Characterizing the role of the structural connectome in seizure dynamics

How the structural connectome influences seizure dynamics is poorly understood. By analyzing high-resolution imaging and intracranial EEG data from patients with focal epilepsy, Shah et al. observe that structure-function coupling increases during the progression from preictal to ictal states, and show that the effect is driven by short-range connectivity.

Abstract

How does the human brain’s structural scaffold give rise to its intricate functional dynamics? This is a central question in translational neuroscience that is particularly relevant to epilepsy, a disorder affecting over 50 million subjects worldwide. Treatment for medication-resistant focal epilepsy is often structural—through surgery or laser ablation—but structural targets, particularly in patients without clear lesions, are largely based on functional mapping via intracranial EEG. Unfortunately, the relationship between structural and functional connectivity in the seizing brain is poorly understood. In this study, we quantify structure-function coupling, specifically between white matter connections and intracranial EEG, across pre-ictal and ictal periods in 45 seizures from nine patients with unilateral drug-resistant focal epilepsy. We use high angular resolution diffusion imaging (HARDI) tractography to construct structural connectivity networks and correlate these networks with time-varying broadband and frequency-specific functional networks derived from coregistered intracranial EEG. Across all frequency bands, we find significant increases in structure-function coupling from pre-ictal to ictal periods. We demonstrate that short-range structural connections are primarily responsible for this increase in coupling. Finally, we find that spatiotemporal patterns of structure-function coupling are highly stereotyped for each patient. These results suggest that seizures harness the underlying structural connectome as they propagate. Mapping the relationship between structural and functional connectivity in epilepsy may inform new therapies to halt seizure spread, and pave the way for targeted patient-specific interventions.

Introduction

Epilepsy is a neurological disorder characterized by recurrent, unprovoked seizures. It affects over 50 million subjects worldwide (World Health Organization, 2018) and will afflict ∼1 in 26 subjects during their lifetime (Hesdorffer et al., 2011). The most common subtype is focal or localization-related epilepsy, in which seizures arise from a specific region in the brain (French, 2007). Patients with localization-related epilepsy often experience uncontrolled seizures despite medication, leading to neurological and psychiatric co-morbidities, deterioration in quality of life, and up to an 11-fold increase in mortality rate (Kwan et al., 2011; Fazel et al., 2013).

Structural brain lesions are considered to be at the core of the epileptogenic zone in localization-related epilepsy (Bernasconi, 2017). Indeed, targeted surgical removal of contiguous regions of abnormal brain tissue has high seizure-freedom rates in drug-resistant epilepsy patients, up to 80% (Spencer et al., 2005; De Tisi et al., 2011; Hussan et al., 2012; Wiebe, 2012; Jette and Wiebe, 2013). However, seizures also may involve recruitment of and spread to multiple, often distant brain regions, thereby involving distributed brain networks (Kramer and Cash, 2012; Bernhardt et al., 2013). As a result, researchers are applying graph theoretical methods from the rapidly growing field of network neuroscience to identify brain network abnormalities in epilepsy, in the hope of finding targets for therapeutic interventions. In this approach, investigators map whole-brain structural and functional networks, or ‘connectomes’, by characterizing connectivity between brain regions based on multi-modal neuroimaging data (Bullmore and Sporns, 2009; Rubinov and Sporns, 2010; Bassett and Sporns, 2017). Structural brain networks are most commonly derived from diffusion tensor imaging (DTI) tractography (Hagmann et al., 2008). Functional brain networks are most commonly derived from correlations in signal fluctuations across multiple recording sites from modalities such as resting state functional MRI (Biswal et al., 1995; Salvador et al., 2004), magnetoencephalography (MEG) (Stam, 2004), and EEG (Micheloyannis et al., 2006). These approaches reveal a wide variety of network disruptions in epilepsy patients, both structurally (Raj et al., 2010; Vaessen et al., 2012; Taylor et al., 2015) and functionally (Pittau et al., 2012; Pedersen et al., 2015; de Campos et al., 2016; Shah et al., 2019). While still nascent, this work shows promise for clinical applications, as network-based measures may serve as biomarkers for predicting seizure onset and spread (Burns et al., 2014; Khambhati et al., 2016; Jirsa et al., 2017; Proix et al., 2017), cognitive impairments (Vlooswijk et al., 2011; Vaessen et al., 2012), and outcome following surgical therapy (Goodfellow et al., 2016; Sinha et al., 2017; Lopes et al., 2018).

Most studies of epileptic networks focus solely on either structural or functional connectivity. However, it is commonly understood that the two are tightly linked. In fact, there is great interest in the neuroscience community in elucidating the relationship between brain structure and function. Recent evidence shows that structural and functional brain networks are correlated at multiple temporal and spatial scales, that structural connectivity constrains functional connectivity, and that functional connectivity can modulate structural connectivity via mechanisms of plasticity (Skudlarski et al., 2008; Greicius et al., 2009; Honey et al., 2009; Rubinov et al., 2009; van den Heuvel et al., 2009; Zhang et al., 2010; Hagmann et al., 2010; Hermundstad et al., 2013, 2014; Chu et al., 2015; Finger et al., 2016).

Given the robust coupling between structure and function in healthy brains, disruptions in structure-function coupling can serve as biomarkers of neurological disease, including epilepsy. For example, Zhang et al. (2011) report that the degree of coupling between resting-state functional MRI networks and DTI tractography networks is lower in idiopathic generalized epilepsy patients compared with healthy controls, and is negatively correlated with epilepsy duration. Using a similar approach, Chiang et al. (2015) report decreased structure-function coupling in patients with left temporal lobe epilepsy compared with healthy subjects. These two studies use resting-state functional MRI, which characterizes the static, interictal functional epileptic network. However, little is known about the correlation between structural and functional connectivity during seizures. How does structure-function coupling change over the course of seizure evolution? And which particular connections drive these changes? Clinically, it is well understood that focal seizures often quickly spread to distant brain regions, but the relationship of this spread to underlying structure has not been quantified. Understanding where seizures are generated and how they spread has been hampered by sparsely sampled intracranial EEG and lesion-negative clinical brain images, and yet remains vital for planning surgical treatments for epilepsy.

To address these questions, we studied structure-function coupling in 45 seizures from nine drug-resistant localization-related epilepsy patients undergoing routine evaluation for epilepsy surgery. To construct time-varying functional connectivity (FC) networks, we used clinical recordings from intracranial EEG (iEEG), an invasive method that captures electrical activity from the brain in the form of aggregate local field potentials, at high spatial and temporal resolution (Penfield and Jasper, 1954). To construct structural connectivity (SC) networks, we used high angular resolution diffusion imaging (HARDI), an advanced diffusion imaging method that can produce robust tractography results in regions of crossing white matter pathways (Tuch et al., 2002). We characterized relationships between these two modalities across time, frequency, and space. We hypothesized that there would be an increase in structure-function coupling during the progression from pre-ictal to ictal states, as seizures spread along structural pathways. Our findings shed light on the pathophysiological processes involved in seizure dynamics, which can ultimately inform new approaches for clinical intervention. We detail these investigations below.

Materials and methods

Subjects

We studied nine patients undergoing pre-surgical evaluation for drug-resistant epilepsy at the Hospital of the University of Pennsylvania. Inclusion criteria for these patients consisted of all patients who agreed to participate in our research scanning protocol and allowed their de-identified iEEG data to be publicly available for research purposes on the International Epilepsy Electrophysiology Portal (www.ieeg.org, IEEG Portal) (Wagenaar et al., 2013; Kini et al., 2016). Seizure localization was determined via comprehensive clinical evaluation, which included multimodal imaging, scalp and intracranial video-EEG monitoring, and neuropsychological testing. This study was approved by the Institutional Review Board of the University of Pennsylvania, and all subjects provided written informed consent prior to participating.

Intracranial EEG acquisition

Cortical surface and depth electrodes were implanted in patients based on clinical necessity. Electrode configurations (Ad Tech Medical Instruments) consisted of linear cortical strips and two-dimensional cortical grid arrays (2.3 mm diameter with 10 mm inter-contact spacing) and linear depths (1.1 mm diameter with 10 mm inter-contact spacing). Continuous iEEG signals were obtained for the duration of each patient’s stay in the epilepsy monitoring unit. Signals were recorded at 500 Hz. For each clinically identified seizure event, a board-certified epileptologist precisely annotated the onset time, termination time, seizure type, and electrodes recording artefact signals. Seizure onset times were defined by the earliest electrographic change (Litt et al., 2001). Seizure types were classified using ILAE 2017 criteria (Fisher et al., 2017) as focal aware (previously known as simple partial), focal impaired awareness (previously known as complex partial), or focal to bilateral tonic-clonic (previously known as complex partial with secondary generalization). Furthermore, the onset time of bilateral spread was noted for focal to bilateral tonic-clonic seizures. All annotations were verified and consistent with detailed clinical documentation. To ensure consistency and validity of the captured seizures, we discarded seizures that contained substantial artefacts in all electrodes, events that were short (<15 s), or those that occurred during sleep.

Image acquisition

Prior to electrode implantation, MRI data were collected on a 3 T Siemens Magnetom Trio scanner using a 32-channel phased-array head coil. High-resolution anatomical images were acquired using a magnetization prepared rapid gradient-echo (MPRAGE) T₁-weighted sequence (repetition time = 1810 ms, echo time = 3.51 ms, flip angle = 9°, field of view = 240 mm, resolution = 0.94 × 0.94 × 1.0 mm³). HARDI was acquired with a single‐shot EPI multi-shell diffusion-weighted imaging (DWI) sequence (116 diffusion sampling directions, b-values of 0, 300, 700 and 2000 s/mm², resolution = 2.5 × 2.5 × 2.5 mm³ resolution, field of view = 240 mm). The same HARDI sequence was acquired in nine healthy adult control subjects for the purpose of comparison. Following electrode implantation, spiral CT images (Siemens) were obtained clinically for the purposes of electrode localization. Both bone and tissue windows were obtained (120 kV, 300 mA, axial slice thickness = 1.0 mm).

Region of interest selection

A brain network consists of nodes representing regions of interest within the brain, and edges representing the strength of connectivity between these regions of interest. To carry out direct quantitative comparisons of structural and functional networks, it was necessary to establish a direct correspondence between functional network nodes and structural network nodes. We therefore determined the location of each electrode in Montreal Neurological Institute (MNI) space and assigned each electrode to its nearest structural region of interest.

Structural regions of interest were defined by an upsampled version of the Automated Anatomical Labeling Atlas (Tzourio-Mazoyer et al., 2002), which consisted of 600 roughly equally sized (region of interest sizes averaging 2.14 ± 0.28 cm³) anatomically constrained regions covering the entire brain with the exception of the cerebellum. We chose this atlas (AAL-600) because it has regions of interest of the same order of resolution as iEEG, obeys gross anatomical boundaries, and has successfully been used in prior studies to evaluate structural and functional connectivity patterns in the brain (Hermundstad et al., 2013, 2014).

To determine electrode MNI coordinates, electrodes were first identified via thresholding of the CT image and labelled using a semi-automated process. Each patient’s CT and T₁-weighted MRI images were aligned using 3D rigid affine registration, with mutual information as the similarity metric. The T₁-weighted MRI images were then aligned to the standard MNI brain using diffeomorphic registration with the symmetric normalization (SyN) method (Avants et al., 2008). The resulting transformations were used to warp the coordinates of the electrode centroids into MNI space. Co-registrations and transformations were carried out using Advanced Normalization Tools (ANTS) software (Avants et al., 2009, 2011), and the accuracy of each step was confirmed via visual inspection. In our final framework, electrodes served as nodes of the functional networks and the associated structural regions of interest served as nodes of the structural networks.

Structural network generation

Diffusion-weighted images were skull-stripped via the FSL brain extraction tool and underwent eddy current and motion correction via the FSL eddy tool (Andersson and Sotiropoulos, 2016). Next, DWI susceptibility distortions were mitigated using the structural T₁-weighted image as follows: (i) T₁-weighted images were registered to the b0 image from the DWI scans using FSL FLIRT boundary-based registration (Greve and Fischl, 2009); (ii) T₁-weighted images were contrast inverted and intensity matched to the DWI image; and (iii) the DWI scans underwent non-linear transformation to the T₁-weighted scan (Wang et al., 2017). Following these preprocessing steps, DSI-Studio (http://dsi-studio.labsolver.org) was used to reconstruct the orientation density functions within each voxel using generalized q-sample imaging with a diffusion sampling length ratio of 1.25 (Yeh et al., 2010). Deterministic whole-brain fibre tracking was performed using an angular threshold of 35 degrees, step size of 1 mm, and quantitative anisotropy threshold based on Otsu’s threshold (Otsu, 1979). Tracks with length shorter than 10 mm or longer than 400 mm were discarded, and a total of 1 000 000 tracts were generated per brain. Deterministic tractography was chosen based upon prior work indicating that deterministic tractography generates fewer false positive connections than probabilistic approaches, and that network-based estimations are substantially less accurate when false positives are introduced into the network compared with false negatives (Zalesky et al., 2010).

Subject-level AAL-600 atlases were generated in DWI space by applying the previously generated registration transformations from MNI to T₁-weighted space and from T₁-weighted space to DWI space. Finally, structural networks were generated by computing the number of streamlines connecting each pair of structural regions of interest identified above. The distribution of mean streamline lengths between each pair of structural regions of interest for each patient is illustrated in Supplementary Fig. 1. As the structural regions of interest were selected based on presence of electrodes, the range and distributions of mean streamline lengths were inherently highly dependent on the number and anatomical locations of electrodes. Streamline counts were subsequently log-transformed to improve normality of the distribution, as is common in prior studies (Bonilha et al., 2015; Wirsich et al., 2016; Park et al., 2017; Taylor et al., 2018).

Functional network generation

Each seizure event consisted of an ictal period spanning the time between seizure onset (earliest electrographic change) and termination, and an associated pre-ictal period of equivalent duration immediately prior to seizure onset. For the purpose of subsequent analyses, for each ictal period we also selected a corresponding interictal period of equivalent duration at least 6 h away from seizure activity, and a 5 min postictal period immediately following seizure termination. Following removal of artefact-ridden electrodes, intracranial EEG signals for each period were common-average referenced to reduce potential sources of correlated noise (Ludwig et al., 2009). Next, each period was divided into 1 s non-overlapping time windows in accordance with previous studies (Kramer et al., 2010; Khambhati et al., 2015, 2016, 2017).

To generate a functional network representing broadband functional interactions between iEEG signals for each 1-s time window, we carried out a method described in detail previously (Khambhati et al., 2017). Namely, signals were notch-filtered at 60 Hz to remove power line noise, low-pass and high-pass filtered at 115 Hz and 5 Hz to account for noise and drift, and pre-whitened using a first-order autoregressive model to account for slow dynamics. Functional networks were then generated by applying a normalized cross-correlation function $\rho$ between the signals of each pair of electrodes within each time window, using the formula:

$${\rho }_{xy}(k)=\begin{array}{c}argmax\\ \tau \end{array}\left[\frac{1}{T}\hspace{0.17em}\sum _t\hspace{0.17em}\frac{(x_k(t)-\hspace{0.17em}{\overline{x}}_k)(y_k\left(t+\hspace{0.17em}\tau \right)-{\overline{y}}_k)}{{\sigma }_{x_k}{\sigma }_{y_k}}\right]$$ (1)

where $x$ and $y$ are signals from two electrodes, $k$ is the 1 s time window, $t$ is one of the $T$ samples during the time window, and $\tau$ is the time lag between signals, with a maximum lag of 250 ms. Next, to gain an understanding of the frequency dependence of structural–functional connectivity (SC-FC) relationships, we generated functional networks across physiologically relevant frequency bands as described in detail in a previous study (Khambhati et al., 2016). Specifically, multitaper coherence estimation (time-bandwidth product of 5, 8 tapers) was used to compute functional coherence networks for each 1 s window across four frequency bands: α/θ (5–15 Hz), β (15–25 Hz), low-γ (30–40 Hz), and high-γ (95–105 Hz). Both broadband and frequency-specific networks were represented as full-weighted adjacency matrices for each 1-s window in each period.

Structure-function coupling analysis

To quantify the relationship between structure and function in the epileptic brain, we computed the Pearson correlation coefficient between the edges of each structural connectivity network and the edges of each broadband functional connectivity network, followed by Fisher r-z transformation for variance stabilization (Fisher, 1921). This led to a time series of SC-FC correlations for each seizure event in each subject. To understand the frequency-dependence of SC-FC coupling better, we repeated the same analysis using the frequency-specific functional networks.

Next, to understand the extent to which the resulting SC-FC time series evolve similarly within each subject, we computed the Euclidean distances between these time series for all pairs of seizure events. Importantly, we first time-normalized the time series for each seizure event to span 200 evenly spaced time bins (100 pre-ictal and 100 ictal). Next, for each seizure event, we generated a single vector consisting of the SC-FC time series for all five frequency bands: broadband, α/θ, β, low-γ, and high-γ. Euclidean distances were then computed between all pairs of vectors, composed of pairs belonging to the same patient and pairs belonging to different patients.

Finally, we wished to assess which edges in the structural network were responsible for the changes in SC-FC correlation between pre-ictal and ictal periods. We therefore first computed a mean ictal and mean pre-ictal broadband functional network for each subject by averaging across seizures events and across windows within each time period. Next, we carried out a virtual edge resection approach, in which we removed an edge from the network and computed the change in SC-FC correlation, $\Delta z\left(i\right)$, as follows:

$$\Delta z\left(i\right)=N[z-\hspace{0.17em}{z}^i]$$ (2)

where $z$ is the SC-FC correlation, $z^i$ is the SC-FC correlation following removal of edge $i$, and $N$ is the number of edges in the network. We chose to multiply by N to normalize the scale of $\Delta z$ across subjects with different numbers of edges. We performed this calculation for both pre-ictal and ictal time periods. Since we were specifically interested in edges that statistically contribute to the increase in SC-FC correlation during seizures, we defined a measure of contribution, $\sigma (i)$, for each edge $i$ in which a structural connection exists on the increase in SC-FC correlation during seizures as follows:

$$\sigma (i)=\left[\Delta z_{ictal}(i)-\Delta z_{pre\hspace{1em}ictal}(i)\right]$$ (3)

where $\Delta z_{ictal}(i)$ and $\Delta z_{pre\hspace{1em}ictal}(i)\hspace{0.17em}$ are the relative changes in SC-FC correlations following removal of edge $i$ during the ictal and pre-ictal periods, respectively.

We defined ‘contributors’ of SC-FC correlation during seizures as structural edges with $\Delta z_{ictal}(i)>\hspace{0.17em}0$ and $\sigma \left(i\right)>\hspace{0.17em}0$. This is because we wanted to identify regions that positively contributed to SC-FC correlation ictally, and more so ictally than pre-ictally. To understand the properties of contributor edges better, we computed the lengths of both the contributor edges and non-contributor edges, in terms of both streamline length and Euclidean distance. The purpose of this analysis was to determine whether the increased SC-FC correlation during seizures was due to long- or short-range connections. The Euclidean distance of an edge was calculated using the mean voxel coordinates of two regions of interest connected by that edge. The streamline length of an edge was calculated using the mean length of all tracts between the pair of regions of interest connected by that edge. To understand the relationship between structure-function coupling and functional seizure spread, for each structurally connected edge $i$ we computed the correlation between contribution and the change in function edge weight between ictal and pre-ictal periods.

A summary of our patient-level SC-FC analysis pipeline is illustrated in Fig. 1.

Figure 1.

Summary of patient-level SC-FC analysis pipeline. (A) HARDI preprocessing and whole-brain tractography was carried out. (B) iEEG data were preprocessed and seizures were annotated, with each seizure event consisting of an ictal period and an associated pre-ictal period of equivalent duration. (C) Regions of interest (ROIs) were selected via a one-to-one spatial correspondence between electrode centroids and atlas regions. (D) The structural connectivity (SC) network was generated using log-normalized streamline counts between atlas regions of interest associated with each electrode location. (E) Time-varying broadband functional connectivity (FC) networks were generated for each 1 s time window by computing correlation between iEEG signals across electrode pairs. Frequency-specific functional connectivity networks were similarly computed using coherence between iEEG signals across electrode pairs. (F) SC-FC relationships were quantified across time, frequency, and space (see ‘Materials and methods’ section for details).

Characterization of structural properties in relation to structure-function changes

We wanted to probe whether there were any factors in patients’ brain structure, both in terms of global structural connectivity and local microstructure, which might account for the observed structure-function coupling dynamics. First, to determine whether global structural network topology was significantly different in patients compared to healthy controls, we generated structural networks as described above in nine healthy adult subjects. Next, in both groups, we computed and compared global clustering coefficient, global efficiency, and small-worldness, network properties that have proven particularly useful in characterizing brain graph topology and quantify the brain’s capacity to minimize biological while maximizing topological integration (Bullmore and Sporns, 2009; Bassett and Bullmore, 2017) (see Supplementary material for equations and further details).

Next, to determine whether seizure spread is affected by local structure in addition to structural connectivity, we computed DTI-derived microstructural indices for each structural region of interest and correlated them with the degree of ictal versus pre-ictal changes in functional connectivity and structure-function coupling. Specifically, we computed fractional anisotropy (FA) and mean diffusivity (MD), the two most commonly studied DTI metrics which quantify the magnitude and preferred directionality of water diffusion within each voxel. For each region of interest, we then computed the mean SC-FC contribution of that region of interest by averaging the contributions of all edges emanating from that region of interest. Similarly, we computed the mean change in functional connectivity between ictal and pre-ictal periods for each region of interest. For each patient, we then correlated the mean value of each microstructural measure with both the mean contribution and mean functional connectivity change, across regions of interest.

Statistical analyses

To determine whether the SC-FC correlations were significantly greater than chance, for each 1-s window we generated a null distribution of correlations via random permutation of the functional network edges (10 000 permutations). We then compared the mean SC-FC correlations during ictal and preictal periods with the null correlations. Next, to determine whether there was a significant increase in SC-FC correlation between pre-ictal and ictal periods, we computed the difference between the mean ictal z and the mean pre-ictal z for each seizure event. We modelled these paired differences using a linear mixed effects model with subject assignment as the random effect, and determined whether the difference was significantly greater than zero using the parametric bootstrap method (1000 bootstrapped samples), which is robust to small sample sizes (Davison and Hinkley, 1997; Halekoh and Højsgaard, 2014). To assess whether the findings were robust to our choice of non-ictal period, we repeated the above analysis substituting the pre-ictal periods with interictal periods of equivalent duration that were at least 6 h away from seizure activity. To further compare findings during pre-ictal and interictal periods, we also carried out the above statistical analysis to determine significant differences between mean preictal z and mean interictal z. Finally, to better understand the pattern of SC-FC coupling during the early post-ictal period, we also carried out the above statistical analysis to determine significant differences between mean ictal z and mean postictal z. The 5 min postictal period was divided into two subperiods: one consisting of the first 1 min following seizure termination, and one consisting of the subsequent 4 min.

To assess the degree of intra-subject similarity of SC-FC evolution across the pre-ictal and ictal periods, we compared the between-subject time series Euclidean distances to the within-subject time series Euclidean distances and tested the significance of the difference using permutational multivariate ANOVA (PERMANOVA) (999 permutations) (Anderson, 2017).

To characterize the properties of edges that contribute to the increase in SC-FC correlation during seizures, we computed the mean length of all contributor edges and the mean length of all non-contributor edges for each subject. Edge length was computed using two metrics: mean streamline length, and Euclidean distance. We compared the mean contributor and non-contributor edge lengths using a paired t-test. Furthermore, to assess the relationship between edge contribution and edge length among the contributor edges, we classified contributor edges into ‘low’, ‘medium’, and ‘high’ contribution levels for each subject using tertiles. The edge lengths in these three categories were compared using paired t-tests. Finally, given prior knowledge that structural connection weights decrease with Euclidean distance (Kaiser and Hilgetag, 2004; Lewis et al., 2009; Rubinov et al., 2015; Donahue et al., 2016), we repeated all analyses after removing the effect of Euclidean distance from the structural networks using linear regression. More specifically, we fit a generalized linear model with the vector of all structural edges as the dependent variable and the vector of Euclidean distances as the independent variable, and took the residuals. The residuals were used for the repeat analysis. Given that this study takes a connectivity-based approach (i.e. focusing on connections/edges between regions of interest rather than the regions of interest themselves), this regression approach accounts for the distance-dependent effects of both the connection weights and the number of different structural connections. This is because each region of interest is associated with a number of different structural connections (i.e. edges), and each edge is associated with a different weight.

Data availability

De-identified iEEG recordings are available online on the International Epilepsy Electrophysiology Portal (www.ieeg.org, IEEG Portal). Our network analysis scripts and associated visualizations are publicly available at https://github.com/shahpreya/EpiConn.

Results

Clinical data

Forty-five clinical seizures (mean duration 71 s ± 44 s), were recorded across the nine patients (mean age 40.2 ± 11.8; five female). All seizures had focal onset, and were characterized as focal aware, focal impaired awareness, or focal to bilateral tonic-clonic. Patient demographic and clinical details, along with final number of regions of interest, are detailed in Table 1.

Table 1.

Patient demographic and clinical information, along with number of regions of interest included in analysis

Subject	Gender	Age of onset, years [epilepsy duration]	Age at MRI, years [at surgery]	Seizure frequency	MRI finding	Localization	Pathology	Treatment	Outcome	Seizures recorded (n)	Regions of interest
1	Female	20 [28]	47 [48]	FIAS: 2–3/week FBTC: 1–2/months	Non-lesional	RTL	HG	ATL + hippocampectomy	IA	FBTC (3)	84
2	Male	27 [12]	37 [39]	FAS: 1–day clusters, 1/months FBTC: 1/months	RTL cortical lesion, possible DNET	RTL/DNET	HG + MTS/HS + tumour	ATL + hippocampectomy	IB	FBTC (2)	55
3	Female	24 [21]	45 [45]	FAS: 2–4/week FIAS: ∼1/week	Non-lesional	LTL	MTS/HS	ATL + hippocampectomy	IA	FIAS (1), FBTC (3)	116
4	Male	5 [31]	36 [36]	FIAS: 5–day clusters, 4/year FBTC: 2 in lifetime	Non-lesional	RTL	Gliosis + MTS/HS	ATL + hippocampectomy	IB	FAS (1), FIAS (5)	118
5	Female	29 [11]	39 [40]	FIAS: 1–2/months	Non-lesional	RTL	Gliosis + MTS/HS	ATL + hippocampectomy	IA	FIAS (5)	101
6	Male	28 [23]	50 [51]	FIAS: 3–5/months	Bilateral PVH	Bilateral PVHa,b	N/A	N/A	N/A	FIAS (4)	70
7	Male	4 [20]	24 [24]	FAS: 10–15/week FIAS: 7/week FBTC: 4/months	Non-lesional	RTL	Gliosis + MTS/HS	ATL + hippocampectomy	IB	FIAS (6)	90
8	Female	12 [46]	57 [58]	FIAS: 2–5/months	Non-lesional	BTLa	N/A	N/A	N/A	FIAS (5)	116
9	Female	22 [5]	23 [27]	FIAS: 3–5/week FBTC: 2 in lifetime	Non-lesional	LTL	N/A	Laser ablation	IA	FIAS (10)	111

Post-surgical outcome was based on Engel classification score (scale: I–IV, seizure freedom to no improvement).

^aintracranial electrodes placed in both hemispheres for these two bilateral focal epilepsy patients.

^bMRI revealed bilateral subependymal nodular heterotopias in bilateral temporal horns and atria of the lateral ventricles. On iEEG, one epileptogenic focus was identified in the left temporal region via a 6-contact strip electrode placed over the left anterior temporal lobe and an 8-contact depth electrode placed in the left PVH.

ATL = anterior temporal lobectomy; BTL = bilateral temporal lobe; DNET = dysembryoplastic neuroepithelial tumour; FAS = focal aware seizure; FBTC = focal to bilateral tonic-clonic seizure; FIAS = focal impaired awareness seizure; GTC = generalized tonic-clonic seizure; HG = hippocampal gliosis; HS = hippocampal sclerosis; LTL = left temporal lobe; MTS = mesial temporal sclerosis; N/A = not applicable; PVH = periventricular heterotopia; RTL = right temporal lobe.

SC-FC coupling using broadband functional connectivity

To assess the overall temporal patterns of SC-FC coupling changes during seizures, we first quantified SC-FC correlations using broadband functional connectivity networks. For each individual seizure event, we determined the degree of SC-FC coupling, as measured by the Fisher-transformed Pearson correlation, z (Fig. 2A). For all seizures in all subjects, SC-FC coupling was significantly greater than chance during interictal, pre-ictal and ictal periods (P < 0.05, permutation-based testing; Fig. 2B). While the temporal progression of SC-FC changes was subject-specific (Fig. 2C), there was a consistent increase between pre-ictal and ictal periods (Fig. 2D). Per-seizure paired differences in mean z values reveal significantly greater SC-FC correlation during ictal periods than pre-ictal periods (P = 0.023, linear mixed effects analysis with subject as random effect). This effect was maintained when substituting pre-ictal periods with randomly chosen interictal clips of equivalent duration at least 6 h away from seizure activity (P = 0.021). It was also maintained after regressing out the effect of distance (P < 0.05, Supplementary Fig. 2). Moreover, there were no significant differences between pre-ictal and interictal period SC-FC correlation values (P = 0.70).

Figure 2.

SC-FC analysis using broadband functional connectivity. (A) Temporal dynamics of SC-FC correlation as measured by Fisher’s z for one example seizure in one patient, along with permutation-based null distribution of z values (mean ± standard deviation). (B) Per-seizure z-values during interictal, pre-ictal, and ictal periods reveal SC-FC correlations significantly greater than chance across all periods (P < 0.05). (C) Temporal dynamics of SC-FC correlation across all subjects (mean ± standard deviation across seizures in each subject). For visualization purposes only, time courses were normalized to span 200 evenly spaced time windows (100 pre-ictal and 100 ictal) and smoothed with a 5-window moving average filter. (D) Per-seizure paired differences in mean z-values reveal significantly greater SC-FC correlation during ictal periods than pre-ictal periods (P = 0.023). This effect holds when substituting pre-ictal periods with interictal periods (P = 0.021), with no significant difference between pre-ictal and interictal period SC-FC correlation values (P = 0.70). *P < 0.05.

Frequency-specific SC-FC analysis

Next, to understand the frequency dependence of the observed increase in SC-FC coupling during seizures better, we repeated the SC-FC coupling analysis across four frequency bands (α/θ, β, low-γ, and high-γ). Similar to the previous analysis, we found that the extent of SC-FC coupling was significantly greater than chance at all time points during pre-ictal and ictal periods (P < 0.05, permutation-based testing) for all frequency bands (Fig. 3A). Moreover, while the pre-ictal SC-FC was lower in higher frequency bands (Fig. 3B), the increase in SC-FC coupling between pre-ictal and ictal periods was significant across all frequency bands (α/θ: P < 0.05; β: P < 0.05; low-γ: P < 0.05; high-γ: P < 0.05) (Fig. 3B and C). This finding was upheld after regressing out the effect of distance (Supplementary Fig. 2). Similar to the findings with broadband functional connectivity, the findings were consistent when substituting pre-ictal periods with interictal periods (α/θ: P < 0.05; β: P < 0.05; low-γ: P < 0.05; high-γ: P < 0.05), and there were no significant differences between pre-ictal and interictal period SC-FC correlation values (α/θ: P > 0.05; β: P > 0.05; low-γ: P > 0.05; high-γ: P > 0.05) (Supplementary Fig. 3).

Figure 3.

Frequency-specific SC-FC analysis. (A) Temporal dynamics of SC-FC correlation as measured by Fisher’s z in α/θ, β, low-γ, and high-γ frequency bands (mean ± standard deviation across seizures in each subject, following interpolation to normalize ictal and pre-ictal durations). (B) Per-seizure z-values during interictal, pre-ictal, and ictal periods (mean ± SD) are significantly greater than chance (P < 0.05, permutation-based testing). (C) The increase in SC-FC correlation between pre-ictal and ictal periods is further illustrated using paired differences for each individual seizure (P < 0.05, linear mixed effects analysis with subject as random effect). (D) Seizures within subjects evolve similarly, as evidenced by higher between-patient Euclidean distances between SC-FC correlation time courses compared to within-patient distances (P < 0.001, R² = 0.50, PERMANOVA). *P < 0.05.

We noted that while the increase was significant across all frequency bands, there were subject-specific frequency-dependent changes in SC-FC correlation. For example, Subject 4 exhibited particularly salient increases in SC-FC_high-γ coupling, while Subject 6 had only moderate increases in SC-FC_high-γ coupling but higher increases in SC-FC_β and SC-FC_low-γ (Fig. 3C and Supplementary Fig. 4). Finally, we characterized the within-subject similarity of the SC-FC time courses across all frequency bands. Using Euclidean distance as a measure of dissimilarity, we determined that the SC-FC time courses were significantly more similar within-patient than between-patient (P < 0.001, R² = 0.50, permutational MANOVA) (Fig. 3D), indicating that the temporal dynamics of SC-FC coupling is stereotyped in each patient across seizure events.

SC-FC analysis during postictal periods

To understand whether the observed increase in SC-FC coupling during seizures persists postictally, we repeated the SC-FC coupling analysis using iEEG data obtained from the first 5 min following seizure termination. Although time courses varied across seizures, we observed three distinct patterns of postictal SC-FC coupling as follows: (i) SC-FC coupling persisted, but did not increase, in the immediate postictal period and subsequently decreased; (ii) SC-FC coupling increased into the immediate postictal period and later decreased; and (iii) SC-FC coupling decreased sharply at or prior to the start of the postictal period (Fig. 4A). Generally, SC-FC coupling ultimately decreased during the postictal period, though not always to the level of SC-FC coupling in the pre-ictal period. Given the different pattern during the immediate postictal period (usually up to 1 min following seizure termination), we separated the postictal period into immediate (Minutes 0–1) and later (Minutes 1–5) subperiods. Per-seizure paired differences in mean z-values revealed significant decreases in SC-FC coupling between ictal periods and later postictal periods across all tested frequency bands, while significant differences between SC-FC coupling between ictal periods and immediate postictal (Minutes 0–1) periods occurred only in α/θ and β frequency bands. (P < 0.05, linear mixed effects analysis with subject as random effect) (Fig. 4B).

Figure 4.

Assessment of SC-FC coupling in postictal periods. (A) Illustration of broadband SC-FC coupling across pre-ictal, ictal, and postictal periods, in three example seizures. Each represents one of three observed distinct patterns of post-ictal SC-FC coupling: (top) SC-FC coupling persists, but does not increase, in the immediate postictal period and subsequently decreases, (middle) SC-FC coupling increases into the immediate postictal period and later decreases, and (bottom) SC-FC coupling decreases sharply at or prior to the start of the postical period. (B) Per-seizure paired differences in mean z-values reveal significant decreases in SC-FC coupling between ictal periods and later postictal (Minutes 1–5) periods across all tested frequency bands, with significant differences between SC-FC coupling between ictal periods and immediate postictal (Minutes 0–1) periods occurring only in α/θ and β frequency bands. (P < 0.05, linear mixed effects analysis with subject as random effect). Pre-ictal period bars included for reference. *P < 0.05.

SC-FC subanalysis in focal to bilateral tonic-clonic seizures

As noted previously, the temporal progression of SC-FC changes was subject-specific (Figs 2C and 3A). More specifically, we observed that in patients who experienced focal to bilateral tonic-clonic seizures (Subjects 1–3), there was a drop in SC-FC coupling after the initial rise following seizure onset. Analysis of the individual SC-FC time courses in these seizures revealed that the drop corresponded with onset of bilateral tonic-clonic activity (Fig. 5A). Furthermore, quantitative analysis revealed significantly greater SC-FC correlation during pre-bilateral tonic-clonic ictal periods than pre-ictal periods (P < 0.05), as well as significantly greater SC-FC correlation during pre-bilateral tonic-clonic ictal periods than post-bilateral tonic-clonic ictal periods (P < 0.05) (Fig. 5B). To focus on the relationship between structure and function prior to the onset of generalized hypersynchronous activity, we limited the ictal periods to the periods prior to bilateral tonic-clonic onset for the subsequent virtual edge resection analysis.

Figure 5.

Assessment of SC-FC coupling in focal to bilateral tonic-clonic seizures. (A) Illustration of SC-FC coupling in two focal to bilateral tonic-clonic seizures, one from Subject 1 and one from Subject 3, reveals decrease in SC-FC coupling following bilateral tonic-clonic (BTC) onset (bilateral tonic-clonic onset indicated by dotted red line). For comparison, SC-FC coupling time course from a focal impaired awareness seizure in Subject 3 (without bilateral tonic-clonic) does not illustrate the same decrease. (B) In all bilateral tonic-clonic seizures, per-seizure paired differences in mean z-values reveal significantly greater SC-FC correlation during pre-bilateral tonic-clonic ictal periods than pre-ictal periods (P < 0.05), as well as significantly greater SC-FC correlation during pre-bilateral tonic-clonic ictal periods than post-bilateral tonic-clonic ictal periods (P < 0.05). *P < 0.05.

Virtual edge resection analysis

Given our finding that SC-FC coupling was significantly higher during ictal periods compared with pre-ictal periods, we wanted to identify and characterize the structural edges that statistically accounted for this increase. After quantifying the contribution $\sigma (i)$ of each edge on the SC-FC coupling, we mapped the contributor edges onto each subject’s brain (Fig. 6) to facilitate subject-specific characterization of SC-FC relationships. Furthermore, at the group level, we determined that contributor edges were predominantly short-range, as quantified by significantly shorter edge lengths in contributors compared with non-contributors, based on both Euclidean distance (P < 0.05, two-tailed paired t-test) (Fig. 7A) and streamline distance (P < 0.05, two-tailed paired t-test) (Fig. 7B). This finding held individually for each subject. Within the contributor edges, we found within each subject that higher contribution edges are shorter-range, both in terms of Euclidean distance (Fig. 7C) and streamline length (Fig. 7D), with significant differences between low and medium contribution edges (P < 0.05, two-tailed paired t-test), and low and high contribution edges (P < 0.05, two-tailed paired t-test). These findings held following distance regression (Supplementary Fig. 2). When relating edge contributions to changes in functional connectivity, we found no significant correlation (Pearson r = −0.04 ± 0.13; P > 0.05) (Supplementary Fig. 7A). While the edges with the largest changes in functional connectivity were typically short-range, these edges were often not the same as those with high contribution; moreover, many longer-range connections also exhibited significant increases in functional connectivity (Supplementary Fig. 7B cf.Fig. 6).

Figure 6.

Subject-specific virtual edge resection approach to determine the contribution, σ($\mathit{i}$), of each structural edge $\mathit{i}$ on the increase in SC-FC correlation during seizures. Results are shown for an example seizure in a patient with left temporal lobe epilepsy. Only ‘contributor’ edges [$\sigma \left(i\right)$ > 0 and $\Delta z_{ictal}\left(i\right)>0]$ are included to highlight edges that are associated with the SC-FC increase, with edge thickness and colour used to representing magnitude of $\sigma \left(i\right)\hspace{0.17em}$.

Figure 7.

Relationship between edge contribution and edge length. Findings reveal that contributor edges are shorter-range in terms of both (A) Euclidean distance and (C) streamline length (P < 0.05, two-tailed paired t-test). Furthermore, there is a trend that edges with higher contribution are shorter-range, in terms of both (B) Euclidean distance and (D) streamline length, with significant differences between low and medium contribution edges (P < 0.05, two-tailed paired t-test), and low and high contribution edges (P < 0.05, two-tailed paired t-test). *P < 0.05.

Global and local structural properties analysis

We analysed global structural network properties in our patient population and compared them to those of healthy controls. We found no significant difference in normalized clustering, (patients: 11.9 ± 1.31; controls: 11.0 ± 1.53; P > 0.05), normalized efficiency (patients: 0.80 ± 0.012; controls: 0.79 ± 0.020; P > 0.05), or small-worldness (patients: 9.43 ± 0.93; controls: 8.60 ± 1.08; P > 0.05) (Supplementary Fig. 5). We also correlated microstructural measures with both nodal SC-FC contribution and nodal FC change across regions of interest in each subject. We found no significant correlation between nodal contribution and mean FA (r = 0.087 ± 0.15; P > 0.05) or mean MD (r = –0.087 ± 0.13; P > 0.05). Similarly, we found no significant correlation between nodal functional connectivity change and mean MD (r = 0.09 ± 0.15; P > 0.05). There was a mild but significant correlation between nodal functional connectivity change and mean FA (r = 0.13 ± 0.06; P < 0.05) (Supplementary Fig. 6).

Discussion

The main goal of this study is to characterize the relationship between structural and functional connectivity during seizure onset and spread. Using network-based analysis of HARDI and iEEG data, we observe significant structure-function coupling at rest and a marked increase in this coupling during the progression from pre-ictal to ictal states. This finding persists across frequency bands, with subject-specific levels of frequency-dependent increases. Furthermore, we present a technique for assessing the impact of individual structural connections to the observed ictal increase in structure-function correlation, and demonstrate that the effect is primarily due to short-range connections. The consistency of findings across seizures within each patient suggests that the spatiotemporal patterns of structure-function coupling are highly stereotyped. Our findings shed light on the dynamics of focal epileptic seizures in relation to underlying structure by demonstrating that seizure spread is tightly controlled by short-range structural connections.

Structure-function coupling across time, frequency and space

We observe greater coupling between structural and broadband functional networks during pre-ictal and interictal periods than expected by chance. This finding is consistent with studies relating DTI-based structural networks to resting-state functional MRI-based functional networks in healthy adults (Skudlarski et al., 2008; Damoiseaux and Greicius, 2009; Honey et al., 2009; van den Heuvel et al., 2009; Zhang et al., 2010; Hermundstad et al., 2013). It is important to note that the functional signals recorded using iEEG are fundamentally different from those recorded using functional MRI. While recent studies suggest that blood oxygen level-dependent (BOLD) signal fluctuations correlate with slow fluctuations in EEG gamma power, the exact relationship between functional MRI (BOLD) signals and electrophysiology has yet to be resolved (Logothetis et al., 2001; He and Liu, 2008; He and Raichle, 2009; Ko et al., 2011) Nonetheless, our finding suggests that the tie between structure and function at rest is robust across diverse measurements of functional connectivity.

Interestingly, we observe that pre-ictal functional connectivity networks in lower frequency bands have higher correlation to structural connectivity networks than pre-ictal functional connectivity networks in higher frequency bands. This relationship decreases during the ictal period, with high SC-FC coupling in all frequency bands. Since it is believed that lower frequencies facilitate long-distance connections in the brain while higher frequencies facilitate shorter connections (Kopell et al., 2000; Miller et al., 2007), our findings may suggest a relative shift to short-range, high-frequency connectivity during seizure generation. However, this observation could be influenced by the spatial distribution of electrodes, which tend to be clustered around the putative seizure onset zone, leading to a bias towards short-range connections within the seizure generating network. Therefore, we plan to corroborate these findings in patients with stereo-EEG, an increasingly popular and less invasive method that records from stereotactically-placed intracranial depth electrodes (Cossu et al., 2005; Varotto et al., 2012; Luders et al., 2013). In comparison to the depth electrodes used to sample the hippocampus and amygdala alongside strips and grids in our study’s patients, stereo-EEG electrodes are more flexible to allow for stereotactic placement. More importantly, because of the ability to place stereo-EEG electrodes without large, highly-invasive craniotomies, stereo-EEG allows for bilateral electrode placement within multiple deep cortical structures and overlying cortex, as well as sampling from multiple non-contiguous lobes (Gonzalez-Martinez et al., 2013). Therefore, stereo-EEG may allow us to sample more regions of the brain and capture longer-range connections.

Despite individual variations inherent to our patient population, the finding of increased SC-FC coupling during ictal periods compared with pre-ictal periods is extremely robust, using both broadband and narrow-band functional connectivity. We compared SC-FC time courses from ictal periods to those of immediately pre-ictal periods to allow for matched pairwise comparisons and to facilitate visualization along a continuous temporal scale. To ensure that activity immediately prior to seizure onset is a good representation of non-ictal activity, we repeated our analysis after substituting the pre-ictal periods with interictal periods far away from seizure activity, and attain consistent results. The rise in SC-FC coupling during seizures indicates that seizures may rely on the brain’s underlying architecture during initial seizure spread. We note that in several of the patients, the rise in SC-FC correlation occurs prior to the clinically-marked earliest electrographic change representative of seizure onset, suggesting that SC-FC coupling may also be a valuable biomarker for seizure prediction or its early generation.

We observed that the only two bilateral focal epilepsy patients, Subjects 6 and 8, had the highest Fisher’s z-values across pre-ictal and ictal periods in all frequency bands, and highest Δz-values in all bands except high gamma. This observation suggests that the extent of structure-function coupling changes may be dependent on the extent of alterations in the underlying seizure network. However, there are clearly a number of factors that may be involved, including the location and extent of tissue involved. Therefore, this observation could be explored in future larger-scale studies with patients of both bilateral and unilateral onset, accounting for possible covariates.

We find that the pattern of SC-FC coupling during the postictal period varies across seizures. In some seizures, there is an initial persistence or increase in SC-FC coupling in the immediate postictal period followed by a decrease, while in some seizures, SC-FC coupling decreases immediately. While the postictal EEG is often characterized by slowing and suppression—particularly in focal to bilateral tonic-clonic seizures—the dynamics of the postictal period are variable, complex, and poorly understood (Kaibara and Blume, 1988; Bateman et al., 2019; Marchi et al., 2019). Additionally, the transition from ictal to postictal is known to be ambiguous, as the end of a seizure is often not well demarcated, neither clinically nor electrophysiologically (Fisher and Engel, 2010). Therefore, our finding of persistence of SC-FC coupling during the first minute following seizure termination may be a consequence of the imprecise boundary between seizure and post-seizure. Additionally, the observation that the degree of postictal SC-FC coupling is higher than that of the pre-ictal period may be due to the fact that postictal EEG can take hours to days to return to baseline (Litt et al., 2001; Fisher and Engel, 2010; So and Blume, 2010). Further studies should be carried out to better understand the dynamics of functional connectivity and structure-function relationships over longer postictal time scales.

We discover that in focal to bilateral tonic-clonic seizures, there is a significant decrease in SC-FC coupling after the onset of bilateral tonic-clonic activity. This finding is not surprising, given that bilateral tonic-clonic periods are associated with generalized hypersynchronous neural activity that is not localized to particular brain regions or pathways. This finding also supports that the observed SC-FC coupling increase during seizures relates to seizure propagation, and is not simply a result of highly synchronous activity.

Of note, the temporal dynamics of SC-FC coupling is highly consistent between seizures within each patient. This indicates that seizures may be ‘hard-wired’ in a sense, and is a macroscopic analogue to the microscale finding of stereotyped ictal progression (Wenzel et al., 2017). However, since our dataset consists of a relatively small group of adult focal epilepsy patients, with the majority having temporal lobe epilepsy, these conclusions may be specific to our dataset and should be confirmed using larger, more diverse patient populations.

To assess the role of each structural connection on the rise in SC-FC coupling during seizures, we implement a virtual edge resection method. Such leave-one-out simulation-based methods have been gaining popularity to probe the role of individual nodes and edges on overall network topology (Honey and Sporns, 2008; Alstott et al., 2009; Rafal et al., 2015; Khambhati et al., 2016). In our case, we determine the contribution of structural connections to SC-FC correlation and generate seizure-specific brain maps of these connections. Group-level analysis reveals that connections with high contribution are predominantly short-range, in terms of both streamline length and Euclidean distance. Of note, the distributions of all streamline lengths (including both contributors and non-contributors) are skewed to the right, indicating that the majority of structural edges are relatively short range. This is due to two phenomena. First, prior studies have demonstrated the brain consists of a large number of short connections and few long-range connections to minimize wiring cost while allowing for efficient communication (Klyachko and Stevens, 2003; Chen et al., 2006; Hagmann et al., 2007). Second, since structural connections analysed in this study are based on electrode locations, and the electrodes are typically clustered around the putative seizure onset location rather than distributed throughout the brain, this leads to a further bias towards shorter range connections. Nonetheless, we see that the edges contributing to SC-FC coupling are statistically shorter than the non-contributors, and that stronger contributors are even shorter-range, indicating that our findings are not simply due to selection of local networks. Interestingly, edge contribution was not significantly correlated to change in functional connectivity. This suggests that our finding of edge contribution is not simply a consequence of functional connectivity changes, and the relationship between functional seizure spread and edge contribution is more complex.

We found no significant differences in global structural network properties between our patient population and healthy controls. Moreover, we found that the observed increases in SC-FC coupling from pre-ictal to ictal periods are not significantly correlated to microstructural properties such as fractional anisotropy and mean diffusivity. This could be partly due to our patient population, which consisted primarily of subjects with no clear lesion on MRI (though several exhibited signs of hippocampal sclerosis on subsequent pathology). Additionally, these findings suggest that multimodal connectivity-based analysis captures unique information about seizure dynamics that are not evident from standard structural image analyses. We plan to repeat our findings in larger datasets to corroborate our observations. Furthermore, further studies in MRI-lesional patient datasets should be undertaken to relate SC-FC coupling changes to the anatomical location and extent of structural lesions.

While the connections themselves are short, the locations of these connections appear distributed across the brain, including connections that are contralateral to seizure onset. This suggests that seizure dynamics rely on a distributed network of locally clustered connections. While further analyses and validation are needed, mapping connections in relation to seizure onset and spread could ultimately be useful in pinpointing networks for therapeutic removal via targeted methods such as laser ablation (Willie et al., 2014) or neurostimulation (Fisher and Velasco, 2014).

Methodological considerations and limitations

An important but inevitable limitation of this work relates to the incomplete sampling of the network via iEEG. Electrode placement is limited by clinical necessity and constrained by the boundaries of the craniotomy, in order to minimize invasiveness and reduce patient morbidity. Therefore, it is not possible to sample functional connectivity from the entire brain at high resolution time scales accessible through iEEG. While clinicians aim to place electrodes around putative seizure onset zones, it is possible that the entire seizure network may not be captured in certain cases. Recent efforts to map whole-brain iEEG using recordings from multiple subjects (Betzel et al., 2017) and to construct models of whole-brain iEEG within individual subjects (Owen and Manning, 2017) may help circumvent this issue. Furthermore, while limited by impedance from the skull and inability to localize subcortical activity, ictal scalp EEG recordings, or ictal MEG recordings could supplement our intracranial analysis as both allow for consistent, grid-like spatial sampling with temporal resolution comparable to iEEG. The feasibility of such approaches has already been demonstrated in a recent paper revealing significant overlap between DTI networks and scalp EEG functional networks in the interictal state (Chu et al., 2015), and in early work on ictal MEG.

Another consideration lies in the method of establishing correspondence between functional network nodes and structural network nodes. We chose to make the assignment based on anatomical location of the electrode centroids. This decision was based on prior research demonstrating that the field created by neurons more than 1 cm away from an electrode contributes minimally to the recorded signal, and that the weight of contribution of a brain signal source is inversely proportional to the square of the distance separating the source from the electrode contact (Morris and Lüders, 1985; Lachaux et al., 2003). Therefore, it is reasonable to assume that the majority of signal recorded by an iEEG electrode likely arises from neighbouring brain tissue. Nonetheless, it is possible that a strong signal from a remote location can contribute the recorded signal. In scalp EEG and MEG studies, source localization methods are often used to circumvent this issue by locating signal sources (Cohen et al., 1990; Mosher and Leahy, 1998). However, while source localization in intracranial EEG has been investigated, it is not commonly used because of many unknowns, such as the number of iEEG electrodes needed for reconstruction, the model to be used for the sources, and the volume conduction properties of the brain tissue (Lachaux et al., 2003). More generally, because of the lack of unique solution to the inverse problem and the wide variety of modelling methods (Plummer et al., 2008; Zhang et al., 2008; Caune et al., 2014), the reliability of the methodology should be explored further prior to incorporating it into our approach.

Our structural network findings are also limited by the capacity of our imaging methods. While HARDI has demonstrated superiority over conventional DTI in terms of its ability to resolve crossing fibres in regions of high fibre heterogeneity (Tuch et al., 2002), HARDI tractography is still only a proxy for true white matter pathways. Similar to other neuroimaging modalities, it is subject to partial volume effects and artefacts such as eddy current and susceptibility distortions (Le Bihan et al., 2006; Assaf and Pasternak, 2008). Diffusion-based tractography is documented to recapitulate known pathways types including the short and long association fibres linking cortical gyri, the projection fibre connecting the cortex to lower portions of the brain, and the commissural fibres linking the two hemispheres (Mamata et al., 2002), but may not reconstruct unmyelinated intracortical axons. Furthermore, streamline count may not be a direct measure of the strength of anatomical connectivity.

We decided to include medically-refractory patients with a range of clinical findings (in terms of laterality, lesional status, and seizure types) in our study, rather than restricting to a particular subtype epilepsy. Notably, our findings were robust across patients despite heterogeneity. While we included one patient with periventricular nodular heterotopia (PVH), a malformation of cortical development, histological evidence suggests that these patients manifest with an altered arrangement of fibre tracks and microstructural abnormalities beyond visible lesions that may displace the axonal tracts from their expected location (Kakita et al., 2005; Meroni et al., 2009; Liu et al., 2017). Therefore, in future work, the anatomical locations of salient structure-function changes should be analysed carefully in the context of these alterations.

Because of the strong relationship between spatial proximity and structural connection strength, it is not possible to entirely disentangle the effects of Euclidean distance on our findings. Given prior work that epileptiform activity propagates within layer V of the neocortex (Badawy et al., 2009), it is possible that local functional connections could partially be attributed to local cortical spreading phenomena rather than white matter propagation along short-range arcuate fibres. Local functional connectivity could also be due to measurement of a common source of signal. Despite these concerns, our finding of higher SC-FC coupling during seizures hold after regressing out Euclidean distance from our structural networks. This suggests that SC-FC coupling goes beyond solely distance-based effects.

Finally, while this study considers only direct structural connections, functional connectivity in the brain is also partially attributed to indirect structural connections (Damoiseaux and Greicius, 2009; Honey et al., 2009; Liang et al., 2017). Future studies could use the property of communicability (Estrada and Hatano, 2008) to incorporate path lengths of greater than one into the construction of structural networks while also accounting for the effects of spatial proximity.

Conclusions

We present a comprehensive approach to understanding the relationship between structure and function in the epileptic brain. Our work provides important insights into the structural underpinnings of seizure dynamics. Our network analysis scripts, associated visualizations, and data are publicly available at https://github.com/shahpreya/EpiConn. It is our hope that by openly sharing our data, code and pipeline that we can accelerate translating this nascent field of network analysis in clinical epilepsy to help patients.

Funding

This work was supported by National Institutes of Health grants 1R01NS099348, K23-NS073801, 1R01NS085211, and 1R01MH112847. We also acknowledge support by the Thornton Foundation, the Mirowski Family Foundation, the ISI Foundation, the John D. and Catherine T. MacArthur Foundation, the Sloan Foundation, and the Paul Allen Foundation.

Competing interests

The authors report no competing interests.

Glossary

Abbreviations

DTI

diffusion tensor imaging

DWI

diffusion-weighted imaging

HARDI

high angular resolution diffusion imaging

iEEG

intracranial EEG

MEG

magnetoencephalography

SC-FC

structural-functional connectivity