Multi-day rhythms modulate seizure risk in epilepsy

Transcription

1 DOI:.38/s y OEN Multi-dy rhythms modulte seizure risk in epilepsy Mxime O. Bud,,3,4, Jonthn K. Kleen, Emily A. Mirro 5, Json C. Andrechk 6, Dvid King-Stephens 7, Edwrd F. Chng 8 & Vikrm R. Ro ():,; Epilepsy is defined y the seemingly rndom occurrence of spontneous seizures. The ility to nticipte seizures would enle preventtive tretment strtegies. A centrl ut unresolved question concerns the reltionship of seizure timing to fluctuting rtes of interictl epileptiform dischrges (here termed interictl epileptiform ctivity, IEA), mrker of rin irritility oserved etween seizures y electroencephlogrphy (EEG). Here, in 37 sujects with n implnted rin stimultion device tht detects IEA nd seizures over yers, we find tht IEA oscilltes with circdin nd suject-specific multidien (multi-dy) periods. Multidien periodicities, most commonly 3 dys in durtion, re roust nd reltively stle for up to yers in men nd women. We show tht seizures occur preferentilly during the rising phse of multidien IEA rhythms. Comining phse informtion from circdin nd multidien IEA rhythms provides novel iomrker for determining reltive seizure risk with lrge effect size in most sujects. Deprtment of Neurology nd Weill Institute for Neurosciences, University of Cliforni, Sn Frncisco, CA 9443, USA. Deprtment of Neurology, University Hospitl Genev, Rue Grielle-erret-Gentil 4, 5 Genev, Switzerlnd. 3 Wyss Center for Bio nd Neuroengineering, Genev, Switzerlnd. 4 Sleep-Wke-Epilepsy-Center, Deprtment of Neurology, Inselspitl, University of Bern, 3 Bern, Switzerlnd. 5 Neuroce, Inc., 455N. Bernrdo Ave, Mountin View, CA 9443, USA. 6 Deprtment of Chemicl nd Biomoleculr Engineering, University of Delwre, Newrk, DE 976, USA. 7 Deprtment of Neurology, Cliforni cific Medicl Center, Sn Frncisco, CA 945, USA. 8 Deprtment of Neurologicl Surgery nd Weill Institute for Neurosciences, University of Cliforni, Sn Frncisco, CA 9443, USA. Correspondence nd requests for mterils should e ddressed to M.O.B. (emil: mxime.ud.neuro@gmil.com) NATURE COMMUNICATIONS (8) 9:88 DOI:.38/s y

2 NATURE COMMUNICATIONS DOI:.38/s y Dily to monthly ptterns in seizure occurrence hve een descried since ntiquity ut only recently quntified, reveling circdin 4, nd cluster orgniztion 5,6. The existence of such ptterns suggests tht rin ctivity is regulted over long timescles. Despite recent progress in using fetures of interictl rin ctivity to forecst imminent seizures 7, controversy remins regrding the reltionship etween seizures nd interictl epileptiform dischrges (e.g., spike-wves, polyspikes, nd fst oscilltions) 3. The rte of these pthologicl dischrges (here termed interictl epileptiform ctivity, IEA) fluctutes over time nd my increse or decrese efore seizures. This suggests tht IEA nd seizures re dissocile ut influenced y common process 4, one tht my e periodic. Oservtion of such process requires chronic recordings of rin ctivity cpturing multiple cycles 5. Recently, n FDA-pproved closed-loop implntle rin stimultor for detecting nd treting seizures (Neuroce, Inc. RNS System, herefter referred to s RNS System ) hs fforded n unprecedented opportunity to monitor humn rin ctivity with intrcrnil recordings continuously over mny yers. The RNS System involves progrmmle neurostimultor connected to intrcrnil electrodes recording neurl ctivity t the seizure focus or foci. Storge of rw EEG on the device is limited, ut customizle lgorithms re used to record hourly counts of epileptiform dischrges (IEA) nd timestmps of seizures. These dt sets re well-suited for nlysis of IEA rhythms t long timescles. Here, using wvelet trnsform to decompose IEA time-series, we identify multidien rhythms 6 with period lengths tht re vrile cross, ut reltively stle within, mle nd femle sujects over yers of recording. Seizures occur preferentilly on the dys-long up-slope of the multidien rhythm, independent of period length. Specific circdin timing of seizures is more vrile cross sujects, ut we show tht, t the individul level, multidien nd circdin IEA rhythms re codeterminnts of seizure risk. Results Sujects. We studied 37 sujects ( mles; ge rnge 58) with epilepsy who hd een implnted with the RNS System (Fig. ) for pproved clinicl indictions. Led plcements included mesil temporl (N = 3) nd neocorticl regions (N = 4) nd were ilterl in sujects (Supplementry Tle ). Recording durtions were 3 months to 9.9 yers (medin:.3 y). For this study, IEA is defined s hourly rtes of detections of epileptiform dischrges using suject-specific lgorithms designed y clinicins (Supplementry Fig. ). Chrcteriztion of circdin nd multidien rhythms of IEA. We formtted IEA rte (Fig., c) into continuous time-series nd pplied wvelet trnsform to resolve component rhythmicity of the IEA (signl processing steps depicted in detil in Supplementry Figs. nd 3). Individul sujects showed cler circdin vrition (Fig. d, h), nd multidien rhythms were lso pprent in dily verges of IEA plotted over long periods (Fig. e, i, j, Supplementry Fig. 4). Spectrl decomposition (Fig. f, g) reveled the expected peks in ultrdin ( h) nd circdin (4 h) rhythms 3,7,8, s well s longer periodicities ( dys) in most sujects (Fig., Supplementry Fig. 4). The medin rtio of multidien to circdin pek mplitude ws.4 (rnge.4 5.7; >. in 7 sujects), suggesting tht the multidien rhythm ws s roust s the circdin rhythm in most sujects. The most common periodicities were 6 3 dys (N = 8) followed y dys (N = 6, Fig. ). Intr-suject utocorreltion coefficients in the frequency-domin over time were ove.5 for ll (.7 ±.7, Supplementry Fig. 5,, e), reflecting reltive stility of these rhythms. Intr-suject correltion of periodogrms derived from ihemispheric recordings ws.93 ±.5 (N = 8, Supplementry Fig. 5c, d), suggesting tht IEA rhythms in ntomiclly distinct seizure foci re co-regulted. All sujects exhiited -h hrmonic of the circdin rhythm nd some sujects lso hd hrmonics of multidien rhythms, for exmple with peks t 7.5 nd 5 dys (Supplementry Fig. 6). Unsupervised clustering of the periodogrms sed on their coefficients for principl components (Supplementry Fig. 7) showed three ptterns of multidien rhythms: (i) out weekly nd iweekly (N = 9), (ii) out tri-weekly (N = ), nd (iii) out monthly (N = 6) peks (Fig. ). This nlysis ws done minly for visuliztion purposes, s there ws no strong ctegoricl seprtion of the dt. Rther, the rnge of periods ws continuum, sometimes with two or three peks in the sme suject (Fig., Supplementry Fig. 4). Sujects demonstrting these ptterns did not differ significntly y region of seizure onset (p =.87, χ -test). Mle nd femle sujects showed similr distriution of periodicities (p =.87, χ -test, Fig. ). Multidien rhythms remined pprent during times when the stimultion function of the RNS System ws disled (Supplementry Fig. 4). hse nlysis of IEA pek in reltion to circdin time. To complement this power nlysis with time informtion, phse nlysis of the circdin IEA rhythm reveled tht the pek ligned consistently with given hour in ll sujects (p <., Omnius test, Fig. 3). Unsupervised clustering showed three groups with peks round 4: M, : AM, nd 6: AM, which my represent different IEA chronotypes 9 (Fig. 3). These findings re consistent with prior study showing pek nocturnl occurrence of IEA independent of the region of seizure onset (p =.4, χ -test) 3. hse nlysis of seizure timing reltive to IEA rhythms. Next, we investigted the reltionship of seizures to the phse of the underlying circdin nd multidien IEA rhythms in suset of sujects (N = 4) for whom seizure detection y the RNS System ws highly relile (estimted ~% flse positives, see Methods section). Averge seizure rte cross these sujects rnged from one seizure every 7 dys to 3 seizures per dy, with medin totl numer of seizures of 35 (rnge 74 5,54). Circulr sttistics of seizure timing confirmed significnt entrinment to circdin nd multidien rhythms in nd 3 out of 4 sujects, respectively (Omnius test, p-vlues in Fig. 4). Across sujects, the verge phse-locking vlue (LV, equl to the resultnt vector length) ws similr for circdin nd multidien rhythms (Fig. 4, ; p =.63, Wilcoxon test), suggesting tht seizures were tied s strongly to given phse of multidien rhythms s to circdin rhythms. However, the popultion of ngles ws significntly different (p =., Kuiper test), spnning from trough to pek of circdin rhythms nd from up-slope to pek of multidien rhythms. Seizures were therefore coupled to multidien rhythms over more nrrow rnge of phses thn to circdin rhythms. Circdin nd multidien LVs correlted wekly (erson r =.36, p =.). To further explore the reltionship etween circdin nd multidien timing, individul seizures were mpped on the circdin vs. multidien phse-spce (see Methods section nd Fig. 5), reveling uncorrelted grouping of seizures t preferred circdin nd multidien phses independent of the underlying period (Fig. 5). Multidien LVs inversely correlted with seizure rte (erson r =.7, p =.5, Supplementry Fig. 8). Thus, seizures re more tightly coupled to the preferred multidien phse in sujects with low or moderte seizure rtes (the mjority in this study) thn in sujects with high seizure rtes. NATURE COMMUNICATIONS (8) 9:88 DOI:.38/s y

3 ARTICLE NATURE COMMUNICATIONS DOI:.38/s y c Count = Count = 8 Voltge e e Electrocorticogrm Epileptiform dischrge e e s s s 7, 7 Neuroce, Inc. Hourly counts d IEA Seizures Ferury Mrch Hourly counts dily verge e Inset f Wvelet components (.u.) d rhythm 6 d rhythm -45 d reconstruction Seizures Septemer April 3 h 4 h 3 d 7 d 5 d 3 d eriod d 6 d July i h Normlized counts ower index g Jnury j 6 AM 6 M Time of dy 6 AM 7. ±. d 9 8 hse 5.6 ± 4.4 d hse 7 Fig. Representtive suject demonstrting circdin nd multidien rhythms in IEA, s well s preferentil timing of seizures. RNS System comprising crnilly implnted neurostimultor connected to intrcrnil leds (imge used with permission from Neuroce, Inc.). EEG showing singleepileptiform dischrge (spike) in chnnels corresponding to left (e) nd right (e) hippocmpl leds. c EEG recorded week lter t the sme time of dy showing higher count of epileptiform dischrges, i.e., higher IEA. Inset mgnifies one typicl element to show wveform morphology. Hourly (d, cyn inset) nd dily (e) fluctution in IEA in one suject over nd months, respectively. Red dots indicte times of seizure occurrence. f Wvelet decomposition reveling two component multidien rhythms with periodicities of nd 6 dys. Comining ll multidien wvelet coefficients reconstructs the dily IEA time-series (gry curve, 45 d, erson correltion r =.93, p = ). g Corresponding periodogrm showing ultrdin ( h), circdin (4 h), nd multidien ( nd 6 d) peks in periodicity. eriod length displyed on the x-xis, nd power index (squre root of spectrogrm power) on the y-xis. Horizontl doule-rrows show spn of corresponding wvelet coefficients included for (f) (pek period ± 33%). h Averge normlized mplitude of the circdin rhythm s function of time of the dy showing phse preference of seizures ner the trough t 5 M (n = 74 seizures, men ± SD in red, p = 4, Omnius test, see Methods section). Blck nd white rectngles (d, h) represent night (6M 6AM) nd dy (6AM 6M), respectively. i, j Averge normlized mplitude of the d nd 6 d IEA rhythms s function of their underlying phse (x-xis, full 36 degrees phse; y-xes hve different scles). Seizures demonstrte phse preference for the up-slope of oth rhythms ( nd 6 dys, n = 66 seizures, men ± SD in red, p =. nd p =., respectively, Omnius test) Seizure risk modultion y circdin nd multidien rhythms. We estimted differences in effect size cross sujects y clculting the risk of hving seizure t given circdin or multidien phse reltive to the risk of not hving seizure t the sme phse. When comining phse informtion from the underlying circdin nd multidien rhythms, we found smll (risk rtio (RR) NATURE COMMUNICATIONS (8)9:88., 95% CI:..3) to very lrge effect sizes (RR 4.5, 95% CI: ) in sujects with high nd low seizure rtes, respectively, nd lrge effect-size summry cross sujects (unweighted RR 6.8, 95% CI: 3. 5., Fig. 5). Although the reltive modultion of seizure occurrence y circdin nd multidien rhythms vried cross sujects, the highest risk rtio ws DOI:.38/s y 3

4 NATURE COMMUNICATIONS DOI:.38/s y ower index Numer of sujects n = 6 n = n = 9 ek 7.5 d 5 d 6 d d h 4 h 3 d 7 d 5 d 3 d Mle Femle h 4 h 3 d 7 d 5 d 3 d eriod Fig. eriodogrms nd peks of IEA rhythms. Averge periodogrms cross ll sujects (N = 37) showing ultrdin, circdin, nd multidien peks. For etter visuliztion, unsupervised clustering cross ll sujects reveled three ptterns: (i) out weekly-to-iweekly rhythm (peks t 7.5 nd 5 dys, N = 9), (ii) out tri-weekly rhythm (pek t dys, N = ), nd (iii) out monthly rhythm (pek t 6 dys, N = 6). Shding indictes ± SD. Histogrms showing the numer of sujects with pek in the periodogrm t given period. The distriutions re similr (p =.87, χ -test) in mle (N = ) nd femle (N = 5) sujects found when the two criticl phses were comined (Fig. 6). When multidien nd circdin rhythms were oth nti-phse, seizures were rre in 5 out of 4 sujects (S3, S5, S4, S3, nd S33). Discussion Our results revel tht, in ddition to well-known circdin rhythms, IEA fluctutes with slower multidien rhythms tht vry cross sujects ut re reltively stle within sujects over mny yers. Furthermore, seizures occur preferentilly during nrrow phses of these circdin nd multidien rhythms. Thus, seizures re orgnized y underlying iologicl rhythms tht operte over multiple timescles nd jointly modulte seizure risk. revious pplictions of quntittive methods to chronic intrcrnil recordings hve elegntly chrcterized distriutions of seizure durtions nd inter-seizure intervls 5,, estlished power-lw reltionships linking pst nd future seizures 6, nd identified circdin nd ultrdin ptterns 4. One study using n utocorreltion method in the time-domin found cyclicl ptterns of IEA rnging in durtion from weeks to month in limited numer of sujects 4. Here we took dvntge of longer recordings nd frequency-domin sttisticl nlyses designed for the study of oscilltions t ny scle. Our study is distinguished y the elucidtion of multidien rhythms in most sujects, often with greter mgnitude thn circdin modultion. This is remrkle s multidien rhythms were present covertly in ll-comers, even though most did not hve ovious periodicity of their epilepsy, underscoring the vlue of monitoring IEA s iomrker of disese ctivity. In comprison with previous contriutions 4, the key insight from our work is tht, cross sujects with diverse focl epilepsies, seizure timing depends on the phse of the multidien rhythm, explining how seizures tend to form clusters with long-rnge dependencies 5,6,. This phenomenon could only e elucidted with long timescle recordings of IEA nd seizures, nd the importnce of using this wider temporl lens to view nd nticipte seizure dynmics represents mjor conceptul dvnce. Indeed, the time window of pre-seizure ctivity relevnt for seizure prediction my e on the scle of dys rther thn hours s previously thought,. Overll, seizure occurrence ws est explined y incorporting informtion out circdin nd multidien rhythms. Relile rel-time seizure prediction will likely involve comintoril function of multiple fetures of n individul s epilepsy, including pst nd present seizure chrcteristics nd short nd long-term IEA trends. Multidien nd circdin rhythms my e most predictive in sujects with low or moderte seizure rte where phse preference is highest. The dt presented here, sed on nlysis of thousnds of seizures, help reconcile conflicting evidence regrding the reltionship etween IEA nd seizures. revious studies hve reported tht IEA increses, decreses, or remins unchnged efore seizures 4,,, nd IEA trends fter seizures re lso vrile,3,4. Seizures preferentilly occur during the rising phse of multidien IEA cycles, ut, in given suject, this could coincide with the pek or the trough of the circdin IEA cycle 4, perhps explining how shorter timescle studies, looking t hour-to-hour chnges in IEA, could drw seemingly contrdictory conclusions. Similrly, dy-to-dy chnges in IEA my not explin seizure timing s well s the phse of the underlying slow oscilltion. A mjor dvntge of our study is tht chronic recordings were mde in multory sujects under nturl conditions, i.e., without tpering nticonvulsnt medictions, which is typicl of cute inptient recordings nd known to ffect IEA 4. Our findings chllenge the concept of direct, generlizle reltionship etween IEA nd seizures nd fvor hypothesis tht these epilepsy phenomen covry under differentil influence of fctors operting t multiple timescles. A slow permittivity vrile ws recently identified in n elegnt mthemticl model of epilepsy 5, nd our results support the existence of n unidentified fctor (or fctors) regulting slow epileptic fluctutions 6, possily through chnges in rin metolism 7 or circuit function 8. Further nlysis of the rise nd decy kinetics of IEA fluctutions my e informtive with regrd to underlying iologicl mechnisms. We speculte tht the seemingly independent circdin nd multidien oscilltors my in fct e co-modulted y hormonl, genetic, environmentl 9, sleep-wke cycle 3, nd ehviorl fctors 3. Hormonl influence on seizures occurs in ctmenil epilepsy 3,33, nd one of the 5 femle sujects hd seizures relted to menstrul cycles 3,33 with IEA cycling t 3 nd 6 dys. However, we oserved similr rhythmicity in men, so ctmenil cycling cnnot explin our results. This study hs limittions. Our sujects, who hve mediclly refrctory focl epilepsy, my not e representtive of ll ptients with epilepsy. These sujects lso received therpeutic rin stimultion. We cnnot exclude the possiility tht stimultion influenced the rhythms we oserved, ut the stility of these rhythms despite prmeter chnges, including turning stimultion off, strongly rgues ginst this. Given tht ptient sujective reports re notoriously inccurte for seizure quntifiction 34, with systemtic negtive is for certin seizure types (mnestic nd nocturnl), we focused our study on ojective quntifiction of electrogrphic seizures recorded with the device nd not on clinicl seizures. It is possile tht clinicl seizures hve unique reltionships to IEA rhythms, ut our findings re consistent 4 NATURE COMMUNICATIONS (8) 9:88 DOI:.38/s y

5 NATURE COMMUNICATIONS DOI:.38/s y ARTICLE Resultnt length/ngle Neocorticl Mesiotemporl Averge n = 8 M LV.8 8% c n = 8 4%.4 6 AM 6 M d 4 n = AM 4 6 AM M 6 M AM Time of dy 6 AM Fig. 3 Circdin timing of pek IEA. hse entrinment of pek circdin rhythm to time of dy for ech suject (N = 37, dys, resultnt ngle nd phse-locking vlue (LV), p <. for ll, Omnius test, see Methods section) grouped into three clusters (group men ngle nd LV in old, corresponding time s dot in ( d). Normlized verge circdin mplitude (±SD) with pek in the lte fternoon (), erly night (c), nd erly morning (d) were independent of seizure locliztion (mesil temporl vs. neocorticl, p =.4, χ -test) ut my represent three chronotypes with the nerly 8-yer-old oservtion tht clinicl seizures demonstrte multidien periodicities in men nd women 6. IEA counts nlyzed here depend on detection prmeters tht were dynmiclly djusted sed on clinicl indictions, nd the RNS System stores limited continuous rw EEG. Chnges in detection sensitivity impct the solute IEA count, ut our sttisticl pproch ccounts for this y relying on reltive fluctutions within periods of constnt detection settings. Finlly, our study ws retrospective, ut leverging knowledge of suject-specific multidien nd circdin rhythms for prospective seizure prediction remins mjor gol of future work. Multidien rhythms hve een identified in mood disorders 35, sleep ptterns 3, nd crdiovsculr physiology 36, nd their role in epilepsy will further fuel investigtions into the underlying iologicl mechnisms. An endocrine sis seems likely 37,38. For exmple, cortisol levels re positively correlted with IEA in some forms of epilepsy 39, nd endogenous neurosteroids, hormonl modultors of GABA receptors, fluctute over time nd possess nticonvulsnt properties 4. Knowledge of these mechnisms nd the ility to nticipte epochs of heightened seizure risk my enle dynmic, personlized tretment strtegies 4. Methods Sujects. We recruited 37 sujects ( mles) who hd een implnted with the RNS System for purely clinicl indictions for t lest 3 months nd up to 9.9 yers (medin:.5 yers) cross two neurology centers (University of Cliforni, Sn Frncisco, N =, nd Cliforni cific Medicl Center, N = 6). The two Institutionl Review Bords pproved the study nd written informed consent ws otined from ll sujects. Sujects hd vriety of focl epilepsies (Supplementry Tle ). Indictions for tretment with the RNS System s opposed to resective surgery included ilterl seizure locliztion (temporl nd frontl), seizures rising from eloquent cortex (motor nd visul), nd previous contrlterl resection. Dt selection. Detection of epileptiform ctivity y the RNS System relies on user-configurle tools (line length, re under the curve, nd ndpss filtering) for which thresholds re optimized to detect seizure onset ptterns 4. Exmples of suject-specific epileptiform ctivity detected y the RNS System hve een reported previously 3 nd re shown in Supplementry Fig.. Hourly detection counts re stored y the RNS System for the lst 8 dys nd re continuous s long s sujects downlod device dt t lest this often. For ech suject, we discrded dt recorded from the dy of implnt until relile detection of seizures nd IEA ws chieved during the first few outptient visits (medin numer of visits:, rnge: ) few months lter (medin: 9 dys, rnge: 9 dys; Supplementry Fig. 4). Sixteen sujects who did not downlod device dt regulrly hd resultnt gps in detection counts. The dt contining gps longer thn 6 dys ws considered discontinuous nd nlyzed in seprte segments. The dt of <9 dys surrounded y gps ws discrded. Gps up to 6 dys were interpolted (see elow). One suject (S4) underwent resective surgery nd the device continued to record. This dt were discrded. For visuliztion purposes dily counts were otined y verging 4 h of dt on the sme clendr dte, ut ctul nlyses were performed on the originl hourly count dt. Due to memory constrints, the RNS System cn store only limited numer of rw EEGs t given time. Seizure detection with the RNS System relies insted on surrogte mrker, long-epileptiform ctivity (LEA; lso termed Long Episode y others 3,4 ), which occurs when the EEG signl meets detection criteri for clinicin-specified length of time (typiclly, the minimum durtion of ech suject s electrogrphic seizure; LEA durtions for this study rnged from 5 to 4 s, with n verge of 6.8 s). Like detection counts, LEA timestmp informtion is stored y the device nd ville for nlysis. Although generlly relile proxy for seizures 43, LEA cn lso represent epochs of undnt IEA tht do not meet criteri for electrogrphic seizures 44 (Supplementry Fig. ). To void contminting seizure nlysis with such flse positives, we clculted for ech suject the positive predictive vlue (V) of LEA for electrogrphic seizures (Supplementry Fig. c). For ech suject, Bord-certified epileptologist (V.R.R.) ssessed whether individul LEA corresponded to true electrogrphic seizures y visully reviewing corresponding EEGs. When possile (<3 LEA, sujects), ll individul EEGs were reviewed nd ech ws leled s n electrogrphic seizure (true positive) or s LEA other thn n electrogrphic seizure (flse positive). For sujects with too mny LEA EEGs for comprehensive review (N > 3, 7 sujects), EEGs were rndomly selected from epochs with stle detection settings nd V ws clculted for ech epoch. Sujects (N = 3) who hd < LEA were excluded from sttisticl nlysis, ecuse this ws too low numer for histogrm-sed sttisticl technique (see elow). In totl, we included 4 sujects for whom LEA ws relile surrogte for seizures (V >9%; men 98%, rnge 9 %; Supplementry Tle ). Thus, we estimte tht <% of LEA used here my ctully e sustined trins of IEA nd tht the rest represent true electrogrphic seizures. Time-series nd wvelet nlysis. Hourly IEA counts were normlized (z-score) seprtely y lock of recording etween clinic visits so s to ensure stility of detection settings nd nticonvulsnt medictions for ech lock. Continuous time-series were otined y conctenting these individul locks. ower nd NATURE COMMUNICATIONS (8) 9:88 DOI:.38/s y 5

6 NATURE COMMUNICATIONS DOI:.38/s y p Circdin ek Multidien ek 3 6 m Time of dy Up LV.4.8 Down Up LV.4.8 Down eriod (dys) 6 pm Trough Trough c S3.7/m S5./m S9.3/w S4 5.9/d S./d S3 3./w S33.9/w S4 3.5/w S 6./w S6 9.7/d S3.4/w S37./d S7.5/d S9 3./d Trough Up ek Down Trough e N Sz yr LV 5 5 S hse of circdin rhythm Time (yers) d Up ek Down hse of multidien rhythm % % Trough Fig. 4 hse preference of seizures in reltion to underlying IEA rhythm. Seizure timing reltive to phse of the underlying circdin () or multidien () rhythm for ech suject shown s the LV nd resultnt ngle (N = 4; p-vlues in (c,d), Omnius test, see Methods section). On verge, the LV ws not different (p =.63, Wilcoxon test), ut the ngles were more tightly distriuted nd closer to the pek for the multidien s compred to the circdin rhythm (p =., Kuiper two-smple test, see Methods section). For visuliztion purposes, individul circulr histogrms of seizure counts (percentge of totl count) for circdin (c) nd multidien (d) rhythms re shown, rnked ccording to incresing multidien verge phse (verticl r position). p- vlues for the Omnius test shown in Figure. p <.. Color codes in () nd (c) re the sme s in Fig. 3 nd represent hour of the dy of pek circdin rhythm. Color codes in () nd (d) represent pek periodicity of multidien rhythm, illustrting tht the preferred multidien phse is similr, regrdless of the exct period length. e Fether nd polr plots showing stle direction nd mgnitude of phse preference ssessed every 3 months in one suject (S3). Color-coding estlishes dt correspondence etween fether (left) nd polr plot (right) nd does not refer to color-rs in (). The nnul numer of seizures is displyed to show the decrese over yers of tretment with the RNS System nd the numer of seizures included in ech clcultion 6 NATURE COMMUNICATIONS (8) 9:88 DOI:.38/s y

7 ARTICLE NATURE COMMUNICATIONS DOI:.38/s y phse of the hourly IEA counts time-series were otined using Morlet wvelet trnsform for 89 period ins (scles) with incresing spcing:. h etween.4 nd 3. h,.4 h etween 33.6 nd 48 h, 4.8 h etween. nd 4 d, h etween 4.5 nd d, nd 4 h etween nd 45 d. Gps in recordings, if reltively short, were interpolted y method similr to kriging in geosttisticl nd climtology reserch45 (Supplementry Fig. 3). For ech gp, the vrince ws clculted for Circdin phse S3 T Multidien phse T T T T T T T S9 two windows, efore nd fter the gp (ech with sme length s the gp itself). This vrince ws used to cst the normliztion curves for pseudo-rndom dt generted round centrl tendency line directly connecting the mens of the two peri-gp windows ove. This process ws performed for ech gp, nd only for gps shorter thn % of the period eing nlyzed (e.g., up to dys of interpoltion llowed for period of dys). Gps were processed in incresing c Risk rtio ¼ ½ 4 S5 Risk rtio S3 N = 66 S5 N = S4 S9 N = 6 S4 N = 39 S S3 S N = 49 S3 N = 33 S33 Incresing IEA in hours preceding seizure Decresing IEA in hours preceding seizure S S4 S33 N = 85 S4 N = 46 S6 S N = 73 S6 N = 856 S3 S37 S3 N = 668 S37 N = 66 S7 S9 S7 N = Circdin preferred ngle ± 9 RR Multidien preferred ngle ± 9 RR Multidien nd circdin comined Circdin IEA pek Multidien IEA pek RR NATURE COMMUNICATIONS (8)9:88 Effect summry Weighted d Unweighted S9 N = 567 DOI:.38/s y 7

8 NATURE COMMUNICATIONS DOI:.38/s y durtion order, so tht higher frequencies were not ffected y interpoltions performed t lower frequencies. In ddition, cone of influence the region of the wvelet spectrum, shped ccording to period length, in which edge effects impede ccurte periodic estimtion ws discrded t the extremities nd round gps too wide to e interpolted. The dt could then e represented s spectrogrm of power or phse over time (time-frequency nlysis) with excluded dt t the extremities nd round gps (Supplementry Fig. ). ower index in periodogrms Circdin phse Z-score 48 h 4 h h + RR > RR < Multidien phse Dys Fig. 6 Averge risk rtio (RR) mp in the circdin vs. multidien phsespce. Averge of individul RR mps shown in Fig. 5 fter lignment to the preferred phses ( in xes lels; red verticl line, multidien; cyn horizontl line, circdin). Blue nd green contour lines indicte RR > nd <, respectively, (95% CI excluding RR of one). To illustrte the concept of time-vrying seizure risk, white lines depict the hypotheticl circulr trjectory of suject with 4 h circdin nd 8-dy multidien cycle. Ech line covers two circdin cycles nd qurter multidien cycle. When strting on the left line, the suject mostly crosses res of low seizure RR with the exception of medium RR t times of fvored circdin timing (rrowhed). In the second qurter (second line from left), the suject crosses n re where multidien nd circdin timing jointly increse seizure RR (rrowhed). In the third qurter (third line from left), the suject stys on n re of incresed risk for two circdin cycles y trveling on verticl nd of fvored multidien phse (rrowhed). The fourth qurter line joins the ottom of the first line to close the cycle. Averge multidien mplitude (z-scored) nd pek position (just right of the preferred phse). Averge circdin cycle is not displyed ecuse the preferred phse ws too vrile cross sujects, ut circdin time is leled 4 48 h 4 ½ ¼ Risk rtio ws estimted for ech individul scle (period in) s the squre root of the verge over time of the solute vlue of complex wvelet coefficients. rincipl component nlysis of ll individul periodogrms (Supplementry Fig. 3) ws used to extrct recurrent ptterns. The six first components were selected s they explined 98.7% of the totl vrince in the frequency domin. Averge periodogrms were clculted for three seprte clusters otined y K-mens (cosine distnce, rnk of 3) on the principl components coefficients (Fig. ). eks in periodicity were defined s positive-to-negtive zero-crossing of the derivtive of the periodogrm. Instntneous phse nlysis. hse t every time-point ws clculted in the frequency domin for single nd of wvelet coefficients corresponding to the pek period ±33.3% (e.g., 4 ± 8 h, or 5 ± 5 d), so s to ccommodte vrition in periodicity. Thus, t ech time-point, the most powerful frequency within rnge would most influence the phse. The verge nd vrince in period length were clculted using the distnce etween two successive phse vlues of zero, excluding gps. Circdin epileptiform pek ctivity histogrms were otined y counting occurrences within -h ins (4 ins, Fig. 3). Seizure phse histogrms were otined y counting occurrences within -degree phse ins (8 ins from π to +π) for circdin nd multidien rhythms (Fig. 4). Similrly, verge mplitude ws otined y clculting the men nd stndrd devition of normlized dt for ll time-points with phse contined within these ins. If more thn one multidien pek ws present in the periodogrm, we used the shortest (first) multidien periodicity to evlute instntneous phse. For visuliztion purposes, signl ws reconstructed for the pek periods ±33.3% using n inverse wvelet trnsform (Fig. nd Supplementry Fig. ). The phse-spce representtion llowed for the study of seizure risk s it reltes to circdin vs. multidien phse. Sctterplots help visulize these reltions strcted from the fct tht multidien periods vry cross sujects. Sttistics. The smple size ws determined y the vilility of dt. revious studies hve demonstrted quntittive nlyses of these dt sets with reltively smll numer of sujects 5 (though our smple size is considerly lrger in oth numer of sujects nd recording durtions). Circulr sttistics cn e pplied within-suject, nd we investigted replicility cross ll sujects in our dt set. The only pre-estlished exclusion criterion ws length of continuous recording of <3 months, nd we excluded seven recently implnted sujects for this reson. Given the oservtionl nture of the study, there ws no repliction of mesurements over time per se, though these long recordings nd utocorreltion nlyses (Supplementry Fig. 5) serve s technicl mesures of within-suject replicility. Vlues were expressed s men ± stndrd devition (SD) nd plotted s dots nd error-rs, unless specified otherwise. For ctegoricl distriutions (gender nd seizure locliztion), we performed χ -test. For continuous vriles, we performed Wilcoxon test. Autocorreltions to the verge periodogrm were ssessed t ech time-point in the frequency domin using erson coefficient nd verged over the totl length of recording for ech individul. For eight sujects with ilterl implnts nd >3 months of ilterl recordings, erson coefficients were clculted on the periodogrms derived from ech site. Other correltions were ssessed using liner model with intercept nd the F-sttistic vs. constnt model. Seizure rte ws log-trnsformed for regression models, s it hd logrithmic distriution. hse nlyses were done using the Mtl circulr sttistics toolox y Dr. hilipp Berens 46 including functions for circulr men, circulr stndrd devition, nd resultnt vector. We used the circulr vrint of k- mens for clustering of ngles. We used the Omnius (or Hodges-Ajne) test to clculte sttisticl significnce for non-uniform ngulr distriution (ginst the null hypothesis of uniform distriution), s opposed to the more clssicl Ryleigh test, ecuse some ngulr distriutions were imodl, especilly in circdin rhythms. We used the Kuiper test (nlog to the Kolmogorov Smirnov test for circulr dt) to clculte the sttisticl difference etween two ngle popultions, Fig. 5 Individul risk rtio (RR) mps in the circdin vs. multidien phse-spce. Sctterplots of circdin vs. multidien phse t time of seizures (totl numer of seizures on the right of (c), N). Note tht dt hve een duplicted on the x nd y-xes to emphsize complete cycles. Ech dot represents one to few seizures hppening during the sme hour. : pek, T: trough of underlying rhythms lso represented with purple lines. The lck (night, 6M 6AM) nd white (dy, 6AM 6M) oxes on the right y-xis represent pproximte time of the dy. Note the lck of correltion etween the circdin nd multidien ngles (i.e., they do not lign on digonl). ink oxes in S33 highlight tht, for given multidien phse, IEA could go up or down in the hours efore or fter seizure, depending on the circdin phse reltive to pek (pink ). Corresponding density plots representing risk rtio (color-coded logrithmic scle) for ins of -degree circdin nd multidien phse comintion. Ech pixel represents the risk of hving seizure t this point in phse-spce s compred to the risk of not hving seizure t this point. Green nd cyn lines in () with corresponding green nd cyn shding in () (±9 ) represent preferred phses of seizures in reltion to underlying IEA rhythms (lso visile in Fig. 4). In some sujects, seizures cn occur t ny time of the dy if in the t-risk multidien phse (S, S5, S7, S3, nd S4) nd, conversely, in other sujects, seizures cn occur on ny dy of the multidien cycle if t specific times of the dy (S4, S6, nd S37). c Forest plot showing the risk rtio for hving seizure when in-phse vs. nti-phse with the preferred phse of the underlying circdin or multidien rhythm or the comintion of the two. d Effect summry for ll 4 sujects. Overll, seizure occurrence ws est explined y incorporting informtion out circdin nd multidien rhythms 8 NATURE COMMUNICATIONS (8) 9:88 DOI:.38/s y

9 NATURE COMMUNICATIONS DOI:.38/s y ARTICLE s it mkes no ssumption on the underlying distriutions. These descriptive sttistics, clustering methods, nd tests in the circulr domin hve equivlents in the liner domin ut they tke into ccount the fct tht ngles flip from π to π, creting numericl discontinuity. The men resultnt vector is metric of phse consistency of popultion of ngles. It is constructed y vectoril verging of phse vectors ech of unitry length equl to one. Thus, the ngle of the men resultnt vector represents the men ngle of the popultion nd its length (hse- Locking Vlue, LV) represents dispersion (vlues close to zero) or concentrtion (vlues close to one) of constituting ngles. Given tht the LV is continuous vrile linerly vrying from zero to one, we used Wilcoxon test to compre popultion medins. To study the stility of this metric over time, we computed repeted LVs every 3 months including dt over yer (±6 months t ech timepoint, Fig. 4f). To study the mp of seizure risk for ech individul suject, we inned seizure counts in the phse-spce into 34 (8 8) -degrees circdin nd multidien phse comintion elements. To reduce noise, we smoothed this result with D Gussin kernel spnning two stndrd-devitions over ±4 degrees. Ech single in, contining the numer of seizures tht occurred t given phse comintion, successively represented true positives (T), wheres seizure counts in the 33 other ins represented flse negtives (FN). Flse positive (F) were the numer of occurrence of given phse comintion (without seizures), nd True Negtive (TN) were ll the other phse comintions (without seizures). The risk rtio ws clculted s T=ðTþFÞ FN=ðTNþFNÞ. This ws done for ech in resulting in mp of risk fctor-seizure ssocition (Fig. 5). Thus, the risk rtio tkes into ccount the numer of seizures oserved t given phse comintion, the seizure rte of given suject, nd the proility of finding given comintion of phses. These mps were verged cross sujects fter lignment to the preferred circdin nd multidien phses (Fig. 6). In ddition to this visuliztion of riskrtio mps, we estimted the glol effect size with confidence intervls for ech individul, y grouping ins of the mp tht were in-phse (the risk fctor ) or nti-phse with the preferred ngle (±9 ) nd clculting risk-rtio etween these two ctegories (Fig. 5). This ws done for circdin nd multidien rhythms independently nd for the comintion of the two phses (using union Boolen opertor). Finlly, we displyed risk rtios s Forest plot nd computed n effect size summry metric cross sujects using two methods: (i) simple unweighted verge of the risk rtio nd stndrd error, nd (ii) rndom effect weighted verge of the risk rtio nd stndrd error (vrince in risk-rtio ws ssumed to e non-rndom, Fig. 5) 47. Dt vilility. The dt nd code utilized in this study re ville from the corresponding uthor upon resonle request. Received: 6 Ferury 7 Accepted: Decemer 7 References. 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Cortisol fluctutions relte to interictl epileptiform dischrges in stress sensitive epilepsy. Brin 39, (6). 4. Reddy, D. S. & Rogwski, M. A. Neurosteroids endogenous regultors of seizure susceptiility nd role in the tretment of epilepsy. (). 4. Rmgopl, S., Thome Souz, S. & Loddenkemper, T. Chronophrmcology of nti-convulsive therpy. Curr. Neurol. Neurosci. Rep. 3, 339 (3). 4. Sun, F. T. & Morrell, M. J. The RNS system: responsive corticl stimultion for the tretment of refrctory prtil epilepsy. Expert. Rev. Med. Devices, (4). 43. Quigg, M. et l. Interrter reliility in interprettion of electrocorticogrphic seizure detections of the responsive neurostimultor. Epilepsi 56, (5). 44. Durzzo, T. S. et l. Temporl distriutions of seizure occurrence from vrious epileptogenic regions. Neurology 7, 65 7 (8). 45. Choudhury, N. H., Rhmn, A. & Ferdousi, S. Kriging infill of missing dt nd temporl nlysis of rinfll in North Centrl region of Bngldesh. J. Climtol. Wether Forecst. doi:.47/ (5). 46. Berens,. CircStt: MATLAB toolox for circulr sttistics. J. Stt. Softw. 3, Issue (9). 47. Neyeloff, J. L., Fuchs, S. C. & Moreir, L. B. Met-nlyses nd Forest plots using microsoft excel spredsheet: step-y-step guide focusing on descriptive dt nlysis. BMC Res. Notes 5, 5 (). Acknowledgements This work ws supported y the Ntionl Institutes of Helth (NIH) grnts R5NS768-7 (J.K.K.) nd R-DC379 (E.F.C.). The uthors re grteful to hil Thornton for technicl ssistnce during dt collection. NATURE COMMUNICATIONS (8) 9:88 DOI:.38/s y 9

10 NATURE COMMUNICATIONS DOI:.38/s y Author contriutions M.O.B. nd V.R.R. designed nd initited the study. V.R.R., D.K.-S., nd E.F.C. recruited sujects from their clinicl prctices. V.R.R., E.A.M., nd J.C.A. performed the dt collection. M.O.B. nd J.K.K. performed the dt nlyses. V.R.R., M.O.B., nd J.K.K. wrote the mnuscript. Additionl informtion Supplementry Informtion ccompnies this pper t Competing interests: V.R.R. nd D.K.-S. hve received honorri from Neuroce, Inc. for consulting nd speking enggements. E.A.M. is n employee of Neuroce, Inc. M.O.B. is prt-time employee of the Wyss Center for Bio nd Neuroengineering. The uthors declre no trgeted funding or compenstion from Neuroce, Inc. for this study. The remining uthors declre no competing finncil interests. Reprints nd permission informtion is ville online t reprintsndpermissions/ ulisher's note: Springer Nture remins neutrl with regrd to jurisdictionl clims in pulished mps nd institutionl ffilitions. Open Access This rticle is licensed under Cretive Commons Attriution 4. Interntionl License, which permits use, shring, dpttion, distriution nd reproduction in ny medium or formt, s long s you give pproprite credit to the originl uthor(s) nd the source, provide link to the Cretive Commons license, nd indicte if chnges were mde. The imges or other third prty mteril in this rticle re included in the rticle s Cretive Commons license, unless indicted otherwise in credit line to the mteril. If mteril is not included in the rticle s Cretive Commons license nd your intended use is not permitted y sttutory regultion or exceeds the permitted use, you will need to otin permission directly from the copyright holder. To view copy of this license, visit licenses/y/4./. The Author(s) 7 NATURE COMMUNICATIONS (8) 9:88 DOI:.38/s y