Analysis of Dynamic Brain Imaging Data

arXiv:q-bio/0309028v1[q-bio.NC]20Apr1998AnalysisofDynamicBrainImagingData1P.P.Mitra2andB.PesaranBellLaboratories,LucentTechnologies700,MountainAve.MurrayHill,NJ079741SubmittedtoTheBiophysicalJournal2CorrespondingAuthor:Room1D-268,BellLaboratories,LucentTechnologies,700,MountainAve.,MurrayHill,NJ079741AbstractModernimagingtechniquesforprobingbrainfunction,includingfunctionalMagneticRes-onanceImaging,intrinsicandextrinsiccontrastopticalimaging,andmagnetoencephalography,generatelargedatasetswithcomplexcontent.Inthispaperwedevelopappropriatetechniquesofanalysisandvisualizationofsuchimagingdata,inordertoseparatethesignalfromthenoise,aswellastocharacterizethesignal.Thetechniquesdevelopedfallintothegeneralcategoryofmultivariatetimeseriesanalysis,andinparticularweextensivelyusethemultitaperframeworkofspectralanalysis.WedevelopspecificprotocolsfortheanalysisoffMRI,opticalimagingandMEGdata,andillustratethetechniquesbyapplicationstorealdatasetsgeneratedbytheseimagingmodalities.Ingeneral,theanalysisprotocolsinvolvetwodistinctstages:‘noise’characterizationandsuppression,and‘signal’characterizationandvisualization.Animpor-tantgeneralconclusionofourstudyistheutilityofafrequency-basedrepresentation,withshort,movinganalysiswindowstoaccountfornon-stationarityinthedata.Ofparticularnoteare(a)thedevelopmentofadecompositiontechnique(‘space-frequencysingularvaluedecom-position’)thatisshowntobeausefulmeansofcharacterizingtheimagedata,and(b)thedevelopmentofanalgorithm,basedonmultitapermethods,fortheremovalofapproximatelyperiodicphysiologicalartifactsarisingfromcardiacandrespiratorysources.Keywords:SpectralAnalysis,functionalmagneticresonanceimaging(fMRI),opticalimaging,magnetoencephalography(MEG),multivariatetimeseriesanalysis,singularvaluedecomposition.1IntroductionThebrainconstitutesacomplexdynamicalsystemwithalargenumberofdegreesoffreedom,sothatmultichannelmeasurementsarenecessarytogainadetailedunderstandingofitsbehavior.Suchmulti-channelmeasurements,madeavailablebycurrentinstrumentation,includemulti-electroderecordings,opticalbrainimagesusingintrinsic(BlasdelandSalama,1986),(Grinvaldetal.,1992)orextrinsic(Davilaetal.,1973)contrastagents,functionalmagneticresonanceimaging(fMRI)(Ogawaetal.,1992),(Kwongetal.,1992)andmagnetoencephalography(MEG)(Hamalainenetal.,1993).Duetoimprovementsinthecapabilitiesofthemeasuringapparatus,aswellasgrowthincomputationalpowerandstoragecapacity,thedatasetsgeneratedbytheseexperimentsareincreasinglylargeandmorecomplex.Theanalysisandvisualizationofsuchmultichanneldataisanimportantpieceoftheassociatedresearchprogram,andisthesubjectofthispaper.Thereareseveralcommonproblemsassociatedwiththedifferenttypesofmultichanneldataenumeratedabove.Firstly,preprocessingisnecessarytoremovenuisancecomponents,arisingfrombothinstrumentalandphysiologicalsources,fromthedata.Secondly,anappro-priaterepresentationofthedataforpurposesofanalysisandvisualizationisnecessary.Thirdly,thereisthetaskofextractinganyunderlyingsimplicitiesfromthesignal,mostlyinabsenceofstrongmodelsforthedynamicsoftherelevantpartsofthebrain.Iftherearesimplefeaturesthatarehiddeninthecomplexityofthedata,thentheanalyticalmethodologyshouldbesuchastorevealsuchfeaturesefficiently.Withthecurrentexponentialgrowthincomputationalpowerandstoragecapacity,itisincreasinglypossibletoperformtheabovestepsinasemi-automatedway,andeveninrealtime.Infact,thisisalmostapre-requisitetothesuccessofmulti-channelmeasurements,sincethelargedimensionalityofthedatasetseffectivelyprecludeexhaustivemanualinspectionbythehumanexperimenter.Anadditionalchallengeistoperformtheabovestepsasfaraspossibleinrealtime,thusallowingquickfeedbackintotheexperiment.Theintimateinterplaybetweenthebasicexperimentalapparatusandsemi-automatedanalysisandvisualizationisschematicallyillustratedinFig.1.Notethatevengiventheincreasesinstoragecapacity,itisdesirabletohavewaysofcompressingthedatawhileretainingtheappropriateinformation,soastopreventsaturationoftheavailablestorage.Problemssuchastheaboveareclearlynotuniquetoneuroscience.Automatedanalysisplaysanimportantroleintheemergentdisciplineofcomputationalmolecularbiology.Despitethecurrentrelevanceoftheseproblems,theappropriateanalyticalandcomputationaltoolsareinanearlystageofdevelopment.Inaddition,investigatorsinthefieldaresometimesunawareoftheappropriatemodernsignalprocessingtools.Sincelittleisunderstoodaboutthedetailedworkingsofthebrain,astraightforwardexploratoryapproachusingcrudeanalysisprotocolsisusuallyfavored.However,giventheincreasingavailabilityofcomputationalresources,thisunnecessarilylimitsthedegreeofknowledgethatcanbegainedfromthedata,andatworstcanleadtoerroneousconclusions,forexamplewhenstatisticalmethodsareappliedinappropriately(cf.(Cleveland,1993)p.177).Ontheotherhand,asuperficialapplicationofcomplexsignalprocessingorstatisticaltechniques,canleadtoresultsthataredifficulttointerpret.Anaspectofthethedatainquestionthatcannotbeemphasizedenoughisthefactthatthedataconstitutetimeseries,mostlymultivariate.Whiletechniquesfortreatingstatichigh-dimensionaldataarewidelykno