 25 patients with unilateral mesial temporal lobe epilepsy. Strong indications of nonlinear determinism were found in recordings from within the epileptogenic zone, while EEG signals from other sites mainly resembled linear stochastic dynamics. In all investigated cases, this differentiation allowed to retrospectively determine the side of the epileptogenic zone in full agreement with results of the presurgical workup.