Introduction
The concept of an epileptic network is based on the long-standing clinical observation that ictal electroencephalography (EEG) patterns cannot be easily explained by the traditional model of a single seizure focus triggering activity that spreads to uninvolved brain regions.1 Accumulating evidence suggests that the pathophysiological underpinnings of focal seizure generation and propagation may involve large-scale networks, which are characterized by 1- and 2-way communication (often undergoing time delays via signal transmission2) across sites in multiple lobes of the brain. Focal seizures evolve over multiple cortical and subcortical structures often with remarkable reproducibility from one seizure to the other in a given patient; however, even when stereotyped, seizures commonly evolve in a distributed fashion with delayed secondary discharges and complex propagation patterns.3-8 In such cases, the traditional model of the epileptogenic focus is too simplistic to capture the spatiotemporal organization of the epileptic network, which has spurred many to start applying complex system approaches used in data and network to understand the underlying neurophysiological mechanisms in epilepsy.
Epileptic networks are mapped onto a network defined by nodes (brain regions) and edges (connections between the nodes). These connections can be defined for each patient structurally (ie, nerve fiber tracts) or functionally (ie, examining the coupling of different brain regions during activity recorded with different modalities, such as EEG or functional MRI (fMRI)). In some cases, directionality of the edges may also be assessed. Together, the defined nodes and edges comprise a complete set of structural or functional links, the so-called connectome, that can then be subject to network analysis. This conceptual framework has been used extensively to characterize epileptic networks in terms of structural and dynamic, state-dependent properties.9-12 When the connectome is linked to a dynamic model, it represents a large-scale brain network model, which can be used for data analysis or the simulation of patient-specific brain activation data. The organizational scale of the network model determines its applicability to data and may cover wide ranges, spatially from the subcellular to the full-brain scale and temporally from milliseconds for action potentials to days/years for modeling seizure occurrence.13,14 Despite its simplicity, connectome-based analyses have yielded potentially important observations, such as elucidating the role of widespread pathological excitation, clarifying the loss of inhibition in modulating seizure severity and extent of spread,15-18 and quantifying the degree of connectome patient-specificity for the prediction of seizure propagation.19,20 Microelectrode recordings in small cell populations in the human are well-situated to address questions on pathophysiology and mechanisms of localized seizure spread and interaction between different seizure territories, whereas intracranial macroelectrode recordings sample large-scale network organizational features used in clinical decision-making. This field bears promise, especially when shifting its focus from simply identifying generic large-scale networks toward characterizing such connections across temporal and spatial scales. We discuss this progress in the following for macroscopic and micro-/mesoscopic networks.
Networks Across Scales: Macroscale EEG and Imaging
Complex system theory provides a fundamental organizing principle of seizure dynamics, capturing characteristics in electrophysiological recordings comprising seizure onset and termination. The set of a seizure’s dynamic properties is called the dynamotype, which leads naturally to a Taxonomy of Seizure Dynamics providing practical, objective metrics for classification into 16 theoretically possible classes.21 This taxonomy coupled with the underlying connectome of the brain is the basis for computational brain network models simulating the range of possible seizure propagation profiles.14 Recognizing that different biological processes might have similar outcomes, as well as the fact that the same (nonlinear) systems may produce a range of different behaviors, the connectome-based brain model presents a strategy to identify what those processes might be experimentally. The capacity to individualize the brain model opens up the possibilities for a personalization of diagnostic and curative approaches. Personalized network modeling is currently being studied by multiple investigators to predict outcome in patients undergoing epilepsy surgery.20,22-24
Currently, when evaluating a patient for epilepsy surgery, the seizure-onset zone region is defined qualitatively based on clinical, EEG, and imaging features. For surgeries outside the temporal lobe, even when there is a clear hypothesis for the area of seizure origin, less than half of patients achieve complete seizure freedom.25 A third of these candidates have a complex pattern of remission or relapse.25 Often this is attributed to an error in identifying the seizure focus. It is also not uncommon for the focus to be incompletely resected,26 or for seizures to be multifocal, with some seizure foci going undetected. Personalized brain network models address these issues as they allow a large number of clinical hypotheses to be tested and may help overcome sampling limitations as they are not limited by the number of intracranial electrodes that can be implanted. Initial retrospective studies indicate good precision in detecting the epileptogenic networks using this approach, underlying the importance of ongoing prospective multicenter trials to estimate the impact of virtual epileptic patient models on improving surgical prognosis. The analysis of factors limiting prospective model performance is critical for future clinical application outside of clinical trials.
Another intriguing possibility for surgical failure is a reorganization of the large-scale pathological network postsurgically to produce seizures from sites that were previously dormant. In the current clinical state, physicians do not know if they selected the optimal resection or ablation size and location even in patients who are seizure free after surgery. Could a better understanding of the patient-specific brain network improve care?27 This question has spurred multiple studies of novel biomarkers or computational models of personalized networks with the goal of improving the outcomes of epilepsy surgery and exploring minimally invasive interventions. For example, using data collected from intracranial monitoring done for presurgical evaluation, and a network analysis approach, a computational model for neocortical focal seizures was generated that categorized the observed networks of individuals into 3 discrete network types.28 The classification, if verified, could be clinically relevant, as it also suggested 3 different treatment approaches based on the network classification (pharmaceutical, surgical, or neurostimulation). This concept of network analysis having predictive value for surgery has been also studied in other computational models derived from electrocorticographic patient data to reconstruct networks.7,23,24 Computational modeling has also been applied in other whole-brain imaging modalities such as fMRI functional networks, which suggest network changes over the course of disease progression.5,29,30 Aberrant structural networks based upon diffusion tractography have been shown to predict outcome and structural node-based abnormalities in unresected brain region have been associated with poor surgical outcomes.31,32 In addition, seizure spread as measured by intracranial EEG has been shown to be constrained by the underlying white matter networks as measured by diffusion tractography.33 These network changes in the different models suggest that there may be dynamic network biomarkers for predicting surgical treatment outcome. A caveat to this work is that it has all been done retrospectively, and the true test of computational models will be in whether they can inform clinicians prospectively.
Networks Across Scales: Micro and Mesoscale
Although microelectrodes provide highly specific data for small cell populations, any investigations into large-scale network activity in humans proposing to take advantage of these data must take into account their limited spatial coverage, as well as the relatively limited number of such recordings available. Current microelectrode systems approved for human use cover a few square mm (the “Utah” microelectrode array, Blackrock Microsystems Inc) or a small number of cells sampled at a limited number of brain sites (Behnke-Fried microwire depth arrays, Ad-tech Medical Instrument Corp). Due to these limitations, such recordings are perhaps best used to test specific hypotheses or to validate animal experiments or computational models. Animal studies have several noted advantages, for example, the ability to employ widefield calcium or GCaMP imaging, perturbation techniques such as optogenetics or pharmacological intervention, and the ability to conduct longitudinal and well-powered studies in a homogeneous data set. Unfortunately, there are few established epilepsy models that have been shown to reproduce the large-scale network effects seen in humans, particularly for focal neocortical syndromes. Existing work includes a focal brain tumor model explored during spontaneous epileptiform activity and seizures using widefield GCaMP imaging,34 a post-stroke epilepsy model in which thalamic connectivity with the seizure focus site in primary somatosensory cortex was demonstrated to have an important role in seizure generation,35 and studies of the effects of optogenetic cell-type specific activation on pilocarpine-induced seizures,36,37 with stimulation of interneurons in the fastigial nucleus of the cerebellum preventing seizures in a mouse pilocarpine model.38 As these models all have important limitations in terms of relevance for patients with chronic focal epilepsy syndromes, there is an urgent need for further work in this area.
Returning to human recordings, there remains considerable controversy regarding such basic issues as the cellular signature of seizures, or indeed how to determine whether a given brain site is actively seizing. Two contrasting models have been put forward. One proposes that seizure activity across the brain is driven from a relatively small, migrating cortical region exhibiting a well-defined seizure signature analogous to those seen in animal models,18,39-42 with a predominantly inhibitory response in brain sites outside of this area,39,43,44 and the second proposes that heterogenous firing activity across large brain regions operate in synchrony to produce seizures, through an as yet unexplained mechanism.45,46
If it is the case that seizures are driven from small cortical regions, a large gap in knowledge remains: how does this localized activity translate to the large-scale seizure effects that have been well documented in EEG studies? The focal-seizure hypothesis was recently extended to account for this effect, due to the dual role for inhibition inherent in this model. At the seizing brain site, inhibition has failed and a runaway excitation effect emerges.18,39 Outside of this region, inhibition is not only intact but is driven to high levels due to the strong excitatory synaptic currents generated from the seizing brain area. This results in weakly synchronized or possibly asynchronous oscillatory activity which may be interpreted as ictal spread.41,43,44 Another possibility is the recruitment of disparate seizure sites, which may potentiate overall epileptic network effects and severity. This is clinically a well-recognized phenomenon,47 but has been only minimally explored in animal studies17 and computational models.20 Capturing this effect in human microscale recordings is an important goal that could help to elucidate the cellular mechanisms and effects of such a scenario and provide crucial validation for high level network analyses.
Conclusion
Once a computational model has been created, predictions can be formulated and validated on new data sets that were not used to train the initial model. This approach allows researchers to glean new mechanistic insights and create models which can then be tested prospectively. There are many different types of mathematical approaches that can be applied to modeling a dynamic nonlinear network such as the brain, which is constantly plastic. However, mathematical modeling of epilepsy network topology is still an emerging field. The field would benefit from an influx of new mathematical perspectives on analyzing network topologies that could be applied to modeling seizure spread across the brain. For example, one could consider symmetries within the network topology or emerging theories on control principles of complex systems.48,49 An interdisciplinary group including neuroscientists, computer scientists, and mathematicians assembled in late 2018 at the Epilepsy Foundation My Brain Map Innovation Institute Workshop intended to facilitate bringing together different perspectives in these early days of network modeling. Major conclusions from this workshop included (1) large curated data sets from multiple institutions are required to validate computational network models, (2) interdisciplinary approaches will facilitate advancing the field, and (3) for clinicians to understand and incorporate network analyses as clinical decision-making tools (for surgery, neurostimulation, or other activities) we need visualization tools that are ergonomic, intuitive to clinicians, and recommend an action for the clinician to take. Therefore, clinical tools to visualize the results of network based analyses will be key for successful clinical implementation.
Acknowledgments
The authors would like to acknowledge the participants in the 2018 Epilepsy Foundation My Brain Map Innovation Institute Workshop including the workshop chairs and planning committee: Brandy E. Fureman, PhD, Jacqueline A. French, MD, Viktor K. Jirsa, PhD, Sonya B. Dumanis, PhD, and Catherine A. Schevon, MD, PhD.
Declaration of Conflicting Interests: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding: The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: KAD is supported by NIH R01 NS116504, R01 NS110347, and R01 NS113366; VKJ is supported by European Union’s Horizon 2020 research and innovation program under Grant Agreement Number 945539 (SGA3) Human Brain Project, and the Recherche Hospitalo-Universitaire EPINOV (Grant ANR-17-RHUS-0004) funded by the “Investissements d’Avenir” French Government program managed by the French National Research Agency (ANR); CAS is supported by NIH R01 NS084142 and R01 NS110669.
- Focal epilepsy syndromes prominently feature network interactions between sites in multiple lobes of the brain.
- Multiscale analyses conducted simultaneously at the cellular, local and brain network level are essential for the discovery of seizure origination, spread, and termination mechanisms.
- Network models guide development of patient-specific surgical interventions.
ORCID iDs
Kathryn A. Davis https://orcid.org/0000-0002-7020-6480
Catherine A. Schevon https://orcid.org/0000-0002-4485-7933
References
- 1.Spencer SS. Neural networks in human epilepsy: evidence of and implications for treatment. Epilepsia. 2002;43(3):219–227. [DOI] [PubMed] [Google Scholar]
- 2.Petkoski S, Palva JM, Jirsa VK. Phase-lags in large scale brain synchronization: methodological considerations and in-silico analysis. PLoS Comput Biol. 2018;14(7):doi:10.1371/journal.pcbi.1006160 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 3.Luo C, Qiu C, Guo Z, et al. Disrupted functional brain connectivity in partial epilepsy: a resting-state fMRI study. PLoS One. 2012;7(1). Sporns O. (editor). doi:10.1371/journal.pone.0028196 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 4.Morgan VL, Rogers BP, Sonmezturk HH, Gore JC, Abou-Khalil B. Cross hippocampal influence in mesial temporal lobe epilepsy measured with high temporal resolution functional magnetic resonance imaging. Epilepsia. 2011;52(9):1741–1749. doi:10.1111/j.1528-1167.2011.03196.x [DOI] [PMC free article] [PubMed] [Google Scholar]
- 5.Morgan VL, Conrad BN, Abou-Khalil B, Rogers BP, Kang H. Increasing structural atrophy and functional isolation of the temporal lobe with duration of disease in temporal lobe epilepsy. Epilepsy Res. 2015;110:171–178. doi:10.1016/j.eplepsyres.2014.12.006 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 6.Zaveri HP, Pincus SM, Goncharova II, Duckrow RB, Spencer DD, Spencer SS. Localization-related epilepsy exhibits significant connectivity away from the seizure-onset area. NeuroReport. 2009;20(9):891–895. doi:10.1097/WNR.0b013e32832c78e0 [DOI] [PubMed] [Google Scholar]
- 7.Englot DJ, Hinkley LB, Kort NS, et al. Global and regional functional connectivity maps of neural oscillations in focal epilepsy. Brain. 2015;138(8):2249–2262. doi:10.1093/brain/awv130 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 8.Englot DJ, Konrad PE, Morgan VL. Regional and global connectivity disturbances in focal epilepsy, related neurocognitive sequelae, and potential mechanistic underpinnings. Epilepsia. 2016;57(10):1546–1557. doi:10.1111/epi.13510 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 9.Kramer MA, Cash SS. Epilepsy as a disorder of cortical network organization. Neuroscientist. 2012;18(4):360–372. doi:10.1177/1073858411422754 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 10.Scott RC, Menendez de la Prida L, Mahoney JM, Kobow K, Sankar R, de Curtis M.WONOEP appraisal: the many facets of epilepsy networks. Epilepsia. 2018;59(8):1475–1483. doi:10.1111/epi.14503 [DOI] [PubMed] [Google Scholar]
- 11.Richardson MP. Large scale brain models of epilepsy: dynamics meets connectomics. J Neurol Neurosurg Psychiatry. 2012;83(12):1238–1248. doi:10.1136/jnnp-2011-301944 [DOI] [PubMed] [Google Scholar]
- 12.van Diessen E, Diederen SJH, Braun KPJ, Jansen FE, Stam CJ. Functional and structural brain networks in epilepsy: what have we learned? Epilepsia. 2013;54(11):1855–1865. doi:10.1111/epi.12350 [DOI] [PubMed] [Google Scholar]
- 13.Markram H. The blue brain project. Nat Rev Neurosci. 2006;7(2):153–160. doi:10.1038/nrn1848 [DOI] [PubMed] [Google Scholar]
- 14.Jirsa VK, Proix T, Perdikis D, et al. The virtual epileptic patient: individualized whole-brain models of epilepsy spread. NeuroImage. 2017;145(Pt B):377–388. doi:10.1016/j.neuroimage.2016.04.049 [DOI] [PubMed] [Google Scholar]
- 15.Khambhati AN, Davis KA, Lucas TH, Litt B, Bassett DS. Virtual cortical resection reveals push-pull network control preceding seizure evolution. Neuron. 2016;91(5):1170–1182. doi:10.1016/j.neuron.2016.07.039 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 16.Wang Y, Trevelyan AJ, Valentin A, Alarcon G, Taylor PN, Kaiser M. Mechanisms underlying different onset patterns of focal seizures. PLoS Comput Biol. 2017;13(5). doi:10.1371/journal.pcbi.1005475 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 17.Liou J-Y, Ma H, Wenzel M, et al. Role of inhibitory control in modulating focal seizure spread. Brain. 2018;141(7):2083–2097. doi:10.1093/brain/awy116 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 18.Liou J-Y, Smith EH, Bateman LM, et al. A model for focal seizure onset, propagation, evolution, and progression. Elife. 2020;9. doi:10.7554/eLife.50927 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 19.Hashemi M, Vattikonda AN, Sip V, et al. The Bayesian virtual epileptic patient: a probabilistic framework designed to infer the spatial map of epileptogenicity in a personalized large-scale brain model of epilepsy spread. NeuroImage. 2020;217. doi:10.1016/j.neuroimage.2020.116839 [DOI] [PubMed] [Google Scholar]
- 20.Proix T, Jirsa VK, Bartolomei F, Guye M, Truccolo W. Predicting the spatiotemporal diversity of seizure propagation and termination in human focal epilepsy. Nat Commun. 2018;9(1):1088. doi:10.1038/s41467-018-02973-y [DOI] [PMC free article] [PubMed] [Google Scholar]
- 21.Saggio ML, Crisp D, Scott JM, et al. A taxonomy of seizure dynamotypes. Elife. 2020;9. doi:10.7554/eLife.55632 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 22.Wendling F, Benquet P, Bartolomei F, Jirsa V. Computational models of epileptiform activity. J Neurosci Methods. 2016;260:233–251. doi:10.1016/j.jneumeth.2015.03.027 [DOI] [PubMed] [Google Scholar]
- 23.Goodfellow M, Rummel C, Abela E, Richardson MP, Schindler K, Terry JR. Estimation of brain network ictogenicity predicts outcome from epilepsy surgery. Sci Rep 2016;6(1). doi:10.1038/srep29215 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 24.Sinha N, Dauwels J, Kaiser M, et al. Predicting neurosurgical outcomes in focal epilepsy patients using computational modelling. Brain. 2017;140(2):319–332. doi:10.1093/brain/aww299 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 25.de Tisi J, Bell GS, Peacock JL, et al. The long-term outcome of adult epilepsy surgery, patterns of seizure remission, and relapse: a cohort study. Lancet. 2011;378(9800):1388–1395. doi:10.1016/S0140-6736(11)60890-8 [DOI] [PubMed] [Google Scholar]
- 26.Weiss SA, Lemesiou A, Connors R, et al. Seizure localization using ictal phase-locked high gamma: a retrospective surgical outcome study. Neurology. 2015;84(23):2320–2328. doi:10.1212/WNL.0000000000001656 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 27.Spencer DD, Gerrard JL, Zaveri HP. The roles of surgery and technology in understanding focal epilepsy and its comorbidities. Lancet Neurol. 2018;17(4):373–382. doi:10.1016/S1474-4422(18)30031-0 [DOI] [PubMed] [Google Scholar]
- 28.Wang Y, Goodfellow M, Taylor PN, Baier G. Dynamic mechanisms of neocortical focal seizure onset. PLoS Comput Biol. 2014;10(8). doi:10.1371/journal.pcbi.1003787 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 29.Morgan VL, Abou-Khalil B, Rogers BP. Evolution of functional connectivity of brain networks and their dynamic interaction in temporal lobe epilepsy. Brain Connect. 2015;5(1):35–44. doi:10.1089/brain.2014.0251 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 30.Shah P, Bassett DS, Wisse LEM, et al. Mapping the structural and functional network architecture of the medial temporal lobe using 7 T MRI. Hum Brain Mapp. 2018;39(2):851–865. doi:10.1002/hbm.23887 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 31.Sinha N, Wang Y, de Silva NM, et al. Node abnormality load predicts chances of seizure recurrence after epilepsy surgery. Neurology. 2020;96;e758–e771. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 32.Sinha N, Wang Y, Moreira da Silva N, et al. Structural brain network abnormalities and the probability of seizure recurrence after epilepsy surgery. Neurology. 2021;96(5):e758–e771. doi:10.1212/WNL.0000000000011315 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 33.Shah P, Ashourvan A, Mikhail F, et al. Local structural connectivity directs seizure spread in focal epilepsy. Brain. 2019;142:1955–1972. doi:10.1101/406793 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 34.Montgomery MK, Kim SH, Dovas A, et al. Glioma-induced alterations in neuronal activity and neurovascular coupling during disease progression. Cell Rep. 2020;31(2):107500. doi:10.1016/j.celrep.2020.03.064 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 35.Paz JT, Davidson TJ, Frechette ES, et al. Closed-loop optogenetic control of thalamus as a tool for interrupting seizures after cortical injury. Nature Neurosci. 2012;16(1):64–70. doi:10.1038/nn.3269 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 36.Krook-Magnuson E, Armstrong C, Oijala M, Soltesz I. On-demand optogenetic control of spontaneous seizures in temporal lobe epilepsy. Nat Commun. 2013;4(1):1376. doi:10.1038/ncomms2376 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 37.Krook-Magnuson E, Szabo GG, Armstrong C, Oijala M, Soltesz I. Cerebellar directed optogenetic intervention inhibits spontaneous hippocampal seizures in a mouse model of temporal lobe epilepsy. eNeuro. 2014;1(1). doi:10.1523/ENEURO.0005-14.2014 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 38.Streng ML, Krook-Magnuson E. Excitation, but not inhibition, of the fastigial nucleus provides powerful control over temporal lobe seizures. J Physiol. 2020;598(1):171–187. doi: 10.1113/JP278747 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 39.Schevon CA, Weiss SA, McKhann G, et al. Evidence of an inhibitory restraint of seizure activity in humans. Nat Commun. 2012;3(1):1–11. doi:10.1038/ncomms2056 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 40.Weiss SA, Banks GP, McKhann GM, et al. Ictal high frequency oscillations distinguish two types of seizure territories in humans. Brain. 2013;136(pt 12):3796–3808. doi:10.1093/brain/awt276 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 41.Smith EH, Liou J, Davis TS, et al. The ictal wavefront is the spatiotemporal source of discharges during spontaneous human seizures. Nat Communs. 2016;7:11098. doi:10.1038/ncomms11098 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 42.Diamond JM, Diamond BE, Trotta MS, Dembny K, Inati SK, Zaghloul KA. Traveling waves reveal a dynamic seizure source in human focal epilepsy [Published online March 9, 2021]. Brain. 2021. doi:10.1093/brain/awab089 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 43.Eissa TL, Dijkstra K, Brune C, et al. Cross-scale effects of neural interactions during human neocortical seizure activity. PNAS. 2017;114(40):10761–10766. doi:10.1073/pnas.1702490114 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 44.Tryba AK, Merricks EM, Lee S, et al. Role of paroxysmal depolarization in focal seizure activity. J Neurophysiol. 2019;122(5):1861–1873. doi:10.1152/jn.00392.2019 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 45.Truccolo W, Donoghue JA, Hochberg LR, et al. Single-neuron dynamics in human focal epilepsy. Nat Neurosci. 2011;14(5):635–641. doi:10.1038/nn.2782 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 46.Bower MR, Buckmaster PS. Changes in granule cell firing rates precede locally recorded spontaneous seizures by minutes in an animal model of temporal lobe epilepsy. J Neurophysiol. 2008;99(5):2431–2442. doi:10.1152/jn.01369.2007 [DOI] [PubMed] [Google Scholar]
- 47.Tobochnik S, Bateman LM, Akman CI, et al. Tracking multisite seizure propagation using ictal high-gamma activity. J Clin Neurophysiol. 2021. doi:10.1097/WNP.0000000000000833 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 48.MacArthur BD, Sánchez-García RJ, Anderson JW. Symmetry in complex networks. Discret Appl Math. 2008;156(18):3525–3531. doi:10.1016/J.DAM.2008.04.008 [Google Scholar]
- 49.Liu Y-Y, Barabási A-L. Control principles of complex systems. RMP. 2016;88(3). doi:10.1103/RevModPhys.88.035006 [Google Scholar]