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Anatomy and Cell Biology Publications Anatomy and Cell Biology Department

3-1-2017

A method for independent component graphanalysis of resting-state f MRIDemetrius Ribeiro de PaulaWestern University, dribeir2@uwo.ca

Erik ZieglerUniversity of Liege

Pubuditha M. AbeyasingheWestern University

Tushar K. DasWestern University

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Citation of this paper:de Paula, Demetrius Ribeiro; Ziegler, Erik; Abeyasinghe, Pubuditha M.; and Das, Tushar K., "A method for independent componentgraph analysis of resting-state fMRI" (2017). Anatomy and Cell Biology Publications. 11.https://ir.lib.uwo.ca/anatomypub/11

Brain and Behavior. 2017;7:e00626. wileyonlinelibrary.com/journal/brb3 | 1 of 12https://doi.org/10.1002/brb3.626

Received:9May2016  |  Revised:28October2016  |  Accepted:18November2016DOI:10.1002/brb3.626

M E T H O D S

A method for independent component graph analysis of resting-­state­fMRI

Demetrius­Ribeiro­de­Paula1 | Erik­Ziegler2 | Pubuditha­M.­Abeyasinghe1 | Tushar­K.­Das1 |  Carlo Cavaliere2,3 | Marco­Aiello3 | Lizette­Heine2 | Carol­di­Perri2 |  Athena­Demertzi2,4 | Quentin­Noirhomme2 | Vanessa­Charland-Verville2 |  Audrey­Vanhaudenhuyse5 | Johan­Stender6 | Francisco­Gomez7 |  Jean-Flory­L.­Tshibanda8 | Steven­Laureys2,8 | Adrian­M.­Owen9 | Andrea­Soddu1

ThisisanopenaccessarticleunderthetermsoftheCreativeCommonsAttributionLicense,whichpermitsuse,distributionandreproductioninanymedium,providedtheoriginalworkisproperlycited.©2017TheAuthors.Brain and BehaviorpublishedbyWileyPeriodicals,Inc.

1DepartmentofPhysics&Astronomy,Brain&MindInstitute,WesternUniversity,London,ON,Canada2ComaScienceGroup,GIGAResearch,UniversitéetCentreHospitalierUniversitairedeLiège,Liège,Belgium3IRCCSSDN,IstitutodiRicercaDiagnosticaeNucleare,Naples,Italy4BrainandSpineInstitute(ICM),HôpitalPitié-Salpêtrière,Paris,France5DepartmentofAlgologyandPalliativeCare,UniversitédeLiège,Liege,Belgium6DepartmentofNeuroscienceandPharmacology,UniversityofCopenhagen,Copenhagen,Denmark7DepartmentofMathematics,UniversidadNacionaldeColombiasedeBogotá,Bogotá,Colombia8DepartmentofNeurology,UniversitédeLiège,Liège,Belgium9DepartmentofPsychology,Brain&MindInstitute,WesternUniversity,London,ON,Canada

AbstractIntroduction:­Independentcomponentanalysis(ICA)hasbeenextensivelyusedforre-ducingtask-freeBOLDfMRIrecordings intospatialmapsandtheirassociatedtime-courses.Thespatiallyidentifiedindependentcomponentscanbeconsideredasintrinsicconnectivitynetworks(ICNs)ofnon-contiguousregions.Todate,thespatialpatternsofthenetworkshavebeenanalyzedwithtechniquesdevelopedforvolumetricdata.Objective:­Here,wedetailagraphbuildingtechniquethatallowsthese ICNstobeanalyzedwithgraphtheory.Methods:­First,ICAwasperformedatthesingle-subjectlevelin15healthyvolunteersusing a 3TMRI scanner. The identification of nine networks was performed by amultiple-template matching procedure and a subsequent component classificationbasedonthenetwork“neuronal”properties.Second,foreachoftheidentifiednet-works, the nodes were defined as 1,015 anatomically parcellated regions. Third,between-nodefunctionalconnectivitywasestablishedbybuildingedgeweightsforeachnetworks.Group-levelgraphanalysiswasfinallyperformedforeachnetworkandcomparedtotheclassicalnetwork.Results:­Networkgraphcomparisonbetweentheclassicallyconstructednetworkandtheninenetworks showed significantdifferences in the auditory andvisualmedial

CorrespondenceDemetriusRibeirodePaulaandAndreaSoddu,DepartmentofPhysics&Astronomy,Brain&MindInstitute,WesternUniversity,London,ON,Canada.Emails:dribeir2@uwo.caandasoddu@uwo.ca

Funding­informationCanadaExcellenceResearchChairs(CERC);JamesS.McDonnellFoundation(JSMF)Program;NaturalSciencesandEngineeringResearchCouncilofCanada(NSERC);BelgianNationalFundforScientificResearch;UniversityofLiege;QueenElisabethMedicalFoundation;LeonFredericqFoundation;BelgianInter-UniversityAttractionProgram;WalloonExcellenceinLifeSciencesandBiotechnologyprogram;MarieCurieInitialTrainingNetworkinNeurophysics,Grant/AwardNumber:PITN-GA-2009-238593

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1  | INTRODUCTION

Theevaluationoffunctionalconnectivityfromresting-statefMRIdatais broadlybasedon two familiesof analyticalmethods. Seed-basedcorrelationanalysisestimatestherelationshipbetweenapredefinedregion(the“seed”)andallothervoxelsaroundthebrain(Biswal,Yetkin,Haughton,&Hyde, 1995; Fox&Raichle, 2007; Fox etal., 2005).Acommonlyemployedalternative is independent componentanalysis(ICA;Beckmann,DeLuca,Devlin,&Smith,2005;Damoiseauxetal.,2006; Esposito etal., 2008; Hyvärinen, Karhunen, & Oja, 2001), adata-drivenapproachtodecomposewhole-brainBOLDsignalintoanumberofcontributingvolumetricspatialmapsandtheirassociatedtime-courses,suchthatthespatialindependenceofthecomponentsismaximized.ICAhasproventobeaneffectiveandrobusttoolfortheisolationof low-frequencyresting-statepatternsfromdataacquiredatvariousspatialandtemporal resolutions (DeLuca,Beckmann,DeStefano, Matthews, & Smith, 2006). The ICA-generated volumetricmapsaregenerallyreportedasz-scoresinordertoshowthecontri-butionofeachcomponent’stime-coursetotheBOLDsignalineachvoxel.Thesemapsarethencommonlyanalyzedinavoxel-wiseman-nerinordertoshowbetweenorwithin-groupconnectivitydifferences(Greicius,Srivastava,Reiss,&Menon,2004).Thenumberofcompo-nentsisgenerallyuser-definedandmanyoftheresultingcomponentsmay be due to non-neuronal activity (such as cardiovascular signal,eyemovements,muscleactivityinthevicinityoftheheadandheadmovement).Classically10 functionalnetworks canbe reliably iden-tifiedfromICA(Beckmannetal.,2005;Damoiseauxetal.,2006;DeLucaetal.,2006;Fox&Raichle,2007)bydecomposingthesignalandto separate neuronal from non-neuronal components. Apart fromvoxel-wisestatistics,graphtheorycouldbeappliedtothefunctionalnetworkswhichprovidestoolsforanalysisofnetworktopographyandconnectivity(Rubinov&Sporns,2010).Functionalandstructuralcon-nectomeanalysishasbecomeincreasinglycommoninneuroscience.Inthesemethods,thebrainisdefinedabstractlyasanetworkofnodeswithedgesconnectingthem.Nodesareoftenanatomicallydefinedre-gions,whereasedgestypicallycarryweightsdescribingthecorrelation,

similarity,ordegreeofconnectivitybetweennodes.Adjacencygraphs,inwhich the edge’s existence is binary and carry no representativeweight, are also common, as data-driven approaches for brain par-cellation(Bullmore&Bassett,2011).Usually,aweightedgraphW iscreatedbycalculatingaconnectivitymeasurebetweeneverypairofregions;subsequently,themeaningfulpropertiesofthegrapharecar-riedoutbynetworkanalysismethods,suchassummarystatistics(e.g.,degree, small-worldness) and permutation testing (Zalesky, Fornito,&Bullmore,2010).Toourknowledge,nographtheoryapproachhasbeendevelopedtoevaluatetheorganizationpropertieswithinbrainnetworks derived from ICA.A graphical method permits to extractpropertiesofaregionofinterestinthecontextofthefullnetwork.Acomparisonofgraphicalpropertiesgoes farbeyondthecomparisonofthezvalues,ascommonlydonewiththecomparisonofICspatialmapsvoxel byvoxel,where eachvoxel is treated as a separate en-tityandnot considered in thecontextof the full brain spatialmap.Themethodwepresenthereincorporatespiecesofbothfamiliesofmethodsanditisageneralizationtotheentirebrainofapreviouslyintroducedapproachrestrictedtothedefaultmodenetwork (DMN)to study functional connectivity changes in patientswith disordersof consciousness (Soddu etal., 2012). Following, this approach hasbeenalsoappliedinpatientssufferingfromtinnitusfocusingontheauditorynetwork(Maudouxetal.,2012a,2012b).Wedobelievethatourmethod,fortheveryfirsttime,permitsacomparisonofICspatialmapsusingtheadvantageofgraphtheory.

2  | METHODS

In short,weused ICAandmachine learningclassification to isolateasetofneuronalcomponents(Demertzietal.,2014),andthencon-structweighted graphs for each of these components. As in otherfunctionalandstructuralconnectivitymappingmethods,wedefinedour regionsbasedonstructuralparcellation (Cammounetal.,2012;Gerhard etal., 2011). As the parcellation concerned cortical areasonly,thecerebellumwasnothereconsideredasanetworkofinterest,

networkswithregardtotheaveragedegreeandthenumberofedges,whilethevisuallateralnetworkshowedasignificantdifferenceinthesmall-worldness.Conclusions:­Thisnovelapproachpermitsustotakeadvantageofthewell-recognizedpowerof ICA inBOLDsignaldecompositionand,at thesametime,tomakeuseofwell-establishedgraphmeasures toevaluateconnectivitydifferences.Moreover,byproviding a graph for each separate network, it can offer the possibility to extractgraphmeasuresinaspecificwayforeachnetwork.Thisincreasedspecificitycouldberelevantforstudyingpathologicalbrainactivityoralteredstatesofconsciousnessasinducedbyanesthesiaorsleep,wherespecificnetworksareknowntobealteredindifferentstrength.

K E YWORD S

BOLDfMRI,graphtheory,independentcomponentanalysis,restingstate

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reducingthenumberofICAmapsanalyzedtonine.Theedgeweight-inginthegraphswasfairlyuniquetothismethod,anddependedonanode-basedcalculationofthecontributionofthespecificcompo-nenttotheaverageBOLDsignal inthatregion.Wethencalculatedtheweight (dependenton themagnitude and typeof contribution)betweeneachpairofnodesthatreflectsthesimilaritybetweenthemthroughacommonsimilaritywiththetimecourseofthecomponentof interest. This approach provided weighted within-componentgraphsthatarerelatedtodistinctandknowncognitivefunctionsandcouldbequantifiedbyusinggraphtheory.Inprinciple,thistechniquecanbeappliedtoanyindependentcomponentmap.

2.1 | Subjects

Fifteen(meanage=43±15,7women)healthysubjects,freeofpsy-chiatricorneurologicalhistory,werestudied.TheEthicsCommitteeoftheMedicalSchoolattheUniversityofLiègeapprovedthestudy.Informedconsenttoparticipateinthestudywasobtainedfromeverysubject.

2.2 | Data­acquisition­and­preprocessing

FunctionalMRI time serieswere acquired on a 3T head-only scan-ner (Siemens Trio, Siemens Medical Solutions, Erlangen, Germany)operatedwithastandardtransmit-receivequadrateheadcoil.Threehundred multislice T2*-weighted functional images were acquiredwith a gradient-echo echo-planar imaging sequence using axialsliceorientationandcovering thewholebrain (32 slices;voxel size:3 × 3 × 3 mm3;matrix size64×64×32; repetitiontime=2,000ms;echo time=30ms; flip angle=78°; field ofview=192×192mm2).The three initialvolumeswerediscarded to avoidT1 saturationef-fects.Thesubjectswereinstructedtoclosetheireyes,relaxwithoutfallingasleepandrefrainfromanystructuredthinkingsuchascount-ing, singing etc. A high-resolution T1-weighted imagewas also ac-quiredforeachsubject (120slices,repetitiontime=2,300ms,echotime=2.47ms, voxel size=1×1×1.2mm3, flip angle=9°, field ofview=256×256mm2). Data preprocessing was performed usingStatisticalParametricMapping8(RRID:nif-0000-00343;www.fil.ion.ucl.ac.uk/spm).Preprocessingstepsincludedrealignmentandadjust-mentformovement-relatedeffects,coregistrationoffunctionalwithstructural images, segmentationof structuraldata, spatialand func-tionalnormalizationintostandardstereotacticMontrealNeurologicalInstitute space, and spatial smoothing of the fMRI data with aGaussiankernelof8mmfull-widthathalf-maximum.Furthercorrec-tionforsmall,large,andrapidmotions,noisespikes,andspontaneousdeepbreathswasappliedusingArtRepair (RRID:SCR-005990;cibsr.stanford.edu/tools/human-brain-project/artrepair-software.html).

2.3 | Independent­component­analysis­and­component­classification

Single-subjectindependentcomponentanalysiswasperformedusingtheInfomaxalgorithmwithintheGroupICAoffMRIToolbox(RRID:

SCR-001953; http://mialab.mrn.org/software/gift/) with a prede-finednumberofcomponentsequaltothirty.Thecomponentspatialimageswerecalibratedtotherawdatasothatthe intensityvalueswereinunitsofpercentsignalchangefromthemean.Componentsweresubsequentlyassignedtotheputativeintrinsicconnectivitynet-works using amultiple-templatematching procedure. Thismethodextends the single-template goodness-of-fit approach by assigningtheindependentcomponentthatmaximizesthegoodness-of-fittoabinarypredefinedtemplatewhileconsideringalloftheRSNssimul-taneously.Thisprocedurehasbeendescribedpreviously (Demertzietal.,2014).

For the discrimination between “neuronal” and “non-neuronal”independentcomponents,abinaryclassificationapproachusingsup-portvectormachine(SVM)wasperformed.ThetrainingoftheSVMclassifierwasperformedonthefingerprintsoftheindependentcom-ponents obtained from ICA decompositionwith 30 components in19 independently studied healthy subjects (Demertzi etal., 2014).The classifier with highest overall classification rate was selectedand subsequently used to label neuronal independent components.Independent components that failed to pass the “neuronality” testwereexcluded.SeeFigure1aforapictorialdescriptionoftheabove-describedprocedure.

2.4 | Regional­parcellation

Segmentation of each subject’s T1-weighted imagewas performedwith Freesurfer’s automatic segmentationpipeline and theDesikanKilliany atlas (De Luca etal., 2006). Further parcellation, using theLausanne2008atlas and its1,015 individually labeled regions,wasdonewithfunctionsfromtheConnectomeMappingToolkit,inordertoseparatedifferentICA-derivednetworksintonon-overlappingspa-tialcomponents(Cammounetal.,2012;Daduccietal.,2012;Gerhardetal.,2011;Gorgolewskietal.,2011).Tofacilitatethecreationofthefunctionalnetworks,thistypeofparcellationwasperformedforboththeoriginalandspatiallynormalizedT1imagesforeachsubject.SeeFigure1bforanillustrativedescriptionofthefinalparcellation.

2.5 | Functional­network­construction

Inthefollowing,thelettersN,PandRwillrefertothenumberofICAneuronalcomponents(N),thenumberofBOLDsignaltimepoints(P)andthenumberofparcellatedregions(R),respectively.

LetX a N × PmatrixstoringattheithrowthetimecourseoftheithindependentcomponentandY a R × PmatrixcontainingattheithrowthetimecourseoftheBOLDsignalaveragedoverthevoxelbelong-ingtotheithregion.Theprocessofidentifyingregionaltime-coursesacrossasetofanatomicallydefinedvoxelsisshowninFigure1c.Wesolvethesimpleequation:

for theN × Rmatrix β, using the least squares solution (Worsley&Friston,1995).Thismeansminimizingthevalueof:

(1)Y=Xβ

(2)‖Y−Xβ‖2

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withanerrortermε,foreveryregionandeachcomponent:

The regression value βij describes how the time course of thejthregioncanbeexplainedbythe ith independentcomponenttimecourseplusanerrorterm.Theregressionvaluesare,however,valuesof arbitrary size andvariance and cannot be interpreteddirectly. Inordertodealwiththisissue,wechosetotransformthesevaluesintot-values(Worsley&Friston,1995),usingthefollowingequation:

where c isavectorindexingeachcomponent,andT isthematrixoft-values by region and IC. At this point, we have regional t-values

for each component,which can be used to buildweighted graphs,Figure1c.Thegoalistochooseanappropriateweightingschemesuchthatedgesarestrongbetweenregionswhichbothcontributelargely,andwithsimilarstrengths,totheregionalfMRItimecourse.Forthisreason,wehavechosenastraightforwardweightingequationforthedegreeofconnectionbetweentwonodes:

where Wa,brepresentstheedgeweightbetweennodesaandb,andta,tbarethet-valuesfornodeaandb,respectively.

Equation5 produces a zero weight for ta and tb with oppositesigns.Here,werestraintheanalysistopositivecorrelationnetworksonly,forwhichaconnectionisconsideredonlybetweennodeswitht-valuesofthesamesign.Itisalsopossibletoconstructthecomple-mentaryanti-correlationnetworks,bydrawingedgesbetweenregions

(3)ε=Y−Xβ

(4)T=cTβ

√Var(ε)cT(XTX)

−1c

(5)Wa,b= |ta|+ |tb|− |ta− tb|

F IGURE  1 Processingworkflowforfunctionalnetworks:(a)1,preprocessing:registrationtoT1(SPM8);2,independentcomponentanalysis(GIFT)and3,neuronalitycheckandtemplatematching.(b)1,SpatialnormalizationofT1(SPM8),2,Atlas-basedsegmentation(FreeSurfer)and3,parcellation(Nipype/CMTK,Lausanne1,015atlas).(c)1,ExtractregionalfMRItimecourses(Y),2,leastsquaressolutiontoestimateβvaluesusingaspredictorsthetimecoursefromICAasin(a)and3,transformβvaluestotvalues.(d)1,Calculateedgeweightsanddrawnetworksforeachindependentcomponentand2,thresholdcorrelationandanti-correlationnetworksandanalyzeseparately

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withopposingsigns.Forcreatingweightededgesbetweennodesofoppositesign,thefollowingequationcanbeused:

2.6 | Thresholding­network­edges

Weestimatedthedegrees-of-freedombyconsideringthenumberoffunctional image volumes and the number of independent compo-nentsinournetworkconstructionprocedure.Thisledtotheequation:

Given thedegreesof freedomand thedesiredsignificance level(p<.001), we calculated the t-value with which to threshold ourgraphs.Wechose to thresholdournetworks to removeall t-valuesthatwerenotinthe99thpercentile.Thisledtothecalculation:

Following the weighting scheme described in Equation5, thenodescanhaveedgeweightsrangingfromzerotothesumoftheirt-values.Forthisreason,wechosetodiscardedgesabove2×tthresh-oldwith2×tthresholdbeingthemaximumvalueforWa,bgiventheas-sumed tthreshold.Group levelnetworks, aspresented inFigures2–6,werecreatedbythresholdingeachsubjectweightedmatrixWa,bandby subsequently keeping the edgeswhichwere present in at least25%ofthesubjects.

2.7 | Classical­network­connectivity­matrix

Withtheaimofthecreationofawhole-brainconnectivitymatrix,wereconstructedthefunctionalMRIsignalateachvoxelbya lin-earcombinationofthecomponentsdeemed“neuronal”bytheclas-sifierwithweights coming from the corresponding scalarmapsof

each component. The resulting signal, cleaned off “non-neuronal”noise,wasthenaveragedoverallthevoxelsbelongingtothesameparcellatedregiontoobtaintimecoursesforeachofthe1,015re-gions.TheWmatrix, representingtheclassicalnetwork,was thencalculated.

2.8 | Network­analysis­and­statistics

Nodesforeachnetworkofinterestwerepreviouslyextractedasthenon-isolatednodesofthecorrespondinggrouplevelnetworksprevi-ouslyintroducedandpresentedinFigures2–6.Wehaveconsideredseveralnetworksummarystatisticsforthegraphs.Wecomputedthenumberofedges(E),averagedegree(k),averagenumberoftrianglesandsmall-worldness (Rubinov&Sporns,2010)asshowninTable1.A graph is a formalmathematical representation of a network andeach object in a graph is called a node. The number of edges rep-resentsthenumberofconnectionsbetweeneachpairofconnectednodes.The averagedegree represents the averagenumberof con-nections(edges)pernode.Isolatednodes(nodeswithoutedges)werediscardedandallthepropertieswerecalculatedfortheconstellationof connected nodes. The number of triangles represents triplets ofnodesinwhicheachnodeisconnectedtothetwoothers.Thesmall-worldnesswascalculatedby:

where CandCrandaretheclusteringcoefficientsandLandLrand are the characteristic path lengths of the network of interest and thecorrespondingrandomnetwork(Humphries&Gurney,2008).Small-worldness is an extremely important property of networks. Thesenetworks are “highly clustered, like regular lattices, yet have smallcharacteristicpathlengths,likerandomgraphs”makingthemveryef-ficientininformationtransfer(Watts&Strogatz,1998).

(6)WACa,b

= |ta|+ |tb|− |ta+ tb|

(7)DOF=Nvolumes−Ncomponents−1

(8)tthreshold= tINV(Confidence, DOF)

(9)σ=C∕Crand

L∕Lrand

F IGURE  2 SagittalandaxialrepresentationofthenetworkandcorticalextentoftherelativeICfortheDMN.Thedegreeofeachoneofthe1,015regionsisrepresentedbythenode’ssizeandorangetoyellowgradient.Ontheright,corticalparcellationforDMNextractedbygroup-ICAsuperimposedtoastructuralT1image

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Thepropertieswere calculated at subject-level producing adis-tributionofgraphicalvaluesforthenetworkofinterest.Thismethodwasusedtocomparethegraphproperties(Table1)amongthediffer-entnetworksasshowninFigure7.AnANOVAtestwasperformedtocompareallthenineweightedfunctionalnetworkswiththeweightedclassical network.The calculation for both networkswas restrictedonly to the nodes belonging to the network of interest due to thenumberofnodesofanetworkhaveanstrongeffectinresultingtopol-ogy(Zalesky,Fornito,Harding,etal.,2010).Column3inTable1showsthenumberofnon-isolatednodesforeachnetwork.Forthenumberoftriangles,thecomparisonwasperformedbyfirstlynormalizingthenumberoftrianglesbyarandomnetworkcontainingthesamenumberofnodes.

Todeterminewhich networks are different from theothers,weconductedaposthocpairedcomparison(Tukeyposthoctestasim-plementedinR),whichisdesignedtoevaluatethedifferencebetweeneachpairofnetworks,Figure7.

3  | RESULTS

3.1 | Component­classification

Thetemplate-matchingandfingerprintselectioncriteriaidentifiedthepredefinedneuronalcomponentswithinthegroupofhealthycontrols.Thepercentageofsubjects inwhichtheywerefound ispresentedinthesecondcolumninTable1.TheSensorimotorwasthehighestrecognizednetwork,withthescoreofdetectionequalto87%ofthesubjects.Theexecutivecontrolleftandvisualoccipi-talnetworkswerethelowestrecognizednetworks,beingpresentin33%of the subjects. ICAwasused to separate the signal intonon-overlapping spatial and time components. This data-drivenmethodwasabletoextract theDMNaswellasmanyothernet-works with very high consistency, that can be verified by com-paring Figures2–6with the z-maps produced using the classicalapproach.

F IGURE  3 GraphicalrepresentationofthenetworkandcorticalextentoftherelativeICsfortheleftandrightexecutivecontrolnetworks.Thedegreeofeachoneofthe1,015regionsisrepresentedbythenode’ssizeandcolorgradient.Ontherightcolumn,corticallocationforeachnetworkwasextractedbygroup-ICAsuperimposedtoastructuralT1image

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3.2 | Network­properties

The network properties were calculated for the nine independentcomponentnetworksof interest forall the15subjects.The resultsareshowninTable1.

Whencomparingeachoftheninenetworkswiththeclassicalnet-work,focusingonlyontheconstellationofnodescharacterizingthenetworkofinterest,seeFigure7,wefoundthattheauditoryandthevisualmedialnetworkshadasignificantlydifferentnumberofedgesanddegreewithrespecttotheclassicalnetwork.Alternatively,whencomparingsmall-worldnessitwasthevisuallateralnetworkshowingasignificantlydifferentvaluefromtheclassicalnetwork.Nosignificantdifferenceswerefoundforthenormalizednumberoftriangles.(SeeintheTableS1forgraphpropertiesandFigureS1forasimilarANOVAanalysisperformedthistimeoverallthe1,015nodes).

The sagittal and axial graphical representationsof thenetworks,as created from the respective group level matrixW, are shown in

Figure8 (all nine overlapping networks and the classical network).Theywerealsopresentedseparately,DMNinFigure2,executivecon-trolleftandexecutivecontrolrightinFigure3,auditoryandsalienceinFigure4,sensorimotorandvisuallateralinFigure5andvisualmedialandvisualoccipitalinFigure6.AsshowninFigure8,thenodeswiththehighestdegreeoftheclassicalnetworkarealsothenodeswiththehighestaveragedegreesharedby theninedifferentnetworks.FromFigures2–6itisalsopossibletorecognizethattheclustersofnodeswithhigherdegreetendtobespatiallydistributedasthehighz-valueinthecorrespondingindependentcomponentz-mapforthespatialpat-ternsofthenineindependentcomponents(Damoiseauxetal.,2006).

4  | DISCUSSION

Wepresentedanovelmethod forapplyinggraph theorymetrics torestingstatefMRIbrainnetworksderivedfromdata-drivenICA.With

F IGURE  4 GraphicalrepresentationofthenetworkandcorticalextentoftherelativeICsforauditoryandsaliencenetworks.Thedegreeofeachoneofthe1,015regionsisrepresentedbythenode’ssizeandcolorgradient.Ontherightcolumn,corticallocationforeachnetworkwasextractedbygroup-ICAsuperimposedtoastructuralT1image

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thiswithin-componentapproach,thebetween-grouptopologicaldif-ferencesinconnectivestructureoffunctionalnetworkscanbestud-iedwithwell-establishednetworkmeasuresemployedingraphtheory.

ClassicalapproachesarebasedontherecognitionofRSNsfromdifferent ICAprocessingresults,suchasmultipletemplate-matching(Demertzietal.,2014),highdimensionalICA(Dipasqualeetal.,2015)and fully exploratory network ICA (Schöpf etal., 2010); once eachRSN is estimated, their spatial distributions are usually comparedvoxel-wisebetweensubjectsorgroupsfortheassessmentofwithin-networkdifferences.Ontheotherhand,atthebestofourknowledge,thereisnotyetaneffectiveprocedurefortheanalysisandcomparisonofgraphpropertiesbetweennetworkcomponentsderivedfromspa-tialICAprocedures.

Asimilarapproachhasbeenproposedfortheanalysesofwithin-networkorganization.In(Parketal.,2014),analternativemethodfortheestimationofeachRSNisemployed.Asourmethod,itprovidesinformation on the connectivity among each component, but eachcomponent isnotderivedwithaconventionalspatial-ICAapproach.

Therefore,ourmethodoffersmoreflexibility,sinceitdealswithcom-monly derived ICA components, exploiting thewell-established ad-vantageofspatialICAfortherejectionofartifactualcomponents.

Comparisonbetweentheninenetworksandtheclassicalnetworkdidnot show, formost of the comparisons, significant differences inthestudiedgraphproperties,which indicatessimilarity in theirgraphstructure.Theabsenceofmaindifferences is also indicating the factthatwhenrestrictingtonetwork’sregions,connectivityduetothetimecoursebehaviorrepresentativeoftheICofinterestiscapturingalmostentirelythefullneuronalbehavior.(FigureS1insupplementarymaterialshows clearly thatwhenextending the analysis to the full brain, i.e.,1,015nodes,deviationof theclassicalnetwork from thenetworkofinterestbecomemorerelevant,consideringthatnow,asexpected,out-sidetheconstellationofnodesrepresentativeofthenetworkofinteresttheclassicalnetworkgetscontributionsfromalltheothernetworks).

Thesignificantdifferencesinthenumberofedgesanddegree,forthe auditory andvisualmedial networks togetherwith the significantsmall-worldnessfor thevisual lateralnetwork,aresuggestingthat the

F IGURE  5 GraphicalrepresentationofthenetworkandcorticalextentoftherelativeICsforsensorimotorandvisuallateralnetworks.Thedegreeofeachoneofthe1,015regionsisrepresentedbythenode’ssizeandcolorgradient.Ontherightcolumn,corticallocationforeachnetworkwasextractedbygroup-ICAsuperimposedtoastructuralT1image

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Type % No.­of­nodes E (103) k Triangles­(103) σ

AUD 80 265 15±2 144±9 1.13±0.02 1.18±0.03

DMN 47 356 26±4 167±14 1.28±0.03 1.41±0.05

ECL 33 153 6±1 84±5 1.53±0.04 1.88±0.07

ECR 80 131 9±1 105±7 1.51±0.03 1.86±0.06

SA 80 116 17±7 115±30 1.10±0.04 1.14±0.06

SM 87 102 5±1 80±13 1.44±0.09 1.68±0.16

VL 60 133 14±3 121±15 1.34±0.06 1.58±0.10

VM 73 277 22±2 174±12 1.24±0.04 1.38±0.06

VO 33 183 10±1 123±10 1.38±0.09 1.61±0.18

Thepropertieswerecalculatedforeachsubject.Themeasureofvariabilityisreportedwiththemean.Networks:AUD,auditory;DMN,defaultmodenetwork;ECL,executivecontrol left;ECR,executivecontrolright;SA,salience;SM,sensorimotor;VL,visuallateral;VM,visualmedialandVO,visualoccipi-tal.Theproperties:%,percentageofsubjectsthathavetherespectivenetwork;No.ofnodes,numberofconnectednodesamongthe1,015possiblenodes;E,NumberofEdges;k,averagedegreeandσ,Small-WorldnessIndex.

TABLE  1 Graphtheoreticalmetricsforthenineindependentcomponentmaskednetworks

F IGURE  6 GraphicalrepresentationofthenetworkandcorticalextentoftherelativeICsforvisualmedialandvisualoccipitalnetworks.Thedegreeofeachoneofthe1,015regionsisrepresentedbythenode’ssizeandcolorgradient.Ontherightcolumn,corticallocationforeachnetworkwasextractedbygroup-ICAsuperimposedtostructuralT1image

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timecoursebehaviorofeachseparateindependentcomponentiscon-tributingtothetotalneuronalsignalinalessdominantfashion,especiallyintheregionsofsensorynetworks.Inparticularahighervalueforsmall-worldnessindicatesthatthenetwork,basedontheseparatetimecourse

behaviorofvisuallateralnetwork,hashigherglobalandlocalefficiencyofparallel informationprocessing, sparseconnectivitybetweennodesandlowwiringcosts(Bassett&Bullmore,2006)withrespecttothecor-respondingclassicalnetworkderivedfromthefullneuronalsignal.

F IGURE  7 Weightednetworkpairsandsignificantdifferenceanalysisusingposthocpairedcomparisonforeachnetworkproperty.Thecolorsredandorangerepresentp-values≤.05and≤.01,respectively.Networks:X_CN(XrepresentsthemaskusedtokeepjustthenodesbelongingtotherespectivenetworkandCNistheclassicalnetwork),DMN(defaultmodenetwork),AUD(auditory),ECL(executivecontrolleft),ECR(executivecontrolright),SA(salience),SM(sensorimotor),VL(visuallateral),VM(visualmedial)andVO(visualoccipital)

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Adrawbackof theprocedure is that it reliesona spatiotempo-ral “neuronality” check and template matching procedure prior tonetworkcreation. It isobvious that the templatematchingwillonlyworkproperlyifthesubjects’brainactivitypatternsfitthepredefinedtemplates. Pathological brain morphology may affect network pre-sentation, however, we do not know inwhich form the functionalnetworkswill appear. Itmaybeattractive toperform some typeofcomponentclusteringtoobtaindata-drivensetsofthegroups’mostcommon graph types. Component clustering has been performedrepeatedly inICAanalysesusingvolumetricdata,aswellas inothergraph-theoreticalstudies (vandenHeuvel,Mandl,&Pol,2008). It isnotclearwhichparameterstheclusteringalgorithmwouldneedtobebasedon,butsomesuitablecandidatescouldbelocaledgeweightandnodalnetworkmetrics.Finally,itisclearthatnewmethodcouldbede-velopedatthesinglesubjectleveltoselectthecomponentofinterest.Infact,forexample,giventheselectionofnodesthatformanetwork(aprioriknowledge)foracomponentof interest,an ICcouldbese-lectedasthecomponentwiththehighestaveragenumberofedgesintheselectedconstellationofnodes.Therefore,thisapproachcouldbe quite appealing to patients suffering severe brain injury, consid-eringthatthenetworksmightbehighlyaffected.Forthesepatients,structuralinformationcouldbeusedtoindicatethepartialselectionofnodeswhichwewouldliketofocuson,andsimplyselectthecom-ponentbasedonthehighestaveragenumberofedgesforthenewlyselectedconstellationofnodes.

5  | CONCLUSIONS

Wepresentedanapproachfortheanalysisofrestingstatenetworkscarriedoutbydissectingtheconnectivitypatternsoftask-freefMRIdatabyusingICA.Ourresultssuggestthat,byevaluatingindependentcomponentnetworksusinggraphtheoryinsteadofusingvolumetric

data,onecouldtakefulladvantageofgraphicalmethods,whichper-mitthecomparisonoflocalpropertiesinthecontextofthefullbrain.Moreover,ourapproachisthebasisforfurtherrefinementssuchasacomponentclusteringbasedonnetworktopology.Similarly,theinitialinvestigation into the anti-correlationnetworks for the15 subjectsstudied here showed wide variability in structural topology, and itneedstobefurtherinvestigated.Infuture,onecouldselectivelycon-nectedgesbasedonthesignoftwonodest-valuesandexplorethedifferencesbetweengraphscreatedwithdifferingparity.

ACKNOWLEDGMENTS

This research was supported by the Canada Excellence ResearchChairs (CERC), the James S. McDonnell Foundation (JSMF) pro-grams,adiscoverygrantfromtheNaturalSciencesandEngineeringResearch Council of Canada (NSERC), the Belgian National FundforScientificResearch,theUniversityofLiege,theQueenElisabethMedical Foundation, the Leon Fredericq Foundation, the BelgianInter-UniversityAttractionProgram, theWalloon Excellence in LifeSciences and Biotechnology program, and the Marie Curie InitialTrainingNetworkinNeurophysics(PITN-GA-2009-238593).

CONFLICT­OF­INTEREST

Nonedeclared.

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How­to­cite­this­article:RibeirodePaulaD,ZieglerE,AbeyasinghePM,etal.Amethodforindependentcomponentgraphanalysisofresting-statefMRI.Brain Behav. 2017;7:e00626. https://doi.org/10.1002/brb3.626