Dynamics of intracranial electroencephalographic recordings from epilepsy patients using univariate and bivariate recurrence networks

Reliable detection of directional couplings using cross-vector measures

Detecting directional couplings from time series is crucial in understanding complex dynamical systems. Various approaches based on reconstructed state-spaces have been developed for this purpose, including a cross-distance vector measure, which we introduced in our recent work. Here, we devise two new cross-vector measures that utilize ranks and time series estimates instead of distances. We analyze various deterministic and stochastic dynamics to compare our cross-vector approach against some established state-space-based approaches. We demonstrate that all three cross-vector measures can identify the correct coupling direction for a broader range of couplings for all considered dynamics. Among the three cross-vector measures, the rank-based variant performs the best. Comparing this novel measure to an established rank-based measure confirms that it is more noise-robust and less affected by linear cross-correlation. To extend this comparison to real-world signals, we combine both measures with the method of surrogates and analyze a database of electroencephalographic (EEG) recordings from epilepsy patients. This database contains signals from brain areas where the patients' seizures were detected first and signals from brain areas that were not involved in the seizure onset. A better discrimination between these signal classes is obtained by the cross-rank vector measure. Additionally, this measure proves to be robust to non-stationarity, as its results remain nearly unchanged when the analysis is repeated for the subset of EEG signals that were identified as stationary in previous work. These findings suggest that the cross-vector approach can serve as a valuable tool for researchers analyzing complex time series and for clinical applications.

The part and the whole: how single nodes contribute to large-scale phase-locking in functional EEG networks

OBJECTIVE

The application of signal analysis techniques to electroencephalographic (EEG) recordings from epilepsy patients shows that epilepsy involves not only altered neuronal synchronization but also the reorganization of functional EEG networks. This study aims to assess the large-scale phase-locking of such functional networks and how individual network nodes contribute to this collective dynamics.

METHODS

We analyze the EEG recorded before, during and after seizures from sixteen patients with pharmacoresistant focal-onset epilepsy. The data is filtered to low (4-30 Hz) and high (80-150 Hz) frequencies. We define the multivariate phase-locking measure and the univariate phase-locking contribution measure. Surrogate signals are used to estimate baseline results expected under the null hypothesis that the EEG is a correlated linear stochastic process.

RESULTS

On average, nodes from inside and outside the seizure onset zone (SOZ) increase and decrease, respectively, the large-scale phase-locking. This difference becomes most evident in a joint analysis of low and high frequencies.

CONCLUSIONS

Nodes inside and outside the SOZ play opposite roles for the large-scale phase-locking in functional EEG network in epilepsy patients.

SIGNIFICANCE

The application of the phase-locking contribution measure to EEG recordings from epilepsy patients can potentially help in localizing the SOZ.

High expectations on phase locking: Better quantifying the concentration of circular data

The degree to which unimodal circular data are concentrated around the mean direction can be quantified using the mean resultant length, a measure known under many alternative names, such as the phase locking value or the Kuramoto order parameter. For maximal concentration, achieved when all of the data take the same value, the mean resultant length attains its upper bound of one. However, for a random sample drawn from the circular uniform distribution, the expected value of the mean resultant length achieves its lower bound of zero only as the sample size tends to infinity. Moreover, as the expected value of the mean resultant length depends on the sample size, bias is induced when comparing the mean resultant lengths of samples of different sizes. In order to ameliorate this problem, here, we introduce a re-normalized version of the mean resultant length. Regardless of the sample size, the re-normalized measure has an expected value that is essentially zero for a random sample from the circular uniform distribution, takes intermediate values for partially concentrated unimodal data, and attains its upper bound of one for maximal concentration. The re-normalized measure retains the simplicity of the original mean resultant length and is, therefore, easy to implement and compute. We illustrate the relevance and effectiveness of the proposed re-normalized measure for mathematical models and electroencephalographic recordings of an epileptic seizure.

An empirical study on network conversion of stock time series based on STL method

A complex network has been widely used to reveal the rule of a complex system. How to convert the stock data into a network is an open issue since the stock data are so large and their random volatility is strong. In this paper, a seasonal trend decomposition procedure based on the loess ( S T L) method is applied to convert the stock time series into a directed and weighted symbolic network. Three empirical stock datasets, including the closing price of Shanghai Securities Composite Index, S&P 500 Index, and Nikkei 225 Index, are considered. The properties of these stock time series are revealed from the topological characteristics of corresponding symbolic networks. The results show that: (1) both the weighted indegree and outdegree distributions obey the power-law distribution well; (2) fluctuations of stock closing price are revealed by related network topological properties, such as weighting degree, betweenness, pageranks, and clustering coefficient; and (3) stock closing price, in particular, periods such as financial crises, can be identified by modularity class of the symbolic networks. Moreover, the comparison between the S T L method and the visibility graph further highlights the advantages of the S T L method in terms of the time complexity of the algorithm. Our method offers a new idea to study the network conversion of stock time series.

Phase irregularity: A conceptually simple and efficient approach to characterize electroencephalographic recordings from epilepsy patients

The severe neurological disorder epilepsy affects almost 1% of the world population. For patients who suffer from pharmacoresistant focal-onset epilepsy, electroencephalographic (EEG) recordings are essential for the localization of the brain area where seizures start. Apart from the visual inspection of the recordings, quantitative EEG signal analysis techniques proved to be useful for this purpose. Among other features, regularity versus irregularity and phase coherence versus phase independence allowed characterizing brain dynamics from the measured EEG signals. Can phase irregularities also characterize brain dynamics? To address this question, we use the univariate coefficient of phase velocity variation, defined as the ratio of phase velocity standard deviation and the mean phase velocity. Beyond that, as a bivariate measure we use the classical mean phase coherence to quantify the degree of phase locking. All phase-based measures are combined with surrogates to test null hypotheses about the dynamics underlying the signals. In the first part of our analysis, we use the Rössler model system to study our approach under controlled conditions. In the second part, we use the Bern-Barcelona EEG database which consists of focal and nonfocal signals extracted from seizure-free recordings. Focal signals are recorded from brain areas where the first seizure EEG signal changes can be detected, and nonfocal signals are recorded from areas that are not involved in the seizure at its onset. Our results show that focal signals have less phase variability and more phase coherence than nonfocal signals. Once combined with surrogates, the mean phase velocity proved to have the highest discriminative power between focal and nonfocal signals. In conclusion, conceptually simple and easy to compute phase-based measures can help to detect features induced by epilepsy from EEG signals. This holds not only for the classical mean phase coherence but even more so for univariate measures of phase irregularity.

Fractal analysis of recurrence networks constructed from the two-dimensional fractional Brownian motions

In this study, we focus on the fractal property of recurrence networks constructed from the two-dimensional fractional Brownian motion (2D fBm), i.e., the inter-system recurrence network, the joint recurrence network, the cross-joint recurrence network, and the multidimensional recurrence network, which are the variants of classic recurrence networks extended for multiple time series. Generally, the fractal dimension of these recurrence networks can only be estimated numerically. The numerical analysis identifies the existence of fractality in these constructed recurrence networks. Furthermore, it is found that the numerically estimated fractal dimension of these networks can be connected to the theoretical fractal dimension of the 2D fBm graphs, because both fractal dimensions are piecewisely associated with the Hurst exponent H in a highly similar pattern, i.e., a linear decrease (if H varies from 0 to 0.5) followed by an inversely proportional-like decay (if H changes from 0.5 to 1). Although their fractal dimensions are not exactly identical, their difference can actually be deciphered by one single parameter with the value around 1. Therefore, it can be concluded that these recurrence networks constructed from the 2D fBms must inherit some fractal properties of its associated 2D fBms with respect to the fBm graphs.

Detecting Abnormal Pattern of Epileptic Seizures via Temporal Synchronization of EEG Signals

OBJECTIVE

Synchronization phenomena of epileptic electroencephalography (EEG) have long been studied. In this study, we aim at investigating the spatial-temporal synchronization pattern in epileptic human brains using the spectral graph theoretic features extracted from scalp EEG and developing an efficient multivariate approach for detecting seizure onsets in real time.

METHODS

A complex network model is used for representing the recurrence pattern of EEG signals, based on which the temporal synchronization patterns are quantified using the spectral graph theoretic features. Furthermore, a statistical control chart is applied to the extracted features overtime for monitoring the transits from normal to epileptic states in multivariate EEG systems.

RESULTS

Our method is tested on 23 patients from CHB-MIT Scalp EEG database. The results show that the graph theoretic feature yields a high sensitivity (  ∼ 98%) and low latency (  ∼ 6 s) on average, and seizure onsets in 18 patients are 100% detected.

CONCLUSION

Our approach validates the increased temporal synchronization in epileptic EEG and achieves a comparable detection performance to previous studies.

SIGNIFICANCE

We characterize the temporal synchronization patterns of epileptic EEG using spectral network metrics. In addition, we found significant changes in temporal synchronization in epileptic EEG, which enable a patient-specific approach for real-time seizure detection for personalized diagnosis and treatment.

Multifractality in individual honeybee behavior hints at colony-specific social cascades: Reanalysis of radio-frequency identification data from five different colonies

Honeybees (Apis mellifera) exhibit complex coordination and interaction across multiple behaviors such as swarming. This coordination among honeybees in the same colony is remarkably similar to the concept of informational cascades. The multifractal geometry of cascades suggests that multifractal measures of individual honeybee activity might carry signatures of these colony-wide coordinations. The present work reanalyzes time stamps of entrances to and exits from the hive captured by radio-frequency identification (RFID) sensors reading RFID tags on individual bees. Indeed, both multifractal spectrum width for individual bees' inter-reading interval series and differences of those widths from surrogates significantly predicted not just whether the individual bee's hive had a mesh enclosure but also predicted the specific membership of individual bees in one of five colonies. The significant effects of multifractality in matching honeybee activity to type of colony and, further, matching individual honeybees to their exact home colony suggests that multifractality quantifies key features of the colony-wide interactions across many scales. This relevance of multifractality to predicting colony type or colony membership adds additional credence to the cascade metaphor for colony organization. Perhaps, multifractality provides a new tool for exploring the relationship between individual organisms and larger, more complex social behaviors.

Time evolution of interhemispheric coupling in a model of focal neocortical epilepsy in mice

Epilepsy is characterized by substantial network rearrangements leading to spontaneous seizures and little is known on how an epileptogenic focus impacts on neural activity in the contralateral hemisphere. Here, we used a model of unilateral epilepsy induced by injection of the synaptic blocker tetanus neurotoxin (TeNT) in the mouse primary visual cortex (V1). Local field potential (LFP) signals were simultaneously recorded from both hemispheres of each mouse in acute phase (peak of toxin action) and chronic condition (completion of TeNT effects). To characterize the neural electrical activities the corresponding LFP signals were analyzed with several methods of time series analysis. For the epileptic mice, the spectral analysis showed that TeNT determines a power redistribution among the different neurophysiological bands in both acute and chronic phases. Using linear and nonlinear interdependence measures in both time and frequency domains, it was found in the acute phase that TeNT injection promotes a reduction of the interhemispheric coupling for high frequencies (12-30 Hz) and small time lag (<20 ms), whereas an increase of the coupling is present for low frequencies (0.5-4 Hz) and long time lag (>40 ms). On the other hand, the chronic period is characterized by a partial or complete recovery of the interhemispheric interdependence level. Granger causality test and symbolic transfer entropy indicate a greater driving influence of the TeNT-injected side on activity in the contralateral hemisphere in the chronic phase. Lastly, based on experimental observations, we built a computational model of LFPs to investigate the role of the ipsilateral inhibition and exicitatory interhemispheric connections in the dampening of the interhemispheric coupling. The time evolution of the interhemispheric coupling in such a relevant model of epilepsy has been addressed here.

Signatures of chaotic and stochastic dynamics uncovered with ε -recurrence networks

An old and important problem in the field of nonlinear time-series analysis entails the distinction between chaotic and stochastic dynamics. Recently, ε -recurrence networks have been proposed as a tool to analyse the structural properties of a time series. In this paper, we propose the applicability of local and global ε -recurrence network measures to distinguish between chaotic and stochastic dynamics using paradigmatic model systems such as the Lorenz system, and the chaotic and hyper-chaotic Rössler system. We also demonstrate the effect of increasing levels of noise on these network measures and provide a real-world application of analysing electroencephalographic data comprising epileptic seizures. Our results show that both local and global ε -recurrence network measures are sensitive to the presence of unstable periodic orbits and other structural features associated with chaotic dynamics that are otherwise absent in stochastic dynamics. These network measures are still robust at high noise levels and short data lengths. Furthermore, ε -recurrence network analysis of the real-world epileptic data revealed the capability of these network measures in capturing dynamical transitions using short window sizes. ε -recurrence network analysis is a powerful method in uncovering the signatures of chaotic and stochastic dynamics based on the geometrical properties of time series.

MRI characterization of temporal lobe epilepsy using rapidly measurable spatial indices with hemisphere asymmetries and gender features

INTRODUCTION

The paucity of morphometric markers for hemispheric asymmetries and gender variations in hippocampi and amygdalae in temporal lobe epilepsy (TLE) calls for better characterization of TLE by finding more useful prognostic MRI parameter(s).

METHODS

T1-weighted MRI (3 T) morphometry using multiple parameters of hippocampus-parahippocampus (angular and linear measures, volumetry) and amygdalae (volumetry) including their hemispheric asymmetry indices (AI) were evaluated in both genders. The cutoff values of parameters were statistically estimated from measurements of healthy subjects to characterize TLE (57 patients, 55% male) alterations.

RESULTS

TLE had differential categories with hippocampal atrophy, parahippocampal angle (PHA) acuteness, and several other parametric changes. Bilateral TLE categories were much more prevalent compared to unilateral TLE categories. Female patients were considerably more disposed to bilateral TLE categories than male patients. Male patients displayed diverse categories of unilateral abnormalities. Few patients (both genders) had combined bilateral appearances of hippocampal atrophy, amygdala atrophy, PHA acuteness, and increase in hippocampal angle (HA) where medial distance ratio (MDR) varied among genders. TLE had gender-specific and hemispheric dominant alterations in AI of parameters. Maximum magnitude of parametric changes in TLE includes (a) AI increase in HA of both genders, (b) HA increase (bilateral) in female patients, and (c) increase in ratio of amygdale/hippocampal volume (unilateral, right hemispheric), and AI decrease in MDR, in male patients.

CONCLUSION

Multiparametric MRI studies of hippocampus and amygdalae, including their hemispheric asymmetry, underscore better characterization of TLE. Rapidly measurable single-slice parameters (HA, PHA, MDR) can readily delineate TLE in a time-constrained clinical setting, which contrasts with customary three-dimensional hippocampal volumetry that requires many slice computation.

Recurrence network analysis of multiple local field potential bands from the orofacial portion of primary motor cortex

Local field potentials (LFPs), which have been considered as aggregate signals that reflect activities of a large number of neurons in the cerebral cortex, have been observed to mediate gross functional activities of a relatively small volume of the brain tissues. Historically there have been several frequency bands observed and defined across various brain areas. However, detailed analysis, either spectral analysis or any dynamical analysis of LFPs particularly in the orofacial part of the primary motor cortex (MIo) has not been done before. Here, we recorded LFPs from MIo using an electrode array from a non-human primate during feeding behavior. Then we performed spectral analysis during the whole feeding sequences and to characterize temporal evolution of spectrum around the time of swallow cycles. The spectrogram over the β range showed dynamical change in its power around the swallow cycle onsets. We then characterized dynamical behaviors of LFPs over multiple bands, α, β, low γ, and high γ using two measures from the recurrence network (RN) method, network transitivity, T and average path length L. Temporal profile of T in α and β indicated that there was a sudden change in the dynamical properties around the swallow cycle onsets, while temporal profile of L indicated that a range of -200 to -150 ms and 200 ms to the swallow cycle onsets exhibited large changes both in α and β ranges. Therefore, to further understand the involvement of cortical oscillation to behavior, particularly swallowing, the combination of traditional spectral methods and various dynamical methods such as RN method would be essential.