braph: a graph theory software for the analysis of brain … · the first step of a graph theory...

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BRAPH:AGraphTheorySoftwarefortheAnalysisofBrainConnectivityMiteMijalkov1,EhsanKakaei1, JoanaB.Pereira2,EricWestman2,GiovanniVolpe1,3*, fortheAlzheimer'sDiseaseNeuroimagingInitiative**1UNAM -NationalNanotechnologyResearch Center&Department of Physics, BilkentUniversity,Ankara,Turkey2 Department of Neurobiology, Care Sciences and Society, Karolinska Institutet,Stockholm,Sweden3DepartmentofPhysics,GoteborgUniversity,Goteborg,Sweden*Correspondingauthor:Giovanni Volpe // Email: [email protected] // Address: Origovägen 6b,41296,Göteborg,Sweden//Phone:+46317869137**Dataused inpreparationof thisarticlewereobtained fromtheAlzheimer’sdiseaseNeuroimagingInitiative(ADNI)database(adni.loni.ucla.edu).Assuch,theinvestigatorswithintheADNIcontributedtothedesignandimplementationofADNIand/orprovideddatabutdidnotparticipate in analysis orwritingof this report.A complete listingofADNI investigators can be found at: http://adni.loni.ucla.edu/wp-content/uploads/how_to_apply/ADNI_Acknowledgement_List.pdfAbstractThe brain is a large-scale complex network whose workings rely on the interactionbetweenitsvariousregions.Inthepastfewyears,theorganizationofthehumanbrainnetwork has been studied extensively using concepts from graph theory, where thebrain is represented as a set of nodes connectedby edges. This representation of thebrain as a connectome can be used to assess important measures that reflect itstopologicalarchitecture.WehavedevelopedafreewareMatLab-basedsoftware(BRAPH– BRain Analysis using graPH theory) for connectivity analysis of brain networksderived from structural magnetic resonance imaging (MRI), functional MRI (fMRI),positron emission tomography (PET) and electroencephalogram (EEG) data. BRAPHallows building connectivitymatrices, calculating global and local networkmeasures,performingnon-parametricpermutationsforgroupcomparisons,assessingthemodulesin the network, and comparing the results to random networks. By contrast to othertoolboxes, it allows performing longitudinal comparisons of the same patients acrossdifferentpointsintime.Furthermore,eventhoughauser-friendlyinterfaceisprovided,the architecture of the program is modular (object-oriented) so that it can be easilyexpanded and customized. To demonstrate the abilities of BRAPH, we performedstructural and functional graph theory analyses in two separate studies. In the firststudy,usingMRIdata,weassessedthedifferencesinglobalandnodalnetworktopologyinhealthycontrols,patientswithamnesticmildcognitiveimpairment,andpatientswithAlzheimer’s disease. In the second study, using resting-state fMRI data,we comparedhealthycontrolsandParkinson’spatientswithmildcognitiveimpairment.Keywords: graph theory analysis, object-oriented software, network topology,longitudinalanalysis

was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprint (whichthis version posted February 7, 2017. ; https://doi.org/10.1101/106625doi: bioRxiv preprint

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1.IntroductionGraph theory studies the properties and behavior of networks, which are systemsconsisting of a set of elements (nodes) linked by connections or interactions (edges).ManysystemsfoundinNature,rangingfromsocial interactionstometabolicnetworksandtransportationsystems,canbemodeledwithinthisframework,pointingtoasetofunderlyingsimilaritiesamongtheseverydiversesystems.Thehumanbraincanalsobemodeledasanetwork(thehumanconnectome) [1],wherebrainregionsare thenodesand the connections between them are the edges. The human brain is thus an idealcandidateforgraphtheoreticalanalysis.Thenodescanbedefinedasthebrainregionsunderlying electrodes or using an anatomical, functional or histological parcellationscheme.Theedgesareobtainedasmeasuresofassociationbetweenthebrainregions,such as connection probabilities (diffusion tensor imaging, DTI), inter-regionalcorrelations in cortical thickness (magnetic resonance imaging, MRI) andelectrophysiological signals (electroencephalography, EEG; magnetoencephalography,MEG)or statisticaldependencies in time series (functionalMRI, fMRI) andblood flow(arterialspinlabeling,ASL).After compiling all pairwise associationsbetween thenodes into aconnectivitymatrix(orbraingraph),severalnetworkpropertiescanbecalculatedinordertocharacterizetheglobal and localorganizationof the connectome.For instance, the small-worldnesscanbeusedtoassessthebalancebetweenshort-distanceandlong-distanceconnectivity[2],whilethemodularitydefineshowwellthenetworkcanbedividedintosubnetworks(ormodules)[3,4],whichgenerallycorrespondtowell-knownbrainsystemssuchasthedefault-mode or fronto-parietal networks [5,6]. These network properties and manyothers can be used to reveal fundamental aspects of normal brain organization andhighlight important aspects of underlying brain pathology in diseases such asAlzheimer'sdisease(AD)[7]orParkinson'sdisease(PD)[8].Severaltoolboxeshavebeendevelopedtostudybrainconnectivity,includingtheBrainConnectivity Toolbox [9], eConnectome [10], GAT [11], CONN [12], BrainNet Viewer[13],GraphVar[14]andGRETNA[15].Whileallofthemmadeimportantcontributionsbyprovingnewoptionstobuild,characterizeandvisualizebrainnetworktopology,theyrequiresomeprogrammingexperience,ordealonlywithsomeaspectsoftheanalysis,or are coded in such away that their adaptation is hard to achieve.Hence, a reliable,streamlined, user-friendly, fast, and scalable software that deals with all aspects ofnetworkorganizationisstilllacking.In this article, we present BRAPH – BRain Analysis using graPH theory(http://www.braph.org/), a softwarepackage toperformgraph theoryanalysisof thebrain connectome.BRAPH is the firstobject-orientedopen-source softwarewritten inMatLabforgraphtheoreticalanalysiswithagraphicaluserinterface(GUI).Incontrastto previous toolboxes, BRAPH takes advantage of the object-oriented programmingparadigm to provide a clear modular structure that makes it easy to maintain andmodifyexistingcode,sincenewobjectscanbeaddedwithouttheneedforanextensiveknowledge of the underlying implementation. From the clinical point of view, BRAPHpresents the following strengths: (a) it allows comparing regional node values beforetheactualnetworkanalysis,whichisimportanttogetafirstimpressiononthedata;(b)itvisualizesindividualconnectivitymatricesandindividualnetworkmeasures,whichiscrucial to detect potential outliers, a major confound in neuroimaging studies; (c) itcarries out longitudinal graph theory analyses that provide an important insight intotopologicalnetworkchangesovertime;(d)itassessesmodularstructureusingdifferentalgorithms and allows performing subnetwork analyses within the defined modules,


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which is important for studies testing hypotheses within a particular structural orfunctionalbrainnetwork;(e)itprovidesutilitiesformulti-modalgraphtheoryanalysesbyintegratinginformationfromdifferentnetworkmodalities,whichisarguablythenextchallengeinimagingconnectomics.Fromtheuserpointofview,BRAPHistheonlyfullyvertically integrated software that allows carrying out all the steps of a graph theoryanalysis,fromimportingtheneuroimagingdatatosavingthefinalresultsinasinglefile.Importantly, this is not only practical but also increases the reliability andreproducibility of the results, which is an increasingly important issue within theresearch community. In addition, BRAPH offers a comprehensivemanual, continuousrelease of new utilities, and a support forum, all of which can be accessed athttp://www.braph.org/.Finally,BRAPHoffersonlinevideosthatprovideastep-by-stepguideonhowtoperformgraphtheoryanalyses,allowingtheusersasimpleandquickstartfortheirbrainconnectivitystudies.Belowwe describe in detail the different options that BRAPH offers for graph theoryanalyseswhenitcomestobuildingconnectivitymatrices,applyingthresholdstrategies,performingweightedorbinarynetworkanalysesandcomputingrandomnetworks.Oursoftwarehasalreadybeensuccessfullyappliedinpreviousgraphtheorystudies[16,17]but to further demonstrate its abilities, in this articlewe assess network topology onstructuralMRIdata frompatientswithamnesticmildcognitive impairment(MCI)andAD,andonfMRIdatafromPDpatientswithMCI.2.MaterialsandMethods2.1.OverviewofBRAPHBRAPHisacompletesoftwarepackagethatallowscarryingoutallthestepsofagraphtheoretical analysis, visualize the results and generate high-quality publication-readyimages.Itcanobtainundirectedbinaryandweightedbrainconnectivitygraphsstartingfrom data acquired using various neuroimagingmodalities, includingMRI, fMRI, EEG,andpositronemissiontomography(PET).BRAPHcanalsoassessthemodularstructureof the brain graph, employing various algorithms and extractingmodules for furtheranalysis. To test for significant differences between groups, BRAPH carries out non-parametricpermutationtestsandallowscorrectingtheresultsformultiplecomparisonsusingfalsediscoveryrate(FDR)[18].Italsoprovidesoptionstocarryoutlongitudinalgraphtheoryanalysesandtonormalizethenetworkmeasuresbyrandomgraphs.As shown inFigure1, thesoftwareconsistsof three independent layers connectedbysoftware interfaces: Graph, Data Structures and Graphical User Interfaces (GUIs). TheGraphpackage includes the fundamental functions toperformagraph theoryanalysisand calculating the global andnodalmeasures. TheData Structures package providesthecorefunctionalitiesofthesoftwareandallowsdefiningthebrainatlas,thecohortofsubjects, and the type of graph analysis; importantly, all these functionalities can beaccessedbycommand-lineandcanthereforebescriptedbyadvancedusers.Finally,theGUIspackageprovidesastreamlinedwaytocarryoutgraphtheoryanalysesbasedonaseries of GUIs for userswithout a computational background: (a) theGUIBrainAtlasallowsselectingandeditingthebrainatlas;(b)theGUICohortallowsdefiningthecohortofsubjectsbyuploadingtherelevantdata;(c)theGUIGraphAnalysisallowsbuildingtheconnectivitymatricesbyselectingthetypeofgraph(weighted,binary,seealsoFigure2)andthresholdingmethod(threshold,density)aswellascalculatingtopologicalmeasuresandvisualizingtheresults.FortheGUICohortandGUIGraphAnalysis, fouroptionscanbe selected (MRI, fMRI, PET, EEG) depending on the nature of the analysis. Figure 3shows an overview of these different steps. Thanks to this three-layered structure,


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BRAPH can be easily expanded and customized to address any needs, e.g., byimplementingnewgraphmeasuresornewapproachesforbuildingbraingraphs.2.2.DefiningthenodesThefirststepofagraphtheoryanalysisconsistsofdefiningthenodes,whichgenerallycorrespondtotheregionsincludedinabrainatlas.Thisatlasshouldcontainthenamesand labelsof thebrain regionsaswell as their spatial coordinates (x,y,z) inorder toproject themona3Dsurfaceandcreateavisualrepresentationof thebraingraph. Inthecaseoftheanalysisofstructuralnetworks(e.g.obtainedfromstructuralMRIdataorT1-weighted images), the nodes are usually defined using an anatomical parcellationschemethatdividesthebrainintoregionsusingthebrainsulciandgyriasanatomicallandmarks.Examplesofanatomicalatlasesaretheautomatedanatomicallabeling(AAL)[19],Desikan[20]orDestrieux[21]atlases.BRAPHalreadyprovidestheseatlasesreadyfor upload on the GUIBrainAtlas interface. In the case of the analysis of functionalnetworks(e.g.obtainedfromfMRIdata),theatlasmaybedefinedusingananatomicalparcellationscheme,ameta-analysis,oraclustering-basedmethodofspatiallycoherentand homogenous regions. Examples of functional atlases are the Dosenbach [22], thePower[23]andtheCraddock[24]atlases,allofwhicharealsoprovidedbyBRAPH.Theusermayalsouploadadifferentatlasfromanexternalfile(in.xml,.txtor.xlsformat)orcreateanentirelynewoneintheGUI.Theresultingatlascanbesavedasa.atlasfile(seemanualandwebsiteforanexampleofa.atlasfile).After the atlas has been created or uploaded into the software, the user should thenuploadthesubjectdataintotheGUICohortinterface.Thisdatamayconsist,forexample,ofcorticalthickness,surfaceareaorvolumemeasuresinstructuralMRI;regionaltime-series in resting-state fMRI; glucose metabolism or blood flow in PET and ASL; andelectrophysiologicalsignalsinEEGorMEG.Theseregionalvaluescanbeobtainedusingthe Statistical Parametric Mapping (SPM; http://www.fil.ion.ucl.ac.uk/spm/), FMRISoftware Library (FSL; https://fsl.fmrib.ox.ac.uk/fsl/fslwiki), FreeSurfer(https://surfer.nmr.mgh.harvard.edu/) or any other image preprocessing software. Inaddition,theymaybecorrectedfortheeffectsofnuisancevariablessuchasage,genderor scanner site bymeans, for example, of linear regression (in this case the residualvaluesshouldsubstitutetherawvaluesinthenetworkanalysis)[25].2.3.DefiningtheedgesOnce the nodes of the network have been defined, the edges representing therelationshipbetweenthemneedtobecomputed.InBRAPH,theedgesarecalculatedinGUIGraphAnalysisasthestatisticalcorrelationbetweenthevaluesofallpairsofbrainregions for an individual or for a group of subjects, depending on the neuroimagingtechnique. Different types of parametric and non-parametric correlations may beselected for thispurpose:Pearson, Spearman,Kendall rankcorrelation coefficients, or(PearsonorSpearman)partialcorrelationcoefficients.Notethatallself-connectionsareeliminatedfromtheanalysisbysettingthediagonalentriesintheconnectivitymatrixtozero. In addition, the user can also choosewhether to retain the negative correlationcoefficients,substitutethemwiththeirabsolutevalueorreplacethembyzero.2.3.NetworkconstructionTo minimize the computation time, the graph measures can be calculated usingoptimizedalgorithmsbasedonlinearalgebra.Therefore,agraphismoreconvenientlyrepresented as a connectivitymatrix,where the rows/columns denote the nodes and


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the matrix elements represent the edges between the nodes. Each row of theconnectivitymatrix represents theedges thataregoingout fromanode; forexample,row j represents theedges that aregoingout fromnode j. Each columnof thematrixrepresentsthenodesthatarrivetoanode;forexample,columnkrepresentstheedgesthatarearrivingtonodek.Thus,theelement(j,k)representstheedgethatgoesfromnode j to node k. The specific order of the nodes in the matrix does not affect thecalculationof thegraph theorymeasures,butonly thegraphical representationof theconnectivitymatrix.AsillustratedinFigure2,basedonthenatureoftheedge’sweightanddirectionality, fourtypesofgraphscanbedefined.Weighteddirected (WD)graphshaveedgesassociatedwitharealnumber,indicatingthestrengthoftheconnection,andaredirected(i.e.,nodejcanbeconnectedtonodekwithoutnodekbeingconnectedtonode j). The edges in theweightedundirected (WU) graphs are associatedwith a realnumber indicating the strength of the connection and are undirected (i.e., if node j isconnectedtonodek,thennodek isalsoconnectedtonodej),resultinginasymmetricconnectivitymatrix.Binarydirected (BD)graphshavedirectededges,whichcaneitherbe 0 or 1, indicating the absence or presence of a connection. The edges in a binaryundirected (BU) network can also be either 0 or 1 and they have no preferentialdirectionality. In order to transform a directed graph into an undirected graph, theconnectivitymatrixneedstobesymmetrized.InBRAPH,theconnectivitymatrixcanbesymmetrizedviacommandlineby:(a)takingthesumbetweenthematrixitselfanditstranspose;(b)takingthedifferencebetweentheprevioustwo;(c)comparingthematrixto its transposeandselectingeitherthesmallerorthe largervalue foreachentry.Weremarkthat,eventhoughthedirectedmeasuresarenotcurrentlyusedintheanalysesperformedbyBRAPH,theyarealreadyavailableintheGraphpackageandreadytobeusedinfutureversionsofthesoftware.To transform aweighted graph into a binary one, BRAPH assigns a value of 1 to theedgesaboveagiventhresholdand0tothosebelowit.Therearetwowaysofapplyingathreshold:(a)byselectingacorrelationcoefficientasthecut-offvaluebelowwhichallconnections are excluded from the analysis (binary undirected threshold (BUT)interfaces); or (b) by fixing the fraction of edges (i.e., a specific density) that will beconnected (binaryundirecteddensity (BUD) interfaces).The choicebetween these twooptionsbecomessignificantwhencomparingdifferentgroupsofsubjects,asitmayleadto different results; currently the density approach is more often employed in theliterature, because it permits analyzing differences in network architecture, whilecontrollingforthedifferentnumberofedgesacrossindividualsorgroups.ForMRIorstaticPETdata,asingleconnectivitymatrix iscalculatedforeachgroupofsubjects;therefore,thegraphtheorymeasuresreflectthegroup’sproperties.ForfMRIdataandotherneuroimagingsequencesthatprovideameasureofbrainfunctionovertime, an individual connectivity matrix is calculated for each subject; therefore, thegraph theory measures reflect the characteristics of each subject, which can then beaveragedwithinaparticulargroup.2.4.NetworkanalysisBRAPH allows calculating both global and nodal network measures, on weighted orbinary networks, using different thresholds or densities. To test for significantdifferences between groups (cross-sectional analysis) or two different points acrosstime (longitudinal analysis), BRAPH performs non-parametric permutation tests,reportingone-tailedandtwo-tailedp-valuesbasedon95%confidenceintervals.


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The network measures can also be compared with the corresponding measurescalculatedonrandomgraphswiththesamedegreeorweightdistribution.Thesecanbeused,forexample,tonormalizeweightednetworkmeasures.Regardingnodalnetworkmeasures,thepermutationtestsarecarriedoutforeachbrainregion, assessing simultaneously multiple null hypotheses, which consequentlyincreasestheriskoffindingfalsepositives.BRAPHdealswiththisissuebyprovidingtheadjusted p-values that should be considered to correct the results for multiplecomparisonswith falsediscoveryrate(FDR)using theBenjamini-Hochbergprocedure[18].2.5.GraphtheorymeasuresBRAPH can calculate several graph theory measures that assess the topology of thewholebrainnetworkaswellasofitsregions.Here,weexplainbrieflysomeofthemostrelevantones; foracomplete listwithformulasanddetails,pleaserefertotheBRAPHmanual andwebsite. The codewe used to calculate the graphmeasureswas adaptedfromtheBrainConnectivityToolbox(http://www.brain-connectivity-toolbox.net/)[9],which is regarded as the most important reference in the field since it provided theseminalgroundworkfortheuseofgraphtheorybyneuroimagingresearchers.The simplest, yet most fundamental, measure that can be assessed in a graph is thedegree,whichisthenumberofconnectionsanodehaswiththerestofthenetwork.Inweighted graphs, we calculate the degree of the nodes by ignoring the weights andbinarizing thematrix. The degree distribution in the brain follows a power law [26],meaningthathighlyconnectedareastendtocommunicatewitheachother.Another importantmeasure is the shortestpathlength,which is the shortest distancebetweentwonodes.Inabinarygraph,distanceismeasuredastheminimumnumberofedgesthatneedtobecrossedtogofromonenodetotheother.Inaweightedgraph,thelength of an edge is a function of its weight; typically, the edge length is inverselyproportional to the edgeweightbecause ahighweight implies a stronger connection.Theaverageoftheminimumpathlengthsbetweenonenodeandallothernodesisthecharacteristicpathlength[2].Onecanalsodefinetworelatedmeasuresofcentrality:theclosenesscentrality,whichistheinverseoftheshortestpathlength,andthebetweennesscentrality,whichisthefractionofallshortestpathsinthenetworkthatpassthroughagivennode [9]. These and othermeasures can be used to assesswhether a node is abrainhub[27],regulatingmostoftheinformationflowwithinthenetwork.The closer the nodes are to each other, the shorter is the path length and the moreefficient is the transfer of information between them. Therefore, one can define theglobalefficiencyofanodeastheinverseoftheshortestpathfromthatnodetoanyothernodeinthenetwork[28].Toassessthecommunicationefficiencybetweenanodeandits immediate neighbors, the local efficiency can be calculated. Both global and localefficiencymeasurescanbeaveragedoverallnodestodescribeglobalpropertiesofthebrainnetwork[28].Theclusteringcoefficientisameasurethatassessesthepresenceofcliquesorclustersinagraph[2].Foreachnode,thiscanbecalculatedasthefractionofthenode'sneighborsthat are also neighbors of each other. For the whole network, the nodal clusteringcoefficientsofallnodescanbeaveragedintothemeanclusteringcoefficient.Acloselyrelatedmeasuretotheclusteringisthetransitivity,whichisdefinedastheratioofpathsthattransversetwoedgesbythenumberoftriangles.Ifanodeisconnectedtoanothernode,whichinturnisconnectedtoathirdone,thetransitivityreflectstheprobabilitythatthefirstnodeisconnectedtothethird.


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The small-worldness is given by the ratio between the characteristic path length andmean clustering coefficient (normalized by the corresponding values calculated onrandom graphs) [2]; this is an important organizational property that describes anoptimalnetworkarchitecture.Comparedtoarandomgraph,asmall-worldnetwork ischaracterizedbysimilarlyshortpathsbutasignificantlyhigherclusteringcoefficient.Anetworkcanalsobedividedintoseparatecommunitiescorrespondingtoanatomicalproximityor to a specific function sharedby a groupof nodes.The extent towhich anetworkcanbedividedintothesecommunitiesormodulescanbecalculatedusingthemodularity,whichmaximizes thenumberofedgeswithincommunitiesandminimizesthe number of edges between different communities [29]. Thewithin-module z-scorequantifieshowwellanodeisconnectedwithothernodesfromthesamemodule,whiletheparticipationcoefficient assesses if a nodehasmany connectionswith nodes fromdifferent modules. If a node has a high within-module degree it is classified as aprovincialhub;ifithasahighparticipationcoefficientitisconsideredtobeaconnectorhub.2.6.SubjectsTodemonstrate theabilitiesofBRAPH,weperformedstructural and functional graphtheoryanalysesintwoseparatestudies.Inthefirststudy,weassessedthedifferencesinglobalandnodalnetworktopologyinhealthycontrols,patientswithamnesticMCI,andpatients with AD (see Table 1) from the Alzheimer’s Disease Neuroimaging Initiative(ADNI)database(adni.loni.usc.edu).TheADNIwaslaunchedin2003asapublic–privatepartnership, ledbyPrincipal InvestigatorMichaelW.Weiner,MD.TheprimarygoalofADNIhasbeentotestwhetherserialMRI,PET,otherbiologicalmarkers,andclinicalandneuropsychologicalassessmentcanbecombinedtomeasuretheprogressionofMCIandearlyAD.Allparticipantswerescannedona1.5TeslaMRIsystemusingasagittal3DT1-weightedMPRAGEsequence:repetitiontime(TR)=9–13ms;echotime(TE)=3.0–4.1ms;inversiontime(IT)=1000ms;flipangle(FA)=8°;voxelsize=1.1×1.1×1.2mm3.In the second study,we carried out a graph theory analysis on the resting-state fMRIdataofhealthy controls andPDpatientswithMCI (seeTable2) from theParkinson’sProgressionMarkersInitiative(PPMI)(2011)[30](www.ppmi-info.org/data;accessedinNovember,2015),aninternational,multicenterstudylaunchedin2010toidentifyPDprogressionbiomarkers.EachparticipatingPPMIsitereceivedapprovalfromanethicalstandards committee before study initiation and obtained written informed consentfromallparticipants.PDpatientswereclassifiedashavingMCI(PD-MCI)iftheyscored1.5 standard deviations below the scaled mean scores on any two cognitive tests,following previously published procedures for PD-MCI diagnosis in the PPMI cohort[31]. PD-MCI patients and controls were scanned on a 3 Tesla Siemens scanner(Erlangen, Germany). Resting-state functional images were acquired using an echo-planarimagingsequence(repetitiontime=2400ms;echotime=25ms;flipangle=80⁰;matrix=68x68;voxelsize=3.25x3.25x3.25mm3).Thescanlasted8minutesand29secondsandincluded210volumes.2.7.NetworkconstructionandanalysisTo assess structural network topology in controls, amnestic MCI patients, and ADpatientsfromADNI,theT1-weightedimagesofthesesubjectswerepreprocessedusingFreeSurfer (version 5.3), as published elsewhere [17]. The cortical thickness andsubcorticalvolumesof82regionswereextractedandincludedasnodesinthenetworkanalysis.TheedgesbetweentheseregionswerecomputedasPearsoncorrelationsand


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the network analyses were carried out on the binary undirected graphs, whilecontrollingforthenumberofconnections,acrossarangeofdensities:from5%to25%,instepsof0.5%.To assess functional network topology in PD-MCI patients and a group of elderlycontrols from PPMI, fMRI images were preprocessed using SPM8(http://www.fil.ion.ucl.ac.uk/spm) using the following steps: removal of first fivevolumes, slice-timing correction, realignment, normalization to the MontrealNeurological Institute(MNI)template(voxelsize3x3x3mm3), temporal filtering(0.01-0.08 Hz), regression ofwhitematter, cerebrospinal fluid signals and six headmotionparameters.Theregionaltime-seriesofthe200brainregionsincludedintheCraddockatlas[24]wereextractedfromeachsubject.Tocomputetherelationshipbetweentheseregions, we used Pearson correlations and performed the network analyses on theweightedundirectedgraphs.Inbothstudies,non-parametricpermutationtestswerecarriedouttoassessdifferencesbetween groups, which were considered significant for a two-tailed test of the nullhypothesis at p

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The functional connectivitymatrices of controls andPD-MCI patients can be found inFigure7.ThecomparisonoftheweightedaveragedegreeshowedthatPD-MCIpatientspresented a significantly lower number of connections compared to controls (PD-MCI=172.6; controls=183.7; p-value=0.027), suggesting that their network was moredisconnected. Then, we performed a modularity analysis on the weighted graphs ofthesesubjectstoassessthepresenceofsmallercommunitiesofregions(modules).Thisanalysis showed there were fivemodules in controls and patients, which were quitesimilarinthetwogroups.ModuleIincludedmedialfrontalareas,theposteriorcingulateandbilateralangulargyri, resembling thedefault-modenetwork.Module II comprisedtemporalandcerebellarareas.Module III includedseveralmiddle, inferior frontalandparietal regions,similarly to the fronto-parietalnetworkusually found inresting-statestudies[5,6].ModuleIVconsistedofmostofthevisualcortexsimilarlytothepreviouslyreported visual network. Finally,Module V includedmainly subcortical regions and afewtemporalandcingularareas.Whenweassessedthenodaldegreesoftheregionsincludedineachmodule(subgraphanalysis,Figure8),weobservedthattheonlydifferencesbetweenthecontrolandPD-MCIgroupswerefoundinthefronto-parietalnetwork.Withinthisnetwork,theregionsshowingasignificantlylowerdegreeinPD-MCIpatientsafterFDRcorrectionswerethebilateral superior frontal, superior parietal gyri and precuneus in addition to the leftmiddleandinferiorfrontalgyriandanteriorcingulate.4.DiscussionGraph theory has introduced new opportunities for understanding the brain as acomplex system of interacting elements. Thanks to this framework,we have come toappreciatethatthehumanbrainreliesonfundamentalaspectsofnetworkorganizationsuch as a small-world architecture, modular structure and vulnerable hubs. Thesepropertiesallowourbrainstoevolve,growandadaptwithinanenvironmentpresentingincreasingcognitivedemands,andtheirdisruptionaccountsforsomeofthekeyaspectsunderlying pathology in neurological diseases. In this report, we present BRAPH, thefirst object-oriented software for graph theory analysis intended for all researchers,regardless of their scientific background. As modern network science continues todevelopatanamazingspeed, it is important tohaveasoftware thatallowsmodifyingexistent code in a structuredmanner so that past knowledge canbe easily integratedwithnewtopologicalanalysesandgraphtheorymeasures.Wearecurrentlyworkingonsome of these developments with a particular focus on multimodal analyses andeffectiveconnectivitymeasures.AmongstBRAPH’sstrengthsisthefactthatitdealswithalltheaspectsofgraphtheoryanalysis,byprovidingtheuserwithextensiveassistance,fromthefirstbasicstepssuchasdefiningthenodesoredgestoproducingthefinalend-stage figures of the results as well as to archiving the results and relative analysisprocedure in a dedicated file. To get an impression on BRAPH’s abilities, below wediscuss some of the results we obtained in two different studies in patients withamnesticMCI,ADandPD-MCI.4.1.Large-scalestructuralnetworksinamnesticMCIandADAD is currently one of the most prevalent neurodegenerative disorders, with asignificant impact on society and caregiver burden [32]. Although the devastatingimpact of this condition has pushed forward a large research effort towards a moreaccurate diagnosis, the underlying effects of AD on network topology remain poorlyunderstood.There is increasingevidencesuggestingthatthepathologicalhallmarksof


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AD, consisting of amyloid plaques neurofibrillary tangles, could spread in the brainthroughsynapsesandneuralconnections.Hence,theapplicationofgraphtheorytothestudyofbrainconnectivitycouldshedlightonthemechanismsofdiseasepropagationinAD.Inthecurrentstudy,wefoundthatADpatientspresentedanabnormalglobalnetworktopologyasreflectedbyincreasesinthepathlength,localefficiencyandmodularity,andbydecreasesof transitivity.Thesechanges indicate that the regionsof theirnetworkscommunicated less efficiently with other brain regions and between different brainmodules. In particular, the most widespread changes in network organization wereobservedforthetransitivityandmodularity.Thedecreases intransitivity foundinADsuggestthattheregionsof theirnetworkwerepoorlyconnectedtoneighboringareas,whereas the increases in modularity indicate that their modules had higher within-moduleconnectivityandworseinter-moduleconnectivity.PatientswithamnesticMCI,whoarepotentiallyonthepathtodevelopAD,alsoshowedsimilar,albeitlessextensive,network changes suggesting that amnesicMCJmight be indeed an intermediate stagebetweenhealthyaginganddementia.Thesefindingsagreewiththeresultsobtainedinpreviousstudies[7,17].TheassessmentofthenodaldegreeinADshowedwidespreadchangesinthenumberofconnections of regions that belong to thedefault-modenetwork, including themedialorbitofrontal, theanteriorcingulateandposteriorcingulategyri,comparedtocontrolsorpatientswithMCI.ThisnetworkhasbeenstronglyassociatedwithADasitsregionscoincidewith theareas showingamyloiddeposition, graymatteratrophyandglucosehypometabolisminthesepatients[33].Hence,thechangeswefoundinthisstudymaypartially reflect pathological and metabolic abnormalities that usually occur in ADpatients.Incontrasttothenodaldegree,thenodallocalefficiencyshowedalterationsbothinMCIand AD patients. Whereas in MCI patients, these changes were confined to a singleregion in the left temporal lobe, inADpatients the local efficiencywas altered acrossseveral frontal, temporalandparietalareas, includingthehippocampusandamygdala,whichareinvolvedinADpathology[34].Thelocalefficiencyreflectshowefficientlyisthe communication between a region and its neighboring areas. Decreases in thismeasuremight indicate a loss of local connections, whereas increases could reflect acompensatory mechanism by which the number of connections between close brainareasincreasestocompensateforthelossofconnectionsbetweendistantbrainareas.Hence, altogetherour findings indicate thatgraph theory is ausefulmethod toassessabnormalitiesinbrainconnectivityandtopologyintheprodromalandclinicalstagesofAD.4.2.Large-scalefunctionalnetworksinPD-MCICognitive impairment is one of the most important non-motor symptoms in PD thatgreatly affects quality of life. During the course of the disease, most PD patients willdevelop impairment in one ormore cognitive domains, for which theywill receive adiagnosis of MCI. The presence of MCI in PD is associated with an increased risk toprogress to dementia [35]. Hence, there is a pressing need to identify the underlyingmechanisms of MCI to prevent cognitive decline in PD patients. Using a weightednetworkapproachinBRAPH,wefoundthatPD-MCIpatientspresentedalowernumberofconnectionsinthewholebrainnetworkcomparedtocontrols.Thisindicatesthatingeneral theirregionsweremoredisconnected.However,after identifying themodularstructureandperformingthesameanalysiswithineachmodule,weobservedthatthese


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effectsweremostlydrivenbyalowerdegreeinthefronto-parietalnetworkinthePD-MCI group. The regions that were most affected in this network were the superiorfrontal gyri, superior parietal gyri and precuneus. All of these regions have beenpreviouslyshowntodisplayreducedconnectivityinPD[8].Inaddition,theyhavealsobeen identifiedas importantbrainhubs inpreviousgraph theorystudies [27].Withinthegraphtheoryframework,thebrainhubsarethemostimportantandcentralregionsof anetworkas theymediatenumerous long-distance connections.This characteristicalso suggests they might have higher metabolic costs and a greater vulnerability tooxidativestress[27].Inapreviousstudy[36],itwasshownthatthepathologicalbrainlesionsareconcentratedinhubregionsoftheconnectomeinseveralneurodegenerativedisorders,includingPD,inlinewithourfindings.4.3.BRAPHfeaturesTheapplicationofgraphtheorytothefieldofimagingconnectomicsisstill initsearlybeginnings.Thereare several important challenges thatneed tobeaddressedsuchaswhether thenodesandedgesareanaccuratedescriptionof the trueunderlyingbrainconnectomeinallitscomplexityofmillionsofneuronsandsynapses.Althoughwehavelimited knowledge on how to address this particular issue, there are several otherchallengesthatcanbeaddressedthroughtheuseofBRAPH.Forinstance,giventhatthetrue connectome is a sparse network, it is important to threshold the structural orfunctional edges, which typically consist of continuous association indices [37]. Thisthresholdingcanbecarriedoutusingdifferentmethods.Ontheonehand,a thresholdcan be applied so that only the connections that are below a significance level areincludedintheanalysis.Inthisway,theweakerconnectionsofthegraphareeliminatedand considered spurious. This approach will yield different numbers of connectionsacross different individuals or groups. On the other hand, a threshold can be appliedsuch that allnetworkshave the samenumberof connections througha fixedvalueofdensity. In thisway, only a percentage of edges are included in the analyses and thegraph theorymeasuresare independentof thenumberof edges [37]. InBRAPH,boththresholdingoptionsareavailablesothattheusercaneasilycomparethem.Another important challenge is the choice of a given value of threshold since there iscurrentlynowaytoestablishwhichisthebestvalue.Tosolvethisissue,BRAPHallowstestingahypothesisacrossdifferentlevelsofsignificanceordensitiestodeterminetherobustness of the results. Some authors consider choosing a range of thresholds anarbitraryprocess thatproducesvaluesthatarestronglydependentonthischoice.Forthis reason, we also provide an option for weighted network analysis, which allowsassessingbothstrongandweakconnectionspresentinagraphandisnotdependentonaparticularthresholdingscheme.Another challenge that is beginning to emerge in the scientific community is therealization that different node definitions can lead to different network findings.CurrentlyBRAPHprovidessixanatomicalandfunctionalbrainatlasesthattheusercanapplywithin the same study to assess the consistency of the results against differentparcellationschemes.Inaddition,anewbrainatlascanbeeasilycreatedoruploadedinBRAPHthatadjuststotheuserneeds.Finally,thelastchallengethatcanbeaddressedthroughBRAPHisthenormalizationofgraph theory measures by reference to random networks that have a randomorganization (with the same degree and/or weight distribution). BRAPH providesvariousoptionstoperformthisnormalization.


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In conclusion, the study of the brain connectome is a growing field that will provideimportantinsightsintobrainorganizationinhealthanddisease.Amongstitsnumerousapplications, there is thepossibility itmighthelppredictingthepathologicalspreadofdisease proteins in neurodegenerative disorders, which are becoming increasinglyprevalent in theworld’s aging population. To address the increasing demands in thisgrowing fieldweprovideBRAPH, the firstobject-oriented software thatwill integratenewtopologicalanalysesandmeasuresinastructuredmanner,allowingtheuserstobeupdated with the latest developments in graph theory. BRAPH can be found athttps://www.braph.orgwithonlinevideos, a comprehensivemanual, a support forumandrelevantlinks.Itisfreeforallresearchersandcanbeusedinalloperatingsystems.5.AcknowledgementsDatausedinthepreparationofthisarticlewereobtainedfromtheAlzheimer’sDiseaseNeuroimaging Initiative (ADNI) and the Parkinson’s Progression Markers Initiative(PPMI).Data collection and sharing of ADNI was funded by the National Institutes of HealthGrantU01AG024904andDepartmentofDefenseawardnumberW81XWH-12-2-0012.ADNIis fundedbytheNationalInstituteonAging,theNationalInstituteofBiomedicalImaging and Bioengineering, and through generous contributions from the following:Alzheimer’s Association; Alzheimer’s Drug Discovery Foundation; BioClinica, Inc.;Biogen Idec Inc.;Bristol-MyersSquibbCompany;Eisai Inc.;ElanPharmaceuticals, Inc.;EliLillyandCompany;F.Hoffmann-LaRocheLtdanditsaffiliatedcompanyGenentech,Inc.; GEHealthcare; Innogenetics, N.V.; IXICO Ltd.; JanssenAlzheimer ImmunotherapyResearch & Development, LLC.; Johnson & Johnson Pharmaceutical Research &Development LLC.; Medpace, Inc.; Merck & Co., Inc.; Meso Scale Diagnostics, LLC.;NeuroRxResearch;NovartisPharmaceuticalsCorporation;PfizerInc.;PiramalImaging;Servier; Synarc Inc.; andTakeda Pharmaceutical Company. The Canadian Institutes ofHealth Research is providing funds to support ADNI clinical sites in Canada. Privatesector contributions are facilitated by the Foundation for the National Institutes ofHealth(www.fnih.org).ThegranteeorganizationistheNorthernCaliforniaInstituteforResearch and Education, and the study is coordinated by the Alzheimer’s DiseaseCooperativeStudyattheUniversityofCalifornia,SanDiego.ADNIdataaredisseminatedbytheLaboratoryforNeuroImagingattheUniversityofCalifornia,LosAngeles.PPMI - a public-private partnership - is funded by theMichael J. Fox Foundation forParkinson’s Research and funding partners, including Abbott, AvidRadiopharmaceuticals, Biogen Idec, Bristol-Myers Squibb, Covance, Elan, GEHealthcare, Genentech, GSK-GlaxoSmithKline, Lilly,Merck,MSD-Meso Scale Discovery,Pfizer, Roche, UCB (www.ppmi-info.org/fundingpartners). For up-to-date informationonthePPMIdatabasevisitwww.ppmi-info.org.Wewouldalso like to thank theSwedishFoundation forStrategicResearch (SSF), theStrategic Research Programme in Neuroscience at Karolinska Institutet (StratNeuro),Hjärnfonden,andBirgittaochStenWesterbergforadditionalfinancialsupport.


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References[1]SpornsO.Thehumanconnectome:originsandchallenges.Neuroimage2013;80:53-61.[2]WattsDJ,StrogatzSH.Collectivedynamicsof 'small-world'networks.Nature1998;393:440-442.[3]HagmannP,CammounL,GigandetX,MeuliR,HoneyCJ,WedeenVJ,etal.Mappingthestructuralcoreofhumancerebralcortex.PLoSBiol2008;6:e159.[4]MeunierD,StamatakisEA,TylerLK.Age-relatedfunctionalreorganization,structuralchanges,andpreservedcognition.NeurobiolAging2014;35:42-54.[5] Damoiseaux JS, Rombouts SA, Barkhof F, Scheltens P, Stam CJ, Smith SM, et al.Consistent resting-state networks across healthy subjects. Proc Natl Acad Sci U S A2006;103:13848-13853.[6] van den Heuvel MP, Hulshoff Pol HE. Exploring the brain network: a review onresting-state fMRI functional connectivity. EurNeuropsychopharmacol 2010; 20: 519-534.[7] Tijms BM, Wink AM, de Haan W, van der Flier WM, Stam CJ, Scheltens P, et al.Alzheimer's disease: connecting findings from graph theoretical studies of brainnetworks.NeurobiolAging2013;34:2023-2036.[8] Baggio HC, Segura B, Junque C. Resting-state functional brain networks inParkinson'sdisease.CNSNeurosciTher2015;21:793-801.[9] RubinovM, Sporns O. Complex networkmeasures of brain connectivity: uses andinterpretations.Neuroimage2010;52:1059-1069.[10]HeB,DaiY,AstolfiL,BabiloniF,YuanH,YangL.eConnectome:AMATLABtoolboxfor mapping and imaging of brain functional connectivity. J Neurosci Methods 2011;195:261-269.[11] Hosseini SM, Hoeft F, Kesler SR. GAT: a graph-theoretical analysis toolbox foranalyzing between-group differences in large-scale structural and functional brainnetworks.PLoSOne2012;7:e40709.[12]Whitfield-GabrieliS,Nieto-CastanonA.Conn:a functionalconnectivitytoolboxforcorrelatedandanticorrelatedbrainnetworks.BrainConnect2012;2:125-141.[13]XiaM,WangJ,HeY.BrainNetViewer:anetworkvisualizationtoolforhumanbrainconnectomics.PLoSOne2013;8:e68910.[14] Kruschwitz JD, List D,Waller L, RubinovM,Walter H. GraphVar: a user-friendlytoolbox for comprehensive graph analyses of functional brain connectivity. JNeurosciMethods2015;245:107-115.[15]WangJ,WangX,XiaM,LiaoX,EvansA,HeY.GRETNA:agraphtheoreticalnetworkanalysistoolboxforimagingconnectomics.FrontHumNeurosci2015;9:386.[16] Pereira JB, AarslandD, Ginestet CE, Lebedev AV,Wahlund LO, Simmons A, et al.AberrantcerebralnetworktopologyandmildcognitiveimpairmentinearlyParkinson'sdisease.HumBrainMapp2015;36:2980-2995.[17] Pereira JB,MijalkovM, Kakaei E,Mecocci P, Vellas B, TsolakiM, et al. DisruptedNetworkTopology inPatientswithStableandProgressiveMildCognitive ImpairmentandAlzheimer'sDisease.CerebCortex2016;26:3476-3493.[18] Benjamini Y, Hochberg Y. Controlling the false discovery rate: a practical andpowerfulapproachtomultipletesting.JRoyalStatSoc.SeriesB(Methodological)1995;289-300.[19]Tzourio-MazoyerN,LandeauB,PapathanassiouD,CrivelloF,EtardO,DelcroixN,etal.AutomatedanatomicallabelingofactivationsinSPMusingamacroscopicanatomicalparcellationoftheMNIMRIsingle-subjectbrain.Neuroimage2002;15:273-289.


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[20] Desikan RS, Segonne F, Fischl B, Quinn BT, Dickerson BC, Blacker D, et al. AnautomatedlabelingsystemforsubdividingthehumancerebralcortexonMRIscansintogyralbasedregionsofinterest.Neuroimage2006;31:968-980.[21]DestrieuxC,FischlB,DaleA,HalgrenE.Automaticparcellationofhumancorticalgyriandsulciusingstandardanatomicalnomenclature.Neuroimage2010;53:1-15.[22]DosenbachNU,VisscherKM,PalmerED,MiezinFM,WengerKK,KangHC,etal.Acoresystemfortheimplementationoftasksets.Neuron2006;50:799-812.[23] Power JD, CohenAL,Nelson SM,Wig GS, BarnesKA, Church JA, et al. Functionalnetworkorganizationofthehumanbrain.Neuron2011;72:665-678.[24]CraddockRC, JamesGA,HoltzheimerPE, 3rd,HuXP,MaybergHS.AwholebrainfMRI atlas generated via spatially constrained spectral clustering. Hum Brain Mapp2012;33:1914-1928.[25]VoevodskayaO,SimmonsA,NordenskjoldR,Kullberg J,AhlstromH,LindL,etal.The effects of intracranial volume adjustment approaches on multiple regional MRIvolumesinhealthyagingandAlzheimer'sdisease.FrontAgingNeurosci2014;6:264.[26]AchardS,SalvadorR,WhitcherB,SucklingJ,BullmoreE.Aresilient,low-frequency,small-worldhumanbrainfunctionalnetworkwithhighlyconnectedassociationcorticalhubs.JNeurosci2006;26:63-72.[27]vandenHeuvelMP,SpornsO.Networkhubsinthehumanbrain.TrendsCognSci2013;17:683-696.[28]LatoraV,MarchioriM.Efficientbehaviorof small-worldnetworks.PhysRevLett2001;87:198701.[29] Girvan M, Newman ME. Community structure in social and biological networks.ProcNatlAcadSciUSA2002;99:7821-7826.[30] Parkinson Progression Marker Initiative. The Parkinson Progression MarkerInitiative(PPMI).ProgNeurobiol2011;95:629-635.[31] Weintraub D, Simuni T, Caspell-Garcia C, Coffey C, Lasch S, Siderowf A, et al.Cognitiveperformanceandneuropsychiatricsymptomsinearly,untreatedParkinson'sdisease.MovDisord2015;30:919-927.[32]WinbladB,AmouyelP,AndrieuS,BallardC,BrayneC,Brodaty,Hetal.DefeatingAlzheimer'sdiseaseandotherdementias: apriority forEuropean scienceand society.LancetNeurol2016;15:455-532.[33] Buckner RL, Snyder AZ, Shannon BJ, LaRossa G, Sachs R, Fotenos AF, et al.Molecular, structural, and functional characterization ofAlzheimer's disease: evidenceforarelationshipbetweendefaultactivity,amyloid,andmemory. JNeurosci2005;25:7709-7717.[34] BraakH, Braak E.Neuropathological stageing of Alzheimer-related changes. ActaNeuropathol1991;82:239-259.[35] Svenningsson P, Westman E, Ballard C, Aarsland D. Cognitive impairment inpatientswithParkinson'sdisease:diagnosis,biomarkers,andtreatment.LancetNeurol2012;11:697-707.[36]CrossleyNA,MechelliA,ScottJ,CarlettiF,FoxPT,McGuireP,etal.Thehubsofthehuman connectome are generally implicated in the anatomy of brain disorders. Brain2014;137:2382-2395.[37] Fornito A, Zalesky A, Breakspear M. Graph analysis of the human connectome:promise,progress,andpitfalls.Neuroimage2013;80:426-444.


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Table1.CharacteristicsofthestructuralMRIsample CTR

(n=42)MCI(n=42)

AD(n=48)

Forχ2(pvalue)

Age(y) 76.1(5.0) 74.5(7.5) 75.6(7.0) 0.017Sex(M/F) 110/100 243/134 97/84 0.005Education(y) 16.0(2.9) 15.7(3.0) 14.8(3.2)

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Figure1.OverviewofBRAPHsoftwarearchitectureBRAPH consists of three layers, from left to right:Graph,DataStructures andGraphicalUserInterfaces(GUIs). These layers are connected by unidirectional software interfaces (arrows). Graph contains thefunctions to perform graph analyses. In Data Structures, BrainAtlas allows defining the nodes of thenetwork, Cohort allows defining the subjects to be studied and dividing them into groups, and GraphAnalysis permits building the connectivitymatrices and calculating networkmeasures; each of these isimplementedinanobject,whosefunctionalitiescanbecalledbycommandline.Foreachoftheseobjects,a GUI is provided (i.e.GUIBrainAtlas,GUICohort andGUIGraphAnalysis). Thanks to this architectureBRAPHcanbeveryeasilymaintained,expandedandcustomized.


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Figure2.TypesofgraphsGraphscanbeclassifiedbasedontheiredgeweights(weightedorbinary)anddirectionality(directedorundirected).Itispossibletotransformadirectedgraphintoanundirectedonebysymmetrization(i.e.byremoving the information about the edge directions), and a weighted graph into a binary one bythresholding (i.e. by assigning a value of 1 to the edges above a given threshold and 0 to those belowthreshold).


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Figure3.BRAPHworkflowWorkflowforagraphtheoryanalysisinBRAPHandrelativegraphicaluserinterfaces(GUIs).A)ThebrainregionsaredefinedintheGUIBrainAtlas.B)ThedataofthesubjectsareimportedintheGUICohortandtheusercandefinegroupsandedittheirage,genderandotherrelevantdata.C)TheconnectivitymatrixiscalculatedintheGUIGraphAnalysisafterselectingtheparametersdefiningthetypeofcorrelation,howtodeal with negative correlation coefficients, and which type of graph to analyze: D) binary undirectedgraphsatafixeddensity(GUIGraphAnalysisBUD);E)binaryundirectedgraphsatafixedthreshold(GUIGraphAnalysisBUT);F)weightedundirectedgraphs(GUIGraphAnalysisWU).


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Figure4.Structuralbrainnetworksincontrols,MCIpatients,andADpatientsFrom left to right:weighted correlationmatrices of 82 regions, binary correlationmatrices after fixingdensityat15%,andcorrespondingbraingraphsfromA)controls(CTR),B)patientswithamnesticmildcognitiveimpairment(MCI),andC)Alzheimer’sdisease(AD)patients.


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Figure5.DifferencesbetweengroupsinglobalstructuraltopologyLeft: differences between controls (CTR) and Alzheimer’s disease (AD) patients; middle: differencesbetween controls (CTR) andpatientswithmild cognitive impairment (MCI); right: differences betweenpatientswithmildcognitiveimpairment(MCI)andAlzheimer’sdisease(AD)patientsforA)characteristicpath length, B) local efficiency, C) transitivity andD)modularity. The plots show the lower and upperbounds (blue circles) of the 95% Confidence Intervals (CI) (gray shade) as a function of density. Theorange circles show the differences between groups and,when falling outside the CI, indicate that thedifferencewasstatisticallysignificantatp

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Figure6.DifferencesbetweengroupsinnodalstructuralmeasuresNodesshowingsignificantdifferencesbetweengroupsinthenodaldegreeandnodallocalefficiencyafterFDRcorrections.Orangeindicatesincreasesinthenodalmeasure,whileblueindicatesdecreases.


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Figure7.FunctionalbrainnetworksandmodulesincontrolsandPD-MCIpatientsWeighted connectivitymatrices andmodules in A) controls (CTR) and B) Parkinson’s disease patientswithmildcognitiveimpairment(PD-MCI).Fivemoduleswereidentifiedineachgroup.


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Figure8.DifferencesbetweengroupsinthenodalfunctionaldegreeSignificant decreases in the nodal degree of regions from Module III or fronto-parietal network inParkinson’sdiseasepatientswithmildcognitiveimpairment(PD-MCI)comparedtocontrols(CTR)afterFDRcorrections.

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braph: a graph theory software for the analysis of brain … · the first step of a graph theory...

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