Identifying sources of human interictal discharges with travelling wave and white matter propagation

C Price Withers; Joshua M Diamond; Braden Yang; Kathryn Snyder; Shervin Abdollahi; Joelle Sarlls; Julio I Chapeton; William H Theodore; Kareem A Zaghloul; Sara K Inati

doi:10.1093/brain/awad259

Brain. 2023 Dec; 146(12): 5168–5181.

Published online 2023 Aug 1. doi: 10.1093/brain/awad259

PMCID: PMC11046055

PMID: 37527460

Identifying sources of human interictal discharges with travelling wave and white matter propagation

C Price Withers, Joshua M Diamond, Braden Yang, Kathryn Snyder, Shervin Abdollahi, Joelle Sarlls, Julio I Chapeton, William H Theodore, Kareem A Zaghloul, and Sara K Inati

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Associated Data

Supplementary Materials: awad259_Supplementary_Data.
awad259_supplementary_data.pdf (1.0M)
GUID: 553FF2EA-2289-4F72-A0DC-85B3568523D8

Data Availability Statement: Processed anonymized patient data will be shared by the corresponding author on reasonable request. All code necessary to replicate source localization is freely available at https://github.com/witherscp/ied-localize.

Abstract

Interictal epileptiform discharges have been shown to propagate from focal epileptogenic sources as travelling waves or through more rapid white matter conduction. We hypothesize that both modes of propagation are necessary to explain interictal discharge timing delays. We propose a method that, for the first time, incorporates both propagation modes to identify unique potential sources of interictal activity.

We retrospectively analysed 38 focal epilepsy patients who underwent intracranial EEG recordings and diffusion-weighted imaging for epilepsy surgery evaluation. Interictal discharges were detected and localized to the most likely source based on relative delays in time of arrival across electrodes, incorporating travelling waves and white matter propagation. We assessed the influence of white matter propagation on distance of spread, timing and clinical interpretation of interictal activity. To evaluate accuracy, we compared our source localization results to earliest spiking regions to predict seizure outcomes.

White matter propagation helps to explain the timing delays observed in interictal discharge sequences, underlying rapid and distant propagation. Sources identified based on differences in time of receipt of interictal discharges are often distinct from the leading electrode location. Receipt of activity propagating rapidly via white matter can occur earlier than more local activity propagating via slower cortical travelling waves. In our cohort, our source localization approach was more accurate in predicting seizure outcomes than the leading electrode location. Inclusion of white matter in addition to travelling wave propagation in our model of discharge spread did not improve overall accuracy but allowed for identification of unique and at times distant potential sources of activity, particularly in patients with persistent postoperative seizures.

Since distant white matter propagation can occur more rapidly than local travelling wave propagation, combined modes of propagation within an interictal discharge sequence can decouple the commonly assumed relationship between spike timing and distance from the source. Our findings thus highlight the clinical importance of recognizing the presence of dual modes of propagation during interictal discharges, as this may be a cause of clinical mislocalization.

Keywords: epilepsy, iEEG, interictal epileptiform discharges, white matter, source localization

Interictal epileptiform discharges can propagate from focal sources as travelling waves that spread across the cortical surface, or through more rapid white matter conduction. Withers et al. develop a new method for identifying sources of interictal activity that incorporates both possible modes of propagation.

Introduction

Interictal epileptiform discharges (IEDs) are brief electrographic events frequently observed between seizures in patients with focal epilepsy.^1,2 They are markers of cortical hypersynchronization, likely arising from similar mechanisms as seizures,³ with a spatial distribution typically including but not limited to the seizure onset zone.^4,5 IED co-spiking between recording electrodes exhibits latencies suggesting propagation of pathologic activity from epileptogenic sources to less epileptogenic, functionally connected brain regions.^6–8 Indeed, the definition of the irritative zone as ‘the area of cortical tissue that generates interictal electrographic spikes’ recognizes the distinction between sources and receivers of interictal epileptiform activity.⁴ IED sources likely correlate more closely with the epileptogenic zone, the brain region indispensable for generating seizures.⁴

Identification of IED sources is an ongoing clinical challenge. In the most straightforward case, epileptiform discharges propagate contiguously and locally from the source across the cortical surface as travelling waves via local synaptic or ephaptic spread.^9–11 Assuming travelling wave propagation, delays in spiking should correlate with distance from the activity source, with the earliest spikes located closest to the generator. Several groups have demonstrated that brain regions exhibiting the earliest spiking, or leading regions, tend to localize to the seizure onset zone. Resection of these regions predicts seizure outcomes more accurately than single electrode spiking characteristics, such as frequency or amplitude alone.^1,12–17 We recently proposed a novel approach in which relative delays in timing of ictal discharges or interictal spiking across electrodes could be used to identify the probable epileptogenic source of travelling waves.^18,19 Similar multilateration approaches are used extensively in fields such as radar and earthquake detection^20–24 with the advantage that sources need not be directly sampled by recording electrodes to be successfully identified.

Although these approaches have accurately predicted outcomes after resective surgery in many patients, they are incomplete models of IED propagation. Both interictal and ictal activity can propagate not only locally in a distance-dependent manner, but also homotopically and non-contiguously through synaptic barrages over white matter pathways.^25,26 Because white matter propagation occurs much more rapidly than travelling wave propagation, spiking delays may not correlate with distance from the source if both modes of propagation occur within the same IED sequence. The sparse spatial sampling provided by intracranial EEG (iEEG) implantations presents an additional challenge, as signals may propagate from distant sources not sampled by implanted electrodes, requiring incorporation of different imaging modalities to provide information about functional or structural connectivity. IED source localization approaches incorporating white matter propagation have been relatively uncommon,^27,28 and to our knowledge, none have accounted for both travelling waves and white matter propagation.

Here, we devise a novel multilateration source localization approach to accommodate both travelling waves and white matter propagation, using patient-specific diffusion tensor imaging-based estimates of structural connectivity. We hypothesized that sources obtained through incorporating both modes of propagation would allow better explanation of timing delays observed in IED sequences and yield distinct potential sources of observed activity. Indeed, we identify sources that are frequently distinct and at times distant from the location of the leading electrode, with greater accuracy of surgical outcome prediction in our patient cohort. Additionally, in sequences involving both modes of propagation, sequence order does not reliably correlate with distance from the source, suggesting a potential mechanism for false localization when relying on the leading electrode to approximate the source of interictal epileptiform activity.

Materials and methods

Participants

We retrospectively identified 38 patients [25 males, age = 35 ± 11 years (mean ± standard deviation, SD), range = 19–61 years] with treatment-resistant focal epilepsy who underwent epilepsy surgery evaluation at the National Institutes of Health Clinical Center (Bethesda, MD) from 2014–2021 and received iEEG implantation, clinical 3 T MRI structural imaging and research-dedicated 3 T MRI for diffusion-weighted imaging that met quality control standards. For analyses requiring evaluation of seizure outcomes, we excluded patients who did not undergo surgical resection or did not have available 1-year postoperative seizure outcome data, resulting in 34 patients (mean follow-up = 20 ± 6 months, range = 11–28 months) (Table 1). These patients were the subset of our previous study cohort who had received diffusion-weighted imaging.¹⁹ Seizure outcomes were reported by Engel class, divided into 17 patients with seizure-free outcome, i.e. Engel class 1, and 17 patients with seizure persistent outcomes (Engel class 2–4).²⁹ Research was approved by the NIH Institutional Review Board and informed consent was obtained from all participants.

Table 1

Patient demographics by seizure outcome

	Seizure free (n = 17)	Seizure persist (n = 17)	P-value
Age at implant, median (IQR)	35 (32–43)	33 (26–36)	0.24^a
Sex, male/female	9/8	12/5	0.48^b
Temporal, n (%)	13 (76%)	10 (59%)	0.47^b
Lesional, n (%)	9 (53%)	8 (47%)	1.00^b
iEEG implant
Subdurals only	5	6	0.56^b
Depths only	3	1	–
Both	9	10	–
Follow-up period months, median (IQR)	19 (12–24)	24 (14–24)	0.89^a

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iEEG = intracranial EEG; IQR = interquartile range.

^aMann-Whitney U-rank test.

^bPearson chi-square test/Fisher’s exact test.

MRI acquisition and processing

Structural magnetic resonance images were acquired on a 3 T Philips Achieva scanner with the following sequences: 3D T₁-weighted MPRAGE (repetition time = 6.8–7.2 ms; echo time = 3.2 ms, flip angle = 9°, voxel size = 0.8 × 0.75 × 0.75 mm³), 3D T₂-weighted FSE (repetition time = 2500 ms, echo time = 225–245 ms, flip angle = 90°, voxel size = 1 × 1 × 1 mm³) and 3D FLAIR (repetition time = 4800 ms, echo time = 271–415 ms, flip angle = 90°, voxel size = 1 × 0.9 × 0.9 mm³ or 0.6 × 1 × 1 mm³). Postoperative structural images were acquired at 1 year follow-up. Diffusion-weighted images were acquired with dual AP-PA phase-encoding using either a 3 T Siemens Magnetom Skyra scanner (repetition time = 11 400 ms, echo time = 92 ms, flip angle = 90°, voxel size = 2 × 2 × 2 mm³, 45 directions, max b-value = 1100 s/mm²) or a 3 T GE Discovery MR750 scanner (repetition time = 9700 ms, echo time = 85 ms, flip angle = 90°, voxel size = 2 × 2 × 2 mm³, 45 directions, max b-value = 1100 s/mm²).

We performed all processing using the publicly available software package Analysis of Functional NeuroImages (AFNI) unless otherwise noted.^30,31 Cortical surfaces were reconstructed with FreeSurfer 6.0.0 (http://surfer.nmr.mgh.harvard.edu/) using the T₁ and T₂ images. We resampled and standardized the surfaces using AFNI’s SUMA package.^32–34 The resulting surfaces each contained 198 812 vertices per hemisphere. To facilitate tractography, surfaces were parcellated into 600 regions per hemisphere based on the Schaefer-Yeo atlas.³⁵ Surface-based Schaefer parcels were sampled onto the volume and then inflated into regions of interest. Using TORTOISE’s DIFFPREP and DR-BUDDI,^36–38 we applied motion, eddy current distortion and EPI distortion corrections to the diffusion-weighted images, before estimating tensors with AFNI’s FATCAT package.³⁹ We performed probabilistic tractography with Monte Carlo simulations, using 1000 iterations, five seeds per voxel, a threshold fraction of 5% per voxel, 0.2 minimum fractional anisotropy, 60° maximum angle and 20 mm minimum tract length.⁴⁰ In patients who underwent resective surgery, we created resection masks using the difference between aligned pre- and postoperative grey and white matter masks (Supplementary material, ‘Methods’ section). Voxel-based resection masks were projected onto the pial surface. We considered a parcel as resected if ≥50% of vertices in that parcel were contained within the resection mask.

Electrode distance estimations

Patients were implanted with a combination of subdural grid and strip electrodes (diameter = 3 mm, inter-electrode distance = 10 mm) and/or depth electrodes (diameter = 2 mm, inter-electrode distance = 3.5–5 mm) (PMT Corporation), with a mean of 118 ± 34 electrodes implanted in each patient (27 ± 32% depth electrodes). We localized electrodes in each participant according to the procedure described in Trotta et al.⁴¹ All electrodes with centre greater than 4 mm from the cortical grey matter ribbon were excluded from source localization analysis (9 ± 9 electrodes per patient).

We then sought to estimate geodesic distances between electrodes which presumably underlie travelling wave propagation. First, we mapped electrode locations to cortical surface vertices (Supplementary material, ‘Methods’ section and Supplementary Fig. 1). Then, we estimated geodesic or grey matter distances in a vertex- wise fashion. We estimated the shortest geodesic distance from each vertex ascribed to an electrode (19 ± 10 vertices) to all other vertices on the cortical surface using the exact geodesic algorithm for triangular meshes⁴² implemented in the pygeodesic toolbox (https://github.com/mhogg/pygeodesic). From this, we retained the minimum and maximum distances from the set of vertices ascribed to each electrode to every vertex on the pial surface.

To estimate white matter distances, we used a lower resolution cortical parcel-based approach, attributing electrodes to the parcels associated with their vertex set (1.7 ± 0.8 parcels per electrode). We estimated the distances between cortical parcels as the mean bundle length ±1σ. For each electrode, we obtained the minimum and maximum white matter distances between parcels ascribed to that electrode and every other parcel on the pial surface in both hemispheres.

Intracranial EEG recordings

We recorded continuous iEEG from subdural grid and strip and/or depth electrodes sampled at 1000 Hz. Raw iEEG signals were referenced to the system hardware reference, set by the recording amplifier (Nihon Kohden) as the average of two intracranial electrode channels. Interictal epochs were selected that were more than 48 h post-implantation, relatively artefact-free and when possible, separated from seizure events by at least six and ideally 24 h. On average, 576 ± 328 min of interictal recordings were included per patient. We re-referenced the raw signals using a separate common average reference for depths and subdurals (Supplementary material, ‘Methods’ section). Electrodes exhibiting obvious artefacts, abnormal signal amplitude or large line noise were manually rejected during visual inspection. For each electrode, we applied a local detrending procedure to remove slow fluctuations and a regression-based approach⁴³ to remove line noise at 60 and 120 Hz. A low-pass type I FIR filter (order = 110, cut-off frequency = 165 Hz) was used to remove higher-order line harmonics, as well as high frequency noise.⁴⁴

IED sequence identification

For automated detection of IEDs, we used a previously described custom-built IED detector (Supplementary material, ‘Methods’ section).^19,45 We defined an IED sequence as an event in which spikes were detected in at least three distinct electrodes within the same 100 ms window (Fig. 1A).^46,47 We used a sliding 100 ms window with 50 ms overlap to detect all spike sequences in a recording epoch. Within a sequence, each unique electrode was permitted one spike; if one electrode had multiple spikes, we retained only the spike occurring closest to the centre of the time window. Because long sequences were computationally intractable using our localization method, we excluded sequences with >10 electrodes spiking consecutively, which comprised <5% of all detections. After this exclusion criterion, there were 3392 ± 2824 sequences per patient with a mean sequence length of 4.3 ± 1.7 electrodes. The electrode spiking earliest in an IED sequence was referred to as the ‘leading’ electrode and all subsequently firing electrodes were ‘following’ electrodes.^{1,12,13,45,48} Spike latencies of following electrodes were calculated with respect to the spike time of the leading electrode.

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Figure 1

IED spike sequence detection and clustering. (A) Detection of an interictal epileptiform discharge (IED) sequence in TT1, TT2, TT3 and PST1 electrodes. Shaded (grey) region represents a 100 ms detection window. TT = temporal tip; PST = posterior subtemporal. (B) Four sample IED sequences with Jaro-Winkler distance calculations. The first sequence is the same IED represented in A. Similar sequences are grouped together through clustering. TG = temporal grid. (C) HDBSCAN clustering of sequences for Subject p39. Left panel shows sequences before clustering and right panel shows emergence of three distinct IED clusters with high intra-similarity and low inter-similarity after clustering. (D) Visualization of Subject p39 spike clustering. Unclustered spiking is displayed on left; clustered spiking is displayed on right. Cluster 1 corresponds to the first two sequences in B and Cluster 2 corresponds to the third and fourth sequences in B.

IED sequence clustering

In many patients we noted spatially independent populations of consistent co-spiking activity, suggesting potential for more than one underlying source of observed interictal epileptiform activity. Because a single electrode could theoretically receive propagation from more than one source, we clustered IED sequences themselves, rather than specific electrodes. We assumed that each focal source of epileptiform activity would generate interictal co-spiking in a relatively consistent subset of recording electrodes with a relatively stable core of early propagation, and more variable later spread as distance from the source increases.⁸ Therefore, we compared the observed IED sequences using a modified Jaro-Winkler string similarity metric, which more closely associates sequences with identical prefixes, consistent with our physiologic hypothesis (Fig. 1B and Supplementary material, ‘Methods’ section).⁴⁹ After calculating the Jaro-Winkler distance between every combination of sequences for a given patient, sequences were clustered using hierarchical density-based spatial clustering of applications with noise (Fig. 1C, Supplementary Fig. 2 and Supplementary material, ‘Methods’ section).⁵⁰

The most frequently appearing electrodes in each cluster were used to carry out clinical validation of the resulting clusters by a board-certified epileptologist blinded to study methodology. Clusters thought to reflect high amplitude intermittent physiologic activity or artifact were manually eliminated, along with clusters containing fewer than 100 sequences. This novel clustering method based on Jaro-Winkler distance allowed for identification of IED sequence groups describing stereotyped patterns of co-spiking across electrodes within each patient (Fig. 1D).

IED cluster source localization

We attempted to identify the most likely source of activity for each clinically validated cluster of IED sequences. We have previously described how time differences in IED receipt across electrodes can be used to estimate source location assuming travelling wave cortical surface propagation.^18,19 We modified this approach to incorporate the possibility of propagation through white matter pathways, assuming that each IED represents a single discharge emitted from a focal source, spreading outward along the grey matter surface as a travelling wave and/or through white matter pathways.

When a focal source, s, emits a discharge that is detected by two electrodes, leading $e_{L}$ and following $e_{F}$ , with conduction velocity v, the observed lag between signal arrival at each electrode $(τ_{F} - τ_{L})$ is related to their relative distances from the source $(d_{s, e_{L}}, d_{s, e_{F}}$ ) as follows:

d_{s, e_{F}} - d_{s, e_{L}} = v (τ_{F} - τ_{L})

(1)

When accounting for grey matter propagation, we assumed approximate conduction velocities of 0.25–0.45 mm/ms.⁵¹ Because we defined an IED sequence as occurring within 100 ms, we limited grey matter propagation to a maximum geodesic distance of 45 mm, the farthest that a discharge could spread at maximal grey matter velocity during our detection window. For white matter propagation we expected faster conduction velocities of 1.7–5.3 mm/ms.^52–54 We hypothesized that a parcel should be considered as a potential source of an IED sequence if computed conduction velocities, based on distance to each electrode and observed time lags across electrodes, were within expected conduction velocity ranges.

Because propagation from the source to each electrode can occur through grey or white matter, we needed to account for four possible propagation patterns for each electrode pair. We created two sets of equations, depending on whether the leading electrode receives signal via grey or white matter propagation. If both leading electrode $e_{L}$ and following electrode $e_{F}$ receive signal via grey matter, grey matter propagation velocity, $v_{(G M)}$ is given by:

v_{(G M)} = \frac{d_{s, e_{F (G M)}} - d_{s, e_{L (G M)}}}{(τ_{F} - τ_{L})}

(2)

Alternately, if $e_{L}$ receives signal through grey matter but $e_{F}$ receives signal through white matter, the observed lag between the time of signal arrival at $e_{L}$ and $e_{F}$ is expressed by $\frac{d_{s, e_{F (W M)}}}{v_{F (W M)}} - \frac{d_{s, e_{L (G M)}}}{v_{(G M)}}$ . Rearranging to solve for the velocity of grey matter propagation, $v_{(G M)}$ :

v_{(G M)} = \frac{d_{s, e_{L (G M)}}}{\frac{d_{s, e_{F (W M)}}}{v_{F (W M)}} – (τ_{F} - τ_{L})}

(3)

Solving Eqs 2 and 3 with a range of velocities ( $v_{F (W M)}$ ) and distances ( $d_{s, e_{L (G M)}}$ , $d_{s, e_{F (G M)}}$ and $d_{s, e_{F (W M)}}$ ) yielded two ranges of possible $v_{(G M)}$ for each vertex. Every following electrode in a sequence imposes an additional constraint on the range of possible $v_{(G M)}$ . Because white matter propagation varies significantly based on differences in fibre myelination and size,⁵⁵ we allowed variable white matter propagation velocities to different electrodes within each particular sequence, while maintaining a fixed velocity of grey matter propagation in all directions, in accordance with previous work.^18,19 Although grey matter velocity was fixed within a single sequence, we allowed it to vary across IED sequences within the range provided. A vertex, along with its associated parcel, was considered as a possible source of a sequence only if some combination of $v_{(G M)}$ intervals overlapped between all following electrodes and if the overlapping range could be found on the interval of allowed grey matter velocities: [0.25, 0.45] mm/ms.

We applied a similar method in the scenario where $e_{L}$ receives signal through white matter:

v_{L (W M)} = \frac{d_{s, e_{L (W M)}}}{\frac{d_{s, e_{F (W M)}}}{v_{F (W M)}} – (τ_{F} - τ_{L})}

(4)

v_{L (W M)} = \frac{d_{s, e_{L (W M)}}}{\frac{d_{s, e_{F (G M)}}}{v_{(G M)}} – (τ_{F} - τ_{L})}

(5)

In these equations, two terms for white matter velocity were included, $v_{F (W M)}$ and $v_{L (W M)}$ , because variable white matter propagation velocities may have occurred within a single discharge. A parcel was considered as the source of a sequence only if some combination of $v_{L (W M)}$ intervals overlapped between all following electrodes and if the overlapping range could be found on the interval of allowed white matter velocities: [1.7, 5.3] mm/ms.

Every parcel that fulfilled the velocity requirements of either set of equations was a cortical source obtained using combined grey and/or white matter propagation (GM+WM source). Parcels fulfilling the velocity requirements of Eq. 2 were grey matter sources and those which solved Eq. 4 were white matter sources. Because we hypothesized that similar IED sequences (i.e. sequences within the same cluster) propagate from the same focal source, we applied this localization procedure to each cluster separately. For subsequent analysis, the single source that explained the largest proportion of sequences for a cluster was considered as the source of that cluster.

We also identified the source parcel that most frequently contained the leading electrodes from sequences occurring within a cluster. This allowed us to compare source parcels obtained using our multilateration source localization algorithm (source parcels) to those obtained by identifying the location of the most frequent leading electrodes (leading parcels).

Classification of IED sequence propagation types

We wished to evaluate whether there were differences between IED sequences relying solely on grey matter propagation and those involving white matter propagation. To investigate this, we used the GM+WM source of each cluster. IED sequences localized through this method may have involved propagation through grey matter only, white matter only, or both modalities simultaneously. To isolate sequences spreading through grey matter, we found the subset of localized IEDs where grey matter propagation was sufficient to identify the GM+WM source parcel (i.e. sequences where the source parcel fulfilled Eq. 2). We classified these sequences as grey matter only sequences (GM sequences). We identified all additional IEDs that localized to the source parcel once white matter was implemented into the model (i.e. sequences where the source parcel fulfilled Eqs 3–5). These sequences were classified as requiring white matter propagation (+WM sequences). They either involved white matter propagation only or combined grey and white matter propagation.

Results

IED sequence clustering reveals independent populations of co-spiking brain regions

Our IED sequence clustering algorithm identified consistently occurring similar sequences of co-spiking electrodes likely arising from a common source of interictal activity. We did not identify clear differences in spike or cluster detection based on recording electrode type, although a significantly lower proportion of sequences were explained when the sequence contained both types of electrodes (Supplementary material, ‘Results’ section). Two patients did not have any clinically validated clusters, so they were excluded from all further analysis (Supplementary Fig. 3). After exclusion of these patients, the study included 32 patients with surgical outcomes and 36 patients overall. Among 36 patients with at least one clinically validated cluster, we identified a total of 67 clusters, averaging 1.9 ± 1.0 clusters per patient (range = 1–4 clusters). One mechanism of surgical failure is the presence of multiple independent or potentially epileptogenic regions.⁵⁶ We found that poor outcome patients had significantly more IED clusters than good outcome patients (median two versus one clusters, respectively, Mann-Whitney U = 85.0, P-value = 0.041 one-tailed).

IED source localization using grey and white matter propagation explains spike latencies

Our multilateration source localization approach for each cluster of IEDs is based on the assumption that differences in timing of epileptiform activity reflect distances from the source, with expected distances and conduction velocities dependent on propagation mode. In individual sequences, we found that relative timing could only be explained using a source localization method in which both grey and white matter propagation were permitted (Fig. 2 and Supplementary Fig. 4). Source localizations obtained in individual patients varied by the type of propagation modelled (Fig. 3A). We did not observe any differences in proportion of sequences explained based on electrode type, although fewer sequences were explained in sequences containing both subdural and depth electrodes (Supplementary material, ‘Results’ section).

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Figure 2

White matter can be necessary to explain IED spike latencies. (A) Lag times between the most frequent leading electrode (RAD17) and three most common followers (RAD18, RAD23 and RPST2) in Cluster 1 of Subject p80. Because RAD17 does not always lead the sequence, there are some instances when lag time is negative. Top (green) and bottom (blue) shaded boxes represent the expected latencies between RAD17 and its three primary follower electrodes, under the assumption of direct propagation from the leading parcel (red) to each follower. Grey matter (GM) and white matter (WM) ranges of estimated lag times are calculated from the min and max distance between electrodes and estimated conduction velocities. The y-axis ranges from −100 to 100 ms based on the IED sequence detection window of 100 ms. There is no white matter connection present between RAD17-RAD18 and RAD17-RAD23 and the estimated grey matter lag range for RAD17-RAD23 exceeds 100 ms. RAD = right amygdala depth; RPST = right posterior subtemporal. (B) Estimated lag times assuming propagation from the grey matter source parcel (red, located primarily within a sulcus, see Supplementary Fig. 4 for inflated brain view). The unfilled box for grey matter propagation to RAD23 indicates that this range exceeds the maximum distance threshold of 45 mm. Latencies between RAD17-RAD23 are unexplained by travelling waves only. (C) Estimated lag times assuming propagation from the white matter source. There is no white matter connection between the source and RAD23, so the lag times are unexplained by white matter propagation only. (D) Estimated lag times assuming grey or white matter propagation from the GM+WM source. For this cluster, the identified source is the same as that of the white matter localization method. Unfilled boxes indicates that the source is >45 mm from the electrode and grey matter propagation is not permitted. Lighter filled box (light blue) represents white matter propagation to the leader (RAD17), followed by grey matter propagation to the follower. Darker unfilled box (purple) represents grey matter propagation to the leader, followed by white matter propagation to the follower. This is the only approach that successfully explains the observed lag times between all three pairs of electrodes.

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Figure 3

Comparison of IED source localization methods across clusters. (A) Results for leading parcel localization, grey matter (GM) source localization, white matter (WM) source localization and GM+WM source localization in clusters 1 (240 sequences) and 2 (170 sequences) of Subject p80. This patient underwent an anterior temporal lobectomy (shaded area Fig. 4F) but experienced occasional disabling seizures postoperatively (Engel 2b). In both clusters 1 and 2, the leading parcel method localizes to the resected anterior temporal lobe. Grey matter source localization explains noticeably fewer sequences than GM+WM source localization across both clusters. The grey matter source for cluster 1 is in a sulcus posterior to the resection territory (Fig. 2B), whereas the grey matter source for cluster 2 is within the resection. White matter source localization creates a non-specific map of possible sources across both clusters, based on structural connectivity; integrating grey matter into the white matter method helps to identify the best source. This is apparent when comparing the white matter and GM+WM sources. GM+WM source localization discovers a source parcel posterior to the resection in both clusters. Notice that, in cluster 1, the maximal GM+WM source is distant from the leading parcel, whereas in cluster 2 the GM+WM source is adjacent to the leading parcel. (B) Comparison of the proportion of sequences explained by each source localization method, among the 67 total clusters. Significance bars represent results of Tukey’s multiple comparisons test after one-way repeated measures ANOVA. ****P < 0.0001; ns = not significant. (C) Histogram of Euclidean distances (in mm) from the leading parcel to the GM+WM source parcel. Distances were calculated between the centre of mass of each parcel. (D) Number of electrodes in the GM+WM source parcel, grouped by concordance with the leading parcel. When the GM+WM source parcel differed from the leading parcel, the number of electrodes per parcel was significantly less than when the GM+WM source parcel was the same as the leading parcel (Mann-Whitney U = 383.5, P-value = 0.002 one-tailed, median = 3 versus 8.5 electrodes per parcel).

Across all patients, sources obtained using white matter propagation explained 44 ± 21% of sequences, grey matter propagation explained 48 ± 19% of sequences and combined GM+WM propagation explained 67 ± 19% of sequences (Fig. 3B). As expected, there was a statistically significant effect of localization method on proportion of sequences explained [repeated measures ANOVA, F(1.628,107.5) = 77.72, P-value < 0.0001]. Using Tukey’s multiple comparisons test, GM+WM sources explained more sequences than grey or white matter sources (both P-values < 0.0001), which performed similarly (P-value = 0.255).

Because of the expanded parameters of the GM+WM approach, it is expected that this model would explain a greater proportion of the observed sequences than the unimodal approaches. For each model, we used a shuffling procedure to determine whether the proportion explained could be simply due to chance (Supplementary material, ‘Results’ section). We found that of 67 clusters, true sources met or exceeded the 95th percentile of shuffled sequences in 30 clusters for the white matter source, 47 clusters for the grey matter source, and 36 clusters for the GM+WM source. Based on this analysis, the obtained sources for each model explain the timing and order of observed sequences significantly more than expected by chance (Supplementary Fig. 5), even taking into consideration the differences in allowable parameters across models. Furthermore, these findings suggest that grey matter sources may be more sensitive to changes in sequence and timing, while white matter localizations may be more influenced by the underlying patterns of connectivity and thus less sensitive to these changes.

Inclusion of white matter propagation yields distinct IED cluster sources

We then compared the concordance of our source localizations with the clinically validated leading electrode locations. GM+WM source parcels were distinct from grey matter sources in 64% of clusters (43/67) and distinct from the leading parcel in 88% of clusters (59/67). Median Euclidean distance between the leading parcel and GM+WM source parcel was 16.8 mm (range 0–98.5 mm) (Fig. 3C). Across source localization methods, we observed significant differences in the spatial distribution of the source parcels identified and proportion of sequences explained. Overall, the leading electrode method yielded the fewest and the GM+WM method the highest mean number of parcels containing at least one successful source (27 ± 14 versus 86 ± 37), with a similar pattern noted for localizations per sequence (1, by definition, versus 13 ± 7). Many fewer parcels, however, explained a high proportion of the explained sequences using the GM+WM approach (Supplementary material, ‘Results’ section).

Limited electrode sampling should be the cause of differences between the earliest spike and the focal source; therefore, we hypothesized that GM+WM source parcels distinct from the leading parcel would have less electrode coverage than those matching the leading parcel. As expected, source parcels discordant with the leading parcel had significantly fewer electrodes than concordant source parcels (Mann-Whitney U = 383.5, P-value = 0.002 one-tailed, median = 3 versus 8.5 electrodes per parcel) (Fig. 3D). In fact, of 59 GM+WM source parcels distinct from the leading parcel, 22% contained zero electrodes, reinforcing that our multilateration approach can identify possible source regions that may not have been directly sampled by implanted electrodes.

White matter pathways underlie distant IED propagation

We then sought to identify differences between sequences that could be explained using grey matter propagation alone versus those requiring white matter propagation (‘Classification of IED sequence propagation types’ section) (Fig. 4A). Of 36 220 sequences explained by GM+WM sources across all patients, 41% required white matter (+WM). Of the most frequently spiking electrodes within these sequences, 34/335 (10%) appeared to receive IED exclusively through grey matter and 11% exclusively via white matter, while 69% appeared more likely to receive grey than white matter propagation (Supplementary material, ‘Results’ section and Supplementary Fig. 7).

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Figure 4

White matter propagation may travel to distant electrodes before grey matter travelling waves reach nearby regions. (A) Depiction of the four possible relationships between leader-follower pairs across sequencers. The star represents the focal source of IEDs. The top row (grey matter propagation to E1) corresponds to Eqs 2–3, and the bottom row (white matter propagation to E1) corresponds to Eqs 4–5. The top left quadrant corresponds to grey matter sequences, whereas the other three quadrants that contain at least one leader-follower pair involving white matter propagation are classified as requiring white matter (+WM). (B) Mean number of sequences classified as grey matter versus +WM across clusters. Error bars for B, C, D and H represent 95% confidence intervals across 67 clusters. Significance bars for B, C and D show results of Wilcoxon signed-rank tests; ns = not significant; ****P < 0.0001. (C) Mean geodesic distances between the source parcel and all electrodes participating in sequences, grouped by sequence type. For all geodesic distance computations, electrodes contralateral to the source were excluded from analysis. (D) Mean lag times of all electrodes participating in sequences, grouped by sequence type. (E) Maximum propagation distances (in mm). For a given sequence, maximum propagation distance is calculated as the geodesic distance between the source parcel and the farthest electrode. The proportion of sequences is normalized by sequence type, such that each group sums to 1.00. (F) Exemplar IED sequence with distant leading electrodes in Subject p80. This patient underwent anterior temporal lobectomy but had occasional disabling seizures postoperatively (Engel 2b). Anterior shaded area (dark grey) = resection zone; posterior shaded area (red) = GM+WM source parcel; RPST = right posterior superior temporal; RAD = right amygdala depth; RPLT = right posterior lateral temporal. (G) Bivariate kernel density estimation (KDE) plots of lag times and propagation distances for all spikes (including leading and following electrodes). Density estimation is log normalized separately for each sequence classification. (H) Bar chart comparing the number of sequences explained by GM+WM propagation, depending on the index of the closest electrode in a sequence. In grey matter source localization, propagation velocity within sequences is fixed in all directions, so the leading electrode will always have a possible geodesic distance closest to the source parcel in its sequence. However, here we find the electrode with the shortest minimum geodesic distance to any part of the source parcel which closer approximates the clinical approach. Significance bars represent results of Tukey’s multiple comparisons test, only showing difference between index 1 (leading electrode) and all other indices. ****P < 0.0001; ns = not significant.

On average, clusters consisted of 1182 grey matter and 930 +WM sequences (Fig. 4B). Grey matter sequences propagated to a mean of 22.4 mm from the source (90% within 33.5 mm), with an average lag time of 12 ms. +WM sequences propagated to a mean distance of 31 mm from the source with an average lag time of 19 ms (Fig. 4C and D). Using Wilcoxon signed-rank tests, there was no significant difference in the number of grey matter and +WM sequences per cluster (P-value = 0.21), but geodesic propagation distances and lag times of grey matter sequences were significantly shorter than +WM sequences (both P-values < 0.0001).

We hypothesized that white matter pathways would be essential for explaining distant IED propagation. For every sequence, we found the minimum geodesic distance from the GM+WM source to each of the spiking electrodes and retained the distance to the farthest electrode for each sequence. We found that 21.5% of +WM sequences propagated beyond the maximum grey matter travel distance of 45 mm (Fig. 4E). Whereas grey matter sequences were distributed around a mode distance of 20–25 mm, propagation distance of +WM sequences was multimodal, with many sequences travelling 80–85 mm or 130–135 mm. Thus, white matter propagation is required to explain most distant spread of IED activity, although a majority of grey matter and +WM sequences involve electrodes relatively close to the source of activity.

IEDs may propagate through white matter to distant electrodes before arriving at local regions

Based on the differences in conduction velocities, it might be expected that IEDs could arrive at distant electrode locations via white matter conduction before closer locations receive signal through slower travelling waves. In fact, we identified multiple patients in whom the earliest spikes, distant from the source, lay within the resection cavity, but the patient continued to have seizures postoperatively (Fig. 4F and Supplementary Fig. 8). This suggests that the presence of distant white matter spread can confound clinical interpretation of the iEEG trace using an ‘earliest spike’ heuristic.

To further investigate this phenomenon across patients, we compared the distribution of lag times and geodesic distances from the putative source to every electrode involved in each sequence type (Fig. 4G). As expected, there was a broader distribution of both lag times and distances in +WM sequences compared to grey matter sequences. +WM sequences involved spikes with short latencies spreading to distant regions and spikes with high latencies that remained relatively close to the source. These findings led us to expect that for grey matter sequences, the order of electrodes in a sequence should reflect distance from the source, while this may not be the case in sequences involving white matter propagation.

We tested the hypothesis that for grey matter, but not +WM sequences, more sequences are explained when the leading electrode is closest to the source parcel (Supplementary material, ‘Methods’ section). We compared the index of the closest electrode in grey matter and +WM sequences (Fig. 4H). We found a significant main effect of index of closest electrode [F(3,264) = 15.17, P-value < 0.0001] and propagation modality [F(1,264) = 6.893, P-value = 0.0092] and a significant interaction effect between index of closest electrode and propagation modality [F(3,264) = 13.69, P-value < 0.0001] on the number of sequences explained (Fig. 4H). In post hoc comparisons, more grey matter sequences were explained if the leading electrode (Index 1) was closest compared to all other electrode indices (1 versus 2: P-value < 0.0001; 1 versus 3: P-value < 0.0001; 1 versus 4+: P-value < 0.0001). In contrast, there was no difference in the number of +WM sequences explained when the leading electrode was closest compared to any other electrode index (1 versus 2: P-value = 0.9891; 1 versus 3: P-value = 0.9051; 1 versus 4+: P-value = 0.2579).

Spikes with high latency tend to be near the IED source

From Fig. 4G, we observed that the majority of IED sequences with high latency spikes were in +WM sequences, presumably due to slower travelling waves following rapid white matter propagation. Therefore, we hypothesized that spikes with high latencies would tend to be close to presumed sources—the opposite of the leading electrode method. We grouped all spikes into four categories based on whether or not their latencies exceeded 50 ms (early/late) and whether or not the electrodes were beyond 50 mm geodesic distance from the source (near/distant). Of 7348 late spikes, only 220 (3.0%) were distant, compared to 8.2% of early spikes (10 365/127 093). There was a statistically significant association between lag times (greater or less than 50 ms) and propagation distance (greater or less than 50 mm), $χ^{2}$ (1, n = 134 441) = 255, P-value < 0.0001. Thus, electrodes spiking with high latencies had a greater likelihood of being close to sources than electrodes spiking with low latencies.

Resection of identified sources predicts surgical outcomes

We assessed the accuracy of our localization models in predicting seizure outcomes based on concordance with the resection (Fig. 5A and Supplementary Tables 1 and 2). Localization using GM+WM propagation had an accuracy of 72% (sensitivity 69%, specificity 75%, positive predictive value 73%), identical to 72% accuracy using grey matter only (69%/75%/73%). Accuracy of the leading parcel was 63% (56%/69%/64%), whereas white matter sources were less accurate at 47%. Although the overall accuracy of the grey matter and GM+WM localization approaches were identical, with two patients having swapped accuracies (Supplementary Fig. 9), the two methods localized to different source parcels in 63% of patients (20/32). In four patients with poor outcomes, both methods yielded a true negative prediction with sources greater than 2.5 cm apart from one another (Fig. 5B). Among these patients, grey matter source parcels contained 16, 4, 5 and 0 electrodes, while GM+WM source parcels contained 2, 0, 0 and 0 electrodes, respectively. Figure 5C provides an example when the GM+WM approach offered multiple source locations outside of electrode coverage that could influence resection planning or guide further implants.

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Figure 5

Source localization comparison with resection zone and surgical outcomes. (A) Concordance of the GM+WM source parcel with the resection cavity for every subject’s clusters. Patients are grouped by surgical outcome, where seizure free means Engel 1. (B) Distance (in mm) between the grey matter source and GM+WM source, grouped by concordance with the resection territory. Euclidean distance is computed between the centre of mass of each parcel. (C) Source localization maps for cluster with highest number of sequences in Subject p39. This cluster is outlined in A and B. The patient underwent a left temporal topectomy but was seizure persistent (Engel 3a) at time of latest follow-up (24 months postoperatively). Both the leading parcel method and grey matter source method yield solutions that remain relatively confined to the anterior temporal lobe. In contrast, the GM+WM source method is inconclusive with multiple putative sources explaining a high proportion of sequences in undersampled cortical regions.

Overall concordance with the seizure onset zone was relatively higher for the leading electrode (66%) and grey matter sources (63%) than GM+WM sources (41%) (Supplementary Table 2). Subgroup analysis was relatively confounded by the overlap between temporal lobe epilepsy (TLE) and surgical intervention, namely increased extent of resection in anterior temporal lobectomies (ATL) compared to neocortical topectomies or lesionectomies (Supplementary Table 3). Accordingly, GM+WM source accuracy was higher in TLE (78%) and ATL (80%) subgroups than extratemporal (56%) and focal cortical resection (67%) subgroups. This can be explained either by improved localization in TLE, or incidental removal of nearby source localizations due to more extensive resection, consistent with literature reporting improved seizure outcomes following anterior temporal lobectomies compared to limited mesial temporal interventions.⁵⁷

Discussion

Despite a long-standing appreciation that interictal spiking in many regions represents propagated activity, it has remained challenging to localize underlying sources of this activity. Here, we incorporate both travelling wave and white matter propagation to localize potential sources of interictal epileptiform activity based on relative timing delays in IED spiking across electrodes. White matter propagation appears to be quite common and to underlie nearby but also rapid distant propagation. In the setting of combined propagation modalities, distant spiking can occur earlier in IED sequences than more local travelling wave propagation.

In this cohort, source localizations based on travelling wave or combined propagation had identical accuracy in predicting surgical outcomes, and greater accuracy than localization of the leading electrode region (72% versus 63%). While accurate, the travelling wave model can only account for local contiguous propagation well sampled by recording electrodes. In contrast, the white matter propagation model alone yielded relatively diffuse and less accurate potential sources (47%). Incorporation of both modes of propagation retains the accuracy of the grey matter model while allowing for the possibility of identifying more distant and frequently poorly sampled potential sources. When these sources explain a high proportion of the observed IED sequence timing, they may be physiologically relevant and clinically important even when distant, particularly when considering re-evaluation in patients with poor seizure outcomes (example in Fig. 5C). Therefore, while source localization accuracy cannot be fully assessed, our findings suggest that our combined multilateration approach may counter some effects of spatial sampling bias inherent in iEEG recordings.

Using our estimated sources, we were able to identify the most likely propagation modes underlying individual IED sequences. Local spread has been proposed to occur through synaptic effects such as collapse of local inhibition^58,59 or a variety of non-synaptic mechanisms.^9,60–63 Distant propagation, meanwhile, appears to occur primarily through excitatory synaptic activity transmitted from the seizure focus via white matter pathways.²⁵ Similar to Smith et al.,¹¹ we found that a majority of IED sequences (59%) could be explained by grey matter propagation only, helping to explain the success of methods utilizing only this mechanism.^18,19 In sequences that could be explained solely by travelling wave propagation, the leading electrode tended to lie closest to the identified source, with propagation usually remaining relatively local. Thus, when electrodes are placed near the IED source, travelling wave propagation likely underlies the efficacy of the leading electrode method as well as our previously reported multilateration approach.

Our new source localization method showed that white matter propagation must be incorporated along with travelling waves to explain observed timing in a substantial proportion of IED sequences. Several previous studies have incorporated estimates of white matter propagation to investigate spike and seizure propagation. Mitsuhashi et al.²⁸ used delays in spike times in combination with diffusion tensor imaging-based connectivity to identify unique potential sources of interictal activity in temporal lobe epilepsy. Proix et al.²⁷ created large-scale personalized brain networks using diffusion tensor imaging to predict seizure propagation pathways and surgical outcomes, although they did not specifically address propagation of interictal activity. Azeem et al.²⁶ showed that interictal spike propagation tends to occur between tract-connected pairs of electrodes. We expand on these approaches by incorporating both travelling waves and white matter propagation into a unified model.

Our multilateration-based approach differs fundamentally from and may be complementary to electrical source imaging (ESI) approaches, which have also been proposed to aid in iEEG IED source localization.⁶⁴ ESI approaches rely explicitly on volume conduction at a particular snapshot in time, while our multilateration approach relies on differences in time of receipt of the signal to estimate the source, explicitly disregarding volume conducted activity. In truth, iEEG signal at any given moment likely represents a combination of volume conducted and propagated activity, and in the setting of radial propagation and adequate spatial sampling, these methods would likely yield similar results. Of note, in our current model of interictal spike propagation, we have assumed primarily radial fixed velocity travelling wave propagation and distant spread constrained by white matter connectivity. However, other research has suggested the possibility of bimodal IED propagation,¹¹ of rotating in addition to radial travelling waves,⁶⁵ or even patterns of activity governed by the overall geometry of the brain.⁶⁶ These topics all merit further investigation.

Our findings illuminate a potential pitfall in clinical interpretation of IED spiking activity when spike latency is assumed to correlate with distance from the source. In sequences involving combined modes of propagation, spikes propagating through white matter occur early regardless of distance from the source, while later spikes, likely propagating as travelling waves, tend to remain closer to the source. This may underlie the observation that focal, consistently organized IEDs, which likely represent well sampled primarily local travelling wave propagation, are associated with good seizure outcomes,^48,67–69 while rapid spread of epileptiform activity is associated with worse seizure outcomes.⁷⁰ Particular caution should be taken in interpreting IEDs with high latencies (>50 ms) from first to last spike, as these sequences likely involve a combination of grey and white matter propagation. In fact, we show that high latency spikes within IEDs may have clinical localization utility because they likely represent local travelling wave propagation. Although this finding is an expected consequence of the differences in conduction velocity, to our knowledge this is a novel insight, as most methods have focused on single modes of propagation.

A major limitation of this study was the difficulty in evaluating source localization accuracy. Poor seizure outcomes may occur due to diffuse or dual pathology, as suggested by the presence of multiple IED clusters in many of our persistent seizure patients (Fig. 5A).^{12,15,16,71–73} Additionally, in patients who continue to have seizures postoperatively, the true source of IEDs remains uncertain. Our accuracy was lower in patients with more limited resections, suggesting that unique but nearby true sources may have been included in the broader resections. This may be supported by the finding of increased concordance with the seizure onset zone compared to the resected area in patients with limited resection and the opposite trend in temporal lobectomy patients (Supplementary Table 3). Alternately, our approach may be less accurate in neocortical epilepsy or when areas of interest are less well sampled by the electrode implantation. Each of these questions requires further prospective study to be fully evaluated, ideally with implantation of these potential sources. Despite these limitations, we provide evidence that estimates of white matter propagation from diffusion-weighted imaging are beneficial for identifying novel potential sources of interictal activity.

Supplementary Material

awad259_Supplementary_Data

Click here to view.^{(1.0M, pdf)}

Acknowledgements

We are grateful to Yasser Tajali for his clinical validation of IED clusters, and we thank Lincoln Chambers for providing mathematical consultation.

Contributor Information

C Price Withers, Neurophysiology of Epilepsy Unit, NINDS, National Institutes of Health, Bethesda, MD 20892, USA.

Joshua M Diamond, Surgical Neurology Branch, NINDS, National Institutes of Health, Bethesda, MD 20892, USA.

Braden Yang, Neurophysiology of Epilepsy Unit, NINDS, National Institutes of Health, Bethesda, MD 20892, USA.

Kathryn Snyder, Neurophysiology of Epilepsy Unit, NINDS, National Institutes of Health, Bethesda, MD 20892, USA.

Shervin Abdollahi, Neurophysiology of Epilepsy Unit, NINDS, National Institutes of Health, Bethesda, MD 20892, USA.

Joelle Sarlls, NIH MRI Research Facility, NINDS, National Institutes of Health, Bethesda, MD 20892, USA.

Julio I Chapeton, Surgical Neurology Branch, NINDS, National Institutes of Health, Bethesda, MD 20892, USA.

William H Theodore, Clinical Epilepsy Section, NINDS, National Institutes of Health, Bethesda, MD 20892, USA.

Kareem A Zaghloul, Surgical Neurology Branch, NINDS, National Institutes of Health, Bethesda, MD 20892, USA.

Sara K Inati, Neurophysiology of Epilepsy Unit, NINDS, National Institutes of Health, Bethesda, MD 20892, USA.

Data availability

Processed anonymized patient data will be shared by the corresponding author on reasonable request. All code necessary to replicate source localization is freely available at https://github.com/witherscp/ied-localize.

Funding

This research was funded through the National Institutes of Neurological Disorders and Stroke Intramural Research Program.

Competing interests

The authors report no competing interests.

Supplementary material

Supplementary material is available at Brain online.

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