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. Author manuscript; available in PMC: 2022 May 1.
Published in final edited form as: Epilepsy Res. 2021 Mar 8;172:106602. doi: 10.1016/j.eplepsyres.2021.106602

Delineation of Epileptogenic Zones with High Frequency Magnetic Source Imaging Based on Kurtosis and Skewness

Jing Xiang a,b,*, Ellen Maue a,b, Hisako Fujiwara b, Francesco T Mangano c, Hansel Greiner b, Jeffrey Tenney a,b
PMCID: PMC8052290  NIHMSID: NIHMS1681151  PMID: 33713889

Abstract

Background:

Neuromagnetic high frequency brain signals (HFBS, > 80 Hz) are a new biomarker for localization of epileptogenic zones (EZs) for pediatric epilepsy.

Methods:

Twenty three children with drug-resistant epilepsy and age/sex matched healthy controls were studied with magnetoencephalography (MEG). Epileptic HFBS in 80-250 Hz and 250-600 Hz were quantitatively determined by comparing with normative controls in terms of kurtosis and skewness. Magnetic sources of epileptic HFBS were localized and then compared to clinical EZs determined by invasive recordings and surgical outcomes.

Results:

Kurtosis and skewness of HFBS were significantly elevated in epilepsy patients compared to healthy controls (p < 0,001 and p < 0.0001, respectively). Sources of elevated MEG signals in comparison to normative data were co-localized to EZs for 22 (22/23, 96%) patients.

Conclusions:

The results indicate, for the first time, that epileptic HFBS can be noninvasively quantified by measuring kurtosis and skewness in MEG data. Magnetic source imaging based on kurtosis and skewness can accurately localize EZs.

Significance:

Source imaging of kurtosis and skewness of MEG HFBS provides a novel way for preoperative localization of EZs for epilepsy surgery.

Keywords: Epilepsy, High Frequency Brain Signals, Kurtosis, Skewness, Magnetic Source Imaging, Magnetoencephalography

Graphical Abstract

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1. Introduction

Invasive recordings (Bragin et al., 2010; Rampp et al., 2010; Weiss et al., 2018; Worrell et al., 2012; Zijlmans et al., 2012a) have provided solid evidence that oscillatory high frequency brain signals (HFBS), which are typically called high frequency oscillations (HFOs, 80-600 Hz), are a epileptogenic biomarker (Lee et al., 2020; Roehri and Bartolomei, 2019). HFOs can be divided into ripples (80-250 Hz) and fast ripples (250-600 Hz) (Bragin et al., 2010; Rampp et al., 2010; Weiss et al., 2018; Worrell et al., 2012; Zijlmans et al., 2012a). The resection of the brain areas generating HFOs, particularly fast ripples, can predict favorable outcomes of epilepsy surgery (Tamilia et al., 2018; van ’t Klooster et al., 2017; Zijlmans et al., 2012b).

One barrier hindering HFOs from wide clinical applications (Engel et al., 2009; Roehri and Bartolomei, 2019) is that the brain generates both epileptic (pathological) and physiological high frequency brain signals (HFBS). Physiological HFBS can be divided into elicited (functional) and endogenous (intrinsic) HFBS. Elicited HFBS, which are also commonly called high gamma, have been widely studied in the somatosensory, language and several other brain areas (Xiang et al., 2003; Xiang et al., 2001). Endogenous HFBS include physiological and pathological signals (Engel et al., 2009; Roehri and Bartolomei, 2019). Though endogenous HFBS in epilepsy were conventionally considered to be pathological, recent reports indicates that endogenous HFBS in epilepsy include both pathological and physiological signals (Engel et al., 2009; Roehri and Bartolomei, 2019). Of note, epileptic HFOs are only one types of HFBS, which typically have four or more oscillations standing out background activities. Unfortunately, there is no criteria that can separate HFOs from HFBS or differentiate pathological from physiological HFBS. From clinical point of view, it is important to separate epileptic from physiological HFBS (Frauscher et al., 2018; Lee et al., 2020; Mooij et al., 2017; Roehri and Bartolomei, 2019; Zijlmans et al., 2012b).

Recent advances in noninvasive detection of HFBS with magnetoencephalography (MEG) opens a new window for the study of HFBS (van Klink et al., 2019; Velmurugan et al., 2019; Xiang et al., 2004; Yin et al., 2019). The noninvasiveness of MEG enables the recording of HFBS from healthy subjects (Xiang et al., 2009b). One potential approach to distinguishing epileptic from physiologic HFBS is to characterize MEG HFBS from epilepsy patients and healthy controls (Xiang et al., 2009b). Since kurtosis is a measure of the “spikiness” (or signal standing out from ongoing background activity) while skewness is a measure of asymmetry of signals(Bullock et al., 1997; Hall et al., 2018; Mooij et al., 2020; Quitadamo et al., 2018), it is possible to use kurtosis and skewness to separate epileptic from physiological HFBS. Kurtosis has been used in localizing low frequency epileptic activity with MEG (de Gooijer-van de Groep et al., 2013; Hall et al., 2018). Two recent reports (Mooij et al., 2020; Xiang et al., 2020) have shown that epileptic HFBS in invasive recordings or virtual sensors can be detected with kurtosis and/or skewness analyses. Up to now, there is no report on kurtosis and skewness based source imaging of MEG HFBS with a focus on pediatric epilepsy.

The objective of this study is to detect and localize epileptic HFBS in MEG with kurtosis and skewness based source imaging. The kurtosis and skewness in MEG signals were quantified with a sliding time window (Letham and Raij, 2011; Prendergast et al., 2013; Quitadamo et al., 2018). To distinguish epileptic HFBS from physiological HFBS, we designed an age and sex matched healthy control group. To rigorously assess the epileptogenicity of HFBS, we studied a group of patients with clearly defined EZs by clinical invasive recordings and surgical outcomes. Since kurtosis and skewness analyses can be done automatically and quantitatively, without the conventional visual identification and mark, the present study may provide an unprecedented approach to noninvasively localizing EZs with MEG.

2. Methods

2.1. Patients

Twenty-three pediatric patients affected by drug-resistant epilepsy were studied. All the 23 patients met the following criteria for the present research. The inclusion criteria for patients were: (1) Drug-resistant epilepsy and a surgical candidates; (2) Underwent clinical intracranial recordings; (3) Had epilepsy surgery, defined as resection or ablation of EZs; (4) Had preoperative magnetic resonance imaging (MRI) scan and MEG recordings; and (5) Post-operative assessments have been obtained at least one year after surgery. The control group included healthy children and adolescents. Controls were recruited to match the children with epilepsy for age and gender and met inclusion criteria of: (1) Healthy without history of neurological disorder; (2) MRI normal. Exclusion criteria for all participants were: (1) Presence of an implant, such as cochlear implant devices, a pacemaker or neuro-stimulator, devices containing electrical circuitry, generating magnetic signals or having other metal that could produce visible magnetic noise in the MEG data; (2) Requiring sedation or unable to keep still. To avoid bias, data from all participants were de-identified. The characteristics and clinical information of all patients, who met inclusion/exclusion criteria, are shown in Table 1. The research protocol was reviewed by the Institutional Review Board (IRB) at Cincinnati Children’s Hospital Medical Center (CCHMC). Informed consents, formally approved by IRB at CCHMC, were obtained from each control subject in accordance with the Declaration of Helsinki.

Table 1.

Clinical Characteristics of Patients with Drug-Resistant Epilepsy

ID Sex/Age Etiology MRI MEG(Spike) Scalp EEG iEEG (ictal) Kurtosis
(80-250 Hz)		 Kurtosis
(250-600 Hz)		 Skewness
(80-250 Hz)		 Skewness
(250-600Hz)		 Resect ES
1 M/1
3		 FCD L Hi L TF LT,LC L TF LTF -- LT,D* -- L TF 1a
2 F/11 TSC R F R F R He R F R F RF -- -- R F 1a
3 M/14 FCD L T L T L T L T L T L T L T L T L T 1a
4 M/14 FCD L TO L TO L He L TO -- -- -- -- L TO 1a
5 F/16 TSC MT L FT L He L FT -- L FT -- -- L FT 1a
6 F/9 Unknown R Hi R T Bi FT R T R T R T R T R T R T 1a
7 M/13 Stroke L P L P L P L P L. P,D L P L P -- L P 1a
8 M/6 Tumor Neg L F L He L F L F L F L F L F L F 1a
9 M/9 TSC MT R FT Bi FT R FT R FT -- -- -- R FT 1b
10 M/10 TSC MT L FT L FT L FT L FT -- -- -- L FT 1a
11 M/11 Stroke Neg L PO L He L PO -- L PO -- -- L PO 1a
12 M/6 TSC MT R FT R FT R FT R FT -- -- -- R FT 1a
13 M/14 FCD L F L F Bi F L F L F -- L F L F L F 1a
14 M/14 Tumor L T L T Bi FT L FT L T L T,D -- L T L T 1a
15 F/16 FCD L F RF,LT* Bi T RF,LT L,F L F L FT* L FT* L F 1a
16 F/13 FCD Neg LF,LC* Bi F LF, LC L F -- -- L F,D L F 1a
17 F/18 FCD Neg L. T L T L T L T L T L T -- L T 1a
18 F/13 Stroke L P L P L P L P -- L P L P -- L P 1a
19 F/15 CA L F L F L FT L F -- LF -- -- L F 1a
20 F/8 FCD Neg R TO* R TPO R TO RTF,D* -- RF,D* RTF* R T II
21 F/16 TSC MT L FT* MF L FT LFT,D* -- LF LFT* L F II
22 F/13 Trauma Neg R O R He R O -- RO -- -- R O 1a
23 F/17 TSC MT Bi FT* MF Bi FT -- LF, D * LF* Bi F Bi F II
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M = Male; F = Female; Neg = Negative; R = Right; L = Left; T = Temporal; F=Frontal; P = Parietal; O = Occipital; Bi = Bilateral; C = Center; He =hemisphere; Hi = Hippocampal; D = Deep brain area; MT = Multiple tubers; MF=Multi-focal; TSC = Tuberous sclerosis; FCD=Focal cortical dysplasia; MTS = Middle temporal sclerosis; CA = Cavernous Angiomas; ES = Engel Surgical Outcome Scale;

*

= Mismatch with surgical resection; -- = No source.

2.2. MEG recording

The MEG recordings were obtained in a magnetically shielded room (MSR) using a whole head MEG system (VSM MedTech Systems Inc., Coquitlam, BC, Canada) in the MEG Center at CCHMC. Before data acquisition commenced, a small coil was attached to the left and right pre-auricular points and nasion of each subject. These three coils were subsequently activated at different frequencies for measuring subjects’ head positions relative to the MEG sensors. The system allowed head localization to an accuracy of 1 mm. All MEG data were recorded with a noise cancellation of third order gradients. The sampling rate of the MEG recordings for the present study was 4,000 Hz. The tolerable limit of head movement during MEG recording was 5 millimeters (mm). Building on previous reports (Scott et al., 2016; Xiang et al., 2009b), MEG data were recorded as multiple epochs. One epochs was 120 seconds. At least two epochs of MEG data without significant head movement (< 5 mm) and/or artifacts (e.g. magnetic noise from swallowing) were recorded for each subject.

2.3. MRI scan

Three-dimensional Magnetization-Prepared Rapid Acquisition Gradient Echo (MP_RAGE) sequences were obtained for all participants with a 3T scanner (Siemens Medical Solutions, Malvern, PA). Three fiduciary points were placed in identical locations to the positions of the three coils used in the MEG recordings to allow for an accurate co-registration of the two data sets. Subsequently, all anatomical landmarks digitized in the MEG study were made identifiable in the MR images.

2.4. Pipeline for data processing

Figure 1 shows the schema of the four-step pipeline from raw MEG waveforms to the final magnetic source imaging. The first step was preprocessing of raw MEG signals. The second step was to identify epileptic activities by performing kurtosis and skewness analyses. The third step was to localize sources of MEG signals. The last step was to determine the epileptogenic signatures by comparing MEG sources with clinical EZs. The following sections describe each step in greater detail.

Figure 1. Workflow for preprocessing, analyzing, localizing and validating epileptic high frequency brain signals (HFBS) in MEG data.

Figure 1.

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After removing noise/artifacts and preprocessing, the left column shows kurtosis analysis while the right column shows the skewness analysis. Both approaches quantify the abnormalities and localize sources of epileptic HFBS. Epileptic sources are then compared to clinical epileptogenic zones (EZs).

2.5. Data preprocessing

Data preprocessing was the first step in kurtosis and skewness analyses. Similar the previous reports (Xiang et al., 2015; Xiang et al., 2014), all MEG data were visually inspected for artifacts and noise. For each subject, two epochs of MEG data, each had 120 seconds, without artifacts were selected, preliminarily pre-processed and filtered (Butterworth filter, 3rd order, the slope was -24 dB/oct) for following quantitative analyses with MEG Processor (Xiang et al., 2015; Xiang et al., 2014). MEG data were filtered with bandpass filters in 80-250 Hz and 250-600 Hz. We analyzed MEG waveforms in ten groups, categorized by sensor location. Figure 2 shows the ten groups of sensors for quantitative measurements.

Figure 2. Sensor groups for quantifying the kurtosis and skewness of MEG signals.

Figure 2.

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High frequency neuromagnetic signals from epileptic activities in the brain are typically very weak and appear only in a group of sensors. Analyses of MEG signals in each group of sensors enables precise detection of high frequency epileptic activities and provide spatial information for localizing epileptic regions.

2.6. Kurtosis and Skewness Analyses

Kurtosis and skewness analyses were performed for MEG signals in 80-250 Hz and 250-600 Hz. Kurtosis provided a measure of spikiness of signals (Prendergast et al., 2013; Quitadamo et al., 2018). The mathematic algorithms of kurtosis has been described in previous reports (Prendergast et al., 2013; Quitadamo et al., 2018). The formulas of kurtosis can be described as:

G2(X)=1TΣt=1T(Xt−X¯)4(1TΣt=1T(Xt−X¯)2)2−3 (1)

Where X¯ is the mean of X. T is the length of time series t for a sliding window. The size of the window was determined with results from pilot study and previous reports (Scott et al., 2016; Xiang et al., 2020). G2(X) represents a kurtosis measurement and is used to find spikiness in the data. Specifically, epileptic neuromagnetic activity in 80-250 Hz and 250-600 Hz were assessed by computing kurtosis for all channels.

Skewness provided a measure of the asymmetry of signals (Letham and Raij, 2011). The mathematical algorithms of skewness has been described in previous reports (Letham and Raij,2011). The formulas of skewness can be described as:

S(X)=1(T−1)δ3Σt=1T(Xt−X¯)3 (2)

Where X¯ is the mean of X. T is the length of time series t for a sliding window. S(X) represents a skewness measurement and is used to find skewness in the data. Elevation of skewness in the data distribution indicates epileptiform activity. In this work, epileptic activity in 80-250 Hz and 250-600 Hz were assessed by computing skewness for all channels. Building on our pilot study and previous reports (Hall et al., 2018; Scott et al., 2016), we calculated kurtosis and skewness values over a successive sliding window of 1 second with 50% overlap. The functions of kurtosis and skewness analyses were implemented in MEG Processor, a software package used in the present study (Xiang et al., 2015).

2.7. Source localization

Source localization of kurtosis and skewness for high frequency MEG data was performed with a grid beamformer described in previous reports (Xiang et al., 2015; Xiang et al., 2014). Briefly, the beamformer use the relative position and orientation of sensors to scan each source (voxel) in the brain by spatially filtering (or minimizing) signals from other places. Mathematically, the source signals are computed by using the follow equation:

Sr=BW (3)

Where B is measured signals while W is the weight. Sr is the source signal at a positon r. The weight can be computed with the following equation:

Wx_y_z(x,y,z)=C−1Lx_y_z(x,y,z)Lx_y_z(x,y,z)TCf−1Lx_y_z(x,y,z) (4)

Where Wx_y_z(x,y,z) represents the weight matrix at a position that is defined with x, y and z in a 3D coordinate. Lx_y_z(x,y,z) is the lead field matrix (forward solution) for a unit current virtual sensor at a location (x,y,z), which represents a location vector. Each location provide a set of signals. C is the covariance matrix of MEG signals. Building on previous findings in partial sensor coverage and coherent source region suppression (Xiang et al., 2015), the covariance matrix of MEG signals was computed with MEG sensors whose MEG signals had high kurtosis and skewness values (optimal sensor number was 90). This procedure was different from the conventional beamformer because the conventional beamformer do not use the kurtosis and skewness for source analyses. Once the weights were computed, the procedures for computing source signals are identical to the beamformer described in previous studies (Hall et al., 2018; Scott et al., 2016; Xiang et al., 2015). The kurtosis and skewness of source signals over the time course were also analyzed for assessing the kurtosis and skewness at source levels. We reconstructed the source time series for each grid and then computed the kurtosis and skewness value for each voxel in the source imaging (one grid generate one signal at source voxel). This results in a volumetric image whereby each voxel could be represented by kurtosis and skewness values. The kurtosis and skewness values from the healthy controls were used as normative data. Similar to previous reports (Prendergast et al., 2013; Scott et al., 2016), if kurtosis and skewness values in epilepsy patients were higher than the normal mean plus 3 standard deviation (SD) (> normal mean ± 3 x SD), the kurtosis and skewness were considered to be altered or abnormal. To precisely analyze MEG sources, MEG and MRI were co-registered with three fiducial points. A 3D brain mask was created with MEG Processor for generating a realistic head model for computation of the forward solution (Xiang et al., 2014). To assess the reproducibility, we analyzed at least two epochs of MEG data for each subject.

2.8. Clinical EZs

The seizure onset zones in epilepsy patients were defined with invasive recordings, which included clinical stereo-electroencephalography (SEEG) and/or electrocorticography (ECoG). Digital photos were taken before and during the operation to record the placements of the electrodes for delineating EZs. All SEEG and ECoG data obtained during preoperative workup for epilepsy surgery. Similar to previous reports (Xiang et al., 2010), the clinical data included clinical history, scalp EEG, MRI, positron emission tomography-computed tomography (PET-CT). EZs at lobar levels were defined by analyzing ictal and interictal invasive data. To confirm EZs, we also obtained post-operative assessments. Only EZs, whose resection resulted in freedom from disabling seizures or almost seizure-free for at least one year after surgery (Engel Surgical Outcome Scale ≤ II; ILAE Outcome Scale ≤ 3), were considered to be true clinical EZs.

Conventional epileptic spikes were visually identified for patients. Low-frequency epileptic spikes (3-80 Hz) were localized using the traditional ECD (equivalent current dipole) localization. Specifically, spikes in the sensor time series were identified and a single ECD model was calculated at each sample from half-way up the ascending limb of the spike until the peak. ECD models with goodness of fit (GOF) values above 85% (residual error< 15%) were accepted for clinical purposes.

The compassion between clinical EZs and the MEG source imaging was performed by overlapping MEG source imaging and the electrodes of invasive recordings on to individual 3D MRI. We visually determined the overlap of clinical EZs and MEG sources. Since MEG source imaging was overlapped on individual MRI with three fiducial points (nasion, left and right pre-auricular points) at a same 3D coordinate, the overlapping of MEG sources and clinical EZs were also been quantitatively measured. Only clinical EZs and MEG sources appeared in the same lobar or the center distance between two partial overlap was less than 5 mm were consider to be matched. The center of MEG sources were determined by finding the peak (highest kurtosis and skewness values. The center of clinical EZs were determined by finding the electrode(s), which showed the initialization of ictal spikes.

2.9. Statistical analysis

Normality was checked with the Kolmogorov-Smirnov test, significance level was set at p < 0.05. False discovery rate (FDR) correction for multiple comparison was applied (Benjamini and Hochberg, 1995). The measurements of kurtosis and skewness in patients and controls were compared using the Student T-test. To exclude age/sex effect, we used analysis of variance (ANOVA) to analyze the measurements from the two groups of participants. All statistical analyses were performed in IBM SPSS software package version 22.0.0.0 and Microsoft Excel 2013.

3. Results

3.1. Characteristics of patients and controls

The demographic information of the remaining 23 patients are shown in Table 1(age range: 6-18 years; mean age: 13 years; 12 females and 11 males). Though the patients had heterogeneous medical conditions, their EZs were clinical defined by invasive recordings and surgical outcomes. Healthy controls included age/gender matched children and adolescents (age range: 6-18 years; mean age: 13 years; 12 females and 11 males). There were no significant differences between patient and control groups in age and gender. There were no significant differences between epochs in each subjects in terms of source location of kurtosis and skewness.

3.2. Measurements of kurtosis and skewness in epilepsy and controls

Figure 3 shows example of epileptic HFBS in an epilepsy patient as compared to normative HFBS in a healthy control. Abnormal kurtosis (> normal mean ± 3xSD) in 80-250 Hz and 250-600 Hz were found in 16 (16/23, 70%) and 14 (14/23, 61%) patients, respectively. Similarly, abnormal skewness in 80-250 Hz and 250-600 Hz were identified in 12 (12/23, 52%) and 10 (10/23, 45%) patients, respectively.

Figure 3. Waveforms and contour maps of MEG signals in 80-250 Hz) and 250-600 Hz in an epilepsy patient and a healthy control.

Figure 3.

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In comparison to MEG data recorded from a healthy control (green arrow), the waveforms in the epilepsy patient show epileptic high frequency activities (red arrows), which include signals in 80-250 Hz and 250-600 Hz. A contour map from a patient shows the spatial distributions of epileptic high frequency activities. The blue arrows indicate the time points at which the contour maps are taken. In the contour map, cyan and red indicate the output and input of the magnetic field of magnetic signals. Each small circle represents a sensor. Epileptic signals appears in seven sensors, which provide important spatial information for source analysis.

In comparison to healthy subjects, epilepsy patients showed significantly elevation of kurtosis. Figure 4 shows the detailed differences of kurtosis between epilepsy patients and healthy controls. In comparison to healthy subjects, epilepsy patients also showed significant alteration of skewness. Figure 5 shows the detailed differences of skewness between epilepsy patients and healthy controls. The results of ANOVA indicated that the significant differences between epilepsy patients and healthy controls held even when the age, gender and channel group were taken as confounding factors for adjustment of statistical analysis.

Figure 4. Column charts showing the kurtosis of high frequency MEG signals in 80-250 Hz and 250-600 Hz.

Figure 4.

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In comparison to healthy controls (red), children with epilepsy (blue) show elevated kurtosis of MEG signals in 80-250 Hz and 250-600 Hz. The stars indicate that the difference between epilepsy (blue) and normal (red) in the corresponding measurements is statistically significant (* p < 0.001; ** p < 0.0001).

Figure 5. Column charts showing the skewness of high frequency MEG signals in 80-250 Hz and 250-600 Hz.

Figure 5.

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In comparison to healthy controls (red), children with epilepsy (blue) show altered skewness of MEG signals in 80-250 Hz and 250-600 Hz. The alteration in positive side (increase in Y axis) is statistically significant; the alteration in negative side does not reach a statistical significance. The stars indicate that the difference between epilepsy (blue) and normal (red) in the corresponding measurements is statistically significant (* p < 0.001; ** p < 0.0001).

3.3. Kurtosis and Skewness based source imaging

Kurtosis based source imaging of MEG signals in 80-250 Hz and 250-600 Hz were localized to cerebral cortices overlapping with EZs for 14 (14/16, 88%) and 13 (13/14, 93%) patients, respectively. Figure 6 shows kurtosis based source imaging of HFBS in an epilepsy patient.

Figure 6. Kurtosis and skewness source imaging of high frequency epileptiform activity in a patient.

Figure 6.

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The MEG high frequency signals in 80-250 Hz and 250-600 Hz in the patients are localized to the left occipital region with both kurtosis and skewness source imaging (yellow arrow). The minor differences between kurtosis and skewness source imaging are marked with cyan (*). Since MEG is sensitive to surface (cortical) sources but not deep sources, the present study focuses on the sources in the cerebral cortex, source activity in the deep brain areas (green arrow) is not analyzed.

Skewness based source imaging of MEG signals in 80-250 Hz and 250-600 Hz were localized cerebral cortices overlapping with EZs for 8 (8/12, 67%) and 7 (7/10, 70%) patients, respectively. Figure 6 shows skewness based source imaging in an epilepsy patient.

Table 1 shows the details of kurtosis and skewness based source imaging for epilepsy patients. Kurtosis based source imaging of MEG signals in 80-250 Hz and 250-600 Hz correctly revealed clinical EZs for patient ID-2, but skewness failed. However, skewness based source imaging of MEG signals in 80-250 Hz and 250-600 Hz correctly revealed clinical EZs for patient ID-13, but kurtosis failed in 250-600 Hz. It seemed that kurtosis and skewness were slightly different in localizing EZs. If both kurtosis and skewness were used in source localization, EZs in twenty two out of the twenty three patients could be localized (22/23, 96%).

3.4. High frequency signals and low-frequency spikes

Conventional low-frequency epileptic spikes were identified in 23 (23/23, 100%) patients. Low-frequency epileptic spikes were localized to EZs in 18 (18/23, 78%) patients using the traditional ECD (equivalent current dipole) localization. In comparison to the conventional low-frequency spikes, skewness and skewness based source imaging were highly localized to EZs (22/23, 96%). Table 1 shows the localizations of low frequency spikes as well as kurtosis and skewness based source imaging.

4. Discussion

The present study has demonstrated that kurtosis and skewness based source localization of MEG signals in 80-600 Hz can localize clinical EZs. It is necessary to clarify that high frequency MEG signals in 80-600 Hz do not mean these signals are HFOs. However, since HFOs are typically defined as 4 or more oscillations in 80-600 Hz (or 500 Hz vary among reports), we consider HFBS in 80-600 Hz include HFOs. Consequently, analyses of high frequency MEG signals in 80-250 Hz and 250-600 Hz frequency bands include or go beyond merely analyzing ripples (80-250 Hz) and fast ripples (250-600 Hz). Since high frequency MEG signals can be noninvasively obtained, we postulate that kurtosis and skewness based source imaging of MEG is an unprecedented method for pre-operative evaluation of epilepsy patients. This approach does not need visual identification of HFOs.

4.1. Localizing EZ with kurtosis and skewness analyses

One of the main findings of this study is that high frequency epileptic activity are characterized with elevation of kurtosis and skewness in MEG data. Elevation of kurtosis in low frequency MEG data has been found in epilepsy patients (Hall et al., 2018). Alteration of skewness in epileptic HFBS has also been found in intracranial electroencephalography (iEEG) (Mooij et al., 2020) and virtual sensors (Xiang et al., 2020). To our knowledge, this is the first study focusing on both kurtosis and skewness of high frequency MEG data. More specifically, this is the first study showing the usefulness of kurtosis and skewness based magnetic source imaging for localization of clinical EZs. The findings of this study are in agreement of previous reports (Mooij et al., 2020; Xiang et al., 2020), which strongly support that kurtosis and skewness analyses are a new way to automatically and quantitatively detect epileptic activity. Similar to previous report (Xiang et al., 2009b), we have noted that two minutes of MEG data can show consistent source localization of high frequency MEG signals in epilepsy patients. Our observation is concordant with recent findings from Scott and colleagues (Scott et al., 2016). Scott and colleagues have also found that kurtosis values of epileptic activity stabilizes at 2 minutes and remains consistent for longer runs.

Kurtosis and skewness are both measures for deviation from a normal distribution (Hall et al., 2018; Mooij et al., 2020; Xiang et al., 2020). Kurtosis describes how many counts can be found in the tails; many counts in the tails result in a “peaked” distribution. In our MEG data, kurtosis provide quantitative information about the spikiness of neuromagnetic signals. Skewness is a measure of asymmetry, i.e., if there are more counts on one side of the distribution than on the other. The skewness in MEG data reflect asymmetric of the ingoing and outgoing magnetic fields. Since the skewness of MEG signals recorded from epileptic regions is very high, the results indicate that epileptic HFBS is very asymmetrical. Though there are some similarity between kurtosis and skewness in the MEG results, taken all kurtosis and skewness results together (Table 1), we have found that kurtosis and skewness may have some differences in localizing EZs.

4.2. Characteristic of MEG high frequency signals in epilepsy

The epileptogenic nature of epileptic high frequency signals in the present study was determined with kurtosis/skewness and then validated with clinical EZs. These epileptic high frequency signals might not meet the criteria for HFOs, consequently, epileptic high frequency signals identified in the present study are not equal to epileptic HFOs. According to our observation, epileptic high frequency signals might include HFOs. Since Kurtosis and skewness quantitatively measure the spikiness and asymmetric nature of signals(Hall et al., 2018; Letham and Raij, 2011; Scott et al., 2016) while HFOs are typically defined as at least four oscillations standing out from ongoing background activity, more discussion of high frequency signals and HFOs might be out of the focus of the present study. From our point of view, kurtosis and skewness analyses of high frequency signals were alternative techniques to the identification of epileptic high frequency activity that may include HFOs. Kurtosis and skewness based detection of epileptic high frequency signals without considering HFOs has several advantages. First, kurtosis and skewness analyses with a sliding window enables processing long data periods or many data point at a time. The entire procedure can be quantitatively and automatically done without making subjective criteria (e.g. number of oscillations). Second, some measurements of kurtosis and skewness can be directly integrated into source scan that enables to localize EZs efficiently (Hall et al., 2018). Third, the spikiness and skewness of high frequency signals provide unique description of high frequency signals (e.g. spikiness and skewness), which cannot be obtained by identifying HFOs. Since the present study has shown very promising results in localization of EZs with high frequency signals, we postulate that quantitative assessment of MEG signals in 80-600 Hz with kurtosis and skewness may play a unique and important role in guiding preoperative recordings and surgical resection for epilepsy surgery in the future.

4.3. Multi-frequency analyses and epilepsy surgery

Careful analyses of the sources of high frequency signals in 80-250 Hz and 250-600 Hz reveal that EZs may be localized by high frequency signals in 80-250 Hz or 250-600 Hz (see Table 1). This observation indicates that there is frequency specific information encoded in MEG high frequency signals. The frequency-specific alteration has been noted in the assessment of kurtosis and skewness. We noted that high frequency signals in 250-600 Hz with elevated kurtosis were highly localized to the EZ (92.9%, respectively). It seems that epileptic activities in 250-600 Hz are more epileptogenic than the activities in 80-250 Hz. Our observation is consistent with previous reports on HFOs (Lee et al., 2020; Xiang et al., 2009a; Xiang et al., 2010). Previous invasive recordings have shown that the resection of electrical fast ripples (250-600 Hz) correlates with favorable outcomes (Holler et al., 2015; Jacobs et al., 2010; Lee et al., 2020; Thomschewski et al., 2019).

The present study has also demonstrated that MEG high frequency signals in 80-250 Hz and 250-600 Hz with elevated kurtosis and skewness are an epileptogenic biomarker and are highly localized to EZs. However, spikes are still the hallmark of epilepsy in clinical practice and epileptic high frequency signals in 80-250 Hz and 250-600 Hz are still biomarkers for research (see Table 1). This observation is supported by an increasing list of publications indicating that high frequency signals are a new biomarker for epilepsy(Bragin et al., 2010; Rampp et al., 2010; Weiss et al., 2018; Worrell et al., 2012; Zijlmans et al., 2012a). One question remains unanswered is whether high frequency signals are superior to the conventional spikes (< 70 Hz) for guiding epilepsy surgery. Since conventional spikes are still the hallmark for epilepsy surgery (Weiss, 2018), if there was no spike on MEG/EEG or invasive recordings, patients were more than likely to be excluded from surgical treatment in current clinical practice. It is reasonable to postulate that kurtosis/skewness analyses of high frequency signals may contribute even more for surgical treatment of epilepsy patients who do not have conventional spikes. Unfortunately, these patients are typically not surgical candidates in current clinical practice. Building on the results from this study, it seems that conventional spikes and epileptic high frequency signals should be studied simultaneous in the future. Since multiple frequency analyses of both high frequency signals and spikes can be done easily (see Table 1), the superiority of high frequency signals in comparison to spikes could be addressed in the future by using multi-frequency data. The results of the present study support the notion that there is an urgent need for multi-center studies to determine if and how high frequency signals can be used with the conventional low frequency source localization to aid the delineation of epileptogenic regions (Weiss et al., 2018). It is more than likely that multi-frequency analyses of both low and high frequency signals may open a new avenue for clinical management of epilepsy.

4.4. MEG detection of high frequency signals for pediatric epilepsy

Although invasive recordings provide solid and convincing high frequency signals data, in particularly, HFO data, its applications are limited to surgical patients (Bragin et al., 2010; Rampp et al., 2010; Weiss et al., 2018; Worrell et al., 2012; Zijlmans et al., 2012a). In comparison to invasive recordings, MEG recordings have several advantages. First, MEG is noninvasive, which is very safe to patients. Second, MEG tests enable the recordings of high frequency signals from healthy subjects, which provides the possibility to quantitatively investigate the abnormalities of high frequency signals. For example, the separation between physiological and pathological HFBS is an obstacle in applications of HFBS (Cimbalnik et al., 2018; Frauscher et al., 2018; Lee et al., 2020; Matsumoto et al., 2013). The results of the present study indicate that epileptic high frequency signals are associated with elevation of kurtosis and skewness. This approach can circumvent the need to visually identify HFOs, let alone of separation of pathological from physiological HFOs. Of note, MEG detection of high frequency signals with kurtosis and skewness may play a key role in applications of high frequency signals.

In comparison to many previous reports on high frequency signals in adult epilepsy (Frauscher et al., 2017; Gonzalez Otarula et al., 2019), the present study focused on high-frequency neuromagnetic signals in childhood epilepsy. Several features have been noted in pediatric MEG data. First, high frequency epileptic activities are typically found within 10-15 minutes after the beginning of MEG recordings, which is probably due to children becoming drowsy or entering slow wave sleep. Second, kurtosis/skewness of high frequency signals varied among channel groups in children with epilepsy. These variations might be a result of the variation of the spatial location of epileptic areas and the head position related to the MEG sensor array. Third, the elevation of kurtosis/skewness might appear in a small groups of channels due to the weakness of neuromagnetic signals in children. Of note, neuromagnetic high frequency signals in pediatric patients are noninvasive detectable with some unique characteristics.

5. Conclusions

In comparison to normative controls, MEG high frequency signals from epilepsy patients have significantly elevated kurtosis and skewness. The elevation of kurtosis and skewness in MEG data is a new objective and quantitative biomarker for epilepsy. The source imaging of high frequency MEG signals based on kurtosis and skewness can accurately localize EZs. Different from conventional invasive recordings, the MEG method developed in the present study is noninvasive and safe. Though additional verification is necessary, the findings of the present study may serve to encourage the development and refinement of kurtosis and skewness based MEG source imaging for preoperative evaluation for epilepsy surgery in the future.

Key Points.

  • Epileptic high frequency brain signals have significantly elevated kurtosis and skewness

  • Sources of epileptic high frequency brain signals pinpoint to epileptogenic zones

  • Magnetoencephalography can noninvasively localize epileptic high frequency activity

Acknowledgements

The authors would like to thank Drs. Douglas Rose and Nat Hemasilpin for MEG data acquisition, Dr. James Leach for reviewing MRI, and Drs. Kimberly Leiken, Yingying Wang and Mr. Kendall O’Brien for MRI scan. This work was supported by the National Institute of Neurological Disorders and Stroke (NINDS), the National Institutes of Health (NIH) [Grant Number R21 NS104459]. The normative database used in the present study was partially supported by NINDS/NIH [Grant Number R21NS081420 and R21NS072817]. This project described was partially supported by funding from the State of Ohio, Ohio Development Services Agency, Ohio Third Frontier [Grant Control No. TECG20170361 and TECG20190159].

Footnotes

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The research work was done at Cincinnati Children’s Hospital Medical Center.

Declaration of Competing Interest

The authors declare no conflicts of interest. The work is consistent with the Journal’s guidelines for ethical publication. All co-authors have been substantially involved in the study and/or the preparation of the manuscript. No undisclosed persons have had a primary role in the study. All co-authors seen and approved the submitted version of the paper and accept responsibility for its content.

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