brain-age prediction longitudinal and cross-sectional study using advanced diﬀusion models and White matter microstructure across the adult lifespan: A mixed NeuroImage

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ContentslistsavailableatScienceDirect

NeuroImage

journalhomepage:www.elsevier.com/locate/neuroimage

White matter microstructure across the adult lifespan: A mixed

longitudinal and cross-sectional study using advanced diﬀusion models and brain-age prediction

Dani Beck

^a^,^b^,^c^,^∗

, Ann-Marie de Lange

^a^,^b^,^d

, Ivan I. Maximov

^a^,^b

, Geneviève Richard

^b

, Ole A. Andreassen

^b^,^e

, Jan E. Nordvik

^f

, Lars T. Westlye

^a^,^b^,^e^,^∗

aDepartment of Psychology, University of Oslo, PO Box 1094 Blindern, 0317 Oslo, Norway

bNORMENT, Division of Mental Health and Addiction, Oslo University Hospital & Institute of Clinical Medicine, University of Oslo, Oslo, Norway

cSunnaas Rehabilitation Hospital HT, Nesodden, Oslo, Norway

dDepartment of Psychiatry, University of Oxford, Warneford Hospital, Oxford, United Kingdom

eKG Jebsen Centre for Neurodevelopmental Disorders, University of Oslo, Oslo, Norway

fCatoSenteret Rehabilitation Center, Son, Norway

a r t i c le i n f o

Keywords:

Ageing White matter Multi-shell Longitudinal, Diﬀusion Brain age

a b s t r a ct

Themacro-andmicrostructuralarchitectureofhumanbrainwhitematterundergoessubstantialalterations throughoutdevelopmentandageing.Mostofourunderstandingofthespatialandtemporalcharacteristicsof theselifespanadaptationscomefrommagneticresonanceimaging(MRI),includingdiffusionMRI(dMRI),which enablesvisualisationandquantificationofbrainwhitematterwithunprecedentedsensitivityanddetail.However, withsomenotableexceptions,previousstudieshavereliedoncross-sectionaldesigns,limitedageranges,and diffusiontensorimaging(DTI)basedonconventionalsingle-shelldMRI.Inthismixedcross-sectionalandlongitudinalstudy(meaninterval:15.2months)including702multi-shelldMRIdatasets,wecombinedcomplementary dMRImodelstoinvestigateagetrajectoriesinhealthyindividualsaged18to94years(57.12%women).Using linearmixedeffectmodelsandmachinelearningbasedbrainageprediction,weassessedtheage-dependence ofdiffusionmetrics,andcomparedtheagepredictionaccuracyofsixdifferentdiffusionmodels,includingdif- fusiontensor(DTI)andkurtosisimaging(DKI),neuriteorientationdispersionanddensityimaging(NODDI), restrictionspectrumimaging(RSI),sphericalmeantechniquemulti-compartment(SMT-mc),andwhitematter tractintegrity(WMTI).TheresultsshowedthattheageslopesforconventionalDTImetrics(fractionalanisotropy [FA],meandiffusivity[MD],axialdiffusivity[AD],radialdiffusivity[RD])werelargelyconsistentwithprevious research,andthatthehighestperformingadvanceddMRImodelsshowedcomparableagepredictionaccuracy toconventionalDTI.LinearmixedeffectsmodelsandWilk’stheoremanalysisshowedthatthe‘FAfine’metric oftheRSImodeland‘orientationdispersion’(OD)metricoftheNODDImodelshowedthehighestsensitivityto age.Theresultsindicatethatadvanceddiffusionmodels(DKI,NODDI,RSI,SMTmc,WMTI)providesensitive measuresofage-relatedmicrostructuralchangesofwhitematterinthebrainthatcomplementandextendthe contributionofconventionalDTI.

1. Introduction

Thearchitectureofhumanbrainwhitematterundergoesconstant remodellingthroughout life. Age-relatedtrajectories of whitematter macro-andmicrostructuretypicallyreflectincreasesinanisotropyand decreasesindiffusivityduringchildhood,adolescenceandearlyadult- hood(Krogsrudetal.,2016;Tamnesetal.,2018;Westlyeetal.,2010), andsubsequentanisotropydecreasesanddiffusivityincreasesinadult- hoodandsenescence(Coxetal.,2016;Davisetal.,2009).Whilethe

∗Correspondingauthorsat:DepartmentofPsychology,UniversityofOslo,POBox1094Blindern,0317Oslo,Norway.

E-mailaddresses:dani.beck@psykologi.uio.no(D.Beck),l.t.westlye@psykologi.uio.no(L.T.Westlye).

ﬁeldhasprimarilybeendominatedbycross-sectionalstudies,whichby designlackinformationonindividualtrajectories(Schaie,2005),lon- gitudinalstudiesinthelast decadehave showncorresponding white matterchangesinbothdevelopmentandageing(Barricketal.,2010; Bender et al., 2016; Bender and Raz, 2015; deGroot et al., 2016; Likitjaroen et al., 2012; Racine et al., 2019; Sexton et al., 2014; Storsve etal.,2016;Teipeletal.,2010).However,studiesthathave evaluatedindividualdiﬀerencesinchangeacrossawideagerangeare rare(Benderetal.,2016).

https://doi.org/10.1016/j.neuroimage.2020.117441

Received10July2020;Receivedinrevisedform11September2020;Accepted5October2020 Availableonline9October2020

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Whitematterpropertieshavecommonlybeeninvestigatedusingtra- ditionaldiffusiontensorimaging(DTI),andtheDTI-basedmetricsfrac- tionalanisotropy(FA)aswellasmean(MD),axial(AD),andradial(RD) diffusivityarehighlysensitivetoage(Coxetal.,2016;Sextonetal., 2014;Westlyeetal.,2010;Yapetal.,2013).However,limitationsof conventionalDTI metricssuchastheirinabilitytocapturerestricted non-Gaussiandiffusionandlackofspecificitytodifferentdiffusionpools (Pinesetal.,2020)havemotivatedcontinueddevelopmentofmoread- vanceddiffusionMRI (dMRI)models.Thesemodelsincludediffusion kurtosisimaging(DKI)(Jensenetal.,2005),whichwasdevelopedtoad- dresstherestricteddiffusionornon-Gaussianityinthediffusionsignal;

neuriteorientationdispersionanddensityimaging(NODDI)(Zhangetal., 2012),whichmodelsthreetypesofmicrostructuralenvironments:intra- cellular,extra-cellular,andanisotropicwaterpoolresponsibleforthe spaceoccupiedbycerebrospinalﬂuid(CSF);whitemattertractintegrity (WMTI)(Chungetal.,2018;Fieremansetal.,2011),whichderivesmi- crostructuralcharacteristicsfromintra-andextra-axonalenvironments;

restrictionspectrumimaging(RSI)(Whiteetal.,2013),whichapplieslin- earmixturemodellingtoresolveaspectrumoflengthscaleswhilesimul- taneouslyacquiringgeometricinformation;andsphericalmeantechnique multi-compartment(SMTmc)(Kadenetal.,2016),amethodformicro- scopicdiffusionanisotropyimagingthatisunconfoundedbyeffectsof fibrecrossingsandorientationdispersion.

Usually based on multi-shell acquisitions with several diffusion weightings(Andersson andSotiropoulos,2015; Jbabdietal., 2012), these modelscan be broadlysplitinto “signal” and “tissue” models (Alexanderetal.,2019).Signalrepresentations,suchasDTIandDKI, describe the diffusion signal behaviour in a voxel without assump- tions about underlying tissue, but asthe estimated parameters lack specificity,theircharacterisationof tissuemicrostructureremains in- direct(JelescuandBudde,2017).Tissuemodels(NODDI,RSI,SMT-mc, andWMTI)involveestimationsof thegeometryofunderlying tissue (Novikovetal.,2019),whichmayprovidehigherbiologicalspecificity andmoreprecisemeasuresofwhitemattermicrostructureandarchitec- ture(JelescuandBudde,2017;Novikovetal.,2019;Pinesetal.,2020).

However,despitetissuemodelsbeingdesignedtoincreasespeciﬁcity, theystillrequireassumptionsabouttheunderlyingmicrostructuretobe accurate.

Building on the opportunities from big data in neuroimaging (SmithandNichols,2018),agerelatedbrainchangeshaverecentlybeen investigatedusingmachinelearningtechniquessuchasbrainagepre- diction;theestimationofthe‘biological’ageofabrainbasedonneu- roimagingdata(Coleetal.,2018;deLangeetal.,2019;Kaufmannetal., 2019;Frankeetal.,2010;Richardetal.,2018).Predictingtheageof abrain,andsubsequentlylookingatthedisparitybetweenpredicted andchronologicalage,canidentifyimportantindividualisedmarkersof brainintegritythatmayrevealriskofneurologicaland/orneuropsychi- atricdisorders(Kaufmannetal.,2019).Whilebrainagepredictionhas grownmorepopularinrecentyears,moststudieshaveusedgreymat- terfeaturesforbrainageprediction,whileonlyfewhaveexclusively (Tønnesen etal.,2020),orpartly(Cole,2019;Maximovetal.,2020; Richardetal.,2018;Smithetal.,2019a,b)utiliseddMRI.However,the brain-agepredictionaccuracyofadvanceddiﬀusionmodelssuchasRSI andNODDIarenotknown.

Includingcross-sectionalandlongitudinaldataobtained from573 healthyindividuals(with702 multi-shelldMRIdatasets)aged18–94 years,theprimaryaimofthisstudywastoofferacomprehensivede- scriptionofnormativeage-relatedwhitemattertrajectoriesinadulthood bycomparingrelevantcurveparameterssuchaskeydeflectionpoints andrateofchangeaswellasagepredictionaccuracyofdifferentdMRI metrics,withaparticularfocusonrelativelynovelparametersbased onadvanced(DKI,NODDI,RSI,SMTmc,andWMTI)andconventional (DTI)diffusionmodelsofwhitemattercoherenceandmicrostructure.

First,weestimatedthetrajectoriesofeachofthediﬀusionmetrics acrosstheagerange.Secondly,weutilisedthreeseparatemethodsto comparetheage-sensitivityofthediﬀusionmodels:i)weusedlinear

Table1

Demographicsofdescriptivestatisticspertainingtothestudysample.N referstodatasets.

Age

Mean ± SD Min Max Full (mixed) sample ( n = 702) 50.86 ± 16.61 18.52 94.67 Male (301, 42.88%) 49.45 ± 17.48 18.52 92.05 Female (401, 57.12%) 51.92 ± 15.86 18.63 94.67 Cross-sectional sample ( n = 444) 47.61 ± 16.59 18.52 94.67 Male (214, 48.20%) 46.75 ± 16.71 18.52 92.05 Female (230, 51.80%) 48.57 ± 16.51 18.63 94.67 Longitudinal sample ( n = 258) 56.60 ± 15.03 20.30 85.82 Male (44, 35.11%) 55.72 ± 17.78 20.30 85.82 Female (85, 65.89%) 55.65 ± 13.70 23.37 80.62

mixedeffect(lme)modelsincludingage,sex,andtimepoint,ii)foreach model,we ranfitswithandwithoutagetermsandcomparedthefit likelihoodvaluesusingWilk’stheorem(Wilks,1938),iii)weusedma- chinelearningtopredictagebasedonthediffusionmetrics,andcom- paredthepredictionaccuracyofthemodels.Thirdly,welookedatthe derivativesofeachfunctionofthelmemodels’agecurvetoidentifythe pointofchangeintrajectoryforeachdiffusionmetric.Basedonprevi- ousworkcharacterisingagedifferencesandlongitudinalchangeswith arangeofdiffusionMRImetrics(Benitezetal.,2018;Falangolaetal., 2008; Jelescuetal., 2015;Kodiweeraetal.,2016;Reasetal.,2017; Westlyeetal.,2010),weexpectedtheincludedmetricstoshowcurvi- linearrelationshipswithage,withvaryingtrajectoriesanddeflection points possiblyreflectingdifferentialinvolvementandrateofchange oftheputativebiologicalunderpinningsduringthedifferentphasesof brainageing.

2. Methodsandmaterial 2.1. Descriptionofsample

Theinitialsampleincluded754multi-shelldatasetsofhealthypar- ticipantsfrom twointegratedstudies;theTematiskOmrådePsykoser (TOP)(Tønnesenetal., 2018)andStrokeMRI(Richardetal., 2018).

Followingtheremovalof52datasets afterqualitychecking(QC,see Section2.4),theﬁnalsamplecomprised702datasetsfrom573individ- uals,includinglongitudinaldata(twotime-pointswithmeaninterval= 15.2months)for129oftheparticipants.Demographicinformationis summarisedinTable1andFig.1.

Exclusioncriteriaincludedneurologicalandmentaldisorders,and previous headtrauma. Ethicalguidelinesfollowedthoseinlinewith theDeclarationofHelsinki.ThestudyhasbeenapprovedbytheRe- gionalEthicsCommitteeandallparticipantsprovidedwritteninformed consent.

2.2. MRIacquisition

Imaging wasperformed atOsloUniversityHospitalon aGeneral ElectricDiscoveryMR7503Tscannerwitha32-channelheadcoil.dMRI data wereacquiredwith aspinecho planarimaging(EPI)sequence withthefollowingparameters:TR/TE/ﬂipangle:8150ms/83.1ms/90°, FOV:256×256mm,slicethickness:2mm,in-planeresolution:2mm.

We obtained 10 vol of b= 0anddiﬀusionweighted dataalong 60 (b=1000s/mm²)and30(b=2000s/mm²)diﬀusionweightedvolumes.

Inaddition,7b=0volwithreversedphase-encodingdirectionwereac- quiredforcorrectionofsusceptibilitydistortions.

2.3. DiﬀusionMRIprocessing

Processing steps followed a previously described pipeline (Maximovetal.,2019),includingnoisecorrection(Veraartetal.,2016),

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Fig.1. Intervalbetweentimepoint1andtimepoint2forcompletelongitudinalsample,n=258(129subjects).Histogramrepresentingdensityofdatapoints.

Gibbsringingcorrection(Kellneretal.,2016),correctionsforsuscepti- bilityinduceddistortions,headmovementsandeddycurrentinduced distortions using topup (http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/topup) andeddy (http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/eddy) (Andersson and Sotiropoulos, 2016). Isotropic smoothing was carried out with a Gaussian kernel of 1 mm³ implemented in the FSL func- tion fslmaths. DTI was estimated using FSL tool dtifit and ex- cluded the b = 2000 shell from the fit. Employing the multi-shell data, DKI and WMTI metrics were estimated using Matlab code (https://github.com/NYU-DiffusionMRI/DESIGNER),(Fieremansetal., 2011). NODDI metrics were derived using AMICO in Matlab (https://github.com/daducci/AMICO). SMT mc metrics were estimated with the original code(https://github.com/ekaden/smt). RSI metricswereestimatedusingin-houseMatlabtools.

Weselected20scalarmetricsfromthesixmodels(DTI,DKI,NODDI, RSI, SMTmc, WMTI) based on recentstudies (Benitez et al., 2018; DeSantisetal.,2011;Hopeetal.,2019;Jelescuetal.,2015;Kadenetal., 2016;Maximovetal.,2019;Pinesetal.,2020).Modelswerealsose- lectedbasedonfeasibilityinrelationtoouracquisitionprotocoland availabilityof opensourcescripts. Fig.2showseachof theincluded metricsforone participant,forillustrative purposes.Allmetricsand their corresponding abbreviationsare summarisedin Supplementary Table1).Brain age predictionwas performedforeach model, using allavailablemetricsextractedfromarangeofregions-of-interest(see Section2.5).

2.4. Qualitycheckingprocedure

WeimplementedarigorousQCproceduretoensuredataqualitywas notcontaminatedbymotion,noise,orartefacts.Usingapublishedap- proach(Roalfetal.,2016),wederivedvariousqualityassurance(QA) metrics(seeSupplementarymaterial;SITable2),includingtemporal- signal-to-noise-ratio(TSNR). Outliersweremanuallycheckedandre- movedif deemed tohave unsatisfactory dataquality. A total of 52

datasetswereremoved,leavingthedatasetatn=702scans.Thisdataset wasputthroughthesamevisualinspection.Asanadditionalstep,im- agesweremanuallyinspectedifTSNRZscoresdeviatedminusorplus 2.5standarddeviationsfromthemean.Followingthisstep,theﬁnal datasetremainedat702scansfrom573individuals.

2.5. Tract-based-spatial-statistics

VoxelwisestatisticalanalysisoftheFAdatawascarriedoutusing Tract-BasedSpatialStatistics(TBSS)(Smithetal.,2006),aspartofFSL (Smithetal.,2004).First,FAimageswerebrain-extractedusingBET (Smith,2002)andalignedintoacommonspace(FMRI58_FAtemplate) using thenonlinear registrationtoolFNIRT (Andersson etal., 2010; Jenkinsonetal.,2012),whichusesab-splinerepresentationofthereg- istrationwarpfield(Rueckertetal.,1999).Next,themeanFAimageof allsubjectswascreatedandthinnedtocreateameanFAskeletonthat representsthecentresofalltractscommontothegroup.Eachsubject’s alignedFAdatawas thenprojectedontothisskeleton.ThemeanFA skeletonwasthresholdedatFA>0.2.Thisprocedurewasrepeatedfor allmetrics.fslmeantswasusedtoextractthemeanskeletonand20re- gionsofinterest(ROI)basedonaprobabilisticwhitematteratlas(JHU) (Huaetal.,2008)foreachmetric.Includingthemeanskeletonvalues, 420featuresperindividualwerederived(20metricsx20+1ROIs).Of these,20metricswereusedforfittingofagecurvetrajectories,lmeanal- ysis,andWilk’stheoremanalysis,whileall420MRIfeatureswereused forageprediction. NumberofMRIfeaturescanbe foundinTable4. Additionalvoxelwiseanalysiswerecarriedoutonthe573participants (excludinglongitudinalmeasures)usingtheFSLtoolRandomisewith permutation-basedstatistics (Winkleretal.,2014) andthreshold-free cluster enhancementmethod(TFCE;SmithandNichols,2009).5000 permutationswererun,whereeachdiffusionmetricwastestedforits associationwithage.TBSSfillwasusedtocreatevoxelwisestatistical mapsforeachmetric,whichcanbefoundinSIFig.10.

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Fig.2. Diffusionmetricsfromoneparticipant.DTI:FA(fractionalanisotropy),MD(meandiffusivity),AD(axialdiffusivity),RD(radialdiffusivity).DKI:AK(axial kurtosis),MK(meankurtosis),RK(radialkurtosis).NODDI:ICVF(intracellularvolumefraction),ISOVF(isotropicvolumefraction),OD(orientaldispersion).RSI:

CI(cellularindex),Fine(FAfinescale/slowcompartment),rD(restricteddiffusivitycoefficient).SMTmc:exMD(extracellularspace),exTr(extra-cellularspace transverse),Intra(intraaxonaldiffusivity).WMTI:Awf(axonalwaterfraction),aEAD,aIAD(axialextraandintraaxonaldiffusivity),rEAD(radialextraaxonal diffusivity).

2.6. Diﬀusionmetricreproducibility

Thevalidityandsensitivityofthedifferentdiffusionmodelsessen- tiallyrelyontherichness,qualityandspecificpropertiesofthedata usedformodelfitting.Inordertoassessthereproducibilityofthein- cludedadvancedmetrics(Maximovetal.,2015),weestimatedthedMRI modelsusingdataobtainedfromdifferentacquisitionschemesvarying thenumberofdirectionsandmaximumbvaluein23healthypartici- pantswithmeanage35.77years(SD=8.37,56.5%women).Thisrep- resentedasub-sampleofthefullsample.Thefollowingthreeacquisi- tionschemeswerecompared:i)b=[1000,2000]with[60,30]directions, whichisidenticaltotheacquisitionschemeusedinthemainanalysis, ii)b=[1000,2000]with[60,60]directionsandiii)b=[1000,2000,3000]

with[60,60,60]directions.Foreachschemeweprocessedthedataus- inganidenticalpipeline(Maximovetal.,2019)asdescribedaboveand extractedthemeanskeletonvaluesforeachmetric.Thecomparisonsbe- tweenacquisitionprotocolswereperformedusingboxplots(SIFig.4), scatterplotswithageasafunctionofmeanskeletonvalues(SIFig.5), andPearson’scorrelationcoeﬃcientplots,whereprotocol1isfactored byprotocol3(SIFig.6).

2.7. Statisticalanalysis

Allstatisticalanalyseswerecarriedoutusingthestatisticalenviron- mentR,version3.6.0(www.r-project.org/)(RCoreTeam,2012)and Python3.7.0(www.python.org/).

2.8. Linearmixedeﬀectsmodels(lme)

Toinvestigatetherelationshipbetweenageandglobalmeanskele- tonvaluesforeachdiﬀusionmetric,lmeanalyseswereperformedusing thelmefunction(BatesandPinheiro,1998)inR(RCoreTeam,2012).

Infittingthemodel,wescaled(znormalised)eachvariableandentered age,orthogonalisedage²,sex,andtimepoint(TP)asfixedeffects.Sub- jectIDwasenteredasarandomeffect.ForeachdiffusionmetricM,we employedthefollowingfunction:

𝑀=𝐴+𝐵×𝐴𝑔𝑒+𝐶 × 𝐴𝑔𝑒²+𝑆𝑒𝑥+𝑇𝑃 (1)

whereAistheintercept,Bistheagecoeﬃcient,andCisthecoeﬃcient oftheorthogonalisedquadraticageterm(expressedaspoly(age,2)[,2]

inR).Agecurveswereobtainedwithpredictionsfromtheﬁttedmodel usingthepredictfunctioninRandusedforagecurvetrajectoryﬁgures.

Visualinspection ofresidual plotsdidnot revealany obviousdevia- tionsfrom homoscedasticityornormality. Thesigniﬁcancethreshold wassetatp<0.05,andtheresultswerecorrectedformultiplecompar- isonsusingthefalsediscoveryrate(FDR)adjustment(Benjaminiand Hochberg,1995).

Toinvestigatetherateofchangeforeachoftheagecurvesatany point, wecalculatedtheirderivativesusing numericaldifferentiation withfinitedifferences(BurdenandFaires,2011).Tocomparetheage- sensitivityofthemodels,weranlmefitswithandwithoutageterms,and calculatedthedifferenceinlikelihoodratios(GloverandDixon,2004).

ThesigniﬁcanceoftheagedependencewascalculatedusingWilk’stheorem(Wilks,1938)as√

2(𝐿2 − 𝐿1),whereL₂isthelikelihoodratio

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Table2 Linearmixedeffectmodelresultsforeachmetric,wherevariablesaredisplayedwithcorrespondingfixedeffectestimates(𝛽),(standarderror),t-statistic,andFDRcorrectedPvalue. FAMDADRDDKIakDKImkDKIrkNODDIicvfNODDIisovfNODDIODRSICIRSIfafineRSIrDSMTmcextramdSMTmcextratransSMTmcintraWMTIawfWMTIaxEADWMTIaxIADWMTIradEAD Age−0.66∗∗∗0.46∗∗∗0.030.59∗∗∗−0.12∗−0.24∗∗∗−0.32∗∗∗−0.33∗∗∗0.48∗∗∗0.67∗∗∗−0.48∗∗∗−0.69∗∗∗−0.54∗∗∗0.50∗∗∗0.56∗∗∗−0.26∗∗∗−0.49∗∗∗0.15∗∗∗−0.58∗∗∗0.57∗∗∗ (0.03)(0.04)(0.04)(0.03)(0.04)(0.04)(0.04)(0.04)(0.04)(0.03)(0.04)(0.03)(0.04)(0.04)(0.03)(0.04)(0.04)(0.04)(0.04)(0.03) −20.7613.190.7118.02−3.21−5.95−8.09−8.5213.3121.6213.79−21.97−14.8914.3116.66−6.68−13.333.51−16.4317.11 4.96x10−413.92x10−2412.95x10−350.012.56x10−079.15x10−124.29×10−132.02x10−249.16x10−431.44x10−251.87×10−433.60x10−288.41×10−273.01x10−327.14x10−091.87x10−246.16×10−031.02x10−312.97x10−33 Age2−0.17∗∗∗0.34∗∗∗0.40∗∗∗0.29∗∗∗−0.44∗∗∗−0.26∗∗∗−0.18∗∗∗−0.33∗∗∗0.10∗−0.08−0.37∗∗∗−0.15∗∗∗−0.11∗0.21∗∗∗0.35∗∗∗−0.27∗∗∗−0.26∗∗∗0.14∗∗∗0.11∗0.21∗∗∗ (0.03)(0.03)(0.04)(0.03)(0.04)(0.04)(0.04)(0.04)(0.03)(0.03)(0.03)(0.03)(0.03)(0.03)(0.03)(0.04)(0.03)(0.04)(0.03)(0.03) −5.5710.3010.639.37−12.34−7.15−4.77−9.043.11−2.66−11.04−4.93−3.166.4610.99−7.42−7.513.633.366.91 1.48x10−062.22x10−176.84x10−184.00x10−154.47x10−221.26x10−095.00x10−055.00x10−140.020.093.46x10−192.60×10−050.022.15x10−084.59x10−193.12×10−109.88x10−116.16x10−030.012.17x10−09 Sex−0.09∗∗0.060.030.07∗0.14∗∗∗0.16∗∗∗0.13∗∗∗0.080.10∗0.070.02−0.050.080.10∗−0.030.15∗∗∗0.070.06−0.030.09∗ (0.03)(0.03)(0.04)(0.03)(0.04)(0.04)(0.04)(0.04)(0.03)(0.03)(0.03)(0.03)(0.03)(0.03)(0.03)(0.04)(0.03)(0.04)(0.03)(0.03) −3.121.750.782.164.004.193.482.202.902.480.62−1.552.242.90−1.074.101.881.56−1.002.86 1.52x10−020.5510.221.06x10−033.54x10−044.53x10−030.190.030.1010.820.180.0314.91x10−040.410.8110.03 Timepoint0.010.020.030.010.070.040.020.040.050.020.030.001−0.010.06−0.020.040.030.03−0.020.05 (0.01)(0.01)(0.02)(0.01)(0.03)(0.03)(0.03)(0.03)(0.03)(0.01)(0.01)(0.01)(0.02)(0.03)(0.01)(0.03)(0.02)(0.03)(0.02)(0.02) 0.881.551.721.022.361.210.641.621.641.331.950.05−0.302.31−1.441.321.411.03−0.662.19 10.620.8910.10110.570.520.930.35110.1110.950.80110.15 Observations702702702702702702702702702702702702702702702702702702702702 LogLikelihood−651.72−741.08−853.38−671.25−885.78−941.80−945.41−885.92−882.34−678.79−748.66−662.96−829.12−832.39−703.69−932.36−849.65−965.60−816.35−795.04 AkaikeInf.Crit.1317.441496.151720.761356.501785.561897.601904.811785.841778.691371.581511.331339.911672.241678.791421.391878.731713.301945.201646.691604.09 BayesianInf.Crit.1349.271527.981752.591388.331817.391929.431936.641817.671810.521403.401543.151371.741704.061710.621453.211910.551745.131977.021678.521635.92 Note:Age2representstheorthogonalisedpolynomialquadraticageterm(Eq.(1)). ∗p<0.05;∗∗p<0.01;∗∗∗p<0.001.

obtainedfromthemodelswithageterms,andL₁isthelikelihoodratio obtainedfromthemodelswithoutageterms.

2.9. Brain-ageprediction

TheXGBoostregressor modelwas usedtorunthebrainagepre- diction (https://xgboost.readthedocs.io/en/latest/python/index.html), including a decision-tree-based ensemble algorithm that has been used in recent large-scale brain age studies(de Lange et al., 2019; Kaufmannetal.,2019).Parametersweresettomaxdepth=3,num- berof estimators=100,andlearningrate=0.1(defaults).Foreach diffusionmodel(DTI,DKI,NODDI,RSI,SMTmc,WMTI),predictedage wasestimatedina10-foldcrossvalidation,assigningamodel-specific brainageestimate toeach individual,aswellasamultimodal brain ageestimatebasedonalldiffusionfeatures.Toinvestigatethepredic- tionaccuracyofeachmodel,correlationanalyseswererunforpredicted versuschronologicalage,andmodel-specificR²,rootmeansquareerror (RMSE)andmeanabsoluteerror(MAE)werecalculated.Tostatistically comparethepredictionaccuracyofthemodels,Ztestsforcorrelated samples(Zimmerman,2012)wererunon themodel-specific correla- tionsbetween predictedandchronologicalage inapairwisemanner using

𝑍=(𝛽m1−𝛽m2)∕

√𝜎_m1² +𝜎²_m2−2𝜌𝜎m1𝜎m2,

where“m1” and“m2” representmodel1andmodel2,the𝛽termsrep- resentthebetavaluefromtheregressionfit,the𝜎termsrepresenttheir errors,and𝜌representsthecorrelationbetweenthetwosetsofassocia- tions.Inordertoassessthecomplementaryvalueofthedifferentmod- els,wecomputed thecorrelationsbetweenthebrainagepredictions (Fig.6).Thepredictionswerefirstcorrected forage-biasusinglinear models(Leetal.,2018),andtheresidualswereusedinthecorrelation analysis.

Toevaluatetheimportanceofeachdiﬀusionmodalityinthemul- timodalmodel,werananadditionalpredictionmodelincludingonly mean-skeletonvaluestoreducethenumberofhighlycorrelatedfeatures intheregressorinput,andcalculateda)theproportionofthetotalweight contributedbyeachmodality,whereweightrepresentsthenumberof timesafeatureisusedtosplitthedataacrossalltrees,andb)gainvalues,whichrepresenttheimprovementinaccuracyaddedbyafeature tothebranchesitison.Toassessthesigniﬁcanceofthegeneralmodel performance,averageRMSEwascalculatedforthemultimodalmodel usingcrossvalidationwithtensplitsandtenrepetitionsandcompared toanulldistributioncalculatedfrom1000permutations.

3. Results

3.1. Diﬀusionmetricreproducibility

Thereproducibilityoftheestimateddiﬀusionmetricsbasedondata obtainedwithdiﬀerentacquisitionschemes(describedin2.6)revealed overallhighcorrelationsbetweenthemeanskeletonvaluesforallthe modelmetrics.HighestoverallreproducibilitywasobservedforNODDI OD(r(22)=0.96,p<0.001)andRSIrD(r(22)=0.97,p<0.001).The lowestreproducibilitywasobservedforWMTIradEAD(r(22)=0.44, p=0.597).SupplementaryTable4andSupplementaryFigs.4–7show theresultsfromthecomparisons.

3.2. Agetrajectories

Fig.3showsthelinearmixedeffectmodel-derived agecurvesfor eachdiffusionmetricplottedasafunctionofage,whereagecurvesare fittedwiththepredictedvaluesofthelmemodels.Fig.4showsalllme model-derivedagecurvesfromFig.3instandardisedforminoneplot.

Fig.5showsthederivativesofthelmeﬁts,providingtheestimatedrate

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Fig. 3. Age curves where each diﬀusion metric’s standardised(z-score)meanskeletonvalue(y-axis)is plottedasafunctionofage(x-axis).Fittedlinesmade withlme-derivedpredictedvalues.Shadedareasrep- resent95%CI.Pointsconnectedbylinesrepresent longitudinaldatawherecircleisTP1andtriangleis TP2.Malesubjectsarerepresentedbypinkandfe- malesubjectsbygreen.

ofchangeateverypoint(ofage),includingthepointofchangeintrajec- toryforeachmodelcurveandthesteepnessoftheturningpoint.Corre- lationsbetweenthemetricsareavailableinthesupplementarymaterial (SIFigs.2and3)forbothrawandstandardisedvaluesrespectively.

3.3. Comparingagecurves

Fig.3showstheestimatedagecurvesforallmetrics.Brieﬂy,FAde- creasedsteadilyaftertheageof30,withasteeperdeclineaftertheage

of50.MD,AD,andRDfollowedareverseprofile,withdecreasesindif- fusivityuntilthe40s,wherebythetrajectoriessubsequentlyincreased thereafter. DKImetricsrevealedcurvilineartrajectories,withNODDI ICVF,RSICI,SMTmcintra,andWMTIawfmetricsfollowingsimilar trajectories.RSIrD,NODDIISOFV,RSIFAfine,andWMTIaxIADmet- ricsfolloweddecreasingtrajectoriesfromtheoffset.SMTmcextramd andextratrans,andWMTIradEADfollowedsimilartrajectoriestoMD andRD.NODDIODrevealedasteadyincreaseuntilolderagewherethe slopestabilisedthereafter.Lastly,WMTIaxEADshowedu-trajectories.

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Fig.3. Continued

3.4. Agesensitivityestimatedusinglmemodels

Resultsfromthelmemodelsrevealedsignificantmaineffectsofage ontheglobalmeanskeletonvaluesforalldiffusionmetrics(seeTable2).

Anexaminationofthefixedeffectsestimates(𝛽)andt-statisticsforthe agetermallowsfor interpretationof theextentanddirectionof the linearassociationwithage.Overall,theFAfinecompartmentofthe RSImodelwasmostsensitivetoage(𝛽(125)=−0.69,t=−21.97,p<

0.001).NODDIODwasthesecondmostsensitivetoage(𝛽(125)=0.67,

t=21.62,p< 0.001).Themodelleastsensitivetoagewas DTIAD (𝛽(125)=0.03,t=0.71,p=1).ForconventionalDTImetrics,FAwas themostagesensitive(𝛽(125)=−0.66,t=−20.76,p<0.001).Nomain eﬀectsoftimepointsurvivedcorrectionformultiplecomparisons.

3.5. AgesensitivityestimatedusingWilk’stheorem

Table 3 showsthe strength of theoverallage variationfor each metric estimatedbythediﬀerencein likelihoodvalues (describedin

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Fig.4.Plotdisplayingalllme-modelderivedagecurvesfromFig.3instandardisedform.

Table3.

Likelihoodvaluesfromthelmemodelswithoutageterms(L₁)andwithageterms(L₂).The signiﬁcanceoftheagedependenceisestimatedbythediﬀerenceinlikelihoodvaluesusing Wilk’stheorem.FDRcorrectedp-values=p^corr.

Model L 1 L 2 Diﬀerence (z) p-value p ^corr

DTI FA − 815.86 − 651.72 18.12 5.22 ×10 ⁻⁷² 1.04 ×10 ⁻⁷⁰ MD − 848.36 − 741.08 14.65 2.55 ×10 ⁻⁴⁷ 5.10 ×10 ⁻⁴⁶ AD − 900.66 − 853.38 9.72 2.93 ×10 ⁻²¹ 5.86 ×10 ⁻²⁰ RD − 820.44 − 671.25 17.27 1.62 ×10 ⁻⁶⁵ 3.24 ×10 ⁻⁶⁴ DKI AK − 952.44 − 885.78 11.55 1.12 ×10 ⁻²⁹ 2.25 ×10 ⁻²⁸ MK − 977.09 − 941.80 8.40 4.71 ×10 ⁻¹⁶ 9.42 ×10 ⁻¹⁵ RK − 981.65 − 945.41 8.51 1.83 ×10 ⁻¹⁶ 3.65 ×10 ⁻¹⁵ NODDI ICVF − 948.54 − 885.92 11.19 6.40 ×10 ⁻²⁸ 1.28 ×10 ⁻²⁶ ISOVF − 957.61 − 882.34 12.27 2.06 ×10 ⁻³³ 4.13 ×10 ⁻³² OD − 850.84 − 678.79 18.55 1.90 ×10 ⁻⁷⁵ 3.80 ×10 ⁻⁷⁴ RSI CI − 866.73 − 748.66 15.37 5.28 ×10 ⁻⁵² 1.06 ×10 ⁻⁵⁰ FA ﬁne − 839.53 − 662.96 18.79 2.07 ×10 ⁻⁷⁷ 4.15 ×10 ⁻⁷⁶ rD − 922.24 − 829.12 13.65 3.62 ×10 ⁻⁴¹ 7.24 ×10 ⁻⁴⁰ SMT mc Extra md − 929.01 − 832.39 13.90 1.10 ×10 ⁻⁴² 2.20 ×10 ⁻⁴¹ Extra trans − 848.79 − 703.69 17.03 9.71 ×10 ⁻⁶⁴ 1.94 ×10 ⁻⁶² Intra − 973.21 − 932.36 9.04 1.82 ×10 ⁻¹⁸ 3.64 ×10 ⁻¹⁷ WMTI AWF − 942.66 − 846.37 13.88 1.52 ×10 ⁻⁴³ 3.04 ×10 ⁻⁴¹ axEAD − 973.15 − 962.32 4.65 1.98 ×10 ⁻⁰⁵ 3.97 ×10 ⁻⁰⁴ axIAD − 930.26 − 816.35 15.09 3.38 ×10 ⁻⁵⁰ 6.76 ×10 ⁻⁴⁹ radEAD − 922.92 − 795.04 15.99 2.91 ×10 ⁻⁵⁶ 5.81 ×10 ⁻⁵⁵

Section2.8).Allmetricsshowedsigniﬁcantagedependence,withRSI FAﬁneasthemostagesensitive(z=18.79),followedbyNODDIOD (z=18.55)andDTI-basedFA(z=18.12).WMTIaxEAD(z=4.65)was theleastage-dependantmetric.

3.6. Agesensitivityestimatedusingbrainage

The model performances for the multimodal and model-speciﬁc brainagepredictionsareshowninTable4.SIFigs.8and9showtheas- sociationsbetweenpredictedageandchronologicalageforeachofthe models.Fig.6showsthepairwisecorrelationsbetweenpredictedage foreachmodel.Pairwisediﬀerencesintheagepredictionaccuracyof themodelsareshowninFigs.7and8.SIFig.1showstheRMSEofthe

multimodalmodelpredictioncomparedtoanulldistributionobtained fromcalculating1000permutations.

AsvisiblefromTable4,themultimodalmodelshowedthemostac- curateageprediction(r=0.85,p<0.001,95%CI=[0.83,0.87]),while theDKImodelperformedtheworst(r=0.68,p<0.001,95%CI=[0.64, 0.72]).AsshowninFigs.7and8,themultimodalpredictionaccuracy wassignificantlyhigherthantheaccuracyofeachof theothermod- els,withthelargestdifferenceseenbetweenthemultimodalmodeland DKI.ThedifferencesinpredictionaccuracybetweenDTIandRSI,and WMTIandNODDIdidnotsurvivecorrectionformultiplecomparisons.

Fig.6showedcorrelationcoeﬃcientsofmeanr=0.59(Std=0.09) betweentheDTI,RSI,NODDI,SMTandWMTIpredictions,whilethe DKIshowedlowercorrelationswiththeothermodelpredictions(mean r=0.29,Std=0.04).

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Fig.5. Thederivativeforeachdiﬀusionmodel,providingtheestimatedrateofchangeateverypoint.Thepointonthex-axiswheretheﬁttedlinecrosses0onthe y-axisrepresentstheturningpointoftheagetrajectoryforeachmetric.

Table4

Number ofMRIvariables(correspondingtothesumofmetricfeatures),rootmean squareerror(RMSE),meanabsoluteerror(MAE),correlationbetweenpredictedand chronologicalage(Pearson’sr),andR²foreachofthemodels.CI=conﬁdenceinterval.

Model MRI variables RMSE MAE r [95% CI] R ²[95% CI]

DTI 84 9.35 7.30 0.83 [0.80, 0.85] 0.68 [0.64, 0.72]

DKI 63 12.19 9.82 0.68 [0.64, 0.72] 0.46 [0.41,0.52]

NODDI 63 9.15 7.31 0.83 [0.81, 0.86] 0.70 [0.65, 0.74]

RSI 63 9.84 7.68 0.81 [0.78, 0.83] 0.65 [0.61,0.69]

SMT mc 63 11.30 9.01 0.73 [0.70, 0.76] 0.54 [0.50, 0.58]

WMTI 84 9.37 7.40 0.83 [0.80, 0.85] 0.68 [0.64, 0.72]

Multimodal 420 8.80 6.99 0.85 [0.83, 0.87] 0.72 [0.69, 0.76]

Toevaluatetherelativeimportanceofeachmodality,werananaddi- tionalmultimodalmodelincludingonlymean-skeletonvaluestoreduce thenumberofhighlycorrelatedfeaturesintheregressorinput.Table5 showsthetotalgainandtheproportionofweightcontributedbyeach modalitytothetotalweight, indicatingtheirrelativecontributionin themodeltraining.Theresultsrevealedthatthemachinefavouredthe NODDImodelinthetraining.

4. Discussion

Ageing confers a range of structural brain alterations, aﬀecting micro- andmacrostructuralproperties of the neurocircuitrysupport-

ingcognitiveandothercomplexbrainfunctions.Inthecurrentmixed cross-sectionalandlongitudinalstudy,wecomparedagesensitivityand brainwhitematteragetrajectoriesacrosstheadultlifespanbasedon advanced andconventional dMRImodels.Theresults fromourcom- prehensive analysisapproach, includingage-curve trajectories,linear mixedeffectsmodels,Wilk’stheoremanalysis,andbrainageprediction, showedhighagesensitivityforalldiffusionmetrics,withcomparable sensitivitybetweenthehighestperformingadvanceddMRImodelsand conventionalDTI,andamoderatebenefitofincludingallmetricsinthe samemodel.Themixedeffectsanalysesandcorrespondingderivatives revealedvariationsinagetrajectoriesbetweenmodels,indicatingthat theymaybe sensitivetodifferentunderlyingaspectsofwhitematter ageing.

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Fig.6.Correlationmatrixforpredictedbrainageofeachmodalityandthe multimodalmodel.Toaccountforage-bias(Leetal.,2018;Smithetal.,2019), thepredictedagevalueswereresidualisedforchronologicalageusinglinear models.

Table5

Featureimportanceevaluatedusinga reducedmultimodal modelthat included only mean skeleton values for each modality.Number of MRIvariables(correspondingtothe sumofmetricfeatures),percentagecontributiontothetotal weight,andtotalgainforeachmodality.

Model MRI variables % of total weight Total gain

DTI 4 20.09 163473.25

DKI 3 5.13 41747.63

NODDI 3 45.48 370129.31

RSI 3 4.85 39463.11

SMT mc 3 11.74 95534.98

WMTI 4 12.72 103545.15

Fig.7.Matrixshowingpairwisediﬀerencesbetweenthemodelpredictionaccu- racies(correlationsbetweenpredictedandchronologicalage),basedonztests forcorrelatedsamples.

OurresultsshowedthatFAplateauedaroundthethirddecadewith a steadydecline in slopefollowing theage of ~40,andanacceler- ateddecreaseinsenescence(Fig.3).TheotherDTImetricsofMD,AD, andRDrevealeddecreasesindiffusivityupuntilthe40–50-yearage mark,wherethetrajectoriessubsequentlyincreasefollowingasteady period.Whiletheseresultstoalargeextentcorrespondwithtrajecto- riesobservedinpreviousstudies(Coxetal.,2016;Davisetal.,2009; Westlyeetal.,2010),amoredefinedinvertedU-shape(Westlyeetal., 2010)waslessprominentinourstudy,likelyduetoalackofyounger participantsbelowtheage of 20.Interestingly,FAbasedontherel- atively simpleDTI modelutilisingonly single-shell dataoffered one of thehighest sensitivitiestoage,supportingthat DTI providessen- sitivemeasuresofgrosswhitematteranatomyandneuropathological changes(Alexanderetal.,2008).Thecharacteristiccurvilineartrajec- toriesoflifespandifferencesinconventionalDTImetrics(Westlyeetal., 2010)havepreviouslybeensuggestedtoreflectacombinationofpro-

Fig.8. Log10(p)valuesofthepairwisedifferencesbetweenthemodelpredictionaccuracies.Highernumbersrepresentmoresignificantdifferences.Left:uncorrected p-values.Right:P-valuescorrectedformultiplecomparisonsusingFDR,withnon-significant(>0.05)valuesmaskedout.

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tractedmyelin-relatedmaturationduringchildhood,adolescenceand earlyadulthood (Lebel et al., 2008; Tamnes et al., 2010) and sub- sequentmyelin lossduring laterstagesof adulthoodandsenescence (Bartzokisetal.,2004).However,DTImetricsareunabletodifferentiate betweenintra-andextra-axonalcompartments,and,inadditiontothe idiosyncraticchangesinmyeloarchitecture,theymaybeinfluencedby individualdifferencesandchangesingrossfibrearchitecture(e.g.cross- ingfibres)andaxonalpackinganddensity(Paus,2010;Simmondsetal., 2014).ThespecificbiologicalinterpretationofDTImetricsessentially dependsuponthelocalfibrearchitecture,andsignalchangesfromDTI requirecareful interpretation,astheexactneurobiologicalunderpin- ningscannotbedirectlyinferred.Whilespeculative,utilisingadvanced dMRImodelsinadditiontoconventionalDTImayprovidemorespeci- ficityintheinterpretationoftheresults,andimprovethedescriptive precisionofthetissuepathologybydisentanglingthevariousbiological sourcesthatarehappeningconcurrently.

WhileseveraloftheadvanceddMRImodelsshowedcomparablere- sultstoDTIintermsofagesensitivity,theyalsoshowedvisiblydifferent agetrajectories(Fig.3),includingvariationinturningpoints(Fig.4), indicatingtheageatwhichanisotropyanddiffusivitymeasureschange direction,andgradientofchange(Fig.5),indicatingrateofdecline.The variationinturningpointsandgradientofchangecalculatedusingthe derivatesofeachmodelinformsusabouttheestimatedrateofchangeat specificages,inadditiontothedifferentialsensitivitybetweendifferent metricsduringdifferentlifephases.Althoughdiffusionimagingcannot givedirectaccesstoneuronalprocessesonacellularlevel,thevarying estimatedtrajectoriesinadvanceddMRImodelspotentiallyreflectdif- ferentialinvolvementoftheputativebiologicalunderpinningsduring thedifferentphasesofbrainageing.Thus,metric-specificdifferences mayreflectage-relatedpathologicalchangesbehindeachdMRImodel, helpingusbetterpinpointtheageatwhichdeclineinwhitemattermi- crostructurebegins,whichhasimportantimplicationsforinterventive strategiesaimedatpromotinghealthyageing.

AlthoughrecentresearchhasvalidatedFAandRDmetricsofDTIas beingsensitivemarkerstomyelin(LazariandLipp,2020),cautionmust beexertedininterpretingspecificunderlyingbiologyonthebasisofDTI alone(Novikovetal.,2018).Withthisinmind,combiningtissuemodels suchasNODDI,WMTI,RSI,andSMTmcmayholdpromiseinjointlyre- flectingmeasuresmorerelatabletotheneurobiologicalunderpinnings ofbrainageing.TheWMTImetricsforexamplehavebeenvalidatedfor reflectingunderlyingbiologybothinvivo(Jelescuetal.,2015,2016) andexvivo(Falangolaetal.,2014;Kelmetal.,2016).WMTIawfwas foundtorelatetoaxonaldensity,whereasWMTIradEADtosomeex- tentdescribesthedegreeofmyelination(Kelmetal.,2016)andrelates totheextracellularenvironmentfilledwithinterstitialfluidandcircu- latingmacromolecules,aswellasbloodvesselsandperivascularspaces (NicholsonandHrabětová,2017).TheparametermapsfromtheNODDI modelhavebeenclaimedtoexhibitaspatialpatternof tissuedistri- butionconsistentwiththeknownbrainanatomy(Zhangetal.,2012), with existingmaps showing theexpected pattern of neurite density (Jespersenetal.,2010),servingasanexampleofthefeasibilityprovided byadvanceddiffusionmodelstodisentangleneuritedensityandorien- tationdispersion,twomajorfactorscontributingtoFA(Zhangetal., 2012).TheRSImodeldiametercalculationshavebeenshowntocorre- spondwiththediameterofunmyelinatedandmyelinatedaxonsinthe ratbrain(Whiteetal.,2013),suggestingadirectbiologicalinterpreta- tion.Likewise,histologicalanalyseshaveshownthattheSMTmcmi- croscopicdiffusionindicesofferdirectsensitivitytopathologicaltissue alterations(Kadenetal.,2016).Whilenotatissuemodel,DKIprovides aspecificmeasureofcellularcompartmentsandmembranesandisrel- ativelyunconfoundedbyconcentrationofmacromolecules,potentially providingamore specificindicatorof tissuepropertiesthanconven- tionalDTI(Jensenetal.,2005).

Intheory,thepartlynon-overlappingassumptionsandbiophysical propertiesofthedifferentdiffusionMRImodelsofferamorecompre- hensiveandcompleteviewofthemanifoldbiologicalprocessesinbrain

development,ageing,anddisorderswhenconsideredjointly.Ingeneral, ourfindingsofhigheragepredictionaccuracywhencombiningdifferent modelssupportsthisview.However,notsurprisingly,therelativelyhigh correlationsandsimilarage-relatedtrajectoriesofseveralofthediffer- entmetricsalsosuggestacertainlevelofredundancy.Furtherstudies areneededtotestthehypothesisthatcombiningvariousdiffusionMRI modelsofbrainmacro-andmicrostructureincreasesthefeasibilityand precisionofmultimodaldata-drivenbrainphenotypingapproaches(e.g.

“fingerprinting”)towardsmorespecificclinicalapplicationsandpredic- tion(Alnæsetal.,2018).Withthisinmind,includingtheadvancedmod- elsmaynotonlyimprovespecificitycomparedtoconventionalDTI,but potentiallyprovidesadditionalinformationrelatedtochangesinmyeli- nationandaxonalrewiring,whilespecificallymodellingmicrostructural featurestypicallyconflatedbyDTI,suchasneuritedensity,axonaldiam- eter,andneuriteorientationdispersion(Alexanderetal.,2019).Further researchisneededtovalidateanddevelopdMRImodelstobetterre- flectthedifferentbiologicalandgeometricalpropertiesofwhitematter.

Ifassumptionsofunderlyingmicrostructurearevalid,theseadvanced modelsrepresentapromisingcontributiontotheinvestigationofbrain developmentandageing,andaberrantbrainbiologyinvariousclinical conditions(Alexanderetal.,2019).

Whileconsideringarangeofdiffusionmodels,itisimportanttonote thateachcomeswithitsrespectivelimitations.NODDIhasbeenpar- ticularlycriticisedinrecentyears,withresearchsuggestingthemodel assumptionsareinvalid(Lampinenetal., 2017).NODDIprovideses- timatesofgeometricparametersonly,withtherebeinganabsenceof anydirectdiffusivityestimation(Jelescuetal.,2015).DKI,likeDTI,is limitedinspecificityasitcanbeaffectedbydifferentfeaturesoftissue microstructure.Thus,thebiophysicalmodelthatrelatesDKIparameters directlytowhitemattermicrostructure(WMTI,Fieremansetal.,2011) wasproposed.However,assumptionsmadeinWMTImaybeoversim- plifying,whichcouldleadtobiasintheestimatedparametersinaddi- tiontoreducedinformationaboutthemicrostructure.WMTIparameter estimationaccuracyisalsosaidtoprogressivelydegradewithhigher orientationdispersion(Jelescuetal.,2015).

TheSMTmcmodelovercomeslimitationsinWMTI(Fieremansetal., 2011)andNODDI(Zhangetal.,2012)asitmakesnoassumptionsabout theneuriteorientationdistribution(Kadenetal.,2016).However,itis limitedbyassumingthattheeffectivetransversediffusivityinsidethe neurites is zero,anapproximationwhich maynotholdforunmyeli- natedaxonsanddendrites(Kadenetal.,2016)duetopossibleneurite undulationonthemicroscopicscale(Nilssonetal.,2012).RSI,likemost diffusion-basedtechniques,suffersfromlowresolutionandmaybestbe utilisedin supplementtohighspatialresolutionsequencesaspartof amultimodal imagingprotocol(Brunsingetal.,2017).Forexample, theDTImodel’slimitationofbeingblind tocrossingandbendingfi- bresmayberesolvedbytheRSImodel’smulti-directionpropertiesand abilitytomeasurediffusionorientationandlengthscale(Whiteetal., 2013).Despitethelimitationsofeachmodel,andpossibleredundancy betweenthem,assessingage-relatedwhitemicrostructuralchangesus- ingacombination ofdiffusionmodelscanbe advantageousin order tozeroinon idiosyncraticneuroanatomicalandmicrostructuralpat- terns(Alnæsetal.,2018).BiophysicalmodelsofWMTIandSMTmc for example, add the possibility for assessing the separate effect of diffusionin intra-andextra-axonalspace(JelescuandBudde,2017; Voldsbekketal.,2020).

Somemethodologicallimitationsmustalsobeaddressed.Onecon- cernisthatofaveragingoverregionsofinterestsandtheentirewhite matterskeleton,whichiscomplicatedbythedirectionandmagnitude ofageassociationsvaryingregionally.Recentﬁndings(Tønnesenetal., 2020)foundthattheglobalmeanskeletonmodeloutperformedregion ofinterest-basedsingle-metricmodels,providingevidenceforrelevant informationrequiredforbrainagepredictionis capturedat aglobal level.Indeed,previousstudieshavesuggestedthatregionalDTI-based indicesofbrainageingreﬂectrelativelyglobalprocesses(Penkeetal., 2010; Westlye et al., 2010), which is also supported by a geneti-