Multilayer brain networks can identify the epileptogenic zone and seizure dynamics

  1. Hossein Shahabi  Is a corresponding author
  2. Dileep R Nair
  3. Richard M Leahy
  1. Signal and Image Processing Institute, University of Southern California, United States
  2. Epilepsy Center, Cleveland Clinic Neurological Institute, United States

Abstract

Seizure generation, propagation, and termination occur through spatiotemporal brain networks. In this paper, we demonstrate the significance of large-scale brain interactions in high-frequency (80–200Hz) for the identification of the epileptogenic zone (EZ) and seizure evolution. To incorporate the continuity of neural dynamics, here we have modeled brain connectivity constructed from stereoelectroencephalography (SEEG) data during seizures using multilayer networks. After introducing a new measure of brain connectivity for temporal networks, named multilayer eigenvector centrality (mlEVC), we applied a consensus hierarchical clustering on the developed model to identify the EZ as a cluster of nodes with distinctive brain connectivity in the ictal period. Our algorithm could successfully predict electrodes inside the resected volume as EZ for 88% of participants, who all were seizure-free for at least 12 months after surgery. Our findings illustrated significant and unique desynchronization between EZ and the rest of the brain in the early to mid-seizure. We showed that aging and the duration of epilepsy intensify this desynchronization, which can be the outcome of abnormal neuroplasticity. Additionally, we illustrated that seizures evolve with various network topologies, confirming the existence of different epileptogenic networks in each patient. Our findings suggest not only the importance of early intervention in epilepsy but possible factors that correlate with disease severity. Moreover, by analyzing the propagation patterns of different seizures, we demonstrate the necessity of collecting sufficient data for identifying epileptogenic networks.

Editor's evaluation

This valuable work proposes new network-based algorithms for brain seizure characterisation that could improve the effectiveness of existing clinical treatment paradigms. The approach is supported by solid evidence. If validated and compared against existing biomarkers, it could shed light on mechanisms of disease progression. This work will be of interest to clinicians and researchers in epilepsy alike.

https://doi.org/10.7554/eLife.68531.sa0

Introduction

Investigating brain connectivity in epilepsy has attracted considerable attention (Kramer and Cash, 2012) since multiple different networks are involved in this neurological disorder (González Otárula et al., 2019; Kramer et al., 2010; van Diessen et al., 2013b). Large-scale epileptogenic networks consist of cortical and subcortical areas that are involved in seizure generation and propagation (Bartolomei et al., 2017). These networks can either represent an increase or decrease in brain synchrony (Khambhati et al., 2017; Kramer et al., 2010; Wendling et al., 2003; Yaffe et al., 2015) or elucidate regions traversed by ictal propagation which is referred to as traveling waves in studies with microscopic recordings (Martinet et al., 2017; Muller et al., 2018; Proix et al., 2018; Schevon et al., 2012; Smith et al., 2016; Weiss et al., 2013). This underlying association between brain areas in epilepsy can describe the seizure spread and termination processes (Kramer and Cash, 2012), explain seizure semiology (Chauvel and McGonigal, 2014), or assist in identifying the seizure onset zone (SOZ) (Burns et al., 2014). Traditionally, seizures have been considered to be characterized by a state of hypersynchrony. Yet recent work (Kramer and Cash, 2012) describes an early stage of desynchronization (Kramer et al., 2010; Schindler et al., 2010; Wendling et al., 2003) followed by synchronization amid seizure termination (Schindler et al., 2007; Schindler et al., 2008). Constructing connectivity maps with various recording techniques and different computational measures over a wide range of frequencies has given rise to different controversial perspectives on how seizures should be characterized (Jiruska et al., 2013). Few studies have examined the functional connectivity between SOZ and other areas of the brain during ictal periods. Electrocorticographic (ECoG) data suggested that for some patients the SOZ is isolated from the rest of the network early in the seizures allowing for SOZ detection in this way (Burns et al., 2014). It has also been suggested that ictal periods can be delineated by a steady series of states (Burns et al., 2014), although whether this is true in all patients remains controversial. Others have shown a decreased synchrony between SOZ and normal brain regions (Warren et al., 2010). It remains unclear how the degree of desynchronization is correlated with physiological parameters such as age and duration of epilepsy (van Diessen et al., 2013a).

Several studies have used multiunit recordings to explore ictal propagation networks (Martinet et al., 2017; Schevon et al., 2019; Schevon et al., 2012; Smith et al., 2016; Weiss et al., 2013). At the microscopic spatial scale, the hypersynchronous ictal core with high neural firing can be distinguished from the penumbra with relatively small and sparse firings (Schevon et al., 2012). In the early part of the seizure, the slow-moving ictal wavefront involves the core and surrounding areas. After recruitment, the low-frequency traveling waves rapidly propagate to other cortical regions (Smith et al., 2016) in a two-dimensional spatial scale (Martinet et al., 2017). However, the mechanism by which ictal discharges spread in the brain volume is still undetermined. The intense firing of neurons in the ictal core is characterized by high-frequency oscillations (HFOs) (Jefferys et al., 2012) in local field potentials (LFPs) (Weiss et al., 2013). The term HFOs has been attributed to brain activity, with multiple possible physiological and pathological neural mechanisms, between 80–500 Hz (Jacobs et al., 2012) or 30–600 Hz (Engel and da Silva, 2012). This includes high-gamma neural activities (80–200 Hz) (Ray and Maunsell, 2011) and broad-band high frequency (Arnulfo et al., 2020).

These oscillations have been analyzed for their value in SOZ localization (Höller et al., 2015; Liu et al., 2018) during ictal (Weiss et al., 2013) and interictal (Fedele et al., 2017; Gliske et al., 2018) periods. Nevertheless, manual HFO (ripple) detection is time-consuming (Gliske et al., 2018) and automatic approaches produce a large number of false positives (Bénar et al., 2010). Moreover, some interictal analyses of slow-wave sleep questioned the utility (Roehri et al., 2018) and accuracy (Jacobs et al., 2018) of HFOs to serve as a biomarker for epileptogenic tissue identification. These observations can be further supported by a resting-state SEEG study which has delineated the long-range high-frequency synchronization of physiological HFOs among the non-epileptogenic regions (Arnulfo et al., 2020). While HFOs have been employed in analyzing functional (Schindler et al., 2010) and propagation (González Otárula et al., 2019) networks, the spatiotemporal dynamics of ictal high-frequency synchronization (HFS) at macroscopic scales remain largely unknown.

In this paper, we analyzed SEEG recordings of cortical and subcortical regions. In SEEG, the EZ not only takes into account the earliest ictal EEG change, it emphasizes an anatomo-electro-clinical analysis (Kahane et al., 2006). This concept incorporates both the anatomic region that initiates the epileptic discharge as well as the ‘primary organization’ (Talairach and Bancaud, 1966) that leads to the manifestation of the clinical seizure itself (Wyllie et al., 2015). The gold standard method of confirming EZ localization is based on whether seizure freedom has been achieved by resection or ablation. The actual ground truth for the EZ location is unknown since in many cases the resection volumes may extend well beyond the EZ. In recent work, the EZ has been considered as part of a network (Jehi, 2018). These epileptogenic networks in focal epilepsy have been invoked in explaining the underlying pathogenesis of epilepsy, seizure initiation, ictal propagation, and disease progression as well as various associated comorbidities (Nair et al., 2004). This perspective is utilized in our work to analyze seizures in the context of a distributed network of interacting regions that include the EZ. Because of the importance of HFOs in epilepsy and SOZ localization, we construct synchronization networks in the 80–200 Hz range, to be in line with similar studies (Höller et al., 2015; Schindler et al., 2010). Fast rhythmic bursting neurons, which have the highest tendency to initiate seizures, are largely responsible for generating ultra-fast oscillations or ripples (80–200 Hz) (Timofeev and Steriade, 2004). We hypothesize that during seizures, the EZ has an abnormal and unique pattern of connectivity with other brain areas.

Graph analysis provides a mathematical framework for the quantification of brain connectivity (Bullmore and Sporns, 2009). Brain networks may be represented as a graph, G=(V, E), in which nodes (V) characterize anatomical regions or electrodes, and edges (E) reflect structural or functional connections among them. Traditionally, brain connectivity in each time sample (layer) of dynamic networks has been evaluated independently, via single graph analysis. However, multilayer analysis allows us to model the entire data with a single super-graph, in which individual graphs for each time-sample are linked. Assuming there are T single graphs (time-samples) with N nodes in each, the super-graph has NT nodes. The multilayer structure has considerable methodological advantages over single-layer analysis (Betzel and Bassett, 2017). First, the interlayer coupling between neighboring time points in this model allows us to incorporate the continuity in neural dynamics. Second, by tuning the coupling parameter, processes with different timescales can be distinguished. Third, the extracted measures on these networks are less susceptible to noise in the data or spurious connectivity. Additionally, there exist several neurological rationales for employing a multilayer approach in seizure analysis. First, the concept of dynamic network reconfiguration has been studied in brain networks (Bassett et al., 2011; Braun et al., 2015). Previous research has shown state transitions during seizures, either through brain connectivity analysis (Burns et al., 2014) or microelectrode recordings (Smith et al., 2016). Multilayer networks have the capability to delineate these transitions and identify network reconfiguration (Mucha et al., 2010). Second, electrophysiological signals are highly non-stationary during ictal periods. As a result, traditional analysis of time-varying networks based on isolated graphs would be affected by instantaneous fluctuations rather than the underlying spatiotemporal networks. Third, seizure propagation is one of the key elements of ictal activity. Recent work has indicated the importance of multilayer modeling of complex systems when encountering spreading processes (De Domenico et al., 2016).

Consequently, we modeled spatiotemporal high-frequency connectivity using multilayer networks. We explore the question of whether the EZ can be identified by unsupervised clustering of nodes (representing SEEG contacts) in the feature space of these multilayer networks. Our connectivity-based EZ identification results show reasonable consistency with a previous approach (described as the fingerprint of the EZ) (Grinenko et al., 2018; Li et al., 2020) which uses three ictal features for EZ localization, namely: low-voltage fast activity (LFD), preictal spiking, and suppression of lower frequencies.

Understanding the connectivity dynamics of EZ and surrounding areas with the rest of the brain can shed light on underlying processes including seizure propagation and termination. We evaluate these interactions in different frequency bands. To use consistent terminology, here the term ‘high-frequency synchrony’ is mostly utilized to describe brain networks at higher frequencies (80–200 Hz). On the other hand, the word ‘connectivity’ has been assigned to both propagation networks in low frequency (3–50 Hz) and synchronization networks in high frequency (80–200 Hz). Our findings illustrate early high-frequency desynchronization and late increase in brain connectivity during seizures. Although, seizures usually initiate with a loss of synchronization in a small area, their termination process demands widespread brain connectivity across multiple scales. During seizure cessation, the brain experiences a critical transition with a hysteresis behavior (Kramer et al., 2012), indicating the future state depends on the current one. Accordingly, we hypothesize that post-termination high-frequency synchrony is correlated with pre-termination connectivity in low frequency.

Results

Multilayer modeling of ictal networks discerns the EZ

SEEG data were recorded using implanted intracranial electrodes in 16 patients who underwent resective surgery and were seizure-free for at least 12 months post-resection (Table 1). We studied the dynamics of brain connectivity during seizures via multilayer networks (Mucha et al., 2010) which captures continuity in neural interactions during the ictal period. A schematic of a multilayer network with inter and intralayer edges is depicted in Figure 1. SEEG contacts were defined as graph vertices while the lagged-coherence (Pascual-Marqui, 2007) was used to define edge strength in each layer as a measure of the macroscopic HFS (see Methods). We investigated two broad bands of HFOs: 80–140 Hz and 140–200 Hz, similar to related studies (Arnulfo et al., 2020; Weiss et al., 2013). Several studies have applied phase-based connectivity metrics on broad-band high-frequency oscillations. For instance, (Zweiphenning et al., 2016) computed the phase lag index (PLI) in two high-frequency bands: ripple (80–250 Hz) and fast ripple (250–500 Hz). Another study used PLI to compute brain connectivity in broad band 80–250 Hz (Nissen et al., 2016). Last, Burns et al., 2014 used coherence to investigate ictal networks in gamma (25–90 Hz) band.

Schematic of a multilayer network and measure of multilayer eigenvector centrality (mlEVC).

Four consecutive layers (time-points) of a simulated network with intralayer (solid lines) and interlayer (dashed lines) edges. Nodes in each layer represent the set of stereoelectroencephalography (SEEG) contacts and are colored and categorized into two clusters (red and blue). Interlayer edges (couplings) were included between the same contacts at adjacent time points. The diameter of each node represents the relative value of mlEVC, in which larger nodes are the more connected nodes and smaller nodes are more isolated.

Table 1
Clinical characteristics of patients.
IDAge (years)ED (years)MRI lesionResection/ablation detailsSurgical pathologyFollow-up(months)Anatomical location of the EZNumber of nodes in the networkNumber of nodes inside the resection areaDuration of seizures (seconds)
14337FCD, insular/frontal operculumAnterior insular/ frontal operculumFCD type 2B13Insular/frontal operculum8811(41, 39, 39)
33317Hippocampal sclerosisAnterior temporal lobeHippocampal sclerosis48Temporal7922(147, 150, 141)
4178NegativeLaser ablation, superior frontal gyrusNo pathology19Frontal715(25, 24, 25)
5161Benign neoplasm, posterior para-hippocampal gyrusPosterior para- hippocampus gyrus and neoplasmLow grade glial/ glioneuronal neoplasm39Basal posterior temporal488(55, 115, 140)
64641FCD, mesial frontalPrefrontal lobeNon-specific38Frontal8832(100, N/D, N/D)
751NegativeSuperior frontal gyrus, superior frontal sulcus, frontal poleFCD type 2B21Superior frontal gyrus/superior frontal sulcus7333(14, 15, 15)
86314NegativeOrbitofrontalFCD type 144Orbitofrontal/ pars orbitalis10519(61, 267, 62)
93319Gliotic postoperative changesAnterior temporal lobeFCD type 1B40Temporal9946(85, 64, 81)
102111NegativeOccipital lobeGray matter heterotopia,
FCD type 1B
12Cuneus12357(106, 98)
113227FCD, precentral gyrusPrecentral gyrusNon-conclusive77Precentral gyrus8213(26, 78, 12)
12223FCD, superior frontal sulcusSuperior and middle frontal gyri, anterior cingulateFCD type 2B78Frontal5831(18, 25, 31)
131918NegativeMiddle frontal gyrusFCD type 148Inferior frontal sulcus/middle frontal gyrus4126(36, 36, 35)
143018NegativeFrontal operculumFCD type 2B47Frontal operculum/ subcentral region7010(49, 21, 78)
152011NegativeFrontal lobeFCD type 182Superior frontal gyrus/superior frontal sulcus9932(65, 86, 86)
166525NegativeAnterior temporal lobeFCD type 1 C39Temporal13923(56, 65, 142)
17659NegativeAnterior temporal lobeFCD type 1 C36Temporal9035(55, 63, 59)
  1. Follow-up information is current as of July 2017.

  2. ED: epilepsy duration, FCD: focal cortical dysplasia, N/D: Not defined.

As discussed in the introduction, we aimed to model ictal brain connectivity by multilayer networks. Additionally, we were interested in quantifying network dynamics using centrality metrics (Rubinov and Sporns, 2010). Among those measures, eigenvector centrality (EVC), a rank-based metric that assesses the importance of each node in the network (Bonacich, 1972), has been employed in studying seizures (Burns et al., 2014). Mathematically, the leading eigenvector of the adjacency (connectivity) matrix has been assigned as the EVC of the graph when there is one clique (component) in the matrix (Bonacich, 1972). However, in our multilayer model of time-varying brain connectivity, a single vector cannot explain the complex structure of the spatiotemporal networks. Therefore, we introduced a new measure called mlEVC that incorporates the top T eigenvectors of the adjacency matrix of the super-graph (see Methods). This allows us to evaluate patterns of nodal centrality and identify regions with similar connectivity characteristics to the rest of the graph. Further, because mlEVC is a function of the interlayer coupling parameter (c), we can explore neural processes at different timescales by varying c. The mlEVC represents the prominence of a node in multiplex networks evolving over time (Figure 1). Nodes with high connectivity over time and space in the multilayer network display larger values in mlEVC than isolated vertices. Figure 2b displays this measure for one seizure of patient 17.

Figure 2 with 4 supplements see all
Identification of epileptogenic zone (EZ) based on multilayer eigenvector centrality (mlEVC) (Patient 17).

(a) Stereoelectroencephalography (SEEG) signals during the ictal period. The red signals are a sample of contacts inside the EZ as identified by our method, and the blue signals depict non-EZ contacts outside the resection zone. (b) The mlEVC during the ictal period. Each row represents a channel (contact). Contacts are categorized and organized into two groups: resected and non-resected as indicated on the right. They are also categorized into two groups based on the proposed clustering algorithm: target and non-target. The blue elements of mlEVC describe the isolated nodes of the super-graph (brain network) while red values describe highly connected contacts. (c) The first three left singular vectors of the mlEVC. The mlEVC spectra of different seizures were first quantized and concatenated before performing singular value decomposition. The red nodes are those identified as predicted EZ based on unsupervised clustering.

Figure 2—source data 1

Comparing SEEG channels identified as true positives between the two methods, mlEVC in this paper vs. those identified using the Fingerprint in Grinenko et al., 2018.

Common channels among the two methods are highlighted.

https://cdn.elifesciences.org/articles/68531/elife-68531-fig2-data1-v2.docx
Figure 2—source data 2

This table summarizes the prediction performance for the proposed method and Fingerprint algorithm on 16 patients.

Important note: 16 out of 17 misidentified electrodes in our method are from three patients only.

https://cdn.elifesciences.org/articles/68531/elife-68531-fig2-data2-v2.docx
Figure 2—source data 3

This table compares the prediction performance of the proposed method with a single-layer network and a multilayer network with a fixed coupling parameter for all subjects.

https://cdn.elifesciences.org/articles/68531/elife-68531-fig2-data3-v2.docx

Algorithm for predicting EZ using mlEVC

We hypothesize that the EZ can be identified as the set of nodes in the graph that exhibit a characteristic and distinct pattern of connectivity to other areas during the seizure. To explore this question, we first quantized the mlEVC of each seizure into three levels based on percentile thresholding (d). The top d/2-portion of elements was assigned a value of ‘1,’ the bottom d/2-portion a value of ‘–1,’ and the remainder a value of ‘0.’ For each subject, quantized measures of mlEVC for two high-frequency bands and all seizures were concatenated to a single matrix with dimension N by Ttot (twice the total number of sample points) (see Methods). We applied the singular value decomposition (SVD) to the concatenated matrix and used the left singular vectors (uiRN) to identify nodes (SEEG channels) with similar features. As an illustration, Figure 2c depicts u1 , u2, and u3 for patient 17.

Next, we applied an unsupervised clustering algorithm using the ui vectors to detect a target cluster that represents the EZ. Following our initial hypothesis, the target cluster should portray a dense and distinctive set of nodes in the feature space with a significant distance from nodes in the non-target group (Figure 2c). We describe the clustering algorithm in detail in the method section. Briefly, we designed a data-driven framework to cluster nodes into two groups using an agglomerative hierarchical clustering technique (function linkage in MATLAB). This process was performed for different combinations of ui as features of the clustering algorithm and a range of values for c and d, resulting in 440 clustering runs. We weighted each run using a performance function (Halkidi et al., 2001) that examines the tightness of the target cluster and its separation from other nodes. Finally, using the weighted sum of performance metrics for all runs, SEEG contacts were divided into two groups; target and non-target.

Assessing the accuracy of the prediction algorithm

By comparing the clustering results with information about which contacts were included in the resected volume (Figure 2b), we defined three categories: ‘EZ,’ ‘resected non-EZ,’ and ‘non-resected.’ The EZ included the nodes in the target cluster, resected non-EZ consists of nodes in the non-target cluster removed during surgery, and non-resected comprises the rest of the nodes, which were neither resected nor clustered in the target group (Figure 2—figure supplement 1). Ideally, the predicted EZ or target cluster should only contain nodes in the resected area for these participants since all patients were seizure-free after surgery. However, the clustering algorithm and proposed technique are not flawless so there are a small number of electrodes outside the resection region selected as EZ, i.e., false positives.

Our approach identified electrodes inside the resected volume as EZ for 88% of participants, i.e., all but two (patients 8 and 11). For patient 11, 2 out of 3 available seizures were short (25 s and 12 s) and the sampling rate was relatively low (500 Hz). Lack of sufficient samples might be the source of miss identification for this patient and a limitation of our approach. The false-positive rate (FPR) was calculated by dividing the number of predicted electrodes as EZ outside the resection zone over the total number of electrodes in the non-resected region. Only four participants had electrodes falsely identified as EZ and the FPR was 1.79% across all 16 patients. The details of predicted electrodes for each patient are given in Figure 2-source data 1. We compared our results with Fingerprint (Grinenko et al., 2018) analysis that employs time-frequency features of pre- and post-seizure onset, to predict the EZ. Although these two algorithms are fundamentally different in their assumptions, contacts/nodes identified in our approach as EZ have 41% overlap (same contact labels) with those found using the Fingerprint. Interestingly, the mlEVC algorithm could identify electrodes inside the resection zone for two patients in which Fingerprint was not able to predict the EZ (participants 6 and 16). In contrast, the latter could localize EZ for two patients (8 and 11) on which our method failed. For several patients, the two approaches identified different but adjacent areas inside the resection region. Nonetheless, 67% of patients had common electrodes labeled as EZ in the resected volume by both algorithms. Since both analyses were retrospective and the actual ground truth is unknown, these techniques can perhaps be used to complement each other. (see Figure 2-source data 1 and Figure 2—source data 2 for a detailed comparison). Finally, Figure 2—source data 3 demonstrates that the proposed method utilizing weighted consensus clustering outperforms single-layer networks and multilayer networks with fixed coupling.

It was striking that for most of the patients, the EZ was distinguishable based on the singular vectors of mlEVC (Figure 2—figure supplement 1). Consistent with other studies, we found out that possibly only a portion of the resected area is responsible for epileptogenicity. Figure 2b captures the discrepancies between the EZ, resected non-EZ, and non-resected areas. Furthermore, it distinctly displays various brain states (phases) during the ictal period. Nodes experience isolated and fully connected phases with respect to the rest of the network. These results confirm the importance of the entire ictal period for EZ identification. For the rest of the paper, we utilize the categorization of nodes introduced above with the following small modifications: removing false positives from the EZ groups (defined as those contacts lying outside the resected volume) and discarding patients 8 and 11 in whom we were unable to observe any unique pattern of connectivity in electrodes inside the resected area.

Evaluating the validity of the proposed method

To explore the validity of our approach, we constructed a null model by also computing the mlEVC from phase-randomized SEEG signals (Prichard and Theiler, 1994). In Figure 2—figure supplement 2, we show typical results of the mlEVC measures calculated from the original time-series and phase-randomized data for a single subject. These results show significant differences between original and randomized data in which the characteristic patterns of brain connectivity both in resected and non-resected areas are lost when signals are phase-randomized. We performed this analysis for different patients and seizures with similar findings.

To investigate whether apparent high-frequency networks were produced as a result of ictal spikes rather than true oscillations, we examined the time-frequency representation of seizures. Figure 2—figure supplement 3 displays time-frequency plots for two sample seizures. The upper plot shows the spectrum averaged among nodes predicted as EZ and the lower spectrum shows the case for randomly selected nodes outside the resection region, with the number of nodes in both groups equal. We observed pre-ictal spikes in the time-frequency plot for nodes inside the EZ, a previously reported feature of the EZ (Grinenko et al., 2018). However, the figure shows that non-spiking high-frequency oscillations were the dominant activity after seizure onset. This observation supports our hypothesis that HFOs, rather than ictal spiking, are the main contributor to observed synchronization during seizures.

Furthermore, we examined the effect of multilayer modeling and adjusting the coupling parameter on EZ prediction and super-graph structure. In Figure 2—figure supplement 1, we display the left singular vectors of mlEVC. For illustration purposes, we showed projections with respect to the singular vectors for the parameter set (c, d) for which the prediction of EZ (binary labeling) was closest to the assumed ground truth (resection information). We observed that the optimal coupling value is different between patients, which supports our primary rationale for choosing a multilayer framework with an adaptive interlayer coupling parameter. In our initial analysis, we ran the algorithm for the single-layer case and EZ identification results were poor (see Figure 2—source data 3).

Figure 2—figure supplement 4 presents the changes in super-graph eigenvalues by adjusting the coupling parameter. For c≤1, there is a falloff when the number of eigenvalues (ne) meets the number of layers (T), indicating a super-adjacency matrix with effective rank T. This is an expected result since the coupling is relatively small. When c increases, the eigenvalues become larger, and their corresponding eigenvectors would comprise several neighboring layers. Although the rate of decline in the magnitude of eigenvalues accelerates as c increases, falloff can be detected when ne ≤2 T. By increasing the coupling value, the super-adjacency matrix transforms from a block diagonal matrix with an effective rank T, to a matrix with major non-diagonal blocks and an effective rank far greater than T. In the computation of mlEVC, we considered the top T eigenvectors for all coupling parameters to avoid erroneous assumptions about the rank of super-graphs.

Seizures evolve with divergent network topologies

In our multilayer modeling of epileptogenic networks, the left singular vectors of mlEVC were used to cluster nodes into two categories, predicted EZ and non-EZ. Here, the associated right singular vectors were employed to display seizure evolution. In clinical epileptology, stereotypy in seizures is defined as similarities in both seizure semiology and ictal EEG recordings over repeated seizures (Schevon et al., 2012). Multiunit recordings have shown that stereotypical firing patterns occur when micro-electrodes are implanted in recruited areas (Schevon et al., 2012). To evaluate stereotypy in this study, we clustered ictal dynamics into different states using the four features from a pool of six-dimensional feature vectors, including the top three right singular vectors of mlEVC split into the two high-frequency bands (see Methods).

Figure 3 compares different seizures for patient 16. Quantized mlEVC are depicted in Figure 3b with corresponding state changes in part c. Results indicate that ictal brain activity evolves through diverse phases during different seizures. In the first seizure, the EZ is mostly isolated with respect to the other nodes and ictal activity advances through three states (E, D, A). In contrast, the EZ exhibits strong connectivity in the second seizure while the centrality measure passes through four states (C, B, D, F). Figure 3d illustrates the ictal dynamics using the four selected features extracted from the top three right singular vectors of mlEVC in two frequency bands (see Methods). In this case, seizure one evolves quite differently from seizures two and three whose traces share similar ictal dynamics.

Figure 3 with 1 supplement see all
Evolution of seizures through high-frequency states (Patient 16).

(a) Time series of a channel inside the predicted epileptogenic zone (EZ) for two different seizures (onset to termination). (b) The low-rank estimation of quantized multilayer eigenvector centrality (mlEVC) plots (80–140 Hz). For a clearer representation, only channels in predicted EZ and resected non-EZ are depicted. (c) State transitions during seizures. The time vector is adjusted based on the seizure onset (t=0 s) (d) Evolution of seizures in the feature space. Capital letters show the center of each brain state. The space and states are created by four features (v-a, v-b, v-c , and v-d) extracted from the right singular vectors of mlEVC in the two high-frequency bands (see Methods – Here, only two features are illustrated). Comparing three ictal periods, we see that the brain can exhibit a different seizure evolution – here between seizure one and seizures two and three.

The same analysis was performed for all patients and results for several of these participants are shown in Figure 3—figure supplement 1. We observed that stereotypy, here considered as similar state transitions among all recorded seizures, does not necessarily occur, especially at high frequencies. In fact, the brain experiences divergent topologies, which might be the result of dissimilar EEG recordings. While previous studies suggested stereotypy in focal firing (Schevon et al., 2012) and brain connectivity (Burns et al., 2014), our multilayer analysis of epileptogenic networks does not imply stereotypy in macroscopic HFS. Our findings confirm the necessity of collecting adequate seizures and large-scale recordings for a better understanding of seizure evolution.

EZ desynchronization occurs in the ictal period

We were interested in exploring the fundamental question of how HFS changes throughout the seizures. To do this, three synchrony measures were computed. The first measure, EZ-nR, quantifies the synchrony between EZ and non-resected (nR) areas. The second metric, RnEZ-nR, computes the connectivity of resected nonEZ and nR. Lastly, we computed interactions between non-resected regions, labeled nR-nR. Figure 4a presents the dynamics of these measures during the ictal period. Collectively, 39 seizures and two frequency bands were analyzed. Seizures with different durations were resampled/rescaled to a zero to one interval, where zero indicates the onset and one indicates the termination time. In general, among the three measures, EZ-nR exhibited a substantial decline in synchrony during early and mid-seizure while widespread synchronization occurred during seizure termination (Figure 4a). Based on this observation, we compared the HFS in three time periods: pre-ictal, mid-seizure, and post-ictal (Figure 4a). Data for all seizures were extracted for statistical analysis in RStudio (Rstudio Team, 2018). To handle possible outliers, the paired percentile bootstrap with a one-step M-estimator (Wilcox, 2011) was employed and p-values were computed for pairwise comparison between and within the three measures at each of the three periods, corrected using Hochberg’s algorithm (B=104 number of bootstraps, J=18 tests, see Methods). All tests and their corresponding corrected p-values can be found in Figure 4—source data 1 .

Figure 4 with 1 supplement see all
High-frequency synchrony during the ictal period.

(a) Time-varying high-frequency synchrony values for three defined measures. The ictal period is normalized to a zero to one scale. The solid lines represent the median and shaded plots display the normalized median absolute deviation (MAD), based on 104 bootstrap tests. The gray rectangles display the periods of special interest. Note that EZ-nR connectivity drops substantially towards mid-seizure and increases to match nR-nR and RnEZ-nR at seizure termination and post-ictally. (b) Connectivity measures in pre-ictal, mid-seizure, and post-ictal. To give a pairwise visual comparison, we subtracted the average synchrony between all pairs of contacts in the pre-ictal interval from nine connectivity measures. The centers of error bars show the median of all seizures in two frequency bands and lines depict the MAD. Scatter circles exhibit the actual values (n=78 for each group). To handle possible outliers, the paired percentile bootstrap with a one-step M-estimator was employed and p-values were computed for pairwise comparison between and within the three measures at each of the three periods, corrected using Hochberg’s algorithm (B=104 number of bootstraps, J=18 tests, see Methods). Asterisks display corrected p-values; *p<0.05, **p<0.01, ***p<0.001. Only the mid-seizure interval shows significant differences between EZ-nR and other measures. All measures are considerably higher in post-ictal than their corresponding values in the mid-seizure and pre-ictal periods. EZ-nR drops significantly in mid-seizure from pre-ictal.

Figure 4—source data 1

Corrected p-values for all pairwise comparisons.

Post-hoc tests on network measures in high-frequency. p-values smaller than 0.05 are bolded.

https://cdn.elifesciences.org/articles/68531/elife-68531-fig4-data1-v2.docx

Figure 4b presents the extracted connectivity values for the above measures in selected periods. To give a pairwise visual comparison, we subtracted the average synchrony between all pairs of contacts in the pre-ictal interval from nine connectivity measures (Figure 4b). Unsurprisingly, there was no difference between measures in the pre-ictal period (p≈1 for all pairwise comparisons). In mid-seizure, EZ-nR was significantly smaller than RnEZ-nR (p=0.0108) and nR-nR (p<10–4), indicating that the EZ is maximally desynchronized from the rest of the brain. Early-onset and late-ictal HFOs have been considered biomarkers for seizure onset zone identification (Weiss et al., 2013), with the latter found to be a more reliable metric (Modur et al., 2011). Our EZ localization technique considers both features. The substantial decrease in EZ connectivity with the entire network in mid-seizure might be the result of these pathological HFOs in the EZ. At a smaller scale, EZ-nR desynchronization could be the result of heterogeneous neuronal spiking activity during seizures (Truccolo et al., 2011). Microelectrode recordings of the ictal core presented a dramatic rise in the Fano factor, a statistical measure of spiking desynchronization (variance of spiking divided by the mean), in the early and mid-phases of seizures (Schevon et al., 2012; Truccolo et al., 2011). Theoretical modeling of neuronal assemblies has shown that asynchrony is necessary to maintain a high firing rate (Gutkin et al., 2001). We further studied the variations of each measure among different periods. Between pre-ictal and mid-seizure, EZ-nR connectivity declined considerably (p≈0.002), followed by a marginally significant fall for RnEZ-nR (p=0.056). In contrast, all measures were substantially elevated during seizure termination and the post-ictal period in comparison to mid-seizure and pre-ictal intervals (p<10–4 for all tests). This observation is well aligned with other studies, suggesting a widespread synchronization during seizure termination (Kramer and Cash, 2012), especially in the range 80–200 Hz (Schindler et al., 2010).

We do not include the connectivity between the EZ and RnEZ in Figure 4 for the following reason. The three measures we do compute are all relative to the non-resected region which we know to definitely be outside the EZ. Within the resection, there is some ambiguity as to which contacts are within EZ and which are not. Second, a measure between EZ and RnEZ would be more susceptible to noise as the number of RnEZ electrodes is typically much smaller than the number in the non-resected region so that establishing statistical significance is difficult. Nevertheless, this measure is computed for the interested reader in Figure 4—figure supplement 1. It can be perceived by visual inspection that EZ-RnEZ has a pattern similar to EZ-nR, suggesting again that the EZ is functionally disconnected from surrounding areas up to mid-seizure (Warren et al., 2010).

The EZ becomes isolated by aging and the duration of epilepsy

Although the EZ exhibited a general pattern of desynchronization, it was not the case for all patients. In mid-seizure, several participants showed larger EZ-nR values when compared with the average connectivity in the entire network. This observation is expected since patients have dissimilar seizure types, etiology, and electrode implantations. Consequently, we postulated that a patient’s demographics might explain differences in EZ connectivity with the rest of the brain. Patients’ age and duration of epilepsy were assessed as predictors for the EZ-nR synchrony in the middle of seizures. For each seizure and patient, the average synchrony between all pairs of contacts in mid-seizure was subtracted from the EZ-nR to reduce inter-subject and inter-seizure variabilities. We constructed a three-dimensional vector consisting of EZ-nR connectivity for each seizure (n=39) along with the corresponding age and duration of epilepsy. We utilized a robust regression estimator based on bootstrap sampling and the Theil-Sen algorithm (Wilcox, 2011). The correlation between patients’ age and normalized EZ synchronization is shown in Figure 5a. Results indicate a strong negative association, suggesting the EZ becomes increasingly desynchronized with age (p<10–4, r = − 0.414). Similarly, we observed a reduction in connectivity between the EZ and non-resected areas with a longer duration of epilepsy (Figure 5b, p=0.032, r = − 0.229).

Correlation between normalized EZ-nR values and patients’ history.

(a) Correlation between patients’ age and normalized EZ-nR synchronization in high frequency. Each data point indicates the average of normalized EZ-nR values in mid-seizure among two high-frequency bands for each seizure (n=39). We utilized a robust regression estimator based on bootstrap sampling and the Theil-Sen algorithm (Wilcox, 2011). (b) The same plot as (a) except where the x-axis indicates the duration of epilepsy among patients.

These findings suggest possible variables that can modify the epileptogenic networks (van Diessen et al., 2013a). Recently, interictal ECoG recordings of patients with temporal lobe epilepsy (TLE) have shown a negative correlation between TLE duration and overall PLI at low frequencies (van Dellen et al., 2009). A resting-state fMRI study also found a negative correlation between epilepsy duration and functional connectivity between two contralateral ROIs in the inferior frontal gyrus (Liao et al., 2010). However, our findings delineate the correlation in a specific pathological pathway among patients with medically intractable focal epilepsy with different SEEG electrode implantations. A decrease in functional connectivity with age might also be observed in a control group. However, the fact that we normalize by subtracting the overall synchronization in each patient from EZ-nR values weakens the influence of that factor in our findings.

Expansive connectivity in low-frequency emerges before seizure termination

Low-frequency brain signals (3–50 Hz) are mainly shaped by rhythmic synaptic currents (Schevon et al., 2012), which in many cases traverse to other regions. These traveling waves are involved in different sensory processes and brain states (Muller et al., 2018; Smith et al., 2016). In epilepsy, ictal discharges exhibit this activity during seizures. Recently, two scenarios have been proposed for seizure spread and termination (Martinet et al., 2017). The first theory postulates that ictal discharges emerge from a fixed cortical source in EZ, while the second hypothesis asserts that the moving ictal wavefront generates traveling waves (Smith et al., 2016). This process dominates when the ictal wavefront recruits the seizure core and penumbra, i.e., the area around the core in which low-voltage signals spread, roughly during the mid-seizure period. These scenarios have contradictory explanations for how seizure termination occurs. The fixed source theory assumes inactivation of a small region would end the seizure while the active wavefront requires a mechanism that affects an expansive area.

We analyzed connectivity in low-frequency during seizures. Brain networks were constructed using the PLI. The PLI is recognized for its superiority to measures such as phase locking value (PLV). By discarding interactions with a phase difference of zero, the PLI quantifies phase coupling between two signals while excluding volume conduction as a confounding factor. Compared to other functional connectivity metrics, PLI is, therefore, less susceptible to common sources. Since a major part of low-frequency (<50 Hz) brain activity during seizures is derived from ictal discharges, which exhibit distance-dependent delays (Smith et al., 2016), true neurological zero-lag connectivity is highly unlikely in this scenario. Because of its robustness to volume conduction, PLI has been widely used in studies of low-frequency (<50 Hz) brain connectivity in epilepsy (Nissen et al., 2016; Schevon et al., 2012; van Diessen et al., 2013b; Zweiphenning et al., 2016). Similarly to high-frequency networks, these connectivity matrices were normalized to the pre-ictal period (see Methods). Previously defined measures were computed, and their dynamics are depicted in Figure 6a. In comparison to HFS, we observed a stronger resemblance in PLI among the three interaction measures (EZ-nR, RnEZ-nR, and nR-nR) other than in a short early-seizure period. Additionally, ictal discharges displayed an expanding coverage after mid-seizure, which was maximized before seizure termination. As a result, early-seizure and pre-termination along with pre-ictal periods were chosen for statistical analyses as analogs to HFS (n=39, see Figure 6—source data 1 ). We did not find any difference between measures in pre-ictal and pre-termination PLI (p>0.05 for all cases). However, EZ-nR was distinguishable from RnEZ-nR (p=0.0374) and nR-nR (p<10–4) in early seizure. This observation can be linked to early-onset suppression in low-frequency, reported as a possible signature of the EZ (Grinenko et al., 2018). Compared with early-seizure and pre-ictal periods, all measures were significantly elevated in pre-termination (p<10–4 for all tests). Consistent with our findings, a recent study showed that an increased temporal and spatial correlation along with flickering, the condition when a system fluctuates between two attractors, are signatures of a critical transition when seizures self-terminate (Kramer et al., 2012).

Low-frequency brain connectivity during the ictal period.

(a) Time-varying low-frequency connectivity values for three defined measures. The ictal period is normalized to a zero to one scale. The solid lines represent the median and shaded plots display the normalized median absolute deviation (MAD) based on 104 bootstrap tests. The gray rectangles display the periods of special interest. EZ-nR connectivity drops in early seizure and a widespread brain connectivity occurs in the pre-termination period. (b) Connectivity measures in pre-ictal, early-seizure, and pre-termination. To give a pairwise visual comparison, we subtracted the average synchrony between all pairs of contacts in the pre-ictal interval from nine connectivity measures. The centers of error bars show the median of all seizures in two frequency bands and lines depict the MAD. Scatter circles exhibit the actual values (n=39 for each group). To handle possible outliers, the paired percentile bootstrap with a one-step M-estimator was employed and p-values were computed for pairwise comparison between and within the three measures at each of the three periods, corrected using Hochberg’s algorithm (B=104 number of bootstraps, J=18 tests, see Methods). Asterisks display corrected p-values; *p<0.05, **p<0.01, ***p<0.001. Only the early-seizure interval shows significant differences between EZ-nR and the two other measures. All measures are considerably higher in pre-termination than their corresponding values in early-seizure and pre-ictal periods.

Figure 6—source data 1

Corrected p-values for all pairwise comparisons.

Post-hoc tests on network measures in low-frequency. p-values smaller than 0.05 are bolded.

https://cdn.elifesciences.org/articles/68531/elife-68531-fig6-data1-v2.docx

Pre-termination connectivity predicts post-ictal synchronization

It has been hypothesized that the brain manifests hysteresis between the two states before and after termination (Kramer et al., 2012). In other words, the post-ictal state is dependent on pre-termination. Consequently, we were interested to examine how the brain changes between these two states. Pre-termination connectivity in low-frequency and post-termination synchrony in high-frequency were among the distinctive features of the results presented above. To test the hypothesis of possible dependency, we computed overall brain connectivity for these two measures. Figure 7 illustrates the correlation between pre-termination and post-ictal intervals. Each point in the graph belongs to one seizure in which the two values for two high-frequency bands are averaged. There is a strong association between the two states (p<0.02, r=0.452, n=34) after removing outliers using the projection method and the MAD-median rule (Wilcox, 2011), supporting the existence of hysteresis in the system. In other words, the brain state in the post-ictal period can be predicted using its condition in pre-termination.

Correlation of overall pre-termination low-frequency connectivity and post-ictal high-frequency synchrony during the critical transition.

Each point in the graph belongs to one seizure in which the two values for two high-frequency bands are averaged (n=34). Outliers were removed using the projection method and MAD-median rule (Wilcox, 2011).

Discussion

Our results investigate large-scale ictal brain connectivity as it relates to EZ localization and seizure generation, propagation, and termination. We showed that the EZ exhibits differential dynamics compared to other brain regions during seizures. This observation is independent of seizure type, etiology, presence or absence of MRI lesion, and occurred in both temporal and extra-temporal lobe epilepsy. High-frequency oscillations have been widely studied as a potential biomarker in epilepsy (Zijlmans et al., 2012), including both early- and delayed-onset ictal HFOs (Weiss et al., 2013). However, there is still some debate on their spatial specificity, timing, and appropriate detection algorithms. As an alternative marker, we computed high-frequency synchrony (HFS) over the entire seizure period. HFS was first modeled using a multilayer network and the potential EZ was identified using a novel measure of centrality. Our approach to identifying the EZ is complementary to other approaches avoiding explicit assumptions regarding seizure patterns and dynamics.

The multilayer network approach used here for EZ prediction and identification of state transitions allows us to explore seizure dynamics in a graph-theoretic context. Traditionally in brain network studies, researchers explore graph measures like clustering and centrality, in single-layer (non-dynamic) networks (Ridley et al., 2015; van Diessen et al., 2014). However, the multilayer framework with an adjustable coupling parameter can reveal processes with different timescales and facilitate defining of new measures (Betzel and Bassett, 2017). By adjusting the coupling between layers, we can overcome the current challenges of selecting an appropriate time interval between different samples of a temporal network. Here, we assumed a relatively short time interval between layers (500 ms) to have a high temporal resolution. By increasing the coupling parameter between adjacent layers, we can investigate processes with slower timescales.

We used an unsupervised clustering algorithm to find a set of nodes among all channels, i.e., the target cluster, as the predicted EZ. The presented method was based on hierarchical clustering and a cost function that combines the separation of clusters and the compactness of the target group. The optimized coupling parameter varies substantially between patients (Figure 2—figure supplement 1), verifying the necessity of analyzing multiple timescales. In some cases, this automatic unsupervised clustering may fail to find all nodes (contacts) with features that would identify them as belonging to the EZ using other methods, such as the fingerprint method that finds a distinctive combination of pre-ictal spiking, low-frequency suppression, and low-voltage fast activity (LFD). This is reflected in the differences in contacts identified as EZ between the two approaches, which is reported in Figure 2—source data 1. However, the complementary dynamic-synchrony-based approach described here also finds plausible EZ contacts in cases where the fingerprint does not, as mentioned in the result section. Finally, based on the predicted EZ and information regarding the resection areas, the SEEG electrodes were categorized into three groups; EZ, Resected non-EZ (RnEZ), and non-resected (nR). We employed this categorization to compute the dynamics of regional ictal connectivity in low and high-frequency bands.

There is substantial evidence of multiscale alterations in structural and functional brain networks in epilepsy (Bernhardt et al., 2016; Englot et al., 2016; Tavakol et al., 2019). A meta-analysis of a dozen interictal studies with variant imaging methodologies showed increased clustering and path length (van Diessen et al., 2014). Resting-state fMRI research has revealed decreased inter-hemispheric functional connectivity in medial and lateral temporal regions among patients with TLE (Maccotta et al., 2013; Pittau et al., 2012). Ictal SEEG recordings of focal cortical dysplasia (FCD) type II have shown that nodes within the lesion have higher values of out-degree and betweenness centrality in the gamma range (30–80 Hz)(Varotto et al., 2012). Using cortico-cortical evoked potentials (CCEPs), we recently presented the differences in effective connectivity between FCD types I and II (Shahabi et al., 2021). These observations have created a new field of research known as connectivity-based biomarkers in epilepsy (Larivière et al., 2021), which is mostly performed by automatic approaches and machine learning algorithms. Applications include estimating neurocognitive performance (Mazrooyisebdani et al., 2020), lesion detection in FCD type II (Jin et al., 2018), lateralization of seizure focus (Barron et al., 2015), and ictal onset zone identification (Van Eyndhoven et al., 2019). Although these measures have been extracted using non-invasive resting-state imaging techniques, in many cases they are limited to specific types of epilepsy, such as FCD type II or lesional patients. On the other hand, we demonstrated that during seizures nodes belonging to the EZ share a unique pattern of centrality, which was verified in the majority of our patients with different etiologies. Our results are consistent with iEEG (Warren et al., 2010) and ECoG (Burns et al., 2014) studies that demonstrated the isolation of SOZ from the rest of the network. More importantly, we investigated the relation between EZ-nR connectivity and patient demographics. We observed a negative correlation between these parameters, in which the EZ and non-resected regions become more desynchronized by aging and the duration of epilepsy (Figure 5). This finding can be explained by abnormal neuroplasticity, where the continuous recruitment of epileptogenic networks intensifies their anomaly (Tavakol et al., 2019). Related work has shown a negative correlation between TLE duration and overall interictal PLI at low frequencies (0.5–48 Hz) (van Dellen et al., 2009). A resting-state fMRI study indicated that the connectivity between two contralateral regions in the mesial temporal lobe is negatively correlated with the duration of epilepsy (Liao et al., 2010). Our results along with the studies cited suggest that network abnormalities can portray the disease severity (Tavakol et al., 2019). To further verify these findings, additional studies should be performed on a larger dataset while considering other influencing factors, including sex, handedness, and lateralization of the SOZ.

The origin and frequency range of HFOs in ictal and interictal states are still disputable (González Otárula et al., 2019; Jacobs et al., 2012; Korzeniewska et al., 2014; Tamilia et al., 2018; Weiss et al., 2013). Recent research has emphasized that narrow-band physiological HFOs, not pathological HFOs or broad-band multi-unit activity (MUA), are responsible for long-range high-frequency synchronization in interictal recordings (Arnulfo et al., 2020). Also, it has been suggested that widespread HFO synchronization should be a characteristic of healthy brain activity (Arnulfo et al., 2020). In our findings, the ictal HFS between the EZ and non-resected areas was the most distinctive pattern among others and showed a significant desynchronization in the early and middle parts of the seizure (Figure 4). In this period, the exclusive presence of pathological HFOs inside the EZ resulted in decreased EZ-nR synchrony while the nR-nR connectivity was left intact. Towards seizure termination, this unique activity faded (Smith et al., 2016) and elevated the similarity of signals in the EZ and non-resected areas, which is consistent with a previous study in the same frequency range (Schindler et al., 2010). Once the seizure terminated and the brain resumed a healthy activity, we observed a widespread HFS irrespective of pathology, a possible outcome of physiological HFOs.

We used the right singular vectors in mlEVC decomposition to explore the network topology during seizures (Figure 3). This feature demonstrated the reconfiguration of brain networks and was later used for clustering these dynamics into brain states. The profound alterations of these features revealed the extensive changes in network topology, even when the nR-nR connectivity was relatively stable. Several studies have also displayed the presence of different brain states in the ictal period (Burns et al., 2014; Khambhati et al., 2015). However, our findings are distinctive in that they present dissimilar brain states among different seizures of the same individual, suggesting variant structures for seizure generation and propagation. It has been shown that TLE seizures can be divided into several categories and in an overwhelming majority of patients they belong to more than one category (Bartolomei et al., 2010). Consequently, in each individual, seizures can be generated by various and separate epileptogenic structures (Bartolomei et al., 2017; Bartolomei et al., 2010). Another study of TLE has identified patients with different seizure semiologies (Loesch et al., 2015), a possible outcome of variations in propagation networks. Recently, the Fingerprint features of the EZ were employed for clustering the seizures of each patient. In the presence of these variations in epileptogenic networks, it is essential to record multiple seizures (Struck et al., 2015) and prolonged interictal (Gliske et al., 2018) data. Also, seizure dissimilarities have been assessed by brain network measures in a wide frequency range (Schroeder et al., 2020). Here, we presented a new approach to group seizures based on the features of high-frequency synchronization networks. Additional work can be done to associate these findings with the patient’s semiology.

While we mainly focused on the dynamics of high-frequency synchrony, the low-frequency (3–50 Hz) propagation networks were also computed, to have a better understanding of large-scale brain interactions during seizures. Here, the PLI was used to address delays between ictal discharges in different channels. In early-seizure, the EZ-nR PLI was significantly smaller than connectivity among non-resected areas. This finding can be related to early-onset suppression of low frequencies in the EZ, as demonstrated in recent studies (Aupy et al., 2019; Grinenko et al., 2018). The low-frequency suppression can be described by rapid inhibitory synaptic currents which resist the seizure spread, causing inhibitory restraint (Schevon et al., 2012; Trevelyan, 2009). By mid-seizure, the ictal wavefront has recruited more areas and ictal discharges are traversing farther regions (Smith et al., 2016). Our results indicated an extensive increase in brain connectivity approaching seizure termination (Figure 6). This observation is consistent with multiscale recordings, reporting an increase in spatial and temporal correlation before seizures cease (Kramer et al., 2012; Martinet et al., 2017), as well as macroscopic cortical networks (Jiruska et al., 2013; Kramer et al., 2010; Schindler et al., 2007). The underlying mechanisms of seizure generation, evolution, and termination remain a matter of debate (Martinet et al., 2017). In addition to studies based on microscopic recordings and modeling, macro-electrode studies and a large-scale explanation of brain dynamics are necessary to develop a full understanding of this issue. Our findings suggest that at seizure-onset, the EZ loses synchronization with the rest of the network and the brain enters a desynchronized state. This condition continues through mid-seizure until the ictal wavefront has recruited many areas, including the core and penumbra (Smith et al., 2016). Subsequently, brain connectivity increases temporally and spatially, indicating an upcoming critical transition (Kramer et al., 2012). It has been shown theoretically and experimentally that brain networks require a higher coupling strength to restore synchronization than to lose synchronization (Kim et al., 2018). Our results support this idea since considerably stronger connectivity was needed to terminate seizures in comparison to that in the pre-ictal period.

It is important to remember that the recording techniques, signal processing approaches, and frequencies of interest are crucial in any study of brain connectivity. These parameters can be the reasons for current controversies (Jiruska et al., 2013). Recent research has investigated the effect of incomplete electrode sampling on network metrics (Conrad et al., 2020), in which EVC showed the highest reliability in comparison to other network metrics when randomly removing network nodes. However, they also showed that confidence intervals in network measures can vary significantly between patients. For this reason, care should be taken when interpreting and comparing different studies.

Employing the bipolar montage and a robust measure of synchrony, helped us to eliminate the effect of volume conduction and muscle artifacts (see Methods). In contrast, classic measures like coherence strikingly increase spurious connectivity. Additionally, our findings do not simply reflect the distance among the electrodes. We normalized the synchronization matrices with respect to the pre-ictal period based on an element-wise approach, previously suggested in Burns et al., 2014. This process reduces the chance of distance alone affecting the value of connectivity.

Limitations and Considerations

We should point out that cross-validation was not performed in this study for several reasons. First, resection labels were not used as part of the prediction algorithm, and the same performance function and ranges of coupling and thresholding values were applied to all subjects. Second, as shown in this manuscript and similar works, parameters such as coupling or active frequency bands are patient-specific. By using cross-validation, we would have to fix these parameters based on a subset of patients, which may not be ideal as the actual range of these parameters could differ from the training dataset. While this study was primarily conducted to propose the multilayer network methodology during seizures, a more rigorous investigation is necessary to evaluate the broader validity of our algorithm. Future research could use data from different clinical centers to assess the generalizability of the proposed technique and identify optimal parameters.

Filtering and subsequent analysis of HFOs should be performed with extra caution due to the possibility of producing false or spurious ripples. Research has shown that high-pass (>80 Hz) filtering of sharp transitions in EEG (such as artifacts and spikes) or harmonics of non-sinusoidal signals can result in such false ripples (Bénar et al., 2010). Several approaches have been suggested to investigate this phenomenon. These include visually inspecting the epileptic waveform alongside the filtered signal, using the time-frequency transform of the original signal since real and false ripples have different spectra, and employing automated spectral decomposition techniques such as Matching Pursuit (Bénar et al., 2010). In our analysis, we visually evaluated several seizures in both the time and time-frequency domains. However, it would be beneficial to use one of these mentioned algorithms in a systematic manner in future studies.

Materials and methods

Patients and recordings

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This retrospective study was approved by the institutional review board at the Cleveland Clinic. Single pulse electrical stimulation-induced cortico-cortical evoked potentials are collected as a part of the routine clinical care of patients undergoing SEEG at Cleveland Clinic. The ictal data is also collected during the presurgical SEEG evaluation. The full procedure for participant selection and data recording is described in our previous work (Grinenko et al., 2018). Briefly, we selected 16 patients who underwent SEEG implantation in the Epilepsy Center at Cleveland Clinic. SEEG placement (Gonzalez-Martinez et al., 2014) used multi-lead depth electrodes (AdTech, Integra, or PMT). Post-implanted 3D computed tomography (CT) images were aligned to T1-weighted MRI for anatomical localization of electrode leads. Patients were monitored for up to two weeks and their seizures were recorded by the Nihon Kohden EEG system with a sampling rate of 500 Hz (before 2012) or 1000 Hz (after 2012). After a thorough evaluation, the identified EZ was resected or ablated. The contacts (electrode leads) inside the resection or ablated region were determined by coregistration of the post-implant CT to a post-resection MRI 1–6 months after surgery. Based on follow-up information, all patients were determined to be seizure-free (Table 1).

We preprocessed SEEG signals before further analyses. First, we constructed bipolar channels by subtracting unipolar signals recorded from each pair of adjacent contacts. For analysis, we included bipolar channels only if both contacts were inside gray matter. Next, any DC offset was removed from each bipolar channel. Thereafter, using the Brainstorm software (Tadel et al., 2011), bipolar EEG signals were bandpass filtered in the 3–200 Hz range and notch filtered at 60, 120, and 180 Hz. Bandpass filtering was performed using a Kaiser-window linear phase FIR filter of order 7252 (for a sample rate of 1000 Hz), using the fir1 MATLAB function. We compensated for filter-induced delay by shifting the filtered sequence, resulting in a zero-delay filter. The notch filtering used an IIR filter of order 6 with a 3dB bandwidth of 1 Hz around the notch frequencies. We used the filtfilt function in MATLAB to compensate for group delay. The resulting preprocessed data were employed in all analyses in this paper. When analyzing low-frequency and high-frequency brain connectivity, we bandpass the preprocessed data using the same filter type (Kaiser-window linear phase FIR filter) with different ranges and orders.

High-frequency ictal networks

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The time-varying brain networks were computed in two frequency bands, 80–140 Hz, and 140–200 Hz. Briefly, we first applied the Hilbert transform to compute analytical signals in each frequency band. Dynamic connectivity matrices were calculated using pair-wise lagged-coherence (Pascual-Marqui, 2007) between signals in 2.5 s windows with 80% overlaps. Here, the term ‘synchrony’ is employed interchangeably with brain connectivity in high-frequency. Lagged-coherence removes spurious coherence values caused by volume conduction. As a result, we have time-varying N×N networks in two frequency bands for each seizure, in which N denotes the number of bipolar channels. Network calculation was performed using Brainstorm (Tadel et al., 2011). The connectivity matrices were z-scored with respect to the pre-ictal period and their values were mapped into the interval (0 1) using an exponential transform (Burns et al., 2014). Assuming a total of T overlapping 2.5 s windows during a seizure, in which T depends on the length of the seizure and window parameters, results in a three-dimensional (N×N×T) matrix or network for each frequency band.

mlEVC and its decomposition

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We constructed an NT ×NT super-adjacency (connectivity) matrix A with coupling effects between layers (Kivela et al., 2014). The diagonal N×N blocks were the adjacency matrices at different time points. Off-diagonal terms were identity matrices multiplied by a coupling parameter c, in which c{1, 2,, 10, 15}. Matrix A is irreducible for any c>0. The weighted identity blocks represent ordinal interlayer links between nodes corresponding to a particular contact (neighboring time points). One can consider the leading eigenvector of matrix A (φ1RNT) as the EVC of this super-graph (Solá et al., 2013). However, in our work, this vector was focused on a few adjacent layers and did not visually capture the centrality across all layers. This is because of the time-varying nature of ictal networks and the relatively weak coupling across time in our model. Historically, the EVC is defined as a weighted sum of all eigenvectors of the matrix but simplified to the leading eigenvector for matrices with one clique (Bonacich, 1972). In our model of time-varying brain connectivity, this simplification does not hold because of the time-varying nature of connectivity during the seizure that is embodied in the super-adjacency matrix. We, therefore, defined a mlEVC that combines the eigenvectors corresponding to the largest eigenvalues. As discussed in the results section, we chose T eigenvectors irrespective of the coupling parameter. In our observations, the eigenvectors φ1, , φT were each restricted to significant values across a few layers only. The Perron-Frobenius theorem asserts the positivity of σ1 (the largest eigenvalue) and φ1 but the elements of other eigenvectors can be non-positive (φi0 for 2iT). Since EVC is a measure of ranking between nodes, we considered the absolute values for all vectors. To extract the mlEVC for matrix A, the T largest eigenvalues were multiplied by their corresponding eigenvectors and the absolute values of the results summed,

mlEVC=σ1φ1+σ2φ2++σTφT

This vector was then reshaped to an N×T matrix, representing the variation in each node’s centrality over time, which we refer to as the mlEVC. In the case where c=0, mlEVC represents the concatenated EVC of the adjacency matrices computed separately for each time point. Elements with the smallest or highest values show isolated or strongly connected instances in time, respectively. Since EVC provides a connectivity ranking among nodes, the mlEVC of each seizure was quantized based on a percentile thresholding (d). The top d/2-portion of elements was assigned a value of ‘1,’ the bottom d/2-portion a value of ‘–1,’ and the remainder a value of ‘0.’ We concatenated the quantized mlEVC matrices into an N×Ttot matrix, in which Ttot= s=1If=12Tsf , where Tsf denotes the number of samples in the network for the sth seizure and fth frequency band. This matrix contains the centrality measure for I ictal periods in two frequency bands. The singular value decomposition (SVD) was applied to this matrix to find the left and right singular vectors : uiRN and viRTtot . The left singular vectors summarize each node’s characteristics across all seizures in the context of centrality.

Unsupervised clustering for EZ identification

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To identify candidate contacts for the EZ, weighted consensus clustering (Kiselev et al., 2017; Li and Ding, 2008) was employed, using combinations of the first four left singular vectors. These vectors were z-scored and used as features in a hierarchical clustering algorithm. This approach clusters the nodes in a bottom-up agglomerative fashion. Based on our hypothesis, the EZ should have a distinctive pattern of connectivity and therefore centrality. Our goal is, therefore, to find a dense target cluster of nodes (X=1) whose feature vectors have a significant distance from the centroid of the feature vectors of the other nodes (Y=0). As a result, we trace the dendrogram to the last step where the final two groups merge. For a fixed coupling and threshold, c and d, respectively, feature vectors were selected from a pool of normalized singular vectors, consisting of the five combinations:

K={{u1,u2},{u1,u3},{u2,u3},{u1,u2,u3},{u1,u2,u3,u4}}

For each combination, κrK, r={1,,5}, the feature vectors of dimensions 2–4 were integrated into the MATLAB hierarchical clustering function linkage (centroid with Euclidean distance). Nodes were divided into two groups before the last linkage. We assigned a binary label ‘1’ to nodes in the smaller cluster (presumptive target X) and ‘0’ to other channels (presumptive Y). Since hierarchical clustering is prone to outliers, we went one step back in the dendrogram if the minor cluster consisted of less than 5% of the nodes. In other words, we divided the nodes into three groups and selected the second minor group as the presumptive target.

Ideally, we would like to see a tight target cluster that is well separated. Consequently, one can evaluate a clustering technique by computing the quotient (Halkidi et al., 2001),

perf(r)=sep(r)comp(r)

where the separation index for the rth combination is defined as the Euclidean distance:

sep(r)=Y¯rX¯r22

where X¯r and Y¯r are the centroids of target and not-target clusters. Compactness is defined as the product of two measures of intra-cluster distance in the target group,

comp(r)= (1Mij>ixirxjr2)(maxi xirX¯r2)

in which xir is the feature vector of the ith point in the target cluster and M is the total number of pairs. The first term calculates distances between all nodes and the second term finds the farthest distance of a point from the center of the cluster.

We combined the hierarchical clustering results for all sets of feature vectors. The vector wRN is calculated as the probability that each node is a candidate for EZ,

w= 1r=1nperf(r)r=1nperf(r)lr

where lrRN is the hierarchical labeling result for the rth case. The parameter n≤5 is defined as the number of feature vector sets that lead to clustering where comp(r)0 which in turn requires a minimum of two contacts in the EZ cluster. Since we need a EZ vs non-EZ label for each node, the vector w was binarized using a threshold θ=n-1n . For the specific case n=1, θ=0.5. We constructed the binary vector lRN by thresholding w,

li={1               wi>θ0         otherwise

We repeated the above procedure for a range of parameter values: c{1, 2,, 10, 15} and d{0.1, 0.2,, 0.8}. The final consensus vector wRN was then computed to represent the overall chance of a node being in the target (EZ) cluster as

w=cdperf(c,d)lcd

The vector w is continuous where larger values indicate increasingly likely candidates for the EZ. We applied k-means clustering (k=3) on vector w and took the cluster with the largest average value as the final target (EZ) group of contacts. Note that in Figure 2 and Figure 2—figure supplement 1 we use a single fixed c and d for illustration purposes.

Brain states

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The seizure evolution is captured by the right singular vectors (viRTtot). To preprocess the data, the singular vectors were separated into distinct seizures and frequency bands. For each vector, the MATLAB outlier removal function hampel was then used to remove outliers, with 15 neighboring points and three scaled median absolute deviations (1.4826 × MAD). These vectors were then reconcatenated in two frequency bands (vifRTtot/2) where Ttot was defined as two times the length of seizures. We then applied K-means clustering, separately for each possible combination of four drawn from the six vectors corresponding to the first three pre-processed singular vectors in each of the two frequency bands. In other words, selecting from the following set,

S={v11,v12,v21,v22,v31,v32}

We repeated the analysis for different numbers of clusters and used the MATLAB silhouette function to determine the optimal number of clusters and best set of vectors. This metric compares the distance of each point with other points in its cluster to the distances to other clusters. The clustering with the highest Silhouette value was selected to construct the transition matrices and find the transitions among brain states (clusters) shown in Figure 3 and Figure 3—figure supplement 1. The final four selected vectors from S were denoted v-a, v-b, v-c , and v-d .

Statistical analysis of functional connectivity in high-frequency

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To quantify brain dynamics, time-varying connectivity measures were constructed for each seizure and frequency band, based on the connectivity between brain regions as follows: EZ-nR, RnEZ-nR, and nR-nR, where EZ, RnEZ, and nR represent respectively predicted EZ (identified using the methodology described above), resection region not in the EZ, and non-resected areas. Each measure was defined by averaging all connectivity values between nodes in the two regions. As a result, we have three synchrony time-series vectors for each seizure/patient/frequency (s/p/f) at 2 samples/s.

We examined these time series over three sub-intervals: pre-ictal (−0.3,–0.1) L, mid-seizure (0.3, 0.5)L, and post-ictal (1, 1.2)L. For each synchrony measure, we computed the average value of connectivity in these intervals, resulting in nine values for each s/p/f (39 seizures in total and two frequency bands). We employed a robust percentile bootstrap test (Wilcox, 2011) with a one-step M-estimator to perform statistical tests for pairwise comparison between and within the three measures at each of the three periods (function rmmcppb in WRS2 package (Wilcox, 2011) for R). Computed p-values were corrected using Hochberg FDR correction for J=18 comparisons. The results are shown in Figure 4 and Figure 4—source data 1 . The EZ-nR connectivity in the mid-seizure was the most remarkable characteristic of the ictal period. Consequently, we used this to explore how the feature changes among patients. For each participant, we averaged the value of EZ-nR among all seizures. We then performed robust regression of these values using bootstrap sampling and the Theil-Sen algorithm (Wilcox, 2011) against both patient age and duration of epilepsy as shown in Figure 5.

Low-frequency propagation networks

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Data was filtered in the range of 3–50 Hz. Propagation networks were computed using the PLI over a moving window with a 2.5 s length and 90% overlap. Connectivity matrices were computed from normalized PLI values using element-wise z-scoring with respect to the pre-ictal period and their values were mapped into the interval (0 1) using an exponential transform (Burns et al., 2014). We used the previously defined measures, EZ-nR, RnEZ-nR, and nR-nR, to explore interactions among brain regions at these lower frequencies. An analogous analysis to the last section was performed except the selected time intervals were pre-ictal (−0.3,–0.1) L, early-seizure (0,0.2)L, and pre-termination (0.8,1)L. These results are presented in Figure 6 and Figure 6—source data 1.

Data availability

The results and codes generated during the current study are available in the following repository, https://data.mendeley.com/datasets/t8bvh5m8bp/1.

The following data sets were generated

References

    1. Kahane P
    2. Landré E
    3. Minotti L
    4. Francione S
    5. Ryvlin P
    (2006)
    The Bancaud and Talairach view on the epileptogenic zone: a working hypothesis
    Epileptic Disorders 8:S16–S26.
  1. Conference
    1. Li T
    2. Ding C
    (2008) Weighted Consensus Clustering
    Proceedings of the 2008 SIAM International Conference on Data Mining. pp. 798–809.
    https://doi.org/10.1137/1.9781611972788.72
    1. Nair DR
    2. Mohamed A
    3. Burgess R
    4. Lüders H
    (2004)
    A critical review of the different conceptual hypotheses framing human focal epilepsy
    Epileptic Disorders 6:77–83.
  2. Book
    1. Wyllie E
    2. Gidal BE
    3. Goodkin HP
    4. Loddenkemper T
    5. Sirven JI
    (2015)
    Wyllie’s treatment of epilepsy: Principles and practice (6th ed)
    Lippincott Williams & Wilkins.

Decision letter

  1. Alex Fornito
    Reviewing Editor; Monash University, Australia
  2. Michael J Frank
    Senior Editor; Brown University, United States
  3. Mangor Pedersen
    Reviewer; Auckland University of Technology, New Zealand
  4. Christian Benar
    Reviewer; Aix-Marseille University, INSERM, France

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Decision letter after peer review:

Thank you for submitting your article "Multilayer brain networks can identify the epileptogenic zone and seizure dynamics" for consideration by eLife. Your article has been reviewed by 3 peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Michael Frank as the Senior Editor. The following individuals involved in review of your submission have agreed to reveal their identity: Mangor Pedersen (Reviewer #2); Christian Benar (Reviewer #3).

The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.

Essential revisions:

1. The prediction of the EZ seems to be completely within-sample. Please provide some indication of cross-validated out-of-sample prediction accuracy.

2. Please evaluate network properties with respect to appropriate null models. An important component of assessing the presence of network structure is to evaluate whether that same structure or nodal importance is not evident in null model where the underlying network structure is randomized. This is key to making sure that clustering results are not just sensitive to random fluctuations in the data. One suggestion is to use a phase-randomization of the voltage trace before computation of HFS to help better evaluate the null distribution of the mlEVC metric. A related reference is: https://pubmed.ncbi.nlm.nih.gov/22343126/

3. The authors may consider that at least one recent study has discussed the challenges and considerations of different recording and electrode sampling techniques on network metrics. And may explain discrepancies in the findings across studies: https://pubmed.ncbi.nlm.nih.gov/32537538/

4. The methods used in this study are complex, and rationale behind the series of steps used to perform the study are not provided. Given that this paper is primarily showcasing a novel method, the authors may want to consider incorporating more methodological details and rationale in-line with the Results.

5. Providing intuition behind abstract mathematical concepts would be helpful. For example (lines 139-141): Help the reader interpret the hierarchical unsupervised clustering applied to the left singular vectors of the concatenated and quantized mlEVC.

6. Line 96: Consider describing the concepts of graph/super-graph, and single/multi-layer in a general sense, first, as this is the first use of these terms in the manuscript.

7. Line 262: Typo, should "EZ-RnRZ" read "EZ-RnEZ".

8. The seizure evolution and state transition plots can be difficult to follow, due to the combination of colors and hues. Please consider a flow field or separate plots per seizure help demonstrate the overlapping and non-overlapping dynamics between seizures?

9. The authors may want to consider incorporating additional details in Table 1, pertaining to: (a) size of the network; (b) number of nodes overlapping with the resected tissue; (c) durations of the seizures; (d) seizure type.

10. One previous study motivated the application of phase and lagged-based connectivity metrics on the analytical amplitude of the broadband signal to avoid computing phase relationships within the asynchronous broadband range of the voltage signal. See: https://pubmed.ncbi.nlm.nih.gov/12631571/. Note that this is distinct from applying phase-based connectivity metrics directly to the high-frequency broadband component of the voltage signal or to high-frequency narrowbands (such as HFOs).

11. If I understand the methodical approach correctly, the authors generate an ordinal graph optimal when using fast intracranial electrophysiological data (500 or 1000Hz). It would be interesting to see a correlation plot between the current eigenvector centrality with an ordinal coupling parameter and cross-correlation of this data at multiple time-lags. In addition to tuning the coupling strength, the current work would be improved to quantify the optimal time interval between matrix 'layers'. It would be useful for the authors to consider/discuss this point in detail.

12. Related to the previous comment, it would be good to head further why the authors choose to use the Phase Lag Index for slow frequency estimation, a measure that does not operate proximately to the zero-lag.

13. A clearer rationale for using a spatiotemporal graph if warranted in this paper. The authors outline and justify the use of multilayer graphs from a methodological point of view, but it would also be good to hear why the authors choose this methodology from a clinical point of view. i.e., what can multilayer metrics tell us about epilepsy that single-layer cannot?

14. Related to the previous point, have the authors thought about comparing eigenvector centrality between multilayer and single-layer graphs, to see whether the results differ between the two?

15. Please provide more details about the filtering procedure, conducted before the Hilbert transform, including the type (and order) of filtering, how the DC offset was accounted for and whether the Hilbert transform in the given frequencies satisfy the Bedrossian's criteria for narrow-band frequency estimation (Xu and Yan, 2006).

16. It would have been nice to see in more detail examples from one or two patients with the actual resection area and the detected networks in volume. Figure 1 would benefit from an intuitive description of the method.

17. P7 It seems to me the term 'primary organization' has to be credited to Talairach and Bancaud. Also, early work on network organization were performed by Wendling and Bartolomei and could be cited (including the desynchronization at seizure onset in Wendling et al. 2003).

18. P8 it is very interesting to see that in a few patients one method fails whereas the other gives good results. This pleads for a complementarity of strategies to cope with inter-patient variability. Can the authors make hypotheses on which signal features/seizure patterns could explain the difference in results across methods and patients?

19. P11 « false positives from the EZ » this really depends on the definition of the EZ. If this is the minimum of cortex to be resected to render the patient seizure free, then the statement may hold. If this is the « primary region of organization of seizures » (definition of Bancaud, given p7), it is possible that not all these regions need to be resected. It would be useful to clarify the two definitions.

20. p17 it would be very interesting to perform a comparison of HF and LF synchrony in predicted the EZ. Moreover, as mentioned below too, part of the HF synchrony can arise from trains of sharp spikes that have energy in all frequencies, which would not be synchrony of high frequency oscillations but an emphasis on the sharp part of ictal spikes. This is not a problem per se, but more an issue of interpretation of the results.

21. Is data processing on monopolar or bipolar montage? Please clarify

22. Is it possible that part of the synchrony arises from filtered spikes? Can the authors provide a (normalized across frequencies) time-frequency representation of a representative seizure in order to assess the relative contribution of oscillations and spikes?

23. P25, eigenvalue centrality. While the rank of the matrix is likely to be T, wouldn't one expect some kind of temporal correlation across points (arising from both the high overlap and some actual temporal persistence of the networks), which would result in an elbow in the eigenvalues after some dimension? If it is not the case, and each time point is independent from the other ones (linear eigenvalue spectrum), what is the added power of multilayer method? Wouldn't a more simple method as summing the degrees across time be equivalent? Please clarify.

24. It would be interesting to visualize the eigenvalues of a representative example in order to measure this. Also, and importantly, it would be useful to compare the multilayer method to a simple mean degree across time (Wilke et al. 2010, van Mierlo et al. 2013, Courtens et al. 2016, Li et al. 2016, Balatskaya et al. 2020).

References:

Kramer, M.A., Eden, U.T., Kolaczyk, E.D., Zepeda, R., Eskandar, E.N., Cash, S.S., 2010. Journal of Neuroscience. 30, 10076-10085.

Schindler, K.A., Bialonski, S., Horstmann, M.-T., Elger, C.E., Lehnertz, K., 2008. Chaos 18, 033119.

Xu, Y and Yan, D, 2006. Proceedings of the American Mathematical Society 134, 2719-2728

Reviewer #1:

In this study, Shahabi and colleagues develop a new computational algorithm based on graph theory to study changes in brain network connections during drug-resistant, epileptic seizures. The structure and organization of these network connections have been the subject of many studies over the past two decades with the principal purpose of mapping seizures and identifying targets for resective surgery. A novel analysis of distributed brain network interactions between the local epileptogenic zone and remote, healthy brain areas outside of this zone is facilitated by invasive stereo-electroencephalographic (sEEG) recordings, which are a key asset to the present study. The authors construct time-dependent functional brain networks based on inter-areal synchrony in the high-frequency band and combine a new graph theory metric called multilayer eigenvector centrality (mlEVC) to quantify the changing pattern of connectivity amongst brain areas within and outside the epileptogenic zone. Using their innovative technique, the authors recapitulate a widely reported result that seizure progression invokes a robust alteration in network organization in which connectivity between the epileptogenic zone and healthy brain areas desynchronize. However, a key contribution of the present study is that the network nodes in the epileptogenic zone whose subsequent surgical resection led to seizure freedom could be predicted using unsupervised machine learning. These findings suggest that nodes involved in desynchronization during seizures may serve as putative surgical targets for epilepsy treatment. The authors also demonstrate that if patients are left untreated, then this abnormal desynchronization process during seizures intensifies with age and duration of epilepsy. This is a compelling scientific advancement in the field that begins to tackle the long-standing question of whether seizures beget seizures.

Generally, the study and analysis are presented as exploratory and proof-of-principle. A major strength of this study is the development of a new methodology to describe complex properties of seizures. However, I have concerns regarding possible overfitting of the data as no cross-validation nor testing was performed. Key claims could be better motivated with concrete hypotheses that are contextualized by prior work. My specific comments are detailed below:

1. Key questions posed in the study are provided and/or stated in the introduction but in many cases the importance or relevance in the broader context are not fully developed. Examples below:

a. Lines 50-52: "It has also been suggested that ictal periods can be delineated by a steady series of states(Burns et al., 2014), although whether this is true in all patients remains controversial."

b. Lines 52-55: "It remains unclear how the degree of desynchronization is correlated with physiological parameters such as age and duration of epilepsy(Van Diessen et 55 al., 2013a)"

2. Much of the introduction focuses on high frequency oscillations and pros/cons of their utility in localizing seizure foci. The authors present ictal high frequency synchronization as a phenomenon of interest, but to the general audience the differences between HFO and HFS are not concretely provided. The rationale for studying ictal HFS over HFOs is also not provided. Are these the same phenomenon? Are they distinct? Why do authors deem HFS analysis important for this study?

a. Lines 75-77: "While HFOs have been employed in analyzing functional(Schindler et al., 2010) and propagation(González Otárula et al., 2019) networks, the spatiotemporal dynamics of ictal high frequency synchronization (HFS) at macroscopic scales remain largely unknown."

b. Lines 238-240: A later point conflates HFOs and HFS as the same phenom: "Early-onset and late ictal HFOs have been considered biomarkers for seizure onset zone identification (Weiss et al., 2013), with the latter found to be a more reliable metric (Modur et al., 2011). Our EZ localization technique considers both features."

3. The interpretation of connectivity in the high-frequency broadband is unclear in the context of previous studies that demonstrate that the broadband activity is due to asynchronous, non-oscillatory neural firing (see references below). Consequently, it is unclear how one should interpret the notion of "synchronization" in the broad 80-200 Hz frequency range.

a. https://pubmed.ncbi.nlm.nih.gov/23283342/

b. https://pubmed.ncbi.nlm.nih.gov/29167419/

4. Was a null network model employed to ascertain whether the clustering procedure and the mlEVC metric identified target epileptogenic zone areas more reliably than chance?

5. What was the trade-off in the sensitivity and specificity of the EZ prediction algorithm? A receiver-operator curve analysis would help here.

6. One concern is that the analysis corresponding to the prediction of the epileptogenic zone is performed at the population level – aggregating nodes across all patients (line 160). What was the mean and standard error of the performance across patients?

7. The comparison between the present method and Fingerprinting method is of great value here. However, a clear conclusion regarding the comparison is not provided because the two algorithms provided results that only partially overlapped. How do these results compare to more conventional measures of the epileptogenic zone such as HFOs or spikes derived from the same dataset?

8. Results regarding the occurrence of different states of connectivity during the ictal period (lines 177-180) are certainly very interesting, but it is not clear how this finding advances previous studies:

a. https://pubmed.ncbi.nlm.nih.gov/20668192/

b. https://pubmed.ncbi.nlm.nih.gov/23366973/

9. A related worry regarding statistical power of the study is reflected in the stereotypy analysis (lines 192-195). To what extent is the stereotypy / lack of stereotypy in the network a function of the dimensionality of the feature space and overfitting of the data? Specifically, as the number of features / complexity of the model increases, are you more likely to find that each seizure event network is different from the others? A cross-validation and out-of-sample prediction approach would help mitigate these concerns.

10. The finding that stereotypy does not necessarily occur at high-frequencies is very interesting (lines 206-209), but the claim is not supported by any statistical testing. Furthermore, the explanation provided "the brain experiences divergent topologies, which might be the result of dissimilar EEG recordings" (line 209) is rhetorical as the topologies are based on features derived from the EEG recordings.

11. Why was the mid-seizure period used to normalize network measures for age/epilepsy duration-related analysis? How is this baseline period more advantageous than a pre-seizure baseline?

12. Were any other connection groups tested as being predictive of age or duration of epilepsy? In particular, is it possible that prolonged epilepsy might reorganize areas that are purely outside the EZ? Was there any relationship between the size of the EZ and age/duration?

13. Can the authors be sure that the emergence in low-frequency connectivity is not related to an increase in the rate or amplitude of ictal spiking? Are they independent phenomena?

14. How are the phases of the seizure (pre-termination, termination, early-seizure) defined? Are they based on the state analysis or on expert ratings of the seizures? A clear definition of these periods would be helpful.

15. Specific steps and choice of parameters in the unsupervised clustering pipeline described in the Methods are not justified. Such as

a. Usage of just the first four singular vectors

b. Limited combinations of the singular vectors

c. Determination of the rank T for the A matrix

d. How the mlEVC approach compares to the traditional EVC approach similar to that studies in the Burns et al. (2014).

Reviewer #2:

The authors combines intracranial EEG data with multilayer network modelling to delineate the seizure onset zone and spatiotemporal network activity during seizures. The major strength of this study is that the networks in this study incorporates spatial and temporal connectivity during seizures, and the relative importance of different intracranial electrodes. This is a novel and interesting approach that is likely to have an impact in the field. Below I discuss two topics (near zero-lag connectivity and previous research in the field) that is worth bearing in mind regarding the current manuscript.

- The authors generate an ordinal graph (connectivity between two adjacent time-points) to quantify spatiotemporal connectivity from intracranial electrophysiological data with a high sampling rate. An ordinal graph computes the connectivity between two adjacent time points, which may represent synchronicity close to a zero-lag in this data. It is worth bearing in mind graphs with connectivity data where time-points that are further apart, and how this may reflect neuronal connectivity at different time-scales.

- The current set of findings are interesting and they show good clinical accuracy at predicting the seizure onset zone. Spatio-temporal connectivity during seizures in this study also align with previous graph theoretical research using intracranial electrophysiological with single-layer graphs. Previous studies show distinct time-varying peri-seizure changes in the clustering coefficient and path length metrics. During seizure initiation and propagation, there is an increase of clustering coefficient and shortest path length, resembling a regularized, or isolated, network topology (Kramer et al., 2010; Schindler et al., 2008). In a network that is regularized, local clusters of neurons may isolate themselves from the rest of the network. It would be good to evaluate the current findings in the context of previous graph theoretical research using intracranial electrophysiological data in epilepsy.

Reviewer #3:

This manuscript introduces a new method for identifying the epileptogenic zone from intracerebral EEG data, based on graph measures in high frequency bands, multilayer graph analysis and clustering.

Graph measures and multivariate methods are promising tools in the electrophysiological characterization of the epileptogenic zone; the strategy proposed here falls within this timely topic. The strength of the approach is to be fully automatic, and to rely on multivariate measures that can capture the overall structure of the data better than the usual monovariate measures. The method identified electrodes within the resected area in 88% of the patients, with only few contacts detected outside of the resection.

It could be interesting to also test the method versus the clinician EZ, as the resected area may be larger this would be consistent with the fact that the 'target' area found by clustering is much smaller that the resected contacts. This would be a further probe of the sensitivity of the method. Another interesting measure would be to probe whether the proportion of contacts outside the resected area increase in non seizure-free patients. Yet another interesting test would be to see whether the multivariate method outperforms more classical measures such as graph strength. In other words, it what does the multilayer approach add to the single layer measures?

[Editors' note: further revisions were suggested prior to acceptance, as described below.]

Thank you for resubmitting your work entitled "Multilayer brain networks can identify the epileptogenic zone and seizure dynamics" for further consideration by eLife. Your revised article has been evaluated by Michael Frank (Senior Editor) and a Reviewing Editor.

The manuscript has been improved but there are some remaining issues that need to be addressed, as outlined below. Please address these comments comprehensively in your response.

1. In their response and amendments to the main text, the authors claim that their method does not require cross-validation and testing over independent datasets since the approach does not involve training the model parameters across patients and does not access information regarding the resection zone. While it is true that the method is applied to each patient, separately, the methodological choices including, but not limited to, functional connectivity metrics, frequency band selection, percentile threshold selection, still effectively "train" the general algorithm and may be highly specific to the cohort studied here. This issue presents itself as a driver of inter-patient variability, as demonstrated by the conflicting findings between the mlEVC method and Fingerprint method. While this limitation detracts from the methodological advances put forth by this study, but some caution in making the claim that cross-validation/testing is not necessary is warranted. Specifically, the manuscript should include a rationale for why cross-validation was not applied in this context, coupled with an acknowledgement that such an approach in future will be important to verify the current results.

2. The relationship between the coupling parameter and network time-scale should be further elaborated, given the importance of this parameter to the authors' claim that patients may have different rates of network change. Please present data examining how sensitive the findings of the EZ are to the choice of this parameter. Please also provide examples of how different coupling parameters would yield more insight into the different time-scales of network change

3. The findings comparing a single-layer model to the multi-layer model should be explicitly quantified to concretely justify the claim in the Discussion section that single-layer models yielded poorer EZ identification than multi-layer models. How much more accurate was the multi-layer model to the single-layer model?

4. More attention should be paid in the text to the risk of contamination of high frequency synchrony by two processes: (1) Filtering of spikes; and (2) Harmonics of non-sinusoidal oscillations. These topics are addressed in the following study, which could be cited in support of the discussion.

Pitfalls of high-pass filtering for detecting epileptic oscillations: a technical note on "false" ripples. Bénar CG, Chauvière L, Bartolomei F, Wendling F. Clin Neurophysiol. 2010 Mar;121(3):301-10

5. The time frequency figures should be accompanied by a presentation of the signal time course in order to fully appreciate the presence/absence of spikes. While there indeed seems to be spikes in the preictal period (vertical lines) , they present much less energy than the high frequency activity during the seizure. This large increase is quite blurred and indistinct and it is not clear what this actually represents. The original signal time course would help understand which seizure pattern this corresponds to.A consideration of the potential effect of harmonics would also be helpful.

https://doi.org/10.7554/eLife.68531.sa1

Author response

Essential revisions:

1. The prediction of the EZ seems to be completely within-sample. Please provide some indication of cross-validated out-of-sample prediction accuracy.

We were inspired by (Burns et al., 2014) while working on our hypothesis. They state, based on exploratory observations, that:

“We found that, in patients with positive surgical outcomes (i.e., patients who were seizure-free after surgery; Table 1), the focal areas were the least connected in the network (least important) shortly after the onset time of the seizure and we denoted this state as the “isolated focus” (IF) state. We also found that, in many of these patients, the focal areas became most connected in the network in a brain state that occurred during the middle or end of the seizures, and we defined this state as the “connected focus” (CF) state.”

They used the clinical resection information to investigate the dynamics of eigenvector centrality in the seizure onset zone. They observed specific patterns of centrality among different groups of patients. However, (Burns et al., 2014) did not introduce an algorithm that directly predicts the seizure onset zone. We believed that there is a gap in this part of literature and an automated algorithm could be developed to help predict the epileptogenic zone (EZ) from ictal network measures separately in each subject.

We therefore proposed an unsupervised framework that aims to identify the epileptogenic zone without any knowledge about the actual resection volume. Based on the observations in (Burns et al., 2014) and other studies, we hypothesized that the EZ should have a unique pattern of brain connectivity. Our algorithm for EZ identification is the same for all patients and does not involve training using resection labels. Since the algorithm was not trained across subjects, there is no need for a separate out-of-sample validation.

The steps employed for unsupervised clustering are common in the literature. For example, thresholding and quantization have been widely used in different brain network studies. For selecting a proper coupling parameter in our multilayer model, we followed the guidelines in (Betzel and Bassett, 2017).

“Without strong evidence to select one weighting scheme over another, interlayer links are usually assigned the same value, ω, that is sometimes varied over a narrow range. Ideally, there would be a principled, data-driven approach for selecting this value.”

Considering neural mechanisms with different timescales, we hypothesized that the proper interlayer parameter might be different among patients. As a result, in our data-driven approach, we first defined a performance function (Halkidi, 2001) for the unsupervised clustering algorithm linkage in MATLAB. As we describe in the method section, the performance function was defined based on our hypothesis that nodes inside the “presumptive EZ” should have a similar pattern of brain connectivity. For the final analysis, we combined the results of performance function over the full range of values for thresholding and interlayer coupling parameter, in an identical manner for each subject. These ranges were held constant among all patients.

To clarify this point in the paper, we added the following to the Results section:

“Cross-validation and testing over a separate independent set were not required for our EZ identification technique since the unsupervised approach was applied independently to each subject without training within or across subjects. Furthermore, resection labels were not employed as part of the prediction algorithm. The same performance function and ranges of coupling and thresholding values were used for all subjects.”

In addition to examining the accuracy of our method on 16 patients, we also performed several other analyses to evaluate validity of our technique, which are described later in this response, with associate modifications in the manuscript. Finally, we note that in the initial version of this manuscript, we used “classification” or “classify” interchangeably with “grouping” or “clustering”. We have clarified the text to make it clearer that all clustering was performed in an unsupervised manner.

2. Please evaluate network properties with respect to appropriate null models. An important component of assessing the presence of network structure is to evaluate whether that same structure or nodal importance is not evident in null model where the underlying network structure is randomized. This is key to making sure that clustering results are not just sensitive to random fluctuations in the data. One suggestion is to use a phase-randomization of the voltage trace before computation of HFS to help better evaluate the null distribution of the mlEVC metric. A related reference is: https://pubmed.ncbi.nlm.nih.gov/22343126/

We consulted the suggested reference (Zalesky et al., 2012) and a related paper for generating surrogate data by time series randomization using Fourier transform and phase scrambling (Prichard and Theiler, 1994). The latter article was employed to create surrogate data for several patients, using their SEEG signals during seizures. The mlEVC metric for phase-randomized signals was calculated with several coupling parameters. We compared results of original times series and surrogate data. Results are presented in new Figure 2—figure supplement 2 – see added text below. The left column portrays the mlEVC for the original data and the right column depicts the same metric when the phase scrambled data was used. We sorted nodes such that those inside the resected volume are on the top of the figures. We observe a clear distinction between the two scenarios, in which the mlEVC of the original time series displays characteristic patterns both in resected and non-resected regions that are not apparent in the scrambled data.

We added this paragraph to the results:

“To explore the validity of our approach, we constructed a null model by also computing the mlEVC from phase-randomized SEEG signals (Prichard and Theiler, 1994). In figure 2—figure supplement 2, we show typical results of the mlEVC measures calculated from the original time-series and phase-randomized data for a single subject. These result show significant differences between original and randomized data in which the characteristic patterns of brain connectivity both in resected and non-resected areas are lost when signals are phase-randomized. We performed this analysis for different patients and seizures with similar findings.”

3. The authors may consider that at least one recent study has discussed the challenges and considerations of different recording and electrode sampling techniques on network metrics. And may explain discrepancies in the findings across studies: https://pubmed.ncbi.nlm.nih.gov/32537538/

In the introduction and discussion, we note possible sources of discrepancies among the results of studies on ictal connectivity. In particular, based on the reviewers’ suggestion we added the following:

“Recent research has investigated the effect of incomplete electrode sampling on network metrics (Conrad et al., 2020), in which eigenvector centrality showed the highest reliability in comparison to other network metrics, when randomly removing network nodes. However, they also showed that confidence intervals in network measures can vary significantly between patients. For this reason, care should be taken when interpreting and comparing different studies.”

4. The methods used in this study are complex, and rationale behind the series of steps used to perform the study are not provided. Given that this paper is primarily showcasing a novel method, the authors may want to consider incorporating more methodological details and rationale in-line with the Results.

5. Providing intuition behind abstract mathematical concepts would be helpful. For example (lines 139-141): Help the reader interpret the hierarchical unsupervised clustering applied to the left singular vectors of the concatenated and quantized mlEVC.

6. Line 96: Consider describing the concepts of graph/super-graph, and single/multi-layer in a general sense, first, as this is the first use of these terms in the manuscript.

The reviewers suggested adding more description regarding the methodology in the results and introduction section of this paper. Before explaining our changes in detail, we note that the proposed methodology in this paper is dominantly focused on EZ identification. Following the eLife format, we incorporated the detailed algorithm description at the end of the paper. In Response 1 above, we elaborated how these steps were chosen based on published studies and common practice in the current literature. To improve the readability of the manuscript, we made the following modifications:

In the introduction, we introduce mathematical concepts including graphs/super-graphs/multilayer.

“Graph analysis provides a mathematical framework for quantification of brain connectivity (Bullmore, 2009). Brain networks may be represented as a graph, G=(V, E),­ in which nodes (V) characterize anatomical regions or electrodes, and edges (E) reflect structural or functional connections among them. Traditionally, brain connectivity in each time sample (layer) of dynamic networks has been evaluated independently, via single graph analysis. However, multilayer analysis allows us to model the entire data with a single super-graph, in which individual graphs for each time-sample are linked. Assuming there are T single graphs (time-samples) with N nodes in each, the super-graph has NT nodes.”

In the Results section, we added references to the eigenvector centrality (EVC) and its formulation. EVC usage in ictal studies and its limitation is also discussed. We then describe why and how a new measure (mlEVC) has been defined based on our multilayer model:

“As discussed in the introduction, we aimed to model ictal brain connectivity by multilayer networks. Additionally, we were interested in quantifying network dynamics using centrality metrics (Rubinov and Sporns, 2010). Among those measures, eigenvector centrality, a rank-based metric which assesses the importance of each node in the network (Bonacich, 1972), has been employed in studying seizures (Burns et al., 2014). Mathematically, the leading eigenvector of the adjacency (connectivity) matrix has been assigned as the eigenvector centrality of the graph when there is one clique (component) in the matrix (Bonacich, 1972). However, in our multilayer model of time-varying brain connectivity, a single vector cannot explain the complex structure of the spatiotemporal networks. Therefore, we introduced a new measure called multilayer eigenvector centrality (mlEVC) that incorporates the top T eigenvectors of the adjacency matrix of the super-graph (see Methods). This allows us to evaluate patterns of nodal centrality and identify regions with similar connectivity characteristics to the rest of the graph. Further, because mlEVC is a function of the interlayer coupling parameter (c), we can explore neural processes at different timescales by varying c.”

In the results, a new section entitled “Algorithm for predicting EZ using mlEVC” was inserted to explain our algorithm, the rationale behind each step, and the way it was executed:

“We hypothesize that the EZ can be identified as the set of nodes in the graph that exhibit a characteristic and distinct pattern of connectivity to other areas during the seizure. To explore this question, we first quantized the mlEVC of each seizure into three levels based on percentile thresholding (d). The top d/2-portion of elements were assigned a value of ‘1’, the bottom d/2-portion a value of ‘-1’, and the remainder a value of ‘0’. For each subject, quantized measures of mlEVC for two high-frequency bands and all seizures were concatenated to a single matrix with dimension N by Ttot (twice the total number of sample points) (see Methods). We applied the singular value decomposition (SVD) to the concatenated matrix and used the left singular vectors (uiRN) to identify nodes (SEEG channels) with similar features. As an illustration, Figure 2c depicts u1, u2, and u3 for patient 17.

Next, we applied an unsupervised clustering algorithm using the ui vectors to detect a target cluster that represents the EZ. Following our initial hypothesis, the target cluster should portray a dense and distinctive set of nodes in the feature space with a significant distance from nodes in the non-target group (Figure 2c). We describe the clustering algorithm in detail in the method section. Briefly, we designed a data-driven framework to cluster nodes into two groups using an agglomerative hierarchical clustering technique (function linkage in MATLAB). This process was performed for different combinations of ui as features of the clustering algorithm, and a range of values for c and d, resulting in 440 clustering runs. We weighted each run using a performance function (Halkidi, 2001) that examines the tightness of the target cluster and its separation from other nodes. Finally, using the weighted sum of performance metric for all runs, SEEG contacts were divided into two groups; target and non-target.”

In the methods, we added the following description:

“Historically, the EVC is defined as a weighted sum of all eigenvectors of the matrix, but simplified to the leading eigenvector for matrices with one clique (Bonacich, 1972). In our model of time-varying brain connectivity, this simplification does not hold because of the time-varying nature of connectivity during the seizure that is embodied in the super-adjacency matrix.”

7. Line 262: Typo, should "EZ-RnRZ" read "EZ-RnEZ".

Thanks for pointing this out. Corrected.

8. The seizure evolution and state transition plots can be difficult to follow, due to the combination of colors and hues. Please consider a flow field or separate plots per seizure help demonstrate the overlapping and non-overlapping dynamics between seizures?

We updated the state transition plots based on your recommendation. Please check figure 3d and figure 3—figure supplement 1.

9. The authors may want to consider incorporating additional details in Table 1, pertaining to: (a) size of the network; (b) number of nodes overlapping with the resected tissue; (c) durations of the seizures; (d) seizure type.

We updated Table 1 with the requested information for parts a, b, and c. Unfortunately, we do not have the seizure type in our database.

10. One previous study motivated the application of phase and lagged-based connectivity metrics on the analytical amplitude of the broadband signal to avoid computing phase relationships within the asynchronous broadband range of the voltage signal. See: https://pubmed.ncbi.nlm.nih.gov/12631571/. Note that this is distinct from applying phase-based connectivity metrics directly to the high-frequency broadband component of the voltage signal or to high-frequency narrowbands (such as HFOs).

We understand the reviewers’ questions about the terminology, relation of HFOs and high-frequency synchronization and applying phase-based connectivity metric on broad-band signals.

To clarify the terminology and justify the methods and approach used in our analysis, we first added the following description to the introduction.

“The term HFOs has been attributed to brain activity, with multiple possible physiological and pathological neural mechanisms, between 80-500 Hz (Jacobs et al., 2012) or 30-600 Hz (Engel and da Silva, 2012). This includes high-γ neural activities (80-200 Hz) (Ray and Maunsell, 2011) and broad-band high frequency (Arnulfo et al., 2020).”

Although some epilepsy studies have investigated HFOs with specific patterns (e.g. ripples and fast ripples in the time-domain), the broad definition of HFOs remains unchanged. Our analysis of brain connectivity uses the standard HFO definition and is computed using a synchrony metric.

Regarding use of phase-based measures on broad-band signals we added references to several studies that employ them (see Results section):

“Several studies have applied phase-based connectivity metrics on broad-band high-frequency oscillations. For instance, (Zweiphenning et al., 2016) computed phase lag index (PLI) in two high-frequency bands: ripple (80-250 Hz) and fast ripple (250–500 Hz). Another study, used PLI to compute brain connectivity in broadband 80-250 Hz (Nissen et al., 2016). Last, (Burns et al., 2014) used coherence to investigate ictal networks in γ (25-90 Hz) band.”

We also note, as shown in (Aydore et al., 2013) for intracranial recordings, phase-based measures provide essentially the same information as coherence in most cases.

Importantly, we first divided the 80-200 Hz into two narrower frequency ranges (80-140 Hz, and 140-200 Hz) and then computed the connectivity matrices based on the lagged-coherence metric for each frequency range separately. The mlEVC measure was computed for each frequency range separately and the results then concatenated.

11. If I understand the methodical approach correctly, the authors generate an ordinal graph optimal when using fast intracranial electrophysiological data (500 or 1000Hz). It would be interesting to see a correlation plot between the current eigenvector centrality with an ordinal coupling parameter and cross-correlation of this data at multiple time-lags. In addition to tuning the coupling strength, the current work would be improved to quantify the optimal time interval between matrix 'layers'. It would be useful for the authors to consider/discuss this point in detail.

13. A clearer rationale for using a spatiotemporal graph if warranted in this paper. The authors outline and justify the use of multilayer graphs from a methodological point of view, but it would also be good to hear why the authors choose this methodology from a clinical point of view. i.e., what can multilayer metrics tell us about epilepsy that single-layer cannot?

14. Related to the previous point, have the authors thought about comparing eigenvector centrality between multilayer and single-layer graphs, to see whether the results differ between the two?

We respond to these three comments together since they are highly relevant. In summary the reviewers requested (a) A discussion about the optimal time interval between different layers of the network, (b) Comparison of results between single-layer and multilayer networks, and (c) A rationale for employing a multilayer approach in epilepsy specifically during seizures.

The common approach to analyzing time-varying brain connectivity is using sliding windows with a constant window size and overlap between windows across time. If the interval between windows is small, instantaneous fluctuations will dominate processes with slower timescales. In the case of large intervals between windows, fast dynamics might be discarded. As a result, choosing an optimal interval, is a challenging issue. Applying the same interval for all participants will exacerbate the problem since seizure dynamics are highly variable across subjects.

In our multilayer model of brain networks, we use a 500ms time interval between layers to allow us to capture fast seizure dynamics. By increasing the coupling parameter among adjacent layers, we can incorporate processes with slower time scales. Using this approach, we only need to tune the coupling parameter to extract desired spatiotemporal processes. So, rather than finding an optimal time interval for the multi-layer network, we instead focus on finding an appropriate coupling parameter. We use a data-driven approach to evaluate the cost function for EZ identification over a range of values for the coupling parameter (See Response #1).

We added the following explanation to the discussion.

“By adjusting the coupling between layers, we can overcome the current challenges for selecting an appropriate time interval between different samples of a temporal network. Here, we assumed a relatively short time interval between layers (500ms) to have a high temporal resolution. By increasing the coupling parameter between adjacent layers, we can investigate processes with slower timescales.”

To assert the importance of a multilayer approach when compared to single-layer, we inserted this paragraph into the results.

“Furthermore, we examined the effect of multilayer modeling and adjusting the coupling parameter on EZ prediction and super-graph structure. In figure 2—figure supplement 1, we display the left singular vectors of mlEVC. For illustration purposes, we showed projections with respect to the singular vectors for the parameter set (c,d) for which the prediction of EZ (binary labeling) was closest to the assumed ground truth (resection information). We observed that the optimal coupling value is different between patients, which supports our primary rationale for choosing a multilayer framework with an adaptive interlayer coupling parameter. In our initial analysis, we ran the algorithm for the single-layer case and EZ identification results were poor.”

After discussing the methodological reasons for using a multilayer framework, we also explained the neurophysiological rationales. The details as appeared below were added to the introduction:

Additionally, there exist several neurological rationales for employing a multilayer approach in seizure analysis. First, the concept of dynamic network reconfiguration has been studied in brain networks (Bassett et al., 2011; Braun et al., 2015). Previous research has shown state transitions during seizures, either through brain connectivity analysis (Burns et al., 2014) or microelectrode recordings (Smith et al., 2016). Multilayer networks have the capability to delineate these transitions and identify network reconfiguration (Mucha et al., 2010). Second, electrophysiological signals are highly non-stationary during ictal periods. As a result, traditional analysis of time-varying networks based on isolated graphs would be affected by instantaneous fluctuations rather than the underlying spatiotemporal networks. Third, seizure propagation is one of the key elements of ictal activity. Recent work has indicated the importance of multilayer modeling of complex systems when encountering spreading processes (De Domenico et al., 2016).

12. Related to the previous comment, it would be good to head further why the authors choose to use the Phase Lag Index for slow frequency estimation, a measure that does not operate proximately to the zero-lag.

In addition to the brief justification for choosing this measure in the initial version of the manuscript, we added the following description to the result section:

“The PLI is recognized for its superiority to measures such as phase locking value (PLV). By discarding interactions with a phase difference of zero, the PLI quantifies phase coupling between two signals while excluding volume conduction as a confounding factor. Compared to other functional connectivity metrics, PLI is therefore less susceptible to common sources. Since a major part of low-frequency (<50Hz) brain activity during seizures is derived from ictal discharges, which exhibit distance-dependent delays (Smith et al., 2016), true neurological zero-lag connectivity is highly unlikely in this scenario. Because of its robustness to volume conduction, PLI has been widely used in studies of low-frequency (<50 Hz) brain connectivity in epilepsy (Nissen et al., 2016; Schevon et al., 2012; Van Diessen et al., 2013; Zweiphenning et al., 2016).”

15. Please provide more details about the filtering procedure, conducted before the Hilbert transform, including the type (and order) of filtering, how the DC offset was accounted for and whether the Hilbert transform in the given frequencies satisfy the Bedrossian's criteria for narrow-band frequency estimation (Xu and Yan, 2006).

21. Is data processing on monopolar or bipolar montage? Please clarify.

Thanks for bringing up these important issues. Regarding the signals montage and preprocessing, we added the following paragraph to the “Patients and recordings” subsection in the methods:

“We preprocessed SEEG signals before further analyses. First, we constructed bipolar channels by subtracting unipolar signals recorded from each pair of adjacent contacts. For analysis we included bipolar channels only if both contacts were inside gray matter. Next, any DC offset was removed from each bipolar channel. Thereafter, using the Brainstorm software (Tadel et al., 2011), bipolar EEG signals were bandpass filtered in the 3-200 Hz range and notch filtered at 60, 120, and 180 Hz. Bandpass filtering was performed using a Kaiser-window linear phase FIR filter of order 7,252 (for a sample rate of 1000 Hz), using the fir1 MATLAB function. We compensated for filter-induced delay by shifting the filtered sequence, resulting in a zero-delay filter. The notch filtering used an IIR filter of order 6 with a bandstop of 1 Hz in notch frequencies. We used the filtfilt function in MATLAB to compensate for group delay. The resulting preprocessed data were employed in all analyses in this paper. When analyzing low-frequency and high-frequency brain connectivity, we bandpassed the preprocessed data using the same filter type (Kaiser-window linear phase FIR filter) with different ranges and orders.”

In Author response image 1 we show the frequency response of the bandpass and notch filters and their characteristics. The low transition band (2.5-3 Hz) is also magnified for a better visualization. In the early version of this manuscript, we listed (2-200 Hz) as the range of the bandpass filter. This has been corrected to (3-200 Hz) in the revised manuscript. The data were filtered over a sufficiently long interval either-side of the seizure window that transient effects of filters was not a matter of concern. Author response image 2 demonstrates the frequency response for the notch filter.

As stated in response #10, we bandpassed preprocessed signals in two narrower frequency ranges, (80-140 Hz) and (140-200 Hz), before applying Hilbert transform, satisfying the Bedrosian identity (Xu and Yan, 2006).

Author response image 1
Magnitude and impulse response of the FIR bandpass preprocessing filter.

The upper figure shows an expanded view of the low-frequency response of the filter.

Author response image 2
Magnitude and impulse response of the notch filter.

The upper figure shows an expanded view of one of the notch bands.

16. It would have been nice to see in more detail examples from one or two patients with the actual resection area and the detected networks in volume. Figure 1 would benefit from an intuitive description of the method.

We appreciate your suggestion. Unfortunately, we did not have access to MRIs with co-registered electrodes and resected volumes while preparing this response letter.

17. P7 It seems to me the term 'primary organization' has to be credited to Talairach and Bancaud. Also, early work on network organization were performed by Wendling and Bartolomei and could be cited (including the desynchronization at seizure onset in Wendling et al. 2003).

Thanks for the suggestions. We now cite the following publications in the article.

Talairach J, Bancaud J. 1966. Lesion, “irritative” zone and epileptogenic focus. Confin Neurol 27:91–94. doi:10.1159/000103937

Wendling F, Bartolomei F, Bellanger JJ, Bourien J, Chauvel P. 2003. Epileptic fast intracerebral EEG activity: Evidence for spatial decorrelation at seizure onset. Brain 126:1449–1459. doi:10.1093/brain/awg144

18. P8 it is very interesting to see that in a few patients one method fails whereas the other gives good results. This pleads for a complementarity of strategies to cope with inter-patient variability. Can the authors make hypotheses on which signal features/seizure patterns could explain the difference in results across methods and patients?

The result section mentioned that insufficient data (short seizures) might be one reason for mlEVC's failure. Here, we added another analysis to look for signal features. For patient 8, mlEVC could not identify any nodes inside the resected area as EZ, while Fingerprint predicted two nodes as EZ (one false positive). We looked at the time-frequency spectrum and mlEVC for one seizure of this subject, which is illustrated in Author response image 3. In the upper figure, we can see the main features of the Fingerprint algorithm (suppression, fast activity, and pre-ictal spikes) in the predicted nodes. However, we do not observe any significant HFOs for those nodes (see also our response to comments #20 & #22 regarding HFOs). As a result, the mlEVC does not have a distinctive pattern in any nodes in the resected region (Author response image 3, lower). Lack of dominant HFOs in the EZ can be another factor attributes to mlEVC's failure.

On the other hand, Fingerprint can fail for different reasons. First and foremost, its features might not be present for some seizures or patients. Second, since Fingerprint uses a trained model for predicting the EZ in the new patient, the new features can be quite different from the base model, or the detection process falls short of the presumed threshold for EZ identification.

Seizure types and locations can also affect the results in both methods, but it is hard to draw conclusions with a small number of patients in each cohort. Additional studies on a larger dataset are needed to further investigate these issues, which is beyond the scope of the current paper.

Author response image 3
Time-frequency spectra and mlEVC for one seizure of patient 8.

19. P11 « false positives from the EZ » this really depends on the definition of the EZ. If this is the minimum of cortex to be resected to render the patient seizure free, then the statement may hold. If this is the « primary region of organization of seizures » (definition of Bancaud, given p7), it is possible that not all these regions need to be resected. It would be useful to clarify the two definitions.

We use the first definition since with this, we can definitively state that the EZ was not resected in those patients who are not seizure free. The EZ is discussed in the Introduction as follows:

“In using SEEG to identify the epileptogenic zone (EZ) we attempt to take into account the earliest ictal EEG change based on an anatomoelectroclinical analysis (Kahane et al., 2006). This concept incorporates both the anatomic region that initiates the epileptic discharge as well as the “primary organization” (Talairach and Bancaud, 1966) that leads to the manifestation of the clinical seizure itself (Wyllie et al., 2015). The gold standard method of confirming EZ localization is based on whether seizure freedom has been achieved by resection or ablation. However, the actual ground truth for EZ location, in the sense of the minimal resection volume needed to achieve seizure freedom, is unknown since in many cases the resection volumes may extend well beyond the EZ.”

20. p17 it would be very interesting to perform a comparison of HF and LF synchrony in predicted the EZ. Moreover, as mentioned below too, part of the HF synchrony can arise from trains of sharp spikes that have energy in all frequencies, which would not be synchrony of high frequency oscillations but an emphasis on the sharp part of ictal spikes. This is not a problem per se, but more an issue of interpretation of the results.

22. Is it possible that part of the synchrony arises from filtered spikes? Can the authors provide a (normalized across frequencies) time-frequency representation of a representative seizure in order to assess the relative contribution of oscillations and spikes?

We appreciate your suggestion on using LF connectivity features to predict EZ and comparing the results with HF. While that can be a valuable investigation, we chose HF features based on the literature. Mainly, (Schevon et al., 2012) showed that core and penumbral might share similar low-frequency activity patterns. However, the high-frequency oscillations are the unique characteristics of the core. Importantly, our findings in Figures 4 and 6 in the main article presented that EZ-nR connectivity in mid-seizure has changed significantly for HF compared to the pre-ictal period. At the same time, this change was not significant in LF.

To investigate the contribution of ictal spikes and oscillations in SEEG signals, we computed the time-frequency representation (normalized across frequencies) of all signals in several seizures and patients. The following discussion and related figure (Figure 2—figure supplement 3) were added to the Results section of the manuscript.

“To investigate whether apparent high-frequency networks were produced as a result of ictal spikes rather than true oscillations, we examined the time-frequency representation of seizures. Figure 2—figure supplement 3 displays time-frequency plots for two sample seizures. The upper plot shows the spectrum averaged among nodes predicted as EZ, and the lower spectrum shows the case for randomly selected nodes outside the resection region, with the number of nodes in both groups equal. We observed pre-ictal spikes in the time-frequency plot for nodes inside the EZ, a previously reported feature of the epileptogenic zone (Grinenko et al., 2018). However, the figure shows that non-spiking high-frequency oscillations were the dominant activity after seizure onset. This observation supports our hypothesis that HFOs, rather than ictal spiking, are the main contributor to observed synchronization during seizures.”

23. P25, eigenvalue centrality. While the rank of the matrix is likely to be T, wouldn't one expect some kind of temporal correlation across points (arising from both the high overlap and some actual temporal persistence of the networks), which would result in an elbow in the eigenvalues after some dimension? If it is not the case, and each time point is independent from the other ones (linear eigenvalue spectrum), what is the added power of multilayer method? Wouldn't a more simple method as summing the degrees across time be equivalent? Please clarify.

24. It would be interesting to visualize the eigenvalues of a representative example in order to measure this. Also, and importantly, it would be useful to compare the multilayer method to a simple mean degree across time (Wilke et al. 2010, van Mierlo et al. 2013, Courtens et al. 2016, Li et al. 2016, Balatskaya et al. 2020).

Previously in this response letter, we scrutinize the virtues of a multilayer framework in response to comments (#11, #13, and #14). We mentioned why a single-layer method cannot extract the neural processes with timescales slower than the time intervals between layers. Our EZ identification method showed that by increasing the coupling between layers we can explore across temporal scales.

We performed the requested analysis for the magnitude of the eigenvalues based on different coupling parameters. We inserted the following discussion and figure in the Results section:

“Figure 2—figure supplement 4 presents the changes in super-graph eigenvalues by adjusting the coupling parameter. For c≤1, there is a falloff when the number of eigenvalues (ne) meets the number of layers (T), indicating a super-adjacency matric with effective rank T. This is an expected result since the coupling is relatively small. When c increases, the eigenvalues become larger, and their corresponding eigenvectors would comprise several neighboring layers. Although the rate of decline in magnitude of eigenvalues accelerates as c increases, falloff can be detected when ne2T. By increasing the coupling value, the super-adjacency matrix transforms from a block diagonal matrix with effective rank T, to a matrix with major non-diagonal blocks and an effective rank far greater than T. In the computation of mlEVC, we considered the top T eigenvectors for all coupling parameters to avoid erroneous assumptions about the rank of super-graphs.”

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[Editors' note: further revisions were suggested prior to acceptance, as described below.]

The manuscript has been improved but there are some remaining issues that need to be addressed, as outlined below. Please address these comments comprehensively in your response.

1. In their response and amendments to the main text, the authors claim that their method does not require cross-validation and testing over independent datasets since the approach does not involve training the model parameters across patients and does not access information regarding the resection zone. While it is true that the method is applied to each patient, separately, the methodological choices including, but not limited to, functional connectivity metrics, frequency band selection, percentile threshold selection, still effectively "train" the general algorithm and may be highly specific to the cohort studied here. This issue presents itself as a driver of inter-patient variability, as demonstrated by the conflicting findings between the mlEVC method and Fingerprint method. While this limitation detracts from the methodological advances put forth by this study, but some caution in making the claim that cross-validation/testing is not necessary is warranted. Specifically, the manuscript should include a rationale for why cross-validation was not applied in this context, coupled with an acknowledgement that such an approach in future will be important to verify the current results.

We thank reviewers for their due diligence in examining the external validity of our algorithm.

Regarding the methodological choices, we would like to emphasize that the rationale for selecting the "connectivity metric" (lagged Coherence) was mentioned in the paper. Coherence is one of the most utilized connectivity metrics in neuroscience. It is also used in the article that we were inspired by (Burns et al., 2014) when performing this research. However, Coherence is prone to spurious connectivity due to volume conduction. Although, in comparison to scalp EEG, volume conduction is less of an issue in intracranial recordings, we were still interested in avoiding it in our study. As a result, we selected lagged Coherence in our analysis. The elementwise normalization of connectivity matrices with respect to the pre-ictal period was also followed by (Burns et al., 2014).

For "frequency band selection", the main question of our study was to investigate the brain connectivity in HFOs, as these oscillations are widely analyzed in epilepsy and are considered a biomarker of the epileptogenic zone. Since the sampling rate of the data was 500 Hz for several patients, we decided to choose the 80-200 Hz range to be consistent among patients. We then divided this band in half to have narrower frequency bands. Although we noticed that in some seizures or patients, only one band (80-140 Hz or 140-200 Hz) was informative, we did not drop any frequency band to avoid adding complexity to our algorithm. A future study can design an algorithm for tailoring the proper frequency band for each patient (Arnulfo et al., 2020).

Regarding our prediction and Fingerprint algorithm, we emphasized that the two methods use different features and can be complementary. Both algorithms have a small number of false positives, and the main differences are in electrodes predicted as true positives, which in both cases they were a subset of the electrodes in the resected area. Since both studies are performed retrospectively, the actual EZ is unknown. One probability can be that the union of the predicted regions by two algorithms is part of the actual EZ and its resection was necessary for seizure freedom among those patients.

Finally, we carefully edited our previous response and added more explanations to address the reviewers' concerns. These descriptions are written under a new section in the discussion titled as "limitations and considerations", which reads as follows:

"We should point out that cross-validation was not performed in this study for several reasons. First, resection labels were not used as part of the prediction algorithm, and the same performance function and ranges of coupling and thresholding values were applied to all subjects. Second, as shown in this manuscript and similar works, parameters such as coupling or active frequency band are patient-specific. By using cross-validation, we would have to fix these parameters based on a subset of patients, which may not be ideal as the actual range of these parameters could differ from the training dataset. While this study was primarily conducted to propose the multilayer network methodology during seizures, a more rigorous investigation is necessary to evaluate the external validity of our algorithm. Future research could use data from different clinical centers to assess the generalizability of the proposed technique and identify optimal parameters."

2. The relationship between the coupling parameter and network time-scale should be further elaborated, given the importance of this parameter to the authors' claim that patients may have different rates of network change. Please present data examining how sensitive the findings of the EZ are to the choice of this parameter. Please also provide examples of how different coupling parameters would yield more insight into the different time-scales of network change

We will address both comments at the same time. In summary, the reviewers requested that we quantify the performance of EZ identification if we used a single-layer model for all patients. Additionally, they asked whether employing different coupling values will result in a better understanding of brain dynamics.

We ran the EZ identification algorithm using both a single-layer model (with coupling set to 0) and a multilayer model with different coupling values (c = 1, … 10). We then compared these results to our proposed method, which involves analyzing a range of coupling parameters and weighting them based on clustering performance. Figure 2-source data 3 presents three performance measures for each case. These include the number of electrodes predicted as true positive, the number of electrodes predicted as false positive, and the number of patients with zero true positives. Our results demonstrate that the proposed approach yields superior EZ identification performance when compared to both the single-layer and multilayer models with fixed coupling values across all patients.

In addition to improving EZ identification, using the appropriate coupling parameter for each patient can also provide valuable insights into seizure dynamics. Author response image 4 compares the brain state dynamics during three seizures in two conditions: using c = 1 and the best-matched coupling parameter (c = 10 for this patient), as discussed in the main manuscript. With c = 1, there is no clear distinction between brain states, making it challenging to observe transitions between them. In contrast, when clustering is performed using the proper coupling parameter, the brain states become separable, allowing us to distinguish between neural state transitions. Although seizure semiology information was not available in our dataset, exploring its correlation with brain state transitions can reveal further insights into brain dynamics in future studies. Author response image 5 displays the same plot for patient 3.

Author response image 4
Brain state transition during three seizures of patient 15 for two coupling values.
Author response image 5
Brain state transition during three seizures of patient 3 for two coupling values.

3. The findings comparing a single-layer model to the multi-layer model should be explicitly quantified to concretely justify the claim in the Discussion section that single-layer models yielded poorer EZ identification than multi-layer models. How much more accurate was the multi-layer model to the single-layer model?

4. More attention should be paid in the text to the risk of contamination of high frequency synchrony by two processes: (1) Filtering of spikes; and (2) Harmonics of non-sinusoidal oscillations. These topics are addressed in the following study, which could be cited in support of the discussion.

Pitfalls of high-pass filtering for detecting epileptic oscillations: a technical note on "false" ripples. Bénar CG, Chauvière L, Bartolomei F, Wendling F. Clin Neurophysiol. 2010 Mar;121(3):301-10

5. The time frequency figures should be accompanied by a presentation of the signal time course in order to fully appreciate the presence/absence of spikes. While there indeed seems to be spikes in the preictal period (vertical lines) , they present much less energy than the high frequency activity during the seizure. This large increase is quite blurred and indistinct and it is not clear what this actually represents. The original signal time course would help understand which seizure pattern this corresponds to.A consideration of the potential effect of harmonics would also be helpful.

Author response image 6 shows the EEG signal of a single node predicted as the EZ, along with two time-frequency spectra. Two sections of this data are enlarged to better illustrate pre-ictal spikes and HFOs after seizure onset (Author response image 7).

As expected, the pre-ictal spikes display broadband activity across frequencies. In contrast, the HFOs, especially between 5-10s after onset, do not exhibit any spikes in the time domain and show a transparent "blob" in the frequency domain at 90-140 Hz. This frequency range falls within the first range we analyzed, but we did not observe significant activity in the 45-70 Hz range. These oscillations cannot be harmonics of non-sinusoidal components.

While we did not visually inspect the spectra in all seizures, our observations are consistent with the "ripple" described in the referenced article (Bénar et al., 2010).

Regarding the power comparison between HFOs and spikes, please note that we normalized these spectra for each frequency bin, as per your request. We performed this normalization to the pre-ictal period to better emphasize the changes that occur after the onset. Since there are stronger low-frequency components (such as spikes) before the onset, and more high-frequency oscillations after the seizure starts, these plots amplify the energy related to HFOs.

To address your concern, we added the following paragraph under the section of “limitations and considerations”:

“Filtering and subsequent analysis of HFOs should be performed with extra caution due to the possibility of producing false or spurious ripples. Research has shown that high-pass (> 80Hz) filtering of sharp transitions in EEG (such as artifacts and spikes) or harmonics of non-sinusoidal signals can result in such false ripples (Bénar et al., 2010). Several approaches have been suggested to investigate this phenomenon. These include visually inspecting the epileptic waveform alongside the filtered signal, using the time-frequency transform of the original signal since real and false ripples have different spectra, and employing automated spectral decomposition techniques such as Matching Pursuit (Bénar et al., 2010). In our analysis, we visually evaluated several seizures in both the time and time-frequency domains. However, it would be beneficial to use one of these mentioned algorithms in a systematic manner in future studies.”

Author response image 6
EEG signal of one node inside the predicted EZ before and after seizure onset in the time domain (top), time-frequency using MATLAB (middle), and time-frequency using Brainstorm (bottom).
Author response image 7
Pre-ictal spikes (top) and ictal HFOs (bottom) of one node inside the predicted EZ.
https://doi.org/10.7554/eLife.68531.sa2

Article and author information

Author details

  1. Hossein Shahabi

    Signal and Image Processing Institute, University of Southern California, Los Angeles, United States
    Contribution
    Conceptualization, Data curation, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing – original draft, Writing – review and editing
    For correspondence
    shahabi.h27@gmail.com
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-3600-8007
  2. Dileep R Nair

    Epilepsy Center, Cleveland Clinic Neurological Institute, Cleveland, United States
    Contribution
    Conceptualization, Resources, Data curation, Supervision, Funding acquisition, Investigation, Writing – original draft, Project administration, Writing – review and editing
    Competing interests
    No competing interests declared
  3. Richard M Leahy

    Signal and Image Processing Institute, University of Southern California, Los Angeles, United States
    Contribution
    Conceptualization, Resources, Formal analysis, Supervision, Funding acquisition, Validation, Investigation, Methodology, Writing – original draft, Project administration, Writing – review and editing
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-7278-5471

Funding

National Institute of Neurological Disorders and Stroke (R01NS089212)

  • Dileep R Nair

National Institute of Biomedical Imaging and Bioengineering (R01EB026299)

  • Richard M Leahy

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

Research reported in this paper was supported in part by the National Institutes of Health under awards R01NS089212 and R01EB026299.

Ethics

This retrospective study was approved by the institutional review board at the Cleveland Clinic. Single pulse electrical stimulation induced cortico-cortical evoked potentials are collected as a part of the routine clinical care of patients undergoing SEEG at Cleveland Clinic. The ictal data is also collected during the presurgical SEEG evaluation. The full procedure for participant selection and data recording is described in our previous work (Grinenko et al., 2018).

Senior Editor

  1. Michael J Frank, Brown University, United States

Reviewing Editor

  1. Alex Fornito, Monash University, Australia

Reviewers

  1. Mangor Pedersen, Auckland University of Technology, New Zealand
  2. Christian Benar, Aix-Marseille University, INSERM, France

Version history

  1. Received: March 18, 2021
  2. Accepted: March 16, 2023
  3. Accepted Manuscript published: March 17, 2023 (version 1)
  4. Version of Record published: March 31, 2023 (version 2)

Copyright

© 2023, Shahabi et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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  1. Hossein Shahabi
  2. Dileep R Nair
  3. Richard M Leahy
(2023)
Multilayer brain networks can identify the epileptogenic zone and seizure dynamics
eLife 12:e68531.
https://doi.org/10.7554/eLife.68531

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