HREEPARIETALCIRCUITSFORNUMBERStanislasDehaene,ManuelaPiazza,PhilippePi - PDF document

HREEPARIETALCIRCUITSFORNUMBERStanislasDehaene,ManuelaPiazza,PhilippePinel,andLaurentCohenINSERM-CEA,ServiceHospitalierFrédéricJoliot,Orsay,FranceDidevolutionendowthehumanbrainwithapredispositiontorepresentandacquireknowledgeabout Houillier,1961;Henschen,1919).Subsequently,asystematicactivationoftheparietallobesduringcalculation,togetherwithprecentralandprefrontalcortices,wasdiscovered(Roland&Friberg,1985)andextensivelyreplicatedusingpositronemissiontomography(PET)(Dehaeneetal.,1996;Pesenti,Thioux,Seron,&DeVolder,2000;Zago,Pesenti,Mellet,Crivello,Mazoyer,&Tzourio-Mazoyer,2001)andlaterfMRI(Burbaud,Camus,Guehl,Bioulac,Caille,&Allard,1999;Rueckertetal.,1996).Onthisbasis,someofusproposedthattheparietallobecontributestotherepresentationofnumericalquantityonamental“numberline”(Dehaene&Cohen,1995).Unfortunately,duetopoorspatialresolutionandlimitsonexperimentaldesigns,thosestudiesdidnotpermitafinerexplorationoftheregionsinvolvedindifferentkindsofnumericaltasks.Thishasbecomecritical,however,becauserecentbehaviouralstudieshavemadeitclearthatmentalarithmeticreliesonahighlycom-positesetofprocesses,manyofwhichareprobablynotspecifictothenumberdomain.Forinstance,studiesoflanguageinterferenceinnormalsubjectssuggestthatlanguage-basedprocessesplayanimportantroleinexactbutnotapproximatecalcu-lation(Spelke&Tsivkin,2001).Likewise,concur-rentperformanceofaspatialtaskinterfereswithsubtraction,butnotmultiplication,whileconcur-rentperformanceofalanguagetaskinterfereswithmultiplication,butnotsubtraction(Lee&Kang,2002).SuchbehaviouraldissociationssuggestthattheneuralbasesofcalculationmustbeThetriple-codemodelofnumberprocessingpredictsthat,dependingonthetask,threedistinctsystemsofrepresentationmayberecruited:aquantitysystem(anonverbalsemanticrepresentationofthesizeanddistancerelationsbetweennumbers,whichmaybecategoryspecific),averbalsystem(wherenumeralsarerepresentedlexically,phonologically,andsyntactically,muchlikeanyothertypeofword),andavisualsystem(inwhichnumberscanbeencodedasstringsofArabicnumerals)(Dehaene,1992;Dehaene&Cohen,1995).Weinitiallyproposedthattheparietalactivationsduringnumberprocessingreflectedsolelythecontributionofthequantitysystem.However,itisnowclearthatthishypothesisrequiresfurtherelaboration.First,theleftperisylvianlanguagenetworkclearlyextendsintotheinferiorparietallobe.Second,theposteriorsuperiorparietallobesarestronglyengagedinvisualattentionprocessesthatmaycontributetothevisualprocessingofnumbers.Itisthuscrucialtodistinguish,withintheobservedparietallobeactivationsduringnumberprocessing,whichactivationsites,ifany,areassociatedwithasemanticrepresentationofnumericalquantityandwhichcorrespondtononspecificverbalorvisual/attentionalsystems.Fortunately,functionalmagneticresonanceimaging(fMRI)hasrecentlyallowedmuchfiner-grainedstudiesoftheneuroanatomyofnumberprocessing,usingparadigmsadaptedfromcognitivepsychology.Thepresentreviewfocusesentirelyontheparietallobeactivationsidentifiedbythoserecentneuroimagingstudies.Weusethree-dimensionalvisualisationsoftwaretoinves-tigatehowtheparietalactivationsreportedbyvariousstudiesrelatetooneanotherincorticalspace.Onthisbasis,weproposethatthreecircuitscoexistintheparietallobeandcapturemostoftheobserveddifferencesbetweenarithmetictasks:abilateralintraparietalsystemassociatedwithacorequantitysystem,aregionoftheleftangulargyrusassociatedwithverbalprocessingofnumbers,andaposteriorsuperiorparietalsystemofspatialandnonspatialattention.Itshouldbeemphasisedthatourdescriptionprovidesonlyatentativemodel.Althoughitisbasedonasynthesisoftheexistingliterature,thismodelremainsspeculativeandwillrequirefurthervalidationbydirectexperimentation.Foreachpostulatedcircuit,wefirstexaminetherelevantneuroimagingliterature,andthenconsiderhowthosebrain-imagingresultsimpingeonourunderstandingofneuropsychologicalimpairmentsofnumberprocessing.Ouraccountpredictsthatdependingonlesionlocalisation,threedifferentcategoriesofnumericalimpairmentsshouldbeobserved:genuinesemanticimpairmentsofthenumericaldomainfollowingintraparietallesions;impairmentsofverbalfactretrievalfollowinglesionstotheleftperisylviancortices,includingtheleftangulargyrus;andimpairmentsofspatialDEHAENEETAL.COGNITIVENEUROPSYCHOLOGY,2003,20(3/4/5/6) attentiononthenumberlinefollowinglesionstothedorsalparietalattentionsystem.THEBILATERALHORIZONTALSEGMENTOFTHEINTRAPARIETALSULCUSANDQUANTITYPROCESSINGNeuroimagingevidenceThehorizontalsegmentoftheintraparietalsulcus(hereafterHIPS)isamajorsiteofactivationinneuroimagingstudiesofnumberprocessing.AsshowninFigure1a,thisregionliesattheintersectionoftheactivationsobservedinmanydifferentnumberprocessingtasks(seeTable1).Whatseemstobecommontothosetasksistherequirementtoaccessasemanticrepresentationofthequantitythatthenumbersrepresent.Weproposethatanonverbalrepresentationofnumericalquantity,perhapsanalogoustoaspatialmapor“numberline,”ispresentintheHIPSofbothhemispheres.Thisrepresentationwouldunderlieourintuitionofwhatagivennumericalsizemeans,andoftheprox-imityrelationsbetweennumbers.Insupportofthisview,severalfeaturesofitsresponsivenesstoexperi-mentalconditionsareworthnoting.Mentalarithmetic.TheHIPSseemstobeactivewheneveranarithmeticoperationcallsuponaquantitativerepresentationofnumbers.Forexample,itismoreactivewhensubjectscalculatethanwhentheymerelyhavetoreadnumericalsymbols(Burbaudetal.,1999;Chochon,Cohen,VandeMoortele,&Dehaene,1999;Pesentietal.,2000),suggestingthatitplaysaroleinthesemanticmanipulationofnumbers.Itsactivationincreases,atleastintherighthemisphere,whensubjectshavetocomputetwoadditionorsubtractionoperationsinsteadofone(Menon,Rivera,White,Glover,&Reiss,2000).Furthermore,evenwithincalculation,theHIPSismoreactivewhensubjectsestimatetheapproximateresultofanadditionproblemthanwhentheycomputeitsexactsolution(Dehaene,Spelke,Stanescu,Pinel,&Tsivkin,1999).Finally,itshowsgreateractivationforsubtractionthanformultiplication(Chochonetal.,1999;Lee,2000).Multiplicationtablesandsmallexactadditionfactscanbestoredinroteverbalmemory,andhenceplaceminimalrequirementsonquantitymanipulation.Contrariwise,althoughsomesubtractionproblemsmaybestoredinverbalmemory,manyarenotlearnedbyroteandthereforerequiregenuinequantitymanipulations.Inanotherstudy,relativetofivedifferentvisuospatialandphonologicalnon-numericaltasks,subtractionwastheonlytaskthatledtoincreasedactivationoftheHIPS(Simon,Cohen,Mangin,Bihan,&Dehaene,Numbercomparison.TheHIPSisalsoactivewheneveracomparativeoperationthatneedsaccesstoanumericalscaleiscalledfor.Forinstance,itismoreactivewhencomparingthemagnitudesoftwonumbersthanwhensimplyreadingthem(Chochonetal.,1999).Thesystematiccontribu-tionofthisregiontonumbercomparisonprocessesisreplicatedinmanyparadigmsusingtomographicimaging(LeClec’Hetal.,2000;Pesentietal.,2000;Pinel,Dehaene,Riviere,&LeBihan,2001;Thioux,Pesenti,Costes,DeVolder,&Seron,2002)aswellasscalprecordingsofevent-relatedpotentials(Dehaene,1996).Parietalactivationinnumbercomparisonisoftenlargerintherightthaninthelefthemisphere(Chochonetal.,1999;Dehaene,1996;Pineletal.,2001).Thismaypointtoapossibleright-hemisphericadvantageincomparisonandinothertasksrequiringanabstractionofnumericalrelations(Langdon&Warrington,1997;Rosselli&Ardila,1989).However,incomparison,theparietalactivation,althoughitmaybeasymmetric,isalwayspresentinbothhemispheres,compatiblewiththeobservationthatnumericalcomparisonisaccessibletobothhemispheresinsplit-brainpatients(Cohen&Dehaene,1996;Seymour,Reuter-Lorenz,&Gazzaniga,1994).Specificityforthenumberdomain.SeveralstudieshavereportedgreaterHIPSactivationwhenprocessingnumbersthanwhenprocessingothercategoriesofobjectsonnon-numericalscales(suchascomparingtheferocityofanimals,therelativepositionsofbodyparts,ortheorientationoftwoCOGNITIVENEUROPSYCHOLOGY,2003,20(3/4/5/6)PARIETALNUMBERPROCESSINGCIRCUITS DEHAENEETAL.COGNITIVENEUROPSYCHOLOGY,2003,20(3/4/5/6) z=44 x=39 x=-48 x=54 x=-49 z=30x=12 B.C. 50 % 22% z=49z=61x=-26 Figure1.Regionsofoverlappingactivityforthreegroupsofstudies,superimposedonaxialandsagittalslicesofanormalisedsingle-subjectanatomicalimage.Theoverlapwascalculatedbyaveragingbinarisedcontrastimagesindicatingwhichvoxelsweresignificantforagivencontrast(studiesandcontrastsarelistedinTable1).Thecolourscaleindicatesthepercentageofstudiesshowingactivationinagivenvoxel.Thesamecolourscale(from22%to50%ofoverlap)isappliedtoallimages.Althoughnosinglevoxelwassharedby100%ofstudiesinagroup,probablyduetovariabilityacrossgroupsofsubjects,laboratories,andimagingmethods,Table1revealedahighconsistencyofactivations.(A)Thehorizontalsegmentoftheintraparietalsulcus(HIPS)wasactivatedbilaterallyinavarietyofcontrastssharingacomponentofnumericalquantitymanipulation.Thebarycentreoftheregionofmaximumoverlap�(50%)wasatTalairachCoordinates(TC)41,–42,49inthelefthemisphere,and–48,–41,43intherighthemisphere.Activationoverlapisalsovisibleintheprecentralgyrus.(B)Theangulargyrus(AG)wasactivatedwithastrongleftlateralisation(TC–48,–59,30)in5studiesofarithmetictaskswithastrongverbalcomponent.Posteriorcingulateaswellassuperiorfrontalregionsalsoshowsomedegreesofoverlap.(C)Theposteriorsuperiorparietallobule(PSPL)wasactivatedbilaterallyinafewnumericaltasks(leftandrightbarycentresatTC–26,–69,61and12,–69,61;andseeTable1).Toemphasisethenonspecificityofthisregion,theimageshowstheintersectionoftheoverlapbetweenfournumericaltaskswithanimageofposteriorparietalactivityduringanon-numericalvisualattentionshifttask(Simonetal.,2002). visuallypresentedcharacters:LeClec’Hetal.,2000;Pesentietal.,2000;Thiouxetal.,2002).Event-relatedpotentialshavealsorevealedgreaterparietalactivationfornumbersthanforothercategoriesofwordssuchasactionverbs,namesofanimals,ornamesoffamouspersons(Dehaene,1995).Inthisstudy,thefirstpointintimeinwhichcategory-specificsemanticeffectsemergeduringvisualwordprocessingwasfoundtobe250–280msfollowingstimulusonset.OnestudydirectlytestedthespecificityoftheHIPSforthenumericaldomaininmultipletasks(Thiouxetal.,2002).Subjectswerepresentedwithnumberwordsandnamesofanimalsmatchedforlength.TheHIPSshowedgreateractivation,bilaterally,tonumbersthantoanimalnames.Thiswastruewhethersubjectswereengagedinacomparisontask(largerorsmallerthan5;moreorlessferociousthanadog),acategorisationtask(oddoreven;mammalorbird),orevenavisualjudgementofcharactershape.Thus,theHIPSshowscategoryspecificityindependentlyoftaskcontext.Furtherresearchwillbeneeded,however,todecidewhetheritisstrictlyspecificfornumbersorwhetheritCOGNITIVENEUROPSYCHOLOGY,2003,20(3/4/5/6)PARIETALNUMBERPROCESSINGCIRCUITS Table1.StudiesandcontrastsusedtoisolatethethreeparietalregionsinFigures1and2 CoordinatesofmaximaLeftRight——————————ReferenceContrastxyzxyz Horizontalsegmentofintraparietalsulcus(HIPS)Chochonetal.(1999)Comparisonofone-digitnumbersvs.letternaming–45–423939–4242Chochonetal.(1999)Subtractionofone-digitnumbersfrom11vs.comparison–42–484839–4242Dehaeneetal.(1999)Approximatevs.exactadditionofone-digitnumbers–56–445244–3652Lee(2000)Subtractionvs.multiplicationofone-digitnumbers–31–524928–5452NaccacheandDehaene(2001)Subliminalquantityprimingacrossnotations–44–565636–4444Piazzaetal.(2002)Numerosityestimationvs.physicalmatchingn.s.44–5654Pineletal.(2001)Distanceeffectincomparisonoftwo-digitnumbers–40–443644–5648Simonetal.(2002)Subtractionofone-digitnumbersfrom11vs.letternaming–48–445252–4452Stanescu-Cossonetal.(2000)Sizeeffectinexactadditionofone-digitnumbers–44–5248n.s.–44–484741–4748756775 Angulargyrus(AG)Chochonetal.(1999)Multiplicationvs.comparisonofone-digitnumbers–30–6939n.s.Dehaeneetal.(1999)Exactvs.approximateadditionofone-digitnumbers–44–723640–7620Lee(2000)Multiplicationvs.subtractionofone-digitnumbers–49–5431n.s.Simonetal.(2002)Intersectionofsubtractionandphonemedetectiontasks–31–7043n.s.Stanescu-Cossonetal.(2000)Inversesizeeffectinexactadditionofone-digitnumbers–52–6832n.s.–41–6636 Posteriorsuperiorparietallobule(PSPL)Dehaeneetal.(1999)Approximatevs.exactadditionofone-digitnumbers–32–685620–6060Lee(2000)Subtractionvs.multiplicationofone-digitnumbers–29–646921–6165NaccacheandDehaene(2001)Subliminalquantityprimingacrossnotationsn.s.12–6048Pineletal.(2001)Distanceeffectincomparisonoftwo-digitnumbers–4–72448–7252–22–685615–635615412668Ineachcase,wereportthecoordinatesofactivationmaxima,theirmean,andtheirstandarddeviation(n.s.=notsignificant).Insomestudies,wereportthecoordinatesofsubpeaksnotreportedinthedigitalpapers,whichonlyreportedasingleglobalmaximumforeachcluster. extendstoothercategoriesthathaveastrongspatialorserialcomponent(e.g.,thealphabet,days,months,spatialprepositions,etc.).Parametricmodulation.ParametricstudieshaverevealedthattheactivationoftheHIPSismodulatedbysemanticparameterssuchastheabsolutemagnitudeofthenumbersandtheirvaluerelativetoareferencepoint.Thus,intraparietalactivityislargerandlastslongerduringoperationswithlargenumbersthanwithsmallnumbers(Kiefer&Dehaene,1997;Stanescu-Cosson,Pinel,VandeMoontele,LeBihan,Cohen,&Delaene,2000).Itisalsomodulatedbythenumericaldistanceseparatingthenumbersinacomparisontask(Dehaene,1996;Pineletal.,2001).Ontheotherhand,theactivationoftheHIPSisindependentoftheparticularmodalityofinputusedtoconveythenumbers.Arabicnumerals,spelled-outnumberwords,andevennonsymbolicstimulilikesetsofdotsortonescanactivatethisregionifsubjectsattendtothecor-respondingnumber(LeClec’Hetal.,2000;Piazza,Mechelli,Butterworth,&Price,2002a;Piazza,Mechelli,Price,&Butterworth,2002b;Pineletal.,2001).Inonestudy,subjectsattendedeithertothenumerosityortothephysicalcharacteristics(col-our,pitch)ofseriesofauditoryandvisualevents.TherightHIPSwasactivewheneverthesubjectsattendedtonumber,regardlessofthemodalityofthestimuli(Piazzaetal.,2002b).Inanotherstudy,theactivationofthebilateralHIPSwasfoundtocorrelatedirectlywiththenumericaldistancebetweentwonumbersinacomparisontask,andthiseffectwasobservedwhetherthenumberswerepresentedaswordsorasdigits(Pineletal.,2001).ThoseparametricstudiesareallconsistentwiththehypothesisthattheHIPScodestheabstractquantitymeaningofnumbersratherthenumericalsymbolsthemselves.Unconsciousquantityprocessing.QuantityprocessingandHIPSactivationcanbedemonstratedevenwhenthesubjectisnotawareofhavingseenanumbersymbol(Dehaeneetal.,1998b;Naccache&Dehaene,2001).Inthisexperiment,subjectswereaskedtocomparetargetnumberstoafixedreferenceof5.Unbeknownsttothem,justpriortothetarget,anothernumber,theprime,wasbrieflypresentinasubliminalmanner.FMRIrevealedthattheleftandrightintraparietalregionsweresensitivetotheunconsciousrepetitionofthesamenumber.Whentheprimeandtargetcorrespondedtothesamequantity(possiblyintwodifferentnotations,suchasONEand1),lessparietalactivationwasobservedthanwhentheprimeandtargetcorrespondedtotwodistinctquantities(e.g.,FOURand1).Thisresultsuggeststhatthisregioncomprisesdistinctneuralassembliesfordifferentnumericalquantities,sothatmoreactivationcanbeobservedwhentwosuchneuralassembliesareactivatedthanwhenonlyoneis.ItalsoindicatesthatthisregioncancontributetonumberprocessinginasubliminalTakentogether,thesedatasuggestthattheHIPSisessentialforthesemanticrepresentationofnumbersasquantities.Thisrepresentationmayprovideafoundationforour“numericalintuition,”ourimmediateandoftenunconsciousunderstand-ingofwhereagivenquantityfallswithrespecttoothers,andwhetherornotitisappropriatetoagivencontext(Dehaene,1992,1997;Dehaene&Marques,2002).NeuropsychologicalevidenceNeuropsychologicalobservationsconfirmtheexis-tenceofadistinctsemanticsystemfornumericalquantitiesanditsrelationtothevicinityoftheintraparietalsulcus.Severalsingle-casestudiesindicatethatnumbersdoublydissociatefromothercategoriesofwordsatthesemanticlevel.Ontheonehand,sparedcalculationandnumbercomprehensionabilitieshavebeendescribedinpatientswithgrosslydeterioratedsemanticprocessing(Thioux,Pillon,Samson,DePartz,Noel,&Seron,1998)orsemanticdementia(Butterworth,Cappelletti,&Kopelman,2001;Cappelletti,Butterworth,&Kopelman,2001).Inbothcases,thelesionsbroadlyaffectedthelefttemporo-frontalcorticeswhilesparingtheintraparietalregions.Ontheotherhand,Cipolotti,Butterworth,andDenes(1991)reportedastrikingcaseofapatientwithasmallleftparietallesionandanalmostcompletedeficitinallspheresofnumberprocessing,sparingDEHAENEETAL.COGNITIVENEUROPSYCHOLOGY,2003,20(3/4/5/6) onlythenumbers1through4,inthecontextofotherwiselargelypreservedlanguageandsemanticfunctions.Althoughsuchasevereandisolateddegradationofthenumbersystemhasneverbeenreplicated,othercasesconfirmthattheunderstandingofnumbersandtheirrelationscanbespecificallyimpairedinthecontextofpreservedlanguageandsemantics(e.g.,Dehaene&Cohen,1997;Delazer&Benke,1997).Inmanycases,thedeficitcanbeextremelyincapacitating.Patientsmayfailtocomputeoperationsassimpleas2+2,3–1,or3×9.Severalcharacteristicsindicatethatthedeficitarisesatanabstract,notation-independentlevelofprocessing.First,patientsmayremainfullyabletocomprehendandtoproducenumbersinallformats.Second,theyshowthesamecalculationdifficultieswhethertheproblemispresentedtothemvisuallyorauditorily,andwhethertheyhavetorespondverballyorinwriting,orevenmerelyhavetodecidewhetheraproposedoperationistrueorfalse.Thus,thecalcu-lationdeficitisnotduetoaninabilitytoidentifythenumbersortoproducetheoperationresult.Third,thedeficitoftenextendstotasksoutsideofcalcula-tionperse,suchascomparisonorbisection.Forinstance,patientMAR(Dehaene&Cohen,1997)showedamildimpairmentindecidingwhichoftwonumbersisthelarger(16%errors),andwasalmosttotallyunabletodecidewhatnumberfallsinthemiddleoftwoothers(bisectiontask:77%errors).Heeasilyperformedanalogouscomparisonandbisectiontasksinnon-numericaldomainssuchasdaysoftheweek,months,orthealphabet(WhatisbetweenTuesdayandThursday?FebruaryandApril?BandD?).Thistypeofdeficitsseemsbestdescribedasacategory-specificimpairmentofthesemanticrepresentationandmanipulationofnumericalquantities(Dehaene&Cohen,1997),ratherthanwiththemereclinicallabelofInsuchpatients,calculationimpairmentsoftenco-occurwithotherdeficits,formingaclusterofdeficitscalledGerstmann’ssyndrome(Benton,1992;Gerstmann,1940),whichcomprisesagraphia,fingeragnosia,andleft–rightdistinctiondifficulties(towhichonemayoftenaddconstructiveapraxia).ThelesionsthatcauseacalculiaoftheGerstmann’stypearetypicallycentredinthedepthoftheleftintraparietalsulcus(Mayer,Martory,Pegna,Landis,Delavelle,&Annoni,1999;Takayama,Sugishita,Akiguchi,&Kimura,1994).Thisiscompatiblewiththeabovebrain-imagingresultsshowingintraparietalactivationduringvariousnumericalmanipulationtasksindependentlyoflanguage.Resultsfromarecentbrain-imagingstudy(Simonetal.,2002)shedsomelightonwhythevariouselementsofGerstmann’ssyndromeoftenco-occurfollowingleftintraparietallesions.Inthisstudy,fMRIwasusedtocompare,inthesamesubjects,thelocalisationofparietalactivationsduringanumbersubtractiontaskwiththoseobservedduringvarioustasksthatalsoinvolvetheparietallobe,suchaseyeorattentionmovements,fingerpointing,handgrasping,andalanguagetaskofphonemedetection.Theresultsrevealedasystematictopographicalorganisationofactivationsandtheirintersections.Inparticular,theintraparietalsulcusappearstocontainsa“four-cor-ners”regioninwhichfourareasofactivationarejuxtaposed:calculationonly,calculationandlan-guage,manualtasksonly,andanareaactivateddur-ingthefourvisuospatialtasks(eyeandattentionmovements,pointing,andgrasping).Thesimulta-neouslesionofthosefourareaswouldpredictablyresultinjointimpairmentsofcalculation,wordprocessing(possiblyincludingagraphia),fingerknowledgeandmovement,andhigh-levelspatialreference(possiblyincludingunderstandingofleft–rightcoordinates).Suchajointlesionmightbefrequentbecausethiscorticalterritoryisjointlyirrigatedbyabranchofthemiddlecerebralartery,theangulargyrusartery.Inter-individualvariabilityintheboundariesbetweencorticalterritoriesaswellasinthebranchingpatternsofthisarterywouldexplainthatthedifferentelementsofGerstmann’ssyndromecanbedissociated(Benton,1961,1992).Notethatthisinterpretationimpliesthat,contrarytoafrequentspeculation,Gerstmann’ssyndromedoesnotresultfromahomogeneousimpairmenttoasinglerepresentationthatwouldsomehowinterminglefingers,numbers,andspace(Butterworth,1999;Gerstmann,1940;Mayeretal.,1999).Rather,thesyndromemayrepresentahappenstanceconjunctionofdistinct,butdissociable,COGNITIVENEUROPSYCHOLOGY,2003,20(3/4/5/6)PARIETALNUMBERPROCESSINGCIRCUITS deficitsthatfrequentlyco-occurduetoacommonvascularisation,andthatareonlylooselyconnectedatthefunctionallevelduetotheoverarchingspatialandsensorimotorfunctionsoftheparietallobe.THELEFTANGULARGYRUSANDVERBALNUMBERMANIPULATIONSNeuroimagingevidenceTheleftangulargyrus(hereafterAG)isalsooftenactivatedinneuroimagingstudiesofnumberprocessing(seeFigure1bandTable1).Thisregionisleft-lateralisedandlocatedposteriorandinferiortotheHIPS(seeFigure2fortheirrespectivelocations).Acloserlookatthetypesofnumericaltasksthatactivatethisregion,detailedbelow,revealsthatitsfunctionalpropertiesareverydifferentfromthepropertiesoftheHIPS.TheleftAGdoesnotseemtobeconcernedwithquantityprocessing,butshowsincreasinglygreateractivationasthetaskputsgreaterrequirementonverbalprocessing.Wethereforeproposethatthisregionispartofthelanguagesystem,andcontributestonumberprocessingonlyinasmuchassomearithmeticoperations,suchasmultiplication,makeparticularlystrongdemandsonaverbalcodingofnumbers.Insupportofthishypothesis,theleftAGisnotmerelyinvolvedincalculation,butindifferenttypesoflanguage-mediatedprocessessuchasreadingorverbalshort-termmemorytasks(forreviews,seeFiez&Petersen,1998;Paulesu,Frith,&Frackowiak,1993;Price,1998).InSimonetal.’s(2002)fMRIstudyofsixdifferenttasks,theleftangulargyruswastheonlyparietalsitewherethereDEHAENEETAL.COGNITIVENEUROPSYCHOLOGY,2003,20(3/4/5/6) LefthemisphereTopview leftangulargyrus(AG) bilateralposteriorsuperiorparietallobe(PSPL) bilateralhorizontalsegmentofintraparietalsulcus(HIPS) RighthemisphereFigure2.Three-dimensionalrepresentationoftheparietalregionsofinterest.Forbettervisualisation,theclustersshowallparietalvoxelsactivatedinatleast40%ofstudiesinagivengroup. wasoverlappingactivityforcalculationandphonemedetection,butnoactivationduringtheotherfourvisuospatialtasks.ThisclearlyindicatesthattheleftAGisnotspecificforcalculation,butjointlyrecruitedbylanguageandcalculationprocesses.Evenwithincalculation,severalstudiesindicateamodulationofAGactivationindirectproportiontotheverbalrequirementsofthetask.First,theAGismoreactiveinexactcalculationthaninapproximation(Dehaeneetal.,1999).Thisfitswithbehaviouraldataindicatingthatexactarithmeticfactsarestoredinalanguage-specificformatinbilinguals,whileapproximateknowledgeislanguage-independentandshowstheclassicalnumericaldistanceeffectassociatedwiththenonverbalquantitysystem(Xu&Spelke,2000).Second,withinexactcalculation,theleftAGshowsgreateractivationforoperationsthatrequireaccesstoaroteverbalmemoryofarithmeticfacts,suchasmultiplication,thanforoperationsthatarenotstoredandrequiresomeformofquantitymanipulation.Forinstance,theleftAGshowsincreasedactivationformultiplicationrelativetobothsubtractionandnumbercomparison(Chochonetal.,1999;Lee,2000),formultiplicationanddivisionrelativetoalettersubstitutioncontrol(Gruber,Indefrey,Steinmetz,&Kleinschmidt,2001),andformultidigitmulplicationrelativetoadigit-matchingcontrol(Fulbright,Molfese,Stevens,Skudlarski,Lacadie,&Gore,2000).Evenwithinagivenoperation,suchassingle-digitaddition,theleftangulargyrusismoreactiveforsmallproblemswithasumbelow10thanforlargeproblemswithasumabove10(Stanescu-Cosson,Pinel,VandeMoortele,LeBihan,Cohen,&Dehaene,2000).Thisprobablyreflectsthefactthatsmalladditionfacts,justlikemultiplicationtables,arestoredinroteverbalmemory,whilebehaviouralevidenceindicatesthatlargeradditionproblemsareoftensolvedbyresortingtovarioussemanticelaborationstrategies(Dehaene&Cohen,1995;Lefevre,1996).Insummary,thecontributionoftheleftangulargyrusinnumberprocessingmayberelatedtothelinguisticbasisofarithmeticalcomputations.Itscontributionseemsessentialfortheretrievaloffactsstoredinverbalmemory,butnotforothernumericaltasks(likesubtraction,numbercomparison,orcomplexcalculation)thatcallforagenuinelyquantitativerepresentationofnumbersandrelatemoretotheintraparietalsulcus.Neuropsychologicalevidence:DissociationsbetweenoperationsThefindingthattheintraparietalsulcusandtheangulargyrusexhibitfunctionallydifferentiatedpropertiescanshedlightontheneuropsychologyofacalculia.Oneofthemoststrikingfindingsistheoccurrenceofsharpdissociationsbetweenarithmeticoperations.Itisnotrareforapatienttobemuchmoreseverelyimpairedinmultiplicationthaninsubtraction(Cohen&Dehaene,2000;Dagenbach&McCloskey,1992;Dehaene&Cohen,1997;Lampl,Eshel,Gilad,&Sarova-Pinhas,1994;Lee,2000;Pesenti,Seron,&VanderLinden,1994;VanHarskamp&Cipolotti,2001),whileotherpatientsaremuchmoreimpairedinsubtractionthaninmultiplication(Dehaene&Cohen,1997;Delazer&Benke,1997;VanHarskamp&Cipolotti,2001).Somehaveproposedthatsuchdissociationsreflectrandomimpairmentsinasys-temwithdistinctstoresofarithmeticfactsforeachoperation(Dagenbach&McCloskey,1992).Here,however,wewouldliketoshowthatthereismuchmoresystematicitybehindthoseobservations.Ourviewssuggestthatdissociationsbetweenoperationsreflectasingle,basicdistinctionbetweenoverlearnedarithmeticfactssuchasthemultiplicationtable,whicharestoredinroteverbalmemory,andthegenuineunderstandingofnumbermeaningthatunderliesnontableoperationssuchassubtraction(Dehaene&Cohen,1997;Delazer&Benke,1997;Hittmair-Delazer,Sailer,&Benke,1995).Accordingtothisinterpretation,multiplicationrequirestheintegrityoflanguage-basedrepresentationsofnumbers,becausemultiplicationfactsaretypicallylearnedbyroteverbalmemorisation.Subtraction,ontheotherhand,istypicallynotlearnedbyrote.Althoughthemechanismsbywhichsimplesubtractionproblemsareresolvedarenotyetunderstood,itislikelythatsomeformofinternalmanipulationofnonverbalquantitiesontheinternalnumberlineisinvolved,asattestedbythefactCOGNITIVENEUROPSYCHOLOGY,2003,20(3/4/5/6)PARIETALNUMBERPROCESSINGCIRCUITS thatverysimplesubtractionsareaccessibletopreverbalinfants(Wynn,1992)andnonhumanprimates(Hauseretal.,2000).Supportforthisviewcomesfromseverallinesofresearch.First,asnotedearlier,imagingstudiesinnormalsconfirmthatdistinctsitesofactivationsunderlieperformanceinsimplemultiplicationandsubtraction(Chochonetal.,1999;Cohen,Dehaene,Chochon,Lehéricy,&Naccache,2000;Lee,2000).Second,allpatientsinwhomsubtractionwasmoreimpairedthansubtractionhadleftparietallesionsand/oratrophy,mostoftenaccompaniedbyGerstmann’ssyndrome,compatiblewithanimpairmenttotheleftHIPSandtothesemanticrepresentationofnumericalquantities(Dehaene&Cohen,1997;Delazer&Benke,1997;VanHarskamp&Cipolotti,2001).Conversely,althoughthisisnotalwaysthoroughlydocumented,patientsinwhommultiplicationismoreimpairedthansubtractiontypicallyhaveassociatedaphasia(e.g.,Cohenetal.,2000;Dehaene&Cohen,1997).Furthermore,thelesionsoftensparetheintraparietalcortexandcanaffectmultipleregionsknowntobeengagedinlanguageprocessing,suchastheleftperisylviancorticesincludingtheinferiorparietallobule(Cohenetal.,2000),theleftparieto-temporalcarrefour(Lampletal.,1994),ortheleftbasalganglia(Dehaene&Cohen,1997).Multiplicationimpairmentswithsparedsubtractionhavealsobeenreportedintwopatientswithreadingdeficitsinwhomthelesionaffectedaccesstothelanguagesystemfromvisualsymbols(Cohen&Dehaene,2000;McNeil&Warrington,1994).Amazingly,oneofthosepatientswasabletosubtractbetterthanshecouldreadthesameproblems(Cohen&Dehaene,2000).Thisconfirmstherelativeindependenceofsubtraction,butnotmultiplication,fromthelanguagesystem.PerhapsthebestevidenceforadissociationbetweenquantityprocessingintheHIPSandverbalnumberprocessingintheleftAGcomesfromtwostudiesofthetemporarycalculationimpairmentscausedbyelectricalbrainstimulation.Inonepatientwithstripsofsubduralelectrodesarrangedovertheleftparietal,superiortemporal,andposteriorfrontalregions,asingleelectrodesitewasfoundwhosestimulationsystematicallydisruptedmultiplicationperformancemuchmorethanadditionperformance(27%vs.87%correct;subtractionwasnottested;Whalen,McCloskey,Lesser,&Gordon,1997).Althoughlimitedinformationisavailableonlocalisation,thiselectrodewaslocatedintheleftinferiorparietalregion,apparentlyclosetotheangulargyrus.Interestingly,multiplicationperformancewasworsewhentheresponsesweregivenorally(27%correct)thanwhentheyweretypedwithakeypad(64%correct),suggestingthatstimulationalsointerferedwiththeverbalcodingofAsecondcasepresentedadoubledissociationbetweensubtractionandmultiplication(Duffauetal.,2002).Corticalstimulationwasperformedintra-operativelyduringtheresectionofaparieto-occipitalglioma.Twoneighbouringsiteswerefoundwithintheleftparietallobe.Thefirst,locatedwithintheangulargyrusproper(approxi-mateTalairachcoordinates–50,–60,+30),dis-ruptedmultiplicationbutnotsubtractionwhenstimulated.Thesecond,locatedmoresuperiorilyandanteriorilywithintheintraparietalsulcus(TC–45,–55,+40),disruptedsubtractionbutnotmul-tiplication.Anintermediatelocationwasalsofoundwherestimulationdisruptedbothopera-tions.Thereportedcoordinates,althoughimpre-cisegiventhedistortionspossiblyinducedbythegliomaandthesurgery,arecompletelycompatiblewiththedissociatedareasofactivationobservedinfunctionalbrainimaging(Chochonetal.,1999;Lee,2000).Tocloseontheissueofdissociationsbetweenoperations,webrieflyconsiderthecaseofaddition(seealsoCohen&Dehaene,2000).Additioniscomplexbecauseitcanbesolvedinatleasttwoways.Itissimilartomultiplicationinthatmanypeoplehavememorisedmostofthebasicadditiontable(singledigitadditionfactswithasumbelow10).However,additionisalsosimilartosubtractioninthatsimpleadditionproblemscanalsobesolvedbyquantitymanipulationstrategies,somethingthatwouldbeutterlyimpracticalwithmultiplication.Thus,additionperformanceishardtopredict.Indeed,inourexperience,itvariesconsiderablyDEHAENEETAL.COGNITIVENEUROPSYCHOLOGY,2003,20(3/4/5/6) acrosspatientsorevenwithinpatients,dependingonthestrategythattheyadopt.Theonlyclearpredictionfromourmodelisthatadditionperformancecannotdissociatefromsubtractionandmultiplicationtogether.Thatistosay,apatientcannotbeimpairedinaddition,butnotinsubtractionnorinmultiplication(sincethelatterwouldimplythatboththeverbalandthequantitycircuitsareintact);norcanapatientshowpreservedadditionwithimpairedsubtractionandmultiplication(sincethelatterwouldimplythatbothsystemsareIfdissociationsbetweenoperationsfollowedachancepattern,thispredictionshouldbeviolatedinaboutonethirdofcases.Infact,however,itisconfirmedbyessentiallyallpatientstodate(10outof11patients:Cohen&Dehaene,2000;Dagenbach&McCloskey,1992;Dehaene&Cohen,1997;Delazer&Benke,1997;Lampletal.,1994;Lee,2000;Pesentietal.,1994;VanHarskamp&Cipolotti,2001).Theonlyexception(patientFS,VanHarskamp&Cipolotti,2001)isworthdis-cussing.Overall,thispatientwas96.3%correct(156/162)insingle-digitsubtractionandmultipli-cation,butonly61.7%correct(100/162)insingle-digitaddition,thussuperficiallyqualifyingasastraightforwardviolationofourhypothesis.How-ever,thepatternoferrorsinthispatientwasquitedifferentfromothercasesofacalculia;87%ofhisadditionerrorsconsistedofselectingthewrongoperation(healmostalwayssolvedthecorrespondingmultiplicationproblem,e.g.,3+3=9).Thisisverydifferentfromtheothertwopatientsreportedinthesamepaper:patientDT,whowasimpairedinsubtraction,madeonly12.5%operationerrors,andpatientVP,whowasimpairedinmultiplication,only3.5%.Inareanalysis,weexcludedpatientFS’soperationerrorsandanalysedonlytheremainingtrials,inwhichhewaspresumablyreallyattemptingtoaddtheoperands.Inthisway,wecanestimatepatientFS’sconditionalsuccessrateinaddition,giventhatheisreallytryingtoadd.Thissuccessrateis92.6%correct(100/108),avaluewhichdoesnotdifferfromtheperformanceobservedintheothertwooperations(96.3%correct).Thus,itcanbearguedthatpatientFSexperienceslittledifficultywitharithmeticoperationsperse,butexhibitsaselectivedeficitinchoosingtheappropriateoperation.Exactlyhowsubjectstransformthetaskinstructionsandoperationsignsintotheselectionofanappropriateinformation-processingcircuitisleftlargelyunspecifiedincurrentmodels.Nevertheless,deficitsaffectingthistask-settinglevelshouldbekeptconceptuallydistinctfromthegenuineimpairmentsinarithmeticalcomputationitself.Insummary,areviewofneuropsychologicaldissociationsbetweenarithmeticoperationsindicatesthatitisnotnecessarytopostulateasmanybraincircuitsastherearearithmeticaloperations(Dagenbach&McCloskey,1992).Rather,mostifnotallcasessofarcanbeaccommodatedbythepostulateddissociationbetweenaquantitycircuit(supportingsubtractionandotherquantity-manipulationoperations)andaverbalcircuit(supportingmultiplicationandotherrotememory-basedoperations).THEPOSTERIORSUPERIORPARIETALSYSTEMANDATTENTIONALPROCESSESNeuroimagingevidenceAthirdregion,observedbilaterallyintheposteriorsuperiorparietallobule(hereafterPSPL),withafrequentmesialextensionintotheprecuneus,isalsoactiveinseveraltasksrequiringnumbermanipulations.ThisregionisposteriortotheHIPS,andoccupiesalocationsuperiorandmesialtotheAGinthesuperiorparietallobule(seeFigure1candFigure2).Itisactiveduringnumbercomparison(Pesentietal.,2000;Pineletal.,2001),approximation(Dehaeneetal.,1999),subtractionoftwodigits(Lee,2000),andcounting(Piazzaetal.,2002a).Italsoappearstoincreaseinactivationwhensubjectscarryouttwooperationsinsteadofone(Menonetal.,2000).However,thisregionisclearlynotspecifictothenumberdomain.Rather,italsoplaysacentralroleinavarietyofvisuospatialtasksincludinghandCOGNITIVENEUROPSYCHOLOGY,2003,20(3/4/5/6)PARIETALNUMBERPROCESSINGCIRCUITS reaching,grasping,eyeand/orattentionorienting,mentalrotation,andspatialworkingmemory(Corbetta,Kincade,Ollinger,McAvoy,&Shulman,2000;Culham&Kanwisher,2001;Simonetal.,2002).Forexample,WojciulikandKanwisher(1999)haveobservedoverlappingactivationsinthisregioninthreetasksthatallsharedacomponentofattention-orienting.Similarly,Simonetal.(2002)observedthatthisregionwasactivatedduringeyemovement,attentionmovements,grasping,andpointing.Thecontributionofthisregiontospatialattentionand/oreyeorientingprobablyexplainsitsactivationduringcounting,wheresubjectsaresequentiallyattendingtotheenumeratedobjects.However,spatialattentiondoesnotseemtoexplainitsactivationduringpurelynumericaloperationsofcomparison,approximation,orsubtraction.Inallofthosetasks,number-relatedactivationinthePSPLwasobservedrelativetoacontrolthatusedthesamespatialdistributionofstimulionscreen,aswellasaverysimilarmotorresponse.Obviously,anyreconciliationofthosesparseanddisparatedatasetmustremaintentative.Thehypothesisthatwewouldliketoproposeisthatthisregion,inadditiontobeinginvolvedinatten-tionorientinginspace,canalsocontributetoattentionalselectiononothermentaldimensionsthatareanalogoustospace,suchastime(Coull&Nobre,1998;Wojciulik&Kanwisher,1999)ornumber.Psychologicalexperimentsindicatethatthecoresemanticrepresentationofnumericalquantitycanbelikenedtoaninternal“numberline,”aquasispatialrepresentationonwhichnumbersareorganisedbytheirproximity(Dehaene,Bossini,&Giraux,1993;Moyer&Landauer,1967).Itisthenconceivablethatthesameprocessofcovertattentionthatoperatestoselectlocationsinspacecanalsobeengagedwhenattendingtospecificquantitiesonthenumberline.Suchnumber-basedattentionwouldbeparticularlyneededintasksthatcallfortheselectionofoneamongstseveralquantities,forinstancewhendecidingwhichoftwoquantitiesisthelarger(Pesentietal.,2000;Pineletal.,2001),orwhichoftwonumbersapproximatelyfitsanadditionproblem(Dehaeneetal.,1999).Neuropsychologicalevidence:JointimpairmentsofattentionandnumberOnlyafewneuropsychologicalandbrainstimulationfindingsprovidesomesupportforouradmittedlyspeculativetheory.Inarecentstudyusingtranscranialmagneticstimulationwithnormalsubjects,Gobel,Walsh,andRushworth(2001)firstlocatedleftandrightdorsalposteriorparietalsiteswherestimulationinterferedwithperformanceinavisualserialsearchtask.Thecoordinatesofthoseregionscorrespondtothoseofthebilateralposteriorparietalregionsfoundactiveinneuroimagingstudiesofeyeandattentionorienting(Corbettaetal.,2000;Simonetal.,2002;Wojciulik&Kanwisher,1999).Theythentestedtheeffectofmagneticstimulationatthoselocationsonatwo-digitnumbercomparisontask.Onstimulatedtrials,comparisonperformancewassignificantlyslower.Interestingly,thenumericaldistanceeffectitselfwasstillpresentandrelativelyunchanged(althoughstimulationonthelefttendedtointerferemorewithnumbersclosetothereference,particu-larlythosethatwerelargerthanthereference).Thissuggeststhatthestimulationdidnotdirectlyinter-ferewithacorerepresentationofnumericalquan-tity,butratherwiththeresponsedecisionprocessitself.Attheveryleast,thisexperimentconfirmsthatspatialattentionorientingandnumericalcomparisonbothengagethisparietalregion,thusconfirmingpreviousbrain-imagingevidence(Pineletal.,2001).Furthersupportforacloseinterplaybetweentherepresentationsofspaceandnumbersisprovidedbyastudywithunilateralneglectpatients(Zorzi,Priftis,&Umiltà,2002).Itisawell-known,indeedalmostadefiningfeatureofthosepatientsthattheyperformpoorlyinspatialbisectiontests.Whenaskedtolocatethemiddleofalinesegment,neglectpatientswithrightparietallesionstendtoindicatealocationfurthertotheright,consistentwiththeirfailuretoattendtotheleftsideofspace.Zorzietal.testedtheirperformanceinatask,wheretheywereaskedtofindthemiddleoftwoorallypresentednumbers.Strikingly,patientserredsystematically,oftenselectinganumberfarDEHAENEETAL.COGNITIVENEUROPSYCHOLOGY,2003,20(3/4/5/6) largerthanthecorrectanswer(e.g.,Q:Whatnumberfallsinbetween11and19?A:17).Thissuggeststhatspatialattentioncanbeorientedontheleft-to-rightorientednumberline,andthatthisattention-orientingprocesscontributestotheresolutionofsimplearithmeticproblemssuchasthebisectiontest.Interestingly,thesepatientsweresaidnottobeacalculicanddidnotshowanydeficitinothernumericaltaskssuchassimplearithmeticfactretrieval.Indeed,VuilleumierandRafal(1999)demonstrated,onadifferentgroupofpatientswithneglect,thataposteriorparietallesiondoesnotimpairthemerequantificationofsmallnumberofitems.Neglectpatientswereabletoestimatenumerositywithsetsofuptofourobjectsevenwhensomeofenumerateditemsfellintheneglectedfield.Again,thissuggeststhatattentionalandnumericalsystemsaredissociable.However,Zorzietal.’sfindingof“representationalneglect”onthenumericalcontinuumindicatesthatspatialattentionprocessesdocontributetosomenumericaltasks.DEVELOPMENTALDYSCALCULIAANDTHEONTOGENYOFNUMBERWhetherornotourfunctionalcharacterisationofthreeparietalsubsystemsiscorrect,itisananatomicalfactthatthoseactivationssitesarestrikinglyreproducible.ItisremarkablethattheHIPS,AG,andPSPLaresystematicallyactivatedindifferentsubjects,oftenfromdifferentcountries,withdifferenteducationalstrategiesandachievementsinmathematics(Stevenson&Stigler,1992),andwithadiversityoflinguisticschemesforexpressingnumber(Hurford,1987).EventhefinedissociationbetweensubtractionandmultiplicationisreproduciblewithFrenchvs.Koreansubjects(Cohenetal.,2000;Lee,2000).Suchsystematicityintheanatomicalorganisationofparietalnumericalprocessesmustbereconciledwiththeobviousfactthatarithmeticis,inpart,arecentculturalOurhypothesisisthattheculturalconstructionofarithmeticismadepossiblebypre-existingcerebralcircuitsthatarebiologicallydeterminedandareadequatetosupportspecificsubcomponentsofnumberprocessing(Dehaene,1997).Thishypothesissupposesaninitialprespecialisationofthebraincircuitsthatwillultimatelysupporthigh-levelarithmeticinadults.Itimpliesthatitshouldbepossibletoidentifyprecursorsofthosecircuitsininfancyandchildhood.Indeed,quantityprocessingispresentataveryyoungage.Infantsintheirfirstyearoflifecandiscriminatecollectionsbasedontheirnumerosity(Dehaeneetal.,1998a;Starkey&Cooper,1980;Wynn,1992),evenwhenthenumbersareaslargeas8vs.16(Xu&Spelke,2000).Althoughnobrain-imagingevidenceisavailableininfantsyet,wespeculatethatthisearlynumericalabilitymaybesupportedbyaquantityrepresentationsimilartoadults’(Dehaene,1997;Spelke&Dehaene,1999).Thisrepresentationwouldserveasafoundationfortheconstructionofhigher-orderarithmeticalandmathematicalconcepts.Thehypothesisofanearlyemergenceofquantity,verbal,andattentionalsystemsleadstoseveralpredictionsconcerningnormalandimpairednumberdevelopment:Brainactivationininfancyandchildhood.Aprecur-soroftheHIPSregionshouldbeactiveininfantsandyoungchildrenduringnumerositymanipula-tiontasks.Atpresent,thispredictionhasonlybeentestedwith5-year-oldchildreninanumbercomparisontask(E.Temple&Posner,1998).Event-relatedpotentialsrevealedthescalpsignatureofanumericaldistanceeffect,withatopographysimilartoadults,commontonumberspresentedasArabicnumeralsorassetsofdots.Thereisaclearneedtoextendthosedatatoanearlierageandwithagreateranatomicalaccuracy.Developmentaldyscalculiaandtheparietallobe.Deficitsofnumberprocessingshouldbeobservedincaseofearlyleftparietalinjuryordisorganisation.Developmentaldyscalculiaisrelativelyfrequent,affecting3–6%ofchildren(Badian,1983;Kosc,1974;Lewis,Hitch,&Walker,1994).Wepredictthatafractionofthosechildrenmaysufferfromacoreconceptualdeficitinthenumericaldomain.Indeed,a“developmentalGerstmannsyndrome”COGNITIVENEUROPSYCHOLOGY,2003,20(3/4/5/6)PARIETALNUMBERPROCESSINGCIRCUITS hasbeenreported(Benson&Geschwind,1970;Kinsbourne&Warrington,1963;Spellacy&Peter,1978;C.M.Temple,1989,1991).Inthosechildren,dyscalculiaisaccompaniedbymostorallofthefollowingsymptoms:dysgraphia,left–rightdisorientation,andfingeragnosia,whichsuggestaneurologicalinvolvementoftheparietallobe.Interestingly,eveninasampleof200normalchildren,atestoffingerknowledgeappearstobeabetterpredictoroflaterarithmeticabilitiesthanisatestofgeneralintelligence(Fayol,Barrouillet,&Marinthe,1998).Tworecentreportsdirectlyrelatedevelopmentaldyscalculiatoanunderlyingleftparietaldisorganisation.Levy,Reis,andGrafman(1999)reportthecaseofanadultwithlifelongisolateddyscalculiatogetherwithsuperiorintelligenceandreadingability,inwhomthestandardanatomicalMRIappearednormal,yetMRspectroscopytechniquesrevealedametabolicabnormalityintheleftinferiorparietalarea.Similarly,Isaacs,Edmonds,Lucas,andGadian(2001)usedvoxel-basedmorphometrytocomparegraymatterdensityinadolescentsbornatequallyseveregradesofprematurity,halfofwhomsufferedfromdyscalculia.Theyfoundasingleregionofreducedgraymatterintheleftintraparietalsulcus.TheTalairachcoordinatesofthisregion(–39,–39,+45)arequiteclosetothecoordinatesoftheHIPS.Subtypesofdevelopmentaldyscalculia.Asinadultacalculia,atleasttwosubtypesofdevelopmentaldyscalculiashouldbeobserved,andthoseshouldbetraceabletoadifferentialimpairmentofquantityvs.languageprocessingcircuits.Althoughseveraldistinctionsbetweensubtypesofdevelopmentaldyscalculiahavebeenproposed(e.g.,Ashcraft,Yamashita,&Aram,1992;Geary,Hamson,&Hoard,2000;Rourke&Conway,1997;C.M.Temple,1991),mostarebasedongroupstudiesandstandardisedbatteriesoftests,whichareinappropriatefortestingthepredictedsubtledistinctionsbetween,e.g.,subtractionandmultiplication.Oneexceptionisthesingle-casestudyofpatientHM(C.M.Temple,1991),whosufferedfromdevelopmentalphonologicaldyslexia.Hisdeficitinarithmeticwasmostlylimitedtomultiplicationfacts,whileheexperiencednodifficultyinsolvingsimpleadditionandsubtractionproblemswithnumbersofthesamesize.Ourviewpredictsthattheassociationofverbalandmultiplicationimpairmentsobservedinthisstudyshouldbegeneralisable.Multiplicationdeficitsshouldbepresentincasesofdyscalculiaaccompaniedbydysphasiaand/ordyslexia,whilesubtractionandquantity-manipulationdeficitsshouldbepresentinpatientswithdyscalculiabutwithoutanyaccompanyingdyslexiaorlanguageretardation.Althoughthisproposalremainslargelyuntested,Gearyetal.(2000)doreportinterestingdifferencesbetweendevelopmentaldyscalculicswithorwithoutassociateddyslexia.Whenfacedwiththesamesimpleadditionproblems,nondyslexicstendtousefactretrievalmuchmoreoftenthandodyslexics,whoratherusefinger-countingstrategies.Thisisconsistentwiththehypothesisthatanimpairmentofroteverbalmemoryispartiallyresponsiblefordys-calculiainchildrenwithdyslexia.Geneticsofdevelopmentaldyscalculia.Ifthebiologi-calpredispositionviewiscorrect,specificcombina-tionsofgenesshouldbeinvolvedinsettinguptheinternalorganisationoftheparietallobeand,inparticular,thedistinctionbetweenquantityandlanguagecircuits.Thus,itshouldbepossibletoidentifydyscalculiasofgeneticorigin.Theavailabledata,indeed,indicatethatwhenachildisdyscalculic,otherfamilymembersarealsofrequentlyaffected,suggestingthatgeneticfactorsmaycontributetothedisorder(Shalevetal.,2001).Althoughthesearchfordyscalculiasofgeneticoriginhasonlyveryrecentlybegun,thepossibilitythatTurnersyndromemayconformtothistypologyhasrecentlyattractedattention.TurnersyndromeisageneticdisordercharacterisedbypartialorcompleteabsenceofoneXchromosomeinafemaleindividual.Thedisorderoccursinapproximately1girlin2000andisassociatedwithwell-documentedphysicaldisordersandabnormaloestrogenproductionandpubertaldevelopment.Thecognitiveprofileincludesdeficitsinvisualmemory,visual-spatialandattentionaltasks,andsocialrelations,inthecontextofanormalverbalIQ(Rovet,1993).MostinterestinglyinthepresentcontextisDEHAENEETAL.COGNITIVENEUROPSYCHOLOGY,2003,20(3/4/5/6) thedocumentationofamildtoseveredeficitinmathematics,particularlyclearinarithmetic(Mazzocco,1998;Rovet,Szekely,&Hockenberry,1994;C.M.Temple&Marriott,1998).Anatomically,thedatasuggestpossiblebilateralparieto-occipitaldysfunctioninTurnersyndrome.Apositronemissiontomographystudyoffiveadultwomendemonstratedaglucosehypometabolisminbilateralparietalandoccipitalregions(Clark,Klonoff,&Hadyen,1990).TwoanatomicalMRstudies,onewith18andtheotherwith30affectedwomen,demonstratedbilateralreductionsinparieto-occipitalbrainvolume,togetherwithothersubcorticalregions(Murphyetal.,1993;seealsoReissetal.,1993;Reiss,Mazzocco,Greenlaw,Freund,&Ross,1995).Interestingly,thephenotypeofTurnersyndromecandifferdependingonwhethertheremainingXchromosomeisofpaternalormaternalorigin(XmorXpsubtypes;Bishop,Canning,Elgar,Morris,Jacobs,&Skuse,2000;Skuse,2000;Skuseetal.,1997).Suchagenomicimprintingeffectwasfirstdemonstratedontestsofsocialcompetence(Skuseetal.,1997).Itwillbeinterestingtoseeifasimilareffectexistsinthearithmeticdomain.Wehavereviewedtheevidenceforasubdivisionofcalculation-relatedprocessesintheparietallobe.Abroaderdiscussionofthespecificityofthenumberprocessingsystemshouldalsoconsiderthesatellitesystemsthatserveasinputandoutputstocalculationprocesses.Atthevisualidentificationlevel,purealexicpatientswhofailtoreadwordsoftenshowalargelypreservedabilitytoreadandprocessdigits(Cohen&Dehaene,1995;Déjerine,1891,1892).Conversely,acaseofimpairednumberreadingwithpreservedwordreadingisonrecord(Cipolotti,Warrington,&Butterworth,1995).Inthewritingdomain,severeagraphiaandalexiamaybeaccompaniedbyafullypreservedabilitytowriteandreadArabicnumbers(Anderson,Damasio,&Damasio,1990).Evenwithinthespeechproductionsystem,patientswhosufferfromrandomphonemesubstitutions,thusresultingintheproductionofanincomprehensiblejargon,mayproducejargon-freenumberwords(Cohen,Verstichel,&Dehaene,1997).Thesedissociations,however,neednotimplyadistinctsemanticsystemfornumber.Rather,theycanprobablybeexplainedbyconsideringthattheparticularsyntaxofnumberwordsandthepeculiaritiesofthepositionalnotationforArabicnumeralplacespecialdemandsonvisualrecognition,speechproduction,andwritingEvenwithintheparietallobe,ourreviewofnumber-relatedactivationssuggeststhatmuchofthehumancapacityfornumberprocessingreliesonrepresentationsandprocessesthatarenotspecifictothenumberdomain.Atleasttwooftheparietalcircuitsthatwehavedescribed,theposteriorsuperiorparietalattentionsystemandtheleftangularverbalsystem,arethoughttobeassociatedwithbroaderfunctionsthanmerecalculation.Thethirdcircuit,inthebilateralhorizontalintraparietalregion(HIPS),isamoreplausiblecandidatefordomainspecificity.Asreviewedabove,itissystem-aticallyactivatedduringmentalarithmetic;itismoreactivatedbynumberwordsthanbyotherwordssuchasnamesofanimals;anditsactivationincreaseswiththeamountordurationofquantitymanipulationrequired,butiscompletelyinde-pendentofthenotationusedfornumbers.Still,wearereluctanttousetheterm“category-specific”forthisbrainregion,andprefertheterms“corequantitysystem”or“number-essential”regioninstead.Forapurelyempiricalpointofview,decidingwhetheragivenregionis“specific”fornumbersseemsanextremelydifficultyenterprise.Testingforspecificitywouldseemtorequireasystematiccomparisonofthetargetcategory(e.g.,number)againstapotentiallyinfinitelistofalternatives.Itisalsocomplicatedbythelimitedresolutionofbrain-imagingtechniques,whichcannotyetresolvethefine-grainedneuronalandcolumnarorganisationofhumancortex.Comparisonofgroupstudies,aswasdonehere,mayoverestimatetheamountofoverlapbetweentasks.Studiesofmultipletaskswithinthesamesubjectswillberequiredtoexaminewhether(1)theverysamevoxelscanbeactivatedbymultiplequantity-relatedparadigms,and(2)thosevoxelscannotbeactivatedbyanyothernon-COGNITIVENEUROPSYCHOLOGY,2003,20(3/4/5/6)PARIETALNUMBERPROCESSINGCIRCUITS 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