Localization of epileptogenic zone based on graph analysis of stereo-EEG

Epilepsy Research 128 (2016) 149–157

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Research paper

Localization of epileptogenic zone based on graph analysis of stereo-EEG Yong-Hua Li a , Xiao-Lai Ye b , Qiang-Qiang Liu b , Jun-Wei Mao a , Pei-Ji Liang a , Ji-Wen Xu b,∗∗ , Pu-Ming Zhang a,∗ a b

School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China Department of Functional Neurosurgery, Renji Hospital, School of Medicine, Shanghai Jiao Tong University, Shanghai 200001, China

a r t i c l e

i n f o

Article history: Received 1 April 2016 Received in revised form 10 October 2016 Accepted 25 October 2016 Available online 4 November 2016 Keywords: Epileptogenic zone Stereo-EEG Focal epilepsy Graph theory Partial directed coherence

a b s t r a c t Localization of the epileptogenic zone (EZ) is essential for the successful surgical treatment of medically intractable epilepsy. In the present study, stereo-EEG (SEEG) recordings were obtained from seven patients underwent presurgical evaluation for treatment of intractable epilepsy. Partial directed coherence (PDC) analysis was applied to construct peri-ictal effective connectivity networks. The graphic measures, in-degree, out-degree and betweenness centrality, were evaluated to localize the EZ. A receiver operating characteristic (ROC) analysis was used to quantify the localization accuracy. We found that the in-degree coincided well with the EZ identified by epileptologists’ visual inspection in all seven patients who had a significant improvement in seizure outcomes, however, the other two measures were effective only in some cases. Furthermore, in all seven patients the electrode contact with the highest in-degree was always located within the EZ identified by epileptologists’ visual inspection. These results indicate that the graph theory is an effective method to localize the EZ when suitable graphic measures were chosen. Furthermore, the in-degree was the most effective measure among the three graphic measures in localizing the EZ when the PDC method was used. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Focal epilepsy is a neurological disorder, in which the seizures originate within networks limited to one hemisphere (Berg et al., 2010), and approximately 30% cases are resistant to anti-epileptic drugs (Beleza, 2009). Patients with focal drug-resistant epilepsy can be considered as candidates for surgical removal of the epileptogenic zone (EZ) which is the brain region involved in the generation of seizures (Bartolomei et al., 2008). For these patients, the precise localization of the EZ is essential to achieve successful surgical outcomes. Although the EZ can sometimes be adequately localized by non-invasive techniques including scalp EEG, magnetic reso-

∗ Corresponding author at: School of Biomedical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Minhang District, Shanghai 200240, China. ∗∗ Corresponding author at: Department of Functional Neurosurgery, Renji Hospital, School of Medicine, Shanghai Jiao Tong University, 145 Middle Shandong Road, Huangpu District, Shanghai 200001, China. E-mail addresses: [email protected] (Y.-H. Li), [email protected] (X.-L. Ye), [email protected] (Q.-Q. Liu), [email protected] (J.-W. Mao), [email protected] (P.-J. Liang), [email protected] (J.-W. Xu), [email protected] (P.-M. Zhang). http://dx.doi.org/10.1016/j.eplepsyres.2016.10.021 0920-1211/© 2016 Elsevier B.V. All rights reserved.

nance imaging (MRI), positron emission tomography (PET) and magnetoencephalography (MEG), intracranial electrocorticography (ECoG) or stereo-EEG (SEEG) is still required in 25–50% of the cases for the pre-surgical evaluation (Cardinale et al., 2013; Yuan et al., 2012). Compared with ECoG, SEEG enables precise recordings from deep cortical structures, multiple noncontiguous lobes, as well as bilateral explorations while avoiding large craniotomies (Cossu et al., 2005; Enatsu et al., 2014; Gonzalez-Martinez et al., 2013). At present, EZ localization using SEEG signals is generally based on the visual inspection by epileptologists, which is subjective and can be inaccurate in quite a proportion of patients (Jeha et al., 2007; Jehi et al., 2009). In recent years, considerable efforts have been made to develop advanced signal analysis methods to improve the precision of the EZ localization, including methods based on frequency analysis (Bartolomei et al., 2011; Gnatkovsky et al., 2014, 2011), nonlinear signal analysis (Andrzejak et al., 2015, 2012), statistical parametric mapping of epileptogenicity indices (David et al., 2011), and connectivity-graph analysis (Panzica et al., 2013). Since recent studies have proposed that epilepsy is a network-level disorder, even for focal epilepsy (Bertram, 2013; Jehi, 2012; Kramer et al., 2008), particular attention has been paid to the methods based on

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the graph theory, which is a formalism to quantify topological properties of complex systems and is quite suitable to investigate the network dynamics (Chiang and Haneef, 2014). In the last decade, graph theory techniques have been applied to characterize the brain networks generating seizures using scalp EEG (Chowdhury et al., 2014; Douw et al., 2010; Ponten et al., 2009; Quraan et al., 2013; Vecchio et al., 2015), ECoG (Burns et al., 2014; Wilke et al., 2011), SEEG (Courtens et al., 2016; Hao et al., 2014; van Mierlo et al., 2013; Varotto et al., 2012), MEG (Jeong et al., 2014; Niso et al., 2015), MRI (Bernhardt et al., 2011; Mueller et al., 2014) and functional MRI (Doucet et al., 2015a, 2015b; Ibrahim et al., 2014; James et al., 2013; Ridley et al., 2015). These studies mostly investigated either the changes of segregation and integration (local and global efficiency) of the brain networks, or the graphic measures correlated with post-surgical seizure frequency and cognitive performance. On the other hand, only a few studies have investigated the issue of EZ localization. van Mierlo and his colleagues applied the graph theory to investigate the epileptic network using SEEG signals in patients with refractory temporal lobe epilepsy and found that the electrode contact with the highest out-degree always laid within the resected brain region (van Mierlo et al., 2013). Similarly, Varotto and his colleagues proved that both out-density and betweenness centrality were effective graphic measures to localize EZ in patients with type II focal cortical dysplasia (Varotto et al., 2012). Another group of researchers proposed that eigenvector centrality could also be used to localize the EZ (Hao et al., 2014). These studies suggest that graph theory might be a promising method to localize the EZ, whereas the feasibility of this method should be further examined because of the variety types of epilepsy. In the present study, SEEG recordings were obtained from seven patients with focal epilepsy. Partial directed coherence (PDC) analysis was applied to construct effective connectivity networks. The graphic measures, in-degree, out-degree and betweenness centrality, were evaluated. We found that the in-degree was the most effective measure among the three graphic measures in localizing the EZ.

by epileptologists. Visual inspection was performed on the periseizure time series and the channels exhibiting the presence of artifact were discarded from the analysis. Then the PDC was calculated to construct the effective connectivity networks. 2.2. Partial directed coherence PDC is an effective connectivity measure derived from the Granger causality (Baccala and Sameshima, 2001). It can be used to qualify the causal interactions (or information flow direction) between neural structures. Compared with the directed transfer function (DTF, another widely used effective connectivity measure derived from the Granger causality), the PDC can distinguish the direct from the indirect connections and can correctly identify interactions even in relatively noisy data (Fasoula et al., 2013; Florin et al., 2011). To calculate the PDC, the first step is to construct the multivariate autoregressive (MVAR) model. Let X(t) = (X1 (t), X2 (t), ..., XN (t)) be a set of SEEG signals. Here t refers to the time and N is the number of recording channels. The MVAR model is defined as X(t) =

p 

A(r)X(t − r) + E(t),

(1)

r=1

Where A(1), A(2), . . ., A(p) are N × N coefficient matrices to be estimated; E(t) is a vector of multivariate zeros-mean white noise; p is the model order which was determined by Akaike information criterion (Akaike, 1974). Once the MVAR coefficients are estimated, the PDC from the jth channel to the ith channel at frequency f can be calculated from the Fourier transform of the MVAR coefficients as: |A¯ (f )|

 ij 

ij (f ) =

2 |A¯ (f )| k kj

,

(2)

where ¯ )=I− A(f

p 

A(r)e−2ifr .

(3)

r=1

2. Methods 2.1. Data acquisition and selection Seven patients with refractory focal epilepsy, who underwent presurgical video-SEEG monitoring at the Department of Functional Neurosurgery, Renji Hospital (Shanghai, China) between 2013 and 2015 were recruited in the retrospective study. All the patients had a significant improvement in seizure outcomes (seizure free or >80% reduction in seizure frequency) during a minimal post-surgery follow-up of 6 months. The patients’ information is summarized in Table 1. All patients gave written informed consent that their clinical data might be used for research purposes. Five to ten SEEG electrodes (HKHS Healthcare, Beijing, China) were implanted into target regions for each patient on the basis of available clinical symptoms, scalp EEG findings and imaging data. Each electrode contained 5–18 contacts (0.8 mm in diameter, 2 mm in length), and the gap between adjacent contacts was 1.5 mm. SEEG data were recorded for a few days under video monitoring to examine electro-clinical features of seizures with the NicoletOneTM Neurodiagnostic system (Nicolet, USA; sample rate, 512 Hz). A referential montage was used to record SEEG data with the reference electrode at sphenoid bone. For data analysis, a bipolar montage between adjacent contacts of the same electrode was used to improve the sensitivity to local electrical activities. For each patient, two to four seizures were available for analysis. The seizure onset and termination time were manually identified

The PDC value,ij (f ), describes the directional flow of information from channel j to i, ranging from 0 to 1. It represents the fraction of information flow from the jth channel directed towards the ith channel, in comparison with all of j’s information flow directed towards all the other channels. In order to assess the statistical significance of the PDC values at each frequency, a surrogate data method was used (Dolan and Spano, 2001). The original time series was Fourier transformed and the phases of the Fourier coefficients were randomly shuffled to create a new surrogate time series. Following the phase shuffling, the data was inverse Fourier transformed and the PDC method was applied to the surrogate time series. This process was repeated 1000 times and a distribution of PDC values of the surrogate data was obtained that corresponded to the null hypothesis of no causal interactions. A significance level was set (p = 0.05) for the statistical test and the PDC values below the threshold were discarded. After the surrogate data test, the maximal PDC values along the frequency dimension were selected and transposed to obtain the association matrix T

W = [max(ij (f ))] ,

(4)

f

Where T denotes matrix transposition. Each element wij in the association matrix W denotes the strength of interaction from the channel i to the channel j. Since the MVAR model analysis requires that the time series are quasi-stationary, short-window techniques were used in this

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Table 1 Patient information. Patient

Sex

Age at first seizure/surgery (years)

Seizures analyzed

Seizure type

MRI

Pathology

1 2

M F

15/20 5/5.25

2 3

CPS SPS, SGTCS

3

F

5/34

4

Aura, CPS, SGTCS

4

M

10/19

4

CPS, SGTCS

5 6

F M

9/25 8/28

2 3

Aura, CPS, SGTCS CPS

7

M

5/32

3

CPS, SGTCS

Normal Negative R, PG&PS cortical R, PG&PS FCD thickening L, PO abnormal sulcal L, PO FCD and gyral pattern R, frontal FCD R, frontal abnormal sulcal and gyral pattern Normal Negative L, SFG T2/FLAIR signal L, SFG FCD hyperintensity of grey matter R, frontal cortical Negative thickening

Resection area

Postoperative follow-up (months)

Outcomes

R, TL&IC R, FL

21 20

SF SF

L, OL

14

SF

R, FL

8

SF*

L, IC L, FL

16 9

SF SF

R, FL

12

SF

M, male; F, female; CPS, complex partial seizures; SPS, simple partial seizures; SGTCS, secondarily generalized tonic- clonic seizures; L, left; R, right; PG, precentral gyrus; PS, precentral sulcus; PO, parietal-occipital; SFG, superior frontal gyrus; FCD, focal cortical dysplasia; TL, temporal lobe; IC, insular cortex; FL, frontal lobe; OL, occipital lobe. SF, seizure free; SF*, 80% reduction of seizure frequency, less severe than the baseline seizure.

study. A 5-s sliding window with a time shift of 0.125 s was applied to the selected time series. The processes described above were repeated for each window sequentially, thus an association matrix was obtained every 0.125 s along the time evolution. 2.3. Graph analysis The graph was constructed by the association matrix for each window, in which the nodes were defined as the SEEG channels and the edges were defined as the elements of the association matrix. Since the main aim of this study was to localize the EZ, two centrality measures, degree and betweenness centrality, were chosen to represent the importance of the nodes. Degree: the degree of a node in a directed network consists of the in-degree and the out-degree. The in-degree of node i (idi ) is defined as the sum of the weights of edges pointing towards i (i.e., inward edges). The out-degree of node i (odi ) is accordingly defined as the sum of the weights of edges originating from i (i.e., outward edges). Formally, idi =



wji

and



wij .

(6)

j= / i

Betweenness centrality: the betweenness centrality of a node in a network is defined as the ratio of the number of shortest paths that pass through a specified node to the total number of shortest paths in the network. It is defined as: BC(v) =



2.4. Evaluation of the EZ localization accuracy To quantify the consistency of the estimated EZ with the EZ identified by epileptologists’ visual inspection, the receiver operating characteristic (ROC) curve analysis was used (Grova et al., 2006). The ROC curve was created by plotting the true positive rate (TPR) against the false positive rate (FPR) at different thresholds ranging from 0 to 100%. The TPR is also known as sensitivity, and the FPR can be calculated by (1 − specificity). The sensitivity measures the proportion of positives which are correctly identified and is calculated out of the true positives (TP) and false negatives (FN) as defined by Eq. (8). The specificity measures the proportion of negatives which are correctly identified and is calculated out of the true negatives (TN) and the false positives (FP) as defined by Eq. (9). Therefore, the ROC curve investigates the trade-off between the sensitivity and the specificity of the EZ localization. sensitivity =

TP TP + FN

(8)

specificity =

TN TN + FP

(9)

(5)

j= / i

odi =

An overview of the methods used in the study is shown in Fig. 1.

ij (v)/ij ,

(7)

i= / j= / v

Where ij is the number of shortest paths between nodes i and j; ij (v) is the number of these shortest paths that pass through node v. The path length between nodes i and j is defined as the reciprocal of the edge weight 1/wij . The betweenness centrality accounts for the importance of a node in facilitating interactions between other nodes in a network. The nodes that have a high betweenness centrality act as centralized hubs in a network. To obtain a comprehensive result, the graphic measures within a 5-s window before the seizure onset were summed. Then the summed values were normalized between 0 and its maximal value (set to 1) for each measure. We hypothesized that the electrodes with high graphic measures were correlated to the EZ.

The area under the ROC curve (AUC), ranging from 0 to 1, is an index to assess the localization accuracy. The AUC would equals to 0.5 in completely random guess. The more the AUC approaches to 1, the better localization ability it indicates (Burns et al., 2014; Yang et al., 2011). In the present study, the AUC values of the indegree, out-degree and betweenness centrality were calculated for each seizure. The Kruskal–Wallis ANOVA, post-hoc Dunn’s multiple comparison test (p < 0.01) was performed to test the differences in localization ability between the three measures. 3. Results 21 seizures from seven patients were analyzed in the present study. For each seizure, the effective connectivity networks were obtained by the PDC method. The graphic measures, in-degree, outdegree and betweenness centrality, were calculated to identify the nodes with high centrality in the ictal epileptic networks. 3.1. Individual patient results In Patient 1, a total number of ten depth electrodes were implanted into the hippocampus (Ha, Hp), insular (ISa, ISm, ISp, IIa, IIp), cingulate gyrus (Ca, Cp) and amygdala (Am) (Fig. 2A). The

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Fig. 1. Overview of the methods utilized in the present study. Firstly, SEEG recordings around the seizure onset were selected. Secondly, PDC was applied to analyze the time series to obtain the causal interactions between SEEG channels. Significance test was performed using a surrogate data method to obtain the causal interactions that were statistically significant. Thirdly, the graph was constructed, in which the nodes were defined as the SEEG channels and the edges were defined as the strength of the causal interactions between the nodes. Lastly, graphic measures, degree and betweenness centrality, were evaluated to find the nodes with high centrality in the ictal epileptic network and these nodes were used to localize the EZ.

SEEG signals during one seizure (denoted as seizure 1) are shown in Fig. 2B. The connectivity analysis was applied to the signals in each moving window as described in Methods. Four representative connectivity patterns during the development of the seizure are shown in Fig. 2C. In window W1 (−11.75 s–−6.75 s, with the seizure onset time as 0), the connectivity pattern was approximately random with no obvious highly connected nodes. While in windows W2-W4 (−5.25 s–−0.25 s, −4.25 s–1.25 s, 2.625 s–7.625 s, respectively), the importance of nodes was differentiated and the highly connected nodes appeared, and the information tended to flow into these nodes. Moreover, the location of the highly connected nodes kept moving during the development of the seizure, from Ha1, to Ha1 and Hp1, then to ISm1-3. The corresponding graphic measures, in-degree, out-degree and betweenness centrality, are shown in Fig. 3. The left panels show the measures in each moving window. At the seizure onset, Ha1 and Hp1-2 showed high in-degree values. The in-degree of Ha1 increased at about 4 s before the seizure onset and remained at high values until 2 s after the seizure onset. The in-degree of Hp1-2 also increased before the seizure onset, a bit later than that of Ha1, and decreased gradually after the seizure onset. For the betweenness centrality, the values of Hp1-2 also increased before the seizure onset. These results indicate that the network topology had already changed before the seizure onset and Ha1 and Hp1-2 played an important role in the seizure generation. However, the out-degree did not reveal any node with significant high value than the others. To obtain a comprehensive result, the graphic measures within a 5-s window before the seizure onset were summed and normalized as described in Methods (right panels in Fig. 3). The electrode contacts with the high in-degree values were coincided well with the EZ (pink rectangles in Fig. 3) identified by epileptologists’ visual inspection (AUC = 1.00). The betweenness centrality could only identify a part of the EZ identified by epileptologists’ visual inspection (AUC = 0.77). However, the out-degree did not identify the EZ (AUC = 0.38). In Patients 2 and 3, all the three measures could localized the EZ to some extent (AUC > 0.75). In Patient 2, the localization accuracy of the in-degree and betweenness centrality was higher than that of the out-degree (Fig. 4). In Patient 3, the localization accuracy of the in-degree was highest among the three measures (Fig. S1). In

Patient 4, the ability of the three graphic measures in localizing the EZ was similar to that of Patient 1(Fig. S1). In Patients 5–7, only the in-degree could localized the EZ to some extent (AUC > 0.85), and the other two measures totally got the wrong localizations (AUC < 0.5) (Fig. S1). In summary, the in-degree was effective in localizing the EZ in all seven patients. However, the out-degree was effective only in 2 patients and the betweenness centrality was effective only in 4 patients. Furthermore, the electrode contact with the highest in-degree was always located within the EZ identified by epileptologists’ visual inspection in all seven patients (Figs. 3–4, Figs. S1–S2). But it was not true for the other measures, even in the cases they showed a certain level of localization ability. 3.2. Reproducibility of graph analysis results across seizures in individual patient In each patient, two to four seizures were available for analysis. It is very important to examine the reproducibility of graph analysis results across seizures in individual patient. We examined all the seizures and show an example in Fig. 4. The three seizures from Patient 2 showed very similar seizure patterns, though the seizure duration of seizure 1 was a bit longer than that of the other two seizures. The graph analysis results were also very similar. In all three seizures, the in-degree and betweenness centrality showed high localization accuracy, whereas the out-degree showed a bit lower localization accuracy. The differences of the AUC values were less than 0.1 for each measure across the three seizures. In Patient 1, only two seizures were available for analysis. The seizure patterns and graphic analysis results in seizure 2 were also very similar to that of seizure 1 (Figs. 2 and 3, & Fig. S2). In the other five patients, the reproducibility of graph analysis results across seizures in individual patient also maintained (data not shown). 3.3. Statistics results To quantify the localization accuracy of the three graphic measures, the ROC curve analysis was used and the AUC values were calculated. As shown in Fig. 5, the AUC values of the in-degree were significant larger than that of the out-degree and betweenness centrality (p < 0.01). It suggests that the in-degree had significant

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Fig. 2. The connectivity analysis results of one seizure (denoted as seizure 1) in Patient 1. (A) Electrode positions. The left panel shows the electrode trajectories on a 3D brain scheme. The right panel shows the trajectory of the electrode Ha superimposed on the sagittal, coronal, and axial MRI views, respectively. (B) The SEEG signals during seizure 1. The seizure onset time is marked by an arrow. (C) Connectivity patterns during four 5-s windows marked by W1-W4 in (B). The 100 largest connections in each window are shown for visualization purpose only. The arrows denote a directional connection from one electrode contact to another.

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Fig. 3. The graph analysis results of the seizure shown in Fig. 2. The left panels show the time courses of the in-degree (A), out-degree (B), and betweenness centrality (C) during the seizure shown in Fig. 2. The right panels show the normalized summations of the in-degree (A), out-degree (B) and betweenness centrality (C) within a 5-s window before the seizure onset. The starting points of the windows are marked by green lines, and the ending points of the windows, which are also the seizure onsets, are marked by white lines. The EZ identified by epileptologists’ visual inspection is represented by pink rectangles. The electrode contacts with high in-degree values or high betweenness centrality values that are coincident with the EZ identified by epileptologists’ visual inspection are marked by white arrows. InD, in-degree; OutD, out-degree; BC, betweenness centrality. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 5. The EZ localization accuracy evaluation of the three graphic measures using the AUC index. 21 seizures from seven patients were included in the analysis. The red bar corresponds to the median, and the 25% and 75% percentiles are the lower and upper borders of each box, respectively. The whiskers correspond to the total range of the data. Significant differences were indicated by asterisks (Kruskal–Wallis ANOVA, post-hoc Dunn’s multiple comparison test, and p < 0.01). InD, in-degree; OutD, out-degree; BC, betweenness centrality.

thermore, there were two seizures even got perfect localization accuracy (AUC = 1.00). However, the median AUC values of the outdegree is 0.48, which was similar to random guess. The median AUC values of the betweenness centrality is 0.67. It should be notice that the AUC values distributed in quite large ranges for these two measures, which means an obvious individual variation. 4. Discussion 4.1. The localization ability of the three graphic measures

Fig. 4. Reproducibility of graph analysis results across seizures in an example patient (Patient 2). (A) Electrode positions on a 3D brain scheme. (B) Graph analysis results of three seizures. For each seizure, the left bottom panel shows the SEEG signals. The seizure onset time is marked by an arrow. The right bottom panel shows the normalized summation of the in-degree, out-degree and betweenness centrality within a 5-s window (marked by a bracket) before the seizure onset. The red numbers indicate the AUC values for each measure. The EZ identified by epileptologists’ visual inspection is represented by pink rectangles. InD, in-degree; OutD, out-degree; BC, betweenness centrality. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

higher accuracy in EZ localization than the other two measures. The median AUC values of the in-degree was 0.93 (range 0.77–1.00). The 25% and 75% percentiles were 0.89 and 0.97, respectively. It means that 50% seizures showed AUC values no less than 0.93, whereas 75% seizures showed AUC values no less than 0.89. Fur-

In the present study, we analyzed 21 seizures from seven patients and found that at least one of the three graphic measures (always including the in-degree) was coincident well with the EZ identified by epileptologists’ visual inspection (Figs. 3–5, Figs. S1–S2). This indicates that the graph theory is an efficient method in identifying the EZ when suitable graphic measures were chosen, which is in line with the previous findings (Panzica et al., 2013). However, the ability of the three graphic measures to identify the EZ was quite different. We found that the in-degree was the most sensitive measure in identifying the EZ. The out-degree was effective only in two patients (Patients 2 and 3) (Fig. 4 & S1). This is inconsistent with the previous findings suggesting that the out-going measures are more suitable than the in-going measures for identifying the EZ (Courtens et al., 2016; Dai et al., 2012; van Mierlo et al., 2013; Wilke et al., 2010). The major reason led to the conflicting conclusions might be the different methods used to construct the effective connectivity networks. The majority of the studies mentioned above used the DTF or adaptive DTF to construct the networks (Dai et al., 2012; van Mierlo et al., 2013; Wilke et al., 2010). Although both the DTF and the PDC are derived from the Granger causality, the normalization procedures are quite different. The definition of DFT uses the row-wise normalization, whereas the definition of PDC uses the column-wise normalization. The row-wise normalization bounds the sum of the inflows per channel to one, which will compromise the sensitivity to inflow, whereas the column-wise normalization bounds the quadratic sum of the outflows per channel to one, which will compromise the sensitivity to outflow (Plomp et al., 2014). It was confirmed by our results that the out-degree did not reveal any ‘outstanding node’ even in Patients 2 and 3. Therefore, from a computational perspective, the in-degree is more suitable

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than the out-degree in identifying the EZ when the PDC method is used, though the out-degree is still effective in some cases. In our opinion, the choice of graphic measures should be linked with the connectivity analysis method, and this issue is worthy to be further investigated. For the betweenness centrality, it was effective in four out of seven patients in the present study (Patient 1–4, Figs. 3 and 4, & Fig. S1). It should be noticed that the AUC values of betweenness centrality distributed in a quite large range (larger than 0.9 in some cases, whereas lower than 0.5 in other cases), which means an obvious individual variation. A few studies have shown that the betweenness centrality is an effective measure in localizing the EZ (Burns et al., 2014; Varotto et al., 2012; Wilke et al., 2011). Therefore, it’s an interesting question that in what kind of patients or conditions the betweenness centrality would be effective. It should be further investigated. 4.2. The time window for EZ localizing The normalized summation of the graphic measures within a 5-s window before the seizure onset was used to localize the EZ (Figs. 3–4, Figs. S1–S2). The choice of the window should be very careful, which would have a direct effect on the EZ localization. EZ is the brain region involved in the generation of seizures, thus the window should lay within the seizure generation phase and try to avoid the effect of the seizure diffusion. There is no universal standard in previous studies, in which the window had different lengths and locations. The window may start from a few seconds before the seizure onset to a few seconds after the seizure onset (Guye et al., 2006; van Mierlo et al., 2011) or start from the seizure onset with length of a few seconds to twenty seconds (David et al., 2011; Lu et al., 2012; Wilke et al., 2010). In the present study, we chose the window based on the consideration of seizure evolution. On the one hand, it is believed that the underlying network characteristics have already changed before the seizure onset and the changed network is responsible for the seizure generation. But the changing point is not clear, maybe a few seconds to a few minutes or even longer before the seizure onset, varied from patient to patient. No matter when the network characteristics change, the networks should carry important information that is responsible for the seizure generation within a few seconds before the seizure onset. On the other hand, the seizure may rapidly propagate from the seizure onset zone to other brain regions within a few seconds or even shorter in some patients. Thus the time period after the seizure onset had not been included in the window here to avoid the confusion of seizure onset zone and the brain regions recruited for the seizure propagation. 4.3. Evaluation of the EZ localization accuracy To quantify the EZ localization accuracy, we used the ROC analysis and the AUC index. This method do not bias any calculated graphic measure by artificially assuming a fixed threshold value (Burns et al., 2014; Courtens et al., 2016; van Mierlo et al., 2011). However, for clinical application, it is essential to select a proper threshold. Wilke et al. used the threshold at 50% and 80% of the maximal value, with no detailed description about the criteria of threshold selection (Wilke et al., 2010). Here we discuss the threshold choice for the in-degree since the in-degree was the most effective measure in our study. As shown in Fig. S3, the specificity got higher and the sensitivity got lower with the increase of threshold. But the distribution range was quite large, especially for the sensitivity. It was because that the situation varied from patient to patient. Therefore, we could not get a universal threshold suitable for all the patients. For the perspective of making less mistakes, we advise to choose the initial threshold at 70%. This choice would

keep the specificity higher than 95%, i.e. the FPR lower than 5%, in the present study (Fig. S3). Then the users could lower the threshold step by step to involve more brain regions, as appropriate. It should be further investigated to find a correct null hypothesis in order to threshold the graph measures (Courtens et al., 2016). 4.4. Limitations and future directions The major limitations of the present study lie in the SEEG recordings. The spatial sampling of the SEEG recordings is limited. It is very important to place the electrodes close to the EZ. If the brain region responsible for the seizure generation is located outside of the area covered by the SEEG, the PDC method may produce erroneous results. Therefore, it should be very careful when interpreting the results calculated from SEEG recordings. Another issue we would like to discuss is that we used the maximal PDC values along the whole frequency band (0.5–256 Hz) to construct the effective connectivity network. Previous studies have shown that the gamma band activities were more effective in localizing the EZ or more correlated with improved postsurgical outcome when compared with other frequency bands (Varotto et al., 2012; Wilke et al., 2011). We have constructed the effective connectivity networks using different frequency band activities, including the theta, alpha, beta, gamma and ripple band activities. But we did not find significant difference among these frequency bands in localizing the EZ (data not shown). It might because of our small sample size, or various epilepsy types, or other reasons. It should be further investigated in the future. In addition, the graph theory can be used not only to localize the EZ but also to improve our understanding of ictal phenomenon. It could quantify the network topology that cannot be seen by visual analysis (as shown in Fig. 2C). Therefore, it could be used to investigate the network dynamics responsible for the transition from interictal state to ictal state. It could also be used to find out the common topology characteristics for specific type of epilepsy. These were also our future investigation directions. In summary, we applied the graph theory to the SEEG recordings in seven patients who underwent presurgical evaluation for treatment of intractable epilepsy. We found that the graph theory is an effective method to localize the EZ when suitable graphic measures were chosen. Furthermore, the in-degree was the most effective measure among the in-degree, out-degree and betweenness centrality in localizing the EZ when the PDC method was used. Acknowledgment This work was supported by the Key Basic Research Project of Science and Technology Commission of Shanghai (13DJ1400303). Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.eplepsyres.2016. 10.021. References Akaike, H., 1974. A new look at the statistical model identification. IEEE Trans. Autom. Control 19, 716–723. Andrzejak, R.G., Schindler, K., Rummel, C., 2012. Nonrandomness, nonlinear dependence, and nonstationarity of electroencephalographic recordings from epilepsy patients. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 86, 046206. Andrzejak, R.G., David, O., Gnatkovsky, V., Wendling, F., Bartolomei, F., Francione, S., Kahane, P., Schindler, K., de Curtis, M., 2015. Localization of epileptogenic zone on pre-surgical intracranial EEG recordings: toward a validation of quantitative signal analysis approaches. Brain Topogr. 28, 832–837. Baccala, L.A., Sameshima, K., 2001. Partial directed coherence: a new concept in neural structure determination. Biol. Cybern. 84, 463–474.

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