Discrete and analogue quantity processing in the parietal lobe: A functional MRI study

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Discrete and analogue quantity processing in the parietal lobe: A functional MRI study
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  Discrete and analogue quantity processing in theparietal lobe: A functional MRI study Fulvia Castelli †‡§ , Daniel E. Glaser ‡ , and Brian Butterworth ‡ † Division of the Humanities and Social Sciences, California Institute of Technology, Pasadena, CA 91125; and  ‡ Institute of Cognitive Neuroscience,University College London, London WC1N 3AR, United KingdomCommunicated by Charles R. Gallistel, Rutgers, The State University of New Jersey, Piscataway, NJ, January 20, 2006 (received for review August 5, 2005) The human intraparietal sulcus (IPS) is implicated in processingsymbolicnumberinformationandpossiblyinnonsymbolicnumberinformation. Specific IPS activity for discrete quantities (numerosi-ties)ascomparedwithcontinuous,analoguequantityhasnotbeendemonstrated. Here we use a stimulus-driven paradigm to distin-guish automatic estimation of ‘‘how many things’’ from ‘‘howmuch’’ and ‘‘how long.’’ The discrete analogue response task(DART) uses the perception of hues which can change eitherabruptly (discrete, numerous stimuli) or smoothly (analogue, non-numerousstimuli)inspaceorintime.Subjectsdecidewhethertheysawmoregreenormoreblue.Aconjunctionanalysisofspatialandtemporal conditions revealed that bilateral IPS was significantlymore active during the processing of discrete stimuli than duringanalogue stimuli, as was a parietal-occipital transition zone. Wesuggest that processing numerosity is a distinct process fromprocessing analogue quantity, whether extended in space or time,and that an intraparietal network connects objects’ segmentationto the estimation of their numerosity. discrete stimuli    magnitude processing    nonsymbolic numericalprocessing    numerosity    analogue stimuli J udgments involving symbolic numbers systematically activatethe intraparietal sulcus (IPS) area (see ref. 1 for a review).However, two fundamental questions are still unresolved: First,is the IPS engaged in nonsymbolic numerical representation?Second, does the IPS represent the numerosity of sets of discreteobjects in the same way as it represents analogue quantities? Of course, a set of discrete objects will have analogue propertiesthat extend in space or in time, such as area, perimeter, andduration, but they are distinct from the abstract property of thenumerosity of the set, i.e. how many objects are in it. Ourexperimental question focuses on whether we can identify aspecific neural response tuned to the ‘‘numerosity parameter’’(1) of the stimulus by using nonsymbolic information.There is considerable evidence from neuroimaging studies toindicatethattheIPSisinvolvedinprocessingsymbolicnumericalinformation with tasks that depend on the perception of Arabicdigits or number words, or which require a number–wordresponse (2–7). A few studies have combined digits with non-symbolic stimuli or nonnumerical dimensions. For example, IPSis activated during target–detection tasks by using Arabic digitscompared with letters and colors (8). It is also activated in directproportion to the difficulty of a comparison task based on thesize and the luminance of Arabic digits (9). Left IPS is activatedduring a magnitude comparison task that included Arabic digits,lengths, and angles (10). A recent study based on the perceptionof digits and nonnumerical stimuli, i.e., scrambled digits, hassuggested that numerosity is represented in the parietal cortex;however, in the context of actions made in response to thenumbers, magnitude and action representations might be closelylinked (11).However, the few functional MRI (fMRI) studies investigat-ing specific IPS involvement in nonsymbolic quantity processinghave yielded apparently conflicting results (12, 13). For example,a recent study showed fMRI adaptation in the horizontalsegment of IPS during passive viewing of discrete numerositiesin the form of a fixed sets of dots, from 8 to 32 (12), but, inanother study, the IPS showed no difference in activation duringthe numerical tasks and their control tasks: number and colorcomparison of two arrays of dots, passive viewing of sets of different shapes varying in numerosity, and number and colorcomparison of dots in an array with ‘‘flashes’’ of a single dot (13).Howcanthesediscrepantresultsbeexplained?Onepossibilityis that the precise activation of the IPS depends on the tasksbeing performed and contrasted, so that commonalities aredifficult to find across different studies. This view is supportedby the observation that specialized intraparietal neural popula-tions are differently branched and layered between subjects (14),and that the spatial resolution of fMRI may not be able toseparate distinct but intertwined neural populations. Further-more, single cell recording in monkeys showed that only 10–20%of all IPS neurons respond to displays of different numbers of dots (15). We sought to address this problem by adopting anapproach aimed at tapping a core, nonsymbolic, numerosityprocessing keeping the task constant but exploiting stimulus-driven differences in activation. We reasoned that IPS systemsmight respond automatically to stimulus properties; that is, equalactivation might occur for any number, i.e., salient stimulus,independent of attention or task. Our question was as follows: Isthere a specialized system in the IPS that responds automaticallytothestimuluspropertyofbeingnumerousascomparedwiththemore general property of being extended? That is, is there aspecialized system that responds to ‘‘how many’’ as compared with ‘‘how much’’ by using nonsymbolic stimuli?Previous neuroimaging studies investigating nonsymbolic nu-merosityhavemanipulatedtheareaofthedisplayedstimuli,dotsor shapes, to control for nonnumerical quantity processing.However, the stimuli have always been presented as discreteobjects, hence numerous, in both the experimental and controlconditions. In addition, although the importance of investigating whether numerosity is coded for both simultaneously as well assequentially presented stimuli has been stressed in the past (16,17), previous studies have not ensured that the numerosity task was independent of type of presentation. Therefore, the chal-lenge for creating a paradigm for numerosity processing was tofind a stimulus dimension that can be displayed as eithernumerous or nonnumerous, either in time (sequentially) or inspace (simultaneously). Colors have these following properties:They can be displayed either as discrete, hence numerous, or asanalogue, hence extended in time or in space.Our experimental paradigm, discrete analogue response task(DART), requires the participant to judge whether there is moreblue or more green in the display. The amount of blue and green Conflict of interest statement: No conflicts declared.Abbreviations: DART, discrete analogue response task; fMRI, functional MRI; IPS, intrapa-rietal sulcus. § To whom correspondence should be addressed at: California Institute of Technology,Division of the Humanities and Social Sciences, MC 228-77, Pasadena, CA 91125. E-mail:fulvia@hss.caltech.edu.© 2006 by The National Academy of Sciences of the USA www.pnas.org  cgi  doi  10.1073  pnas.0600444103 PNAS    March 21, 2006    vol. 103    no. 12    4693–4698       N      E      U      R       O       S       C      I      E      N       C      E  can be varied continuously or as discrete areas of blue and green.In ‘‘analogue’’ conditions, the relative amount blue and greencan be assessed only in terms of analogue quantities (how muchblue vs. how much green). However, in the discrete conditions,the assessment can also be made on the basis of numerosity (howmany discrete blue rectangles vs. how many discrete greenrectangles). In addition, both analogue and discrete displays canbe presented in spatial and temporal modalities by using thesamestimulusmanipulations(see  Methods fordetailsandFig.1).We can also manipulate the ratio of the amount of blue andgreen, varying from easy (e.g., 5 green to 15 blue) to moredifficult (e.g., 9 green to 11 blue), allowing for investigation of a difficulty effect within the intraparietal region, as suggested bystudies of numerical comparison tasks (9, 18, 19). We stress thatthe logical relationship between numerosity and extent is asym-metrical; that is, discrete stimuli have both numerosity andanalogue extent, whereas analogue stimuli have only analogueextent. Thus, DART can reveal brain areas showing an addi-tional effect of numerosity over analogue quantity but not thoseareas responding to analogue quantity over numerosity. Results Behavioral Data.  Subjects gave correct responses for 86% of thestimuli (Fig. 2  a  shows accuracy score for each condition anddifficulty level). (For technical reasons, the complete accuracydata from two subjects were not available for analysis, and thebehavioral analyses were conducted on ten subjects.) There wasno significant difference between correct score (max, ninecorrect responses in each condition) for discrete stimuli (88%)and for analogue stimuli (83%) [discrete mean  7.9 (SD  1.6) vs. analogue mean  7.5 (SD  1.6); mean comparison,  F   5.1,  P     0.05)] or for the temporal  spatial presentation [temporalmean  7.45 (SD  1.6) vs. spatial mean  7.5 (SD  1.6); meancomparison,  F     5.1,  P     0.05]. A further analysis showedthat subjects’ accuracy differed over the five difficulty levels(  F  (1,4)  35.8,  P   0.001), which refer to the ratio between thetwo colors: 5:15 (i.e., easiest), 6:14, 7:13, 8:12, and 9:11 (mostdifficult). In particular, subjects gave fewer correct responses asthe difficulty level increased [5:15, mean  8.45 (SD  1.2); 6:14,mean    8.25 (SD    1.2); 7:15, mean    8.05 (SD    1.5); 8:12,mean  7.55 (SD  1.4); 9:11, mean  6.33 (SD  1.6); and  F   55.9,  P     0.0001]. Analysis of 12 subjects’ reaction times (RTs) (in ms) revealedthefollowingdifferenceinthetemporal  spatialdisplay(  F  (1,11)  115.3,  P   0.0001): temporal stimuli (mean  715.4, SD  155)evokedslowerresponsethanspatialstimuli(mean  489.7,SD  187). In addition, subjects’ RTs differ along the difficulty levels(  F  (1,4)  9.27,  P   0.0001). In particular, RTs increased linearlyas the magnitude distance between the two colors decreased asfollows: 5:15 (mean    562.3, SD    188); 6:14 (mean    551.7,SD  209); 7:13 (mean  588.4, SD  203); 8:12 (mean  651,SD    195); 9:11 (mean    718.7, SD    203) (  F     53.6,  P    0.0001). There was no significant interaction between the degreeof difficulty and the stimuli type (analogue vs. discrete) insubjects’ RTs (  F  (1,4)  0.72,  P   not significant). Fig. 2  b  showssubjects’ RTs for each condition and each difficulty level. Neuroimaging Results.  Random effects analysis of neuroimagingdata were carried out to evaluate common and differential areasof response during processing discrete vs. analogue stimuli in thetemporal and spatial presentations. A mixed effects analysis wascarried out treating subject as a random variable. This analysis was implemented by using a two-stage summary statistic ap-proach. In particular, subject-specific contrasts were developedat the first level and then entered into a second level analysis.Thus all inferences are made about the population from whichthe subjects are (assumed randomly) drawn.Because of our  apriori hypothesis regarding the role of the IPS(see  Identification of Activation Loci ) on number processing, welooked at bilateral intraparietal areas without correction for Fig. 1.  Schematic view of DART stimuli arranged in a 2  2 design. The same hues are used in all conditions. ( Upper Left  ) In the discrete temporal condition,asequenceofblueandgreensquaresappearsatrandomintervalsbetween150and400msinthesameplaceonthescreen.( UpperRight  )Inthecorrespondinganalogue temporal condition, the same hues are linked by intermediate hue values, so that a single square appears to be smoothly changing hue. In thecorrespondingdiscretespatialcondition( LowerLeft  ),thesamehuesareformedintodiscreterectanglesseparatedbygraybackground,whereas,intheanaloguespatial condition ( Lower Right  ), a smoothing function blurs the boundaries between the different hues. Every trial of discrete stimuli is transformed into a trialof analogue stimuli. 4694    www.pnas.org  cgi  doi  10.1073  pnas.0600444103 Castelli  et al.  multiple comparisons. A conjunction analysis [(discrete tempo-ral    analogue temporal)    (discrete spatial    analogue spa-tial)] revealed, as predicted, a bilateral activation along thelength of the IPS including the most caudal IPS area, spreadinginto the transverse occipital sulcus region (Fig. 3). The para-metric analyses revealed a linear increase in activation withincreasingtaskdifficultyinbothspatialandtemporalnumerosityprocessing (discrete    analogue) (Table 1). As predicted, theIPS region was activated more as the difference between the twocolors decreased (e.g., from 5 greens and 15 blues to 9 blues and11 greens). In particular, the difficulty of the numerosity esti-mation in space affects the activation in the bilateral IPS, whereas the difficulty of the numerosity estimation in timeaffects the activation of right IPS extending into the postcentralsulcus(Fig.4).Nootheractivationswithalevelofsignificant  P   0.05 corrected for multiple comparisons (FamilyWise Error;FWE) have been found during numerosity comparison. Discussion The starting point of the present experiment is the automatictendency of humans to estimate the numerosity of any set of entities, whether homogeneous or heterogeneous, extended intime or in space (see refs. 20 and 21 for reviews). We distin-guishedtwotypesofquantityprocessinginanefforttoclarifythenature of the representations involved in relative magnitude judgements: numerosity estimation, based on the perception of countable discrete stimuli, and extent estimation, based on theperception of uncountable analogue entities. Extent processingacted as a control condition for numerosity processing. We useda visual paradigm, the DART that presents matched pairs of discrete and analogue stimuli displayed both simultaneously andsequentially.We showed that specific estimation of numerosity activatesbilaterally the IPS by using nonsymbolic stimuli alone, in bothtemporal and spatial modes of display. The greatest challenge inmapping parietal cortex is that many of the functions that itprobably subserves, such as shifting and maintaining attention,directing eye movements, using working memory (23), in addi-tion to number-processing tasks, are a vital component in manycognitive tasks (22). Given the architectonic complexity of thehuman intraparietal neurons (14), the limitation of fMRI tech-niques (16, 24), and contrasting findings relative to IPS involve-ment with nonsymbolic number information (12, 13), it ispossible that the precise activation of this area depends on thetasks being performed and contrasted. We were able to excludecondition-dependent task difficulty as a factor in the IPS acti- Fig. 2.  Behavioral results. ( a ) Subjects’ correct responses for the four tasks and five difficulty levels. Errors bars indicate the range of observed percentages ofcorrect responses (i.e., max  100%). ( b ) Subjects’ reaction time for the four tasks and five difficulty levels. Errors bars indicate 1 SD. Castelli  et al.  PNAS    March 21, 2006    vol. 103    no. 12    4695       N      E      U      R       O       S       C      I      E      N       C      E   vation, because the task was held as far as possible constant inthe paradigm by using the neutral question ‘‘more green or moreblue?’’ for all four tasks. Overall, the difficulty of task for theextent stimuli and the numerosity stimuli were equivalent asmeasured by response accuracy. In addition, we are able toexclude the possibility that the IPS activity is because of theobvious visual differences between temporal and spatial presen-tations by making a ‘‘cognitive conjunction’’ (25) and consider-ing only the higher-order feature of the stimuli, namely, beingcountable or not countable, whether extended in time or inspace.However, it can be argued that subjects might be using anonnumerical intermediate perceptual representation as a basisfor magnitude comparison. We are able to rule out this hypoth-esis because blood oxygenation level-dependent activity in thehorizontal segment of the IPS (hIPS) and postcentral sulcusincreased as the difficulty of the estimation task increased duringthe discrete stimuli processing (i.e., numerosity) compared withthe difficulty of the estimation task during analogue stimuliprocessing (i.e., extent). This finding indicates that the anteriorregion of IPS is engaged by the numerosity properties alone, andthat its activity is modulated according to the changes in thenumerical ratio of the stimuli. This finding replicates previousstudies with numerical comparison tasks where the distanceeffect (i.e., it is easier and quicker to select the larger of twonumbers when they are numerically dissimilar than when theyare similar) (26) revealed activation in bilateral hIPS (1, 9).We report activation along the length of the IPS including itsmost caudal extent spreading into the transverse occipital sulcusregion. This visual region has not been fully characterized inother studies (24). However, human neuroimaging has identifiedthis area during object matching and grasping as well as duringdiscriminations of object size and orientation (24, 27). Interest-ingly, single cell recordings in the monkey parietal lobe indicatedthat most of the neurons that respond to numerosity displays arelocated in the ventral area of the IPS (16). As noted above, wehave excluded specific low level visual aspects of the discretestimuli by use of the conjunction, and so we deduce that we haveidentified a high-level visual feature to which this area issensitive. It is important to note that in the parametric analyses, we could find no evidence that this caudal region was sensitiveto manipulating the relative proportions of the blue and greenstimuli. This result supports the contention that this region isconcerned with segmenting the scene into discrete objects butnot with estimating numerosity. Because we were not able to Fig. 3.  Conjunction analysis (spatial and temporal presentations). BilateralareasalongthelengthoftheIPSweremoreactivatedbynumerosityprocess-ing (discrete, countable stimuli) than extent processing (analogue, uncount-able stimuli). Numerosity processing activates the IPS and the caudal IPSbilaterally. Table 1. Conjunction analysis of numerosity (discrete stimuli) vs.extent (analogue stimuli) and parametric analyses of numerosityvs. extent as the difficulty of the estimation increased revealedclusters of activation along bilateral IPS Brain regionCoordinates  x  ,  y  ,  z Z   scoreCluster size(voxels)Estimating numerosity:In space and cIPS right 33,  78, 24 5.64 102in time 24,  90, 21 5.4433,  78, 15 4.01cIPS left   21,  90, 27 4.64 39IPS left   24,  48, 48 3.73 12  33,  51, 54 3.22IPS right 33,  57, 51 4.00 6Difficulty effect while estimating numerosity:In space Left IPS  Pocs   57,  39, 45 3.97 10Right IPS  Pocs 27,  42, 48In time IPS right 21,  51, 42 3.42 624,  42, 42 3.30 P   0.001. cIPS, caudal IPS; Pocs, postcentral sulcus. Fig. 4.  Parametric analysis of task difficulty. The activity in the more hori-zontal segment of the IPS and in the postcentral sulcus increased as thedifference between the number of green and blue stimuli decreased. Figuresshowtaskdifficultyeffectactivationduringnumerosityprocessingintime( a )and in space ( b  and  c  ). 4696    www.pnas.org  cgi  doi  10.1073  pnas.0600444103 Castelli  et al.  record eye movements in the scanner during the four conditions, we cannot quantify or characterize saccade differences contrib-uting to this increased activation during discrete stimuli process-ing vs. analogue stimuli processing. We can speculate that thisregion serves as a ‘‘location map’’ that, in some computationalmodels of numerosity extraction, serves as a first step of objectsegmentation before numerosity estimation (28). The concept of a countable entity can be therefore defined as a thing that firstlymust be segmented from the background and only then can it becounted or numerically manipulated. It seems therefore that a wide range of properties of the world is processed along thelength of the IPS, beginning with segmenting the visual sceneinto objects and proceeding to representing their number. Theconceptsofobjectandofcountabilityareclearlyrelated,andourfindings therefore suggest that regions responsible for the rep-resentation and processing of numerosities may be built from theperception of ‘‘objecthood.’’How can the specificity of a numerosity system be justified asone of the functions that the parietal cortex subserves? It hasbeen argued by Walsh (29) that the inferior parietal cortex (IPC)is the site engaged by a common magnitude system, whichencompasses estimation of time, space, and quantity. No dis-tinction is made between numerosity and extent, that is, count-able and uncountable quantity. The hypothesis of a generalmagnitude system is based on the view that the linking functionof the parietal cortex is to extract the information about theexternal world for representing the coordinates of action. Thus,according to Walsh, the competence of the IPC, rather thancomputing ‘‘where’’ in space, is computing ‘‘how far, how fast,how much, how long, and how many with respect to action’’ (ref.29, p. 486). The present study provides a complementary evi-dence for a subregion of the magnitude system located along theIPS, which is more active during discrete quantity estimation,both in time and in space, than during analogue quantityestimation. These findings support the view of a functionalparcellation of a magnitude system that, in turn, may reflect thearchitectonic differentiation of the cortex lining the IPS (15, 30).Future investigations are needed to clarify differentiations within IPS neural populations.Interestingly, Walsh (29) points out that it would be maladap-tive for the infant brain not to use a common metric forestimating time, space, and quantity because experience teachesthe infant that there is a covariance of time, space, and quantityin the physical world. However, we further speculate that thiscovariance may represent a confound for correct numerosity judgements. Numerosity abilities in infants have been investi-gated by using control tasks based on perception of continuousextent (31). However, these tasks suffer the same limitations of past neuroimaging studies: The stimuli for the control conditionare presented as discrete objects, hence numerous. Furtherinvestigations are needed to determine whether a differentiationbetween two different systems, numerosity and extent, develops with experience. We propose that an exact representation of numerosity seems to better capture our intuitive understandingof numerosity, because it maps directly onto lower level percep-tual processes (e.g., object identification) and enumerationprocedures (e.g., subitizing, counting).In conclusion, the present study made a clear distinctionbetween discrete and analogue quantities and compared themdirectly by using nonsymbolic stimuli. We suggest that thefundamental ability to compare magnitudes evolved from thecapacity to extract information about the discreteness of a scene. Anobjectcanbedefinedasanentitythatcanbesegmentedfroma background and can also be thought of as a countable entity.Our findings reveal a network along the length of the IPS thatconnects object segmentation to the estimation of numerosityduring a magnitude comparison task. Methods Subjects.  Twelve neurologically healthy subjects (4 females and 8males; mean age, 24.0 years; range, 18.0–34.1 years), all but oneright-handed, gave written informed consent according to pro-cedures approved by the National Hospital and Institute of Neurology Ethics Committee (London). Experimental Design.  The DART visual stimuli were presentedboth sequentially (in time), as discrete entities (DT) or analoguestimuli (AT), and simultaneously (in space), as discrete entities(DS) or analogue stimuli (AS) (see Fig. 1). The stimuli werepresented in nine blocks of four conditions (DT, AT, DS, AS) foreach of the five difficulty levels (in a randomized order). Stimuli Presentation.  Each stimulus was presented on a screensituated outside the scanner and projected onto a mirror 30 cmabove subjects, subtending a visual angle of    10°. The stimuli were created with  MATLAB  (MathWorks, Natick, MA). Thestimulation consisted of a rectangle filled with blue and greenhues.Thebackgroundwasgray.Thestimuliofallfourconditions were shown at the same location, within the rectangle. The fourconditions differed as function of the type of presentation (intime and in space) and of the type of transition between each hue(abrupt or continuous). Twenty hues in total were presented foreach condition. The difficulty of the ‘‘more blue or more green?’’ judgment was controlled by varying the ratios of the amounts of the two hues: 5:15 (easier), 6:14, 7:13, 8:12, 9:11 (more difficult).Within each block, the higher ratio was counterbalanced be-tween the two colors. The speed and the randomization of thepresentation were designed to prevent explicit counting of thetwo sets of hues, as confirmed by subjects’ report at the end of the experiment. Stimuli Presentation in Time (Sequential Presentation).  In the dis-crete condition, the interstimulus interval of each hue variedrandomly from 150 to 400 ms, so that subjects perceived the visual signal as a sequence of twenty blue and green squaresappearing at irregular intervals (Fig. 1  Upper Left ). In theanalogue condition, the transition between the 20 different huesincluded a fixed number of intermediate steps so that subjectsperceived a continuous light changing from blues to greens (Fig.1  Upper Right ). The intermediate steps between the 20 blue andgreen squares were created by a  MATLAB  program to assure theperception of a smooth transition between each pair of squares.The average duration of the display of both discrete andanalogue stimuli in the temporal presentation was of 9 s plus a3-s window within which the subject had to respond. Stimuli Presentation in Space (Simultaneous Presentation).  In thediscrete spatial condition, the hues were presented as a rectan-gular grid composed of blue and green rectangles (5    4) of irregular size separated by gray background (Fig. 1  Lower Left ).In the analogue spatial condition, the hues were presented as asingle large rectangle composed of blurred blue-to-green areasthat correspond to blurred versions of the discrete spatialconfiguration (Fig. 1  Lower Right ). The average duration of thedisplay of both discrete and analogue stimuli in the spatialpresentation was of 0.6 s plus a 3-s window for forced choiceresponse. Instructions.  The subjects were instructed to watch the sequencesand to decide at the end whether they saw more blue or moregreen. They answered by pressing one of two keys (left or rightpress for each response varied and counterbalanced acrosssubjects). Scanning was preceded by a practice session withexamples of the four conditions and a key press. Castelli  et al.  PNAS    March 21, 2006    vol. 103    no. 12    4697       N      E      U      R       O       S       C      I      E      N       C      E
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