Using bivariate signal analysis to characterize the epileptic focus: the benefit of surrogates

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.

Epileptic spasms are associated with increased stereo-electroencephalography derived functional connectivity in tuberous sclerosis complex

OBJECTIVE

Epileptic spasms (ES) are common in tuberous sclerosis complex (TSC). However, the underlying network alterations and relationship with epileptogenic tubers are poorly understood. We examined interictal functional connectivity (FC) using stereo-electroencephalography (SEEG) in patients with TSC to investigate the relationship between tubers, epileptogenicity, and ES.

METHODS

We analyzed 18 patients with TSC who underwent SEEG (mean age = 11.5 years). The dominant tuber (DT) was defined as the most epileptogenic tuber using the epileptogenicity index. Epileptogenic zone (EZ) organization was quantitatively separated into focal (isolated DT) and complex (all other patterns). Using a 20-min interictal recording, FC was estimated with nonlinear regression, h² . We calculated (1) intrazone FC within all sampled tubers and normal-appearing cortical zones, respectively; and (2) interzone FC involving connections between DT, other tubers, and normal cortex. The relationship between FC and (1) presence of ES as a current seizure type at the time of SEEG, (2) EZ organization, and (3) epileptogenicity was analyzed using a mixed generalized linear model. Spike rate and distance between zones were considered in the model as covariates.

RESULTS

Six patients had ES as a current seizure type at time of SEEG. ES patients had a greater number of tubers with a fluid-attenuated inversion recovery hypointense center (p < .001), and none had TSC1 mutations. The presence of ES was independently associated with increased FC within both intrazone (p = .033) and interzone (p = .011) networks. Post hoc analyses identified that increased FC was associated with ES across tuber and nontuber networks. EZ organization and epileptogenicity biomarkers were not associated with FC.

SIGNIFICANCE

Increased cortical synchrony among both tuber and nontuber networks is characteristic of patients with ES and independent of both EZ organization and tuber epileptogenicity. This further supports the prospect of FC biomarkers aiding treatment paradigms in TSC.

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.

More Than Spikes: On the Added Value of Non-linear Intracranial EEG Analysis for Surgery Planning in Temporal Lobe Epilepsy

Epilepsy surgery can be a very effective therapy in medication refractory patients. During patient evaluation intracranial EEG is analyzed by clinical experts to identify the brain tissue generating epileptiform events. Quantitative EEG analysis increasingly complements this approach in research settings, but not yet in clinical routine. We investigate the correspondence between epileptiform events and a specific quantitative EEG marker. We analyzed 99 preictal epochs of multichannel intracranial EEG of 40 patients with mixed etiologies. Time and channel of occurrence of epileptiform events (spikes, slow waves, sharp waves, fast oscillations) were annotated by a human expert and non-linear excess interrelations were calculated as a quantitative EEG marker. We assessed whether the visually identified preictal events predicted channels that belonged to the seizure onset zone, that were later resected or that showed strong non-linear interrelations. We also investigated whether the seizure onset zone or the resection were predicted by channels with strong non-linear interrelations. In patients with temporal lobe epilepsy (32 of 40), epileptic spikes and the seizure onset zone predicted the resected brain tissue much better in patients with favorable seizure control after surgery than in unfavorable outcomes. Beyond that, our analysis did not reveal any significant associations with epileptiform EEG events. Specifically, none of the epileptiform event types did predict non-linear interrelations. In contrast, channels with strong non-linear excess EEG interrelations predicted the resected channels better in patients with temporal lobe epilepsy and favorable outcome. Also in the small number of patients with seizure onset in the frontal and parietal lobes, no association between epileptiform events and channels with strong non-linear excess EEG interrelations was detectable. In contrast to patients with temporal seizure onset, EEG channels with strong non-linear excess interrelations did neither predict the seizure onset zone nor the resection of these patients or allow separation between patients with favorable and unfavorable seizure control. Our study indicates that non-linear excess EEG interrelations are not strictly associated with epileptiform events, which are one key concept of current clinical EEG assessment. Rather, they may provide information relevant for surgery planning in temporal lobe epilepsy. Our study suggests to incorporate quantitative EEG analysis in the workup of clinical cases. We make the EEG epochs and expert annotations publicly available in anonymized form to foster similar analyses for other quantitative EEG methods.

Seizure Onset Zone Lateralization Using a Non-linear Analysis of Micro vs. Macro Electroencephalographic Recordings During Seizure-Free Stages of the Sleep-Wake Cycle From Epilepsy Patients

The application of non-linear signal analysis techniques to biomedical data is key to improve our knowledge about complex physiological and pathological processes. In particular, the use of non-linear techniques to study electroencephalographic (EEG) recordings can provide an advanced characterization of brain dynamics. In epilepsy these dynamics are altered at different spatial scales of neuronal organization. We therefore apply non-linear signal analysis to EEG recordings from epilepsy patients derived with intracranial hybrid electrodes, which are composed of classical macro contacts and micro wires. Thereby, these electrodes record EEG at two different spatial scales. Our aim is to test the degree to which the analysis of the EEG recorded at these different scales allows us to characterize the neuronal dynamics affected by epilepsy. For this purpose, we retrospectively analyzed long-term recordings performed during five nights in three patients during which no seizures took place. As a benchmark we used the accuracy with which this analysis allows determining the hemisphere that contains the seizure onset zone, which is the brain area where clinical seizures originate. We applied the surrogate-corrected non-linear predictability score (ψ), a non-linear signal analysis technique which was shown previously to be useful for the lateralization of the seizure onset zone from classical intracranial EEG macro contact recordings. Higher values of ψ were found predominantly for signals recorded from the hemisphere containing the seizure onset zone as compared to signals recorded from the opposite hemisphere. These differences were found not only for the EEG signals recorded with macro contacts, but also for those recorded with micro wires. In conclusion, the information obtained from the analysis of classical macro EEG contacts can be complemented by the one of micro wire EEG recordings. This combined approach may therefore help to further improve the degree to which quantitative EEG analysis can contribute to the diagnostics in epilepsy patients.

Linear and nonlinear interrelations show fundamentally distinct network structure in preictal intracranial EEG of epilepsy patients

Resection of the seizure generating tissue can be highly beneficial in patients with drug-resistant epilepsy. However, only about half of all patients undergoing surgery get permanently and completely seizure free. Investigating the dependences between intracranial EEG signals adds a multivariate perspective largely unavailable to visual EEG analysis, which is the current clinical practice. We examined linear and nonlinear interrelations between intracranial EEG signals regarding their spatial distribution and network characteristics. The analyzed signals were recorded immediately before clinical seizure onset in epilepsy patients who received a standardized electrode implantation targeting the mesiotemporal structures. The linear interrelation networks were predominantly locally connected and highly reproducible between patients. In contrast, the nonlinear networks had a clearly centralized structure, which was specific for the individual pathology. The nonlinear interrelations were overrepresented in the focal hemisphere and in patients with no or only rare seizures after surgery specifically in the resected tissue. Connections to the outside were predominantly nonlinear. In all patients without worthwhile improvement after resective treatment, tissue producing strong nonlinear interrelations was left untouched by surgery. Our findings indicate that linear and nonlinear interrelations play fundamentally different roles in preictal intracranial EEG. Moreover, they suggest nonlinear signal interrelations to be a marker of epileptogenic tissue and not a characteristic of the mesiotemporal structures. Our results corroborate the network-based nature of epilepsy and suggest the application of network analysis to support the planning of resective epilepsy surgery.

Inferring directed networks using a rank-based connectivity measure

Inferring the topology of a network using the knowledge of the signals of each of the interacting units is key to understanding real-world systems. One way to address this problem is using data-driven methods like cross-correlation or mutual information. However, these measures lack the ability to distinguish the direction of coupling. Here, we use a rank-based nonlinear interdependence measure originally developed for pairs of signals. This measure not only allows one to measure the strength but also the direction of the coupling. Our results for a system of coupled Lorenz dynamics show that we are able to consistently infer the underlying network for a subrange of the coupling strength and link density. Furthermore, we report that the addition of dynamical noise can benefit the reconstruction. Finally, we show an application to multichannel electroencephalographic recordings from an epilepsy patient.

Robustness and versatility of a nonlinear interdependence method for directional coupling detection from spike trains

The detection of directional couplings between dynamics based on measured spike trains is a crucial problem in the understanding of many different systems. In particular, in neuroscience it is important to assess the connectivity between neurons. One of the approaches that can estimate directional coupling from the analysis of point processes is the nonlinear interdependence measure L. Although its efficacy has already been demonstrated, it still needs to be tested under more challenging and realistic conditions prior to an application to real data. Thus, in this paper we use the Hindmarsh-Rose model system to test the method in the presence of noise and for different spiking regimes. We also examine the influence of different parameters and spike train distances. Our results show that the measure L is versatile and robust to various types of noise, and thus suitable for application to experimental data.

Reconstructing networks of pulse-coupled oscillators from spike trains

We present an approach for reconstructing networks of pulse-coupled neuronlike oscillators from passive observation of pulse trains of all nodes. It is assumed that units are described by their phase response curves and that their phases are instantaneously reset by incoming pulses. Using an iterative procedure, we recover the properties of all nodes, namely their phase response curves and natural frequencies, as well as strengths of all directed connections.

WONOEP appraisal: Development of epilepsy biomarkers-What we can learn from our patients?

OBJECTIVE

Current medications for patients with epilepsy work in only two of three patients. For those medications that do work, they only suppress seizures. They treat the symptoms, but do not modify the underlying disease, forcing patients to take these drugs with significant side effects, often for the rest of their lives. A major limitation in our ability to advance new therapeutics that permanently prevent, reduce the frequency of, or cure epilepsy comes from a lack of understanding of the disease coupled with a lack of reliable biomarkers that can predict who has or who will get epilepsy.

METHODS

The main goal of this report is to present a number of approaches for identifying reliable biomarkers from observing patients with brain disorders that have a high probability of producing epilepsy.

RESULTS

A given biomarker, or more likely a profile of biomarkers, will have both a quantity and a time course during epileptogenesis that can be used to predict who will get the disease, to confirm epilepsy as a diagnosis, to identify coexisting pathologies, and to monitor the course of treatments.

SIGNIFICANCE

Additional studies in patients and animal models could identify common and clinically valuable biomarkers to successfully translate animal studies into new and effective clinical trials.

EEG synchronization measures are early outcome predictors in comatose patients after cardiac arrest

OBJECTIVE

Outcome prognostication in comatose patients after cardiac arrest (CA) remains a major challenge. Here we investigated the prognostic value of combinations of linear and non-linear bivariate EEG synchronization measures.

METHODS

94 comatose patients with EEG within 24h after CA were included. Clinical outcome was assessed at 3months using the Cerebral Performance Categories (CPC). EEG synchronization between the left and right parasagittal, and between the frontal and parietal brain regions was assessed with 4 different quantitative measures (delta power asymmetry, cross-correlation, mutual information, and transfer entropy). 2/3 of patients were used to assess the predictive power of all possible combinations of these eight features (4 measures×2 directions) using cross-validation. The predictive power of the best combination was tested on the remaining 1/3 of patients.

RESULTS

The best combination for prognostication consisted of 4 of the 8 features, and contained linear and non-linear measures. Predictive power for poor outcome (CPC 3-5), measured with the area under the ROC curve, was 0.84 during cross-validation, and 0.81 on the test set. At specificity of 1.0 the sensitivity was 0.54, and the accuracy 0.81.

CONCLUSION

Combinations of EEG synchronization measures can contribute to early prognostication after CA. In particular, combining linear and non-linear measures is important for good predictive power.

SIGNIFICANCE

Quantitative methods might increase the prognostic yield of currently used multi-modal approaches.

Coupling strength versus coupling impact in nonidentical bidirectionally coupled dynamics

The understanding of interacting dynamics is important for the characterization of real-world networks. In general, real-world networks are heterogeneous in the sense that each node of the network is a dynamics with different properties. For coupled nonidentical dynamics symmetric interactions are not straightforwardly defined from the coupling strength values. Thus, a challenging issue is whether we can define a symmetric interaction in this asymmetric setting. To address this problem we introduce the notion of the coupling impact. The coupling impact considers not only the coupling strength but also the energy of the individual dynamics, which is conveyed via the coupling. To illustrate this concept, we follow a data-driven approach by analyzing signals from pairs of coupled model dynamics using two different connectivity measures. We find that the coupling impact, but not the coupling strength, correctly detects a symmetric interaction between pairs of coupled dynamics regardless of their degree of asymmetry. Therefore, this approach allows us to reveal the real impact that one dynamics has on the other and hence to define symmetric interactions in pairs of nonidentical dynamics.

Weighted and directed interactions in evolving large-scale epileptic brain networks

Epilepsy can be regarded as a network phenomenon with functionally and/or structurally aberrant connections in the brain. Over the past years, concepts and methods from network theory substantially contributed to improve the characterization of structure and function of these epileptic networks and thus to advance understanding of the dynamical disease epilepsy. We extend this promising line of research and assess-with high spatial and temporal resolution and using complementary analysis approaches that capture different characteristics of the complex dynamics-both strength and direction of interactions in evolving large-scale epileptic brain networks of 35 patients that suffered from drug-resistant focal seizures with different anatomical onset locations. Despite this heterogeneity, we find that even during the seizure-free interval the seizure onset zone is a brain region that, when averaged over time, exerts strongest directed influences over other brain regions being part of a large-scale network. This crucial role, however, manifested by averaging on the population-sample level only - in more than one third of patients, strongest directed interactions can be observed between brain regions far off the seizure onset zone. This may guide new developments for individualized diagnosis, treatment and control.

All together now: Analogies between chimera state collapses and epileptic seizures

Conceptually and structurally simple mathematical models of coupled oscillator networks can show a rich variety of complex dynamics, providing fundamental insights into many real-world phenomena. A recent and not yet fully understood example is the collapse of coexisting synchronous and asynchronous oscillations into a globally synchronous motion found in networks of identical oscillators. Here we show that this sudden collapse is promoted by a further decrease of synchronization, rather than by critically high synchronization. This strikingly counterintuitive mechanism can be found also in nature, as we demonstrate on epileptic seizures in humans. Analyzing spatiotemporal correlation profiles derived from intracranial electroencephalographic recordings (EEG) of seizures in epilepsy patients, we found a pronounced decrease of correlation at the seizure onsets. Applying our findings in a closed-loop control scheme to models of coupled oscillators in chimera states, we succeed in both provoking and preventing outbreaks of global synchronization. Our findings not only advance the understanding of networks of coupled dynamics but can open new ways to control them, thus offering a vast range of potential new applications.

Computing network-based features from intracranial EEG time series data: Application to seizure focus localization

The surgical resection of the epileptogenic zone (EZ) is the only effective treatment for many drug-resistant epilepsy (DRE) patients, but the pre-surgical identification of the EZ is challenging. This study investigates whether the EZ exhibits a computationally identifiable signature during seizures. In particular, we compute statistics of the brain network from intracranial EEG (iEEG) recordings and track the evolution of network connectivity before, during, and after seizures. We define each node in the network as an electrode and weight each edge connecting a pair of nodes by the gamma band cross power of the corresponding iEEG signals. The eigenvector centrality (EVC) of each node is tracked over two seizures per patient and the electrodes are ranked according to the corresponding EVC value. We hypothesize that electrodes covering the EZ have a signature EVC rank evolution during seizure that differs from electrodes outside the EZ. We tested this hypothesis on multi-channel iEEG recordings from 2 DRE patients who had successful surgery (i.e., seizures were under control with or without medications) and 1 patient who had unsuccessful surgery. In the successful cases, we assumed that the resected region contained the EZ and found that the EVC rank evolution of the electrodes within the resected region had a distinct "arc" signature, i.e., the EZ ranks first rose together shortly after seizure onset and then fell later during seizure.

Resected Brain Tissue, Seizure Onset Zone and Quantitative EEG Measures: Towards Prediction of Post-Surgical Seizure Control

BACKGROUND

Epilepsy surgery is a potentially curative treatment option for pharmacoresistent patients. If non-invasive methods alone do not allow to delineate the epileptogenic brain areas the surgical candidates undergo long-term monitoring with intracranial EEG. Visual EEG analysis is then used to identify the seizure onset zone for targeted resection as a standard procedure.

METHODS

Despite of its great potential to assess the epileptogenicty of brain tissue, quantitative EEG analysis has not yet found its way into routine clinical practice. To demonstrate that quantitative EEG may yield clinically highly relevant information we retrospectively investigated how post-operative seizure control is associated with four selected EEG measures evaluated in the resected brain tissue and the seizure onset zone. Importantly, the exact spatial location of the intracranial electrodes was determined by coregistration of pre-operative MRI and post-implantation CT and coregistration with post-resection MRI was used to delineate the extent of tissue resection. Using data-driven thresholding, quantitative EEG results were separated into normally contributing and salient channels.

RESULTS

In patients with favorable post-surgical seizure control a significantly larger fraction of salient channels in three of the four quantitative EEG measures was resected than in patients with unfavorable outcome in terms of seizure control (median over the whole peri-ictal recordings). The same statistics revealed no association with post-operative seizure control when EEG channels contributing to the seizure onset zone were studied.

CONCLUSIONS

We conclude that quantitative EEG measures provide clinically relevant and objective markers of target tissue, which may be used to optimize epilepsy surgery. The finding that differentiation between favorable and unfavorable outcome was better for the fraction of salient values in the resected brain tissue than in the seizure onset zone is consistent with growing evidence that spatially extended networks might be more relevant for seizure generation, evolution and termination than a single highly localized brain region (i.e. a "focus") where seizures start.

Nonlinear dynamics of mood regulation in bipolar disorder

OBJECTIVES

We sought to study the underlying dynamic processes involved in mood regulation in subjects with bipolar disorder and healthy control subjects using time-series analysis and to then analyze the relation between anxiety and mood using cross-correlation techniques.

METHODS

We recruited 30 healthy controls and 30 euthymic patients with bipolar disorder. Participants rated their mood, anxiety, and energy levels using a paper-based visual analog scale; and they also recorded their sleep and any life events. Information on these variables was provided over a three-month period on a daily basis, twice per day. We analyzed the data using Box-Jenkins time series analysis to obtain information on the autocorrelation of the series (for mood) and cross-correlation (mood and anxiety series).

RESULTS

Throughout the study, we analyzed 10,170 data points. Self-ratings for mood, anxiety, and energy were normally distributed in both groups. Autocorrelation functions for mood in both groups were governed by the autoregressive integrated moving average (ARIMA) (1,1,0) model, which means that current values in the series were related to one previous point only. We also found a negative cross-correlation between mood and anxiety.

CONCLUSIONS

Mood can be considered a memory stochastic process; it is a flexible, dynamic process that has a 'short memory' both in healthy controls and euthymic patients with bipolar disorder. This process may be quite different in untreated patients or in those acutely ill. Our results suggest that nonlinear measures can be applied to the study of mood disorders.

Assessing directionality and strength of coupling through symbolic analysis: an application to epilepsy patients

Inferring strength and direction of interactions from electroencephalographic (EEG) recordings is of crucial importance to improve our understanding of dynamical interdependencies underlying various physiological and pathophysiological conditions in the human epileptic brain. We here use approaches from symbolic analysis to investigate--in a time-resolved manner--weighted and directed, short- to long-ranged interactions between various brain regions constituting the epileptic network. Our observations point to complex spatial-temporal interdependencies underlying the epileptic process and their role in the generation of epileptic seizures, despite the massive reduction of the complex information content of multi-day, multi-channel EEG recordings through symbolization. We discuss limitations and potential future improvements of this approach.

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

Recently Andrezejak et al. combined the randomness and nonlinear independence test with iterative amplitude adjusted Fourier transform (iAAFT) surrogates to distinguish between the dynamics of seizure-free intracranial electroencephalographic (EEG) signals recorded from epileptogenic (focal) and nonepileptogenic (nonfocal) brain areas of epileptic patients. However, stationarity is a part of the null hypothesis for iAAFT surrogates and thus nonstationarity can violate the null hypothesis. In this work we first propose the application of the randomness and nonlinear independence test based on recurrence network measures to distinguish between the dynamics of focal and nonfocal EEG signals. Furthermore, we combine these tests with both iAAFT and truncated Fourier transform (TFT) surrogate methods, which also preserves the nonstationarity of the original data in the surrogates along with its linear structure. Our results indicate that focal EEG signals exhibit an increased degree of structural complexity and interdependency compared to nonfocal EEG signals. In general, we find higher rejections for randomness and nonlinear independence tests for focal EEG signals compared to nonfocal EEG signals. In particular, the univariate recurrence network measures, the average clustering coefficient C and assortativity R, and the bivariate recurrence network measure, the average cross-clustering coefficient C(cross), can successfully distinguish between the focal and nonfocal EEG signals, even when the analysis is restricted to nonstationary signals, irrespective of the type of surrogates used. On the other hand, we find that the univariate recurrence network measures, the average path length L, and the average betweenness centrality BC fail to distinguish between the focal and nonfocal EEG signals when iAAFT surrogates are used. However, these two measures can distinguish between focal and nonfocal EEG signals when TFT surrogates are used for nonstationary signals. We also report an improvement in the performance of nonlinear prediction error N and nonlinear interdependence measure L used by Andrezejak et al., when TFT surrogates are used for nonstationary EEG signals. We also find that the outcome of the nonlinear independence test based on the average cross-clustering coefficient C(cross) is independent of the outcome of the randomness test based on the average clustering coefficient C. Thus, the univariate and bivariate recurrence network measures provide independent information regarding the dynamics of the focal and nonfocal EEG signals. In conclusion, recurrence network analysis combined with nonstationary surrogates can be applied to derive reliable biomarkers to distinguish between epileptogenic and nonepileptogenic brain areas using EEG signals.

Network dynamics of the brain and influence of the epileptic seizure onset zone

The human brain is a dynamic networked system. Patients with partial epileptic seizures have focal regions that periodically diverge from normal brain network dynamics during seizures. We studied the evolution of brain connectivity before, during, and after seizures with graph-theoretic techniques on continuous electrocorticographic (ECoG) recordings (5.4 ± 1.7 d per patient, mean ± SD) from 12 patients with temporal, occipital, or frontal lobe partial onset seizures. Each electrode was considered a node in a graph, and edges between pairs of nodes were weighted by their coherence within a frequency band. The leading eigenvector of the connectivity matrix, which captures network structure, was tracked over time and clustered to uncover a finite set of brain network states. Across patients, we found that (i) the network connectivity is structured and defines a finite set of brain states, (ii) seizures are characterized by a consistent sequence of states, (iii) a subset of nodes is isolated from the network at seizure onset and becomes more connected with the network toward seizure termination, and (iv) the isolated nodes may identify the seizure onset zone with high specificity and sensitivity. To localize a seizure, clinicians visually inspect seizures recorded from multiple intracranial electrode contacts, a time-consuming process that may not always result in definitive localization. We show that network metrics computed from all ECoG channels capture the dynamics of the seizure onset zone as it diverges from normal overall network structure. This suggests that a state space model can be used to help localize the seizure onset zone in ECoG recordings.

Detecting determinism with improved sensitivity in time series: rank-based nonlinear predictability score

The rank-based nonlinear predictability score was recently introduced as a test for determinism in point processes. We here adapt this measure to time series sampled from time-continuous flows. We use noisy Lorenz signals to compare this approach against a classical amplitude-based nonlinear prediction error. Both measures show an almost identical robustness against Gaussian white noise. In contrast, when the amplitude distribution of the noise has a narrower central peak and heavier tails than the normal distribution, the rank-based nonlinear predictability score outperforms the amplitude-based nonlinear prediction error. For this type of noise, the nonlinear predictability score has a higher sensitivity for deterministic structure in noisy signals. It also yields a higher statistical power in a surrogate test of the null hypothesis of linear stochastic correlated signals. We show the high relevance of this improved performance in an application to electroencephalographic (EEG) recordings from epilepsy patients. Here the nonlinear predictability score again appears of higher sensitivity to nonrandomness. Importantly, it yields an improved contrast between signals recorded from brain areas where the first ictal EEG signal changes were detected (focal EEG signals) versus signals recorded from brain areas that were not involved at seizure onset (nonfocal EEG signals).

A novel dynamic update framework for epileptic seizure prediction

Epileptic seizure prediction is a difficult problem in clinical applications, and it has the potential to significantly improve the patients' daily lives whose seizures cannot be controlled by either drugs or surgery. However, most current studies of epileptic seizure prediction focus on high sensitivity and low false-positive rate only and lack the flexibility for a variety of epileptic seizures and patients' physical conditions. Therefore, a novel dynamic update framework for epileptic seizure prediction is proposed in this paper. In this framework, two basic sample pools are constructed and updated dynamically. Furthermore, the prediction model can be updated to be the most appropriate one for the prediction of seizures' arrival. Mahalanobis distance is introduced in this part to solve the problem of side information, measuring the distance between two data sets. In addition, a multichannel feature extraction method based on Hilbert-Huang transform and extreme learning machine is utilized to extract the features of a patient's preseizure state against the normal state. At last, a dynamic update epileptic seizure prediction system is built up. Simulations on Freiburg database show that the proposed system has a better performance than the one without update. The research of this paper is significantly helpful for clinical applications, especially for the exploitation of online portable devices.

Brain state evolution during seizure and under anesthesia: a network-based analysis of stereotaxic eeg activity in drug-resistant epilepsy patients

Epilepsy is a neurological condition with a prevalence of 1%, and 14-34% have medically refractory epilepsy (MRE). Seizures in focal MRE are generated by a single epileptogenic zone (or focus), thus there is potentially a curative procedure - surgical resection. This procedure depends significantly on correct identification of the focus, which is often uncertain in clinical practice. In this study, we analyzed intracranial stereotaxic EEG (sEEG) data recorded in two human patients with drug-resistant epilepsy prior to undergoing resection surgery. We view the sEEG data as samples from the brain network and hypothesize that seizure foci can be identified based on their network connectivity during seizure. Specifically, we computed a time sequence of connectivity matrices from EEG recordings that represent network structure over time. For each patient, connectivity between electrodes was measured using the coherence in a given frequency band. Matrix structure was analyzed using singular value decomposition and the leading singular vector was used to estimate each electrode's time dependent centrality (importance to the network's connectivity). Our preliminary study suggests that seizure foci may be the most weakly connected regions in the brain during the beginning of a seizure and the most strongly connected regions towards the end of a seizure. Additionally, in one of the patients analyzed, the network connectivity under anesthesia highlights seizure foci. Ultimately, network centrality computed from sEEG activity may be used to develop an automated, reliable, and computationally efficient algorithm for identifying seizure foci.

Nonrandomness, nonlinear dependence, and nonstationarity of electroencephalographic recordings from epilepsy patients

To derive tests for randomness, nonlinear-independence, and stationarity, we combine surrogates with a nonlinear prediction error, a nonlinear interdependence measure, and linear variability measures, respectively. We apply these tests to intracranial electroencephalographic recordings (EEG) from patients suffering from pharmacoresistant focal-onset epilepsy. These recordings had been performed prior to and independent from our study as part of the epilepsy diagnostics. The clinical purpose of these recordings was to delineate the brain areas to be surgically removed in each individual patient in order to achieve seizure control. This allowed us to define two distinct sets of signals: One set of signals recorded from brain areas where the first ictal EEG signal changes were detected as judged by expert visual inspection ("focal signals") and one set of signals recorded from brain areas that were not involved at seizure onset ("nonfocal signals"). We find more rejections for both the randomness and the nonlinear-independence test for focal versus nonfocal signals. In contrast more rejections of the stationarity test are found for nonfocal signals. Furthermore, while for nonfocal signals the rejection of the stationarity test increases the rejection probability of the randomness and nonlinear-independence test substantially, we find a much weaker influence for the focal signals. In consequence, the contrast between the focal and nonfocal signals obtained from the randomness and nonlinear-independence test is further enhanced when we exclude signals for which the stationarity test is rejected. To study the dependence between the randomness and nonlinear-independence test we include only focal signals for which the stationarity test is not rejected. We show that the rejection of these two tests correlates across signals. The rejection of either test is, however, neither necessary nor sufficient for the rejection of the other test. Thus, our results suggest that EEG signals from epileptogenic brain areas are less random, more nonlinear-dependent, and more stationary compared to signals recorded from nonepileptogenic brain areas. We provide the data, source code, and detailed results in the public domain.

Stability of synchronization clusters and seizurability in temporal lobe epilepsy

PURPOSE

Identification of critical areas in presurgical evaluations of patients with temporal lobe epilepsy is the most important step prior to resection. According to the "epileptic focus model", localization of seizure onset zones is the main task to be accomplished. Nevertheless, a significant minority of epileptic patients continue to experience seizures after surgery (even when the focus is correctly located), an observation that is difficult to explain under this approach. However, if attention is shifted from a specific cortical location toward the network properties themselves, then the epileptic network model does allow us to explain unsuccessful surgical outcomes.

METHODS

The intraoperative electrocorticography records of 20 patients with temporal lobe epilepsy were analyzed in search of interictal synchronization clusters. Synchronization was analyzed, and the stability of highly synchronized areas was quantified. Surrogate data were constructed and used to statistically validate the results. Our results show the existence of highly localized and stable synchronization areas in both the lateral and the mesial areas of the temporal lobe ipsilateral to the clinical seizures. Synchronization areas seem to play a central role in the capacity of the epileptic network to generate clinical seizures. Resection of stable synchronization areas is associated with elimination of seizures; nonresection of synchronization clusters is associated with the persistence of seizures after surgery.

DISCUSSION

We suggest that synchronization clusters and their stability play a central role in the epileptic network, favoring seizure onset and propagation. We further speculate that the stability distribution of these synchronization areas would differentiate normal from pathologic cases.

Assessing directed interactions from neurophysiological signals--an overview

The study of synchronization phenomena in coupled dynamical systems is an active field of research in many scientific disciplines including the neurosciences. Over the last decades, a number of time series analysis techniques have been proposed to capture both linear and nonlinear aspects of interactions. While most of these techniques allow one to quantify the strength of interactions, developments that resulted from advances in nonlinear dynamics and in information and synchronization theory aim at assessing directed interactions. Most of these techniques, however, assume the underlying systems to be at least approximately stationary and require a large number of data points to robustly assess directed interactions. Recent extensions allow assessing directed interactions from short and transient signals and are particularly suited for the analysis of evoked and event-related activity.

Uniform approach to linear and nonlinear interrelation patterns in multivariate time series

Currently, a variety of linear and nonlinear measures is in use to investigate spatiotemporal interrelation patterns of multivariate time series. Whereas the former are by definition insensitive to nonlinear effects, the latter detect both nonlinear and linear interrelation. In the present contribution we employ a uniform surrogate-based approach, which is capable of disentangling interrelations that significantly exceed random effects and interrelations that significantly exceed linear correlation. The bivariate version of the proposed framework is explored using a simple model allowing for separate tuning of coupling and nonlinearity of interrelation. To demonstrate applicability of the approach to multivariate real-world time series we investigate resting state functional magnetic resonance imaging (rsfMRI) data of two healthy subjects as well as intracranial electroencephalograms (iEEG) of two epilepsy patients with focal onset seizures. The main findings are that for our rsfMRI data interrelations can be described by linear cross-correlation. Rejection of the null hypothesis of linear iEEG interrelation occurs predominantly for epileptogenic tissue as well as during epileptic seizures.