Corresponding author: Frank G. Hillary, Department of ... · Graph theory approaches to functional...

Graphtheoryasatooltounderstandbraindisorders

1

Graphtheoryapproachestofunctionalnetworkorganizationinbraindisorders:

Acritiqueforabravenewsmall-world

MichaelN.Hallquist1,2

and

FrankG.Hillary1,2,3

1DepartmentofPsychology,PennsylvaniaStateUniversity,UniversityPark,PA

2SocialLifeandEngineeringSciencesImagingCenter,UniversityPark,PA

3DepartmentofNeurology,HersheyMedicalCenter,Hershey,PA

AcceptedforpublicationinNetworkNeuroscience.

Corresponding author: Frank G. Hillary, Department of Psychology, Penn State University, 140 Moore Building, University Park, PA 16802. Email: [email protected]. This research was supported by a grant from the National Institute of Mental Health to MNH (K01 MH097091). Acknowledgments.WethankZachCeneviva,AllenCsuk,RichardGarcia,MelanieGlatz,andRiddhiPatelfortheirworkcollecting,organizing,andcodingreferencesfortheliteraturereviewandmanuscript.Keywords:graphtheory,braindisorders,networkneuroscience,proportionalthresholding


2

Abstract

Overthepasttwodecades,resting-statefunctionalconnectivity(RSFC)methods

haveprovidednewinsightsintothenetworkorganizationofthehumanbrain.Studiesof

braindisorderssuchasAlzheimer’sdiseaseordepressionhaveadaptedtoolsfromgraph

theorytocharacterizedifferencesbetweenhealthyandpatientpopulations.Here,we

conductedareviewofclinicalnetworkneuroscience,summarizingmethodologicaldetails

from106RSFCstudies.Althoughthisapproachisprevalentandpromising,ourreview

identifiedfourchallenges.First,thecompositionofnetworksvariedremarkablyintermsof

regionparcellationandedgedefinition,whicharefundamentaltographanalyses.Second,

manystudiesequatedthenumberofconnectionsacrossgraphs,butthisisconceptually

problematicinclinicalpopulationsandmayinducespuriousgroupdifferences.Third,few

graphmetricswerereportedincommon,precludingmeta-analyses.Fourth,somestudies

testedhypothesesatonelevelofthegraphwithoutaclearneurobiologicalrationaleor

consideringhowfindingsatonelevel(e.g.,globaltopology)arecontextualizedbyanother

(e.g.,modularstructure).Basedonthesethemes,weconductednetworksimulationsto

demonstratetheimpactofspecificmethodologicaldecisionsoncase-controlcomparisons.

Finally,weoffersuggestionsforpromotingconvergenceacrossclinicalstudiesinorderto

facilitateprogressinthisimportantfield.


3

Introduction

Effortstocharacterizea“humanconnectome”havebroughtsweepingchangesto

functionalneuroimagingresearch,withmanyinvestigatorstransitioningfromindicesof

localbrainactivitytomeasuresofinter-regionalcommunication(Friston,2011).Thebroad

goalofthisconceptualrevolutionistounderstandthebrainasafunctionalnetworkwhose

coordinationisresponsibleforcomplexbehaviors(Biswaletal.,2010).Theprevailing

approachtostudyingfunctionalconnectomesinvolvesquantifyingcouplingoftheintrinsic

brainactivityamongregions.Inparticular,resting-statefunctionalconnectivity(RSFC)

methods(Biswal,Yetkin,Haughton,&Hyde,1995)focusoninter-regionalcorrespondence

inlow-frequencyoscillationsoftheBOLDsignal(approximately0.01-0.12Hz).

WorkoverthepasttwodecadeshasdemonstratedthevalueofRSFCapproachesfor

mappingfunctionalnetworkorganization,includingtheidentificationofseparablebrain

subnetworks(Biswaletal.,2010;Lairdetal.,2009;Poweretal.,2011;Smithetal.,2009;

vandenHeuvel&HulshoffPol,2010).BecauseRSFCmethodsdonotrequirethestudy-

specificdesignsandcognitiveburdenassociatedwithtask-basedfMRIstudies,RSFCdata

aresimpletoacquireandhavebeenusedinhundredsofstudiesofhumanbrainfunction.

Nevertheless,therearenumerousmethodologicalchallenges,includingconcernsaboutthe

qualityofRSFCdata(Poweretal.,2014)andtheeffectofdataprocessingonsubstantive

conclusions(Ciricetal.,2017;Hallquist,Hwang,&Luna,2013;Shirer,Jiang,Price,Ng,&

Greicius,2015).

RSFCstudiesofbraininjuryordiseasetypicallyexaminedifferencesinthe

functionalconnectomesofaclinicalgroup(e.g.,Parkinson’sdisease)comparedtoa

matchedcontrolgroup.Therearespecificmethodologicalandsubstantiveconsiderations


4

thatapplytoRSFCstudiesofbraindisorders.Forexample,differencesintheoveralllevel

offunctionalconnectivitybetweenpatientandcontrolgroupscouldleadtodifferencesin

thenumberofspuriousconnectionsinnetworkanalyses,potentiallyobscuringmeaningful

groupcomparisons(vandenHeuveletal.,2017).Likewise,thereisincreasingconcernin

theclinicalneurosciencesthatanunacceptablysmallpercentageoffindingsarereplicable

(Mülleretal.,2017).Suchconcernsechothegrowingemphasisonopen,reproducible

practicesinneuroimagingmoregenerally(Poldracketal.,2017).

Inthispaper,wereviewthecurrentstateofgraphtheoryapproachestoRSFCinthe

clinicalneurosciences.Basedonkeythemesinthisliterature,weconductedtwonetwork

simulationstodemonstratethepitfallsofspecificanalysisdecisionsthathaveparticular

relevancetocase-controlstudies.Finally,weproviderecommendationsforbestpractices

topromotecomparabilityacrossstudies.

Ourreviewdoesnotdirectlyaddressmanyimportantmethodologicalissuesthat

areactiveareasofinvestigation.Forexample,detectingandcorrectingmotion-related

artifactsremainsacentralchallengeinRSFCstudies(Ciricetal.,2017;Dosenbachetal.,

2017)thatisespeciallyproblematicinclinicalanddevelopmentalsamples(Greene,Black,

&Schlaggar,2016;VanDijk,Sabuncu,&Buckner,2012).Thelengthofresting-statescans

(intermsoftime,numberofmeasurements,andnumberofsessions)alsoinfluencesthe

reliabilityoffunctionalconnectivityestimates(Birnetal.,2013;Gonzalez-Castillo,Chen,

Nichols,&Bandettini,2017)andlikelyhasdownstreamconsequencesonnetworkanalyses

(Abroletal.,2017;Yangetal.,2012).Finally,brainparcellation—definingthenumberand

formofbrainregions—isoneofthemostimportantinfluencesonthecompositionof

RSFCnetworks.Therearenumerousparcellationapproaches,includinganatomicalatlases,


5

functionalboundarymapping,anddata-drivenalgorithmsbasedonvoxelwiseBOLDtime

series(Goñietal.,2014;Honnoratetal.,2015).InordertofocusonRSFCgraphtheory

researchintheclinicalliterature,whererelevant,wereferreaderstomorefocused

treatmentsofimportantissuesthatarebeyondthescopeofthispaper.

ALiteratureReviewofClinicalNetworkNeuroscienceStudies

Graphtheoryisabranchofdiscretemathematicsthathasbeenappliedinnumerous

studiesofbrainnetworks,bothstructuralandfunctional.Agraphisacollectionofobjects,

calledverticesornodes;thepairwiserelationshipsamongnodesarecallededgesorlinks

(Newman,2010).GraphscomposedofRSFCestimatesamongregionsprovideawindow

intotheintrinsicconnectivitypatternsinthehumanbrain.Figure1providesasimple

schematicofthemostcommongraphtheoryconstructsandmetricsreportedinRSFC

studies.Formorecomprehensivereviewsofgraphtheoryapplicationsinnetwork

neuroscience,seeBullmoreandSporns(2009,2012),orFornito,Zalesky,andBullmore

(2016).


6

Figure1.Atoygraphandrelatedgraphtheoryterminology.AdaptedwithpermissionfromHillary&Grafman,2017.

Thegoalofourliteraturesearchwastoobtainarepresentativecross-sectionof

graph-theoreticRSFCstudiesspanningneurologicalandmentaldisorders.Wefocusedon

functionalconnectivity(FC)asopposedtostructuralconnectivity,whereadistinctsetof

methodologicalcritiquesarelikelyrelevant.Also,wereviewedfMRIstudiesonly,

excludingelectroencephalography(EEG)andmagnetoencephalography(MEG).Although

thereareimportantadvantagesofEEG/MEGinsomerespects(Papanicolaouetal.,2017),

wefocusedonfMRIinpartbecausethevastmajorityofclinicalRSFCstudieshaveusedthis

modality.Inaddition,therearefMRI-specificconsiderationsfornetworkdefinitionand

spatialparcellationinRSFCstudies.WeconductedtworelatedsearchesofthePubMed

database(http://www.ncbi.nlm.nih.gov/pubmed)toidentifyarticlesfocusingongraph-

Clustering coefficient: local density of connections, or in this example (A and B), the number of triangles over the number of connected triples (“how many of my friends are friends with each other”). For (A) the clustering coefficient is 1, for (B) it is 0.

Degree (of a node): number of edges incident to that node.

Density: The density of the graph is the ratio of the number of observed connections in the network to the number of possible connections.

Edges: (pairwise) connections between nodes.

Hub: node with high degree or high centrality. Node b (red) has high degree and betweenness, and node c (blue) has high degree within the network. Betweenness centrality of a node reflects the frequency with which it sits along the shortest path between any two nodes in the graph.

Modules/Communities: clusters of nodes densely linked amongst themselves and more sparsely linked to nodes outside the cluster. Three communities circled in red.

Node: brain region of interest.

Path Length: here, the shortest distance (in number of edges) separating two nodes; e.g., in D from a to d = 5

Weight (of an edge): relationship between corresponding pair of nodes (e.g., correlation). In (A) and (B) the network is unweighted, while (C) is weighted.

A

C

0.4 0.20.6

0.7

D

a

bc

d

B


7

theoreticapproachestoRSFCinmentalandneurologicaldisorders(fordetailsonthe

queries,seeMethods).

ThesesearcheswereruninApril2016andresultedin626potentialpapersfor

review(281fromneurologicalquery,345frommentaldisorderquery).Studieswere

excludediftheywerereviews,casestudies,animalstudies,methodologicalpapers,used

electrophysiologicalmethods(e.g.,EEGorMEG),reportedonlystructuralimaging,ordid

notfocusonbraindisorders(e.g.,healthybrainfunctioning,normalaging).After

exclusions,thesetwosearchesyieldeddistinct106studiesincludedinthereview(see

Table1).AfulllistingofallstudiesreviewedisprovidedintheSupplementaryMaterials.

Table1.Clinicaldisordersrepresentedinthereviewof106clinicalnetworkneurosciencestudies

Note.ADHD:attentiondeficithyperactivitydisorder,MCI:mildcognitiveimpairment

ClinicalPhenotype n(frequency)Alzheimer’sDisease/MCI 19(17.9%)Epilepsy/Seizuredisorder 13(12.3%)Depression/Affective 12(11.3%)Schizophrenia 11(10.4%)Alcohol/SubstanceAbuse 7(6.6%)Parkinson’sDisease/Subcortical 6(5.7%)TraumaticBrainInjury 6(5.7%)Anxietydisorders 5(4.7%)ADHD 5(4.7%)Stroke 4(2.8%)Cancer 3(2.8%)MultipleSclerosis 2(1.9%)AutismSpectrumDisorder 2(1.9%)Disordersofconsciousness 2(1.9%)Somatizationdisorder 2(1.9%)DualDiagnosis 2(1.9%)OtherNeurologicaldisorder 3(2.8%)OtherPsychiatricdisorder 2(1.9%)


8

Below,weoutlineimportantgeneralthemesfromtheliteraturereview(ourmajor

concernsaresummarizedinBox1),includingtheheterogeneityofdataanalytic

approachesacrossgraphtheoreticalstudies.Wethenturnourfocustotwocriticalissues

withimportantimplicationsforinterpretingnetworkanalysesincase-controlstudies:1)

networkthresholding(i.e.,determininghowtodefinea“connection”fromacontinuous

measureofFC)and2)matchingthehypothesistothelevelofinquiryinthegraph.Foreach

oftheseissues,weoffernetworksimulationstoillustratetheimportanceoftheseissuesfor

case-controlcomparisons.

Box1:Majorchallengesingraph-theoreticstudiesoffunctionalconnectivityinbrain

disorders

1) There is substantial heterogeneity in defining the nodes and edges of graphs

across resting-state studies that largely precludes quantitative comparisons and formal meta-analyses. Key sources of heterogeneity include: brain parcellations, functional connectivity metrics (e.g., full versus partial correlation), handling of negative FC estimates, and preprocessing decisions (e.g., global signal regression). Furthermore, few graph metrics were reported in common, further undermining an examination of similarities across studies and disorders.

2) Many studies use proportional thresholding to convert a continuous functional connectivity metric (e.g., Pearson correlation) to a binary edge in the graph while controlling for the total number of edges. This approach may obscure the effects of brain pathology in case-control designs, where clinical groups may have changes in the number and strength of functional connections. Proportional thresholding may also identify spurious group differences when groups differ in the connectivity strength of selected brain regions.

3) The link between many graph metrics and neurobiology has been more commonly presumed than established (e.g., neural efficiency).

4) The alignment between study hypotheses and specific graph analyses was often unclear. Moreover, many studies have not considered how findings at one level (e.g., global topology) are contextualized by another (e.g., modular structure).


9

CreatingComparableNetworksinClinicalSamples

Definingnodesinfunctionalbrainnetworks.GraphtheoryanalysesofRSFCdata

fundamentallydependonthedefinitionofnodes(i.e.,brainregions)andedges(i.e.,the

quantificationoffunctionalconnectivity).Fornetworkanalysestorevealnewinsightsinto

clinicalphenomena,investigatorsmustchooseaparcellationschemethatrobustlysamples

theregionsandnetworksofinterest.Ourliteraturereviewrevealedthat76%ofstudies

definedgraphsbasedoncomprehensiveparcellations(i.e.,samplingmostorallofthe

brain),whereas24%analyzedconnectivityintargetedsub-networks(e.g.,motorregions

only;Table2a).Furthermore,wefoundsubstantialheterogeneityinparcellations,ranging

from10to67632nodes(Mode=90;M=1129.2;SD=7035.9).Infact,whereas25%of

studieshad90nodes(mostoftheseusedtheAALatlas;Tzourio-Mazoyeretal.,2002),the

frequencyofallotherparcellationsfellbelow5%,resultinginatleast50distinct

parcellationsin106studies.


10

Table2.Networkconstructionandedgedefinition

a.Networkconstruction n(frequency)Comprehensiveregionsampling 80(75.5%)Targetedregionsampling 26(24.5%)

b.Edgedefinition n(frequency)Weightednetwork 48(45.3%)Binarynetwork 42(39.6%)Both 13(12.3%)Unknown/unclear 3(2.8%)

c.EdgeFCstatistic n(frequency)Correlation(typically,Pearson’sr) 82(77.3%)Partialcorrelation 11(10.4%)Waveletcorrelation 6(5.7%)Causalmodeling(e.g.,SEM) 3(2.8%)Other/unclear 4(3.7%)

d.TreatmentofNegativeedges n(frequency)Notreported/unclear 61(57.5%)Discardnegativevalues 23(21.7%)Absolutevalue 10(9.4%)Maintained/analyzed 9(8.5%)Othertransformation 3(2.8%)Note.FC=functionalconnectivity;SEM=structuralequationmodeling

Althoughitmayseemself-evident,itbearsmentioningthatseveralpopular

parcellationschemesprovideabroad,butnotcomplete,samplingoffunctionalbrain

regions.Forexample,recentparcellationsbasedonthecorticalsurfaceofthebrain(e.g.,

Glasseretal.,2016;Gordonetal.,2016)haveprovidedanewlevelofdetailonfunctional

boundariesinthecortex.Yetifaresearcherisinterestedincortical-subcortical

connectivity,itiscrucialthattheparcellationbeextendedtoincludeallrelevantregions.

Thereareadvantagesandchallengestoeveryparcellationapproach(e.g.,Honnorat

etal.,2015;Poweretal.,2011);here,wefocusontwospecificconcerns.First,agoalof

mostclinicalnetworkneurosciencestudiesistodescribegroupdifferencesinwhole-brain


11

connectivitypatternsthatarereasonablyrobusttothegraphdefinition.Thus,investigators

maywishtouseatleasttwoparcellationsinthesamedatasettodetermineifthefindings

areparcellation-dependent.Becauseofthefundamentaldifficultyincomparingunequal

networks(vanWijk,Stam,&Daffertshofer,2010),onewouldnotexpectidenticalfindings.

Inparticular,globaltopologicalfeaturessuchasefficiencyorcharacteristicpathlength

mayvarybyparcellation,butotherfeaturessuchasmodularityandhubarchitectureare

likelytobemorerobust.Applyingmultipleparcellationstothesamedatasetincreasesthe

numberofanalysesmultiplicatively,aswellastheneedtoreconcileinconsistentfindings.

Cassidyandcolleagues(2018)recentlydemonstratedthatpersistenthomology,a

techniquefromtopologicalanalysis,hasthepotentialtoquantifythesimilarityof

individualfunctionalconnectomesacrossdifferentparcellations.Webelievethatsuch

directionsholdpromiseforsupportingreproduciblefindingsinclinicalRSFCstudies

(Craddock,James,Holtzheimer,Hu,&Mayberg,2012;Royetal.,2017;Schaeferetal.,in

press).

Second,differencesinparcellationfundamentallylimittheabilitytocompare

studies,bothdescriptivelyandquantitatively.Asnotedabove,ourreviewrevealed

substantialheterogeneityinparcellationschemesacrossstudiesofbraindisorders.

Extendingourconcernaboutparcellationdependence,suchheterogeneitymakesit

impossibletoascertainwhetherdifferencesbetweentwostudiesofthesameclinical

populationareanartifactofthegraphdefinitionorameaningfulfinding.Moreover,

whereasmeta-analysesofstructuralMRIandtask-basedfMRIstudieshavebecome

increasinglypopular(e.g.,Goodkindetal.,2015;Mülleretal.,2017),suchanalysesarenot

currentlypossibleingraph-theoreticstudiesinpartbecauseofdifferencesinparcellation.


12

Toresolvethisissue,weencouragescientiststoreportresultsforafield-standard

parcellation,apointweelaborateinourrecommendationsbelow.Wealsobelievethereis

valueininvestigatorshavingfreedomtotestandcompareadditionalparcellationsthat

mayhighlightspecificfindings.

Definingedgesinfunctionalbrainnetworks.Parcellationdefinesthenodes

comprisingagraph,butanequallyimportantdecisionishowtodefinefunctional

connectionsamongnodes(i.e.,theedges).Thevastmajority(77%)ofthestudiesreviewed

usedbivariatecorrelation,especiallyPearsonorSpearman,asthemeasureofFC.InCritical

Issue1below,weconsiderhowFCestimatesarethresholdedinordertodefinesedgesas

presentorabsentinbinarygraphs.

Quantifyingfunctionalconnectivity.ThestatisticalmeasureofFChasimportant

implicationsfornetworkdensityandtheinterpretationofrelationshipsamongbrain

regions.Theprevailingapplicationofmarginalassociation(typically,bivariatecorrelation)

doesnotseparatethe(statistically)directconnectivitybetweentworegionsfromindirect

effectsattributabletoadditionalregions.Bycontrast,mostconditionalassociation

methods(e.g.,partialcorrelation)relyoninvertingthecovariancematrixamongall

regions,therebyremovingcommonvarianceanddefiningedgesbasedonunique

connectivitybetweentworegions(Smithetal.,2011).

Atthepresenttime,thereisnoclearresolutiononwhetherFCshouldbebasedon

marginalorconditionalassociation(forusefulreviews,seeFallani,Richiardi,Chavez,&

Achard,2014;Varoquaux&Craddock,2013).Nevertheless,wewishtohighlightthatasthe

averagefullcorrelationincreaseswithinanetwork,partialcorrelationvalues,onaverage,

mustdecrease.Furthermore,partialandfullcorrelationsrevealfundamentallydifferent


13

graphtopologiesinresting-statedata(Cassidyetal.,2018)andmayyielddifferent

conclusionsaboutthesamescientificquestion(e.g.,identifyingfunctionalhubs;seeLiang

etal.,2012).Incasesofneuropathologywhereonemightexpectdistinctgainsorlossesof

functionalconnections,theuseofpartialcorrelationshouldbeinterpretedbaseduponthe

relativeedgedensityandmeanFC.Ofthestudiesreviewedhere,10%usedpartial

correlation,butvirtuallynostudyaccountedforpossibledifferencesinedgedensity(see

Table2c).

Negativeedges.Anotherimportantaspectofdefiningedgesishowtohandle

negativeFCestimates.FullcorrelationsofRSFCdatatypicallyyieldanFCdistributionin

whichmostedgesarepositive,butanappreciablefractionarenegative.Bycontrast,partial

correlationmethodsoftenyieldarelativebalancebetweenpositiveandnegativeFC

estimates(e.g.,Y.Wang,Kang,Kemmer,&Guo,2016).Thereremainslittleconsensusfor

handlingorinterpretingnegativeedgeweightsinRSFCgraphanalyses(cf.Murphy&Fox,

2017).Inourreview,57%ofthestudiesreportedinsufficientornoinformationabouthow

negativeedgeswerehandledingraphanalyses(Table2d).Twenty-onepercentofstudies

deletednegativeedgespriortoanalysis,and9%includedthenegativeweightsaspositive

weights(i.e.,usingtheabsolutevalueofFC).Asdetailedelsewhere,somegraphmetricsare

eithernotdefinedorneedtobeadaptedwhennegativeedgesarepresent(Rubinov&

Sporns,2011).

Importantly,themeanofthemarginalassociationRSFCdistributiondependson

whetherglobalsignalregression(GSR)isincludedinthepreprocessingpipeline(Murphy,

Birn,Handwerker,Jones,&Bandettini,2009).WhenGSRisincluded,thereisoftena

balancebetweenpositiveandnegativecorrelations.IfGSRisincludedasanuisance


14

regressor,alargefractionofFCestimatesmaysimplybediscardedasirrelevanttocase-

controlcomparisons,whichisamajor,untestedassumption.ThemeaningofnegativeFC,

however,remainsunclear,withseveralinvestigatorsattributingnegativecorrelationsto

statisticalartifactsandGSR(Murphyetal.,2009;Murphy&Fox,2017;Saadetal.,2012).

GiventhatnegativecorrelationsareobservableintheabsenceofGSR,however,

othershaveexaminedwhethernegativeweightscontributedifferentiallytoinformation

processingwithinthenetwork(Parenteetal.,2017).Negativecorrelationsmayalsoreflect

NMDAactionincorticalinhibition(Anticevicetal.,2012).Theseconnectionsbear

considerationgiventhatbrainnetworkscomposedofonlynegativeconnectionsdonot

retainasmall-worldtopology,butdohavepropertiesdistinctfromrandomnetworks

(Parenteetal.,2017;Schwarz&McGonigle,2011).Altogether,theomissionof

methodologicaldetailsaboutnegativeFCinempiricalreportsseverelyhampersthe

resolutionofthisimportantchoicepointindefininggraphs.

Degreedistributionasafundamentalgraphmetric.Afterresolvingthe

questionsofnodeandedgedefinition,wealsobelieveitiscrucialforstudiestoreport

informationaboutglobalnetworkmetricssuchascharacteristicpathlength,clustering

coefficient(akatransitivity),anddegreedistribution.AsnotedinTable3,localandglobal

efficiencywerecommonlyreported(71%and74%,respectively)andtypicallyacross

multipleFCthresholds.However,ourreviewrevealedthatonly27%ofstudiesprovided

cleardescriptivestatisticsformeandegree,and16%plottedthedegreedistribution.In

binarygraphs,thedegreedistributiondescribestherelativefrequencyofedgesforeach

nodeinthenetwork.Asimilarpropertycanbequantifiedbyexaminingthestrength(aka

cost)distributioninweightedgraphs.Wearguethatpresentationofthedegree(strength)


15

distributioninpublishedreportsisvitaltounderstandinganyRSFCnetworkforafew

reasons.First,itprovidesasanitycheckonthedata.Onecurrentperspectiveisthathuman

brainsareorganizedtomaximizecommunicationwhileminimizingwiringandmetabolic

cost(Bassettetal.,2009;Betzeletal.,2017;Chen,Wang,Hilgetag,&Zhou,2013;Tomasi,

Wang,&Volkow,2013),Thus,whenexaminingwhole-brainRSFCdata,themosthighly

connectedregionsarerareandshouldbeevidentinthetailofthedegree/strength

distribution(Achard,Salvador,Whitcher,Suckling,&Bullmore,2006).Second,reporting

detailsofthedegreedistributionfacilitatescomparisonsofgraphtopologyacrossstudies,

aswellastheimpactofpreprocessingandanalyticdecisionssuchasFCthresholding.

Finally,examiningthedegreedistributionasafirststepindataanalysismayoffer

otherwiseunavailableinformationaboutthenetworktopologyinhealthyandclinical

samples.Forexample,inpriorwork,weisolatededgesfromthetailofthedegree

distributiontounderstandtheimpactofthemosthighlyconnected,andrare,nodesonthe

network(Hillaryetal.,2014).

Table3.GraphmetricscommonlyreportedinclinicalRSFCstudies

Graphmetrics n(frequency)DegreeDistribution(plotted) 17(16.0%)MeanDegree(weightedorbinary) 29(27.4%)Clustering/Localefficiency 76(71.7%)PathLength/Globalefficiency 79(74.5%)Smallworldness 33(31.1%)Modularity(e.g.,Q-value) 21(19.8%)

Note.Totalfrequencyisgreaterthan100%becausesomestudiesreportedmorethanoneofthesemetrics.


16

CriticalIssue1:EdgeThresholdingandComparingUnequalNetworks

Wenowfocusonedgethresholding—thatis,howtotransformacontinuous

measureofFCintoanedgeinthegraph.Inourreview,39%ofstudiesbinarizedFCvalues

suchthatedgeswereeitherpresentorabsentinthegraph,whereas45%ofstudies

retainedFCasedgeweights(seeTable2b).Regardlessofwhetherinvestigatorsanalyze

binaryorweightednetworks,therearefundamentalchallengestocomparingnetworks

thatdiffereitherintermsofaveragedegree(k)orthenumberofnodes(N)(Fornitoetal.,

2016).Inparticular,comparinggroupsongraphmetricssuchaspathlengthandclustering

coefficientcanbeambiguousbecausethesemetricshavemathematicaldependencieson

bothkandN(vanWijketal.,2010).

Mostbrainparcellationapproachesdefinegraphswithanequivalentnumberof

nodes(N)ineachgroup.Ontheotherhand,connectiondensityisoftenavariableof

interestinclinicalstudieswherethepathologymayalternotonlyconnectionstrength,but

alsothenumberofconnections.IfNisconstant,variationinkbetweengroupsconstrains

theboundariesoflocalandglobalefficiency.Iftwogroupsdiffersystematicallyinedge

density,thisalmostguaranteesbetween-groupdifferencesinmetricssuchasclustering

coefficientandpathlength.Determiningwheretointerveneinthiscircularproblemhas

greatimportanceinclinicalnetworkneuroscience,wherehypothesesoftenfocusonthe

numberandstrengthofnetworkconnections.

Toaddressthisissue,severalinvestigatorshaverecommendedproportional

thresholding(PT)inwhichtheedgedensityisequatedacrossnetworks(Achard&

Bullmore,2007;Bassettetal.,2009;Power,Fair,Schlaggar,&Petersen,2010).

Furthermore,toreducethepossibilitythatfindingsarenotspecifictothechosendensity


17

threshold,29%ofstudieshavetestedforgroupdifferencesacrossarange(e.g.,5-25%;

Table4).However,wearguethatdefiningedgesbasedonPTmaynotbeidealforclinical

studies,wherethereareoftenregionaldifferencesinfunctionalcouplingorpathology-

inducedalterationsinthenumberoffunctionalconnections(Hillary&Grafman,2017).For

example,indepression,thedorsomedialprefrontalcortexexhibitsenhancedconnectivity

withdefaultmode,cognitivecontrol,andaffectivenetworks(Sheline,Price,Yan,&Mintun,

2010).Asdemonstratedbelow,whenFCdiffersinselectedregionsbetweengroups,PTis

vulnerabletoidentifyingspuriousdifferencesinnodalstatistics(e.g.,degree).The

concernsexpressedhereextendfromvandenHeuvelandcolleagues(2017),who

demonstratedthatPTincreasesthelikelihoodofincludingspuriousconnectionsinthe

networkwhengroupsdifferinmeanFC.

Table4.Thresholdingmethodfordefiningedgesingraphs

Natureofthresholding n(frequency)Allconnectionsretained 6(5.7%)Singlebyvalue 25(23.6%)Multiplebyvalue 28(26.4%)Singlebydensity 5(4.7%)Multiplebydensity 31(29.2%)Bothbyvalueanddensity 7(6.6%)Other(connectionslost) 3(2.8%)Unknown/unclear 1(0.9%)

Note.Value:thresholdingdeterminedbyFCstrength,includingstatisticallycorrectedanduncorrectedvalues;Single:analysesreportedatasinglethresholdvalue;Multiple:networkexaminedacrossmultiplethresholds.

SimulationtodemonstrateaproblemwithPTingroupcomparisons:Whack-

a-node.Inthefirstsimulation—‘whack-a-node’—weexaminedtheconsequencesofPT

onregionalinferenceswhengroupsdifferinFCforselectedregions.Unlikeempirical


18

resting-statefMRIdata,wheretheunderlyingcausalprocessesremainrelativelyunknown,

simulationsallowonetotesttheeffectofbiologicallyplausiblealterations(e.g.,

hyperconnectivityofcertainnodes)onnetworkanalyses.Simulationscanalsoclarifythe

effectsofalternativeanalyticdecisionsonsubstantiveconclusionsinempiricalstudies.For

thedetailsofoursimulationapproach,seeMethods.Briefly,weusedanetwork

bootstrappingapproachtosimulateresting-statenetworkdataforacase-controlstudy

with50patientsand50controls.Werepeatedthissimulation100times,increasing

connectivityforpatientsinthreerandomlytargetednodes(hereaftercalled‘Positive’)and

decreasingconnectivityslightly,butnonsignficantly,inthreerandomnodes(‘Negative’).

Oursimulationscapturedbothbetween-andwithin-personvariationinFCchangesfor

targetednodes(seeMethods,Equations5-7).WecomparedchangesinPositiveand

NegativenodestothreeComparatornodesthatdidnotdifferbetweengroups.

Resultsofwhack-a-nodesimulation.

Proportionalthresholding.Inamultilevelregressionofgroupdifferencet-statistics

(patient–control)ondensitythreshold,wefoundthatPTwassensitiveto

hyperconnectivityofPositivenodes,reliablydetectinggroupdifferences,averaget=12.4

(SD=1.15),averagep<.0001(Figure2a).Importantly,however,degreewassignificantly

lowerinpatientsthancontrolsforNegativenodes,averaget=-6.52(SD=1.15),averagep

<.001.WedidnotfindanysystematicdifferencebetweengroupsinComparatornodes,

averaget=-.22(SD=.65),averagep=.47.

Thesegroupdifferenceswerequalifiedbyasignificantdensityxnodetype

interaction(p<.0001)suchthatgroupdifferencesforPositivenodeswerelargerathigher

densities(Figure3,toppanel),B=11.32(95%CI=10.59–12.04),t=30.72,p<.0001.


19

Conversely,wefoundequal,butopposite,shiftsinNegativenodes(Figure3,middlepanel):

groupdifferencesbecameincreasinglynegativeathigherdensities,B=-11.93,(95%CI=-

12.65–-11.2),t=-32.74,p<.0001.However,wedidnotobserveanassociationbetween

densityandgroupdifferencesinComparatornodes,B=.31,p=.40(Figure3,bottom

panel).


20

Figure2.Theeffectofthresholdingmethodongroupdifferencesindegreecentralitywhenthereisstronghyperconnectivityinthreerandomlyselectednodes(Positive)andweakhypoconnectivityinthreenodes(Negative).Threeunaffectednodesaredepictedforcomparison(Comparator).Forparametersofthissimulation,seeTableS1,Whack-a-nodehyperconnectivity.Thecentralbarofeachrectangledenotesthemediantstatistic(patient–control)across100replicationdatasets(patientn=50,controln=50),whereastheupperandlowerboundariesdenotethe90thand10thpercentiles,respectively.Thedarklineatt=0reflectsnomeandifferencebetweengroups,whereasthelightgraylinesatt=-1.99and1.99reflectgroupdifferencesthatwouldbesignificantatp=.05.a)Graphsbinarizedat5%,15%,and25%density.b)Graphsbinarizedatr={.2,.3,.4}.c)Graphsbinarizedatr={.2,.3,.4},withdensityincludedasabetween-subjectscovariate.d)Strengthcentrality(weightedgraphs).

−505

1015

0.05 0.15 0.25Density

Mea

n t

Density thresholda)

−505

1015

0.4 0.3 0.2Pearson r

FC Thresholdb)

−505

1015


Mea

n t

FC threshold, covary densityc)

−505

1015

Node TypePositiveNegativeComparator

Weightedd)


21

Figure3.Theeffectofdensitythresholdongroupdifferencesindegreecentrality.Dotsdenotethemeantstatisticatagivendensity,whereasverticallinesdenotethe95%confidenceinterval.Allstatisticsreflectgroupdifferencesindegreecentralitycomputedongraphsbinarizedatdifferentdensities.

Functionalconnectivity(FC)thresholding.Ingraphsthresholdedatdifferinglevelsof

FC(rsrangingbetween.2and.5),wefoundreliableincreasesinPositivenodesinpatients,

averaget=6.37,averagep<.0001(Figure2b).Negativenodes,however,werenot

significantlydifferentbetweengroups,averaget=-1.75,averagep=.23.Neitherdid

Comparatornodesdifferbygroup,averaget=.05,p=.50.UnlikePT,forFC-thresholded

graphs,wedidnotfindasignificantthresholdxnodetypeinteraction,!2(16)=13.38,p=

.65.

●

●

●

●

●●

●●

●

●

●

●

●

●●

●●

●

●

●

●●

● ●● ● ●

Comparator

Negative

Positive

0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 0.25

11

12

13

−7

−6

−5

−0.4

−0.2

Density threshold

Aver

age

grou

p di

ffere

nce t


22

Functionalconnectivitythresholdingwithdensityascovariate.Bydefinition,FC

thresholdingcannothandletheproblemofgroupdifferencesinmeanFC.Thus,theriskof

FCthresholdingaloneisthatnodalstatisticsmayreflectgroupdifferencesinmeanFCthat

affectinterpretationoftopologicalmetrics(e.g.,smallworldness).Tomitigatethisconcern,

onecouldthresholdatatargetFCvalue,thenincludegraphdensityforeachsubjectasa

covariate(assuggestedbyvandenHeuveletal.,2017).AsdepictedinFigure2c,however,

althoughthisstatisticallycontrolsfordensity,italsoreintroducestheconstraintthatthe

groupsmustbeequalinaveragedegree.Asaresult,thepatternofeffectsmirrorsthePT

graphs(Figures2a,3).Morespecifically,groupdifferencesinPositivenodeswerereliably

detected,averaget=12.39,averagep<.0001.Butpatientsappearedtobesignificantly

morehypoconnectedinNegativenodescomparedtocontrols,averaget=-6.59,averagep

<.001.

Weightedanalysis.Inanalysesofstrengthcentrality,weobservedsignificantly

greaterdegreeinPositivenodes,averaget=5.5,averagep=.0003(Figure2d).Asexpected

givenoursimulationdesign,NegativeandComparatornodeswerenotsignificantly

differentbetweengroups,averageps=.19and.49,respectively.

Discussionofwhack-a-nodesimulation.Inour‘whackanode’simulation,three

nodeswererobustlyhyperconnectedin‘patients’,whilethreenodeswereweakly

hypoconnected.Theprincipalfindingofthissimulationwasthatenforcingequalaverage

degreeusingPTcanspuriouslymagnifychangesingroupcomparisonsofnodalstatistics.

Whenthegroupswereotherwiseequal,hyperconnectivityinselectednodeswas

accuratelydetectedusingPTacrossdifferentgraphdensities.However,nodesthatwere

weaklyhypoconnectedtendedtobeidentifiedasstatisticallysignificant.Theinclusionof


23

lowmagnitude,spuriousconnectionsintothenetworkinheresfromthewayinwhichPT

handlesthetailsoftheFCdistribution.

ByretainingonlyedgesatthehighendoftheFCdistribution,edgesthatareonthe

cuspofthatcriterionaremostvulnerabletobeingremoved.Forexample,atadensityof

25%,smallvariationinFCstrengthnearthe75thpercentilecouldleadtoinclusionor

omissionofanedge.Asaresult,ifFCforedgesincidenttoagivennodetendstobeweaker

inonegroupthantheother,thenbinarygraphsgeneratedusingPTwillmagnifythe

statisticalsignificanceofdifferencesindegreecentrality.Totheextentthatnodal

differencesinFCstrengthrepresentashiftinthecentraltendencyofthedistribution,this

problemisnotsolvedbyapplyingmultipledensitythresholds(Figure3).Weobservedthe

sameproblemifthedirectionofFCchangeswasflippedinthesimulation:underPT,group

comparisonsweresignificantforweaklyhyperconnectednodesifsomenodeswere

robustlyhypoconnected(seeFigureS1).Moreover,ourfindingswerequalitatively

unchangedwhensimulatedchangesinFCwereappliedproportionatetotheoriginal

connectionstrength,ratherthanshiftingconnectivityincorrelationalunits(seeFigureS2).

ThisadditionalsimulationrespectedbiologicallyplausiblevariationinFC(e.g.,greater

averageconnectivityinfunctionalhubs).

WeexaminedFC-basedthresholding(here,usingPearsonrasthemetric)and

weightedanalysesascomparisonstoPT.Thesemethodsdonotsufferfromthespurious

detectionofnodaldifferencesevidentunderPT.Rather,FCthresholdingaccurately

detectedhyperconnectednodesacrossdifferentthresholdswhilenotmagnifying

significanceoftheweaklyhypoconnectednodes.However,asnotedelsewhere(vanden

Heuveletal.,2017;vanWijketal.,2010),iftwogroupsdifferinmeanFC,thresholdingata


24

givenlevel(e.g.,r=.3)inbothgroupswillleadtodifferencesingraphdensity.Thiscould

manifestaswidespreaddifferencesinnodalstatisticsduetoglobaldifferencesinthe

numberofedges.Weconsideredwhetherincludingper-subjectgraphdensityasa

covariateingroupdifferenceanalysescouldretainthedesirableaspectsofFCthresholding

whileaccountingforthepossibilityofglobaldifferencesinFC.Wefound,however,that

statisticallycovaryingfordensitywasqualitativelysimilarinitseffectstoPTbecauseit

constrainsthesumofdegreechangesacrossthenetworktobezerobetweengroups(i.e.,

equalaveragedegree).

ThegoalofoursimulationwastoprovideaproofofconceptthatPTmaynegatively

affectnodalstatisticsincase-controlgraphstudiesbyenforcingequalaveragedegree.We

didnot,however,testarangeofparameterstoidentifytheconditionsunderwhichthis

concernholdstrue.Thesimulationfocusedspecificallyondegreecentralityinthebinary

caseandstrengthintheweightedcase.Whileuntested,weanticipatethattheseeffects

likelygeneralizetoothernodalmeasuressuchaseigenvectorcentrality.Importantly,the

problemswithPThighlightedaboveoccurregardlessofedgedensity(Figure3),sotheuse

ofmultipleedgedensitiesdoesnotadequatelyaddressthe“whack-a-node”issue.

CriticalIssue2:Matchingtheorytoscale:Telescopinglevelsofanalysisingraphs

Thesecondmajormethodologicalthemefromourliteraturereviewconcernsthe

alignmentbetweenneurobiologicalhypothesesandgraphanalyses.Werefertothisas

theory-to-scalematching.RSFCgraphsoffertelescopinglevelsofinformationabout

intrinsicconnectivitypatterns,fromglobalinformationsuchasaveragepathlengthto

detailssuchasconnectivitydifferencesinaspecificedge.Forexample,inmajordepression,

resting-statestudieshavefocusedanalysesonspecificsubnetworkscomposedofthe


25

dorsalmedialprefrontalcortex,anteriorcingulatecortex(ACC),amygdala,andmedial

thalamus(forareview,seeL.Wang,Hermens,Hickie,&Lagopoulos,2012).

Weproposethatgraphanalysesshouldbeconceptualizedandreportedintermsof

telescopinglevelsofanalysisfromglobaltospecific:globaltopology,modularstructure,

nodaleffects,edgeeffects.Ourreviewoftheclinicalnetworkneuroscienceliterature

revealedthatthemajorityofstudies(69%;seeTable5)testedwhethergroupsdifferedon

globalmetricssuchassmall-worldness.Importantly,however,manystudiesprovided

limitedtheoreticaljustificationforwhythepathophysiologyofagivenbraindisorder

shouldaltertheglobaltopologyofthenetwork.Inthefollowing,weprovidemorespecific

commentsonpathlengthandsmall-worldness,andhowinvestigatorsmightideallymatch

hypothesestolevelsofanalysis.

Table5.Levelofgroupdifferencehypothesesingraphanalyses(i.e.,telescoping)

Hypothesislevel n(frequency)Global 73(68.9%)Module(subnetwork) 41(38.7%)Nodal(Region) 52(49.1%)Edge 1(0.9%)Note.Global:examiningwhole-graphnetworkfeatures(e.g.,small-worldness),Module:examiningsubnetworks/modules(e.g.,defaultmodenetwork).Totalfrequencyisgreaterthan100%becausesomestudiestestedhypothesesatmultiplelevels.

Theclinicalmeaningfulnessofsmall-worldness.Inadefiningstudyfornetwork

neuroscience,WattsandStrogatz(1998)demonstratedthattheorganizationofthecentral

nervoussysteminC.elegansreflecteda“small-world”topology(cf.Muldoon,Bridgeford,&

Bassett,2016).Theimpactofthisfindingcontinuestoresonateinthenetwork

neuroscienceliterature20yearslater(Hilgetag&Kaiser,2004;Sporns&Zwi,2004),with


26

manystudiesfocusingon“disconnection”andthelossofnetworkefficiencyasquantified

bysmall-worldness(31%ofthestudiesreviewedhere).Althoughsmall-worldtopologies

havebeenobservedinmoststudiesofbrainfunction(Bassett&Bullmore,2016),the

relevanceofthisorganizationforfacilitatinghumaninformationprocessingremains

unclear.Otherfeaturesofhumanneuralnetworks,suchasmodularity,mayhavemore

importantimplicationsfornetworkfunctioning(Hilgetag&Goulas,2015).Highernetwork

modularityreflectsagraphinwhichtheconnectionsamongnodestendtoformmore

denselyconnectedcommunities,whichtendtoberobusttorandomnetworkdisruption

(Shekhtman,Shai,&Havlin,2015).

Itremainsuncertainthat,asageneralrule,brainpathologyshouldbereflectedina

measureofsmall-worldness.Forexample,asmall-worldtopologyispreservedevenin

experimentsthatdramaticallyreducesensoryprocessingviaanesthesiainprimates

(Vincentetal.,2007)andindisordersofconsciousnessinhumans(Croneetal.,2014).

Recognizingthatconventionalmeasuresofsmall-worldness(e.g.,Humphries&Gurney,

2008)dependondensityanddonothandlevariationinconnectionstrength,recent

researchhasrecastthisconceptanditsquantificationintermsofthe“smallworld

propensity”ofanetwork(Muldoonetal.,2016).

Althoughwedonotdisputethevalueofglobalgraphmetricssuchassmall-

worldnessasimportantdescriptorsofanetworkorganization,bydefinition,theyprovide

informationatonlythemostmacroscopiclevel.Groupdifferencesinglobalmetricsmay

largelyreflectmorespecificeffectsatfinerlevelsofthegraph.Forexample,removing

connectionsinfunctionalhubregionsselectivelytendstoreduceglobalefficiencyand

clustering(Hwang,Hallquist,&Luna,2013).Likewise,failingtoidentifygroupdifferences


27

inglobalstructuredoesnotimplyequivalenceatotherlevelsofthegraph(e.g.,nodesor

modules).Todemonstratethepointthatsubstantialgroupdifferencesinfinerlevelsofthe

graphmaynotbeevidentinglobalmetrics,weconductedasimulationinwhichthegroups

differedsubstantiallyinmodularconnectivity.

Simulationtodemonstratetheimportanceofunderstandinggraphsat

multiplelevels:globalinsensitivitytomodulareffects.Extendingthebasicapproachof

ourwhack-a-nodesimulation,weuseda13-moduleparcellationofthe264-node

groundtruthgraphinasimulationof50‘controls’and50‘patients’(modularstructure

fromPoweretal.,2011).Morespecifically,weincreasedFCinthefronto-parietalnetwork

(FPN)anddorsalattentionnetwork(DAN)incontrols,andincreasedFCinthedefault

modenetwork(DMN)inpatients.Thesimulationprimarilyexaminedgroupdifferencesin

small-worldness(globalmetric)andwithin-andbetween-moduledegree(nodalmetrics).

AdditionaldetailsareprovidedintheMethods.

Resultsofglobalinsensitivitysimulation.Consistentwithcommonmethodsinthe

field,weappliedproportionalthresholding(PT)between7.5%and25%toeachgraph.We

computedsmall-worldness,",ateachthreshold(seeMethods),thentestedforgroup

differencesinthiscoefficient.AsdepictedinFigure4,wedidnotobserveanysignificant

groupdifferencesinsmall-worldnessatanyedgedensity,Mt=.36,ps>.3.


28

Figure4.Groupdifferencesinsmallworldness(")asafunctionofedgedensity.Thecentralbarofeachrectangledenotesthemedian"statistic(patient–control),whereastheupperandlowerboundariesdenotethe90thand10thpercentiles,respectively.

However,consistentwiththestructureofoursimulations,wefoundlargegroup

differencesinwithin-andbetween-moduledegree(Figure5).Inamultilevelregressionof

within-networkdegreeongroup,density,andmodule,wefoundasignificantDMNincrease

inpatientsirrespectiveofdensity,B=1.37,t=33.25,p<.0001.Likewise,controlshad

significantlyhigherwithin-networkdegreeintheFPNandDAN,ts=21.67and13.52,

respectively,ps<.0001.Thesefindingsweremirroredingroupanalysesofbetween-

networkdegreeintheDMN,FPN,andDAN,ps<.0001(seeFigure5).

1.08

1.12

1.16

1.20

1.24

10 15 20 25Density (%)

Smal

l wor

ldne

ss (σ

)

Groupcontrolspatients


29

Figure5.Groupdifferencesinz-scoreddegreestatisticsat10and20%density.Degreedifferencesforconnectionsbetweenmodulesaredepictedinthetoprow,whereaswithin-moduledifferencesareinthebottomrow.Dotsdenotethemeanzstatisticacrossnodes,whereasthelinesrepresentthe95%confidenceintervalaroundthemean.NonsignificantgroupdifferencesintheVisualnetworkaredepictedforcomparison,whereasconnectivityintheDAN,FPN,andDMNwasfocallymanipulatedinthesimulation.DAN=DorsalAttentionNetwork;FPN=Fronto-ParietalNetwork;DMN=DefaultModeNetwork.

Discussionofglobalinsensitivitysimulation.Intheglobalinsensitivitysimulation,

weinducedlargegroupchangesinFCattheleveloffunctionalmodulesthatrepresent

canonicalresting-statenetworks(e.g.,theDMN).Thesimulationdifferentiallymodulated

FCwithinandbetweenregionsoftheDAN,FPN,andDMN.Ingroupanalysesofwithin-and

between-moduledegreecentrality,wedetectedtheselargeshiftsinFC.However,despite

robustdifferencesinnetworkstructure,thetwogroupswereverysimilarinthesmall-

worldpropertiesoftheirgraphs.

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

●●

10% Density 20% Density

Between−Module

Within−M

odule

−0.5 0.0 0.5 −0.5 0.0 0.5

DMN

FPN

DAN

Visual

DMN

FPN

DAN

Visual

Degree (z)

Mod

ule Group

●

●

controlspatients


30

Aswiththewhack-a-nodesimulation,wedidnotseektotesttherangeofconditions

underwhichthesefindingswouldhold.Rather,theglobalinsensitivitysimulationprovides

aproofofconceptthatresearchersshouldbeawarethattheabsenceofgroupdifferences

atahigherlevelofthegraph(here,globaltopology)doesnotsuggestthatthenetworksare

otherwisesimilaratlowerlevels(here,modularconnectivity).Aswehavenotedabove,in

graphanalysesofcase-controlresting-statenetworks,weencourageresearcherstostate

theirstudygoalsintermsthatclearlymatchthehypothesestothescaleofthegraph.

Intheglobalinsensitivitysimulation,failingtodetectdifferencesinsmall-worldness

shouldnotbeseenasanomnibustestofmodularornodalstructure.Likewise,ifgroup

differencesaredetectedatthegloballevel,theremaybesubstantialvalueininterrogating

finerdifferencesinthenetworks,evenifthesewerenothypothesizedapriori.

GeneralSummary

Theoverarchinggoalofthisreviewwastopromotesharedstandardsforreporting

findingsinclinicalnetworkneuroscience.Oursurveyoftheresting-statefunctional

connectivityliteraturerevealedthepopularityandpromiseofgraphtheoryapproachesto

networkorganizationinbraindisorders.Thispotentialisevidentinlarge-scaleinitiatives

foracquiringandsharingresting-statedataindifferentpopulations(e.g.,theHuman

ConnectomeProject;Barchetal.,2013).Publiclyavailableresting-statedatacanalso

supportreproducibilityeffortsbyservingasreplicationdatasetstocorroboratespecific

findingsinanindependentsample(e.g.,Jalbrzikowskietal.,2017).Wesharethefield’s

enthusiasmforsuchworkandanticipatethatwithfurthermethodologicalrefinementand

standardization,thecouplingofnetworkscienceandbrainimagingcanprovidenovel

insightsintotheneurobiologicalbasisofbraindisorders.


31

Ourreview,however,suggestedthattheheterogeneityofmethodsispreventingthe

fieldfromrealizingitspotential.Graphanalysesacrossclinicalstudiesvariedsubstantially

intermsofbrainparcellation,FCquantification,andtheuseofthresholdingmethodsto

defineedgesingraphs.Thesedecisionsarefundamentaltographtheoryandprecede

analysesatspecificlevelssuchasglobaltopology.Inaddition,althoughitwasnotafocusof

ourreview,therewassubstantialvariationinwhatnetworkmetricswerereportedacross

studies.Thelackofstandardizationinmethodsatmultipledecisionpointshas

multiplicativeconsequences:thelikelihoodthatanytwostudiesusedthesameparcellation

scheme,FCdefinition,thresholdingstrategy,andnetworkmetricwasremarkablylow.

Thismakesformalmeta-analysesoftheclinicalnetworkneuroscienceliteraturevirtually

impossibleatthepresenttime,detractingfromeffortstodistinguishdistinct

pathophysiologicalmechanismsortoidentifytransdiagnosticcommonalities.Inaddition,

methodologicalheterogeneityingraphanalysesundercutsthevalueofdatasharingefforts

thathavemademassivedatasetsavailabletothenetworkneurosciencecommunity.For

theimmensepotentialofdatasharingtoberealized,standardizationmustoccurnotonly

indataacquisition,butalsoindataanalysis,withasharedframeworktoguidehypothesis-

to-scalematchingingraphs.

AssummarizedinBox2,webelievethatthefieldshouldworktowardaprincipled,

commonapproachtographanalysesofRSFCdata.Thisisachallengingproposition

becauseoftherapidandexcitingdevelopmentsinfunctionalbrainparcellation(e.g.,

Schaeferetal.,inpress),FCdefinition(e.g.,Cassidy,Rae,&Solo,2015),edgethresholding

(vandenHeuveletal.,2017),andnetworkmetrics(e.g.,Vargas&Wahl,2014).Such

developmentshighlightboththeenthusiasmfor,andrelativeinfancyof,network


32

neuroscienceasafield.Althoughwearesensitivetotheimportanceofcontinuingtorefine

functionalparcellationsofthebrain,wealsoseegreatvalueindevelopingfield-standard

parcellationstopromotecomparability.Indeed,manyaspectsofnetworkstructure(e.g.,

homogeneityoffunctionalconnectivitypatternswithinaregion)arelargelyconvergent

aboveacertainlevelofdetail(likely200-400nodes)inthefunctionalparcellation

(Craddocketal.,2012;Schaeferetal.,inpress).Likewise,theoptimalapproachfor

quantifyingfunctionalconnectivityisanopenquestion(Smithetal.,2011),yetinthe

absenceofmethodologicalconvergence,graphswereoftennotcomparableacrossstudies.

Arelateddilemmawasthatin57%ofstudies,littleornodetailwasprovidedabout

hownegativeFCvalueswereincorporatedintographanalyses.Thiswasespecially

troublinginsofarasglobalsignalregressiontendstoyieldanFCdistributioninwhich

approximatelyhalfofedgesarenegative(Murphyetal.,2009).Furthermore,FCestimates

atthelowendofthedistributionmayhavedifferenttopologicalpropertiessuchasreduced

modularity(Schwarz&McGonigle,2011).Evenamongthe21%ofstudiesinwhich

negativeedgeswereexplicitlydropped,itremainsunclearwhatconsequencesthis

decisionhasonsubstantiveconclusionsaboutgraphstructure.Inrecentyears,therehave

beenadvancesinquantifyingcommongraphmetricssuchasmodularityinweighted

networksthatincludenegativeedges(Rubinov&Sporns,2011),aswellasincreasingcalls

forweighted,notbinary,graphanalyses(Bassett&Bullmore,2016).Regardless,we

believethatgreaterclarityinreportingofnegativeFCwillpromotecomparisonsamong

clinicalstudies.

Methodologicalheterogeneityalsoresultedinveryfewgraphstatisticsthatwere

reportedincommonacrossstudies,anessentialingredientforexaminingthe


33

reproducibilityoffindings.Networksthatareresilienttothedeletionofspecificedges

oftenhaveahighlyskeweddegreedistribution(Callaway,Newman,Strogatz,&Watts,

2000)thatmayrelatetosmall-worldnetworkproperties(Achardetal.,2006).Wepropose

thatstudiesshouldroutinelydepictthisdistribution.Likewise,broadmetricssuchasedge

density,meanFC,transitivity,andcharacteristicpathlengthprovideimportant

informationaboutthebasicpropertiesofgraphsthatcontextualizemoredetailed

inferentialanalyses.Thechallengeofdevelopingreportingstandardsinclinicalnetwork

neuroscienceechoesthebroaderconversationinneuroimagingaboutreproducibility,

especiallytheimportanceofdetailandtransparencyintheanalyticapproach(Nicholset

al.,2017).

Inadditiontothegeneralissuesofstandardizinggraphanalysesandreporting

procedures,ourreviewexaminedtwocriticalissuesingreaterdetail.First,weconsidered

thepotentialbenefitsandrisksofusingproportionalthresholding(PT),acommon

procedureforequatingthenumberofedgesbetweengraphs.Second,wearticulatedthe

valueofconsideringthetelescopinglevelsofgraphstructuresinordertomatcha

hypothesistothecorrespondingscaleofthegraph.

RoughlyonethirdofthestudiesincludedinourreviewappliedPT,thresholding

graphsatsingleormultipleedgedensities.Althoughthisapproachisalignedwithprior

workhighlightingconcernsaboutcomparingunequalnetworks(vanWijketal.,2010),its

applicationinclinicalstudiesisoftenconceptuallyproblematic.Manybrainpathologies

appeartoaffecttargetedregionsornetworks,whileleavingtheconnectivityofother

regionslargelyundisturbed.Forexample,althoughfrontolimbiccircuitryisheavily

implicatedinmooddisorders(Price&Drevets,2010),visualnetworkslargelyappear


34

unaffected.Thereisgrowingevidencethatbraindisordersalterthestrengthoffunctional

couplingandpotentiallythenumberoffunctionalconnections(Hillary&Grafman,2017).

Consequently,ifsomeregionsareaffectedbythepathology,butothersaresimilartoa

matchedcontrolpopulation,PTmayerroneouslyremoveoraddconnectionstographsin

onegroupinordertomaintainequalaveragedegreebetweengroups.Furthermore,ifa

brainpathologyaltersthedensityoffunctionalconnections—forexample,neurological

disruptionisassociatedwithhyperconnectivity(Hillaryetal.,2015)—PTwillpreclude

theinvestigatordetectingdensitydifferencesbetweengroups.If,intruth,thegroupsdiffer

inedgedensity,artificiallyequatingdensityalsodetractsfromtheinterpretabilityofgraph

analyses(cf.vandenHeuveletal.,2017).

Inadditiontotheseconceptualproblems,ourwhack-a-nodesimulation

demonstratedthatPTmayresultinthedetectionofspuriousgroupdifferences(Figure2a).

Altogether,applyingPTinclinicalstudiesmaybeamethodologicaldoublejeopardy,

characterizedbyreducedsensitivitytopathology-relateddifferencesinconnectiondensity

andtheriskofidentifyingnodaldifferencesbetweengroupsthatareastatisticalartifact.

TheserisksmakePTespeciallyunappealingwhenoneconsidersthatFC-based

thresholdingandweightedanalysesaccuratelydetectedgroupdifferences(Figure2b,d)

whilealsoallowingedgedensitytovary.Weacknowledge,however,thataprevious

empiricalstudyfoundthatgroupdifferencesweremoreconsistentacrossmultiple

thresholdsusingproportional,asopposedtoFC-based,thresholding(Garrison,Scheinost,

Finn,Shen,&Constable,2015).

Wethereforehavetworecommendationsforedgethresholdingincase-control

comparisons.First,weightedanalysesorFCthresholdingshouldtypicallybepreferredto


35

PTifoneisinterestedinnodalstatistics.Second,toruleoutthepossibilitythatnodal

findingsreflectglobaldifferencesinmeanFC,onecouldincludemeanFCasacovariatein

weightedanalysesorper-subjectdensityinanalysesofFC-thresholdedbinarygraphs.

Crucially,weproposethatthesebetreatedassensitivityanalysesconductedonlyafter

establishinganodalgroupdifference.Thatis,ifoneidentifiesgroupdifferencesinFC-

thresholdedgraphs(e.g.,greaterdegreeinanteriorcingulatecortexamongpatients),does

includingedgedensityasacovariateabolishthisfinding?Ifso,itsuggeststhatdifferences

inglobaltopologymayaccountforthenodalfinding.However,oneshouldnotinclude

densityasacovariateinFC-thresholdedgraphsasafirststeptoidentifywhichnodesdiffer

betweengroups,asthiscouldfallpreytothe‘whackanode’problem(i.e.,spuriousnodal

effects).

Thesecondcriticalissuewasthatmanystudiesprovidedlimitedtheoretical

justificationforthealignmentbetweenagivenhypothesisandthecorrespondinggraph

analysis.Amajorityofstudies(69%)testedwhethergroupsdifferedinglobalmetricssuch

assmall-worldness,butmostpathologies(e.g.,braininjury,Alzheimer’sdisease)primarily

affectregionalhubswithinnetworks(Crossleyetal.,2014).Ourglobalinsensitivity

simulationfocusedontheimportanceofmatchinghypothesestographanalyses,or

telescoping.Wedemonstratedthatglobalgraphmetrics,specificallysmall-worldness,may

notbesensitivetogroupdifferencesinmoduleornodecentrality.Metricssuchas

modularityandnodalcentralityoffervitalinformationaboutregionalbrainorganization

thatcanbeinterpretedinthecontextofalterationsinaveragedegree.Thegeneralpointis

thatonecannotgeneralizefindingsfromonelevelofagraphtoanother,norshouldnull

effectsatonelevelbeviewedassuggestingthatthegroupsaresimilaratotherlevels.By


36

conceptualizingadataanalysisplanintermsofthetelescopingstructureofgraphs,

researcherscanclearlydelineateconfirmatoryfromexploratoryanalyses,whichis

consistentwiththespiritofreproduciblescienceinneuroimaging(Poldracketal.,2017).

Box2:RecommendationsforBestPracticesandConvergenceinClinicalNetwork

Neuroscience

Challenge Recommendation

Brain parcellations vary substantially across studies

In the absence of a field standard, we recommend that brain parcellations should meet the following minimum requirements:

1) Provide comprehensive coverage of functional regions throughout the brain, including cortical and subcortical structures, as well as cerebellum

2) Divide the brain into at least 200 functional regions (Craddock et al., 2012)

3) Delineate regions based on functional connectivity (as opposed to a structural atlas; Gordon et al., 2016), potentially combined with multi-modal imaging (e.g., Glasser et al., 2016)

4) Ensure that regions exhibit high functional connectivity homogeneity (Gordon et al., 2016; Schaefer et al., in press)

5) Provide clear guidance on the modular structure of regions comprising the parcellation (Yeo et al., 2011). In general, we discourage clinical researchers from attempting to identify functional modules in their data (e.g., using community detection algorithms) when a published modular structure exists.

The quality of RSFC data varies as a function of acquisition length and time

1) Longer resting-state acquisitions help to improve the stability of FC estimates and, therefore, their test-retest reliability (Birn et al., 2013). We encourage clinical researchers to acquire resting-state data for at least nine minutes and to use faster temporal sampling (e.g., 1s TR, potentially using multi-band imaging; Demetriou et al., 2016) when possible.

Edge definition Quantifying functional connectivity: The reliability of functional connectomes based on conditional association (e.g., partial correlation) diminishes as the number nodes increases or the number of measurements decreases (Cassidy et al., 2018), requiring substantially longer scans, both in terms of time and measurements. The stability of bivariate correlations, however, is not dependent on the number of nodes and values typically stabilize around 250 measurements (Schönbrodt & Perugini, 2013). For conventional resting-state data (e.g., 180 volumes with TR = 2s) and comprehensive parcellations, we recommend a shrinkage estimator of marginal correlation (Varoquaux & Craddock, 2013), rather than a conditional association measure.

2)


37

3) Proportional thresholding: We caution against using proportional thresholding to create binary graphs in case-control studies (for more detailed recommendations, see Simulation 1). Negative edge weights: Studies should provide details about how negative FC estimates are handled when constructing graphs, whether weighted or binary. The deletion of negative edges is a largely untested assumption in network neuroscience that deserves greater attention. If researchers have many negative edges (e.g., if global signal regression or partial correlation are used), we encourage analyzing and reporting them, perhaps using a separate graph.

Graph metrics varied across studies

4) To promote formal comparisons across studies, we encourage researchers to report a standard set of graph metrics, even if these are in the form of descriptive tables or supplementary material. As a minimal set, we propose: 1) global clustering coefficient, 2) average path length, 3) modularity, 4) degree, 5) eigenvector centrality, and 6) summary statistics of edge strength.

Need to align neurobiology and the network representation

We encourage researchers to conceptualize and report graph analyses in terms of telescoping levels of analysis, from global to specific. As demonstrated in Simulation 2, global metrics may be insensitive to regional effects of pathology or neurodevelopment. We also advocate articulating the alignment between the level of the graph and the biological account of neuropathology. The relevance of some graph metrics (e.g., small-worldness) to understanding brain disorders remains unclear.

Insummary,thereisaneedforacommonframeworktoinformgraphtheory

analysesofRSFCdataintheclinicalneurosciences.Anyrecommendationsshouldemerge

organicallyfromascientificcommunitywhoseinvestigatorsvoluntarilyadoptprocedures

thatmaximizesensitivitytohypothesizedeffectsandsimultaneouslypermitgraph

comparisonsamongstudies(cf.theCOBIDASeffortinneuroimagingmorebroadly;Nichols

etal.,2017).Theimplementationofbestpracticesintask-basedfMRI(e.g.,handling

autocorrelation;Woolrich,Ripley,Brady,&Smith,2001)hasbeensupportedbypowerful,

usable,andfreesoftware.Althoughsimilarsoftwareisincreasinglyavailableforresting-

statestudies(e.g.,Chao-Gan&ZangYu-Feng,2010;Whitfield-Gabrieli&Nieto-Castanon,

2012),bestpracticesarestillemerging,andwebelievethatsoftwaredeveloperswillbe

crucialtopromotingastandardizedgraphtheoryanalysispipeline.Weanticipatethata


38

commonmethodologicalframeworkwillpromotehypothesis-drivenresearch,alignment

betweentheoryandgraphanalysis,reproducibility,datasharing,meta-analyses,and

ultimatelymorerapidprogressofclinicalnetworkneuroscience.

Methods

PubmedSearchSyntax

Neurologicaldisordersquery:

(graphORgraphicalORgraph-theor*ORtopology)AND(brainORfMRIORconnectivity

ORintrinsic)AND(resting-stateORrestingORrest)AND(neurologicalORbraininjuryOR

multiplesclerosisORepilepsyORstrokeORCVAORaneurysmORParkinson'sORMCIor

Alzheimer'sORdementiaORHIVORSCIORspinalcordORautismORADHDOR

intellectualdisabilityORDownsyndromeORTourette)AND"humans"[MeSHTerms]

Mentaldisordersquery:

(graphORgraphicalORgraph-theor*ORtopology)AND(brainORfmriORconnectivityOR

intrinsic)AND(resting-stateORrestingORrest)AND(clinicalORpsychopathologyOR

mentaldisorderORpsychiatricORneuropsychiatricORdepressionORmoodORanxiety

ORaddictionORpsychosisORbipolarORborderlineORautism)AND"humans"[MeSH

Terms]

GeneralApproachtoNetworkSimulations

Toapproximatethestructureoffunctionalbrainnetworks,weidentifiedayoung

adultfemalesubjectwhocompleteda5-minuteresting-statescaninaSiemens3TTrio


39

Scanner(TR=1.5s,TE=29ms,3.1x3.1x4.0mmvoxels)withessentiallynohead

movement(meanframewisedisplacement[FD]=.08mm;maxFD=.17mm).We

preprocessedthedatausingaconventionalpipeline,including:1)motioncorrection(FSL

mcflirt);2)slicetimingcorrection(FSLslicetimer);3)nonlineardeformationtotheMNI

templateusingtheconcatenationoffunctional→structural(FSLflirt)andstructural→

MNI152(FSLflirt+fnirt)transformations;4)spatialsmoothingwitha6mmFWHMfilter

(FSLsusan);5)andvoxelwiseintensitynormalizationtoameanof100.Afterthesesteps,

wealsosimultaneouslyappliednuisanceregressionandbandpassfiltering,wherethe

regressorsweresixmotionparameters,averageCSF,averageWM,andthederivativesof

these(16totalregressors).Thespectralfilterretainedfluctuationsbetween.009and.08

Hz(AFNI3dBandpass).Wethenestimatedfunctionalconnectivity(FC)of264functional

ROIsfromthePowerandcolleaguesparcellation,whereeachregionwasdefinedbya5mm

radiusspherecenteredonaspecificcoordinate.Theactivityofaregionovertimewas

estimatedbythefirstprincipalcomponentofvoxelsineachROI,andthefunctional

connectivitymatrix(264x264)wasestimatedbythepairwisePearsoncorrelationsof

timeseries.

This264x264adjacencymatrix,W,servedasthegroundtruthforallsimulations,

withspecificwithin-person,between-person,andbetween-groupalterationsapplied

accordingtoamultilevelsimulationofvariationacrossindividuals(detailsofsimulation

parametersprovidedinTableS1).Morespecifically,toapproximatepopulation-level

variabilityinacase-controldesign,wesimulatedresting-stateadjacencymatricesfor50

‘patients’and50‘controls’byintroducingsystematicandunsystematicsourcesof

variabilityforeachsimulatedparticipant.Systematicsourceswereintendedtotest


40

substantivehypothesesaboutproportionalthresholding(whack-a-nodesimulation)and

insensitivitytoglobalversusmodulardifferences(globalinsensitivitysimulation),whereas

unsystematicsourcesreflectedwithin-andbetween-personvariationinedgestrength.

Inthismodel,thesimulatededgestrengthbetweentwonodes,iandj,foragiven

subject,s,is:

$%&' = )%& + +%&' +-%&' + .%&' (1)

where)%& istheedgestrengthfromthegroundtruthadjacencymatrixW.Globalvariation

inmeanFCisrepresentedby+%&' ,whichreflectscontributionsofbothbetween-and

within-personvariation:

+%&' = /' + 0%&' (2)

where/'representsnormallydistributedbetween-personvariationinmeanFC:

1~3(0, "7) (3)

while"7controlsthelevelofbetween-personvariationinthesample.Theterm0%&'

representswithin-personvariationofthisedgerelativetothepersonmeanFC,/'.Within-

personvariationinFCacrossalledgesisassumedtobenormallydistributed:

8..'~3(0, ":) (4)

with": scalingthedegreeofwithin-personFCvariationacrossalledges.

Node-specificshiftsinFCarerepresentedby-%&' ,whichincludesbothbetween-

personandwithin-nodecomponents.Morespecifically,themodulationofFCbetween

nodesiandjisgivenby:

-%&' = ;%' + <%&' (5)

wherebetween-personvariationinFCfornodeiis:

=%.~3(>?@, "?@) (6)


41

with>?%and"?% capturingthemeanandstandarddeviationinFCshiftsfornodeiacross

subjects,respectively.EdgewiseFCvariationofanodeiacrossitsneighbors,j,isgivenby:

AB.C~3(0, "D%) (7)

where"D@representsthestandarddeviationofFCshiftsacrossneighborsofi.Whennodesi

andjwerebothmanipulated,theshiftswereappliedsequentiallysuchthatFCfortheedge

betweeniandjwasnotallowedtohavecompoundingchanges.Thatis,weset-%&' = 0for

i>j.

Finally,.%&'representstherandomvariationinFCfortheedgebetweeniandjfor

subjects.Thisvariationwasassumedtobenormallydistributedacrossalledgesfora

subject:

E..'~3(0, "F) (8)

where"Fcontrolsthestandarddeviationofedgenoiseacrosssubjects.

Whack-a-NoteSimulationMethods

Asmentionedabove,proportionalthresholding(PT)isoftenappliedincase-control

studiestoruleoutthepossibilitythatnetworkdifferencesbetweengroupsreflect

differencesinthetotalnumberofedges.Importantly,ingraphsofequalorderN(i.e.,the

samenumberofnodes),proportionalthresholdingequatesboththedensity,D,and

averagedegree,⟨H⟩betweensubjects:

J = KLM(MNO)

, ⟨H⟩ = KLM⇒ ⟨H⟩ = J(3 − 1) (9)


42

whereEdenotesthenumberofuniqueedgesinanundirectedgraphwithnoself-

loops.AsnotedbyvandenHeuvelandcolleagues(2017),whenoneappliesPT,differences

inaverageconnectivitystrengthcanleadtotheinclusionofweakeredgesinmoresparsely

connectedgroups.Furthermore,weakedgesestimatedbycorrelationaremorelikelyto

reflectanunreliablerelationshipbetweennodes.Thus,ifonegrouphaslowermean

functionalconnectivity,PTcouldintroducespuriousconnections,potentiallyundermining

groupcomparisonsofnetworktopology.

Thatis,whengroupsareotherwiseequivalent,thesumofincreasesindegreein

hyperconnectednodesforagroupmustbeoffsetbyequal,butopposite,decreasesin

degreeforothernodesinthatgroup.Thisphenomenonholdsbecauseofthemathematical

relationshipbetweenaveragedegreeandgraphdensity(Eq.9).Forsimplicity,ourfirst

simulationrepresentsthescenariowheretherearemeaningfulFCincreasesinpatientsfor

selectednodesandunreliableFCdecreasesinothernodes.Thisunreliabilityisintendedto

representsamplingvariabilitythatcouldleadtoerroneousfalsepositives.

Structureofwhack-a-nodesimulation.Asdescribedabove,wesimulated50

patientsand50controlsbasedonagroundtruthFCmatrix.Weestimated100replication

sampleswithequallevelsofnoiseinbothgroups(seeTableS1).Ineachreplication

sample,weincreasedthemeanFCinthreenodes,selectedatrandom,byr=0.14.Wealso

appliedsmallerdecreasesofr=-.04tothreeotherrandomlytargetednodes1.Thislevelof

decreasewaschosensuchthatgroupdifferencesinanalysesofnodalstrength(i.e.,

computedonweightedgraphs)werenonsignificantonaverage(Mp=.19,SDp=.02).We

1ResultsarequalitativelysimilarusingothervaluesforgroupshiftsinFC.


43

appliedPTtobinarizegraphsineachgroup,varyingdensitybetween5%and25%in1%

increments.Likewise,forFCthresholding,webinarizedgraphsatrthresholdbetweenr=

.2and.5in.02increments.Finally,weretainedweightedgraphsforallsimulatedsamples

toestimategroupdifferencesinnodalstrength.Toensurethateffectswerenotattributable

toparticularnodes,weaveragedgroupstatisticsacrossthe100replicationsamples,where

thetargetednodesvariedrandomlyacrosssamples.

Ineachreplicationsample,weestimateddegreecentralityforthePositive

(hyperconnected),Negative(weaklyhypoconnected),andComparatornodes.Comparators

werethreerandomlyselectednodesineachsamplethatwerenotspecificallymodulated

bythesimulation.Theseservedasabenchmarktoensurethatsimulationsdidnotinduce

groupdifferencesincentralityfornodesnotspecificallytargeted.Toquantifytheeffectof

PTversusFCthresholdinginbinarygraphs,weestimatedgroupdifferences(patient–

control)ondegreecentralityusingtwo-samplet-testsforeachPositive,Negative,and

Comparatornode.Forweightedanalyses,weestimatedgroupdifferencesinstrength

centrality.

GlobalInsensitivitySimulationMethods:Hypothesis-to-scalematching

Wesimulatedadatasetof50‘controls’and50‘patients’inwhichthefronto-parietal

network(FPN)anddorsalattentionnetwork(DAN)weremodulatedincontrolscompared

tothegroundtruthmatrix,W.Inthissimulation,thepatientgrouphadincreasedFCinthe

defaultmodenetwork(DMN),acommonfindinginneurologicaldisorders(Hillaryetal.,

2015).Incontrols,weincreasedFCstrengthforedgesbetweenFPN/DANregionsandother

networks,Mr=0.2,SD=0.1.Per-modulevariationinbetween-networkFCchangeswas


44

assumedtobenormallydistributedwithineachsubject,SD=0.1.Wealsoincreased

controls’FConedgeswithintheFPNandDAN,Mr=0.1,between-subjectsSD=0.05,

within-subjectsSD=.05.Inpatients,between-networkFCforDMNnodeswasincreased,M

r=0.2,between-subjectsSD=0.1,within-subjectsSD=0.1.Likewise,within-networkFCin

theDMNwasincreased,Mr=0.1,between-subjectsSD=.05,within-subjectsSD=.05.That

is,weappliedsimilarlevelsofFCmodulationtotheFPN/DANincontrolsandtheDMNin

patients,althoughthesechangeslargelyaffecteddifferentedgesinthenetworksbetween

groups.

Wecomputedthesmall-worldnesscoefficient,",accordingtotheapproachof

HumphriesandGurney(2008):

" =ST/SV?WXYT/YV?WX

Here,STrepresentsthetransitivityofthegraph,whereasSV?WX denotesthe

transitivityofarandomgraphwithanequivalentdegreedistribution.Likewise,YTand

YV?WXrepresentthecharacteristicpathlengthofthetargetgraphandrandomlyrewired

graph,respectively.Valuesof"muchlargerthan1.0correspondtoanetworkwithsmall-

worldproperties.Togeneratestatisticsforequivalentrandomgraphs,weapplieda

rewiringalgorithmthatretainedthedegreedistributionofthegraphwhilepermuting

347,160edges(10permutationsperedge,onaverage).Thisalgorithmwasappliedtothe

targetgraph100timestogenerateasetofequivalentrandomnetworks.Transitivityand

characteristicpathlengthwerecalculatedforeachofthese,andtheiraverageswereused

incomputingthesmall-worldnesscoefficient,".Wealsoanalyzedwithin-andbetween-


45

networkdegreecentralityforeachnode,z-scoringvalueswithineachmoduleanddensity

toallowforcomparisons.


46

References

Abrol,A.,Damaraju,E.,Miller,R.L.,Stephen,J.M.,Claus,E.D.,Mayer,A.R.,&Calhoun,V.D.

(2017).Replicabilityoftime-varyingconnectivitypatternsinlargerestingstate

fMRIsamples.NeuroImage,163,160–176.

https://doi.org/10.1016/j.neuroimage.2017.09.020

Achard,S.,&Bullmore,E.(2007).Efficiencyandcostofeconomicalbrainfunctional

networks.PLoSComputationalBiology,3(2),0174–0183.

https://doi.org/10.1371/journal.pcbi.0030017

Achard,S.,Salvador,R.,Whitcher,B.,Suckling,J.,&Bullmore,E.(2006).Aresilient,low-

frequency,small-worldhumanbrainfunctionalnetworkwithhighlyconnected

associationcorticalhubs.TheJournalofNeuroscience:TheOfficialJournalofthe

SocietyforNeuroscience,26(1),63–72.https://doi.org/10.1523/JNEUROSCI.3874-

05.2006

Anticevic,A.,Cole,M.W.,Murray,J.D.,Corlett,P.R.,Wang,X.-J.,&Krystal,J.H.(2012).The

roleofdefaultnetworkdeactivationincognitionanddisease.TrendsinCognitive

Sciences,16(12),584–592.

Barch,D.M.,Burgess,G.C.,Harms,M.P.,Petersen,S.E.,Schlaggar,B.L.,Corbetta,M.,…WU-

MinnHCPConsortium.(2013).Functioninthehumanconnectome:task-fMRIand

individualdifferencesinbehavior.NeuroImage,80,169–189.


Bassett,D.S.,&Bullmore,E.T.(2016).Small-worldbrainnetworksrevisited.The

Neuroscientist,1073858416667720.


47

Bassett,D.S.,Bullmore,E.T.,Meyer-Lindenberg,A.,Apud,J.a,Weinberger,D.R.,&Coppola,

R.(2009).Cognitivefitnessofcost-efficientbrainfunctionalnetworks.Proceedings

oftheNationalAcademyofSciencesoftheUnitedStatesofAmerica,106(28),11747–

11752.https://doi.org/10.1073/pnas.0903641106

Betzel,R.F.,Medaglia,J.D.,Papadopoulos,L.,Baum,G.L.,Gur,R.,Gur,R.,…Bassett,D.S.

(2017).Themodularorganizationofhumananatomicalbrainnetworks:Accounting

forthecostofwiring.NetworkNeuroscience,1(1),42–68.

https://doi.org/10.1162/NETN_a_00002

Birn,R.M.,Molloy,E.K.,Patriat,R.,Parker,T.,Meier,T.B.,Kirk,G.R.,…Prabhakaran,V.

(2013).Theeffectofscanlengthonthereliabilityofresting-statefMRIconnectivity

estimates.NeuroImage,83,550–558.


Biswal,B.B.,Mennes,M.,Zuo,X.-N.,Gohel,S.,Kelly,C.,Smith,S.M.,…Colcombe,S.(2010).

Towarddiscoveryscienceofhumanbrainfunction.ProceedingsoftheNational

AcademyofSciences,107(10),4734–4739.

Biswal,B.B.,Yetkin,F.Z.,Haughton,V.M.,&Hyde,J.S.(1995).Functionalconnectivityin

themotorcortexofrestinghumanbrainusingecho-planarMRI.MagneticResonance

inMedicine,34(4),537–541.https://doi.org/10.1002/mrm.1910340409

Bullmore,E.,&Sporns,O.(2009).Complexbrainnetworks:graphtheoreticalanalysisof

structuralandfunctionalsystems.NatureReviewsNeuroscience,10(3),186–198.

https://doi.org/10.1038/nrn2575

Bullmore,E.,&Sporns,O.(2012).Theeconomyofbrainnetworkorganization.Nature

ReviewsNeuroscience,13(5),336–349.https://doi.org/10.1038/nrn3214


48

Callaway,D.S.,Newman,M.E.,Strogatz,S.H.,&Watts,D.J.(2000).Networkrobustnessand

fragility:percolationonrandomgraphs.PhysicalReviewLetters,85(25),5468–5471.

https://doi.org/10.1103/PhysRevLett.85.5468

Cassidy,B.,Bowman,D.B.,Rae,C.,&Solo,V.(2018).OntheReliabilityofIndividualBrain

ActivityNetworks.IEEETransactionsonMedicalImaging,37(2),649–662.

https://doi.org/10.1109/TMI.2017.2774364

Cassidy,B.,Rae,C.,&Solo,V.(2015).BrainActivity:Connectivity,Sparsity,andMutual

Information.IEEETransactionsonMedicalImaging,34(4),846–860.

https://doi.org/10.1109/TMI.2014.2358681

Chao-Gan,Y.,&ZangYu-Feng.(2010).DPARSF:aMATLABtoolboxfor“pipeline”data

analysisofresting-statefMRI.FrontiersinSystemsNeuroscience,4.

https://doi.org/10.3389/fnsys.2010.00013

Chen,Y.,Wang,S.,Hilgetag,C.C.,&Zhou,C.(2013).Trade-offbetweenMultipleConstraints

EnablesSimultaneousFormationofModulesandHubsinNeuralSystems.PLOS

ComputationalBiology,9(3),e1002937.

https://doi.org/10.1371/journal.pcbi.1002937

Ciric,R.,Wolf,D.H.,Power,J.D.,Roalf,D.R.,Baum,G.L.,Ruparel,K.,…Satterthwaite,T.D.

(2017).Benchmarkingofparticipant-levelconfoundregressionstrategiesforthe

controlofmotionartifactinstudiesoffunctionalconnectivity.NeuroImage,

154(SupplementC),174–187.https://doi.org/10.1016/j.neuroimage.2017.03.020

Craddock,R.C.,James,G.A.,Holtzheimer,P.E.,Hu,X.P.,&Mayberg,H.S.(2012).Awhole

brainfMRIatlasgeneratedviaspatiallyconstrainedspectralclustering.Human

BrainMapping,33(8),1914–1928.https://doi.org/10.1002/hbm.21333


49

Crone,J.S.,Soddu,A.,Höller,Y.,Vanhaudenhuyse,A.,Schurz,M.,Bergmann,J.,…

Kronbichler,M.(2014).Alterednetworkpropertiesofthefronto-parietalnetwork

andthethalamusinimpairedconsciousness.NeuroImage.Clinical,4,240–248.

https://doi.org/10.1016/j.nicl.2013.12.005

Crossley,N.A.,Mechelli,A.,Scott,J.,Carletti,F.,Fox,P.T.,McGuire,P.,&Bullmore,E.T.

(2014).Thehubsofthehumanconnectomearegenerallyimplicatedintheanatomy

ofbraindisorders.Brain,137(8),2382–2395.

Demetriou,L.,Kowalczyk,O.S.,Tyson,G.,Bello,T.,Newbould,R.D.,&Wall,M.B.(2016).A

comprehensiveevaluationofmultiband-acceleratedsequencesandtheireffectson

statisticaloutcomemeasuresinfMRI.BioRxiv,076307.

https://doi.org/10.1101/076307

Dosenbach,N.U.F.,Koller,J.M.,Earl,E.A.,Miranda-Dominguez,O.,Klein,R.L.,Van,A.N.,…

Nguyen,A.L.(2017).Real-timemotionanalyticsduringbrainMRIimprovedata

qualityandreducecosts.NeuroImage,161,80–93.

Fallani,F.D.V.,Richiardi,J.,Chavez,M.,&Achard,S.(2014).Graphanalysisoffunctional

brainnetworks:practicalissuesintranslationalneuroscience.Philosophical

TransactionsoftheRoyalSocietyB:BiologicalSciences,369(1653),20130521–

20130521.https://doi.org/10.1098/rstb.2013.0521

Fornito,A.,Zalesky,A.,&Bullmore,E.(2016).Fundamentalsofbrainnetworkanalysis.

AcademicPress.

Friston,K.J.(2011).FunctionalandEffectiveConnectivity:AReview.BrainConnectivity,

1(1),13–36.https://doi.org/10.1089/brain.2011.0008


50

Garrison,K.A.,Scheinost,D.,Finn,E.S.,Shen,X.,&Constable,R.T.(2015).The(in)stability

offunctionalbrainnetworkmeasuresacrossthresholds.NeuroImage,118,651–661.


Glasser,M.F.,Coalson,T.S.,Robinson,E.C.,Hacker,C.D.,Harwell,J.,Yacoub,E.,…Van

Essen,D.C.(2016).Amulti-modalparcellationofhumancerebralcortex.Nature,

536(7615),171–178.https://doi.org/10.1038/nature18933

Goñi,J.,vandenHeuvel,M.P.,Avena-Koenigsberger,A.,deMendizabal,N.V.,Betzel,R.F.,

Griffa,A.,…Sporns,O.(2014).Resting-brainfunctionalconnectivitypredictedby

analyticmeasuresofnetworkcommunication.ProceedingsoftheNationalAcademy

ofSciences,111(2),833–838.

Gonzalez-Castillo,J.,Chen,G.,Nichols,T.E.,&Bandettini,P.A.(2017).Variance

decompositionforsingle-subjecttask-basedfMRIactivityestimatesacrossmany

sessions.NeuroImage,154,206–218.


Goodkind,M.,Eickhoff,S.B.,Oathes,D.J.,Jiang,Y.,Chang,A.,Jones-Hagata,L.B.,…Etkin,A.

(2015).Identificationofacommonneurobiologicalsubstrateformentalillness.

JAMAPsychiatry,72(4),305–315.

https://doi.org/10.1001/jamapsychiatry.2014.2206

Gordon,E.M.,Laumann,T.O.,Adeyemo,B.,Huckins,J.F.,Kelley,W.M.,&Petersen,S.E.

(2016).GenerationandEvaluationofaCorticalAreaParcellationfromResting-State

Correlations.CerebralCortex,26(1),288–303.

https://doi.org/10.1093/cercor/bhu239


51

Greene,D.J.,Black,K.J.,&Schlaggar,B.L.(2016).ConsiderationsforMRIstudydesignand

implementationinpediatricandclinicalpopulations.DevelopmentalCognitive

Neuroscience,18,101–112.https://doi.org/10.1016/j.dcn.2015.12.005

Hallquist,M.N.,Hwang,K.,&Luna,B.(2013).Thenuisanceofnuisanceregression:spectral

misspecificationinacommonapproachtoresting-statefMRIpreprocessing

reintroducesnoiseandobscuresfunctionalconnectivity.NeuroImage,82,208–225.


Hilgetag,C.C.,&Goulas,A.(2015).Isthebrainreallyasmall-worldnetwork?Brain

StructureandFunction,221(4),1–6.

Hilgetag,C.C.,&Kaiser,M.(2004).Clusteredorganizationofcorticalconnectivity.

Neuroinformatics,2(3),353–360.https://doi.org/10.1385/NI:2:3:353

Hillary,F.G.,&Grafman,J.H.(2017).InjuredBrainsandAdaptiveNetworks:TheBenefits

andCostsofHyperconnectivity.TrendsinCognitiveSciences.

Hillary,F.G.,Rajtmajer,S.M.,Roman,C.A.,Medaglia,J.D.,Slocomb-Dluzen,J.E.,Calhoun,V.

D.,…Wylie,G.R.(2014).TheRichGetRicher:BrainInjuryElicitsHyperconnectivity

inCoreSubnetworks.PLoSONE,9(8),e104021–e104021.

https://doi.org/10.1371/journal.pone.0104021

Hillary,F.G.,Roman,C.A.,Venkatesan,U.,Rajtmajer,S.M.,Bajo,R.,&Castellanos,N.D.

(2015).Hyperconnectivityisafundamentalresponsetoneurologicaldisruption.

Neuropsychology,29(1),59–75.https://doi.org/10.1037/neu0000110

Honnorat,N.,Eavani,H.,Satterthwaite,T.D.,Gur,R.E.,Gur,R.C.,&Davatzikos,C.(2015).

GraSP:geodesicgraph-basedsegmentationwithshapepriorsforthefunctional

parcellationofthecortex.NeuroImage,106,207–221.


52

Humphries,M.D.,&Gurney,K.(2008).Network‘Small-World-Ness’:AQuantitativeMethod

forDeterminingCanonicalNetworkEquivalence.PLoSONE,3(4),e0002051–

e0002051.https://doi.org/10.1371/journal.pone.0002051

Hwang,K.,Hallquist,M.N.,&Luna,B.(2013).Thedevelopmentofhubarchitectureinthe

humanfunctionalbrainnetwork.CerebralCortex,23(10),2380–2393.

https://doi.org/10.1093/cercor/bhs227

Jalbrzikowski,M.,Larsen,B.,Hallquist,M.N.,Foran,W.,Calabro,F.,&Luna,B.(2017).

DevelopmentofWhiteMatterMicrostructureandIntrinsicFunctionalConnectivity

BetweentheAmygdalaandVentromedialPrefrontalCortex:AssociationsWith

AnxietyandDepression.BiologicalPsychiatry,82(7),511–521.

https://doi.org/10.1016/j.biopsych.2017.01.008

Laird,A.R.,Eickhoff,S.B.,Li,K.,Robin,D.A.,Glahn,D.C.,&Fox,P.T.(2009).Investigating

thefunctionalheterogeneityofthedefaultmodenetworkusingcoordinate-based

meta-analyticmodeling.JournalofNeuroscience,29(46),14496–14505.

Liang,X.,Wang,J.,Yan,C.,Shu,N.,Xu,K.,Gong,G.,&He,Y.(2012).EffectsofDifferent

CorrelationMetricsandPreprocessingFactorsonSmall-WorldBrainFunctional

Networks:AResting-StateFunctionalMRIStudy.PLoSONE,7(3),e32766.

https://doi.org/10.1371/journal.pone.0032766

Muldoon,S.F.,Bridgeford,E.W.,&Bassett,D.S.(2016).Small-worldpropensityand

weightedbrainnetworks.ScientificReports,6,22057–22057.

Müller,V.I.,Cieslik,E.C.,Serbanescu,I.,Laird,A.R.,Fox,P.T.,&Eickhoff,S.B.(2017).

Alteredbrainactivityinunipolardepressionrevisited:Meta-analysesof

neuroimagingstudies.JAMAPsychiatry,74(1),47–55.


53

Murphy,K.,Birn,R.M.,Handwerker,D.a,Jones,T.B.,&Bandettini,P.a.(2009).Theimpact

ofglobalsignalregressiononrestingstatecorrelations:areanti-correlated

networksintroduced?NeuroImage,44(3),893–905.


Murphy,K.,&Fox,M.D.(2017).Towardsaconsensusregardingglobalsignalregressionfor

restingstatefunctionalconnectivityMRI.NeuroImage,154(SupplementC),169–

173.https://doi.org/10.1016/j.neuroimage.2016.11.052

Newman,M.(2010).Networks:AnIntroduction(1sted.).OxfordUniversityPress,USA.

Nichols,T.E.,Das,S.,Eickhoff,S.B.,Evans,A.C.,Glatard,T.,Hanke,M.,…Yeo,B.T.T.(2017).

BestpracticesindataanalysisandsharinginneuroimagingusingMRI.Nature

Neuroscience,20(3),299–303.https://doi.org/10.1038/nn.4500

Papanicolaou,A.C.,Rezaie,R.,Narayana,S.,Choudhri,A.F.,Wheless,J.W.,Castillo,E.M.,…

Boop,F.A.(2017).ClinicalApplicationsofFunctionalNeuroimaging:Presurgical

FunctionalMapping.TheOxfordHandbookofFunctionalBrainImagingin

NeuropsychologyandCognitiveNeurosciences,371–371.

Parente,F.,Frascarelli,M.,Mirigliani,A.,DiFabio,F.,Biondi,M.,&Colosimo,A.(2017).

Negativefunctionalbrainnetworks.BrainImagingandBehavior.

https://doi.org/10.1007/s11682-017-9715-x

Poldrack,R.A.,Baker,C.I.,Durnez,J.,Gorgolewski,K.J.,Matthews,P.M.,Munafò,M.R.,…

Yarkoni,T.(2017).Scanningthehorizon:towardstransparentandreproducible

neuroimagingresearch.NatureReviewsNeuroscience,18(2),115–126.

https://doi.org/10.1038/nrn.2016.167


54

Power,J.D.,Cohen,A.L.,Nelson,S.M.,Wig,G.S.,Barnes,K.A.,Church,J.A.,…Petersen,S.E.

(2011).Functionalnetworkorganizationofthehumanbrain.Neuron,72(4),665–

678.https://doi.org/10.1016/j.neuron.2011.09.006

Power,J.D.,Fair,D.A.,Schlaggar,B.L.,&Petersen,S.E.(2010).Thedevelopmentofhuman

functionalbrainnetworks.Neuron,67(5),735–748.

https://doi.org/10.1016/j.neuron.2010.08.017

Power,J.D.,Mitra,A.,Laumann,T.O.,Snyder,A.Z.,Schlaggar,B.L.,&Petersen,S.E.(2014).

Methodstodetect,characterize,andremovemotionartifactinrestingstatefMRI.

NeuroImage,84,320–341.https://doi.org/10.1016/j.neuroimage.2013.08.048

Price,J.L.,&Drevets,W.C.(2010).Neurocircuitryofmooddisorders.

Neuropsychopharmacology,35(1),192–216.

Roy,A.,Bernier,R.A.,Wang,J.,Benson,M.,FrenchJr,J.J.,Good,D.C.,&Hillary,F.G.(2017).

Theevolutionofcost-efficiencyinneuralnetworksduringrecoveryfromtraumatic

braininjury.PloSOne,12(4),e0170541–e0170541.

Rubinov,M.,&Sporns,O.(2011).Weight-conservingcharacterizationofcomplexfunctional

brainnetworks.NeuroImage,56(4),2068–2079.


Saad,Z.S.,Gotts,S.J.,Murphy,K.,Chen,G.,Jo,H.J.,Martin,A.,&Cox,R.W.(2012).Trouble

atRest:HowCorrelationPatternsandGroupDifferencesBecomeDistortedAfter

GlobalSignalRegression.BrainConnectivity,2(1),25–32.

https://doi.org/10.1089/brain.2012.0080

Schaefer,A.,Kong,R.,Gordon,E.M.,Laumann,T.O.,Zuo,X.-N.,Holmes,A.J.,…Yeo,B.T.T.

(inpress).Local-GlobalParcellationoftheHumanCerebralCortexfromIntrinsic


55

FunctionalConnectivityMRI.CerebralCortex.

https://doi.org/10.1093/cercor/bhx179

Schönbrodt,F.D.,&Perugini,M.(2013).Atwhatsamplesizedocorrelationsstabilize?

JournalofResearchinPersonality,47(5),609–612.

https://doi.org/10.1016/j.jrp.2013.05.009

Schwarz,A.J.,&McGonigle,J.(2011).Negativeedgesandsoftthresholdingincomplex

networkanalysisofrestingstatefunctionalconnectivitydata.NeuroImage,55(3),

1132–1146.https://doi.org/10.1016/j.neuroimage.2010.12.047

Shekhtman,L.M.,Shai,S.,&Havlin,S.(2015).Resilienceofnetworksformedof

interdependentmodularnetworks.NewJournalofPhysics,17(12),123007.

https://doi.org/10.1088/1367-2630/17/12/123007

Sheline,Y.I.,Price,J.L.,Yan,Z.,&Mintun,M.A.(2010).Resting-statefunctionalMRIin

depressionunmasksincreasedconnectivitybetweennetworksviathedorsalnexus.

ProceedingsoftheNationalAcademyofSciences,107(24),11020–11025.

Shirer,W.R.,Jiang,H.,Price,C.M.,Ng,B.,&Greicius,M.D.(2015).Optimizationofrs-fMRI

Pre-processingforEnhancedSignal-NoiseSeparation,Test-RetestReliability,and

GroupDiscrimination.NeuroImage,117,67–79.


Smith,S.M.,Fox,P.T.,Miller,K.L.,Glahn,D.C.,Fox,P.M.,Mackay,C.E.,…Beckmann,C.F.

(2009).Correspondenceofthebrain’sfunctionalarchitectureduringactivationand

rest.ProceedingsoftheNationalAcademyofSciences,106(31),13040–13045.

https://doi.org/10.1073/pnas.0905267106


56

Smith,S.M.,Miller,K.L.,Salimi-Khorshidi,G.,Webster,M.,Beckmann,C.F.,Nichols,T.E.,…

Woolrich,M.W.(2011).NetworkmodellingmethodsforFMRI.NeuroImage,54(2),

875–891.https://doi.org/10.1016/j.neuroimage.2010.08.063

Sporns,O.,&Zwi,J.D.(2004).Thesmallworldofthecerebralcortex.Neuroinformatics,

2(2),145–162.https://doi.org/10.1385/NI:2:2:145

Tomasi,D.,Wang,G.-J.,&Volkow,N.D.(2013).Energeticcostofbrainfunctional

connectivity.ProceedingsoftheNationalAcademyofSciences,110(33),13642–

13647.https://doi.org/10.1073/pnas.1303346110

Tzourio-Mazoyer,N.,Landeau,B.,Papathanassiou,D.,Crivello,F.,Etard,O.,Delcroix,N.,…

Joliot,M.(2002).AutomatedanatomicallabelingofactivationsinSPMusinga

macroscopicanatomicalparcellationoftheMNIMRIsingle-subjectbrain.

NeuroImage,15(1),273–289.https://doi.org/10.1006/nimg.2001.0978

vandenHeuvel,M.P.,deLange,S.,Zalesky,A.,Seguin,C.,Yeo,T.,&Schmidt,R.(2017).

Proportionalthresholdinginresting-statefMRIfunctionalconnectivitynetworks

andconsequencesforpatient-controlconnectomestudies:Issuesand

recommendations.NeuroImage,152,437–449.


vandenHeuvel,M.P.,&HulshoffPol,H.E.(2010).Exploringthebrainnetwork:areview

onresting-statefMRIfunctionalconnectivity.EuropeanNeuropsychopharmacology:

TheJournaloftheEuropeanCollegeofNeuropsychopharmacology,20(8),519–534.

https://doi.org/10.1016/j.euroneuro.2010.03.008


57

VanDijk,K.R.A.,Sabuncu,M.R.,&Buckner,R.L.(2012).Theinfluenceofheadmotionon

intrinsicfunctionalconnectivityMRI.NeuroImage,59(1),431–438.


vanWijk,B.C.M.,Stam,C.J.,&Daffertshofer,A.(2010).ComparingBrainNetworksof

DifferentSizeandConnectivityDensityUsingGraphTheory.PLoSONE,5(10),

e13701–e13701.https://doi.org/10.1371/journal.pone.0013701

Vargas,E.R.,&Wahl,L.M.(2014).Thegatewaycoefficient:anovelmetricforidentifying

criticalconnectionsinmodularnetworks.TheEuropeanPhysicalJournalB,87(7),

161.https://doi.org/10.1140/epjb/e2014-40800-7

Varoquaux,G.,&Craddock,R.C.(2013).Learningandcomparingfunctionalconnectomes

acrosssubjects.NeuroImage,80,405–415.


Vincent,J.L.,Patel,G.H.,Fox,M.D.,Snyder,A.Z.,Baker,J.T.,Essen,D.C.V.,…Raichle,M.E.

(2007).Intrinsicfunctionalarchitectureintheanaesthetizedmonkeybrain.Nature,

447(7140),83.https://doi.org/10.1038/nature05758

Wang,L.,Hermens,D.F.,Hickie,I.B.,&Lagopoulos,J.(2012).Asystematicreviewof

resting-statefunctional-MRIstudiesinmajordepression.JournalofAffective

Disorders,142(1),6–12.

Wang,Y.,Kang,J.,Kemmer,P.B.,&Guo,Y.(2016).AnEfficientandReliableStatistical

MethodforEstimatingFunctionalConnectivityinLargeScaleBrainNetworksUsing

PartialCorrelation.FrontiersinNeuroscience,10.

https://doi.org/10.3389/fnins.2016.00123


58

Watts,D.J.,&Strogatz,S.H.(1998).Collectivedynamicsof“small-world”networks.Nature,

393(6684),440–442.https://doi.org/10.1038/30918

Whitfield-Gabrieli,S.,&Nieto-Castanon,A.(2012).Conn:AFunctionalConnectivity

ToolboxforCorrelatedandAnticorrelatedBrainNetworks.BrainConnectivity,2(3),

125–141.https://doi.org/10.1089/brain.2012.0073

Woolrich,M.W.,Ripley,B.D.,Brady,M.,&Smith,S.M.(2001).Temporalautocorrelationin

univariatelinearmodelingofFMRIdata.NeuroImage,14(6),1370–1386.

https://doi.org/10.1006/nimg.2001.0931

Yang,Z.,Zuo,X.-N.,Wang,P.,Li,Z.,LaConte,S.M.,Bandettini,P.A.,&Hu,X.P.(2012).

GeneralizedRAICAR:Discoverhomogeneoussubject(sub)groupsbyreproducibility

oftheirintrinsicconnectivitynetworks.NeuroImage,63(1),403–414.


Yeo,B.T.T.,Krienen,F.M.,Sepulcre,J.,Sabuncu,M.R.,Lashkari,D.,Hollinshead,M.,…

Buckner,R.L.(2011).Theorganizationofthehumancerebralcortexestimatedby

intrinsicfunctionalconnectivity.JournalofNeurophysiology,106(3),1125–1165.

https://doi.org/10.1152/jn.00338.2011

Supplementarymaterialsfor

Graphtheoryapproachestofunctionalnetworkorganizationinbraindisorders:

Acritiqueforabravenewsmall-world

MichaelN.Hallquist

and

FrankG.Hillary

TableS1.ParametersusedinnetworksimulationsSimulation Parameter Description ValueWhack-a-nodehyper-connectivity

!" Between-personvariationinmeanFC .2!# Within-personvariationinFC .2!$ Edgenoise .2

%&', * ∈ , MeanshiftinPositivenodetargetsinpatientgroup .14 !&', * ∈ , Between-personvariationinFCshiftsforPositivetargets .07 !-', * ∈ , Within-personvariationinFCvariationofPositivenodei

acrossitsneighbors,j.07

%&', * ∈ . MeanshiftinNegativenodetargetsinpatientgroup -.04 !&', * ∈ . Between-personvariationinFCshiftsforNegativetargets .02 !-', * ∈ . Within-personvariationinFCvariationofPositivenodei


Whack-a-nodehypo-connectivity


%&', * ∈ , MeanshiftinPositivenodetargetsinpatientgroup .04 !&', * ∈ , Between-personvariationinFCshiftsforPositivetargets .02 !-', * ∈ , Within-personvariationinFCvariationofPositivenodei


%&', * ∈ . MeanshiftinNegativenodetargetsinpatientgroup -.14 !&', * ∈ . Between-personvariationinFCshiftsforNegativetargets .07 !-', * ∈ . Within-personvariationinFCvariationofPositivenodei


Globalinsensitivity


%&', * ∈ FP, DAN Meanshiftinbetween-moduleconnectivityofF-PandDANnodesincontrolgroup

.1

!&', * ∈ FP,DAN Between-personvariationinbetween-moduleconnectivityofFPandDANnodesincontrolgroup

.05

!-', * ∈ FP, DAN Within-personvariationinbetween-moduleconnectivityofFPandDANnodesincontrolgroup

.05

%&', * ∈ FP, DAN Meanshiftinwithin-moduleconnectivityofF-PandDANnodesincontrolgroup

.2

!&', * ∈ FP,DAN Between-personvariationinwithin-moduleconnectivityofFPandDANnodesincontrolgroup

.1

!-', * ∈ FP, DAN Within-personvariationinwithin-moduleconnectivityofFPandDANnodesincontrolgroup

.1

%&', * ∈ DMN Meanshiftinbetween-moduleconnectivityofDMNnodesinpatientgroup

.1

!&', * ∈ DMN Between-personvariationinbetween-moduleconnectivityofDMNnodesinpatientgroup

.05

!-', * ∈ DMN Within-personvariationinbetween-moduleconnectivityofDMNnodesinpatientgroup

.05

%&', * ∈ DMN Meanshiftinwithin-moduleconnectivityofDMNnodesinpatientgroup

.2

!&', * ∈ DMN Between-personvariationinwithin-moduleconnectivityofDMNnodesinpatientgroup

.1

!-', * ∈ DMN Within-personvariationinwithin-moduleconnectivityofDMNnodesinpatientgroup

.1

Note.P=Positivetargets(3persimulation);N=Negativetargets(3persimulation);FP=frontoparietalnetwork;DAN=dorsalattentionnetwork;DMN=defaultmodenetwork.

FigureS1.Theeffectofthresholdingmethodongroupdifferencesindegreecentralitywhenthereisstronghypoconnectivityinthreerandomlyselectednodes(Negative)andweakhyperconnectivityinthreenodes(Positive).Forsimulationdetails,seeTableS1,Whack-a-nodehypoconnectivity.Thecentralbarofeachrectangledenotesthemediantstatistic(patient–control)across100replicationdatasets(patientn=50,controln=50),whereastheupperandlowerboundariesdenotethe90thand10thpercentiles,respectively.Thedarklineatt=0reflectsnomeandifferencebetweengroups,whereasthelightgraylinesatt=-1.99and1.99reflectgroupdifferencesthatwouldbesignificantatp=.05.a)Graphsbinarizedat5%,15%,and25%density.b)Graphsbinarizedatr={.2,.3,.4}.c)Graphsbinarizedatr={.2,.3,.4},withdensityincludedasabetween-subjectscovariate.d)Strengthcentrality(weightedgraphs).

−15−10−5

05

0.05 0.15 0.25Density

Mea

n t

Density thresholda)

−15−10−5

05


FC Thresholdb)

−15−10−5

05


Mea

n t


−15−10−5

05 Node Type

PositiveNegativeComparator

Weightedd)

FigureS2.Theeffectofthresholdingmethodongroupdifferencesindegreecentralitywhenthereisstronghyperconnectivityinthreerandomlyselectednodes(Positive)andweakhypoconnectivityinthreenodes(Negative).RelativetoFigure1,thissimulationappliedproportionalchangestoFCsuchthatedgeswereshiftedasafractionoftheiroriginalstrength,ratherthanshiftingedgesbyanabsoluteamount(i.e.,incorrelationalunits).Thus,FCforpositivenodeswasincreasedby14%,onaverage,whereasnegativenodesweredecreasedby4%.AllsimulationparametersareidenticaltoTableS1,Whack-a-nodehyperconnectivity,butwithchangesappliedproportionately.Thecentralbarofeachrectangledenotesthemediantstatistic(patient–control)across100replicationdatasets(patientn=50,controln=50),whereastheupperandlowerboundariesdenotethe90thand10thpercentiles,respectively.Thedarklineatt=0reflectsnomeandifferencebetweengroups,whereasthelightgraylinesatt=-1.99and1.99reflectgroupdifferencesthatwouldbesignificantatp=.05.a)Graphsbinarizedat5%,15%,and25%density.b)Graphsbinarizedatr={.2,.3,.4}.c)Graphsbinarizedatr={.2,.3,.4},withdensityincludedasabetween-subjectscovariate.d)Strengthcentrality(weightedgraphs).

−505

1015

0.05 0.15 0.25Density

Mea

n t

Density thresholda)

−505

1015


FC Thresholdb)

−505

1015


Mea

n t


−505

1015

Node TypePositiveNegativeComparator

Weightedd)

Corresponding author: Frank G. Hillary, Department of ... · Graph theory approaches to functional...

Documents

Transcript of Corresponding author: Frank G. Hillary, Department of ... · Graph theory approaches to functional...