The use of functional and effective connectivity techniques to understand the developing brain

ContentslistsavailableatScienceDirect

Developmental

Cognitive

Neuroscience

jo u r n al ho me p ag e :htt p : / / w w w . e l s e v i e r . c o m / l o c a t e / d c n

Review

The

use

of

functional

and

effective

connectivity

techniques

to

understand

the

developing

brain

Diane

Goldenberg

_,

_Adriana

_Galván

a_{DepartmentofPsychology,UniversityofCalifornia,LosAngeles,1285FranzHall,Box951563,LosAngeles,CA90095,USA} b_{BrainResearchInstitute,UniversityofCalifornia,LosAngeles,695CharlesYoungDr.S.,LosAngeles,CA90095,USA}

a

r

t

i

c

l

e

i

n

f

o

Received15July2014

Receivedinrevisedform28January2015 Accepted29January2015

Availableonline11February2015 Keywords: Braindevelopment Functionalconnectivity Effectiveconnectivity Restingstate Graphtheory

Dynamiccausalmodeling

a

b

s

t

r

a

c

t

Developmentalneuroscience,thestudyoftheprocessesthatshapeandreshapethe matur-ingbrain,isagrowingfieldstillinitsnascentstages.Thedevelopmentalapplicationof functionalandeffectiveconnectivitytechniques,whicharetoolsthatmeasurethe inter-actionsbetweenelementsofthebrain,hasrevealedinsighttothedevelopingbrainasa complexsystem.However,thisinsightisgrantedindiscretewindowsofconsecutivetime. Thecurrentreviewusesdynamicsystemstheoryasaconceptualframeworktounderstand howfunctionalandeffectiveconnectivitytoolsmaybeusedinconjunctiontocapturethe dynamicprocessofchangethatoccurswithdevelopment.

©2015PublishedbyElsevierLtd.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).

Contents

1. Introduction... 156

2. Functionalconnectivity:resting-state ... 157

2.1. Principlesandmethodology... 157

2.2. Developmentalapplications... 158

2.3. Limitations... 158

3. Effectiveconnectivity:dynamiccausalmodeling(DCM)... 159

3.1. Principlesandmethodology... 159

3.2. Developmentalapplication... 160

3.3. Limitations... 160

4. Thebrainasalarge,complexnetwork:graphtheory ... 161

4.1. Principlesandmethodology... 161

4.2. Developmentalapplications... 161

4.3. Limitations... 162

5. Conclusionsandfuturedirections... 162

Conflictofinterest... 163

Acknowledgements ... 163

References... 163

∗ Correspondingauthor.Tel.:+13102064850. E-mailaddress:[email protected](A.Galván). http://dx.doi.org/10.1016/j.dcn.2015.01.011

1. Introduction

Thebrain is a complex and dynamic functional sys-tem,characterizedbyconstantactivityandchange.Billions ofneuronsformintricatepatternsthatcanflexibly inte-grate based on sharedfunction, forming networks that areconstrained by,but not limited to,direct structural connectionsofthebrain(Vincentetal.,2007).Functional networkshavetheamassedcapacitytosupportcomplex thoughtandactionthatanysingleelementofthesystem wouldbeunabletosupportalone.However,thetopology offunctionalnetworkshasbeenlargelyintangibleuntilthe relativelyrecentemergenceoffunctionalandeffective con-nectivitytechniques.Respectively,thesetoolsmeasurethe temporalcorrelationbetweenremoteneurophysiological events(Spornsetal.,2007)andtheinfluenceoneneural systemexertsoveranother(Friston,2009).Together, func-tionalandeffectiveconnectivitytechniqueshaveprovided remarkableinsighttothebrainasasetofinterconnected elementsembeddedwithinalargerwhole.

Increasingly,researchers in thefield of developmen-talcognitiveneuroscienceareimplementingconnectivity techniques,makingmethodologicalandconceptualstrides intheunderstandingofthedevelopingbrain(e.g.,Fairetal., 2007,2008;Dosenbachetal.,2010).Thesestudieshave revealedthatthecomplexfunctionalarchitectureofthe brainchangesthroughoutthelifespan.Specifically, func-tionalbrainnetworksinchildrenappeartobecomposed ofmultipledecentralizedclustersatthelocallevel,while adultfunctionissupportedbyamoreintegrated organiza-tiondistributedthroughoutthebrain(forreview,seeVogel etal.,2010).Tocontributetothisburgeoningliterature, thepresentreviewsummarizesandsynthesizes develop-mentalresearchimplementingconnectivitytechniquesto understandtheemergence of networksin thebrain. In otherwords,howmightmaturepatternsofconnectivity ariseasa developmentalproductofprecursorsthat did notcontainthesepatterns?Adynamicsystemsframework mayprovidevaluabletheoreticalprinciplesfor conceptu-alizingthecomplexinterrelationsofphysicalform,time, andprocessthatcontributetotheemergenceofnetworks inthehumanbrain.

Dynamicsystemstheoryhasbeenreferred toas the broadestandmostencompassingofallthe developmen-taltheories(Miller,2002).Asdefinedinthepresentreview, dynamicsystemsisatheoreticalapproachthatdescribesthe behaviorofcomplexnetworks(SmithandThelen,2003). Thisisdifferentfromthemoretechnicaluseoftheterm, dynamicalsystems,whichreferstoaclassofmathematical equationsthatdescribetime-basedsystemswith partic-ularproperties (e.g.,Luenberger, 1979). The qualitative principlesofthisapproacharecontent-independentand havebeenpreviouslyappliedtoarangeof developmen-talquestionssuchaslanguageacquisition(DeBotetal., 2007), emotion(Lewisand Granic,2002), andcognition (Thelen,1996),thoughhavenotyetbeenwidelyappliedto questionsofneurobiologicaldevelopment.Underdynamic systemstheory,developmentcanonlybeunderstoodas the multiple, mutual, and continuous interaction of all levelsofthedeveloping system.Thisconcept singularly resonateswiththegrowingunderstandingofthebrainas

an interconnectedsystem,a series of simplernetworks organizedintoincreasingly complexnetworks, undergo-ingachangingtrajectorythroughoutthelifespan(Power etal.,2010).Theapplicationofthistheorytounderstand thedevelopingbrainmayhelpanswersuchquestionsas: How canthestable and integrated patternof theadult neuralnetworkemergefromthedecentralizedpatterning typicalofachild’sbrain?Howcanthelocalcommunity clustersof a child’s brainemerge froma single neuron communicating to another? According todynamic sys-temstheory,thekeytounderstandingthesefundamental developmentalquestionslieswithintheprocessof self-organization.Someformofglobalorderorcoordination arisesout ofthelocalinteractions betweenthe compo-nents ofan initially disorderedsystem.In otherwords, development of networks may organically emerge as a productofthesystem’sownactivityandtherelationship betweenthesystem’scomponentparts.Connectivity tech-niquesprovidea setoftoolsforresearcherstoexamine interactions betweenelementsof thebrain.The current review describestoolstoassessfunctional andeffective connectivityanddescribesaframeworkfor understand-ing large-scale networks. Although the tools described heredonotrepresenttheentiretyofavailabletechniques implementedtoevaluatefunctionalandeffective connec-tivity, they are widely used and have beenselected to demonstratethepoweroftheseapproachesthematically. Individuallyandtogether,thesetoolshavethepotential tooffersignificantcontributioninthemethodologicaland conceptualstridesbeingmadetowardanunderstanding ofthedevelopingbrainasadynamicsystem.Thereaderis directedtoreviewsdiscussingmethodsnotdiscussedhere, suchasGrangercausality(Fristonetal.,2013).

Thegeneralprinciplesofdynamicsystemstheorymay beusefulforconceptualizingbiologicalself-organization. The first such principle is the tenet of multicausality, whichassumesthattheregularitiesofthematureorganism patentlyemergefrommultiplefactors,includinginternal configurationofthesystemand externalchangesinthe environmentthatthesystemrespondsto.Thestableand distributedfunctionalsystemofthematurebrainmaybe a developmental product of multiplesources, including thesystem’sinternalconfiguration(i.e.,intrinsic architec-ture) anditsresponse totheexternal environment(i.e., extrinsic architecture).The brain’s intrinsic architecture is definedasthespontaneousfluctuationsbetween ele-mentsoftheneuralsystemintheabsenceofanexplicit task,whichcanbeassessedthroughtheacquisitionof func-tionaldatasuchasresting-state.Thisintrinsicarchitecture may provide a framework for the moment-to-moment responsesthattheexternalworldevokes(FoxandRaichle, 2007; Raichle,2010).Extrinsic networks,defined as in-the-momentcouplingofregions inresponsetoexternal stimuli, maybe assessed through task-evoked effective connectivitytechniques,suchasdynamiccausalmodeling (DCM).Individuallyandtogether,theintrinsicand extrin-sicarchitecturesofthebrainhavethepotentialtoshape thedevelopmentoffunctionalnetworksthroughashared history of co-activation. Through the use of functional andeffectiveconnectivitytechniques,researcherscan bet-ter understandthe multipleinfluenceson a developing

network, including (1) the stable interactions between elementsofthesystemthatareaproductoflifetime pro-cesses(Buckneretal.,2009)and(2)themoreephemeral, flexible process of oneelement of thesystem influenc-ingthedynamicsofanotherelementinreal-time(Friston, 2009).

Understandingthewaysinwhichthesemultiple influ-encesinteract,notonlywitheachother,butacrosstime, isattheheartofthecomplexityofdevelopmentalscience. Thesecondtenetofdynamicsystemstheoryisthat devel-opmentcanonlybeunderstoodasnestedprocessesthat unfold over many timescales.For example,neural exci-tationoccursontheorderofamillisecond.Everyneural event is theinitialcondition for thenext slice of time. Developmental change occursover weeks, months, and years.Thecoherenceoftimedictatesthatthedynamics ofthesmallesttimescale(e.g.,neuralactivity)arenested withinthedynamicsof allothertimescales(e.g., devel-opmental growth). Thus, in the study of development, we mustbeconcernedwiththeinteraction ofdifferent timescales.Althoughconnectivitytechniqueshavegiven researchersunprecedentedinsighttothebrainasa com-plexsystem,thisinsightislimitedtoglimpsesofchange throughdiscretewindowsofdevelopmentaltime,eitheron thescaleofmilliseconds(effectiveconnectivity)orlifetime processes (functionalconnectivity). Comparisons among snapshots of the brain throughout developmental time maynoteffectivelycapturetheprocessofchange.Given thattheintrinsicandextrinsicarchitecturesofthebrain shapeeachotherthroughoutthenestedmillisecondsand yearsofdevelopmentaltime,perhapsamoreprecise pic-tureofdevelopmentalchangecanbecapturedthroughthe useoffunctionalandeffectiveconnectivitytoolsin con-junction.

In thecurrent review, thefunctional examination of intrinsic connectivityis described throughresting-state, which is a form of data acquisition during functional magneticresonanceimaging(fMRI).Effectiveconnectivity and subsequentextrinsicarchitectureisdiscussedusing dynamiccausalmodeling(DCM)asanexample,whichis ananalytictechniqueappliedtofMRIdata.Itisworthwhile tomentionthatpsychophysiologicalinteractions(PPI)isa task-basednon-directionalconnectivitytechniquethathas beenusedwidelybutisnotcoveredinthisreview.Graph theory,ananalytictechniquethatcanbeappliedto func-tionaloreffectiveconnectivitydata,isdiscussedtoprovide aframeworkforunderstandinglarge-scalenetworks.The principles and methodology of each technique will be reviewed, as well as their developmental applications; thelimitationsanddevelopmentalconsiderationsofeach approach will be discussed. Finally, current extensions ofthetechnologywillbesummarizedand future direc-tionsforthefieldareproposed.Thereaderisreferredto Poweret al.(2010)and Vogeletal.(2010)forexcellent and detaileddiscussionsontheuseof restingstateand graphtheoryondevelopmentalpopulations.Thepurpose of thecurrent reviewis tousedynamic systemstheory asaconceptualframeworkfortheadvancesbeingmade withfunctionalandeffectiveconnectivitytechniques;to thisend, thestudieshighlightedaredescriptive andnot exhaustive.

2. Functionalconnectivity:resting-state

2.1. Principlesandmethodology

Brainregionsthatoftenworktogetherformafunctional networkwithahighlevelofongoing,stronglycorrelated spontaneousneuronal activity,without thepresence of ataskorstimulus(FoxandRaichle,2007).Resting-state provides a method with which to measure connectiv-itybyexaminingthelevelof co-activationbetweenthe functionaltime-seriesofbrainregionsduringrest(Biswal etal.,1995).Thesepatternsofresting-statecorrelationsare hypothesizedtoreflectthestableandintrinsicfunctional architectureofthebrain(Buckneretal.,2009).

Biswalandcolleaguesfirstdemonstratedthatongoing neuralactivityoccursatrestthroughoutfunctionally con-nectedregions of the brain when theyrevealed a high correlation between the blood oxygenlevel dependent (BOLD)time-seriesoftheleftandrighthemisphericregions of theprimarymotor network in theabsenceof a task (Biswaletal.,1995).Severalstudieshavesincereplicated theseresults,propellingextensiveuseofthetechniquein adult(e.g.,FoxandRaichle,2007;Greiciusetal.,2003)and developmentalpopulations(e.g.,Fairet al.,2007,2008; Koyamaetal.,2011).

The acquisition of resting-state simply involves col-lectingfunctionalimagingdatafromparticipantsasthey layin theMRIscanner,fixatingona cross-hairor with eyesclosed, whilerefrainingfromengagingin any spe-cificcognitivetask.OnestudydemonstratedthattheBOLD responsedifferedwhenparticipantsfixatedonacross-hair comparedtoclosingtheireyes(VanDijketal.,2010),which emphasizestheimportanceofstandardizingdata collec-tiontechniquesgiventheincreasinglywidespreaduseof resting-state.

Oncedataarecollected,oneformofanalysisto exam-inethefunctionalconnectionsofaparticularbrainregion is the seed method. Seed-based ROI analysescorrelate theresting-statetime-seriesofanaprioribrainregionof interestagainstthetime-seriesofallotherbrainregions, resultinginafunctionalconnectivitymap(fcMap;Biswal etal.,1997).ThefcMapprovidesinformationaboutwhich regions the selected seed region is functionally linked to, and to what extent. The simplicity of this analysis affordsastrongadvantageforseed-dependentmethods; however,theinformationofthefcMapislimitedtothe functionalconnections oftheselectedregion,makingit difficulttoexamineconnectionpatternsonawhole-brain scale(BucknerandVincent,2007).Additionally,the selec-tionofaprioriregionsofinterestcanpresentachallenge toresearchers,giventhattherearenostraightforward pre-scriptionsforhowtoselectseeds.

Toexaminewhole-brainconnectivitypatterns, meth-odsdesignedtoevaluategeneralpatternsofconnectivity havebeenintroduced.Thereareseveralmodel-free meth-ods, though the most widely used are independent component analysis (ICA) and clustering. ICA methods requirethattheinvestigatorchoosethenumberof compo-nents,andthenasearchisconductedfortheexistenceof spatialsourcesofresting-statesignalsthatvarytogether overtimeandaremaximallydistinguishablefromother

setsofsignals(Beckmannetal.,2005).Amongthe advan-tages of ICA-based methods are their application to whole-brainvoxel-wise data and a highconsistency of reportedresults(Damoiseauxetal.,2006).Apossible dis-advantageofICAisthecomplexrepresentationofdatathat maycomplicatetranslationofresultstoclinicalrelevance (Fox and Raichle,2007).Clustering, another model-free method, maximizes the similarity between datapoints bygroupingconnectedpointsintonon-overlapping sub-clusters(Salvadoretal.,2005).Althoughclusteringmore directlyreflectsfunctionalconnectionsthanICA,itrequires additionalseed-likeprocessingstepstocomparefunctional connectivity between patients and healthy volunteers. There are several model-free and seed-based methods availablefortheanalysisofresting-statedata,thoughthere isahighdegreeofoverlapandconsistencyamongresults ofthesemethods.

Since theemergence ofresting-state, thesemethods havebeenusedtoidentifymajorfunctionalnetworks,such astheprimarymotor, visual,and auditorynetworks,in additiontohigherordercognitivesystems(Cordesetal., 2000;FoxandRaichle,2007;Greiciusetal.,2003).Of par-ticularinterestisthedefaultmodenetwork(Fig.1),which consistsoftheprecuneus,medialfrontal,andinferior pari-etalregions(Foxand Raichle,2007).Theregions ofthis networkdemonstrateasignificantlyhigherlevelof neu-ronalactivityduringrest,asopposedtowhencognitive tasksareperformed(RaichleandSnyder,2007).This sug-geststhatactivityofthisnetwork isreflecting adefault stateofneuronalactivity.

Theuseofresting-stateingeneralandtheexamination ofthedefaultmodenetworkinparticularcanbeconducted independentof taskperformance.Thismaybe advanta-geous,asdifferentiatingchangesinbrainactivationrelated totaskperformancecompared tothoserelated tobrain maturationhasbeenachallengeindevelopmentalresearch (Caseyetal.,2005).However,itisimportanttonotethat evenintheabsenceofanexplicittask,theacquisitionof resting-statedatainvolvesameta-taskinwhichthe sub-jectliessilentand still inthe scanner(Poldrack, 2014). Thismayengagebrainregionsdifferentiallyinchildrenand adultsthatareunrelatedtointrinsicmaturation,suchas developmentaldifferencesinattention.

2.2. Developmentalapplications

Thoughthetechniqueisstillinitsinfancy,the increas-inglywidespreadapplicationofresting-statehasbegunto clarifyandrevealimportantprinciplesoffunctionalbrain development.Theuseofresting-statehasnotonlydetected thepresenceofastablevisualnetworkininfantsasyoung asthreemonthsold(Kiviniemietal.,2003),ithasrevealed thatsensorimotorandvisualnetworksundergodifferential developmentaltrajectories,withsensorimotorfunctional connectivityprecedingthatinthevisualsystems(Linetal., 2008). Another study comparing network connectivity betweenchildren,adolescents,andadultsfoundthat con-nectivityofnetworksassociatedwithsocialandemotional functions exhibited the greatest developmental effects, while connectivity of networks associated with motor control did not differ between the three groups (Kelly

et al., 2009). These studies used resting-state methods withdifferentagegroupstoconfirmthelong-hypothesized organizational principle of development, demonstrating thatthematurationofmotorsystemsprecedesthe mat-urationofsystemsunderlyinghighercognition(Chugani etal.,1987).Thisideareflectstheself-organizing princi-pleofdynamicsystemstheory,anddemonstrateshowa systemmaydevelopasahierarchical,non-linearprocess.

Severalresting-statestudieshavedemonstratedthatin thedevelopmentoflarge-scalebrainsystems,functional connectivity shifts from a local to distributed architec-ture.For example, intrahemisphericconnectivitywithin localcircuits precedesthedevelopmentof longer-range interhemisphericconnectivity(Franssonetal.,2007;Liu et al., 2008). Others have found that nodes within the defaultmodenetworkaresparselyconnectedinchildren andstronglyfunctionallyconnectedinadults(Fairetal., 2008).Onegroupused5minute-longresting-statescans from a sampleof typically-developingsubjectsacross a rangeofagestomakeaccuratepredictionsabout individ-uals’brainmaturityacrossdevelopment(Dosenbachetal., 2010).Results indicatedthegreatestcontributorto pre-dictingindividual brainmaturity wasthestrengthening oftheadultbrain’smajorfunctionalnetworks,aswellas thesharpeningoftheboundariesbetweenthesenetworks (Dosenbachetal.,2010).

2.3. Limitations

Inthestudydescribedabove(Dosenbachetal.,2010), thegrouplaterdiscoveredthatdespitemeticulous atten-tion to exclusion of high-motion subjects, substantial changesinthetimecoursesofresting-statedataappeared tohavebeenintroducedbyrelativelyminorsubject move-mentsinthescanner(Poweretal.,2012).Thishasbeen a concernthathassincereceivedmuch attentioninthe developmental literature, as motion artifact specifically tendstoenhanceshort-rangeconnectivityanddiminish long-distanceconnectivityamongnetworknodes(Power etal.,2012).Thishasparticularimplicationsforconclusions drawnfromdevelopmentalresting-statestudiesbecauseit isuncleartowhatextentthefindingthatnetworksundergo a localto long-rangetrajectory hasbeen influenced by greatermotioninchildrencomparedtoadults.Giventhe potentiallylargeimplicationstherelativelysmall move-mentsinthescannermayhave,itisofcriticalimportance tounderstand howtobest model andaccount for sub-tlemotion(Poweretal.,2012;Satterthwaiteetal.,2012; VanDijketal.,2012).Foradescriptionofhowdifferent preprocessing strategiesmayalter thewaymotion arti-factmanifests,thereaderisreferredtoSatterthwaiteetal. (2013).

Additionally, raw resting-state data is influenced by physiologicalnoise(Biswaletal.,1995).Researchershave workedtodeveloptechniquestoremovethisnoise,such as spatial smoothing (to improve signal-to-noise ratio), temporalfiltering(toremovesignalcontributedby phys-iological sources),andwhole-brainsignalregression (to accountfornoisesourcessuchasmotion)(Supekaretal., 2009),althoughthedevelopmentofthesepreprocessing

Fig.1.Thedefaultmodenetwork.Correlationsbetweenaseedregionintheposteriorcingulate/precuneus(PCC)andallothervoxelsinthebrainduring rest,revealingthedefaultmodenetwork.Thetimecourseforasinglerunisshownfortheseedregion.Regionspositivelycorrelatedwithseedshownin orange,andregionsnegativelycorrelatedwithseedshowninblue.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferred tothewebversionofthearticle.)

AdaptedfromFoxetal.,2005.Copyright©2005,TheNationalAcademyofSciences. techniqueshasintroducednewconcernsaboutthe

inter-pretationofprocesseddata(Coleetal.,2010).

Resting-state is stilla novelmethod,and acquisition and analysis techniquesundergocontinual standardiza-tionandrefinement.Althoughtheconclusionsdrawnfrom resting-state data appear to be relatively robust, only time willtelltheextentofpotentiallyspurious findings due tomotionasresearcherscontinuetosearchforthe most effectivepreprocessing for raw resting-statedata. Thetechnique,thoughstillevolving,providesinvaluable informationontheintrinsicfunctionalarchitectureofthe developingbrain.

3. Effectiveconnectivity:dynamiccausalmodeling (DCM)

3.1. Principlesandmethodology

Advancements in the area of effective connectivity allowforanexaminationof co-activationbetween neu-ralregionsduringperformanceofataskorexperimental manipulation(Fristonetal.,2003);specifically,dynamic causalmodeling(DCM)providesastatisticaltooltoinfer causalarchitectureofcoupledordistributed systems.In other words, the effect of one neural region influenc-inganother givenanexternal stimuluscanbecaptured in real-time (Friston, 2009;Stephan et al., 2010). Thus, therelationshipsbetweenelementsofthesystemcanbe

examinedinadirectional,task-specificandextrinsic man-ner.

DCMmaybeusedwithdatacollectedduringfunctional magnetic resonance imaging (fMRI) to create a simple modelofneuraldynamicsin anetwork ofninteracting neuralregions(Fristonetal.,2003).Thisdynamicmodel estimateshowchangesinneuronalactivityinonenodeare causedbyactivityinanother.Sinceitsinception(Friston etal.,2003), anumber ofdevelopments haveimproved andextendedDCMasatooltofurnishanexplicit genera-tivemodelofhowobserveddataarecaused(Friston,2009). ThismeansthattheexactformoftheDCMchangeswith eachapplicationandspeakstoitsprogressiverefinement. Dynamic models are created through the use of a general bilinear state equation resulting from a Tay-lorapproximation of how changes in neural activityin one nodex1 are caused byactivity in another nodex2

(Fig. 2a, from Stephan et al., 2007). Within this equa-tion,theA-Matrixreferstothecouplingbetweenregions in the absence of experimental manipulation (called fixedoraverageconnectivity)andtheB-Matrixrefersto changesin couplingstrength causedby the experimen-talmanipulations.TheB-matrix(uj)embodiesinfluences

ofexperimentalmanipulationsthatcauseperturbationsof neuralstatesinthesenodes.Theinputstothemodelare denotedbyuandtheC-Matrixindexesthedirect influ-encesonanarea(Fig.2b,fromStephanetal.,2007).DCMs arecreatedandanalyzedwithconfigurationsofforward andbackwardself-connectionsandtheirmodulations,and

Fig.2. Dynamiccausalmodeling(DCM).ThebilinearstateequationforDCMwithfMRI(a).AnexampleofaDCMconsistingoftwonodes(x1,x2)shown

inblue.Blackarrowsrepresentfunctionalconnections.Grayarrowsrepresentexogenousinputs(u1,u2).Dottedarrowsrepresentchangesfromhidden

neuralstatestomeasurablehemodynamicobservations,showninred.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderis referredtothewebversionofthearticle.)

AdaptedfromStephanetal.(2007).ReprintedwithkindpermissionfromSpringerScienceandBusinessMedia:[JournalofBiosciences]copyright(2007). Bayesianmodelcomparisonisimplementedtoselectthe

modelthatbestfitsthedata.Inaddition,DCMprovidesa parameterestimateofthestrengthoftheconnectionand thestrengthofthemodulationbyanexperimental condi-tion.Inthisway,DCMoffersapowerfulstatisticaltoolthat evaluatesreciprocalandhierarchicalfunctional organiza-tionwithinaparticulardatasetinresponsetoextrinsictask manipulations.

3.2. Developmentalapplication

Beyondtheabilitytoevaluatefunctional communica-tionbetweennodesina causaland directionalmanner, oneofthestrengthsofDCM isthecapacity to incorpo-rateexogenous inputs in the analyses.In this way, the effectsoftaskmanipulationsonhiddenneuronalstatesand theirinteractionsareabletobeassessedand quantified (Stephanetal.,2010).Theseanalysesallowresearchersto investigatefunctionalorganizationandconnectivityinan in-the-momentmanner,examininghowcommunication betweenbrainregionschangesasaresultofexperimental manipulations,context,ortime.Despiteitspotentialutility in characterizing complex, context-dependent develop-mentalprocesses,relativelyfewstudieshaveimplemented DCMdevelopmentally.OnestudyhasimplementedDCMto examinehowthreecomponentsofrewardneurocircuitry, the nucleus accumbens, thalamus, and anterior insula, functionasanetworkduringgainorlossanticipationin adultsandyouth(Choetal.,2013).Bothgroups demon-strated a broader set of significant connections found forthelossconditionthanthegain condition,reflecting context-dependentfindings,thoughnostatistically signif-icantbetween-groupcomparisonswerefound,suggesting thatadultsandadolescentsusethisincentive-processing networkina similarmanner(Choetal.,2013).Another

recentstudyimplementedDCMtoexaminetheeffective connectivityunderlyingincreasesinrelationalintegration duringrelationalreasoningacrossdevelopment(Bazargani etal.,2014).Findingsdemonstrateddistinct developmen-taleffectsonthestrengthoflong-rangeversusshort-range connections,andthemodulatoryconnectionsofrelational integrationincreasedwithage,providingconverging evi-dencefrommultipleconnectivitytechniquesregardingthe segregationandintegrationthatareproposedtooccur dur-ingdevelopment(Vogeletal.,2010).Thereisalsoevidence thateffectivecouplingisassociatedwithbrainmaturation, suchthattop-downmodulatoryeffectsinadolescents dif-feredfromthoseinadults,suggestingtheirslowformation inhumanontogenesis(Fornarietal.,2014).Althoughthere are relatively few studies using DCM in developmental populations,morerecentstudiesarebeginningtoemerge, andtheuseofthisstatisticaltoolappearstobepromising forunderstandingcausalneurodevelopmentalprocesses. 3.3. Limitations

ItisimportanttonotethatDCMisnotanexploratory tool,asitsimplementationrequirestheformulationofa priorihypothesesandthepre-specificationofasetof mod-elsfortesting.However,amethodhasbeendevelopedto explore verylargenumbers ofmodelsusing aposthoc procedureinwhich onlythefullmodelisinverted, and the model evidence for anyreduced model is obtained usinga searchprocedure.Thissearchproceduretakesa subsetofparameterswiththeleastamountofevidence andsearchesoverallreducedmodelswithinthatsubset (Fristonetal.,2011).Additionally,DCMisdependentupon experimental manipulations; in the past,DCM was not suitable forusewithresting-statedata,although recent advancementsallowfortheapplicationofDCManalyses

ontask-freeresting-statedata(i.e.,stochasticDCM)and inexploratorysettings(Fristonetal.,2011).Itisevident that,aswithanynewtechnology,theuseofDCMrelies uponfrequentrefinementsasnewknowledgeis continu-allygainedastotheaccuracyofthetechnique.Anumberof developmentshaveimprovedandextendedDCMsinceits inception(Fristonetal.,2003).ForfMRI,modelsofprecise temporalsampling(Kiebeletal.,2007),multiplehidden statesperregion(Marreirosetal.,2008),arefined hemody-namicmodel(Stephanetal.,2007),andanonlinearmodel (Stephanetal.,2008)havebeenintroduced.Inotherwords, theanalytictechniquehasbeentailoredforusewithfMRI throughtheincorporationofmethodologicalrefinements relatedtotimingandhemodynamicresponseinthemodel, whichwasnotoriginallydevelopedforusewithfMRI.

4. Thebrainasalarge,complexnetwork:graph theory

4.1. Principlesandmethodology

Inadditiontotheformationofmultiplesubnetworks, the brain forms one integrative network that links all brainregions intoa single,complexsystem.Graph the-oryprovidesatheoreticalframeworktoexaminecomplex systems,andcanrevealimportantinformationaboutthe localandglobalorganizationoffunctionalbrainnetworks (BullmoreandSporns,2009).

Graph theory can be used to model many types of dynamicprocessesandrelationshipsinphysical,biological, social,andinformationsystems(BondyandMurty,1976). Theapplicationofgraphtheoryhasaidedinthe examina-tionofsuchvariedgridsasaircraftflightpatterns,biological systems,and theinternet,since complexnetworkstend to consistof similar topologicalpatterns betweentheir constituent parts. With respectto the brain, functional networkscanbedescribedasgraphsthatarecomposedof nodes(i.e.,brainregions)thatarelinkedbyedges, repre-sentingfunctionalconnectivity(i.e.,correlationsbetween timeseries)(Fig.3a,fromBullmoreandSporns,2009).Thus, withinthegraphtheoryframework,thenodesofthebrain networkarerepresentedasregions,whichmaybebasedon apredefinedanatomicalregionofinterestorfMRIvoxels. The level of connectivity betweentwo regions is com-putedasthelevelofcorrelationbetweenthetime-series ofthetwobrainregions.Computingtheleveloffunctional connectivitybetweenallpossiblepairsofnodesand deter-miningtheexistenceofafunctionalconnectionbyusing a predefinedstatisticalthresholdresultsina graph rep-resentation of the functionalbrain network. This graph representationallowsfortheexaminationofnetwork orga-nizationusinggraphtheory.

A network’stopologicalpatternsare evaluatedusing thekeypropertiesofgraphtheory:clusteringcoefficient, characteristic path length, node degree, centrality, and modularity(Spornsetal.,2004).Theclusteringcoefficientof agraphprovidesinformationabouttheleveloflocal clus-teringwithinagraph,expressinghowwelltheneighbors ofanodeareconnectedamongstthemselves.Thisprovides ameasureofhowmuchspatially-closerbrainregionsare connectedwitheachother,orlocalconnectednessofthe

network.Thelevelofglobalconnectivityofthenetworkcan beassessedwiththecharacteristicpathlengthofagraph, whichdescribeshowclose,onaverage,anodeofthe net-workisconnectedtoeveryothernodeinthenetwork.This providesinformationonhowefficientlyinformationcanbe integratedbetweendifferentsystems.Thedegreeofanode describesthenumberofconnectionsofanodeandprovides informationabouttheexistenceofhighlyconnectedhub nodesinthebrainnetwork.Additionally,centrality meas-uresindicatehowmanyoftheshortesttravelrouteswithin anetworkpassthroughaspecificnode,providingfurther informationontheformationofhubswithinnetworks.If anodehasahighlevelofcentrality,itfacilitatesalarge numberofshortestroutesinthenetwork,indicatingthat ithasakeyroleintheoverallcommunicationefficiency ofanetwork.Finally,thelevelofmodularityofanetwork describestheextentthatgroupsofnodesinthegraphare connectedtoothermembersof theirowngroup, estab-lishingsub-networks withinthegreaternetwork.Taken together,thesevaluesofgraphtheoryprovideimportant information about thestructure of a network and may characterizeaspecificorganizationstyle(e.g.,small-world, modular)ofthatnetwork.

Neuroimaging research applying graph theory on resting-statedatahasrevealedsmall-worldarchitecture offunctionalbrainnetworksacrossdevelopment(Achard etal.,2006;Spornsetal.,2004;BassettandBullmore,2006; Poweret al.,2012).Inotherwords,mostnodesarenot directneighbors,butmostnodescanbereachedfromevery otherbya smallnumber ofsteps.Studiesrevealhighly clusteredlarge-scalecorticalnetworks,withmost exist-ing pathwayslinking areas that are spatially close and functionallyrelated(Poweretal.,2010).Theseclusters,or modules,arethenconnectedbyspecializedhubregions. Thelong-rangeconnections betweendifferentmodules, thoughfewinnumber,keeptheoverallpathlengthsacross thenetworklow(Fig.3b,fromBullmoreandSporns,2009). Small-worldnetworkorganizationisanefficient orga-nization for flow of information (Bullmore and Sporns, 2012).Whilebothyoungandolderadultsexhibit small-worldnetworkorganization,thetopologicalrolesofthe specificbrainregionsaswellastheinter-regional connec-tivityappeartodiffersignificantlybetweenthetwogroups (Power etal.,2010).Convergingevidencefrommultiple studiessuggeststhatwhereaschildrendemonstrate sim-ilarsmall-worldarchitectureasadults(Fairet al.,2009; Supekaretal.,2009),theorganizationofindividual sub-networks has a protracted time course. Developmental studiesimplementinggraphtheoryhavethepotentialto reveal thefeatures of large-scale network development withinthebrain(KashtanandAlon,2005).

4.2. Developmentalapplications

The ontogeny of the large-scale functional organi-zationof the brainis still not wellunderstood, though studies have begun to use network analyses to reveal that children and adults display similar small-world architectureatagloballeveltomaximizeefficiency,with specific group differences in hierarchical organization andinterregionalconnectivity(Fairetal.,2009;Supekar

Fig.3. Illustrationofagraph.Graphsaremadeupofnodesandlinescallededgesthatconnectthem(a).Withtheuseofgraphtheory,researchershave characterizedthesmall-worldarchitectureofneuralnetworks.Structurallyandfunctionallyrelatedregionsaredenselyconnectedwithinhubs,ormodules; thesemodulesaresparselyconnectedwitheachother(b).

AdaptedfromBullmoreandSporns(2009).ReprintedbypermissionfromMacmillanPublishersLtd:[NatureReviewsNeuroscience]copyright(2009). etal.,2009).Forinstance,whileadultnetworksconsistof

prominentcortico-corticalconnections, childrentend to havestronger andmore abundantconnections between subcortical and cortical regions (Supekar et al., 2009). Specifically,subcorticalareasappeartobemorestrongly connected withprimary sensory,association, and para-limbicareas in children, whereas adults show stronger cortico-corticalconnectivitybetweenparalimbic, limbic, andassociationareas.Thesmall-worldnatureofthebrain mayallowfortheformationofneuralnetworksthatwork togetherina highlystableyetflexible manner,perhaps to allowfor adaptive change based on experience and environment.

Additionally,morematurebrainsexhibitgreater hier-archical organization, with more regions involved in longer-distanceclustersofactivity.Networkswithgreater hierarchyarecharacterizedbyhighdegreenodes,which exhibitlowclustering.Hierarchicalnetworkscontainsmall denselyconnected clusters that combinetoform large, less interconnected clusters, which further combine to formlargerandlesserinterconnectedclusters(Ravaszand Barabási, 2003).Hierarchical networks form to support top-downrelationshipsbetweennodeswhileminimizing wiringcosts(RavaszandBarabási,2003).Lowerlevelsof hierarchicalorganizationinchildrenmayallowformore flexibilityinnetworkgrowthonthebasisofexperience.

Finally,thedevelopmentoflarge-scaleneuralnetworks is characterized by a weakening of short-range func-tional connectivity and a strengthening of long-range functionalconnectivity.Functionalconnectivitybetween moreproximalanatomicalregionsissignificantlyhigher inchildren,whereasfunctionalconnectivitybetweenmore distalanatomicalregionsissignificantlyhigherinadults (Supekar etal., 2009).Thissuggestsa pattern ofhigher short-rangefunctionalsegregationinchildrenandhigher long-rangefunctional integrationin adults,contributing evidenceforthehypothesisthatthedevelopmentof large-scaleneuralnetworksinvolvesadualprocessoffunctional segregation and integration (Fair et al., 2007). In the first large-scalestudy to examine thelifespan trajecto-riesofbrainnetworkpropertiesbasedongraphtheory,a recentstudy(Caoetal.,2014)revealedlineardecreasesin modularityandinvertedU-shapedtrajectoriesoflocal effi-ciency.Together,thesefindingsprovideinsightsintothe

developmentoflarge-scalebrainorganizationwiththeuse ofnetworksanalysis.Inthisway,graphtheorycanprovide apowerfulstatisticalframeworktocharacterizethe devel-opment of brain systems in a comprehensive manner, consideringnotonlyrelationshipswithinagivensystem, butalsohowtheserelationshipsaresituatedwithinwider networkcontexts(Poweretal.,2010).

4.3. Limitations

Such emerging findings usegraph theory toprovide importantinsightintothedevelopmentoffunctional neu-ralsystems;however,limitationsmustbeaddressed.The functionalnetworkofthebrainiscomprisedofneurons andcolumns,physicalelementsthathavealimited abil-ityofbeingaccuratelymeasuredanddefinedinhumans. For graph theory analyses, inferences must be made when nodes are defined as voxels, or anatomically- or functionally-defined regions of interest. Definitions of nodesareparticularlydifficultindevelopmentalresearch, asthenodesarelikelynotthesameacrossthesample.The useofgraphtheoryrequirescarefulselectionofnodesand anunderstandingthatobtainedgraphsareonlyas accu-rateasthenodes.Giventhatitisimpossibletofullyknow thetruedefinitionoffunctionalnodesinthehumanbrain, graphslikelycontainsomeamountof distortion(Power etal.,2010).

5. Conclusionsandfuturedirections

The implementationof graph theorytoresting-state data has demonstrated that the brain is a remarkable andcomplexhierarchyofmultiplesubsystemswithinone dynamicsystem.Itisimportanttonotethatgraphtheory mayalsobeappliedtoeffectiveconnectivitydata,andas anincreasingnumberofdevelopmentalstudiesbeginto useDCM,adirectionalunderstandingoftheinfluenceof functionalregionswithinthecontextofthelargersystem maybepossible(BullmoreandSporns,2009).The grow-ingunderstandingofthebrainasadeveloping,hierarchical network that hasbeenattained throughthe implemen-tationoffunctionalandeffectiveconnectivitytechniques underscoresthepotentialutilityofconceptualizingthese findingswithintheframeworkofdynamicsystemstheory.

Thebrainhasbeendemonstratedtobeadynamicsystem, asetofinterconnectedelementsembeddedwithinalarger whole.

Thedevelopmentofthebrainisinfluencedbymultiple elements,withnooneelementtakingpriority.Thismeans that nosingle element(e.g.,one neuron, neuralregion, or neural system) drives development; rather, it is the interactionbetweenelementsthatisimportant.Theuse offunctionalconnectivitytechniquessuchasresting-state capturestheintrinsicandstablefunctionalnetworksofthe brain,whileeffectiveconnectivityassessesthe moment-to-momentinfluenceofoneelementofthesystemover another. In the same way that a dynamic system may generatenoveltythroughinteractionsbetweenindividual elements of the system, the combined implementation and interpretationof connectivitytechniquesmay have thepotentialtorevealnewinsightthathasnotyetbeen attainedthroughuseofthesetoolsindividually. Specifi-cally,examiningfunctionalandeffectiveconnectivitydata inconjunctionmaycapturetheprocessofchangeandthe emergenceofnovelpatternsthatmayarisefromactivity within the system itself (Smith and Thelen, 2003).We speculatethattheuseofconnectivitytoolsinconjunction may allowdevelopmental researchers to gain a deeper understandingofthemultipleandreciprocalinteractions that occuracrossmultiplehierarchiesandtimescales of thesystem.

Previousexaminationsofcouplingbetweenthe extrin-sicandintrinsicarchitectureofthebrainhasbeendone throughtheuseoflarge-scalemeta-analyticapproaches (Toroetal.,2008;Smithetal.,2009).Whilethese large-scale approaches arepowerful, theydo notcapturethe moment-to-momentcovariationofBOLDresponseacross trials (Mennes et al., 2013). Asan alternative, a recent studyinvestigatedregionalvariationataparticipantlevel bycomputingthespatialcorrelationbetweenpatternsof intrinsicfunctionalconnectivityacquiredthrough resting-stateandpatternsoftask-evokedfunctionalconnectivity foreachvoxelinthebrain(Mennesetal.,2013).Whilethis studywasdoneinadults,examiningthecouplingbetween thesetwoarchitectureshasthepotentialtocapturethe interactionbetweentwosystemsthatoperatewithin dis-tinctdevelopmentaltime.Theintrinsicarchitectureofthe brain,arelativelystablesystem,mayundergoaslow tra-jectoryof protracted changeover thelifetime. Extrinsic architecturereflectsco-activationofneuralregionstoan externalresponseinthesliceoftimeinwhichitoccurs.By examiningthecouplingofthesearchitecturesacrossthe lifespan,newinsightmaybegainedintotheorganic emer-genceofnewpatternsthroughtheinteractionoflifetime processesandin-the-momentchange.

Conflictofinterest

Therearenoconflictsofinteresttoreport.

Acknowledgements

DGissupportedbytheNationalScienceFoundation. AG is supported by The William T. Grant Foundation (GrantID:181941).TheauthorswouldliketothankDr.

AndrewFuligniforprovidingthoughtsandcommentson themanuscript.

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