# An Explainable Statistical Method for Seizure Prediction Using Brain Functional Connectivity from EEG

Authors: Hao Chen; Taoyun Ji; Xiang Zhan; Xiaoxin Liu; Guojing Yu; Wen Wang; Yuwu Jiang; Xiao-Hua Zhou
Journal: Computational Intelligence and Neuroscience
 (2022)

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## Abstract

Background. Epilepsy is a group of chronic neurological disorders characterized by recurrent and abrupt seizures. The accurate prediction of seizures can reduce the burdens of this disorder. Now, existing studies use brain network features to classify patients’ preictal or interictal states, enabling seizure prediction. However, most predicting methods are based on deep learning techniques, which have weak interpretability and high computational complexity. To address these issues, in this study, we proposed a novel two-stage statistical method that is interpretable and easy to compute. Methods. We used two datasets to evaluate the performance of the proposed method, including the well-known public dataset CHB-MIT. In the first stage, we estimated the dynamic brain functional connectivity network for each epoch. Then, in the second stage, we used the derived network predictor for seizure prediction. Results. We illustrated the results of our method in seizure prediction in two datasets separately. For the FH-PKU dataset, our approach achieved an AUC value of 0.963, a prediction sensitivity of 93.1%, and a false discovery rate of 7.7%. For the CHB-MIT dataset, our approach achieved an AUC value of 0.940, a prediction sensitivity of 93.0%, and a false discovery rate of 11.1%, outperforming existing state-of-the-art methods. Significance. This study proposed an explainable statistical method, which can estimate the brain network using the scalp EEG method and use the net-work predictor to predict epileptic seizures. Availability and Implementation. R Source code is available at https://github.com/HaoChen1994/Seizure-Prediction.


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## Body

## 1. Introduction

Epilepsy is a group of chronic neurological disorders characterized by the abnormal and excessive firing of brain neurons, called epileptic seizures [1]. According to the newest WHO global report on epilepsy, around 50 million people are suffering from epilepsy globally [2, 3]. During epileptic seizures, electrical activities in the brain are disrupted, resulting in dysfunction and communication disorders among brain regions, which in turn lead to many temporary symptoms, such as loss of consciousness, staring, and disturbances of movement [4]. Unpredictable seizures dramatically affect the life of patients and may even lead to death [5]. Therefore, accurate and reliable seizure prediction can be beneficial for treating epilepsy. Patients can use Anti-Seizure Medications (ASMs) for treatment in advance, which would substantially improve the quality of life of these patients and prevent some traumatic events, including a series of life-threatening accidents.Electroencephalography (EEG), as an electrophysiological monitoring approach to detecting brain electrical activity, has been proven to be a critical technique for diagnosing patients with epilepsy. Scalp EEG is typically noninvasive with multiple electrodes placed along the scalp [6]. It records the spontaneous electrical activity generated by brain neurons with high time resolution over a while. Scientists have found that it can be categorized into four different waveforms for scalp EEG records of patients with epilepsy. In the view of brain functional connectivity, these four different waveforms can be represented by four brain functional connectivity structures [7], corresponding to four different states of epilepsy seizures: (1) preictal state, which is the state before a seizure occurs; (2) ictal state, which is the onset state of seizure; (3) postictal state, which refers to the immediate state after a seizure; (4) interictal state, that is the state between postictal state and preictal state [8]. Figure 1 shows the sketch of the four states. Predicting seizures can be realized by detecting the preictal state, which can be achieved through discovering the changes in brain connectivity networks from interictal state to preictal state [9–12]. However, it is clinically difficult to identify the preictal state by visual inspection of scalp EEG signals to observe changes in the structure of brain connectivity networks. Therefore, powerful and explainable statistical methods are needed to determine the preictal state from scalp EEG recordings for seizure prediction.Figure 1
The sketch plot of four different states of epilepsy seizures.Nowadays, brain functional connectivity modeling approaches have been proven to be a crucial tool in the neuroscience research field [12]. The brain can be seen as a complex network in which each brain region communicates and cooperates to carry out different functions [13]. However, the dysfunction in certain areas would interfere with the processing of upcoming information, consequently leading to network disorders and changes in a person’s behavior [14]. Current research has shown that epilepsy is a specific disease related to the brain network abnormalities, and they also suggest that the brain functional connectivity of a particular patient would abnormal dynamic changes during seizures, and the forms of brain functional connectivity are different among four different states of epilepsy seizures [15]. Hence, it is reasonable and adequate to employ brain functional connectivity modeling approaches to predict seizures. Some previous studies have applied brain functional connectivity modeling methods to study epilepsy disease. For example, Williamson et al. [16] constructed multiple spatiotemporal correlation structure features from EEG data to classify the patients’ preictal or interictal states. A potential limitation of this study is that it only used a cortical network rather than a whole-brain network and cannot extract all essential features, making it difficult to achieve excellent predictive performance. Varotto et al. [17] proposed a method that employed a partially directed coherence method to depict the brain functional connectivity network. However, this study did not use the brain network features to predict seizures. Furthermore, a more recent work [18] has proposed an automatic seizure prediction method based on a graph convolutional network. This method could achieve a good seizure prediction performance by exploring the critical brain network features. To the best of our knowledge, this method is an excellent approach for seizure prediction. However, there are two fatal issues with this method. First, since this method is based on the deep learning technique, the interpretability is relatively weak. Second, the algorithm of this method is too complicated to be applied by clinicians.To address the issues mentioned above, we referred to the existing novel statistical analysis framework called simultaneous differential network analysis and classification for matrix-variate data (SDNCMV) [19] and based on the characteristics of scalp EEG data and epilepsy disease, we proposed an explainable statistical model for patient-specific seizure prediction. Before introducing the proposed method, we first briefly described the SDNCMV approach. This method was a two-stage data-driven approach that deals with fMRI data. The first stage estimated each subject’s brain functional connectivity network and converted this network data into vector data for prediction in the next step. In the second stage, an ensemble prediction procedure was used to conduct the prediction results. In our study, we focused on using scalp EEG data to address patient-specific prediction problems. Since EEG data and fMRI data are in the same data format as matrix data [20, 21], we can refer to SDNCMV. However, there are still some differences between the scenarios of this study and those of Chen et al. [19] that used fMRI data to classify Alzheimer’s disease. The fMRI data is a matrix data for each subject, while the EEG data is a matrix data for each epoch [22], which is artificially generated. More specifically, since the scalp EEG data used in this study have higher temporal resolution than fMRI data and the data epochs are small, we cannot use the SDNCMV method directly. We should assume that the brain functional connectivity for each subject is time-varying and then modify the first stage of SDNCMV to estimate the dynamic brain functional connectivity to obtain better performance. More details of our method will be introduced in the following section.The significance of this study is that we proposed an explainable statistical method, which could be used to predict seizures based on the brain functional network. In addition, the proposed method is also computationally efficient, and the results can be easily interpreted. Therefore, this method can be better applied to the clinical and is more conducive to helping more patients with epilepsy.


## 2. Materials and Methods

### 2.1. Scalp EEG Data

The scalp EEG data used in this study are obtained from Children’s Hospital Boston, the Massachusetts Institute of Technology (CHB-MIT) database [23] and Peking University First Hospital (FH-PKU) database.The CHB-MIT database is available with open access athttps://physionet.org/physiobank/database/chbmit/. The EEG recordings were collected from 23 children with intractable seizures, of which five males with age from 3 to 22, 17 females with age from 1.5 to 19, and one child with missing gender and age data. These recordings were grouped into 24 cases since the EEG data of patient ID chb21 was obtained one-half year after chb01 from the same child. The sampling frequency for this database was 256 Hz, and the international 10–20 EEG electrode positions and nomenclature system was used for these recordings. The difference between two adjacent electrodes obtained the signal measurement for each electrode in this scalp EEG data. In most of the 24 cases, there are 21 unique signals, while a few cases contain less or more. Hence, only the recordings that include these 21 unique signals were selected in this study to keep the results consistent.The FH-PKU database is a private database containing 17 patients or cases. This scalp EEG data were recorded at a sampling rate of 500 Hz and used 19 signals in the international 10–20 system. In this database, a different method was used from the CHB-MIT database to measure the signal of each electrode. This method used the signal difference between the electrode and the fixed reference electrode. Furthermore, to ensure the accuracy of the results, the physiological state of the patients in different epochs was roughly the same.In this study, we focus on patient-specific seizure prediction performance. For each patient in these two databases, the ictal state, the period when the patient experienced seizure onset, is easily detected from raw signals by doctors. Although the preictal state is challenging to identify and there is no gold standard, based on the ictal state, the preictal state can be defined by ourselves, which is the 30-minute window before a seizure occurs and is seen as the case state in this study. However, the interictal state, which is seen as the control state, is more difficult to define; it is hard to recognize the period of the postictal state. Hence, to eliminate the noise effect of the postictal state, recordings within 2 hours after the end of the seizure are removed. The period from this time to the next preictal state is defined as the interictal state. Moreover, if the time between two seizure periods is less than 2 hours, only the first one is selected for this study. We consider all epochs as samples in this study and divide the continuous EEG data within a preictal state and interictal state into nonoverlapping 60-second epochs. To reduce computational complexity, we average the data obtained every second for each signal. Then, the data of each epoch is in matrix form with 21 or 19 columns and 60 rows for the patients from CHB-MIT or FH-PKU database.


### 2.2. Dynamic Brain Functional Connectivity Estimation

This section introduces the procedure to estimate the individual-specific dynamic brain functional connectivity measures. For each individual, we denoteXγ∈Rp×q and Yϕ∈Rp×q as the raw scalp EEG data matrix of γ-th epoch for preictal state and ϕ-th epoch for the interictal state, respectively, where p represents the number of electrodes and q represents the number of time points. Based on the assumption that not every region of interest in our brain is connected, we estimate the dynamic brain functional connectivity within γ-th epoch for the preictal state and ϕ-th epoch for the interictal state via sparse precision matrices for Xγ and Yϕ, which estimate the strength measures of brain connectivity via partial correlations. Here we mainly focus on the procedure of how to address the raw scalp EEG data matrix in the preictal state Xγ, while Yϕ can be dealt with similarly.Before introducing the detailed procedure, we follow the classical matrix normal distribution framework to define the distribution ofXγ. Assume Xγ follows a matrix normal distribution for each γ, denoted as Xγ∼MNMXγ,ΣXTγ⊗ΣXSγ, where ΣXTγ=ΣXT,ijγ∈Rq×q and ΣXSγ=ΣXS,ijγ∈Rp×p represent the covariance matrices of p electrodes locations and q time points for γ-th epoch, respectively. Then, for each time point t (1≤t≤q) within the γ-th epoch, we have X⋅tγ∼NMX,⋅tγ,ΣXSγ. If the brain functional network is stable within each epoch, there are lots of existing approaches to estimate the sparse precision matrix ΩXSγ=ΣXSγ−1 in the high-dimensional setting, such as Graphical Lasso [24] and CLIME [25]. However, in the current study of epilepsy, it is more reasonable to assume that the brain functional network is changing over time. Hence, we need to estimate the dynamic sparse precision matrix ΩXSγt for each time point based on time-varying covariance matrices, which can be achieved by(1)Ω^XSγt=argminΩTrΣ^XSγtΩ−logΩ+λΩ1,where Σ^XSγt=∑iwitX·iγX·iγT/∑iwit is a weighted covariance matrix, and we adopt a symmetric non-negative kernel function K⋅ to generate the over time weights as wit=Ki−t/hn. It is easy to find that this objective function is based on the Graphical Lasso and given the estimated Σ^XSγt, we can use the same algorithm to solve this optimization problem. Please refer to Graphical Lasso [24] for details. In practice, to obtain a better prediction performance, we substitute Σ^XSγt by ∑t=1qΣ^XSγt/q, which is the average of Σ^XSγt over q time points and then a unified sparse precision matrix estimation within each epoch, instead of multiple different sparse precision matrices Ω^XSγ, which can be used to estimate the brain functional connectivity measures. Although, here the sparse precision matrix is same for each time points within a specific epoch, it is generated via a time varying covariance matrix, so the brain functional network can be considered dynamic. In addition, we use Gaussian kernel function and set hn=n1/3 to calculate the weights wit in the real application, where n is the sample size.To sum, in this study, we adopt two symmetric matricesW^XSγ=W^XS,ijγ∈Rp×p and W^YSϕ=W^YS,ijϕ∈Rp×p to measure the dynamic brain functional connectivity strengths for γ-th epoch in preictal state and ϕ-th epoch in interictal state, respectively. Here, we vectorize them via extracting the upper triangular elements by row for each matrix and connecting them together, and define these vectors as VXSγ=VecW^XSγ∈Rd and VYSϕ=VecW^YSϕ∈Rd for each epoch in different states, in which each element represent an edge in brain functional network and the dimension d is equal to pp−1/2. Assume there are n1 epochs in preictal state, n2 epochs in interictal state and totally n=n1+n2 epochs. Hence, we can define the predictor matrix used in predictive model as V∈Rn×pp−1/2, where V can be expressed as the stack of matrix VXS∈Rn1×pp−1/2 and matrix VYS∈Rn2×pp−1/2. In the following of this study, we are using V to serve as “Network Predictor Matrix.”


### 2.3. Dynamic Brain Functional Connectivity Estimation

Given the network predictor matrix, due to the complexity and high dimensionality of the data, we adopt a penalized and ensembled logistic regression method to predict seizures. For details, we use Lasso penalty to deal with high-dimension problem and bootstrap procedure to ensemble this penalized logistic regression. LetZ as the binary response variable and its observations are Z1,…,Zn, in which Zk=1k=1,…,n1 means corresponding observations are from preictal state and Zk=0k=n1+1,…,n means corresponding observations are from the interictal state. We denote P as the probability of Z=1 and Bb=1,…,B is the bootstrap times.Now, we introduce this predictive method briefly, and for more details, please refer to Chen et al. [19]. We randomly sample n1 epochs in the preictal state and sample n2 epochs in the interictal state, respectively, with replacement. Then, we repeat the resampling B times, and for each time, we employ the high-dimensional logistic regression model. We define the βb as the corresponding regression coefficients vector estimated by b-th model. If there is the coefficient in βb which is not equal to 0, it indicates that the corresponding edge in the brain network is meaningful for distinguishing between the preictal state and the interictal state. Finally, after whole resampling procedure, we define the estimated coefficients vector as β^bb=1,…,B and outcome for test sample as P^b. Hence, we use P^B=P^b/B to denote the proportion of a new epoch is assigned to preictal state and ψi=1/B∑b=1BIβ^ib≠0 to denote the weight for corresponding edge in the brain network. The greater the weight, the more important this edge is. This demonstrates the interpretability of our method.


### 2.4. Performance Evaluation Measures

The evaluation measures that we adopt for the performance of seizure prediction are Sensitivity Rate (SENS), False Discovery Rate (FDR), and Area Under Curve (AUC). The SENS measures the proportion of epochs from the preictal state with a positive result, and FDR is defined as the proportion of all epochs predicted from the preictal state, which is not. Since the values of these two criteria change with the cutoff value, we select the cutoff with the highest prediction accuracy. To avoid different cutoffs affecting performance, we also present the AUC values, which is a cutoff-independent measure and would be the most comprehensive measure.


## 2.1. Scalp EEG Data

The scalp EEG data used in this study are obtained from Children’s Hospital Boston, the Massachusetts Institute of Technology (CHB-MIT) database [23] and Peking University First Hospital (FH-PKU) database.The CHB-MIT database is available with open access athttps://physionet.org/physiobank/database/chbmit/. The EEG recordings were collected from 23 children with intractable seizures, of which five males with age from 3 to 22, 17 females with age from 1.5 to 19, and one child with missing gender and age data. These recordings were grouped into 24 cases since the EEG data of patient ID chb21 was obtained one-half year after chb01 from the same child. The sampling frequency for this database was 256 Hz, and the international 10–20 EEG electrode positions and nomenclature system was used for these recordings. The difference between two adjacent electrodes obtained the signal measurement for each electrode in this scalp EEG data. In most of the 24 cases, there are 21 unique signals, while a few cases contain less or more. Hence, only the recordings that include these 21 unique signals were selected in this study to keep the results consistent.The FH-PKU database is a private database containing 17 patients or cases. This scalp EEG data were recorded at a sampling rate of 500 Hz and used 19 signals in the international 10–20 system. In this database, a different method was used from the CHB-MIT database to measure the signal of each electrode. This method used the signal difference between the electrode and the fixed reference electrode. Furthermore, to ensure the accuracy of the results, the physiological state of the patients in different epochs was roughly the same.In this study, we focus on patient-specific seizure prediction performance. For each patient in these two databases, the ictal state, the period when the patient experienced seizure onset, is easily detected from raw signals by doctors. Although the preictal state is challenging to identify and there is no gold standard, based on the ictal state, the preictal state can be defined by ourselves, which is the 30-minute window before a seizure occurs and is seen as the case state in this study. However, the interictal state, which is seen as the control state, is more difficult to define; it is hard to recognize the period of the postictal state. Hence, to eliminate the noise effect of the postictal state, recordings within 2 hours after the end of the seizure are removed. The period from this time to the next preictal state is defined as the interictal state. Moreover, if the time between two seizure periods is less than 2 hours, only the first one is selected for this study. We consider all epochs as samples in this study and divide the continuous EEG data within a preictal state and interictal state into nonoverlapping 60-second epochs. To reduce computational complexity, we average the data obtained every second for each signal. Then, the data of each epoch is in matrix form with 21 or 19 columns and 60 rows for the patients from CHB-MIT or FH-PKU database.


## 2.2. Dynamic Brain Functional Connectivity Estimation

This section introduces the procedure to estimate the individual-specific dynamic brain functional connectivity measures. For each individual, we denoteXγ∈Rp×q and Yϕ∈Rp×q as the raw scalp EEG data matrix of γ-th epoch for preictal state and ϕ-th epoch for the interictal state, respectively, where p represents the number of electrodes and q represents the number of time points. Based on the assumption that not every region of interest in our brain is connected, we estimate the dynamic brain functional connectivity within γ-th epoch for the preictal state and ϕ-th epoch for the interictal state via sparse precision matrices for Xγ and Yϕ, which estimate the strength measures of brain connectivity via partial correlations. Here we mainly focus on the procedure of how to address the raw scalp EEG data matrix in the preictal state Xγ, while Yϕ can be dealt with similarly.Before introducing the detailed procedure, we follow the classical matrix normal distribution framework to define the distribution ofXγ. Assume Xγ follows a matrix normal distribution for each γ, denoted as Xγ∼MNMXγ,ΣXTγ⊗ΣXSγ, where ΣXTγ=ΣXT,ijγ∈Rq×q and ΣXSγ=ΣXS,ijγ∈Rp×p represent the covariance matrices of p electrodes locations and q time points for γ-th epoch, respectively. Then, for each time point t (1≤t≤q) within the γ-th epoch, we have X⋅tγ∼NMX,⋅tγ,ΣXSγ. If the brain functional network is stable within each epoch, there are lots of existing approaches to estimate the sparse precision matrix ΩXSγ=ΣXSγ−1 in the high-dimensional setting, such as Graphical Lasso [24] and CLIME [25]. However, in the current study of epilepsy, it is more reasonable to assume that the brain functional network is changing over time. Hence, we need to estimate the dynamic sparse precision matrix ΩXSγt for each time point based on time-varying covariance matrices, which can be achieved by(1)Ω^XSγt=argminΩTrΣ^XSγtΩ−logΩ+λΩ1,where Σ^XSγt=∑iwitX·iγX·iγT/∑iwit is a weighted covariance matrix, and we adopt a symmetric non-negative kernel function K⋅ to generate the over time weights as wit=Ki−t/hn. It is easy to find that this objective function is based on the Graphical Lasso and given the estimated Σ^XSγt, we can use the same algorithm to solve this optimization problem. Please refer to Graphical Lasso [24] for details. In practice, to obtain a better prediction performance, we substitute Σ^XSγt by ∑t=1qΣ^XSγt/q, which is the average of Σ^XSγt over q time points and then a unified sparse precision matrix estimation within each epoch, instead of multiple different sparse precision matrices Ω^XSγ, which can be used to estimate the brain functional connectivity measures. Although, here the sparse precision matrix is same for each time points within a specific epoch, it is generated via a time varying covariance matrix, so the brain functional network can be considered dynamic. In addition, we use Gaussian kernel function and set hn=n1/3 to calculate the weights wit in the real application, where n is the sample size.To sum, in this study, we adopt two symmetric matricesW^XSγ=W^XS,ijγ∈Rp×p and W^YSϕ=W^YS,ijϕ∈Rp×p to measure the dynamic brain functional connectivity strengths for γ-th epoch in preictal state and ϕ-th epoch in interictal state, respectively. Here, we vectorize them via extracting the upper triangular elements by row for each matrix and connecting them together, and define these vectors as VXSγ=VecW^XSγ∈Rd and VYSϕ=VecW^YSϕ∈Rd for each epoch in different states, in which each element represent an edge in brain functional network and the dimension d is equal to pp−1/2. Assume there are n1 epochs in preictal state, n2 epochs in interictal state and totally n=n1+n2 epochs. Hence, we can define the predictor matrix used in predictive model as V∈Rn×pp−1/2, where V can be expressed as the stack of matrix VXS∈Rn1×pp−1/2 and matrix VYS∈Rn2×pp−1/2. In the following of this study, we are using V to serve as “Network Predictor Matrix.”


## 2.3. Dynamic Brain Functional Connectivity Estimation

Given the network predictor matrix, due to the complexity and high dimensionality of the data, we adopt a penalized and ensembled logistic regression method to predict seizures. For details, we use Lasso penalty to deal with high-dimension problem and bootstrap procedure to ensemble this penalized logistic regression. LetZ as the binary response variable and its observations are Z1,…,Zn, in which Zk=1k=1,…,n1 means corresponding observations are from preictal state and Zk=0k=n1+1,…,n means corresponding observations are from the interictal state. We denote P as the probability of Z=1 and Bb=1,…,B is the bootstrap times.Now, we introduce this predictive method briefly, and for more details, please refer to Chen et al. [19]. We randomly sample n1 epochs in the preictal state and sample n2 epochs in the interictal state, respectively, with replacement. Then, we repeat the resampling B times, and for each time, we employ the high-dimensional logistic regression model. We define the βb as the corresponding regression coefficients vector estimated by b-th model. If there is the coefficient in βb which is not equal to 0, it indicates that the corresponding edge in the brain network is meaningful for distinguishing between the preictal state and the interictal state. Finally, after whole resampling procedure, we define the estimated coefficients vector as β^bb=1,…,B and outcome for test sample as P^b. Hence, we use P^B=P^b/B to denote the proportion of a new epoch is assigned to preictal state and ψi=1/B∑b=1BIβ^ib≠0 to denote the weight for corresponding edge in the brain network. The greater the weight, the more important this edge is. This demonstrates the interpretability of our method.


## 2.4. Performance Evaluation Measures

The evaluation measures that we adopt for the performance of seizure prediction are Sensitivity Rate (SENS), False Discovery Rate (FDR), and Area Under Curve (AUC). The SENS measures the proportion of epochs from the preictal state with a positive result, and FDR is defined as the proportion of all epochs predicted from the preictal state, which is not. Since the values of these two criteria change with the cutoff value, we select the cutoff with the highest prediction accuracy. To avoid different cutoffs affecting performance, we also present the AUC values, which is a cutoff-independent measure and would be the most comprehensive measure.


## 3. Results

This section illustrates the results of the proposed method in seizure prediction by applying it to the CHB-MIT and FH-PKU databases.Table1 presents the seizure prediction results for 24 patients in the CHB- MIT database. To prove that features derived via a dynamic brain functional network contain more information and improve prediction accuracy, we convert the raw scalp EEG data matrix for each epoch to a vector and stack these n vectors into a data matrix of dimension n×pq. Then, we feed this data matrix into our ensemble prediction model for comparison. Furthermore, considering that the raw data may contain a small amount of information, we also combine the predictor matrix derived from brain network data (BN Data) and the predictor matrix derived from raw scalp EEG data (Raw Data) as a predictor to observe its prediction performance. The results in Table 1 show that satisfactory prediction results can be obtained by using network features, while the prediction results obtained via using raw data as input are no different from random guessing. In addition, using the combination of brain network data and raw EEG data can also achieve satisfactory prediction. However, it is still worse than using brain network data only. This is because the raw data cannot provide any valuable information for prediction, so increasing these redundant variables from raw data makes prediction performance worse.Table 1
Seizures prediction results for the patients in CHB-MIT database via our method and STS-HGCN-AL method.
Patient IDBN dataRaw dataBN + raw dataSTS-HGCN-ALAUCSENSFDRAUCSENSFDRAUCSENSFDRAUCSENSFDRchb010.96895.00.0600.49647.50.3740.97095.00.0880.9961000.000chb020.9841000.1020.63475.00.4730.97390.00.0590.8971000.145chb030.99295.50.0220.69150.00.1930.98995.50.0290.92883.30.173chb040.86786.70.2900.59550.00.2470.82593.30.362NANANAchb050.83591.50.1730.4581000.9460.77860.00.1350.8751000.000chb060.80484.30.3440.50522.90.1540.77965.70.2050.9061000.162chb070.97893.30.0670.58343.30.2210.97593.30.057NANANAchb080.95385.00.0780.54840.00.2000.93385.00.1000.9991000.000chb090.96390.00.0430.55396.70.8150.95090.00.0690.8431000.092chb100.94786.70.0730.54425.00.1100.92285.00.1270.97783.30.171chb110.99095.00.0390.69680.00.4590.98995.00.0360.9401000.123chb120.91176.80.0950.47996.40.9190.90487.50.162NANANAchb130.99896.30.0000.50622.20.1000.99696.30.0250.91585.70.109chb140.87295.00.0150.49042.50.3350.82692.50.3690.9761000.104chb150.83699.80.2310.43384.60.8380.79373.60.306NANANAchb160.95093.30.1890.48640.00.3220.90496.70.2110.95487.50.187chb170.96095.00.0800.54275.00.5870.95490.00.0730.8261000.237chb180.9121000.3000.55330.00.1430.90187.50.2590.99275.00.138chb190.97691.00.0460.61063.60.3900.9741000.1670.9911000.038chb200.9871000.0770.38633.30.3190.9801000.1170.9821000.184chb210.95790.00.0850.4515.00.0020.92385.00.1150.8331000.156chb220.92496.30.2450.48540.70.2830.86085.20.2190.9971000.000chb230.9941000.0110.40910.00.0430.9901000.0310.9901000.047chb241.0001000.0000.59987.00.6371.0001000.000NANANAAverage0.94093.00.1110.53052.50.3800.92089.30.1380.93895.50.109The seizure prediction results for 17 patients from the FH-PKU database are presented in Table2. As done in Table 1, we compare the prediction performance of our method using three kinds of input features. In Table 2, we show that network features can also achieve accurate predictions. Although the prediction result obtained using the raw data is higher than random guessing, it is still unsatisfactory. Furthermore, unlike the CHB-MIT data, in this dataset, since the raw data can provide some valuable information for prediction, it is found that the best prediction performance can be obtained using the combined data.Table 2
Seizures prediction results for the patients in FH-PKU database via our method.
Patient IDBN dataRaw dataBN + raw dataAUCSENSFDRAUCSENSFDRAUCSENSFDR2000020.9501000.1250.63740.00.0250.94580.00.0002104160.99195.00.0260.9451000.1840.98395.00.0532104430.95790.00.0000.72670.00.3590.96790.00.0002104470.90089.50.2370.74978.90.3420.86594.70.3162104540.89185.00.1050.8341000.4470.93090.00.1322104600.9961000.0710.84790.00.2840.99596.70.0352104650.99295.00.0350.79080.00.3190.9851000.1132104670.93990.00.0290.79570.00.1430.96790.00.0292104700.97590.00.0000.8201000.4470.97890.00.0002104710.92980.00.0250.57950.00.2560.91085.00.1542104770.97187.50.0260.65195.80.6920.92787.50.1032104860.9951000.0250.86965.00.0260.98995.00.0512104890.97890.00.0260.74985.00.3680.98890.00.0262104941.0001000.0000.94992.90.1541.0001000.0002104980.9921000.0280.61170.00.4510.9871000.0562104990.94880.00.0130.73060.00.1970.9701000.1582105030.87780.00.0400.9811000.0670.9861000.080Average0.95891.30.0480.78079.30.2800.96393.10.077


## 4. Discussion

In this study, we have proposed an explainable statistical method to predict epileptic seizures, which is helpful in raising the alarm before seizures. More concretely, our method uses scalp EEG data to construct a dynamic brain functional connectivity network via a time-varying precision matrix estimation approach. Then, we treat these brain functional connectivity measures as predictor variables for the ensembled prediction model. Finally, through the proposed method in this study, we can obtain accurate prediction results by using these electrodes with overactive electrical discharges as predictors. In the following, we would like to discuss the findings of this study, and at the end, we will present some future research directions.


### 4.1. Relationship to Other Studies

Our study is not the first to use scalp EEG data to extract brain connectivity signatures for seizure prediction. There have been lots of state-of- the-art approaches, such as Gemein et al. [26], Tsiouris et al. [27], and Truong et al. [28]. So far as we know, the method called STS-HGCN-AL proposed by Yang et al. [18] can achieve a better seizure prediction performance among these approaches. We speculate that if our method outperforms STS- HGCN-AL, our method will outperform all existing methods. Hence, in this study, we only compare the prediction performance of our method with the method STS-HGCN-AL in the public database CHB-MIT database. It should be noted that it is difficult to draw a direct comparison due to different data preprocessing, such as how to choose the length of the epoch, when the preictal state starts, etc. In addition, the method STS-HGCN-AL has more strict requirements for the raw data, so this method can address part of patients’ data within the CHB-MIT database, while our method can deal with all patients’ data in terms of seizure prediction. We choose the AUC value as a measure of prediction performance to compare these two methods for the part of patients’ data. From the results in Table 1, it is not difficult to see that our method can predict more patients and has a higher AUC value of 94% in these patient data, which can suggest that our method performs better than the existing method STS-HGCN-AL in terms of predicting epileptic seizures.Furthermore, since our method uses brain functional connectivity features to predict seizures, in this study, in addition to the prediction performance, we also briefly discuss the performance of critical feature selection. We randomly select two patients from the FH-PKU database, the patient 210486 and patient 210494. Based on the order of the derived weightsψ for each edge in the brain network, we show the top 10 critical brain functional connectivity features identified by our model in Table 3 and Figures 2 and 3. Then, based on the weights for each edge in Table 3, we may consider the features with larger weights as identifying potential connectome biomarkers. For the identification of potential connectome biomarkers, there are many existing methods, such as Song et al. [29], Lu et al. [30], and Ding et al. [31]. However, there is no gold standard for the public datasets identifying potential connectome biomarkers. We cannot prove the effectiveness of our method for this issue and thereby cannot compare our method with existing methods. We just put the identification results here without evaluating the performance, and for this issue, we will leave it as a direction for future research.Table 3
Epileptogenic focus localization results for the two patients in FH-PKU database.
210486ψ210494ψ1Occipital L ↔ temporal L1.00Parietal L ↔ occipital L1.002Frontal L ↔ frontal R0.91Occipital L ↔ frontal M0.993Frontal R ↔ parietal L0.91Parietal R ↔ parietal M0.894Parietal R ↔ temporal R0.75Frontal M ↔ frontal M0.665Parietal L ↔ occipital L0.69Frontal L ↔ parietal R0.656Temporal L ↔ frontal M0.66Temporal L ↔ parietal M0.567Parietal L ↔ frontal L0.65Occipital R ↔ parietal M0.568Parietal L ↔ frontal M0.65Frontal R ↔ frontal R0.549Parietal R ↔ frontal R0.56Occipital L ↔ occipital R0.5110Frontal L ↔ frontal M0.55Frontal L ↔ frontal R0.50Figure 2
Top 10 brain functional connections that affect seizures for patient 210486.Figure 3
Top 10 brain functional connections that affect seizures for patient 210494.


### 4.2. Limitations and Future Directions

Although our method achieves satisfactory results in terms of seizure prediction, it still leaves much space for improvement to obtain even more realistic models. The limitations of our method proposed in this study mainly concentrated on three aspects. At first, for the sake of simplicity of our model, we have assumed that the raw scalp EEG data of each patient comes from a normal distribution. However, in the real world, we cannot know the actual distribution of the raw data. Hence, we are currently applying some statistical methods to relax the normal assumption for this problem. Secondly, in our model, we have used the same time window to define the preictal state of each patient, while in the real world, each patient has its heterogeneity and the time window of the preictal state is diverse. Hence, we plan to focus on how to estimate an optimal time window of the preictal state in the future. In the end, the study only briefly discussed how to identify potential connectome biomarkers using our method but did not test whether these biomarkers actually affected epilepsy. Therefore, in the future, we will conduct hypothesis tests in this field to demonstrate the efficiency and accuracy of our method in identifying potential connectome biomarkers.


### 4.3. Potential Applications of the Method in Treatment of Epilepsy

Epileptic seizures are sudden and have no apparent signs. The prediction of epileptic seizures can significantly enhance the effect of epilepsy treatment, improve the quality of life of patients with epilepsy, and reduce the mortality due to epileptic seizures, so the accurate prediction of epileptic seizures in the clinical application has a vital significance. Our experimental results and the comparison with previous work demonstrate that the proposed method is efficient. This gives the patient enough time to take action to cope with the seizure and reduce anxiety and trauma.Patients with epilepsy after regular ASMs treatment, there is still one-third of patients with epilepsy that cannot be controlled. Uncontrolled seizures have severe impacts on patients’ cognition, memory, quality of life, social psychology, and the growth and development of children. In recent years, imaging, electroencephalography, genetics, and other diagnostic techniques have been continuously improved, and the efficacy and safety of surgical resection have been recognized. For patients with drug-resistant epilepsy with a clear epileptogenic focus and a low surgical risk, surgical resection should be considered as soon as possible. The accuracy of the connectome biomarker identification may help to determine the epileptic region before epilepsy surgery, which is the key to ensuring the success of epilepsy surgery. Hence, finding the right target remains the essential prerequisite for our new drug development, and accurate connectome biomarker identification can provide potential therapeutic targets. In this study, we have briefly discussed that our method may enable potential connectome biomarker identification, which is essential for physicians to conduct the preoperative evaluation and develop new drugs or treatments for epilepsy, but this needs to be further validated in the future.


## 4.1. Relationship to Other Studies

Our study is not the first to use scalp EEG data to extract brain connectivity signatures for seizure prediction. There have been lots of state-of- the-art approaches, such as Gemein et al. [26], Tsiouris et al. [27], and Truong et al. [28]. So far as we know, the method called STS-HGCN-AL proposed by Yang et al. [18] can achieve a better seizure prediction performance among these approaches. We speculate that if our method outperforms STS- HGCN-AL, our method will outperform all existing methods. Hence, in this study, we only compare the prediction performance of our method with the method STS-HGCN-AL in the public database CHB-MIT database. It should be noted that it is difficult to draw a direct comparison due to different data preprocessing, such as how to choose the length of the epoch, when the preictal state starts, etc. In addition, the method STS-HGCN-AL has more strict requirements for the raw data, so this method can address part of patients’ data within the CHB-MIT database, while our method can deal with all patients’ data in terms of seizure prediction. We choose the AUC value as a measure of prediction performance to compare these two methods for the part of patients’ data. From the results in Table 1, it is not difficult to see that our method can predict more patients and has a higher AUC value of 94% in these patient data, which can suggest that our method performs better than the existing method STS-HGCN-AL in terms of predicting epileptic seizures.Furthermore, since our method uses brain functional connectivity features to predict seizures, in this study, in addition to the prediction performance, we also briefly discuss the performance of critical feature selection. We randomly select two patients from the FH-PKU database, the patient 210486 and patient 210494. Based on the order of the derived weightsψ for each edge in the brain network, we show the top 10 critical brain functional connectivity features identified by our model in Table 3 and Figures 2 and 3. Then, based on the weights for each edge in Table 3, we may consider the features with larger weights as identifying potential connectome biomarkers. For the identification of potential connectome biomarkers, there are many existing methods, such as Song et al. [29], Lu et al. [30], and Ding et al. [31]. However, there is no gold standard for the public datasets identifying potential connectome biomarkers. We cannot prove the effectiveness of our method for this issue and thereby cannot compare our method with existing methods. We just put the identification results here without evaluating the performance, and for this issue, we will leave it as a direction for future research.Table 3
Epileptogenic focus localization results for the two patients in FH-PKU database.
210486ψ210494ψ1Occipital L ↔ temporal L1.00Parietal L ↔ occipital L1.002Frontal L ↔ frontal R0.91Occipital L ↔ frontal M0.993Frontal R ↔ parietal L0.91Parietal R ↔ parietal M0.894Parietal R ↔ temporal R0.75Frontal M ↔ frontal M0.665Parietal L ↔ occipital L0.69Frontal L ↔ parietal R0.656Temporal L ↔ frontal M0.66Temporal L ↔ parietal M0.567Parietal L ↔ frontal L0.65Occipital R ↔ parietal M0.568Parietal L ↔ frontal M0.65Frontal R ↔ frontal R0.549Parietal R ↔ frontal R0.56Occipital L ↔ occipital R0.5110Frontal L ↔ frontal M0.55Frontal L ↔ frontal R0.50Figure 2
Top 10 brain functional connections that affect seizures for patient 210486.Figure 3
Top 10 brain functional connections that affect seizures for patient 210494.


## 4.2. Limitations and Future Directions

Although our method achieves satisfactory results in terms of seizure prediction, it still leaves much space for improvement to obtain even more realistic models. The limitations of our method proposed in this study mainly concentrated on three aspects. At first, for the sake of simplicity of our model, we have assumed that the raw scalp EEG data of each patient comes from a normal distribution. However, in the real world, we cannot know the actual distribution of the raw data. Hence, we are currently applying some statistical methods to relax the normal assumption for this problem. Secondly, in our model, we have used the same time window to define the preictal state of each patient, while in the real world, each patient has its heterogeneity and the time window of the preictal state is diverse. Hence, we plan to focus on how to estimate an optimal time window of the preictal state in the future. In the end, the study only briefly discussed how to identify potential connectome biomarkers using our method but did not test whether these biomarkers actually affected epilepsy. Therefore, in the future, we will conduct hypothesis tests in this field to demonstrate the efficiency and accuracy of our method in identifying potential connectome biomarkers.


## 4.3. Potential Applications of the Method in Treatment of Epilepsy

Epileptic seizures are sudden and have no apparent signs. The prediction of epileptic seizures can significantly enhance the effect of epilepsy treatment, improve the quality of life of patients with epilepsy, and reduce the mortality due to epileptic seizures, so the accurate prediction of epileptic seizures in the clinical application has a vital significance. Our experimental results and the comparison with previous work demonstrate that the proposed method is efficient. This gives the patient enough time to take action to cope with the seizure and reduce anxiety and trauma.Patients with epilepsy after regular ASMs treatment, there is still one-third of patients with epilepsy that cannot be controlled. Uncontrolled seizures have severe impacts on patients’ cognition, memory, quality of life, social psychology, and the growth and development of children. In recent years, imaging, electroencephalography, genetics, and other diagnostic techniques have been continuously improved, and the efficacy and safety of surgical resection have been recognized. For patients with drug-resistant epilepsy with a clear epileptogenic focus and a low surgical risk, surgical resection should be considered as soon as possible. The accuracy of the connectome biomarker identification may help to determine the epileptic region before epilepsy surgery, which is the key to ensuring the success of epilepsy surgery. Hence, finding the right target remains the essential prerequisite for our new drug development, and accurate connectome biomarker identification can provide potential therapeutic targets. In this study, we have briefly discussed that our method may enable potential connectome biomarker identification, which is essential for physicians to conduct the preoperative evaluation and develop new drugs or treatments for epilepsy, but this needs to be further validated in the future.


## 5. Consent

The parents of the patients signed written informed consent and agreed with their children’s participation in this study and allowing the use of the relevant data and information for scientific research.



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*Source: 2183562-2022-12-08.xml*