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1.INTRODUCTIONEpilepsy is a neurological condition that affects the central nervous system. It is characterized by recurrent spontaneous seizures, which are sudden and difficult to predict [1]. Drug-resistant epilepsy accounts for about a third of the 65 million patients worldwide who require surgery [2]. Therefore, accurate localization of the epileptogenic zone (EZ) in preoperative evaluation is imperative. The EZ, which is usually approximately enclosed by the seizure onset zone (SOZ), is a crucial area that needs to be accurately identified for effective treatment [3]. Intracranial electroencephalography (iEEG) helps identify EZ clinically, which can be recorded simultaneously across different cortical regions. Directed graph features based on functional brain networks are expected to be important biomarkers. Fruengel et al. studied local and global network reconfigurations during the four-node centrality pre-seizure period measures, as indicated by changes in different node centrality indices [4]. Yang et al. utilized the overall topology of the graphs, edge weights, and the number of edges in Granger causality (GC) maps to enhance understanding and potential applications in epilepsy surgery planning [5]. Murin et al. applied PageRank on the estimated causal influence graph to calculate a rank for each of the nodes, and the final results for 19 patients show a close match between the SOZ inferred by the proposed approach and expert neurologists (success rate of 17 out of 19) [6]. In clinical practice, the localization of the EZ relies on the capture of multiple seizures during intracranial monitoring, a process that takes several days or even weeks. The interictal period, characterized by abundant data, presents a valuable opportunity for EZ localization, such as significantly reducing medical costs and improving the efficiency of the diagnostic process [7]. Although locating the EZ through interictal periods is difficult, some scholars have made good results. Ye et al. extract pathological brain networks from the interictal period of E/MEG recordings to localize epileptic foci for presurgical evaluation [8]. Coito et al. investigated the fast-varying behavior of epileptic networks during interictal spikes in right and left temporal lobe epilepsy at a whole-brain scale using directed connectivity [9]. Park et al. denoted that maps of the GC network from interictal data might inform about the seizure network and indicated that “causality” in the Granger sense correlated with surgical targets [10]. Inspired by previous work, we want to know how effectively calculating causal networks in the interictal period, combined with graph features, is for locating the EZ. 2.METHODS2.1Dataset and preprocessingFour epilepsy patients were used in this study, with at least one-year follow-up, all from a publicly available dataset (https://www.ieeg.org [11]), and surgical outcome was defined as seizure-free according to the International League Against Epilepsy surgical outcome scale. A standard clinical recording system collected all the Electrocorticography (ECoG) data of the patients, and the electrode array and linear electrode (mesh electrode and strip electrode) were implanted in the subdural under clinical guidance. All patients underwent surgery at the Mayo Clinic. The ECoG recordings used are from apparently ‘healthy’ interictal epochs only, with no obvious epileptiform activity [12]. Patient P1 (iEEG ID: Study 038) had a medial frontal lobectomy and amygdalohippocampectomy, with the record in the 1521 to 1530 minutes, 3.3 hours from the next seizure. Patient P2 (iEEG ID: Study 021) underwent a temporal lobectomy and amygdalohippocampectomy, with the record in the 4951 to 4960 minutes, 20.5 hours from the next seizure. Patient P3 (iEEG ID: Study 023) received an occipital lobectomy, with the record in the 531 to 540 minutes, 4.6 hours from the next seizure. Patient P4 (iEEG ID: Study 026) had a medial frontal lobectomy, with the record in the 415 to 424 minutes, 8.7 hours from the next seizure. The sampling rate of the data was 500 Hz. During data preprocessing, three key steps were undertaken: data from all channels were filtered at a 60 Hz power frequency to eliminate power frequency interference, and then band-pass filtered between 1-80 Hz to isolate the frequency bands of interest. The bipolar method was used to remove the influence of the reference electrode, and channels with minimal amplitudes were excluded. The ECoG signal was divided into consecutive 1-second segments, each overlapping the previous one by 0.5 seconds, and a stationarity test was performed on each 1-second segment to ensure data validity. All channels were split into training and testing sets at 70% and 30%. 2.1Workflow of epileptogenic zone localizationThe research is organized into five sections, as depicted in Fig. 1. Five simulated nodes illustrate the workflow. Fig. 1(a) represents the original interictal ECoG data. Fig. 1(b) illustrates the weighted directed brain networks, where the strongest 10% of nodes are retained to extract information that potentially characterizes epilepsy. Fig. 1(c) presents six parallel features derived from graph theory, including indegree, outdegree, cluster coefficient, PageRank, hubs, and community. Fig. 1(d) details the model training process, where a balanced support vector machine (SVM) approach is employed to address the issue of imbalanced datasets. Fig. 1(e) shows the prediction of the EZ. The red area indicates the true excised electrode determined by the physician, while the yellow area represents the excised electrode predicted by the model. 2.2Autoregressive modelThe autoregressive (AR) model is a basic time series analysis model that uses the existing variables of the series to predict the value of the future time series [13]. The AR-based iEEG model can be described as follows: Where p is the order number, yt = [y1,t, y2,t,…, ym,t]T is m variables in state vector, εt = [ε1,t, ε2,t,…,εm,t]T is the vector of the multivariable zero-mean-uncorrelated white noise process, and Ar is the coefficient matrix of magnitude m × m. The stationary test in pre-processing parts showed that it was reasonable to select the order p = 1 for the model [14]. Due to the low spatial resolution of ECoG, excitatory and inhibitory connections between nodes can not be resolved from the network. The absolute value of the element can be interpreted as the influence between the nodes. Therefore, we define Where T represents the number of fragments, abs (·) represents the absolute value of all the elements of the matrix. 2.3Directed transfer functionDirected transfer function (DTF) is a method of analysis based on AR [15], using the system function of the AR model to estimate the causal effect between channels, which is the application of GC in the frequency domain. After the conversion from complex frequency domain to frequency domain and the conversion from analog angular frequency to digital angular frequency, the following formula is obtained: Where i represents the imaginary number, f represents the analog frequency, and Δt represents the sampling interval. Similar to the AR model, element Hij (f) in the DTF matrix represents the intensity of information flow from j channels to i channels. 2.4DegreeThe degree of a directed graph is divided into two categories, the in-degree and the out-degree, where the indegree is the number of edges pointing to the node, and the outdegree is the number of edges starting from the node. 2.5Cluster coefficientThe clustering coefficient (CC) is the fraction of triangles around a node and is equivalent to the fraction of the node’s neighbors that are neighbors of each other [16]. The following formula can define the CC: Where 2.6PageRank centralityPageRank is a graph node centrality metric to evaluate the importance of web pages [17]. The basic idea of PageRank, which uses random walks to simulate the behavior of users browsing the web and assess the importance of each node, has been used in several fields, including neuroscience. PageRank is calculated as follows: Where d is the damping factor, which is used to simulate the probability that the user will jump to a random page. M (i) is the set of all nodes that point to the node i. L(j) means the outdegree of the node. PR (i) is determined by the PageRank value of all nodes j pointing to node and the output of node i. N is the total number of nodes. 2.7HubsThe hub score is based on the Hyperlink-Induced Topic Search (HITS) algorithm. The HITS algorithm is specifically designed to analyze hyperlink structure and originally used for web page ranking [18]. It assigns two scores to each web page: a hub score and an authority score. Both are initialized to 1. By continuously updating the computation iteratively until the end of convergence, the formula is as follows: Where F(p) is the set of pages that p links to, and aq is the authority score of page r. B(p) is the set of pages that link to p, and hq is the hub score of page q. 2.8CommunityCommunity detection is an important problem in graph theory that aims to divide a network into several subgroups (communities) so that there is a higher density of connections between nodes within the same community and fewer connections between different communities. It adopts a community detection method based on the Louvain algorithm [19]. The Louvain algorithm is a greedy optimization method aimed at maximizing modularity, which measures the quality of community structure in a network. The modularity is defined as: Where Aij is the weight of the edge between node i and node j. ki and kj are the degrees of nodes i and j. m is the total number of edges in the network. ci and cj are the communities of nodes i and j. δ(ci, cj) is the Kronecker delta, which is one if ci = cj and zero otherwise. 2.9Balanced support vector machineGiven the highly imbalanced dataset, we employed a balanced SVM approach for training and classification. This method involves assigning higher weights to the minority class samples. Specifically, the weight adjustment is determined by the ratio of minority class samples to the number of majority class samples, ensuring a balanced influence on the model’s learning process. 3.RESULTSFirstly, we conducted a significance analysis (wilcoxon rank-sum test) on the six generated graph features. Although only indegree and PageRank showed significant differences, the other four features also contributed to EZ localization due to substantial information overlap. The statistical results are shown in Fig. 2. In addition, to ensure the reliability of the results, we conducted the training and test 500 times and averaged the outcomes across these iterations. As shown in Table 1, the AR model outperformed the DTF model in predicting EZ in the interictal period and achieved accuracy, precision, and recall of 0.775, 0.475, and 0.554. Table 1.Network difference differences with using SVM.
Finally, to verify the effectiveness of the proposed method, we generated a graph eigenmatrix from a stochastic matrix simulation. This simulation matrix was designed based on the graph size and the number of valid values. One numerical matric was generated for graph size 177x6, corresponding to the data size from the previous model. Regarding the number of effective values, the non-zero values in the simulated matrices matched the number of graph features in the real graph feature matrices, 327/828. Additionally, the value sizes adhered to the standard Gaussian normal distribution. The final results got the accuracy, precision, recall, specificity, and f1-score with 0.23, 0.08, 0.17, 0.25, and 0.11, respectively. The results of AR and DTF are compared with the baseline by random selection, as illustrated in Fig 3. 4.CONCLUSIONIn this paper, we analyzed two types of functional connectivity networks, each extracted six graph metrics, and employed a balanced SVM model for the localization of EZ. The results indicate that the localization stability of the interictal AR model surpasses that of the DTF model and achieves the accuracy, precision, and recall of 0.775, 0.475, and 0.554. Additionally, the proposed method demonstrates a high degree of overlap between the predicted EZ in the interictal period and the actual EZ, highlighting its significant potential value. ACKNOWLEDGEMENTSThis work was supported by the University Fundamental Research Funds of Liaoning Provincial Department of Education (202434180) and the Research Fund of Liaoning Provincial Natural Science (2021-KF-12-11). REFERENCESKanner, A. M. and Bicchi, M. M.,
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