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Dynamic network drivers of seizure generation,propagation and termination in human epilepsyAnkit N. Khambhati ∗ †, Brian Litt ∗ † ‡, and Danielle S. Bassett ∗ † §

∗Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA,†Penn Center for Neuroengineering and Therapeutics, University ofPennsylvania, Philadelphia, PA 19104, USA,‡Department of Neurology, Hospital of the University of Pennsylvania, Philadelphia, PA 19104, USA, and §Department ofElectrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA

Submitted to Proceedings of the National Academy of Sciences of the United States of America

Drug-resistant epilepsy is traditionally characterized b y patho-logic cortical tissue comprised of seizure-initiating ‘fo ci’. These‘foci’ are thought to be embedded within an epileptic networ kwhose functional architecture dynamically reorganizes du ringseizures through synchronous and asynchronous neurophysi o-logic processes. Critical to understanding these dynamics is iden-tifying the synchronous connections that link foci to surro undingtissue and investigating how these connections facilitate seizuregeneration and termination. We use intracranial recording s fromneocortical epilepsy patients undergoing pre-surgical ev aluationto analyze functional connectivity before and during seizu res. Wedevelop and apply a novel technique to track network reconfig u-ration in time and to parse these reconfiguration dynamics in todistinct seizure states, each characterized by unique patt erns ofnetwork connections that differ in their strength and topog ra-phy. Our approach suggests that seizures are generated whenthe synchronous relationships that isolate seizure ‘foci’ from thesurrounding epileptic network are broken down. As seizuresprogress, foci reappear as isolated subnetworks, marking a shiftin network state that may aid seizure termination. Collecti vely, ourobservations have important theoretical implications for under-standing the spatial involvement of distributed cortical s tructuresin the dynamics of seizure generation, propagation and term ina-tion, and have practical significance in determining which c ircuitsto modulate with implantable devices.

epileptic networks | seizure focus | network state | synchrony | graphtheory | community detection | dynamic network neuroscience

Abbreviations: ECoG, electrocorticography

Significance Statement. Localization-related epilepsy affects≈80%of epilepsy patients and is often resistant to medication. The chal-lenge for treating patients is mapping dynamic connectivity betweencortical structures in the epileptic network during seizures. Whileit is well known that whole-brain functional architecture reconfig-ures during tasks, we hypothesize that epileptic networks recon-figure at the meso-scale leading to seizure initiation, propagation,and termination. We develop new methods to track dynamic net-work reconfiguration amongst connections of different strength asseizures evolve. Our results indicate that seizure onset isprimar-ily driven by the breakdown of strong connections that re-surge inan isolated focal sub-network as seizures transition to termination.These findings have practical implications for targeting specific con-nections with implantable, therapeutic devices to controlseizures.

L ocalization-related epilepsy is traditionally characterized byseizures that arise from one or more abnormal islands of cor-

tical tissue in the neocortex or mesial temporal structures, such ashippocampus [1]. In more severe cases, seizures with focal onsetsecondarily generalize, as pathologic activity spreads across the brain[2]. Localization-related epilepsy represents≈80% of epilepsy casesand is often resistant to medication [3]. For drug-resistant patients,the only treatment options are implantable devices, or moretradition-ally resective surgery to remove enough cortical tissue in the epilepticnetwork to decrease seizure frequency, while preserving brain tissueresponsible for eloquent function. In surgical cases wherediscrete

lesions associated with seizure onset (‘foci’) are not evident on brainMRI, only ≈40% remain seizure-free post-surgery [3]. The modestoutcome associated with these procedures has lead investigators tofurther explore spatial distributions of epileptic activity using mul-tiscale neural signals in ECoG and sub-millimeterµECoG to moreaccurately localize where seizures start and how their pathologic ac-tivity spreads [4, 5, 6, 7, 8, 9]. These approaches have spurred aparadigm shift from localizing epileptic ‘foci’ towards mapping theepileptic network and identifying key regions for intervention.

In a broad sense “functional networks” describe time-dependentcommunication pathways between neural populations. They can bemeasured by metrics that establish statistical relationships betweensensor dynamics. In this framework sensors (nodes) that exhibita significant degree of synchrony are considered functionally con-nected. The notion of an epileptic network stems from the ideathat pathologic synchrony manifests as disruptions in neural func-tion: rhythmic motor activity, altered cognition, or abnormal sensa-tion. While seizures were originally thought to be limited to burstsof hypersynchrony (strong connections between nodes), recent workdemonstrates that seizures are characterized by more complex tem-poral dynamics demonstrating synchrony and asynchrony in tandem[10, 11, 12, 13, 14].

Clinical epileptologists and translational researchers are anx-ious to employ these methods to answer pressing clinical questions:Where do seizures start? Can the epileptic network be modulatedtherapeutically? What can these methods reveal about the underlyingneurophysiologic mechanisms? Answering these questions requiresthe ability to track time-dependent functional connections [15] andto study the geometry of epileptic networks as seizure-generating re-gions interact with the surrounding cortex. Such a capability is vital,because epileptogenic regions cause symptoms not only through theirown dysfunction, but also through their ability to recruit and disruptnormal brain regions.

Based on the complexity of seizure dynamics, we hypothesizethat network reconfiguration explains how seizures begin, spatiallyprogress and self-terminate. In this view, epileptic network recon-figuration forms a causal prediction of activity, rather than a post-hoc description. Our hypothesis is informed by recent work demon-strating that human brain networks dynamically reconfigureprior tochanges in behavior [16, 17]. These reconfigurations can be char-acterized by variations in strong (synchronous) and weak (asyn-chronous) connections, which have been proposed in prior work to

Reserved for Publication Footnotes

www.pnas.org/cgi/doi/10.1073/pnas.0709640104 PNAS Issue Date Volume Issue Number 1–8

Fig. 1. Schematic of Analysis Pipeline for Dynamic Epileptic Networks.(A) (Top) We create functional networks based on electrophysiology by windowingECoG signals collected from patients with medically refractory epilepsy implantedwith intracranial electrodes into 1s time windows. Each sensor is representedas a network node, and weighted functional connectivity between sensors, inter-preted as degree of synchrony, is represented as a network connection. (LowerRight) Functional connectivity is estimated by a magnitude cross-correlation be-tween sensor time series for each time window; non-significant connections areidentified via comparison to surrogate data [20] and removed (see Materials andMethods). (Lower Left) We visualize the resultant data as a connection-by-timematrix that represents all connection weights for all 1s time windows. (B) Foreach seizure, we form a dynamic seizure network from the set of time windowsthat range from the earliest electrographic change characterizing seizure onset[21] to the seizure termination point. Similarly, we form a dynamic pre-seizurenetwork from a set of time windows extracted directly prior to seizure onset. Timewindow size in both epileptic and pre-seizure networks are identical.

support different network functions [18, 19]. We hypothesize that theepileptic network can be characterized by strong connections repre-senting primary propagation pathways, and weak connections thatinitiate seizure onset; these two populations uniquely define the to-pographical extent and propagation dynamics of seizures.

ResultsTo address these hypotheses, we examined ECoG sensor-levelactiv-ity prior to and during seizure epochs. We assessed sensor-sensorfunctional connectivity by constructing dynamic network represen-tations from independent time windows of data (Fig. 1A) for bothseizure and pre-seizure periods (Fig. 1B). In each 1s time window ofECoG data, the sensors were represented as network nodes andinter-sensor magnitude cross-correlations, or synchrony, were representedas weighted network connections.

Functional Network Architecture Reveals Distinct Seizure States.Do functional connectivity patterns change as a seizure progresses?To answer this question, we developed a new method to uncovernet-

work states, defined by unique patterns of sensor-sensor functionalconnectivity betweenT time windows (Fig. 2). We summarizedthe time-dependent fluctuations in connectivity between all sensorsin a configuration matrix (seeMaterials and Methods). To quan-tify similarity in gross network connectivity between timewindows,we calculated the Pearson correlation between pairs of timewin-dows from the configuration matrix, thereby forming a symmetricT × T configuration-similarity matrix (seeMaterials and Methods).We cluster the configuration-similarity matrix to group time win-dows with similar network connectivity patterns into distinct networkstates, which we discuss below.

To test for distinct network states across seizure epochs, we usedan unsupervised network clustering approach known as communitydetection. This detection method maximizes a modularity qualityfunctionQ obtained from the configuration-similarity matrix (Fig. 2;for details, seeMaterials and Methods). When applied to individualseizure epochs from each patient, this procedure revealed “configu-ration communities.” Each community was composed of a groupoftime windows with similar network configurations, and therefore cor-responded to a unique brain state (Fig. 3A). The number of commu-nities in pre-seizure networks and seizure networks were not statisti-cally different (N = 25, T = 0.50, P ≈ 0.62) (Fig. 3B). However,seizure communities were less randomly distributed in time, indi-cating that they captured meaningful temporal structure (seeSI formeasuring temporal dispersion). Seizure networks tended to display3 large communities (seeSI for distilling communities); which we re-fer to asstart, middleandendcommunities, based on their temporalplacement in the seizure (Fig. 3C).

Next we asked whether clustered network configurations withinthese three seizure states were distinct or whether certainpairs ofstates shared more or less similarity than other pairs of states. Toaddress the question of state separability, we calculated the correla-tion between connectivity patterns of different time windows from

Fig. 2. Identifying Network Configuration States. (First) We constructdynamic functional networks; colors represent arbitrary connection strengths.(Second) We track functional connectivity over time using a connection-by-timematrix, or ‘configuration matrix’, that represents the set of connection weightsfor each 1s time window. (Third) We compute a Pearson correlation betweenall possible pairs of time windows to construct a configuration-similarity matrix;colors represent the magnitude of similarity and visually identified clusters aredistinguished by colored, dashed lines. (Fourth) We apply community detec-tion to the configuration-similarity matrix to extract clusters of time windows withsimilar network configurations; colors represent assignments of time windows todifferent network configuration communities.

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Fig. 3. Distinct States of Dynamic Epileptic Networks.(A) Example assignments of sensors to network configuration communities (seizure states) demonstratingnetwork reconfiguration. Assignments are overlaid on a subset of representative ECoG grids during an entire seizure. (B) Number of communities in pre-seizure(gray) and seizure (blue) epochs; t-test (N = 25, t = 0.50, p ≈ 0.62). (C) Distribution of community assignments to temporal time windows for seizure epochs; wenormalize all seizure lengths to 1. (D) Average separation of the start and endcommunities from the middlecommunity compared to separation between start andendover seizure population—connection strengths averaged between all nodes of each community; t-test (N = 21, t = 3.40, p < 0.005).

the configuration matrix, in which each time window was assigned adifferent configuration community. We found that connectivity pat-terns instart andendcommunities were less similar to one another,on average (Fig. 3D). In contrast, connectivity patterns inthe mid-dlecommunity were more similar to bothstartandendcommunities,suggesting that themiddlecommunity plays an intermediary role asa transition state.

Seizure States Display Stereotyped Connectivity. In the previoussection, we observed that seizures progress through distinct statescharacterized by different patterns of sensor-sensor functional con-nectivity. To understand how these patterns differ, we useda two-pronged approach, examining (i) the average and (ii) the distribu-tion of functional connectivity in each time window as a function ofseizure state (Fig. 4). The mean functional connectivity (averagedover all pairs of sensors and over all time windows in a community)increased as the seizure progressed through the 3 states (Fig. 4A),

indicating that the gross epileptic network becomes increasingly syn-chronized.

To investigate the distribution of connection strengths, we sepa-rately trackedstrongandweakconnections through each epoch, de-fined as the 10% largest valued and 10% smallest valued connectionsin each community, respectively. To measure the balance betweenthese connections in each state, we defined a balance indexB (seeMaterials and Methods): values approaching+1 indicate that mostconnections are strong while values close to−1 indicate that mostconnections are weak. Pre-seizure epochs exhibited a balance ofconnection type (Fig. 4B). In seizure epochs, thestart communitywas dominated by weak connections, while theendcommunity wasdominated by strong connections. Themiddlecommunity displayeda large variance in the balance index over seizures, consistent with itsputative role as a transition state betweenstartandendcommunities.These results suggest that a finer examination of network geometryin themiddlecommunity might help to explain how brain networkstransition through seizure states.

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Anatomical Structure of Dynamic Epileptic Networks. In the pre-ceding analyses, we demonstrated that seizures progress through dis-tinct states characterized by different network geometries (patternsof weighted connections). However, whether these reconfigurationsare spatially localized or distributed, and how they relateto seizurefoci, was unclear. To address these questions, we leveragedroutineclinical procedures: A team of neurologists identified the sensors onthe seizure onset zone based on visual inspection of the intracra-nial recordings. We used this information to map connections ineach seizure state to physical electrode locations in stereotaxic space.Throughout pre-seizure and seizure epochs, we observed that clustersof strongconnections lay in close proximity to seizure onset sensors(Fig. 5A).

To quantify this observation and examine its role in seizureprop-agation, we delineated the following three topographical connectionswithin the seizure network: (i) inside the seizure onset zone, (ii) out-side the seizure onset zone, and (iii) between seizure onsetsensorsand all other sensors. We performed a two-way analysis of variance(ANOVA) with location and community as categorical factorsandthe balance index,B, as dependent variable (Fig. 5B). Significantmain effects of location (F = 32.02, df = 2, p ≈ 5 × 10−13)and community (F = 55.40, df = 3, p ≈ 4 × 10−27) indicatedthat anatomical substrates of the epileptic network and temporal stateplay distinct roles in dynamic functional connectivity patterns. Wedid not observe a significant interaction effect (F = 0.86, df = 6,p ≈ 0.52). During pre-seizure epochs, sensors in the seizure on-set zone predominantly displayed strong connections, while sensorsin the surrounding epileptogenic cortex displayed weak connections.Strong connections increased fromstart to middlestates within theseizure onset zone, and between the seizure onset zone and surround-ing epileptogenic cortex. In contrast, strong connectionslinking sen-sors in the surrounding epileptogenic cortex did not increase until theendstate. This pattern of results is consistent with a propagation ofstrong connectivity beginning in the seizure onset zone andemanat-ing to the surrounding cortex towards the end of the seizure.

The change in anatomical location of synchronous activity sug-gests that connections change in physical length throughout theseizure. We observed that weak connections tended to be relativelylong, and remained approximately unchanged in length in thepre-seizure and seizure epochs (Fig. 5C). In contrast, strong connectionstended to be relatively short. The length of strong connections in thestart andmiddlestates was shorter than in the pre-seizure state, sug-gesting a more anatomically focal distribution at seizure onset. Asthe seizure progressed frommiddleto endstates, strong connectionsgrew longer, suggesting a broadening of the anatomical distributionof functional coordination consistent with widespread synchroniza-tion.

DiscussionEpileptic Network Reconfiguration. Intuitively, complex reconfigu-ration of functional brain networks can accompany changes in cog-nitive state or changes in behavior. Prior fMRI studies haveexploredsuch reconfiguration in whole-brain networks constructed from dataacquired during motor skill learning [16] and as task stateschange[22], and in networks impacted by stroke [23, 24]. In contrast, herewe explore the reconfiguration of a local area and use high resolutionECoG data to map the fine-scale temporal dynamics of reconfigu-ration processes. Our approach differs from the conventional one,focused on tracking changes in sensor signals, irrespective of inter-sensor relationships. The dynamic network framework we imposeallows us to study time-dependent changes in connectivity betweensensors through similarities in signal statistics.

In this study, we developed and exercised a novel method fordistinguishing brain states based on differences in time-dependentfunctional network configurations. We applied our technique to a setof human ECoG recordings, and extracted network dynamics dur-

ing seizure and pre-seizure epochs. We found that seizures most of-ten exhibit three stereotyped network configurations and that theseconfigurations correspond to the start, middle and end of a seizure.These data-derived states may provide a fundamental neurophysio-logical explanation for the neurologically-defined onset,propagationand termination states ubiquitous in clinical descriptions. However,the mechanisms supporting these 3 states differ significantly in thetwo definitions. Clinically, seizure propagation is believed to involvethe spreading of pathologic spiking activity outside of a seizure fo-cus [2] followed by aspontaneousshift towards seizure termination.Our results paint a different picture: the middle configuration state,clinically thought to be the seizure propagation stage, plays more of atransitional role that initiates and guides seizure termination bygrad-ually integrating the surrounding neocortex with the seizure onsetzone through strong, synchronous, connections.

Connectivity Imbalance. Our analytical approach utilizes thestrength of functional connections to characterize them as“strong”(synchronous) or “weak” (asynchronous), rather than simply statingthat two sensors are functionally “connected” or “not connected”.Mathematically, this focus corresponds to a study of network ge-ometryas opposed to networktopology. A primary advantage ofthe weighted network approach is the ability to separate connec-tions into classes that differ in strength. Evidence suggests thatstrong and weak connections play different roles in supporting cog-nitive function [25, 19]. Strong connections have traditionally beenthought to represent primary communication pathways between brainareas. However, recent work demonstrates that weak connectionssupport increased network efficiency and may play a large role indistinguishing pathologic [26] and healthy [27, 19] network states.From a dynamical perspective, strong connections may be those thatare engaged consistently throughout neurophysiological processes,whereas weak connections may be engaged transiently to enable tran-sitions of the brain between distinct states.

Prior work has speculated that weak connections present in themiddle of a seizure [11, 13]. However, we believe a more accurateway to address this hypothesis is to consider the strength offunc-tional connections. Using a weighted connectivity approach, we findthat connections in epileptic networks are much weaker at the startand middle of seizures, compared to pre-seizure periods, suggestingthat a distributed profile of weak connectivity accompaniesseizure

Fig. 4. Network Geometry of Seizure States. (A) Distribution of connec-tion strengths over seizure population—connections strengths averaged over alltime windows within each community compared to pre-seizure epoch; one-wayANOVA (N = 21, df = 3, F = 3.41, p < 0.05). (B) Distribution of thefraction of strong to weak connections over seizure population—B within eachcommunity compared to pre-seizure epoch; one-way ANOVA (N = 21, df = 3,F = 25, p < 1 × 10−13). Strong (weak) connections were determined sep-arately for each epoch based on the top (bottom) 10% of the connection weightdistribution. See Materials and Methodsfor a formal definition of B.

4 www.pnas.org/cgi/doi/10.1073/pnas.0709640104 Footline Author

onset. These data-driven findings challenge the conventional clinicalview that seizure onset is characterized predominantly by increasedsynchronization. In contrast, the weak connectivity that we observeat seizure onset may represent an inability of surrounding epilepto-genic cortex to quarantine seizure initiation in the seizure onset zone.

In contrast to the start of the seizure, the middle of the seizure dis-plays a large variability over subjects, with some seizuresdisplayingrelatively weak connectivity and others displaying relatively strongconnectivity. We speculate that the disparity in dominant connectiontype during the middle of the seizure can be described by mixed ex-pression of connectivity patterns from the start and end of the seizure.This explanation is corroborated by our finding that networkconfigu-rations in the start and end of the seizure, which are weak andstrongtype dominant respectively, are statistically similar to configurationsin the middle of the seizure. It follows that reconfigurationduringthe middle of the seizure allows the epileptic network to purge weak,asynchronous, connections from the start of the seizure andto mobi-lize strong, synchronous, connections in a transition to the end of theseizure.

Functional Incorporation of Seizure Onset Sub-Network. Whiletemporal network structure provides rich information regarding

Fig. 5. Dynamics of Network Geometry. (A) Example of network geometrywith preserved 2-D spatial relationships between nodes for categories of weak(< 10%), medium(10-90%) and strong (> 90%) connections; topographicmap represents mean connection strength within a seizure community or pre-seizure epoch. The clinically-determined seizure onset sensors are shown inred. (B) Population average balance index, B, for three connection locations(within seizure-onset zone, outside seizure-onset zone, and between seizure-onset zone and other sensors) across epochs and communities. (C) Physicallength of connections in a large 8x8 grid, normalized to one for longest possi-ble connection, averaged over connections and seizures for each configurationcommunity. Error bars indicate standard error of the mean over seizures.

seizure states, it does not directly provide information regarding thespatial processes involved in seizure dynamics. We therefore comple-mented the temporal network approach by incorporating informationabout sensor location in Euclidean space and sensor role either withinor outside the seizure onset zone. Our results demonstrate that theseadditional spatial features provide new insights into potential neu-rophysiological mechanisms involved in seizure initiation, and mayinform the development of clinical tools for objectively isolating theseizure onset zone directly from seizure or pre-seizure data.

Prior work has demonstrated the presence of low synchroniza-tion between seizure-generating regions and non-seizure generatingregions in epochs at least 2 hours prior to seizure start [28]. However,the temporal dynamics and geometrical roles of these two sets of ar-eas has remained elusive. Our results elucidate the role played byseizure-onset regions during seizures and the accompanying recruit-ment of the surrounding epileptic network during termination. Clearisolation of the onset zone exists in pre-seizure periods, suggestingthe potential to identify foci, niduses of seizure generation, withinthe network from inter-ictal data. Critically, this isolation of the on-set zone diminishes at seizure initiation. As the network transitionsinto the middle state, we observe a resurgence of strong connectionswithin the onset zone, consistent with pre-seizure periods. These re-sults lead us to posit that the incorporation of the onset zone under-lies a shift from seizure initiation to termination that then requiresrecruitment of surrounding epileptogenic cortex. The similarity ofconnection strength and spatial location in pre-seizure and middleseizure states suggests a mechanistic role for functional connectivityin subduing seizure onset.

Network Tightening During Seizures. Our observation that strongconnections are typically short and weak connections are typicallylong, is consistent with results from two lines of research:(i) func-tional studies in healthy individuals that utilize other imaging modal-ities such as fMRI [19] and (ii) structural connectivity studies in non-human primates that utilize tract tracing techniques [18].The lengthof strong connections decreases from the pre-seizure period to themiddle of the seizure, suggesting that strong connections are physi-cally tightening, perhaps into more functionally cohesiveportions ofcortex, before the seizure begins terminating. We speculate that thetightening of strong connections to a localized sub-network mightact as a control mechanism to quench disruptive network activity thatmay have built-up over many hours prior to the seizure through in-creasing frequency of epileptiform discharges [21]. Giventhis expla-nation we theorize that seizures are a neurophysiologic mechanism torelieve a build-up of pathologic activity, akin to a rubber band recoil-ing after having stretched too far. This process occurs in three-stageswhere: (i) seizure-initiation invokes network reconfiguration that, (ii)enables strong connections to tighten and quench pathologic activityas seizures progress, (iii) the tightening spearheads a second reor-ganization event that synchronizes surrounding weak connections inorder to stop the mechanism.

Clinical Impact and Future Work. We have seen that the dynami-cal processes that propel epileptogenic networks into seizures can becomplex and are poorly understood. Yet, clinicians rely on visualinspection to describe spatial and temporal properties of seizures.The lack of standardized clinical measures to mark epileptic eventscalls for the development of automated methods. The networkanal-ysis tools we have built, while generally applicable to any dynamicnetwork, can parse seizure states, localize driver ‘foci’ of seizures,and characterize how seizures terminate. This interpretation can betranslated into useful clinical tools to identify dysfunctional anatom-ical regions that drive the epileptic network and may be particularlyamenable to local interventions, such as surgery or device placement.Of interest, seizure driving ‘foci’ were equally present inthe half ofour study patients who did not have focal lesions on brain imaging,compared to those patients with lesions demonstrated on MRI. We

Footline Author PNAS Issue Date Volume Issue Number 5

plan a more detailed study in the future to correlate mappingof theseseizure-driving regions with brain resection and outcome.

Currently, our tools employ community detection techniques toidentify gross changes in the meso-scale architecture of networkstructure across time. The observed meso-scale reconfiguration pro-cesses may be accompanied by region-specific trends in reconfigu-ration between the epileptic network and surrounding healthy net-works. This work could potentially be used to address cellular mech-anisms by considering micro-scale reconfigurations. Recent studiessuggest that epileptic networks in the neocortex may be composedof distributed micro-domains on the scale of a few cortical columnsgenerating high frequency oscillations and micro-seizures that co-alesce in a network during seizure generation and termination [6].While of great interest, these studies are currently limited by thelack of appropriate implantable high resolution sensors capable ofcovering clinically relevant areas sufficiently to yield comprehensivehigh-resolution maps. Further development of dynamic communitydetection methods to identify and track reconfiguration within net-work sub-regions at both the meso and micro-scales may help de-lineate healthy and pathologic networks and uncover mechanisms ofnetwork recruitment.

An important clinical consideration related to this work istheimpact of sampling error inherent in any intracranial implantationprocedure on our results. Any technique used to map epileptic net-works, subdural electrode strips and grids, more distributed “StereoEEG” implantations, and combinations of these two approaches, usu-ally yield incomplete representations of epileptic networks. It is notpossible to fully record from the entirety of cortex in affected pa-tients. In some cases this might mean that neither seizure onset zonesnor all regions of seizure spread are fully delineated. Despite thisincomplete representation, the presence of three clear states definingseizures in each of the patients presented above, and their objectiveand independently determined relationship to the seizure onset zonesuggest that our findings are important and real. With further val-idation on a larger number of patients with both lesional andnon-lesional epilepsies, we hope to demonstrate the utility of our methodto define functional components of epileptic networks. We believethe method can be useful both in epilepsy surgery and for placing de-vices into regions that drive seizure initiation and termination. Wealso plan to use these methods to compare competing approachesfor localizing epileptic networks, such as subdural and stereo EEG.We hypothesize that each will have advantages in recording compo-nents of epileptic networks in different types of localization-relatedepilepsy.

Conclusion. We have found evidence supporting our hypothesis thatepileptic networks reconfigure through 3 different synchronous statesduring seizures: initiation, propagation, and termination. Gross, uni-form network connectivity preceding seizures was found to redis-tribute primarily as weak connections during seizure initiation andpropagation and strong connections during termination. This indi-cates that an imbalance of connectivity between strong and weak con-nection types plays a mechanistic role in seizure topography. Theseimbalances lead the epileptic network to assimilate the seizure-onsetzone into the surrounding tissue during the beginning of seizures andreassert its isolation as the seizure progresses. Finally,we found thatthese networks physically tighten strong connections intoa focal sub-network during seizures, suggesting a novel mechanism for seizuretermination.

Materials and MethodsSeven patients undergoing surgical treatment for medically refractory epilepsy be-lieved to be of neocortical origin underwent implantation of subdural electrodes tolocalize the seizure onset zone after noninvasive monitoring was indeterminate.De-identified patient data was retrieved from the online International EpilepsyElectrophysiology Portal (IEEG Portal); and all patients gave written informedconsent in accord with the University of Pennsylvania Institutional Review Board

for inclusion in this study [29]. ECoG signals were recorded and digitized at500 Hz sampling rate using Nicolet C64 amplifiers and pre-processed to elimi-nate line noise. Surface electrode (Ad Tech Medical Instruments, Racine, WI)configurations, determined by a multidisciplinary team of neurologists and neuro-surgeons, consisted of linear and two-dimensional arrays (2.3 mm diameter with10 mm inter-contact spacing) and sampled the neocortex for epileptic foci. Sig-nals were continuously recorded for the duration of a patient’s stay in the epilepsymonitoring unit. See Table S1 for demographic and clinical information.

We analyzed a total of twenty-five complex partial seizures, a subset ofwhich exhibited secondary generalization. We excluded simple, partial seizuresand seizures stemming from non-neocortical foci from this study. Seizure onsettime and localization were defined by the point of earliest electrographic change(EEC) and annotated and marked as a part of routine clinical workup [21]. ECoGsignal directly preceding each seizure and equal in duration to that seizure wasalso extracted for balanced comparison and labeled as pre-seizure.

Signals from each epoch were divided into1-second, non-overlapping, wide-sense stationary time-windows in accord with other studies [13]. To test the bias-ing effect of high-amplitude spiking on signal connectivity measurements we alsoinvestigated windows 0.5-seconds in duration to sample more of the non-biasingtemporal space and found similar results.

Dynamic functional networks were formed by applying a normalized cross-correlation similarity function ρ between the time series of two sensors in thesame time window using the formula

ρxy(k) = argmaxτ

E[(xk(t)− µxk)(yk(t+ τ )− µyk)] [ 1 ]

where x and y are signals from one of N sensors or network nodes, k isone of T non-overlapping, one-second time windows, and xk = yk = 0.The NxNxT similarity matrix ρxy was statistically thresholded in each time

window k using a two-step approach [20]. A surrogate distribution of similaritymatrices was constructed for Fourier phase-randomized versions of time seriesin each time window and used to compute two-tailed p-values for the significanceof the cross-correlation between every sensor pair. Finally, a false discovery rate(α = 0.05) technique was applied to each distribution of p-values to retainsignificant connection weights. The collection of significant, weighted dynamicconnections were stored in an NxNxT network adjacency matrix A (Fig. 1A).

Temporal changes in connectivity between nodes was tracked within indi-vidual epochs by determining modules of the configuration-similarity matrix. Weconstruct the configuration-similarity matrix by first unraveling A to a network

evolution matrix A describing the weights ofN(N− 1)

2 connections across

T time windows. Using a Pearson correlation similarity metric, we transform

A to a fully-connected TxT configuration state adjacency matrix S. The con-figuration adjacency matrix is partitioned into communities by maximizing themodularity index Q [30] using a Louvain-like locally greedy algorithm [31]. Weemployed a Newman-Girvan null model [32, 33] and adaptively determined anoptimal structural resolution parameter γ per seizure (see SI; and [20] for a moredetailed discussion of resolution parameters in modularity maximization). Weused a consensus partition method with 1000 optimizations per run until we ob-tained consistent community partitioning [34, 20]. The three largest communitiesfrom each seizure were selected for further analysis and re-labeled in order ofmedian temporal occurrence for population-level comparison.

Connections were classified as strongor weakbased on thresholds de-termined by the distribution of connection strengths for each epoch separatelyfor each seizure. The strong(weak) connections must be >90% (<10%) of allconnection strengths. Non-significant connections (disconnected) were excludedfrom the distribution and not categorized as weak. To measure the dominanceof strongor weakconnections, we defined the balance index as

B =Es −Ew

Es +Ew

[ 2 ]

where Es and Ew are the average number of strong and weak connectionsover possible connections and number of time windows.

Connection topography metrics were computed for only within-grid elec-trodes (configurations of 8× 8), ignoring all other non-grid electrodes such thatinter-electrode spacing in all analyses was kept constant. To measure the topo-graphical tightness of connections, we defined the normalized connection lengthL as the mean Euclidean distance of all connections scaled by the longest pos-sible distance between two nodes.

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ACKNOWLEDGMENTS. AK and BL acknowledge support from the National In-stitutes of Health through awards #R01-NS063039, #1U24 NS 63930-01A1, theCitizens United for Research in Epilepsy (CURE) through Julie’s Hope Award, andthe Mirowski Foundation. DSB acknowledges support from the Alfred P. Sloan

Foundation, the Army Research Laboratory through contract no. W911NF-10-2-0022 from the U.S. Army Research Office, the Institute for Translational Medicineand Therapeutics at Penn, and the National Science Foundation through award#BCS-1441502.

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Footline Author PNAS Issue Date Volume Issue Number 7

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Supporting Information for

Dynamic network drivers of seizure generation, propagation andtermination in human epilepsy

Ankit N. Khambhati1,2, Brian Litt1,2,3, Danielle S. Bassett1,2,4

1Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA2Penn Center for Neuroengineering and Therapeutics, University of Pennsylvania, Philadelphia, PA 19104, USA3Department of Neurology, Hospital of the University of Pennsylvania, Philadelphia, PA 19104, USA4Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA

1 Patient Demographics

Patient (IEEG Portal) Sex Age (Onset/Surgery) Etiology Seizure Type (N) ImagingI002_P002 M 3.5/20 Left frontal onset,

left cortical dysplasiaCPS+Gen (1) Lesional

I002_P003 M 2/36 Right temporal onset CPS+Gen (3) UnclearI002_P006 F 15/26 Symptomatic menin-

gitis,right temporal onset

CPS (1), CPS+Gen (4) Non-lesional

I002_P015 M <1/54 Left anterior tempo-ral onset

CPS (5) Lesional

I002_P016 F <1/22 Symptomatic menin-gitis,occipital lobe

CPS (3) Lesional

I002_P017 F 36/41 Cryptogenic left tem-poral lobe

CPS+Gen (6) Non-lesional

I002_P023 F 18/25 Left temporal lobe CPS+Gen (2) Non-lesional

Table 1: Patient Demographics. Seizure types were either complex partial (CPS) or complex partial with secondary gener-alization (CPS+Gen). M, male; F, female.

2 The Configuration Vector

For dynamic networks there is a lack of approaches to quantify how the pattern of connections between nodes, or thegross network configuration, varies over time. In networks whereN nodes stay constant over allT time windows, we candescribe the state ofN(N−1)

2 possible connections between all nodes in each time windowt = 1 to T by aconfiguration

vector ~vt ∈ RN(N−1)

2 ; collectively forming aconfiguration matrixV ∈ RN(N−1)

2 ×T . Intuitively, changes in~vt betweendifferentt can imply dynamical changes in network connectivity.

While dynamic networks commonly experience meso-scale changes in connectivity over time, there is currently no wayto determine whether these meso-scale changes contribute to gross reconfiguration of the entire network. Using a similarityfunction (herein we use Pearson correlation), we quantify the degree of change in connectivity patterns inV between allT time windows stored in a symmetricconfiguration-similarity matrixS ∈ R

T×T . In this work we are interested inclustering time windows that express similar network configuration patterns. To this end, we employ static communitydetection techniques to group time windows with similar gross network configuration.

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3 Modularity Optimization for Community Detection

3.1 Theory

Community-detection is an often used technique to study meaningful group structure in complex networks by clusteringnodes into ‘modules’ ‘communities’. A community is defined as a set of nodes that are connected among one anothermore densely than they are to nodes in other communities. A popular way to identify community structure is to optimize aquality function known as modularityQ, which has been shown to extract meaningful functional components of networksby comparing the real network to a null model [1, 2, 3, 4]. While these approaches have been mainly applied to bothbinarized and weighted static networks, more recent extensions of the model investigate dynamic communities that groupnodes over time. In our work we apply static community detection to the configuration-similarity matrix, viewed as a fullyconnected graph where each node represents the similarity of configuration vector~vt between time windowst1 and t2wheret1 = t2 = 0, to group gross network configuration patterns into communities.

In general, to perform community detection one begins with anetwork ofN nodes and a given set of connectionsbetween those nodes. A static network is then represented using anN × N adjacency matrixA. The elementAij of theadjacency matrix represents a connection from nodei to nodej wherei = j = 0, and its value indicates the weight of thatconnection. Then,Q is formally defined as:

Q =∑

ij

[Aij − γPij ]δ(gi, gj) , (1)

where nodei is assigned to communitygi, nodej is assigned to communitygj, the Kronecker deltaδ(gi, gj) = 1 ifgi = gj and it equals0 otherwise,γ is thestructural resolution parameter, andPij is the expected weight of the edgeconnecting nodei to nodej under a specified null model. The choiceγ = 1 is very common, but it is important to considermultiple values ofγ to examine groups at multiple scales (seeSI Section 3.2). A commonly chosen null model is theNewman-Girvan null model [3, 4, 1, 2] defined as:

Pij =kikj

2m(2)

whereki =∑

j Aij is the strength of nodei andm = 12

∑ij Aij is the average strength over all connections.

Maximizing Q partitions the network into communities such that the totalwithin-community connection weight ismaximum relative to the null.

3.2 Structural Resolution Parameter for Community Detection

The structural resolution parameterγ of the modularity quality function can be used to identify community structure overdifferent topological or geometric scales [5, 9, 3, 6, 7]. Typically,γ is chosen to be equal to 1. However, by varyingγ, onecan examine fine grain structure in networks by extracting smaller communities. In our application, we were interested indetermining community structure of configuration-similarity matrices with a variable (i) number of sensors implantedperpatient, (ii) seizure duration and (iii) spatial extent of epileptogenic cortex. Each of these factors can potentiallyimpact thescale at which appreciable meso-scale functional reorganization can be detected.

Prior studies have explored a structural resolution parameter limit that represents a trade-off between grouping all nodesinto a single community with large modularity and grouping each node into separate communities with low modularity[9]. This inverse relationship between modularity and structural resolution has been demonstrated in real-networks [7]suggesting that an even trade-off in modularity and number of communities may occur at the inflection point. To determinean optimal structural resolution parameter for each seizure we computed the inflection point in average modularityQ over1000 optimizations at eachγ between0.5 and2.0 in intervals of0.1 (Fig. S1).

4 Network Configuration Communities

4.1 Temporal Dispersion of Community Order

The temporal order of configuration communities can be (i)perfectly cohesive, where the network reconfigures minimallyduring an epoch, or (ii)perfectly random, where the network reconfigures in every time window. Traditionally, the rateof network reconfiguration has been measured by community flexibility F, quantified by the number of community as-signment changes within an epoch divided by the number of possible changes within the epoch [10]. Here we useF tomeasure the temporal dispersion of network configuration patterns, where more ordered community occurrence with lowF is suggestive of rich temporal structure. Our data show thatnetwork configuration communities from dynamic seizurenetworks demonstrated greater clear cohesive reconfiguration compared to pre-seizure networks that demonstrate morerandom dispersion of community assignment (Fig. S2).

2

4.2 Community Ranking and Distillation

In order to compare configuration communities across seizures, we developed a two-step method to re-assign communitiesbased on temporal occurrence. First, we ranked configuration communities within each pre-seizure network and seizurenetwork by community size; defined by fraction of time windows in an epoch assigned to the community. We then sum-marized seizure population distributions of community size based on ranked community labels (Fig. S3). We found thatpre-seizure networks were grouped into at most 3 configuration communities and seizure networks were grouped into atmost 6 configuration communities. We also noted that≈90% or more of the seizure time windows had been assigned toone of the first 3 configuration communities. Therefore, we chose to retain the 3 largest configuration communities fromseizure networks for further analysis.

References

[1] Newman M, Girvan M (2004) Finding and evaluating community structure in networks.Physical Review E69:026113.

[2] Newman M E (2006) Modularity and community structure in networks.Proceedings of the National Academy ofSciences103(23): 8577–8582.

[3] Porter M A, Onnela J-P, Mucha P J (2009) Communities in networks.Notices of the AMS56(9): 1082–1097.

[4] Fortunato S (2010) Community detection in graphs.Physics Reports486(3-5): 75–174.

[5] Reichardt J, Bornholdt S (2006) Statistical mechanics of community detection.Physical Review E74: 016110.

[6] Mucha P J, Richardson T, Macon K, Porter M A, Onnela J-P (2010) Community Structure in Time-Dependent,Multiscale, and Multiplex Networks.Science328: 876–878.

[7] Bassett D S, Porter M A, Wymbs N F, Grafton S T, Carlson J M, Mucha P J (2013) Robust detection of dynamiccommunity structure in networks.Chaos: An Interdisciplinary Journal of Nonlinear Science23: 013142.

[8] Brandes U, Delling D, Gaertler M, Gorke R, Hoefer M, Nikoloski Z, Wagner D (2008) On Modularity Clustering.IEEE Transactions on Knowledge and Data Engineering20(2): 172–188.

[9] Fortunato S, Barthelemy M (2007) Resolution limit in community detection.Proceedings of the National Academy ofSciences104(1): 36-41.

[10] Bassett D S, Wymbs N F, Porter M A, Mucha P J, Carlson J M, Grafton S T (2011) Dynamic reconfiguration of humanbrain networks during learning.Proceedings of the National Academy of Sciences108(18): 7641–7646.

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Figure 1: Structural Resolution Parameter Sweep. Each graph demonstrates the effect of varyingγ on the averagemodularityQ over1000 optimizations per seizure per patient. The red cross denotes theγ chosen for use in the communitydetection results presented in the main manuscript.

Figure 2: Temporal Dispersion of Network Configuration Communities. Distribution of flexibility F over seizurepopulation;t-test (N = 25, t = 11.04, p < 1× 10−14).

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Figure 3:Size Ranking of Network Configuration Communities. (Top) Pre-seizure network distribution of communitysize for size-ranked communities over seizure population.(Bottom) Seizure network distribution of size-ranked communi-ties over seizure population.

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