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A geometric model for 3-D confocal image analysis

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A geometric model for 3-D confocal image analysis
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  AGeometricModelfor3   D  ConfocalMicroscopeImageAnalysis     A.Sarti,C.OrtizdeSolorzano,S.LockettandR.Malladi  MS50A-1148,1CyclotronRoad LawrenceBerkeleyNationalLaboratory UniversityofCalifornia Berkeley,CA94720  Abstract  Inthispaper,weusepartialdierentialequationbasedanalysisasamethodologyfor computer-aidedcytology.Wewishtoaccuratelyextractandclassifytheshapesofnucleifrom noisyconfocalmicroscopyimages.Thisisaprerequisitetoanaccuratequantitativeintranuclear (genotypicandphenotypic)andinternuclear(tissuestructure)analysisofcancerousandpre- cancerousspecimens.Westudytheuseofageometric-drivenschemeforimprovingtheresults obtainedbyanautomatednuclearsegmentationmethod,followedbyobjectreconstructionand interactiveclassication.Webuildachainofmethodsthatincludesanedge-preservingimage smoothingmechanism,anautomaticsegmentationmethod,ageometry-drivenschemetoreg- ularizetheshapesandimproveedgedelity,andaninteractivemethodtosplitshapeclusters andreclassifythem.Wetestthedenoisingandshapeextractionstepsonmanyrealconfocal microscopeimagesandmeasuretheimprovementwhencomparedtoothermethods. Keywords:  Cytology,Imageprocessing,Segmentation,Dynamicsurfaces,LevelSets,Dier- entialgeometry,Riemanniangeometry,Surfaceevolution  Correspondingauthor:Dr.RaviMalladi MS50A-2152 LawrenceBerkeleyNationalLaboratory UniversityofCalifornia Berkeley,CA94720 Phone:(510)-486-6020Fax:(510)-486-6199    Theauthorscanbereachedat  f  asarti,malladi g  @math.lbl.gov,and  f  carlos,lockett  g  @black.lbl.gov. 1   1Introduction  Cytologyshowsthatthecellsinatissuebecomeincreasinglyheterogeneousintheirstructural propertiesduringcarcinogenesis,whilehistologyshowsincreasingdisorganizationofthecells.Fur- thermore,whetherapre-cancerousorcancerouslesionprogresses,isstableorentersremissionis likelytodependonthechemicalandphysicalenvironmentofthecellinthelesion9]12]20]in additiontotheinternalpropertiesofthecells.Inordertounderstandthesestructuralalterations,togetherwiththemolecularmechanismsunderlyingthem,itisnecessarytoanalyzethecellsin- dividuallyandwithintheirnaturaltissuecontext.Sincemanyofthestructuralandmolecular changesoccurwithinthecell'snucleus,theabilitytosegmenttheindividualnucleiinintacttissue isthereforeanimportantandbasictechnicalcapability.Toobtainquantitativelyaccuratemeasurementsattheindividualnucleuslevel,itisnecessary toanalyzeintactnuclei.Therefore,thick(  >  20micron)sectionsmustbeemployed,whichrequires three-dimensional(3  D  )(confocal)microscopicimageacquisition33]followedby3  D  imageanaly- sis.Inordertofacilitatethesegmentationofnucleifromimages,itisusualtolabelthespecimen withauorescentDNAcounterstain,becauseitproducesveryhighcontrastimagescontaininghigh intensitynuclearregionsversuslowintensitynon-nuclear(background)regions.Actualsegmenta- tionofnucleicanbeobtainedbyeitherinteractiveorautomaticalgorithms.Interactivemethods,basedondrawingaroundnucleiinsequence6]25]ororthogonal13]2  D  slicesaresuperiorin performance(denedasthefractionofnucleicorrectlysegmented)basedonvisualjudgementof theresultscomparedtoautomaticalgorithms.However,theyareslow,tedious,andrequireintense humaneort,typicallytakingmanyminutespernucleusandarethuslimitedintheirpractical applicationtosituationswhereonlyfewnucleirequireanalysis.Automaticalgorithms3]10]23],ontheotherhandaremuchfaster,enablingtheanalysisof 100sofofnucleiperstudy:Theperformanceoftheautomaticmethodsisonlyhigh(  >  90%)for specimenscontainingisolatednuclei.Moreover,performancesignicantlydeterioratesformany cancerspecimens,becausethecellsarestructurallydominatedbytheirnucleileavinglittlesepa- ratingcytoplasmandthustheimagesshowclusterednuclei.Thisisthekindofbiologicalspecimen weareinterestedtostudyandthereforetheaccuracyofthesegmentationmethodcallsforim- 2   SAMPLE PREPARATIONANDIMAGE ACQUISITIONSHAPE REFINEMENTBASED PDE-  AUTOMATIC SEGMENTATION3D IMAGE DENOISINGBASED PDE-  CLUSTER SEGMENTATION PDE-  BASED (a)  Figure1:Flowchartdepictingthesequenceofstepsweundertake provement.Tothisend,our3  D  segmentationapproachcombinesthespeedofautomaticimage analysisalgorithmswiththeperformanceofinteractivealgorithmsbyincludingvisualinspection stagesinthemethod.Thisenablesthecorrectsegmentationofahighproportionofindividual nucleiinintacttissue,whilegreatlyreducingusereortandprovidingcomparableaccuracyto thatofmanualmethodsforsegmentingcellnuclei.Themethodstillneedsimprovementsbyway ofbetteredgedelityespeciallyforclustersofhighlyirregularnucleiandfornucleiwithhighly unevenDNAstaining.Encouragedbytherecentadvances15]16]17]18]32]2]26]29]19]inpartialdierentialequa- tionbasedimageanalysistools,inthispaper,weextendandapplysomeofthosemethodsto confocalmicroscopeimageanalysis.Specically,weareinterestedinrstpre-processingagiven 3  D  imagetoreducenoisebypayingcloseattentiontotheedgegeometry,andthenexpressing thenuclearsegmentationasthesolutionofaninitialvaluepartialdierentialequation.Weshow 3   thebenetofusingthegeometricmethodviaadetailedcomparisontoothermethodsandtabu- latingthemeasurementsunderavarietyofnoiseconditionsonbothsyntheticandrealconfocal images.Thethemeofthispaperistostartwithagoverningequationthatisexpressedviaan Euler-Lagrangeofafunctionalandtoexploititsmanyinterpretations;theseincludetasksranging fromedge-preservingimagedenoising,shapeextractionin3  D  ,curvaturebasedmin-owtorida givenshapeofitsholes,andtosplitnuclearclustersinordertore-classifythem.Variousformsof ourequationarethenimplementedusingthelevelset24]methodsandtheecientnarrow-band versions1]15]ofit.TheowchartinFig.1showstheexactsequenceofstepsweundertakein ordertoanalizea3  D  confocalmicroscopeimage.Therestofthepaperisorganizedasfollows:inSection2wedescribetheimageacquisition methodincludingthesamplepreparation.InSection3weintroducethemainequationandwe outlineitsrelevantfeatures.Thissetsthestagefortheworktofollowonpartialdierentialequation basedmethods.InSection4,weinterpretthemainequationasanimageprocessingalgorithmand showitsapplicationtoconfocalmicroscopeimagedenoising.Inthissection,wealsoquantifythe benetofemployingthegeometriclterforimageprocessingbycomparingitsperformancewith thatofamedianlter.InSection5wepresentourautomaticsegmentationmethod.InSection 6,weexaminethegeometricinterpretationofourmainmodelandshowthatitcanbeusedfor shaperenement.Inthepresentcontextitisusedtoimprovethebinarysegmentationprovided bytheautomaticmethod.Finally,inSection7weusevariationsofourmainmodelforcluster classication;specically,weshowhowholeeliminationcanbeperformedviaacurvaturebased ow,andnallyweuseamultipleinterfaceversionofourgeometricmodeltoextracttheshapes ofnucleiavoidingtheirmerger. 2SamplePreparationandImageAcquisition  CellnucleicanbestainedusinguorescentcompoundsthathaveanitywithDNA,suchas PropidumIodide(PI),4',6-Diamidino-2-phenylindole(DAPI),Hoechst33342,etc.SinceDNA occupiesmostofthenucleus,thesourcesofuorescenceexistonlywithinthevolumesoccupied bythenuclei.Therefore,attheopticaluorescemicroscope,nucleicanbeseenasbrightcircles againstablackbackground.Ifthelightemittedbytheuorochromeisimagedusingarecording 4   device,suchasaCCD,theimagessoacquiredwouldcontainbright(white)circles(nuclei)and backgroundunstainedareas.Inconventionalmicroscopyonlythinsectionsoftissue(2-dimensionallayerofcells)canbe observed.Thislimitationderivesfromthefactthatinthicksamples,wherenucleioverlap,light fromnucleithatareoutoffocusblurstheinformationthatisinfocusresultinginpoorimagery.Confocalmicroscopyprovidesaconvenientwaytoovercomethisproblem,andthereforetolookat thicksectionsoftissue.Theunwantedout-of-focusinformationiseliminatedbyusingtwopinholes locatedattheemission(specimen)anddetection(image)endsoftheimagingsystem.Thisway,onlyaclear,sharpimageofthein-focusplaneisobtained.Movingthespecimenintheaxial direction,imagescanbetakenatdierentpositionandstoreasa3  D  imagesetthatcanbeseen asanopticalsectioningofthetissue.Allourspecimensconsistedoftissuebiopsiestakenfromhumanormousetissuerepositories.Typicalexamplesandcorrespondingdetailsareasfollows:   Humanskinspecimens(S)wereobtainedfromthearchivesoftheDermatopathologySections oftheDepartmentsofPathologyandDermatology,UniversityofCalifornia,SanFrancisco.Humanbreastspecimenscontaininginvasivecarcinomainsituparts(I)wereobtainedfrom theDepartmentofPathology,CaliforniaPacicMedicalCenter(CPMC),SanFrancisco.Bothskinandbreastspecimenshadbeenxedin10paran-embeddedbeforereceipt.The tissueblockswerecutinto20micronsectionsandstainedwithPIat0.1mgmL,andmounted inglycerol.   Formalin-xed,paranembeddedMCF7cells(ahumanbreastcancercellline)thathad beengrowninnudemiceasaxenograft(X)wereprovidedbyDr.GailColbern(Geraldine BrushCancerResearchInstitute,CPMC).Thexenograftswerecutto30micronthickness,stainedusingYO-PRO-1(MolecularProbes,Eugene,OR),andmountedonglycerol.   SSpecimenswereimagedusinganMRC-1000confocalimagingsystem(Bio-RadMicro- scienceLtd.HelmelHempstead,U.K.)equippedwithaDiaphot200microscope(NikonInc.,InstrumentGroup,GardenCity,NY)a60x,1.4PlanApoobjectivelens(Nikon)andan Argon/Krypton(Ar/Kr)laser.I&Xspecimenswereimagedusingalaserscanningconfocal 5 
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