Morphometricity: Measuring the Neuroanatomical...
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Morphometricity:MeasuringtheNeuroanatomicalSignatureofaTrait
MertR.Sabuncua,b,TianGea,c,d,AvramJ.Holmesa,e,f,JordanW.Smollerc,d,RandyL.Bucknera,g,and
BruceFischla,b;fortheAlzheimer’sDiseaseNeuroimagingInitiative(ADNI)*
aAthinoulaA.MartinosCenterforBiomedicalImaging,DepartmentofRadiology,Massachusetts
GeneralHospital,Charlestown,MA02129,USA;bComputerScienceandArtificialIntelligence
Laboratory,MassachusettsInstituteofTechnology,Cambridge,MA02138,USA;cPsychiatricand
NeurodevelopmentalGeneticsUnit,CenterforHumanGeneticResearch,MassachusettsGeneral
Hospital,Boston,MA02114,USA;dStanleyCenterforPsychiatricResearch,BroadInstituteofMIT
andHarvard,Cambridge,MA02138,USA;eDepartmentofPsychology,YaleUniversity,NewHaven,
CT,06520,USA;fDepartmentofPsychiatry,MassachusettsGeneralHospital,HarvardMedicalSchool,
Boston,MA02114,USA;gDepartmentofPsychologyandCenterforBrainScience,HarvardUniversity,
Cambridge,MA02128,USA.
*DatausedinpreparationofthisarticlewereobtainedfromtheAlzheimer’sDiseaseNeuroimaging
Initiative(ADNI)database(adni.loni.usc.edu).Assuch,theinvestigatorswithintheADNIcontributed
tothedesignandimplementationofADNIand/orprovideddatabutdidnotparticipateinanalysisor
writingofthisreport.AcompletelistingofADNIinvestigatorscanbefoundat:
http://adni.loni.usc.edu/wp-content/uploads/how_to_apply/ADNI_Acknowledgement_List.pdf
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Abstract
Complexphysiologicalandbehavioraltraits,includingneurologicalandpsychiatricdisorders,often
associatewithdistributedanatomicalvariation.Thispaperintroducesaglobalmetric,called
morphometricity,asameasureoftheanatomicalsignatureofdifferenttraits.Morphometricityis
definedastheproportionofphenotypicvariationthatcanbeexplainedbymacroscopicbrain
morphology.Weestimatemorphometricityviaalinearmixedeffectsmodelthatutilizesan
anatomicalsimilaritymatrixcomputedbasedonmeasurementsderivedfromstructuralbrain
MagneticResonanceImaging(MRI)scans.Weexaminedover3,800uniqueMRIscansfrom9large-
scalestudiestoestimatethemorphometricityofarangeofphenotypes,includingclinicaldiagnoses
suchasAlzheimer’sdisease;andnonclinicaltraitssuchasmeasuresofcognition.Ourresults
demonstratethatmorphometricitycanprovidenovelinsightsabouttheneuroanatomicalcorrelates
ofadiversesetoftraits,revealingassociationsthatmightnotbedetectablethroughtraditional
statisticaltechniques.
Significance
Neuroimaginghaslargelyfocusedontwogoals:mappingassociationsbetweenneuroanatomical
featuresandphenotypes,andbuildingindividual-levelpredictionmodels.Thispaperpresentsa
complementaryanalyticstrategycalledmorphometricitythataimstomeasuretheneuroanatomical
signaturesofdifferentphenotypes.Inspiredbypriorworkonheritability,wedefinemorphometricity
astheproportionofphenotypicvariationthatcanbeexplainedbybrainmorphology,e.g.,as
capturedbystructuralbrainMagneticResonanceImaging(MRI).Inthedawningeraoflarge-scale
datasetscomprisingtraitsacrossabroadphenotypicspectrum,morphometricitywillbecriticalin
prioritizingandcharacterizingbehavioral,cognitive,andclinicalphenotypesbasedontheir
neuroanatomicalsignatures.Furthermore,theproposedframeworkwillbesignificantindissecting
thefunctional,morphological,andmolecularunderpinningsofdifferenttraits.
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Introduction
Thestructural,functional,andmolecularpropertiesofthebrainsupportnumeroustraitsspanning
thebehavioral,cognitiveandclinicalspectra.Neuroanatomicalfeaturesareinturninfluencedby
factorssuchasage,sex,training,andgenetics[1-4].Neuroimagingallowsustocharacterizethese
bidirectionalassociationsbyrevealingvariationinbrainstructureandfunctionacrossindividuals.
Conventionalmethodsthatweusetoprobetheseassociationsaimtoanatomicallymapeffects,build
predictionmodels,ortesthypotheses.Yet,wedonothaveastandardtechniquetomeasureand
comparetheoftenspatiallydistributedandcomplexpatternsofneuroanatomicalcorrelatesof
differentphenotypes.Herewepresentanovelmetriccalledmorphometricitythatoffersthis
capability.
Todate,structuralneuroimagingstudieshaveprimarilyreliedonthreeclassesofanalyticapproaches.
Thefirststrategyishypothesis-drivenandutilizesaregressionmodeltoexamineassociations
betweenbehavioraltraitsorclinicalconditionsandasmallnumberofaprioriimage-derived
measurements,suchasthoserestrictedtoananatomicalregionofinterest(ROI)[5].TheROI-based
approachprovidesusefulinsightsabouttheunderlyingbiologyandcanbeefficientinlimitedsample
sizescenarios,butisrestrictedtothetestedhypothesis.Thesecondapproachisexploratoryandaims
tocomputemapsofassociationsbyconductingbrain-widetests[6],asexemplifiedinvoxel-based
morphometry(VBM)[7],orvertex-wisecorticalthicknessanalysis[seee.g.,8].Suchmassive
univariateanalysescanofferacomprehensivepictureoftheunderlyinganatomicalassociations,yet
theycanalsobeinefficientinrevealingsubtle,multivariatepatternsofassociation,becauseeach
anatomicallocationistypicallyexaminedinisolationandtheburdenofmultipletestingcorrection
canconstrainstatisticalpower.ThethirdclassincludesmultivariatetechniquessuchasCanonical
CorrelationAnalysis(CCA)[9],PartialLeastSquares(PLS)[10],Bayesianinferencealgorithms[11],or
othermachinelearningmethods[12,13].Thesestudiesarefocusedoneitherdiscoveringthe
multivariatepatternsofassociationordemonstratingindividual-levelpredictioncapabilities,butthe
biologicalinterpretationoftrainedmultivariatemodelscanbechallenging[14].Furthermore,these
methodsoftensufferfromhighcomputationaldemand,andcanbesensitivetoimplementation
details,suchasthechoiceoflearningrule,optimizationalgorithm,andlocaloptimaintraining.
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Wepresentmorphometricityanalysisasanovelapproachtoexaminetheglobalstatistical
associationbetweenbrainmorphologyandobservabletraits.Inspiredbypriorworkontrait
heritabilityinpopulationandstatisticalgenetics[15,16],wedefinemorphometricityasthe
proportionofphenotypicvariationthatcanbeexplainedbybrainmorphology,e.g.,ascapturedby
measurementsderivedfromstructuralbrainMagneticResonanceImaging(MRI)scans.UnlikeROI-
basedormassiveunivariateassociationtests,morphometricityanalysisisnotconcernedwithspecific
anatomicalstructuresorthepreciseanatomiclocalizationofeffects.Incontrasttotheapplicationof
machinelearningtopopulationdata,theprimaryaimofmorphometricityanalysisisnottomaximize
individual-levelpredictionaccuracy,butexamineandquantifystatisticalassociations.Theproposed
strategythusaffordsauniqueperspectiveonthebiologicalunderpinningsofdifferentphenotypes,
andallowsustocompareandcontrastimagingmodalities,typesofanatomicalmeasurements,and
processingstreams.
Morphometricityisgroundedinlinearmixedeffects(LME)modeling,aclassicalstatisticalframework
thatwasrecentlyemployedinpopulationgeneticstoquantifytheheritabilityofatraitusinggenome-
widegeneticvariants[17-19].Themodelrelatesthevariationinbrainmorphologycomputedfrom
brain-wide,MRI-derivedmeasurementstothevariationinobservabletraits,andcanbefittedusing
well-established,robustcomputationaltools.Inourimplementation,weuseFreeSurfer[20],afreely
available,widelyused,andextensivelyvalidatedbrainMRIanalysissoftwarepackage,to
automaticallyprocessstructuralMRIscansandobtainavectorofvolumetricmeasurementsacross
subcorticalstructuresandcorticalthicknessmeasurementsacrosstheentirecorticalmantle,which
constituteacomprehensivedescriptionofthestructuralneuroanatomy.
Weappliedthemorphometricityanalysistoover3,800uniquebrainMRIscansfrom9large-scale
studiesandcomputedthemorphometricityofclinicalconditionsincludingAlzheimer’sdisease,
attention-deficithyperactivitydisorder(ADHD),schizophrenia,autismspectrumdisorder,and
Parkinson’sdisease;andnonclinicaltraitsincludingsex,age,intelligence,educationlevel,andan
arrayofcognitivemeasures.Ourresultsdemonstratethatmorphometricityanalysispromisestooffer
auniqueperspectiveontherelationshipbetweenbrainanatomy,andbehavioral,cognitiveand
physiologicaltraits.
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Results
OverviewoftheModel.Theproposedmorphometricityanalysisisbasedonthefollowinglinear
mixedeffects(LME)model:
𝒚 = 𝑿𝜷 + 𝒂 + 𝝐, (1)
where𝒚isan𝑁-dimensionalcolumnvectorofaquantitativephenotypewith𝑁beingthesamplesize
(i.e.,numberofsubjects),𝑿isthe(design)matrixofconfoundingvariables(sometimescalled
covariatesornuisancevariables)suchasageandsex,𝜷isthe(fixedeffect)coefficientvector,𝒂 ∼
N(𝟎, 𝜎/0𝑲/)isan𝑁-dimensionalrandomeffectvectordrawnfromazero-meanmultivariateGaussian
distributionwithacovariancematrixthatisequaltothescaledanatomicsimilaritymatrix(ASM)𝑲/,
andtheelementsofthenoisevector𝝐areassumedtobedrawnfromindependentandzero-mean
Gaussiandistributionswithhomogeneousvariance𝜎30.TheASMencodesglobalmorphological
resemblancebetweenpairsofindividualsinthesample,andinprinciplecanbeanynon-negative
definitematrixwithitsdiagonalelementsconstrainedtobeequalto1onaverage,and𝜎/0canthus
beinterpretedasthetotalvariancecapturedbytheASM.Inthispaper,weconsideredtwotypesof
intuitiveandwidelyusedmetricsthatquantifythesimilarityofvolumetricandcorticalthickness
measurementsextractedfromstructuralbrainMRIscansbetweenpairsofindividuals:(1)alinear
similaritymetric(i.e.,innerproductbetweennormalizedimagingmeasurements);and(2)anonlinear
Gaussian-typesimilaritymetric(seeMethods).Usingamodelselectionapproach,wefoundthatthe
Gaussiansimilaritymetricprovidedconsistentlybetterdescriptionofthedataacrossthetraitswe
studied(seeMethodsandSupplementaryTableS1).Therefore,allreportedmorphometricity
estimateswerebasedontheGaussianmetric.
Formally,wedefinemorphometricitybasedontheLMEmodelofEquation(1)as:
𝑚0 ≐𝜎/0
𝜎/0 + 𝜎30=𝜎/0
𝜎60,(2)
where𝜎60isthephenotypicvariance.Morphometricityisthustheproportionofphenotypicvariation
thatcanbeexplainedbybrainmorphology,thevariationofwhichiscapturedbytheASM.Estimates
ofmorphometricitycanbecomputedbypluggingtherestrictedmaximumlikelihood(ReML)
estimates[21,22]ofthevariancecomponents,𝜎/0and𝜎30,intoEquation(2).
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Weextendthisdefinitiontothecase-controldesign,i.e.,binarydiseasetraits(affectedvs.
unaffected),usingtheclassicalliability-thresholdmodel,whichiswidelyemployedinpopulationand
statisticalgeneticstudies[23,24].Themodelassumesthattheunderlyingdiseaseliability(whichisa
quantitativevariable)followsaGaussiandistributionandindividualsarecases(affected)iftheir
liabilityexceedsathreshold.Themorphometricityestimate𝑚0foradiseasetraitontheobserved
scale,obtainedbyfittingthemodelofEquation(1)tothebinaryphenotypedata,canbeeasily
transformedtotheliabilityscale[24,25]:
𝑚90 = 𝑚0 𝐾(1 − 𝐾)
𝜑(𝑡)0𝐾(1 − 𝐾)𝑃(1 − 𝑃) ,(3)
where𝑚90isthemorphometricityontheliabilityscale,𝐾istheprevalenceofthediseaseinthe
generalpopulation(i.e.,theproportionofthepopulationhavingthedisease),𝑃istheprevalenceof
thediseaseinthestudysample,𝑡 = ΦBC(1 − 𝐾)istheliabilitythreshold,ΦisthestandardGaussian
cumulativedistributionfunction,and𝜑isthestandardGaussiandensityfunction.Inrealdisease
studies,casesareoftenconsiderablyoversampledrelativetotheirpopulationprevalence(knownas
non-randomascertainment),inwhichcase𝑃islargerthan𝐾.Transformingmorphometricity
estimatesfromtheobservedscaletotheliabilityscalemakesthemindependentofpopulationand
sampleprevalence,andthuscomparableacrossdifferentdiseases.
OverviewoftheData.WeanalyzedbrainMRIscansandtraitdatafromover3,800uniqueindividuals
spanning9large-scalestudies:theHarvard/MassachusettsGeneralHospitalBrainGenomic
SuperstructProject(GSP)[26],theHumanConnectomeProject(HCP)[27],theAlzheimer’sDisease
NeuroimagingInitiative(ADNI)[28],theAttention-DeficitHyperactivityDisorder(ADHD200)sample
[29],theOpenAccessSeriesofImagingStudies(OASIS)cross-sectionalsample[30],theCenterfor
BiomedicalResearchExcellence(COBRE)schizophreniasample[31],theMINDClinicalImaging
Consortium(MCIC)schizophreniasample[32],theAutismBrainImagingDataExchange(ABIDE)[33],
andtheParkinsonProgressionMarkerInitiative(PPMI)[34].SeetheMethodssectionforfurther
detailsonthedatasets.Thetraitsofinterestweregroupedintothreecategories:clinicaldiagnoses,
generalnonclinicaltraitsandmeasuresofcognition.
MorphometricityofClinicalDiagnoses.TheclinicaltraitsweexaminedincludedAlzheimer’sdisease,
attention-deficithyperactivitydisorder(ADHD),schizophrenia,autismspectrumdisorder,and
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Parkinson’sdisease.Table1liststhecharacteristicsofthecorrespondingsamples,alongwith
morphometricityestimates(ontheliabilityscale)andassumedpopulationprevalencevalues[35-41].
Figure1showstheestimatedmorphometricityvaluesontheliabilityscale.Ouranalysesrevealed
thatAlzheimer’sdiseaseissubstantiallymorphometric(witha95%confidenceintervalof[0.94-1.00]),
suggestingthatthisclinicalconditionisassociatedwithasubstantialanatomicalsignature.Onthe
otherhand,ADHD,schizophreniaandautismshowedmoderatemorphometricityvalues,allgreater
than0.35.Finally,wefoundthatParkinson’sdiseasewasmodestlymorphometric,withanestimated
liability-scalevalueof0.20.Allexaminedclinicalconditionswerestatisticallysignificantlyassociated
withwhole-brainmacroscopicmorphology,i.e.,theestimatedmorphometricityvalueswere
significantlylargerthanzero(allp-values<0.005).SupplementaryTableS2listspointestimatesof
morphometricityandtheirstandarderrorscomputedviajackkniferesampling[42].Theseresultsare
instrongagreementwiththeparametricestimatesinTable1.
Wehadaccesstotwoindependentsamplesthatallowedustoreplicateourmorphometricity
estimatesofAlzheimer’sdisease(OASIS)andschizophrenia(COBRE).Weobservedthattherewas
strongagreementbetweentheestimatesfromindependentsamples(Figure1).SupplementaryTable
S3providesfurtherdataaboutthesereplicationanalyses.
MorphometricityofGeneral,NonclinicalTraits.Thenonclinicaltraitsweexaminedwereage,general
intelligence(IQ),sex,andeducationlevel.Table2liststhecharacteristicsofthesamplesusedinthe
primaryanalyses,alongwiththeestimatesofmorphometricity.Theseresultsrevealedthatallthe
examinedgeneraltraitsaresignificantlyandsubstantiallymorphometric(Figure2);all
morphometricitypointestimatesweregreaterthan0.8,andallp-values<1e-8.SupplementaryTable
S2listsmorphometricityestimatesandtheirstandarderrorscomputedviajackkniferesampling.
TheseresultsandtheparametricestimatesinTable1arevirtuallyidentical.
Wehadaccesstoindependentreplicationsamplesforallthegeneralnonclinicaltraitsweexamined.
ItcanbeseeninFigure2thatthereplicationanalysesrevealedremarkablyconsistent
morphometricityestimates.SupplementaryTableS4providesfurtherdataaboutthesereplication
analyses.
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ContrastingwithROI-basedAssociationAnalyses.Themostcommonanalyticstrategyintoday’s
neuroimagingstudiesinvolvesexaminingassociationsbetweentraitsandmeasurementsfrom
regionsofinterest(ROIs).Ourgoalinthisanalysiswastocontrasttheproposedwhole-brain
morphometricityanalysiswithsuchROI-basedtechniques.Werestrictedouranalysistothesix
phenotypes(age,IQ,sex,education,Alzheimer’sdisease,andschizophrenia),forwhichwehadtwo
independentdatasets.Wethenusedoneofthesamples(thereplicationsampleintheanalyses
above)forthediscoveryofthemostsignificantlyassociatedROIwiththetrait,andtheothersample
(theprimarysampleintheanalysesabove)toquantifythestrengthandmagnitudeofassociation.
SupplementaryTableS5liststhestructuresthatexhibitedthestrongestassociationwiththetraitsin
thediscoveryanalysis.
Figure3visualizesthemagnitudeofassociationbetweentheROI-basedmeasurementsand
phenotypicvariation,assessedusingthesameLMEmodelingframeworkofwhole-brain
morphometricity.Here,wereplacedtheglobalASMwithonecomputedbasedonROImeasurements
(seeMethodsforfurtherdetails).ItcanbeseenthattheproportionofvarianceexplainedbyROI-
basedmeasurementswasconsistentlylowerthanwhole-brainmorphometricityestimates(with
generalintelligenceexhibitingthesmallestdiscrepancy).Mostnotably,foreducationand
schizophrenia,ROI-basedassociationsweremuchweaker(bothinmagnitudeandstatistical
significance)thanwhole-brainassociations(Figure3andSupplementaryTableS5).Infact,education
andschizophreniadidnotexhibitastatisticallysignificantcorrelationwithindividualROI-based
measurements,whilewhole-brainmorphometricityanalysesrevealedsignificantassociations.
MorphometricityAnalysisofCognitiveMeasures.WeusedthemostrecentreleaseoftheHuman
ConnectomeProject(HCP)data(downloadedonDecember15,2015)tocomputemorphometricity
estimatesforanarrayofcognitivemeasures.Ourprimaryanalysisreliedon190non-twinsubjectsof
non-HispanicEuropeanancestry(28.9+/-3.8years,47.3%female),drawnfromseparatefamilies(i.e.,
therewerenosiblingsinthissample).Figure4showsthemorphometricityestimatescomputedfor
variablesthatmeasuresustainedattention,non-verbalandverbalepisodicmemory,working
memory,executivefunction,delaydiscounting,language(vocabularycomprehensionandreading
decoding),spatialorientation,processingspeed,fluidintelligence,andself-regulation(impulsivity).
Weconductedasecondary(replication)analysison208non-Hispanicwhitetwins(29.4+/-3.2years,
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61.4%female),withonetwindrawnfromeachfamily,andthustherewerenosiblingsinthis
replicationsample.Figure4showstheresultsobtainedfromthissecondaryanalysisaswell.
Ourresultsdemonstratedthatallexaminedvariables,exceptforthemeasureofself-regulation,are
statisticallysignificantlymorphometric.Wenotefurtherthattherewasanimportantamountof
variabilityinthedegreeofmorphometricityacrosscognitivemeasures.Thisvariationwasremarkably
consistentbetweentheprimaryandsecondaryanalyses.Measuresofattention,cognitiveflexibility,
workingmemory,verbalepisodicmemory,andinhibitionweresubstantiallymorphometric(with
estimatesgreaterthan0.80inbothprimaryandsecondaryanalyses).Measuresoflanguage,non-
verbalepisodicmemory,spatialorientation,processingspeed,andfluidintelligenceweremoderately
morphometric(withpointestimatesgreaterthan0.50).
Discussion
Morphometricity:ANovelMetrictoQuantifyWhole-brainAssociationswithaTrait.Inthispaper,
weintroducedanoveltechniqueforanalyzingtheneuroanatomicalunderpinningsofvariousclinical,
physiological,andbehavioraltraitsusinglarge-scaleneuroimagingdata.Incontrastwithassociation
testingtechniqueswidelyusedintoday’sneuroimagingstudies,ourapproachdoesnotfocusona
prioriROIsorconductindependent(massiveunivariate)interrogationsateachcandidateregionor
voxel.Instead,morphometricityisaglobalquantificationofthewhole-brainanatomicalsignatureof
atrait.
Whiletheproposedapproachisintimatelyrelatedtoimage-basedmultivariateprediction
performance,therearetwocharacteristicsofmorphometricitythatmakeitdifferentfromthe
applicationofmachinelearning.Firstly,themetricdoesnotrequirecross-validation,whichisoften
thetechniqueutilizedinmachinelearningtogaugepredictionaccuracy.Cross-validationisusually
computationallydemanding,andreliesontheunbiasedsettingofmodelparameters(whichmightbe
achievedviaanestedcrossvalidationstrategy),andrepeatedandbalancedpartitioningofdatainto
trainandtestsets.Incontrast,theproposedLME-basedapproachexploitstheentiredatasettofit
themodelandestimatetheunknownvariancecomponentparameters,andinturnmorphometricity,
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inanunbiasedfashion.Secondly,morphometricityisaclassicalstatisticalmeasureofexplained
varianceandisthereforefamiliartointerpret.
Morphometricityhasmanyparallelstoheritabilityingenetics[15,16].Bothconcepts,statisticalin
nature,areaboutphenotypicvariationandtheproportionofvarianceexplained.Thus,the
interpretationhastobecarriedoutwithinaprobabilisticframework,islimitedbythestudied
population,dependsonthetechniqueusedtoquantifythetrait,andcanbeconfoundedby
unmeasuredvariablesactingthroughunknownmechanisms.Thebiasesduetoconfoundssuchas
(cryptic)relatednessbetweensubjectsorpopulationadmixturearewell-studiedinheritability
analysis.Asweelaboratebelow,morphometricityalonecannotbeusedtoinfercausalrelationships,
buthastobefollowedupwithfurtherstudiesthatwillhomeinonpotentialmechanisms.Thecore
differencebetweenmorphometricityandheritabilityisthedirectionofassociation.Inheritability,
thisdirectionisknownandfixed,becausethereisnoknownbiologicalmechanismthatwouldallow
thephenotypetoalterthegenotype.Inmorphometricity,however,thedirectionalitycangoeither
wayandhastobedissectedwithfurtherbiologicalstudies.
TraitsCanBeMorphometrictoDifferentDegrees.Virtuallyalltraitsweexaminedinthisstudywere
significantlymorphometric.However,ouranalysesalsorevealedinterestingvariationinthewhole-
brainanatomicalsignatureofdifferenttraits.Certainphenotypes,suchasAlzheimer’sdisease,age,
and(maybesurprisingly)generalintelligence(IQ)weresubstantiallymorphometric(withestimates
exceeding0.90),whileothermeasures,suchasnon-verbalepisodicmemory,spatialorientation,
processingspeed,andfluidintelligenceexhibitedmoderatemorphometricity.Furthermore,the
psychiatricdisordersweexamined(schizophrenia,ADHDandautism)wereallmoderately
morphometric,unequivocallypointingtoaneuroanatomicalsubstratefortheseclinicalconditions.
Theproposedmorphometricityanalysisisthefirstcoherentframeworkthatenablesustodirectly
quantifyandcomparethemorphologicalsignaturesofsuchdiversesetsoftraits.
Thetraitswepresentedinthisstudyhavebeenexaminedextensivelyinpriorstructural
neuroimagingstudiestorevealmorphologicalcorrelates.Whilemanyofthesestudiesreliedon
regionalorvoxel-levelassociationteststhatareconductedateachlocationindependently,thereis
growingevidencethatmultiplebrainregionsareimplicatedincomplex,multivariaterelationships
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withmanycommonphenotypes.Forexample,patternsofatrophyinneurodegenerativeconditions
suchasAlzheimer’sdiseasehavebeenshowntospreadthroughlarge-scale,distributedbrain
networksthatcanbecircumscribedbasedonresting-stateactivity[43].Furthermore,developmental
mechanismssuchasneuronalmigration,synapseformation,myelination,andsynapticpruningfollow
predictableandrobustspatiotemporalpatterns,whicharelikelyassociatedwithbehavioraltraits
suchasintelligenceanddisruptedinpsychiatricdisorderssuchasschizophrenia[44,45].Ourdata
fromROI-basedanalysessupportthepremiseofanalyzingbrain-widepatterns,ratherthanisolated
regions,forassociationsbetweenneuroanatomicalfeaturesandbehavioralorclinicalphenotypes.
MorphometricityEstimatesAreConsistentAcrossIndependentSamples.Formostofthetraitswe
examinedinthisstudy,wereplicatedouranalysesonindependentdata.Allpointestimatesfell
within95%confidenceintervalsoftheestimatescomputedonthecorrespondingindependentdata.
Theseresultssuggestedthatthepresentedmorphometricityestimatesareconsistentacrossdifferent
samples.Wepresenttheseresultswithacautionarynotehowever.Asweemphasizedabove,
morphometricityisastatisticalmetricthatdependsonthestudiedpopulationandthemeasurement
ofthetrait.Thus,variationsinthepatientcompositionforexampleorchangesindiagnosticcriteria
willinevitablyleadtodifferentestimatesofmorphometricity.Inourreplicationanalyses,these
factorsseemedtoplayonlyaminorrole.
Whole-brainMorphometricityAnalysesCanBeMorePowerfulthanROI-basedAnalyses.We
presentmorphometricityanalysisasanalternativetotheclassicalregion-basedinterrogation
conductedinneuroimaging,whichisoftenfocusedondiscoveringorcharacterizingbiomarkersand
mappingbiologicaleffects.Thecentralchallengeinregion-basedapproachesisthatweneedto
eitherconfineouranalysestoaprioriROIs,orexhauststatisticalpowerbyprobingalargenumberof
candidateregions.Inourexperiments,weconductedadirectcomparisonbetweenwhole-brain
morphometricityanalysisandanROI-basedapproach.Toidentifytrait-specificROIs,adiscovery
analysiswasrunonindependentsamplesofeachtrait.TheassociationsbetweentheidentifiedROIs
andtraitswerethentestedinnon-overlappingsamples.IdentifyingthemostassociatedROIand
estimatingthemagnitudeofassociationinindependentsamplesavoidedtheissueofcircularanalysis
[46,47],andproducedunbiasedmorphometricityestimatesforindividualROIs.Ourresults
demonstratedthatwhole-brainmorphologyconsistentlyexplainedmoreofthephenotypicvariation
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thansingleROIs.Furthermore,morphometricityanalysiscouldrevealassociationsthatwerenot
detectablewhenfocusedonisolatedregions.Forexample,educationandschizophreniawerefound
tobenotsignificantlyassociatedwithvolumetric/thicknessmeasurementsofanyoftheindividual
ROIs;yet,bothtraitsweremoderatelyandsignificantlymorphometricinwhole-brainanalyses,which
indicatesthattheymayhavespatiallydistributedneuroanatomicalsignaturesthatcannotbe
capturedbyindividualROIs.Inaddition,whole-brainmorphometricityanalysisoffersthecapabilityof
capturinginteractionsbetweenbrainregionsandthuscanbemorepowerfulthananalyzingeachROI
independently.
PotentialLimitationsandDrawbacksofMorphometricity.Morphometricityisastatisticalmetricand
assumesaparticular,linearmodeloftherelationshipbetweenvariables.Onecriticalcomponentof
themodelistheAnatomicalSimilarityMatrix(ASM),whichcapturesthecovariancestructureofthe
randomeffectthataccountsforthemorphologicalvariationinthesample.Inthiswork,we
consideredalinearmetricandanonlinearGaussian-typemetrictoquantifythesimilarityof
volumetric/thicknessmeasurementsbetweenpairsofsubjects,andemployedamodelselection
techniquetofindthemetricthatbetterdescribesthedata.OuranalysessuggestthattheGaussian
metricisconsistentlybetterthanthelinearmetricacrossthetraitswestudied,andcapturesa
significantportionofrelevantinter-subjectvariationunderdifferentconditions.However,wehave
notattemptedtoexhaustivelyexploreothertypesofsimilaritymetrics,whichmayemphasize
differentaspectsofthedataandproducedifferentresults.Alternatively,theASMcanbebuiltusinga
bottom-upapproachandexpressedasacombinationofelementarymatrices,andtheparametersof
thiscombinationcanbetreatedasunknownvariables.Byincreasingtheunknownsinthemodel,
however,thisapproachwilllikelyreducestatisticalpower.
AnotherimportantpointtoconsideristhatASMshouldreflectbrain-wideglobalmorphologyand
cannotbeoptimizedforaspecifictrait.Thislatterobservationiscriticaltobeabletoobjectively
comparemorphometricityestimatesacrossdifferenttraits.OurglobaldefinitionofASMand
morphometricity,however,constrainstheinterpretationoftheresults.Certaintraitswithvery
dramaticyetfocaleffects,mightnotyieldlargemorphometricityestimates,sincetheproposed
modelisinsensitivetolocalizedeffects.
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Finally,asinanyassociationtestingframework,theinterpretationofmorphometricityanalysis
resultsshouldbedoneverycarefullyandconsiderconfoundingmechanisms.Thisiswellunderstood
inthecontextofheritability,wherenon-genetic(e.g.,dietary,cultural,socioeconomic)influences
thatvaryacrossracialgroupsorfamiliescanconfoundgeneticanalyses.Similardrawbacksapplyto
morphometricity.Forexample,siblingsmighthavesimilarbrainmorphologiesandphenotypic
expressions,yettheremightnotbeanycausallinkbetweenbrainmorphologyandthephenotype.
Therefore,werecommendrunningmorphometricityanalysesonasetofunrelatedsubjects.
Furthermore,weadviseconstrainingtheanalysis(ifpossible)toahomogeneoussampleofuniform
ancestry,andexplicitlycontrollingforotherpotentialconfoundingfactors,suchasage,sex,andscan
site.
PotentialUsesandExtensionsofMorphometricity.Morphometricityanalysiscanbeusedto
prioritizeimagingmodalities,acquisitionparameters,andprocessingpipelines.Forexample,there
areagrowingnumberofsoftwarepackagesthatallowustoautomaticallyextractnumerous
structuralmeasurementsfrombrainimages.Differentconstructionsoffeaturevectorsanddifferent
metricsthatquantifythesimilarityofimagingfeaturesbetweenindividualswillresultindistinct
ASM’s,whichcanbecomparedwiththemodelselectionframeworkemployedinthisstudy.
Therefore,morphometricityanalysisoffersawaytoquantitativelyandobjectivelyidentifythe
imagingfeaturesandinter-subjectsimilaritymetricthatbestdescribethetrait-relevantaspectsof
whole-brainmorphology.
Alternatively,onecanimagineestimatingthefunctional,structural,connectomic,andmolecular
signaturesofatraitwithinasinglestatisticalmodel,whereeachofthesecomponentsisrepresented
witharandomeffectandthecorrespondingsimilaritymatrixcomputedfromarelevantmodality.
Similarly,onecanpartitionthephenotypicvariationintocontributionsfrom,forinstance,corticaland
subcorticalfeatures,ordifferentlarge-scalebrainnetworks.Thisstrategymightoffernovelinsights
abouttheneuralcorrelatesofcertainphenotypesbyintegratingmultiplemodalitiesand/ormodeling
spatialheterogeneityinaunifiedanalyticframework.Thisnovelperspectivemightalsoallowusto
quantifythecomplementaryinformationcontainedindifferentimagingmodalitiesandspatial
locations.
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Aslongitudinalimagingstudiescontinuetogrow,itwillbeinterestingtoextendmorphometricityto
examinetherelationshipsbetweentemporaldynamicsinbrainmorphology(e.g.,globalatrophy
rates)andclinicalorbehavioraltraits.Weenvisionemployingthelinearmixedeffectsstrategyto
modellongitudinaldata[48,49],andwewilldefinethemorphometricityoflongitudinalchangesin
phenotypeswithinthisframework.
Finally,theproposedframeworkcanalsoofferanovelperspectiveonexaminingrelationships
betweendifferentphenotypes.Weplantoextendmorphometricity,whichisessentiallythedegree
ofassociationbetweenglobalbrainmorphologyandaphenotype,toquantifythe“morphological
correlation”betweenphenotypes.Thiswillbeanalogoustogeneticcorrelationanalysis[50],which
quantifiesthegeneticoverlapbetweentraits.Webelievethatmorphologicalcorrelationwillbean
invaluabletooltoexaminethecomplexbiologicalrelationshipsbetweenthevariousdimensionsof
humanbehaviorandwillinformbasicandtranslationalresearchintoexploringandredefiningthe
landscapeofbraindiseases.
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Methods
TheImagingMeasurements.Inthisstudy,weusedtheextensivelystudiedFreeSurfer-derived
measurementstodescribethewhole-brainmorphology.Theimagingmeasurementsincluded
volumesofnon-corticalstructures[51](leftandrightcerebralwhitematter,lateralventricle,inferior
lateralventricle,cerebellumwhitematter,cerebellumcortex,thalamusproper,caudate,putamen,
pallidum,hippocampus,amygdala,andthe3rdand4thventricles)andthicknessmeasurementsof
corticalregions[52](leftandrightsuperiorfrontal,rostralmiddlefrontal,caudalmiddlefrontal,pars
opercularis,parstriangularis,parsorbitalis,lateralorbitofrontal,medialorbitofrontal,precentral,
paracentral,frontalpole,superiorparietal,inferiorparietal,supramarginal,postcentral,precuneus,
superiortemporal,middletemporal,inferiortemporal,banksofthesuperiortemporalsulcus,
fusiform,transversetemporal,entorhinal,temporalpole,parahippocampal,lateraloccipital,lingual,
cuneus,pericalcarine,rostralanteriorfrontal,caudalanteriorfrontal,posteriorparietal,isthmus
parietal,andinsula).
TheAnatomicalSimilarityMatrix.Theanatomicalsimilaritymatrix(ASM)playsacentralroleinthe
proposedmorphometricityanalysis.TheASMisan𝑁×𝑁symmetricmatrix,where𝑁isthenumberof
subjectsintheanalyzedsample.EntriesintheASMquantifythepairwiseglobalsimilaritybetween
thebrainmorphologiesoftwoindividuals.Inprinciple,theASMcanbeanynon-negativedefinite
matrixwithitsdiagonalelementsconstrainedtobeequalto1onaverage.Inthisstudy,we
consideredtwowidelyusedsimilaritymetrics(linearandGaussian)toconstructtheASM.
Assumethat𝑣FGdenotesthe𝑘-thimagingmeasurementsfromsubject𝑖,𝑀isthetotalnumberof
measurements,and𝑠Gisthesamplestandarddeviationofthe𝑘-thmeasurement.ThefirstASMwe
consideredusesalinearkernel.Thus,thesimilarityismeasuredasthelinearcorrelationbetween
pairsofimagingvectorsandthe(𝑖, 𝑗)-thentryiscomputedas:
1𝑀
𝑣FG𝑣MG𝑠G0G
.(4)
Thisisequivalenttomodelingtherandomeffect𝒂inEquation(1)asalinearcombinationofthe
imagingfeatures:𝒂 = 𝒁𝒖,where𝒁isan𝑁×𝑀matrixcomprisingthestandardizedimaging
measurements(i.e.,the(𝑖, 𝑘)-thentryof𝒁is𝑣FG/𝑠G),and𝒖isan𝑀×1randomvectordistributedas
𝒖 ∼ N 𝟎, STU
V𝑰 ,i.e.,eachimagingmeasurementisassociatedwithanindependentandnormally
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distributedeffectsize.Thecovarianceof𝒂canthenbecomputedas𝜎/0 ∙ 𝒁𝒁Y/𝑀,i.e.,𝒁𝒁Y/𝑀isthe
ASMwithitsentriesexplicitlystatedinEquation(4).
ThesecondASMweconsideredwascomputedusingaGaussiankernelonstandardizedimaging
features,withthe(𝑖, 𝑗)-thentrydefinedas:
exp −(𝑣FG − 𝑣MG)0
𝑀𝑠G0G
.(5)
NotethateachASMdefinitioncorrespondstodifferentmodelsoftrait-relevantvariation.For
example,theGaussiankernelcancapturenonlinearandmultivariateassociationsbetweenbrain
morphologyandtraits.Onecanfurtherdecidetoweighdifferentfeaturesdifferently,basedonfor
example,someaprioriinformationabouttraitrelevance.EachoftheseASMchoiceswillcorrespond
toaparticularsemi-parametricregressionmodel,wherethemorphologicalassociationiscaptured
withafunctionthatbelongstoaspecificspaceoffunctionsinducedbytheutilizedkernel[53].Below,
wedescribeanempiricalstrategytochoosethemostappropriateASMmodelfromaselectionof
candidates.
Inthepresentedstudy,foragivensimilaritymetric,wecomputedanASMforthecorticalthickness
measurementsandanASMforthehead-size-normalizedvolumesofnon-corticalstructures(i.e.,
dividedbytotalintracranialvolumeestimates).TheglobalASMwasthencomputedastheaverageof
thecorticalandnon-corticalASM’s.
ModelSelection.ToselecttheASMthatcanbestdescribethedata,weusedamodelselection
techniquederivedforLMEmodelsandproposedin[53].Specifically,foragivenASM𝑲/,ifwe
denote𝑽 = 𝜎/0𝑲/ + 𝜎30𝑰astheReMLestimateofthecovarianceof𝒚,𝑷 = 𝑽B𝟏 −
𝑽B𝟏𝑿(𝑿𝑽B𝟏𝑿)B𝟏𝑿𝑽B𝟏,anddefine𝑺 = 𝑰 − 𝜎30𝑷,itcanbeshownthattr(𝑺),i.e.,thetraceofthe
matrix𝑺,isameasureofmodelcomplexity.Liuetal.[53]thusproposedthefollowingAkaike
InformationCriterion(AIC)andBayesianInformationCriterion(BIC)intheLMEmodelingframework:
AIC = 𝑁log 𝑅𝑆𝑆 + 2tr 𝑺 ,BIC = 𝑁log 𝑅𝑆𝑆 + log 𝑁 ∙ tr 𝑺 ,(6)
where𝑅𝑆𝑆 = (𝒚 − 𝒚)Y 𝒚 − 𝒚 =𝜎30(𝑁 − tr 𝑺 )istheresidualsumofsquares(RSS)oftheLME
model.BothAICandBICrewardthegoodness-of-fit(thefirstterm)ofthemodelandpenalize
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complexmodels(thesecondterm)toavoidoverfitting.BIChasalargerpenaltytermthanAICfor
large𝑁andthusfavorssimplermodels.WeselectedtheASMthatgavesmallerAIC/BICvalues.
TheAnalysisPipeline.WefirstranFreeSurferonallstructuralbrainMRIscansavailableineachofthe
analyzedstudies,anddroppedthesubjectsthatFreeSurferfailedtocompletesuccessfully.Next,we
conductedautomaticqualitycontrolonthemeasurementscomputedbyFreeSurferbyidentifying
outliers–if>25%oftheutilizedmorphometricvariablesexhibitedvaluesthatweremorethan2
standarddeviationsawayfromthepopulationmean,wedeemedthatsubjectanoutlierand
discardedit.Fortheremainingsubjects,wecomputedpairwisesimilaritymeasuresbasedonthe
linearorGaussiankerneldescribedabove.Ifthereweretwosubjectsthatexhibitedacorticaland
non-corticalsimilaritymeasuregreaterthan0.95,wedroppedoneofthosesubjects,accountingfor
thepossibilitythatthiswasaduplicatecaseoracloselyrelatedindividual.Finally,weincludedsex
andageascovariatesinallouranalyses(unlesssexoragewasthetraitofinterest,inwhichcasethat
variablewasnotincluded).WefurtherintroduceddummyvariablesthatindicatedsiteIDswhen
analyzingmulti-sitedata(exceptforADNI,wheretherewerealargenumberofsites,yettheimaging
parameterswerecarefullycalibratedacrosssites[28]).
Givenindividual-leveldataandtheASM,wefitthemodelofEquation(1)toestimatethevariance
componentparametersviatheRestrictedMaximumLikelihood(ReML)algorithm[21,22].InMatlab,
weimplementedanefficientFisherscoringmethodtoiterativelymaximizetherestrictedlikelihood
ofthemodel.Thestandarderrorofthevariancecomponentestimatescanbederivedusingthe
inverseoftheFisherinformationmatrixwhenthealgorithmconverges.Empiricallyweconfirmedthe
parametricestimatesusingjackkniferesampling(seeSupplementaryTableS2).Significanceofthe
morphometricityestimatewasobtainedviaalikelihoodratiotest,comparingLMEmodelswithand
withouttherandomeffects.Becausethenullhypothesis(𝜎/0 = 0)liesontheboundaryofthe
parameterspace,thelikelihoodratioteststatisticfollowsahalf-halfmixtureof𝜒p0(achi-square
distributionwithallprobabilitymassatzero)and𝜒C0(achi-squaredistributionwithonedegreeof
freedom)[54].Implementationsofthedevelopedmorphometricitytoolsareavailableat:
http://people.csail.mit.edu/msabuncu/morphometricity.
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ROI-basedMorphometricityAnalysis.Inordertocomparetheproposedwhole-brain
morphometricityanalysistomoreconventionalROI-basedanalyses,weimplementedanROI-based
adaptationofEquation(1).Here,insteadofcomputingtheASMusinganarrayofvariablesthatspan
thebrain,wecomputedROI-basedASMsonlyusingasingleROIbiomarker–thevariablethathad
thestrongestassociationwiththetraitofinterest.ToidentifytheROIbiomarkerofeachtrait,we
conductedanindependentdiscoveryanalysisonanon-overlappingsample,examiningthe
associationbetweeneachofthecandidateimagingvariablesandthetraitinaregressionanalysis,
whileappropriatelycontrollingforage,sex,andsite.Theimagingvariablethatexhibitedthesmallest
p-valuewasthenidentifiedastheROIbiomarkerforthetraitofinterestandusedinthe
morphometricityanalysis.WenotethatfortheROI-discoveryanalysesweutilizedthereplication
(secondary)samplesofthewhole-brainmorphometricityanalyses.Thisway,wecomputedtheROI-
basedmorphometricityresultsusingtheprimarysamples.
TheData.WeemployedbaselinebrainMRIscans(T1-weightedacquiredon1.5Tmachines),clinical
diagnosis,anddemographicvariablesfromphase1oftheADNI[28].IntheADHD200sample[29],
casesweredefinedasthosewithevidenceofnon-typicaldevelopmentandanADHD-Combined
diagnosis,asperthepublishedphenotypickey
[http://fcon_1000.projects.nitrc.org/indi/adhd200/general/ADHD200_PhenotypicKey.pdf].Inthe
cross-sectionalOASISsample[30],subjects(of60yearsorolder)withaclinicaldementiarating(CDR)
greaterthan0wereclassifiedashavingdementia.Elderlysubjectswitha0CDRwereclassifiedas
healthycontrols.Forthe20controlsubjectswithrepeatscans,weonlyusedthedatafromthefirst
imagingsession.IntheCOBREsample[31],schizophreniasubjectswereidentifiedaccordingtothe
phenotypefile[http://fcon_1000.projects.nitrc.org/indi/retro/cobre.html].TheMCICdatawas
compiledfromasharedrepositoryofmulti-sitebrainimagingdatacollectedfortheclinical
investigationofschizophrenia[32].TheABIDEanalyses[33]wereconductedonsubjectswhowere
olderthan10years,andcasesweredefinedasthosehavinganon-zerodiagnosticgroupentryinthe
phenotypetable[http://fcon_1000.projects.nitrc.org/indi/abide/].InthePPMIanalyses[34],cases
weredeterminedtobethosediagnosedwithParkinson’sDiseaseatbaselineandcontrolswerethose
whowereclinicallyhealthyandnotprodromal,againatbaseline[http://www.ppmi-info.org/access-
data-specimens/download-data/].
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Allgeneraltraitanalyseswereconductedonhealthycontrolsamples(seecriteriaofrelevantstudy).
BoththeOASISandGSPsamplescoverasubstantialportionoftheadultlifespanandthuswereused
toestimatethemorphometricityofage.AllGSPanalyseswereconstrainedtounrelated,healthy
controlsofnon-HispanicEuropeanancestry,withhigh-qualitystructuralbrainMRIscansacquiredon
a12-channelcoil[26].Inthegeneralintelligence(IQ)analyses,weutilizedtheWechslerAbbreviated
ScaleofIntelligenceasthephenotype(bothintheADHD200andABIDEsamples).Forthe
morphometricityanalysisofsex,wecreatedsubsamplesthatweregender-balanced(50%female)
andage-matchedbetweensexes.InthePPMIdata,educationwasmeasuredinyears(minimum9
andmaximum24),whereasintheOASISsample,educationlevelswereencodedas;1:lessthanhigh
schoolgraduate,2:highschoolgraduate,3:somecollege,4:collegegraduate,and5:beyondcollege.
Inthecognitivemeasureanalyses,weemployedthedemographicandbehavioralmeasuresreported
inthe‘openaccess’and‘restricted’subjectinformationspreadsheetsavailablefromtheHCP
databasewebsite[http://www.humanconnectome.org/data].TheHCPcollectedarangeofwell-
validatedandreliablebehavioralmeasures,includingthosefromtheNIHToolboxAssessmentof
NeurologicalandBehavioralFunction,andseveraladditionalmeasurestoassessdomainsnot
coveredbytheNIHToolbox.Formoreinformationontherationalebehindthedevelopmentofthe
behavioralbatteriesusedinHCP,see[55].
AllMRIscansfromADNI,OASIS,ADHD200,MCIC,COBRE,PPMI,andHCPwereprocessedwith
FreeSurferversion5.3.TheGSPMRIscanswereprocessedwithFreeSurferversion4.5.
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Acknowledgements
SupportforthisresearchwasprovidedinpartbytheNationalInstituteforBiomedicalImagingand
Bioengineering(P41EB015896,R01EB006758,R21EB018907,R01EB019956),theNationalInstituteon
Aging(5R01AG008122,R01AG016495),theNationalInstituteforNeurologicalDisordersandStroke
(R01NS0525851,R21NS072652,R01NS070963,R01NS083534,5U01NS086625),andwasmade
possiblebytheresourcesprovidedbySharedInstrumentationGrants1S10RR023401,1S10RR019307,
and1S10RR023043.AdditionalsupportwasprovidedbytheNIHBlueprintforNeuroscienceResearch
(5U01-MH093765),partofthemulti-institutionalHumanConnectomeProject.
DatawereprovidedinpartbytheBrainGenomicsSuperstructProject(GSP)ofHarvardUniversity
andMGH,withsupportfromtheCenterforBrainScienceNeuroinformaticsResearchGroup,
AthinoulaA.MartinosCenterforBiomedicalImaging,CenterforHumanGeneticResearch,and
StanleyCenterforPsychiatricResearch.20individualinvestigatorsatHarvardandMGHgenerously
contributeddatatotheoverallproject.
ThisresearchwasalsofundedinpartbyNIHgrantsR01NS083534,R01NS070963,and
1K25EB013649-01and1R21AG050122-01A1(toMRS);K01MH099232(toAJH);K24MH094614and
R01MH101486(toJWS);anMGHECORTostesonPostdoctoralFellowshipAward(toTG).JWSisa
TepperFamilyMGHResearchScholar.BFhasafinancialinterestinCorticoMetrics,acompanywhose
medicalpursuitsfocusonbrainimagingandmeasurementtechnologies.BF'sinterestswerereviewed
andaremanagedbyMassachusettsGeneralHospitalandPartnersHealthCareinaccordancewith
theirconflictofinterestpolicies.
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TablesandFigures
Figure1:Morphometricityestimatesofvariousdiseases(ontheliabilityscale)computedusingthe
Gaussiananatomicalsimilaritymatrix(ASM)ofEquation(5).Eachbarisannotatedwithstudy
namesusedtocomputetheseestimates.ForAlzheimer’sdiseaseandschizophrenia,wehad
independentsamplesusedtocomputereplicationestimates(purplebars).Errorbarsindicate
standarderroroftheestimates.
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Figure2:MorphometricityestimatesofgeneralnonclinicaltraitscomputedusingtheGaussian
anatomicalsimilaritymatrix(ASM)ofEquation(5).IQdenotesgeneralintelligence.Eachbaris
annotatedwithstudynamesusedtocomputetheseestimates.Bluebarscorrespondtoresultsfrom
theprimaryanalyses,whereaspurplebarscorrespondtoindependentreplicationanalyses.Errorbars
indicatestandarderroroftheestimates.
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Figure3:ROI-basedmorphometricityestimatesofgeneralnonclinicaltraits(age,intelligence,sex,
andeducation),Alzheimer’sdisease(AD),andschizophrenia(SCZ).ForADandSCZ,morphometricity
estimateshavebeentransformedtotheliabilityscale.Redcirclesdenotewhole-brain
morphometricityestimatesforeachtrait.Errorbarsindicatestandarderroroftheestimates.
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Figure4:Morphometricityestimatesofvariousmeasuresofcognitioncomputedondatafromthe
HumanConnectomeProject(HCP)andusingtheGaussiananatomicalsimilaritymatrix(ASM).Blue
andpurplebarscorrespondtoprimaryandsecondaryanalyses,respectively.Errorbarsindicate
standarderroroftheestimates.
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Table1:Samplecharacteristicsandmorphometricityestimatesforanalyzeddiseasetraits.
*P<5e-3,**P<5e-4,***P<5e-5
Disease Case N Case Age (mean±std)
Case Fem% Control N
Control Age (mean±std)
Control Fem %
Study Name
Alzheimer's 154 74.6±7.6 46.8 219 75.9±5 48.4 ADNIADHD 122 11.6±3.2 75.4 384 11.8±2.9 62.2 ADHDSchizophrenia 92 33±11.2 75.0 85 32.8±11.7 67.1 MCICAutism 209 17.6±7.9 14.4 305 17.3±7.2 18.4 ABIDEParkinson's 376 61.4±9.7 35.1 152 60.4±11.4 47.8 PPMI
Assumed Prevalance
Morphometricity (liability scale)
Standard Error
13% 1.00*** 0.031% 0.55** 0.161% 0.50*** 0.031% 0.38*** 0.060.2% 0.20* 0.06
Table2:Samplecharacteristicsandmorphometricityestimatesfortheanalyzedgeneralnonclinicaltraits.
Trait Name Sample
Size Age (mean±std)
[min-max] Female
% Study Name
Age 1073 22±5.8 [18-81] 56 GSPIQ 155 11.3±2.8 [7.2-17.7] 60 ADHDSex 1074 25.3±13.7 [18-84] 50 GSPEducation 152 60.4±11.4 [30-82] 34.8 PPMI
Morhopmetricity Estimate
Standard Error
1.00 0.010.95 0.050.93 0.020.81 0.08
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SupportingInformationfor“Morphometricity:MeasuringtheNeuroanatomical
SignatureofaTrait”
MertR.Sabuncu,TianGe,AvramJ.Holmes,JordanW.Smoller,RandyL.Buckner,andBruceFischl;
fortheAlzheimer’sDiseaseNeuroimagingInitiative(ADNI)*
SupplementaryTableS1:AkaikeInformationCriterion(AIC)andBayesianInformationCriterion(BIC)
values(Equation6)fortheprimarymorphometricityanalysesconductedwiththeLinear(Equation4)
andGaussian(Equation5)kernels.
AIC(x104) BIC(x104)
Disease/Trait Gaussian Linear Gaussian LinearAlzheimer's(ADNI) -1.508 -0.309 -1.362 -0.163ADHD -2.040 -0.655 -1.826 -0.441Schizophrenia (MCIC) -0.772 -0.216 -0.716 -0.160Autism (ABIDE) -2.022 -0.637 -1.804 -0.419Parkinson's -0.522 -0.194 -0.491 -0.163Age (GSP) -2.967 -0.276 -2.433 0.258IQ (ADHD 200) -0.521 -0.107 -0.474 -0.059Sex (GSP) -3.559 -0.992 -3.024 -0.457Education (PPMI) -0.512 -0.188 -0.477 -0.153
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SupplementaryTableS2:Parametricandjackknifeestimatesofmorphometricityandstandarderrors.Morphometricityestimatesfordiseasetraitsareontheliabilityscale.
Morphometricity StandardError
Disease/Trait Parametric Jackknife Parametric JackknifeAlzheimer's(ADNI) 1.00 1.00 0.03 0.03 ADHD (ADHD 200) 0.55 0.55 0.16 0.17 Schizophrenia (MCIC) 0.50 0.50 0.03 0.03 Autism (ABIDE) 0.38 0.38 0.06 0.06
Parkinson's 0.20 0.20 0.06 0.06
Age (GSP) 1.00 1.00 0.01 0.01 IQ (ADHD 200) 0.95 0.95 0.05 0.06 Sex (GSP) 0.93 0.93 0.02 0.02
Education (PPMI) 0.81 0.81 0.08 0.07
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SupplementaryTableS3:Independentreplicationonnon-overlappingdata:samplecharacteristics
andmorphometricityestimatesforanalyzeddiseasetraits.
Disease Case N Case Age (mean±std)
Case Fem% Control N
Control Age (mean±std)
Control Fem %
Study Name
Assumed Prevalance
Morphometricity (liability scale)
Standard Error
Alzheimer's 100 76.8±7.1 59.0 98 75.9±9.0 73.4 OASIS 13% 1.00 0.06Schizophrenia 56 35.8±12.4 16.1 73 35.7±11.6 31.5 COBRE 1% 0.45 0.08
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SupplementaryTableS4:Independentreplicationonnon-overlappingdata:samplecharacteristics
andmorphometricityestimatesforanalyzedgeneralnonclinicaltraits.
Trait Name Sample
Size Age (mean±std)
[min-max] Female % Study Name
Trait (mean±std) [min-max]
Morhopmetricity Estimate
Standard Error
Age 124 68.0±13.7 [33-94] 72.6 OASIS N/A 1.00 0.03IQ 108 17.5±8.0 [10.5-56.2] 14.8 ABIDE 109.33±11.0[84-133] 0.95 0.06Sex 298 11.3±2.9 [7.17-21.74] 50 ADHD N/A 0.90 0.05Education 124 68.0±13.7 [33-94] 72.6 OASIS 3.5±1.2 [1-5] 0.79 0.13
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SupplementaryTableS5:ROI-basedmorphometricityestimatesforthetraitswithtwoindependent
samples.MostassociatedROIswereidentifiedonindependentsample.*Fordiseasetraitswelist
morphometricityestimatesontheliabilityscale.
Trait Name ROI-basedMorphometricity StandardError P-value MostassociatedROIAge 0.82 0.03 <1e-15 3rdVentricleIQ 0.87 0.05 <1e-15 RightLateralVentricleSex 0.44 0.07 1.9e-9 RightThalamusEducation 0.00 0.06 1.00 RightHippocampusAlzheimer's* 0.66 0.16 2.6e-5 RightHippocampusSchizophrenia* 0.06 0.05 0.22 RightInferiorLateralVentricle