The association of magnetoencephalography high‐frequency oscillations with epilepsy types and a ripple‐based method with source‐level connectivity for mapping epilepsy sources

Abstract Objective To explore the association between high‐frequency oscillations (HFOs) and epilepsy types and to improve the accuracy of source localization. Methods Magnetoencephalography (MEG) ripples of 63 drug‐resistant epilepsy patients were detected. Ripple rates, distribution, spatial complexity, and the clustering coefficient of ripple channels were used for the preliminary classification of lateral temporal lobe epilepsy (LTLE), mesial temporal lobe epilepsy (MTLE), and nontemporal lobe epilepsy (NTLE), mainly frontal lobe epilepsy (FLE). Furthermore, the seizure site identification was improved using the Tucker LCMV method and source‐level betweenness centrality. Results Ripple rates were significantly higher in MTLE than in LTLE and NTLE (p < 0.05). The LTLE and MTLE were mainly distributed in the temporal lobe, followed by the parietal lobe, occipital lobe, and frontal lobe, whereas MTLE ripples were mainly distributed in the frontal lobe, then parietal lobe and occipital lobe. Nevertheless, the NTLE ripples were primarily in the frontal lobe and partially in the occipital lobe (p < 0.05). Meanwhile, the spatial complexity of NTLE was significantly higher than that of LTLE and MTLE and was lowest in MTLE (p < 0.01). However, an opposite trend was observed for the standardized clustering coefficient compared with spatial complexity (p < 0.01). Finally, the tucker algorithm showed a higher percentage of ripples at the surgical site when the betweenness centrality was added (p < 0.01). Conclusion This study demonstrated that HFO rates, distribution, spatial complexity, and clustering coefficient of ripple channels varied considerably among the three epilepsy types. Additionally, tucker MEG estimation combined with ripple rates based on the source‐level functional connectivity is a promising approach for presurgical epilepsy evaluation.


| INTRODUC TI ON
About a third of epilepsy are clinically refractory to drug therapy and cause significant morbidity. 1 Surgery is a promising alternative for treating epilepsy. 2 However, about 20%-50% of epileptic patients undergo experience seizures due to inaccurate resection. 3 Currently, temporal lobe epilepsy (TLE) accounts for more than 50% of all focal epilepsy cases, 4,5 while frontal lobe epilepsy (FLE) accounts for approximately 30% of all cases. 6 Therefore, TLE and FLE are clinically challenging to treat, and effective preoperative classification and evaluation are necessary.
There is an urgent need for reliable biomarkers, and more novel and comprehensive evaluation methods to determine the epilepsy type and epileptogenic zone. 7 High-frequency oscillations (HFO) (ripple: 80-250 Hz; fast ripple: 250-500 Hz) have been used as a new biomarker of epilepsy for decades, 8 which is an oscillation with frequencies higher than 80 Hz on electroencephalography (EEG) or magnetoencephalography (MEG). 9 Among all the electrophysiological presurgical evaluation techniques, such as electroencephalography (EEG), video-EEG, head MRI, and magnetoencephalography (MEG), EEG is cheaper than most other technologies used in preoperative epilepsy assessment. [10][11][12] However, EEG has a lower spatial resolution than MEG and is susceptible to noise. 13 While MEG has increasingly become a valuable noninvasive diagnostic tool for preoperative epilepsy evaluation and has a high temporal and spatial resolution. [14][15][16] However, compared with EEG, relatively fewer HFO studies in source locations based on MEG have been conducted in the past decades. 17 So it is a ripe research area. The rates and morphological features of HFO were used to evaluate the seizure status. 18 Varying HFOs have been observed among different seizure types. 19 Resection of the HFO-generating areas is associated with better treatment outcomes than removing the spike-generating areas. On the other hand, retaining most of the HFO-generating tissue is associated with poor treatment outcomes. 20 Compared with spikes, different mechanisms are involved in HFO-associated seizures. 21,22 Moreover, the source location accuracy of ripple was higher than spike. 23,24 The ripples detected from MEG are more specific and sensitive to the activated brain areas than from EEG. 25 Therefore, there is a need to explore whether various HFO characteristics could be used for the preliminary identification of epilepsy types.
Apart from determining the initial epilepsy type, it is difficult to accurately locate seizure foci for successful epilepsy surgery. Currently, it is also challenging to accurately identify the source location due to the ill-posed nature of the inverse problem. 26 Therefore, many techniques have been proposed to solve the inverse problem. 27,28 Beamforming and the improved linearly constrained minimum variance (LCMV) source location algorithms have been proposed to address the inverse problem. 23,[29][30][31] However, the accuracy of this method needs improvement. To solve the problem, Tucker decomposition, a higherorder extension of traditional singular value decomposition (SVD) and Principal Component Analysis (PCA), has been used for multichannel signal analysis and showed advantages. 32,33 Tucker is a method used to estimate the ranks of an N-order input tensor so that the high-and low-frequency noises can be removed synchronously. 23,34 While its application in multichannel bioelectric signals is rare. 35 In addition to considering the new biomarkers and the accuracy of solving the inverse problem, we also innovatively take into account the impaired network activity and connectivity of epilepsy to make a more comprehensive preoperative evaluation. 24,[36][37][38] Analyzing the HFO epileptic network could be used for epilepsy diagnosis. 39 Most studies on functional connectivity for epilepsy have relied on EEG. 40,41 To understand the interrelationships among different brain regions, there is a need to explore source-level functional brain networks. Studies show that the hub state of each region of interest (ROI) in the preoperative evaluation of epilepsy, which relies on betweenness centrality, effectively predicts epilepsy recurrence after surgery. 42 The maximum accuracy of functional connectivity at the source level relies on the improvement of the source location algorithm because the brain is a complex nonlinear system with nontrivial topological and dynamical properties. 43 Therefore, the severity of seizures can be predicted by the nonlinear dynamic dimension of MEG. 44 Mean correlation dimension and Kolmogorov entropy of the nonlinear dynamic system are used to assess the treatment effects of repetitive transcranial magnetic stimulation (rTMS). 45 Apart from that, chaos theory is used in enhancing the accuracy of the presurgical evaluation of epilepsy based on the spatial and temporal interactions between epileptogenic zones and other parts. 46 To make noninvasive classification and accurate preoperative evaluation, we propose a multidimensional approach using MEG HFO (ripple) to precisely localize the epileptic focus of MTLE, LTLE, and NTLE (mainly FLE).
The following were the main objectives and contributions of the study: 1. Innovatively, epilepsy types were preliminarily distinguished by ripple rates, ripple distribution, as well as nonlinear dynamic features, and network collectivization.
2. An improved source location algorithm of LCMV through Tucker decomposition, which could remove the redundant information in the MEG signal, was used for more accurate localization of the seizure foci.

| Preprocessing
The artifacts were removed before ripple detection. Firstly, the line noise was removed using a discrete Fourier transform. Then, electrooculogram and electrocardiograph artifacts were removed through independent component analysis. Lastly, all channels were converted into z-scores using a semi-automatic method of rejecting channels containing artifacts, which were all completed in MATLAB.
To determine the spatial distribution of ripple, the 306 MEG channels were divided into four brain sections (frontal lobe, temporal lobe, parietal lobe, and occipital lobe).

| Automatic detection of ripples
A sliding window algorithm was used as the basis for the automatic detection algorithm. An improved algorithm based on the root mean square (RMS) of MEG was used after wavelet threshold denoising ("db4") of the MEG signal for 0.6 s 47 in MATLAB. To construct the peak points distribution curve (PPDC) with 80-250 Hz ripple signal, all signal peaks were detected during the 0.6 s interval and were ranked from highest to lowest. The distribution curve of the 30%~60% peaks was then fitted into a linear model. An amplitude greater than 5% of the fitted amplitude line was used as the boundary of the ripple threshold and baseline for the PPDC ( Figure 2A). Furthermore, the dynamic thresholds were created using this improved algorithm. Waveforms with four more continuous peaks higher than the threshold and in accordance with the oscillation trend (rising and falling slowly) were classified as ripples ( Figure 2B).

F I G U R E 1
Overview of the preoperative evaluation of lateral temporal lobe epilepsy (LTLE), mesial temporal lobe epilepsy (MTLE), and nontemporal lobe epilepsy (NTLE), including ripple detection and scalp-level analysis, improved source location algorithm based on Tucker decomposition, and source-level analysis

| MEG ripple analysis of LTLE, MTLE, and NTLE on scalp level
During the preoperative assessment of epilepsy, we considered three aspects: (1) ripple rate and channel distribution pattern, (2) nonlinear dynamic feature, and (3) scalp networks.

| Ripple detection rates and channel distribution pattern
To distinguish the different ripple rates of the three epilepsy types (LTLE, MTLE, and NTLE), the number of ripples in 10 min of the 63 patients was calculated using the MATLAB program.
To compute the spatial distribution of ripple, the 306 MEG channels were divided into four brain sections (frontal lobe, temporal lobe, parietal lobe, and occipital lobe). Except for occipital lobe areas, which cover 72 channels, the rest of the brain areas cover 78 channels. The ripple-detecting percentage of each brain section was calculated, and then, we assigned the value of all channels in this section to the value of the percentage, so that the 306 channels have a total of four different values. The topographic distribution over the head of 2-dimensional data representations was plotted using fieldtrip software.

| Nonlinear dynamic analysis of channels detected ripples
The spatial complexity represents the mutual independence of brain areas. After the time points of ripples were marked, the spatial complexity was computed for every channel that could detect ripple. where ' i is the normalized eigenvalues. For every patient, the spatial complexity of the channels, which could detect ripples, was averaged. 63 quantified spatial complexity were obtained at last.

| Scalp-network analysis
The relationship between local aggregation at the scalp level and epilepsy types were investigated. Specifically, the coherence between MEG signals from the Fourier spectrum, in which the MEG segment was the ripple window (0.3 s), was calculated using the  (2): where n is the number of neighbor nodes.
The standardized clustering coefficient was calculated using where C A is the average clustering coefficient of all channels, and C k is the clustering coefficient of the channels, which detected ripples.
On the coherence map, the threshold we used is 0.7, each 306 * 306 matrix is converted into an undirected weighted graph by applying the threshold 0.7, and the 306 MEG electrodes represent the vertices. If the coherence value exceeded 0.7, an edge between the corresponding vertices was established, which are neighbors of each other. Finally, we mainly compare the standardized clustering coefficients of the channels that can detect ripple.

| Preoperative evaluation on source-level
The results in section 2.5 were only used to assess the epilepsy type.
To better pinpoint the foci of the patients, we used the Tucker decomposition and selected the ripple segment as a time window of interest. Additionally, a source-level network indicator was calculated for more precise detection.

| Source localization algorithm
Forward problem: Individual head MRI data were used to construct a realistic-shaped surface (Single shell) inside the skull for MEG.
The anatomical MRI was spatially aligned with head coordinates (Neuromag coordinate system) based on external fiducials markers through rotation, scaling, and translation.
Inverse problem: The covariance matrix was computed based on the approximated data of the MEG data to improve the accuracy of the source location. The high-frequency and low-frequency noises were removed using Tucker decomposition of the 306 channel MEG signals before the inverse problem was solved with linearly constrained minimum variance beamformers (LCMVs). The Tucker decomposition was derived using Equation (4): where  is the core tensor containing the main information, and U (i) are factor matrices of the original tensor. It is an efficient method to calculate the core tensor and the factor matrices, where singular value decomposition (SVD) replaces the eigenvalue decomposition. All the source location processes are completed on fieldtrip.
The pseudo-code of the Tucker method is described as follows: Input: tensor A and rank-R.
Output: core tensor and U. 6. Return core tensor and U.
Then, a new matrix, which includes more useful information of the original signal, is reconstructed by the core tensor and the core tensor.
Lastly, the new matrix was used as input in fieldtrip to perform the LCMV algorithm.

| Source-level network analysis
Brain network analysis and source localization were used to assess whether the results of brain network analysis could improve The dark blue line is the fitting straight line of the 30% ~ 60% peaks, the dotted red line is the threshold of the ripples, while the light blue line is the ordered peaks. (B) representative image of magnetoencephalography (MEG) ripple the accuracy of preoperative assessment. The coherence between source-level signals was calculated using ripple window-based source analysis using an equation in MATLAB Equation (5).
where S xy ƒ is the cross-spectral power density of two signals, S xx ƒ and S yy ƒ represent the auto-power spectral density.
Moreover, the source activity was interpolated onto the voxels of the Anatomical Automatic Labeling(AAL)template from the Montreal Neurological Institute (MNI). A functional network was constructed using 90 ROIs from the source-reconstruction parameters over the parcels.
Finally, a network graph measure (betweenness centrality) between the ROIs was computed. The 90 betweenness values were ranked from the largest to the smallest to evaluate the overlap between the betweenness of ROIs and the surgical operation site.

| Statistical analysis
Data were analyzed using the Origin software version 2022. The difference in the detection rate, spatial complexity, and clustering coefficient among the groups was evaluated using analysis of variance (ANOVA). Besides, we used Bonferroni multiplicity adjustment for multiple comparisons and paired t-tests to compare LTLE, MTLE, and NTLE source-level calculations (LCMV source location, Tucker decomposition source location, and source-level network analysis).
Statistical significance was set at p < 0.05.

| Ripple detection rates and channel distribution pattern
To investigate the differences in ripple rates and distribution of 306 channels among LTLE, LTLE, and NTLE, we calculated the number of ripples in 10 minutes and the brain area where the ripple channels were located.

| Nonlinear dynamic analysis and scalpnetwork analysis
Taking into account the dynamics of ripple channels and the relationship between the three types of ripple channels, the spatial complexity and clustering coefficients were calculated. For nonlinear dynamic analysis, the channels we used were all the channels, which could detect ripples. For scalp-network analysis, we computed the clustering coefficients for 306 channels, and the clustering coefficient for the ripple channel was standardized using the average clustering coefficient of all 306 channels, which were compared among different epilepsy types. Both the results of nonlinear dynamic analysis and the clustering coefficient were averaged across channels for the same patient.
As shown in Figure 4A, the spatial complexity was significantly higher in NTLE than in LTLE and MTLE patients, and the spatial complexity was lowest in MTLE patients. The spatial complexity findings were then compared with the number of ripples in 10 min (p < 0.01) and were found to be opposite. In contrast with Figure   The majority of the top ten betweenness was concentrated in the surgical area using these two ripple windows. Moreover, Figure 5D-E shows the top 10 betweenness in source level by these 2 ripples:

| Source-level network analysis based on the Tucker decomposition
for the yellow ripple 1 and green ripple 2, most areas with top 10 betweenness are in the surgical area: left temporal lobe, hippocampus, and parahippocampal gyrus.
As shown in Figure 6A-C, the percentage of ripples at the surgical site was higher than the Tucker algorithm results, and the source location algorithm gave slightly better results than the LCMV algorithm for all three patient categories. Based on the Tucker source location algorithm, the "betweenness centrality" of the 90 ROIs was calculated at the source level. When the "betweenness centrality" was added, the percentage of ripples at the surgical site increased and were higher than those of Tucker decomposition (p < 0.01). So functional connectivity analysis effectively supplemented the epilepsy preoperative evaluation with MEG. (5)

| DISCUSS ION
In this paper, we investigated the intergroup difference in ripple rates among LTLE, MTLE, and NTLE groups. Specifically, we used a multiangle approach combining ripple rates, ripple distribution, ripple-channel spatial complexity, and clustering coefficient for initial diagnosis. A new source location algorithm was used to estimate indicating that the higher the spatial complexity, the more independent the neural processes, and the lower the functional connectivity.
The localization accuracy of the LCMV method for the ripple window was lower than that of the Tucker LCMV method in the source location. As a consequence, we conclude that Tucker decomposition is more effective at removing redundant noise and keeping the maximum amount of information than LCMV. Functional connectivity at the brain region level revealed that more ripples indicate an area for surgical resection with a higher degree of betweenness centrality.
Using noninvasive MEG recordings at the source level to localize the epileptogenic zone is effective in localizing seizures among patients with intractable epilepsy. Analyzing brain networks revealed details of epileptic seizures because an epilepsy network may not be limited to a few regions. Above all, the proposed framework displays excellent outcomes.
These results are consistent with previous studies, in which ripples were demonstrated to contribute to epilepsy pathology by generating and propagating seizures. Thus, ripples are potentially promising epileptogenic biomarkers. 16 The rates of HFOs with different pathologic substrates were different and were higher in focal cortical dysplasia (FCD), mesial temporal sclerosis, and nodular heterotopia (NH) than in atrophy, polymicrogyria, and tuberous sclerosis. 19  Tucker decomposition based on LCMV provides better source location results than dynamic imaging of coherent sources (DICS), multiple signal classification (MUSIC), and LCMV. 50 The source location results based on LCMV are more reliable. 23 Generally, abnormal brain activity is not confined to a single region but spreads to other brain regions through networks. 51 In this paper, we mapped magnetic field activity onto the source-level functional modules and found that higher betweenness centrality regions are mostly located in or near the surgical region. Within the focal zone, nodes with higher betweenness centrality are important nodes and they spread out over the entire network. Therefore, epilepsy is a network disease caused by abnormal neocortical connectivity spanning multiple regions. 49 Overall, these findings further revealed that the pathological

| CON CLUS ION
In this study, we investigated the differences in ripple parameters, including ripple rates, ripple distribution, ripple-channel nonlinear dynamics, and functional connectivity among LTLE, MTLE, and NTLE. The results showed significant differences in these parameters among the three epilepsy subtypes. Moreover, a modified algorithm called Tucker LCMV was used to improve source localization accuracy using a rippled window based on the source-level network.
The proposed method supplemented the source-level network can be an excellent tool for MEG source localization during the preoperative evaluation of epilepsy. In summary, this study demonstrates that epilepsy types have specific ripple features, and the HFO findings are critical in presurgical assessments.

CO N FLI C T O F I NTER E S T S TATEM ENT
None of the authors have any financial disclosure or conflicts of interest.

DATA AVA I L A B I L I T Y S TAT E M E N T
The data and software code that support the findings of this study are available from the corresponding author upon reasonable request.