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A correction algorithm for partial volume effects in 3D PET imaging: principle and validation

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A correction algorithm for partial volume effects in 3D PET imaging: principle and validation
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  CorrectionforPartialVolumeEffectsinPET:PrincipleandValidation OlivierG.Roussel,YilongMaandAlanC.Evans McConnellBrainImagingCenter,MontréalNeurologicalInstitute,McGillUniversity,Montréal,Québec,Canada TheaccuracyofPETformeasuringregionalradiotracerconcentrationsinthehumanbrainislimitedbythefiniteresolutioncapabilityofthescannerandtheresultingpartialvolumeeffects(PVEs).WedesignedanewalgorithmtocorrectforPVEsbycharacterizingthegeometricinteractionbetweenthePETsystemandthebrainactivitydistribution.Methods:Thepartialvolumecorrection(PVC)algorithmuseshigh-resolutionvolumetricMR¡magescorrelatedwiththePETvolume.WeusedaPETsimulatortocalculaterecoveryandcross-contaminationfactorsofidentifiedtissuecomponentsinthebrainmodel.Thesegeometry-dependenttransfercoefficientsformamatrixrepresentingthefractionoftrueactivityfromeachdistinctbrainregionobservedinanygivensetofregionsofinterest.ThismatrixcanbeinvertedtocorrectforPVEs,independentofthetracerconcentrationsineachtissuecomponent.Aspherephantomwasusedtovalidatethesimulatedpoint-spreadfunctionofthePETscanner.AccuracyandprecisionofthePVCmethodwereassessedusingahumanbasalgangliaphantom.AconstantcontrastexperimentwasperformedtoexploretherecoverycapabilityandstatisticerrorpropagationofPVCinvariousnoiseconditions.Inaddition,adual-isotopeexperimentwasusedtoevaluatetheabilityofthePVCalgorithmtorecoveractivityconcentrationsinsmallstructuressurroundedbybackgroundactivitywithadifferentradioactivehalf-life.Thismodelsthetime-variablecontrastbetweenregionsthatisoftenseeninneuroreceptorstudies.Results:Datafromthethree-dimensionalbrainphantomdemonstratedafullrecoverycapabilityofPVCwithlessthan10 rootmean-squareerrorintermsofabsolutevalues,whichdecreasedtolessthan2 whenresultsfromfourPETsliceswereaveraged.Inaccuracyintheestimationof18Ftracerhalf-lifeinthepresenceof11Cbackgroundactivitywasintherangeof25 -50 beforePVCand0 -6 afterPVC,forresolutionvaryingfrom6to14mmFWHM.Intermsofnoisepropagation,thedegradationofthecoefficientofvariationafterPVCwasfoundtobeeasilypredictableandtypicallyontheorderof25 . Conclusion:ThePVCalgorithmallowsthecorrectionforPVEs simultaneouslyinallidentifiedbrainregions,independentoftracerlevels. KeyWords:correction;partialvolumeeffects;PET;simulation; regionsofinterest JNucÃMed1998;39:904-911 De  espitethewiderangeoftracersavailable,therelativelypoorspatialresolutionofPEThasalwaysbeenamajorlimitingfactorfortheaccuracyofquantitativestudies,particularlycompartmentalanalysisofradioligandkinetics.Thedirectconsequenceoflimitedresolutionisthelossofsignalforstructurespartiallyoccupyingthepoint-spreadfunction(PSF)ofthescanner,i.e.,withdimensionssmallerthanabout2-3timesitsFWHM(1-3).Thiseffectwasfirstestimatedbytheoverlapofthescanner'sPSFwiththeobjectbeingimagedandwasreferredtoasitsrecoverycoefficient(RC),i.e.,theratioofobservedtotrueactivityintheabsenceofsurroundingactivity(7,2).AlthoughthepartialvolumeeffectoriginallyreferredtothelossofsignalduetothelimitedaxialextentoftheobjectwithrespecttotheaxialPSForslicethickness(4),thisconceptbecamemoregeneralandcametoalsodesignatethepartialoverlapoftheobjectwiththetransversecomponentofthePSF  5,6).Thereciprocaleffectofpoorspatialresolutionisthe contaminationofactivityfromneighboringtissuesorspillovereffect(3,6-8).However,partialvolumeeffects(PVEs)usuallyincorporatebothaspectsofpoorspatialresolution(partialvolumeandspillover).Inquantitativestudies,PVEsintroducedistortionsthatdependontracerdistribution,bothinthetargetedregionandinadjacenttissues(8,9).Thischangesboththemagnitudeandtheshapeofthetime-activitycurves(TACs),resultingintypicalerrorsof50%inestimatedrateconstantsformetabolismandtransferoftracerbetweencompartments(10).PhysicalphantomstudiesarecommonlyusedtocharacterizethenatureandmagnitudeofPVEs(1-3,11-14).Asecondclassofmethodsisbasedoncomputer-aidedsimulationofPETscannerresolutionanddigitizedimagesofbrainanatomy.Thiswasfirstintroducedusingpostmortembrainslices(15-17)andwasfurtherdevelopedwithimagescreatedbyanatomicalimagingdevices(18).Invivocorrectionapproachesbasedonhigh-resolutionMRortransmissionCTwerefirstdevelopedtocorrectforbrainactivitydilutionbycerebrospinalfluid(CSF)spaces,intwo(19)andinthreedimensions(20).Later,amethodaccountingforwhitemattercontributiontograymattermeasurementswasdeveloped(21).Thisapproachhasbeenfurtherextendedtoallowforamoreheterogeneoustracerdistributioningraymatter,byincludingadistinctvolumeofinterestforsubcorticalgraystructures(22).Wepreviouslyintroducedacorrectionbasedonregionalestimatesofthecontributionofeachfunctionallydistinctbrainregion(8,10).Inthiswork,thebasicprinciplesofthepartialvolumecorrection(PVC)algorithmarepresented,alongwithvalidationresultsfromamultiple-spherephantomandarealisticthree-dimensionalbrainphantomscannedonthePC-2048systemattheMontréalNeurologicalInstituteandthePC-4096systematJohnsHopkinsHospital(Baltimore,MD). MATERIALSANDMETHODS Theory ProvidingthatthelinearcharacteristicsofPETarepreservedforthelevelsanddistributionsofactivityencountered,thePETimageg(r)representstheweightedintegrationoftheactivitydistributionf(r)presentinthefieldofview(FOV),bytheresponsefunctionofthePETsystemintermsofitsPSFh(r):Eq.1(r)=f(r')h(r,r')dr', FOV ReceivedSep.16,1996;revisionacceptedAug.5,1997.Forcorrespondenceorreprintscontact:OlivierRousset,PhD,McConnellBrainImagingCenter,MontréalNeurologicalInstitute,3801UniversityStreet,MontréalH3A-2B4,Québec,Canada. whererandr'arethree-dimensionalvectorsinimageandobjectreferencespaces,respectively.Iftheactivityf(r)isconsideredtobedistributedoverNfunctionallydistincttissuecomponentsoftrueactivityconcentra-904THEJOURNALOFNUCLEARMEDICINE•ol.39•o.5•May1998  tionT¡,achdefinedoveraspatialdomainD¡,Equation1canbewrittenas:g(r)=T;(r')h(r,r')dr'.Eq.2BecauseT¡(r)sconsideredtobeconstantoverDj(i.e.,homogeneousactivitydistributionwithineachtissuecomponent),Equation2becomes:h(r,r')dr'.Eq.3 D, Theintegrationofthesystem'sPSFh(r)overD|representstheregionalspreadfunction(RSF)oftissuedomainD¡,ssumingaunitactivitydistribution:RSFj(r)=h(r,r')dr'.•'D,Eq.4Inprinciple,tocorrectforpartialvolumeaveragingofvoxelswithdifferentactivity,wecouldconsidereachvoxelasfunctionallyuniqueandperformafullthree-dimensional deconvolution ofthePETimagewiththeinverseofthesystemresponsefunction.Althoughthisisacceptableconceptually,itisimpracticalduetotheresultantnoiseamplification,aswellasitshighcomputationalcost.Ifoneseekstosolvetheimagingequation(Eq.3)forthetrueactivityconcentrations(T¡),tisonlywhenoneisolatedtissuecomponenttakingupthetracerisconsidered(i.e.,n=1)thattheproblemcanbesolveddirectly.Inthiscase,thecorrectedimagebecomesasimpledivisionoftheobservedPETimagebythetissuecomponent'sresponsefunctionRSF,(r).Thishasbeendonewithcorrectionfordilutionofbrainmatteractivitybytracer-freeCSFspaces(19,20).Whenn=2(e.g.,grayandwhitematterregions),theremustbeanaprioriassessmentofoneofthetwounknowns,asinthemethodpresentedbyMüller-Gärtnertal.(27).Theseauthorsidentified true whitematterasaremotelargewhitematterregion,inwhichresolutioneffectswereconsiderednegligibleduetoitsrelativelylargecross-section;theyassumedwhitematteractivitytobeuniformthroughoutthebrain.However,whenthedistributionofactivityisconsideredtobemoreheterogeneous(i.e.,n>2),itbecomesincreasinglydifficulttoaccountforthecontaminationfromatissuecomponentsufferingfromPVEsitself.Forinstance,toaccountforactivityspilledoverfromcorticalgraymatterintoasubcorticalnucleussuchastheamygdala(22),truecorticalgrayactivityisassessedfromthemoreglobalgraymatter-PETimage(21)andisassumedtoreflecttheactivityofgraymatterregionsactuallycontaminatingtheamygdala,withoutbeingitselfcontaminatedbytheamygdalaorotheradjacentstructures.InsteadofconsideringthewholePETimageforsignalrecovery,wecanrestrictthedomainofcalculationofthePSFconvolutionwiththetrueobjectstothelimitedareathatconstitutesaregionofinterest(ROI).ThemeanvalueobservedwithinROIj,isthengivenby:1 Nr 2T¡RSF¡(r)dr, '='•'ROI, Eq.5Equation5canbereexpressedas: tj=2,«ijTi. i=l -if €¢v* RSFi(r)dr.Eq.6Eq.7TheweightingfactorsWyrepresentthecontributionofeachdomainDjtoanyROI¡ftheimageandcanbecomputedforeachcomponentofnonzeroactivitytogenerateamatrixofregionaltransfercoefficients: tlt2IN _=«II «21«12«22«IN«2N «Ml «NN T,T2 Eq.8TheregionalvaluesactuallyobservedwithPET,t¡,andthisknownregionalgeometrictransfermatrix(GTM)representasystemoflinearequationsthatcanbesolvedforthetruevaluesT¡.Whilethediagonaltermsofthismatrixrepresenttissueself-interaction(regionalRC),theoff-diagonaltermso>¡ji1=j)expressthefractionoftrueactivityT¡pilledoverfromdomainD¡ndintegratedinROIj. AccuracyVersusPrecision AlthoughthecalculationoftheinversematrixanddeterminationofthecorrectedvaluesT¡arestraightforward,suchinversionprocedurestendtoincreasethenoisepresentinthecorrectedestimates.ExactdeterminationofthenoiseamplificationrequiresknowledgeofthecovariancestructureoftheGTM(23).However,theerrorattachedtothecorrectedvalueT¡,ntermsofitss.d.dT¡,annotexceedthatobtainedinthecaseofindependentvariables: 1=1 Eq.9whereo>'¡jretheelementsoftheinverseoftheGTMgiveninEquation8,anddtjrepresentsthes.d.attachedtotheobservedvaluetj.AninitialestimateofthenoiseenhancementphenomenonintroducedbythecorrectionprocesscanbederivedfromEquation9,whichrepresentsanupperbound.Wedefinethenoisemagnificationfactor(NMF),astheratioofthecoefficientsofvariation(COVs)afterandbeforePVC:NMF=——.Eq.10BymultiplyingnumeratoranddenominatorbythetrueactivityT,theexpressionoftheNMFbecomes:dTit¡TdT¡and1-|ARCobs-11 dt:i-|ARccor-i| obs NMF=:x--[ARC>0]' wherenpixisthenumberofpixelsinwhereARCistheapparentRC(8),whichrepresentstheratioofregional-to-true(T)activityconcentrationsbefore(ARCohs=t/T)andafter(ARCcor=T/T)PVC.Inmostcases,ARChasavaluesmallerthan1,andtheNMFcanbesimplyexpressed,asinPARTIALVOLUMECORRECTIONNBRAINPET•ousseletal.905  Equation11A,astheproductofthecorrected-to-observedprecisionratio(dT/dtj)andtheobserved-to-correctedaccuracyratio(ARCobs/ARC,.OI.).However,thegeneralexpressionvalidforanyvalueofARCisgivenbyEquation1IB. Implementation MagneticResonanceImaging-BasedModeloftheBrain.With theadventofnewmultimodalityimageregistrationtechniques  24.25),thebrainanatomyanditsunderlyingtraceruptakecanbe accuratelyspatiallyalignedinthreedimensions.TocreateamodelofthebrainprovidingthestructuralinformationnecessaryforPVC,high-resolutionvolumetricMRdataarecollectedusingathree-dimensionalgradient-echosequence(typicallyTE=10ms,TR=18ms,NEX=1,flipangle=30°)andregisteredwiththecorrespondingPETdatausingathree-dimensionallandmark-matchingalgorithm(26).TheregisteredMRIvolumeisthenresampledtothin(1-to2-mm)slicesandprocessedthroughathree-dimensionaltissueclassifier(27)tosegmenttheobjectintoitsmaincomponents,(e.g.,graymatter,whitematterandCSF).Inaddition,becausetissueclassifiersareunsuitablefordiscriminatingbetweencomponentsexhibitingsimilarsignalintensitywithMRI,(e.g.,distinguishingsubcorticalfromcorticalgraymatterregions),theboundariesofsuchstructuresaremanuallyoutlinedfromconsecutiveMRslicescoveringthespecificbrainregion.Theirthree-dimensionalshapeisthenbuiltupfromthestackoftwo-dimensionalROIstocreatevolumesofinterest(8,26,28).TheresultingfullylabeledMRIvolumeisthenassignedwithtracerconcentrationsrepresentingtrueactivitydistributions,assuminguniformuptakewithineachidentifiedtissueorregionalcomponent. PETSimulation.ThePVCalgorithmmakesuseofananalytical three-dimensionalPETsimulatordevelopedbyourgroup,whichincorporatesallthemajorphysicalandstatisticaleffectsthatareinherentinPETdataacquisitionandreconstruction(29,30).ThevariouscomponentsofthepreviouslylabeledMRIvolumeareassignedwithradioactivityconcentrations,andtheresultingidealizedactivitydistributionissampledaccordingtothegeometryofourPC-2048PETscanner(Eq.4).Aspatiallyinvariantthree-dimensionalGaussianfunctionwasusedtoapproximatethethree-dimensionalPSFofthetomograph.ThetrueaxialresolutionofthePC-2048is6.1mmFWHM,whereasthetransverseresolutionrangesfrom4.6mmatthecenteroftheFOVto6.4ataradiusof9cm(31).BecausemoreoftheFOVfallsatlargerdistancefromthecenter,anannular-weightedaveragevaluefortransverseresolutioniscloseto6mm.Therefore,weselectedaGaussianfunctionof6mmFWHMinallthreedirections.ThepropertyofseparabilityofthePETimagingsystemallowsustosimulatethree-dimensionalresolutioneffectsbyfirstconvolvingtheactivitydistributionintheaxialdirectionwithaone-dimensionalGaussianfunction(6mmFWHM),whichmodelstheaxialaperturefunctionofthescanner(i.e.,slicethickness).Idealizedprojectionssinograms(32)ofeachaxiallysmoothedslicearecomputedwithradialandangularsamplingofthescanner,e.g.,128elementsX128anglesX2mmraygeometryforthePC-2048.Theresultingprojectionprofilesarethenconvolvedwithaone-dimensionalGaussianfunction(6mmFWHM)tomodelthetransversedetectorresponsefunction.OtherphysicaleffectsinherenttoPETdataacquisitionsuchasphotonattenuationorscattercountscanbeincludedatthesinogramleveltoproducenoisyPET-likeimages. RegionalSpreadFunctionandGeometricTransferMatrix.To characterizethePETresponsetotheobjectf(r),thedifferenttissuedomainsD¡dentifiedinthecodedMRIvolumeareprocessedseparatelythroughthePETsimulator.ThetissuedomainD¡assignedwithunitactivityisconvolvedwiththethree-dimensionalPSFofthescannerasdescribedabove.Thesimulatedsinogramisthenreconstructedbyuseofthetomograph'sfilteredback-projectionalgorithm,ensuringthesameamountofimagedegradationresultingfromprojectionfilteringandbackprojection(33).TheresultingimagethenrepresentstheresponsefunctionofthescannertocomponentD¡,.e.,RSF¡(r)Eq.4).EachGTMcoefficientü>(¡sthencalculated(Eq.7)astheproportionofthetotalRSF^r)imagedensity(integratedoverallpixelsintheimagevolume)withintheROIjboundary(integratedoverallROIpixels). ExperimentI:SpherePhantom TovalidatetheaccuracyofthesimulatedPSFofthetomograph,weusedawater-filled20-cm-diametercylindercontainingsixhollowsphereswithinnerdiametersrangingfrom4.0to15.5mm.Allthesphereswerefilledwithauniformconcentrationof68Ga(half-life=1.14hr)andscannedwiththeirequatoralignedwithoneoftheringsofthePETscanner.Activityconcentrationatbeginningofscanwas208kBqinl',and2millioneventswerecollected.Imageswerereconstructedwitha5mmFWHMrampfilter,aftercorrectionforattenuationusingatransmission68Garodsourceandforscattercountsusingaone-dimensionaldeconvolu-tionkernelonprojectiondata.Asimulatedversionofthisphantomwasthencreatedthathadgeometricaldimensionsandconfigurationidenticaltothoseofthephysicalphantomandconsistedof2-mm-thickstackeddiskscutfromnumericalspheremodels.Thisprocedurewasdesignedtoavoidthepotentialerrorinobjectsizethatcouldhavebeenintroducedbythesegmentationprocess.Becausewewereonlyinterestedinrelativeintensity,anarbitraryactivityconcentrationwasassignedtothespheremodel,andthecorrectnoiselevelwassetbysimulatingtheacquisitionofatotalof2millioncounts,similartothatrecordedduringtherealPETexperiment.RecoverycoefficientswerecalculatedforeachsphereusingmaximumpixelsandcomparedwiththeoreticalvaluescomputedfromtheGaussianintegraloverasphericalregionofspace(3). ExperimentII:PhysicalBrainPhantom Forvalidationinamorerealisticsetting,aplasticmodelofthebrainprovidedbyDr.DeanWongofJohnsHopkinsUniversity(Baltimore,MD)wasused.Thedesignofthebrainphantomisbasedondigitizedbrainslicesandisintendedtoestimatepartialvolumelossesinneuroreceptorstudies(34).Themodelconsistsofseparatelyfillableplasticcavities,representingthebasalgangliaofthehumanbrain,andplainpolyesterresinmodelsofventricularspaces,locatedinamainTillablechambersimulatingtherestofthebrain,allsurroundedbyahumanskull(Fig.1).Carefultestingofthephantomstructuralintegrityindicatedthattheleftcaudatenucleus(CN)andtheleftglobuspallidus(GP)weredamagedandopentothemaincavity[background(BKG)].Therefore,fortheseexperiments,theleftCNandleftGPcompartmentswerefilledwiththesamesolutionastheBKG.Althoughtheleftputamen(PU)appearedtobestructurallyintact,itsproximitytothedamagedleftCNandleftGPcompartmentsmotivatedourdecisionnottofillitwithradioactivesolutionthatmightleak.Instead,theleftPUcompartmentwasfilledwithwaterandtreatedaspartoftheventricularcompartment. StaticTracerDistribution.Thephantomwascenteredinthe PC-2048PETscannerandunderwentatransmissionscantoaccountforphotonattenuation.ThebrainphantomwasthenfilledwithasolutionoflÃ F-fluorodeoxyglucose(FDG)attwodifferentconcentrations,oneforthesmallcavities(61kBq-ml')andoneforthemainchamber(16kBq-ml').ThePETacquisitionprotocolwastypicalofF-DOPAstudies(35)andwasasfollows:six30-sec,seven1-min,five2-min,four5-minandfive10-minframes.Samplesweretakenfromtheradioactivesolutionsandmeasured 9 6THEJOURNALFNUCLEARMEDICINE€¢ol 39•o 5•May1998  TABLE1 RegionalTransferCoefficientsoftheGeometricTransferMatrix Integrationoftrueactivityconcentration* FIGURE1.Physicalbrainphantomwith top removed,unveilingaplastic modelofthebrainembeddedinadriedskull.IndependentlytillablecavitiesintheshapeofthestriatumallowedfortheassessmentoftheperformanceofthePVCalgorithminconditionsrepresentativetoPETradioligandstudies. withacross-calibratedwellcountertoprovidethetrueisotopeconcentrations.Imageswerereconstructedusinga6mmFWHMManningfilter,aftercorrectionforphotonattenuation,aswellasrandomandscattercounts.Subsequently,atypicalTl-weightedsequenceofthephantomwasacquiredonanMRIunit(GeneralElectric,Milwaukee,WI,1.5T),withthedeepcavitiesfilledwithcoppersulfatesolution(CuSO42-5H2O,0.1mM)toprovidesufficientimagecontrastforfurther tissueclassification. ThevolumetricMRIdatasetwasregisteredwiththehigh-resolution15-slicePETvolumeobtainedbysummingalldynamicframes.TheMRIvolumewasresampledto2-mm-thickimages(26)andsegmentedintoitsvariouscompartments,i.e.,CN,PU,GP,ventriclesandmainchamber(BKG).Thefinitewallthicknessofthephantomcompartmentswasexplicitlydealtwithbyincludinginthesimulationa1-mm-thickboundaryregionaroundeachactivecompartment.ApparentregionalconcentrationswithinfourPETslicesofthephantomweremeasuredusingMRI-basedROIsforeachcompartmentwithnonzeroactivity.SimulatedimagesofeachcomponentwerethengeneratedtoobtainRSFimages(Fig.2),andtheGTMfortheparticularROItemplateandslicewasextracted(Table1).TheobservedregionalvalueswerethencorrectedaccordingtotheestimatedGTM(Eq.8),consideringeitherathree- FIGURE2.ExtractionoftheGTMinthecaseofthephysicalbrainphantom. TheRSFimageofeachcompartment,rightCN(A),rightPU(B),maincavityBKG(C)andrightGP(D),isgeneratedbyassigningunitactivitytothecorrespondingtissuemapidentifiedfromMRimagesandprocessedthroughthePETsimulator.Afterapplicationoftheuser-definedROItemplatenormallyusedforextractingregionaltracerconcentrations,eachRSFimageprovidesacolumnoftheGTM,theelementsofwhichrepresentthefractionoftrueactivityofthetissueineachuser-definedROI.Imageswerereconstructedataresolutionof6mmFWHM.ObservedegionalactivityCNPUBKGGPCN67.243.700.002.15PU1.7748.280.027.04BKG23.3235.*Shownisthepercentageintegrationoftrueactivityconcentrationinselectedregionsintotheobservedregionalactivityinthesameselectedregions.CN=caudatenucleus;PU=putamen;BKG=background;GP=globuspallidus;GTM=geometrictransfermatrix;RSF=regionalspreadfunction.TheGTMwasobtainedfromRSFimagesandROItemplatesshowninFigure2.TheGTMisdependentongeometricalrelationshipsbetweenthestructuresofinterestandontheROIsandimageresolutionusedbutisindependentoftraceractivitydistributionatanytime.Notethat,foragivenstructure,thesumofitsregionaltransfercoefficients^isalwayssmallerthan1duetodilutionofactivityinnonradioactiveregions(e.g.,ventricles). orafour-tissuesystem,i.e.,withorwithoutCN,PU,BKG,GP(Fig.2),dependingonthesliceanalyzed.Wecouldequallyhavechosentoperforma2X2correctioninsteadofa3X3or4X4becausethethreesmallcavitiescontainedthesameconcentrationofradioactivityandcouldberegardedasasingleregion.Thesespacesweretreatedasseparatecompartmentstoevaluatethecross-contaminationfactors,aswouldbethecaseifthetracerdistributionineachoftheCN,PUandGPcompartmentswasdifferent.Analysisoftheimagescollectedwithdifferenttotalcountsalsoallowedforthestudyofstatisticalerrorinthemeasuredmeanregionalvaluesatvaryingnoiseconditions.Therelativedegradationofprecisionwasassessedviathedispersionoftheobserved(corrected)regionalvalueswithrespecttothemeanobserved(corrected)dataovertheentiretimeseries.ThesevalueswerecomparedwithmaximumexpectationsderivedfromEquations9-11B. Dual-IsotopeExperiment.ToinvestigatefurtherPVCperfor mancewithadifferentscannergeometryandchangingtracercontrast,thephantomwasscannedwiththePC-4096systeminstalledatJohnsHopkins.ThemajordifferentphysicalcharacteristictobeaccountedforbetweenthissystemandthatattheMontréalNeurologicalInstitutewasthenumberofdetectors(512insteadof256).MagneticresonancedatawereacquiredonaGeneralElectricSIGNA1.5-Tunitusingaspoiledgradient-recalledacquisitioninthesteady-statesequence(TE=5ms,TR=35ms,NEX=2,flipangle=45°)andstoredasamatrixof256X256X192,withapixelsizeof0.94mm.Tosimulatedifferenttracerkinetics,adual-isotopephantomexperimentwasperformed(11).BoththerightCNandPUcompartmentswerefilledwithanaqueoussolutionofI8F(half-life=110min),whereasthemainchamberwasfilledwitha Csolution(half-life=20min).Tofurthercomplicatethedistributionofactivitywithinthephantom,theGPcompartmentwasfilledwithamixedsolutionofthetwoisotopes.Startingconcentrationswere74kBq-mr'for Cand51.8kBq-ml~'forI8F.Thephantomwasscannedfor85min(~4 Chalf-lives),providingaseriesof60-secframesinterleavedwithtwoshortseriesof15-secframes(oneat10minandtheotherat45min),toobtainnoisierdata.Time-activitycurveswerederivedfromeachstructureononePETslicefromatotalof100reconstructedimageswithoutradioisotopedecaycorrection.ThesameproceduresofsimulationdescribedabovePARTIALVOLUMECORRECTIONNBRAINPET•oussetetal. 907  l I 1.5D/FWHM RGURE3.Real(A)andsimulated(B)imagesofasetofsixspheresof4.0-, 7.5-,8.5-,11.0-,13.0-and15.5-mmdiameters.Theseimageswerereconstructedwitha5-mmFWHMRampfilter.Notethatthesmallestsphereremainspracticallyinvisibleforbothrealandsimulatedcases.(C)RCsasafunctionofspherediameternormalizedtotheimageresolution.ThesolidlineisthetheoreticalintegralofaGaussianoverasphericalregionofspace(3). wereappliedtoprovideaGTMcharacteristicofthegeometricconditionsoftheexperiment.BothobservedandcorrectedTACswerefittedwithmonoexponentialfunctionstoderivethehalf-lifeofbothtracers.Toestimatetheaccuracyofthephysicalhalf-lifeofthetracerbefore/afterPVCforvariousimageresolutions,theanalysiswasrepeatedfordifferentvaluesofreconstructionfilterwidth. RESULTSExperimentI:SpherePhantom Figure3AandB,comparesspherephantomimagesfromrealdataandsimulation.TheRCvaluescorrespondingtotheratioofthepeakvalue(i.e.,5-pixelROI)observedintheimagetotheactualisotopeconcentrationareplottedversusthespherediameternormalizedtotheFWHMofthesystemPSF(Fig.3C).Bothsimulatedandrealdataagreewiththeoreticalcalculations(3)within2%. ExperimentII:PhysicalBrainPhantom StaticTracerDistribution.AtypicalGTMobtainedforthe PETsliceinwhichallthreesmallcavitieswerevisibleispresentedinTable1.Forinstance,ataresolutionof6mmFWHM,theestimatedregionalconcentrationofthecaudatecavity(CN)contains67%ofitsowntrueactivity(trueRC),23%oftrueactivityofthemaincavity(BK.G)and1.8%and0.8%ofPUandGPtrueisotopeconcentrations,respectively(Table1).Thefractionsofcontamination(off-diagonaltermsoftheGTM)mightbeslightlyunderestimatedcomparedtostructuresofcomparablesizeinthebrainduetothewallthicknessofthesmallcavitiesactinglikeanextratracer-freespaceseparatingthesmallcavitiesfromeachotherandfromthemaincompartment.TheprincipalresultsontheaccuracyoftheregionalactivityestimatesbeforeandafterPVCaresummarizedinTable2.Reportedvaluesaremean±s.d.fortheseriesof27images,withthenumberofcountsperslicerangingfrom52,000to1.1million.Therecoveryfactorsfortheobservedvalueswereintherangeof59%-72%forCN,54%-77%forPUand75%forGP,whichwascontainedinasingleslice.Thevaluesforthe volume measurementwereobtainedafterweightedaveragingofthemeanactivitiesfromindividualROIsbytheirrespectiveareaoverfourcontiguousPETslices(Fig.4)andwere67.6%±1.5%forCNand70.1%±0.6%forPU.Partialvolume-correctedestimateswereintherangeof95%-106%oftruevalueforCNand91%-107%forPU.TheanalysisofallfourslicesprovidedanaverageestimateofARCafterPVCof98.5%±2.4%forCNand97.3%±1.1%forPU.FortheGPcompartment,96%recoverywasachievedinthesinglesliceanalyzed(Table2).Therootmean-squaredeviationsfromthemeanobservedvalueswererelativelylowovertheentiretimeseries(<4%;Table2).Asexpected,thefluctuationsaroundthemeanregionalvaluesforsimilarnumberofaccumulatedcountsweremorepronouncedforlowerstatistics(Fig.5).TheNMF,definedastheratioofCOVafterandbeforePVC,wasestimatedexperimentallyfromthemeanregionalactivityvaluesandtheirprecisionobtainedfromtheanalysisofregionalTACs(Table2).ThevaluesoftheNMFforthesmallcavities TABLE2 ApparentRecoveryCoefficientsinDifferentCompartmentsofthePhysicalBrainPhantom SliceVolumeCaudateucleusObservedCorrectedPutamenObservedCorrectedGlobuspallidusObservedCorrectedBackgroundObservedCorrected69.498.254.194.597.097.5±2.6±4.3±3.3±10.7±2.9±2.972.494.775.2107.375.096.197.398.3±2.5±3.8 908THEJOURNALOFNUCLEARMEDICINE•ol.39•o.5•May1998
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