Common and Specific Contributions of the Intraparietal Sulci to Numerosity and Length Processing

Transcription

1 Human Bain Mapping 30: (2009) Common and Specific Contibutions of the Intapaietal Sulci to Numeosity and Length Pocessing Valéie Domal and Mauo Pesenti* Unité de Neuosciences Cognitives, Univesité Catholique de Louvain, Belgique Abstact: Numeical and spatial magnitude pocessing have long been intimately associated, leading to the suggestion that they shae a common system of magnitude epesentation. Although sepaate investigations on the ceebal aeas involved in numeosity and spatial estimation point towad the paietal cotex, the pecise anatomical ovelap, if any, has not yet been diectly established. Hee, functional magnetic esonance imaging was used to localize the ceebal netwok involved in pocessing both numeosity and length. Blood oxygenation level-dependent signal changes wee measued while healthy voluntees wee making numeosity compaisons on linea aays of dots, and length compaisons on discete linea aays of dots and continuous ectangles. The esults show the bilateal involvement of paietal egions aound the intapaietal sulci in explicit and implicit pocessing of numeosity, and a ight latealized occipitopaietal netwok activation in length pocessing; numeosity and length pocessing both activate the ight IPS and the pecental gyus. By excluding the mandatoy intinsic spatial pocessing of aays, we demonstate that the left IPS is involved in numeosity pocessing only, wheeas the ight IPS undelies a common pocessing mechanism o epesentation of spatial and numeical magnitude. Hum Bain Mapp 30: , VC 2009 Wiley-Liss, Inc. Key wods: numeosity pocessing; length pocessing; intapaietal sulcus; functional magnetic esonance imaging INTRODUCTION It has been suggested that the paietal cotices undelie a notation- and task-independent semantic epesentation of numbes [Dehaene et al., 1998]. The ole of the paietal Contact gant sponso: Communauté Fançaise de Belgique Actions de Recheche Concetées (Belgium); Contact gant numbe: 01/ *Coespondence to: Mauo Pesenti, Unité de Neuosciences Cognitives, Univesité Catholique de Louvain, Place Cadinal Mecie, 10, B-1348 Louvain-la-Neuve Belgium. mauo.pesenti@uclouvain.be Received fo publication 17 July 2008; Revised 11 Septembe 2008; Accepted 14 Septembe 2008 DOI: /hbm Published online 17 Mach 2009 in Wiley InteScience (www. intescience.wiley.com). aeas, and moe pecisely the intapaietal sulci (IPS), in numeical pocessing has been demonstated by neuopsychological studies with bain-damaged patients [Dehaene and Cohen, 1997; Takayama et al., 1994]. This finding is suppoted by ecent bain imaging studies using numbe compaison [Kaufmann et al., 2005; Pesenti et al., 2000; Pinel et al., 1999, 2001], paity judgment [Thioux et al., 2005], and vaious aithmetic tasks [Chochon et al., 1999; Lee, 2000; Simon et al., 2002; Zago et al., 2001]. Most neuoimaging and neuopsychological studies in humans have only used symbolic numbe tasks (i.e., tasks with Aabic o vebal numeals), but only a few have investigated whethe the paietal aeas ae also involved in pocessing nonsymbolic discete mateials (e.g., pattens of dots). This was done by using eithe passive habituation paadigms o tasks equiing the paticipants to count. Using an adaptation paadigm o vaiants of it, activations of the IPS VC 2009 Wiley-Liss, Inc.

2 Numeosity and Length Pocessing in the IPS of both hemisphees wee indeed found in esponse to visual numeosity changes while paticipants wee passively exposed to aays of dots o squaes [Ansai et al., 2006; Piazza et al., 2004]. Stict selectivity is had to establish, but the sensitivity of the IPS to numeical changes is suppoted by the fact that this egion does not espond in the same way to othe changes in the stimuli, such as shape o distibution in space [Cantlon et al., 2006]. Moeove, simila neuonal adaptation and ecovey effects have been obseved fo sets of dots and Aabic digits, suppoting the idea that shaed neual populations encode nonsymbolic and symbolic magnitudes [Piazza et al., 2007]. Bilateal implication of the posteio pat of the IPS has also been demonstated in seveal studies using dot enumeation and simple addition tasks equiing explicit counting, iespective of whethe the stimuli wee pesented sequentially o simultaneously [Fink et al., 2001; Piazza et al., 2002, 2003; Sathian et al., 1999; Venkataman et al., 2005]. This may eflect the visuospatial pocesses equied to oient attention to numeically elevant dimensions of the stimuli and tack thei tansfomations. Finally, appoximate nonsymbolic numeosity estimation has been shown to activate a ight-latealized fontopaietal netwok including the IPS when paticipants had to estimate the numeosity of sequential seies of visually and auditoily pesented stimuli [Piazza et al., 2006], and the IPS foci wee activated whethe numeosity extended ove space o ove time [Castelli et al., 2006]. A magnitude-compaison task with nonsymbolic stimuli (i.e., aays of squaes) was used to compae the neual substate of the numeical distance effect in childen and adults [Ansai and Dhital, 2006]. A bilateal IPS implication was obseved in adult paticipants, with an incease in activation with age in the left hemisphee only. Aeas in and aound the IPS have thus been shown to be involved in symbolic and nonsymbolic numeical magnitude pocessing. The paietal cotex is also known to be involved in visuospatial functions such as spatial attention [Coull and Nobe, 1998; Gitelman et al., 1999], peception of nea and fa space [Mashall and Fink, 2001], and mental otation [Kosslyn et al., 1998]. Inteestingly, the IPS, especially in the ight hemisphee, have been found to be activated fo judgments of physical size and oientation [Faillenot et al., 2001; Pinel et al., 2004], and in line bisection tasks [Fink et al., 2000]. Moeove, the left IPS has been found to be common to the compaison of Aabic numeals, lengths of lines, and amplitudes of angles [Fias et al., 2003]. These findings suggest that magnitude might be epesented o pocessed by the same mechanism fo both symbolic and nonsymbolic continuous stimuli. Given the stong spatial dimension involved in nonsymbolic stimuli, space pocessing is a good candidate fo such a common mechanism. The paietal cotex may indeed be engaged in cognitive computations on space and numbes [Walsh, 2003], which could explain why physical size, spatial location, and numbes intefee at the behavioal level [Dehaene et al., 1993; Henik and Tzelgov, 1982], and why patients with paietal damage may show deficits in both spatial and numeical bisection tasks [Rossetti et al., 2004; Vuilleumie et al., 2004; Zozi et al., 2002]. The intefeence of spatial cues on numeosity judgment is found in the well-known consevation of numbe task [Piaget, 1952]; when two aays with the same numbe of elements have diffeent lengths, childen until the age of seven eoneously decide that the longe aay contains moe objects. This eflects a misleading visuospatial length-equals-numbe heuistic that adults still have to inhibit to pefom coectly [Dauignac et al., 2006; Houdé, 1997; Houdé and Guichat, 2001; Leoux et al., 2006]. We ecently investigated the mutual influence of length and numeosity pocessing in a behavioal Stoop expeiment in which healthy paticipants had to compae the length o the numeosity of aays of dots in which the two dimensions wee manipulated independently [Domal and Pesenti, 2007]. The esults showed that the spatial cues intefeed stongly with the numeosity judgment, wheeas the numeical cues only intefeed modeately with the length judgment. We intepeted these findings as eflecting a diffeent mandatoy pocessing of numeosity and length; with the stimuli used, length pocessing appeas to take place automatically, wheeas numeosity pocessing appeas insufficiently automatic to geneate stong intefeence effects. This obseved asymmety in intefeence did not allow us to daw fim conclusions about a possible common mechanism and hence a common bain substate fo length and numeosity pocessing. To test whethe the numeosity-sensitive neuons in the IPS wee also sensitive to line-length discimination, ecodings fom single neuons in the left and ight IPS of macaque monkeys wee ecently made while the monkeys wee pefoming compaisons of eithe the numbe of items in multiple-dot displays o the length of lines [Tudusciuc and Niede, 2007]. The esults showed that some neuons esponded selectively to eithe the numeical magnitude o the length, wheeas othes esponded to both dimensions. This confimed the pesence of highly distibuted epesentations of numeical and nonnumeical magnitudes, patly intemingled at the single-cell level in the monkeys IPS. To date, howeve, a diect compaison of nonsymbolic numeosity and length pocessing has not been caied out using a neuoimaging appoach in humans. Whethe o not numeosity and length pocessing belong to the same geneal magnitude pocessing system and shae the same neuoanatomical substate in the human paietal cotex is thus still an open question. In the pesent study, we used functional magnetic esonance imaging (fmri) to investigate and diectly compae the bain s esponses to numeosity and length-compaison tasks. Paticipants had to compae the numeosity of two discete linea aays of dots, o the length of two discete linea aays of dots, o the length of two continuous black ectangles. If the same epesentational mechanisms and medium undelie numeosity and length pocessing, then the thee types of compaisons should lead to simila activations, possibly in 2467

3 Domal and Pesenti the aeas aound the IPS. This would povide diect suppot to the idea of a magnitude system undelying both (discete) numeosity and (continuous) space pocessing in humans. Moeove, it is woth noting that using discete and continuous stimuli in the length-compaison tasks should allow us to isolate the bain aeas specifically involved in length judgments, egadless of the type discete o continuous of stimuli (by excluding those implicitly involved in the numeosity pocessing of discete aays); convesely, this should also isolate the bain aeas specifically involved in numeosity pocessing (by including those implicitly involved in the length compaison of discete aays). METHODS Paticipants Fouteen healthy Fench-speaking male voluntees (mean age: yeas) paticipated in this study, afte giving thei infomed witten consent. All the paticipants wee ight-handed, as attested by the Edinbugh inventoy questionnaie [Oldfield, 1971], had no histoy of neuological o psychiatic disodes, had coected-to-nomal vision, and wee unawae of the pupose of the study. The expeiment was noninvasive and was pefomed in accodance with the ethical standads laid down in the 1964 Helsinki Declaation; the expeimental potocol was appoved by the Biomedical Ethical Committee of the Univesité catholique de Louvain. Tasks and Stimuli Thee compaison tasks wee used: (1) a numeosity compaison of two linea aays of dots (denoted N, fo numeosity, late), (2) a length compaison of two discete linea aays of dots (DL, fo discete length), and (3) a length compaison of two continuous black ectangles (CL, fo continuous length). Fo the fist two tasks, the aays wee composed of black dots and used nonpeiodic signals so that spatial atios wee not confounded with numeosity, and density biases and patten ecognition wee avoided [Beukelaa and Dalymple-Alfod, 1998; Domal and Pesenti, 2007]. The diamete of each dot (e j ) vaied fom 2.5 to 15 mm, while the intedot spacing (i j ) anged fom 2.5 to 20 mm; to avoid patten ecognition, each seies involved at least one e j and one i j of 2.5 mm, one e j of 15 mm and one i j geate than 15 mm (see Fig. 1A). Pais of aays wee composed of 5 vs. 8 dots fo N and wee 8 cm vs. 9 cm long fo DL. Fo CL, the stimuli wee two black ectangles 1 cm wide and 8 vs. 9 cm long. The position of the aays/ectangles within the pais vaied: fo half of the pais, the smalle/shote aay/ectangle was on the left (S-L pais) and in the othe half it was on the ight (L-S pais). A 1-cm high coss in the cente of the sceen sepaated the two elements of a pai, and the whole display Figue 1. (A) Spatial attibutes of the stimuli shown in a nonpeiodic aay with six dots and a total length of 80 mm (l 5 total length; o j 5 length of one dot and its adjacent spacing; e j 5 dot size; i j 5 intedot spacing). (B) Examples of stimuli composed of two linea aays of dots fo numeosity (uppe panel) and discete length compaison (middle panel), and of two continuous black ectangles fo continuous length compaison (lowe panel). occupied the cente of the visual space (aound 98 of visual angle). The paticipants wee told to look at the coss thoughout the task, so as to pevent possible eye saccades (Fig. 1B). Each pai was pesented fo 650 ms, with a 600-ms intetial inteval between pais (Fig. 2A). The thee efeence tasks used the same stimuli as those in the coesponding expeimental tasks, except fo the fact that one of the two aays o ectangles in each pai was coloed ed; paticipants wee equied to indicate which aay/ectangle was ed. These efeence tasks wee equated with the expeimental tasks in tems of visual complexity and manual foced-choice esponses. 2468

4 Numeosity and Length Pocessing in the IPS Schematic epesentation of the tempoal stuctue of the expeiment. (A) Examples of expeimental (left) and efeence (ight) task: Each tial was composed of a stimulus (a pai of linea aays of dots o a pai of continuous black ectangles) displayed fo 650 ms, and a fixation coss fo the intetial inteval Figue 2. fo 600 ms. Fo the efeence task, one element of the pai was ed. (B) fmri design. Each un consisted of eight altenations of a 12-s fixation peiod (black coss on white backgound) and a 24-s activation peiod. Each activation peiod coesponded to eithe an expeimental condition o its efeence condition. Expeimental Pocedue Backpojected images wee viewed though a tilted mio mounted on the head coil; the pojecto and the mio (Silent Vision TM System, Avotec, Inc., og) wee compatible with the MRI envionment. Stimulus pesentation and esponse ecoding wee contolled with E-Pime [Schneide et al., 2002]. Each paticipant undetook six acquisition uns, each consisting of eight expeimental blocks of 24 s inteleaved with 12 s fixation peiods of a black coss on a white backgound (Fig. 2B). In the numeosity-compaison task, the paticipants had to decide which aay contained moe dots by pessing a lefthand esponse button on a esponse box fo the left aay and a ight-hand esponse button fo the ight aay. In the two length-compaison tasks, they had to decide which aay/ectangle was longe, using the same button pesses. Befoe the fmri expeiment, each paticipant also undetook a peliminay taining session outside the magnet oom to each a stable pefomance level and to check on his capacity to fixate on the cental coss thoughout the task. In the taining session, task and pocedue wee the same as in the fmri session, but thee wee two distances between the pais in the aays: a lage distance (thee dots fo numeosity: pais 6 and 9; 3 cm fo length: pais 9 and 12 cm) and a small distance (one dot fo numeosity: pais 5 and 6; 1 cm fo length: pais 8 and 9 cm). 1 fmri Acquisition and Analysis Functional images wee acquied with a 1.5 T magnetic esonance image and a standad head coil (Gyoscan, Philips Medical Systems) as seies of blood-oxygen-sensitive T2*-weighted echo-plana image volumes (GRE-EPI). Acquisition paametes wee as follows: time to echo 5 50 ms, time fo epetition 5 2,000 ms, flip angle 5 908, field of view mm 2, slice thickness 5 6 mm with no inteslice 1 The esults of the taining session with nine paticipants (fo technical easons, the taining data fom the fist five paticipants could not be used) showed a classical distance effect [Moye and Landaue, 1967] in the thee tasks: pais with a lage distance wee esponded to faste and moe accuately than pais with a small distance (esponse latencies fo lage distance ms, small ms, F(1, 8) , P < 0.02; pecentage of eos fo lage 5 6.3% %, small % %, F(1, 8) , P < 0.001). This demonstates that paticipants actually pefomed the compaisons using the appopiate dimensions (i.e., numeosity in the numeosity compaison, and length in the discete and continuous compaisons). 2469

5 Domal and Pesenti gap. Each image volume compised 20 axial slices acquied in an ascending inteleaved sequence. High-esolution T1- weighted 3D fast field echo anatomical images with mm contiguous axial slices wee also acquied fo each paticipant (TE 5 3 ms, TR 5 30 ms, flip angle 5 308, FOV mm 2 ; in-plane voxel size mm 3 ). Head movement was limited by foam padding within the head coil and a estaining band acoss the foehead. The data wee pocessed and analyzed using statistical paametic mapping (SPM2, Welcome Depatment of Cognitive Neuology, London, UK; spm). Functional images wee (1) coected fo slice acquisition delays, (2) ealigned to the fist scan of the fist un (closest to the anatomical scan) to coect fo within- and between-un motion, (3) coegisteed with the anatomical scan, (4) nomalized to the MNI template using an affine fouth degee ß-spline intepolation tansfomation and a voxel size of mm 3 afte the skull and bones had been emoved with a mask based on the individual anatomical images, and (5) spatially smoothed using a 10-mm FWHM Gaussian kenel. Condition-elated changes in egional bain activity wee estimated fo each paticipant by a geneal linea model in which the esponses evoked by each condition of inteest wee modeled by a standad hemodynamic esponse function. The contasts of inteest wee fist computed at the individual level to identify the ceebal egions significantly activated by numeosity, DL, and CL, elative to the fixation peiods used as a geneal baseline (espectively, [N 2 fix], [DL 2 fix], and [CL 2 fix]), and similaly fo each efeence task. Significant ceebal activations fo these contasts wee then examined at the goup level in andom-effect analyses using one-sample t-tests and analyses of vaiance (ANOVA), with the statistical theshold set at P < 0.05 (FamilyWise Eo coected) and extending to at least 15 contiguous voxels. Given the stong a pioi hypotheses, activations in the paietal cotices wee also sceened at lowe, uncoected, thesholds The conjunction (using the minimum statistic compaed to the conjunction null, MS/CN; [Nichols et al., 2005]) of each expeimental contast with its own efeence contast isolated the ceebal activations elicited by numeosity, DL, and CL compaisons. The conjunction (MS/CN) of the two length tasks was computed in the same way to identify the ceebal activations involved in length compaison. A conjunction (MS/CN) between N and DL masked exclusively by CL evealed the ceebal activations in both explicit and implicit numeosity pocessing, excluding length pocessing. Finally, a tiple conjunction analysis (MS/CN) between the thee efeence tasks, each contasted to its expeimental task, was caied out. RESULTS Behavioal Data An ANOVA was pefomed on the esponse latencies (RLs) of coect answes with condition (expeimental vs. Figue 3. Mean pecentage of eos and esponse latencies in milliseconds fo discete and continuous length and numeosity tasks, as a function of the condition (expeimental vs. efeence). efeence) and task (N vs. DL vs. CL) as within-subject vaiables. Significant main effects wee obseved fo condition (F(1, 13) , P < 0.001) and task (F(2, 26) , P < 0.004). Paticipants esponded faste oveall to the efeence ( ms) than to the expeimental ( ms) tasks, and wee slowe in N and DL compaisons than in the CL compaison (N: ms, DL: ms, CL: ms; N-CL: t(13) , P < 0.001, DL-CL: t(13) , P < 0.003, and DL-N: t(13) , P > 0.9). Moeove, the RLs showed a condition by task inteaction (F(2, 26) , P < 0.007): the CL compaison was pefomed faste than the two othe tasks, these diffeences being geate fo expeimental than fo efeence tasks (see Fig. 3). A simila ANOVA on eo ates evealed significant main effects of condition (F(1, 13) , P < 0.001) and task (F(2, 26) , P < 0.03). Paticipants made moe eos in the expeimental (10.4% 6 6.4%) than in the efeence (1.1% 6 1.2%) tasks. The CL compaison was pefomed moe accuately than the DL and N compaisons (CL: 2.3% 6 2.9%, DL: 5.4% 6 2.4%, N: 9.4% 6 8.9%; CL- DL: t(13) , P < 0.002, CL-N: t(13) , P > 0.01, and DL-N: t(13) , P > 0.1). Thee was also a significant inteaction between condition and task (F(2, 26) , P < 0.04): eo ates did not vay significantly between the thee efeence tasks, but in the expeimental conditions, thee wee significantly fewe eos with the CL compaison than with the DL and N compaisons (see Fig. 3). 2470

6 Numeosity and Length Pocessing in the IPS TABLE I. Bain egions showing significant activation fo (a) numeosity (N), (b) discete length (DL), and (c) continuous length (CL) compaisons each compaed to its own efeence task (Ref) Bain egions L/R k x y z t-statistic a b c [N 2 fix] 2 [RefN 2 fix] Infeio fontal gyus, opecula pat R * Infeio fontal gyus, opecula pat L * Middle fontal gyus R * Middle fontal gyus R * IPS/infeio paietal lobule R 3, * IPS/infeio paietal lobule L * Infeio tempoal gyus L 1, * Supplementay moto aea R * Insula R * [DL 2 fix] 2 [RefDL 2 fix] IPS/infeio paietal lobule R 2, * IPS/infeio paietal lobule L * Supeio paietal lobule L * Infeio fontal gyus, opecula pat R * Infeio fontal gyus, tiangula pat R * Infeio occipital gyus L * Middle occipital gyus L * Supplementay moto aea R * Pecental gyus R * [CL 2 fix] 2 [RefCL 2 fix] Pecental gyus R * IPS/infeio paietal lobule R * Supeio paietal lobule L ** L, left hemisphee; R, ight hemisphee; k, cluste size (numbe of voxels); x, y, z, steeotaxic coodinates of peak-height voxels. * P-values < 0.05 FWE coected fo multiple compaisons. ** P-values < uncoected. Numeosity pocessing Functional Data Contasting the N task to its efeence evealed the aeas involved in explicit numeosity pocessing and compaison. Bilateal activations wee found in the paietal lobes, in the depth and aound the IPS, moe extended in the ight hemisphee. Aeas of activation wee also obseved in the ight middle and infeio fontal gyi and insula, the ight supplementay moto aea (SMA), the left and ight occipitotempoal junction, and the left infeio fontal gyus (Table Ia and Fig. 4A). A conjunction between the N and DL tasks, each contasted to its efeence and exclusively masked by CL minus its efeence, evealed the ceebal aeas commonly involved in explicit (N) and implicit (DL) discete numeosity pocessing, excluding length pocessing (Table IIc). These aeas included the left IPS (peak at 242, 240, 50), the left middle occipital gyus, and the ight occipitotempoal junction. Finally, contasted to DL and CL, the N task activated the left and ight occipitotempoal and occipitopaietal junctions, and the posteio pat of the ight IPS. Length pocessing Contasting the DL task to its efeence evealed a lage focus of activation in the ight infeio and supeio paietal lobules all aound the IPS, and othe lage foci extending fom the occipitotempoal junction to the posteio pat of the supeio paietal lobule, along the dosal steam (Table Ib). Similaly, although less extended, foci wee obseved in the left hemisphee. Othe activation foci wee found in the ight fontal lobe, in the pecental gyus and the insula, and in the SMA. In CL, only two foci wee found to be activated in the ight hemisphee: one in the IPS (with a local maximum at 40, 242, 48) and one in the pecental gyus (Table Ic). A small left supeio paietal lobule activation only appeaed at an uncoected theshold (P < 0.003). The conjunction between DL and CL, each contasted to its efeence and exclusively masked by N minus its efeence, showed no focus of activation at the coected theshold; a tiny focus (k 5 5) was obseved in the depth of the ight infeio paietal lobule only at an uncoected theshold (P < 0.003) (Table IIa). Numeosity and length pocessing A conjunction between N, DL and CL, each contasted to its own efeence, evealed the aeas commonly involved in numeosity and length pocessing. Only the two foci obseved fo CL wee found to be activated in all the tasks, one in the IPS and one in the pecental gyus, both in the ight hemisphee. The latte was slightly but not significantly moe activated in the two tasks using discete stimuli (i.e., 2471

7 Domal and Pesenti Figue 4. (A) Bain egions activated in the numeosity task (N) compaed with its efeence. (B) Bain egions activated in the conjunction of the thee expeimental tasks (N, DL and CL). Uppe panel: Statistical paametic maps supeimposed on a suface ende of the ight hemisphee. Middle panel: Contast estimates fo each condition in the ight IPS (left) and the ight pecental gyus (ight). Lowe panel: Right IPS and pecental gyus foci displayed on sagittal, coonal, and axial slices of the MNI standad bain (all P < 0.05, FWE coected.) N and DL; Table IIb and Fig. 4B). A left IPS focus also appeaed at an uncoected theshold (P < 0.003). Colo pocessing Finally, the conjunction between the thee efeence tasks, each contasted to its own expeimental task showed bilateal activation at the occipitopaietal junction and in the middle tempoal gyus (Table IId), coesponding to the pocessing of colos. DISCUSSION In ou expeience of daily life, numeosity and length ae intimately linked, as moe objects usually occupy moe space. This pivileged elationship shows itself in expeimental conditions though vaious facilitation and intefeence effects [Dempste, 1995; Dixon, 1978; Domal and Pesenti, 2007; Houdé and Guichat, 2001]. Recent theoetical accounts have suggested that numeosity and space may be pocessed and epesented within a common magnitude pocessing system possibly located in the paietal cotex [Walsh, 2003]. Although sepaate investigations on the ceebal bases of numeosity and spatial pocesses do convege on the paietal lobes, the pecise anatomical ovelap, if any, between these two dimensions has not peviously been diectly assessed. In this study we asked paticipants to compae the numeosity o the length of two discete linea aays of dots, o the length of two continuous black ectangles in an fmri expeiment. Fistly, ou esults show the bilateal involvement of the paietal aeas in numeosity pocessing, as aleady suggested by neuopsychological and neuoimaging studies [e.g., Dehaene and Cohen, 1997; Piazza et al., 2004, 2006]. They also extend this paietal involvement to the pocessing of discete linea aays of dots. Moe pecisely, we found that the left IPS was activated by both explicit and implicit pocessing of numeosity, egadless of the judgment (numeosity o length) being pefomed on the stimuli, as demonstated by the conjunction between N and DL compaison. It is woth noting that length pocessing was totally absent fom this conjunction since the CL judgment had been used as an exclusive mask. This ensued that the left IPS focus was involved in the numeical aspects of numeosity pocessing, and not the mandatoy intinsic spatial pocessing. Fo the same eason, the IPS activation should not eflect any possible ovet visual saccades, which might have been left afte contasting the expeimental tasks to thei efeences. This focus is also clealy located moe anteioly than the posteio paietal foci usually associated with the visuospatial pocesses equied to oient attention to the numeically elevant dimension of the stimuli. The vey shot pesentation time used in this expeiment (i.e., 650 ms) and the equiement to fixate the cental coss thoughout the task to avoid eye saccades and scanning the dots make an explicit counting stategy vey unlikely to have been used. Howeve, we cannot totally exclude that the displayed numeosities implicitly tiggeed the vebal numeals system in the left hemisphee, which may be the cause of the obseved leftlatealized activation both in implicit and explicit numeosity judgments. Although pobably not specific to numeosity pocessing, it seems likely that the occipitotempoal and occipitopaietal activations left afte length pocessing has been discaded eflect the modulation of the visuoattentional components that is needed to individualize the dots within the aays [Cobetta, 1998]. This, with the involvement of the fontal aeas sustaining attentional contol, fits with pevious findings on quantifying dots in the same ange of numeosities [Sathian et al., 1999]. Second, the activations obseved in continuous linea length judgment demonstate the impotance of the ight 2472

8 Numeosity and Length Pocessing in the IPS TABLE II. Bain egions showing significant activation in the (a) conjunction of the two length tasks (DL and CL), (b) conjunction of the thee expeimentals tasks (N, DL and CL), (c) conjunction of N and DL tasks masked exclusively by CL, and (d) conjunction of the thee efeence tasks (RefN, RefDL, and RefCL) Bain egions L/R k x y z t-statistic a b c d [DL 2 RefDL] and [CL 2 RefCL] masked exclusively by [N 2 RefN] IPS/infeio paietal lobule R * [N 2 RefN] and [DL 2 RefDL] and [CL 2 RefCL] Pecental gyus R ** IPS/infeio paietal lobule R ** IPS/Supeio paietal lobule L * [N 2 RefN] and [DL 2 RefDL] masked exclusively by [CL 2 RefCL] Middle occipital gyus L ** Infeio tempoal gyus R ** IPS/supamaginal gyus L ** [RefN 2 N] and [RefDL 2 DL] and [RefCL 2 CL] Angula gyus R ** Pecuneus R 1, *** Middle tempoal gyus L *** Middle tempoal gyus L *** Middle tempoal gyus L * Middle tempoal gyus R *** Supeio fontal gyus, medial pat L *** Supeio fontal gyus, medial pat L *** Medial obitofontal gyus L *** L, left hemisphee; R, ight hemisphee; k, cluste size (numbe of voxels); x, y, z, steeotaxic coodinates of peak-height voxels. * P-values < 0.01 uncoected. ** P-values < 0.05 FWE coected fo multiple compaisons. *** P-values < uncoected. paietal aeas in length compaison. 2 This fits with the involvement of the ight paietal cotex in many spaceelated pocesses such as the oientation of attention [Coull and Nobe, 1998], the compaison of sizes [Pinel et al., 2004], and the bisection of lines [Fink et al., 2000]. Neuopsychological studies with bain-damaged patients and tanscanial magnetic stimulation (TMS) expeiments cooboate the dominance of the ight paietal hemisphee found fo the pocessing of lengths. Patients with ight paietal lesions, in addition to spatial neglect, had difficulty with size judgments [Milne and Havey, 1995], length line compaison [Iving-Bell et al., 1999], and line-bisection tasks [Mashall and Halligan, 1989]. Moeove contalateal visuospatial deficits wee obseved in healthy subjects afte tansient disuption of the ight paietal cotex induced by focal TMS, as tested in a line-length judgment task [Fieo et al., 2000, 2001]. Finally, numeosity and length pocessing both ely on the activation of the ight IPS and the ight pecental gyus. The ight paietal aea could be the site of a possible common mechanism o epesentation fo length and 2 In a pevious PET study [Fias et al., 2003], line compaison was only associated with left IPS activation. Howeve, the authos only epoted activations pesent in both line and symbolic numbe (Aabic numeal) compaisons. This may explain this left hemispheic latealization. numeosity pocessing, and be involved in both kinds of cognitive estimation. The idea that numeical and nonnumeical magnitudes ae epesented in ovelapping aeas of the IPS is suppoted by single-cell ecoding studies showing that, when monkeys pefom compaisons of diffeent numeosities o line lengths, some IPS neuons espond to both quantities [Tudusciuc and Niede, 2007]. Inteestingly, it has been suggested that this paietal stuctue in monkeys may be the homologue of the hoizontal segment of the IPS in humans, which is found to be activated in judgments of both physical size and numeical magnitude [Pinel et al., 2004]. The fact that thee is ight paietal activation fo both numeosity and length compaisons could at least patly explain the intefeences obseved in many behavioal studies between the numeical magnitude and the physical size of the stimuli in compaison tasks [Henik and Tzelgov, 1982; Pinel et al., 2004], the numeical magnitude and space location in paity judgments [Dehaene et al., 1993], the numbe of elements and length in numeosity compaison [Houdé, 1997; Houdé and Guichat, 2001], and numeosity and length cues in Stoop paadigms [Domal and Pesenti, 2007]. Behavioal intefeence effects between two physical dimensions have been shown to be stonge when they ely on the same neuonal stuctues [Fias et al., 2001]. The shaed ight paietal activation could explain why the spatial cues intefeed stongly with the pocessing of numeosity in 2473

9 Domal and Pesenti ou Stoop paadigm [Domal and Pesenti, 2007], wheeas numeical cues, pocessed less automatically than length and sustained by bilateal paietal aeas, only geneated weak intefeence with length pocessing. Without the specific time couses of these uni- and bilateal activations, it is had to comment futhe on the mandatoy pocessing of numeosity and/o length. A ecent fmri study compaed the pocessing of discete numeosities and continuous quantities, epesented by displays of hues with colos changing eithe abuptly o smoothly in space and time [Castelli et al., 2006]. Discete numeosity compaison was found to activate the IPS moe than continuous quantity compaison. This was intepeted by the authos as indicating two distinct pocesses. Howeve, this conclusion goes beyond the epoted data: the fact that the IPS wee activated moe by discete numeosities than by continuous ones does not, of couse, mean that they wee not activated at all by continuous quantities. Unfotunately, the activations elated to continuous quantities alone wee not epoted by the authos, and, so the possibility that the IPS was also activated, pehaps to a lesse extent, cannot be excluded. Ou expeiment clealy shows that the ight IPS is activated by length pocessing, in the vey aeas which undelie the pocessing of numeosity. Although the RLs and accuacy of the thee compaison tasks had been equated in a pilot study, 3 the numeositycompaison task tuned out to be moe difficult than the two length tasks, and the CL compaison was pocessed faste than the othe two tasks duing the fmri session. Moeove, the expeimental tasks tuned out to be moe time consuming and moe eo pone oveall than thei efeence tasks. As IPS activation shows some modulation as a function of inceased task difficulty [Göbel et al., 2004], it can be agued that task complexity made some contibution to the patten of activation we obseved. Howeve, the fact that vey simila IPS activations wee obseved in the absence of an explicit task duing passive numeosity changes [Ansai et al., 2006] suggests that esponse-selection equiements and task difficulty [Göbel et al., 2004] cannot be the only souces of IPS activation. This, in tun, makes the possibility that task complexity contibuted to the patten of esults we obseved less plausible. To avoid this poblem, futue studies should ty to ensue a bette match in individual pefomance acoss tasks, by conducting extensive individual taining pio to the expeiment. The idea that vaious types of magnitudes could be pocessed and/o epesented though the same mechanisms and ceebal stuctues has ecently been exploed 3 ANOVAs wee pefomed on the RLs of coect answes and on the eo ates duing the taining session (n 5 9), with task (N, DL, o CL) as the within-subject vaiable, consideing only the distance used in the fmri expeiment. These showed no significant diffeences between the expeimental tasks (RLs fo N: ms, DL: ms, CL: ms; F(2, 16) , P > 0.2; eos fo N: 15.1% %, DL: 27.6% 6 9.9%, CL , F(2, 16) , P > 0.06). Note that the taining session involved moe tials than the fmri session. fo physical and numeical magnitudes in gasping-elated tasks [Andes et al., 2004, 2008; Badets et al., 2007]; fo time, numeosity, o physical size in compaison tasks [Domal et al., 2008; Olivei et al., 2008; Xuan et al., 2007]; and fo semantic and physical quantities [Cohen Kadosh et al., 2006]. The pesent esults add new evidence to this debate, but is woth noting that the spatial esolution of fmri is still seveely limited in compaison with the invasive electophysiological techniques used with monkeys. Thus, it is possible that the ight IPS activation found hee in both discete (i.e., numbe of dots) and continuous (i.e., length of lines) magnitude pocessing might be due to neuons that code specifically fo one dimension. Futue studies using multivoxel patten analyses might help to claify the ovelap between epesentations of numeical and nonnumeical magnitude in the IPS [Ansai, 2008]. TMS would be anothe ideal complementay technique fo fomulating infeences about the causal elationship between the activity of these egions and the cognitive pocesses unde investigation. By inducing a tansient vitual lesion in healthy subjects while pefoming numeosity o lengthcompaison tasks, the necessay and citical contibution of these paietal aeas could be diectly tested. ACKNOWLEDGMENTS MP is a eseach associate at the National Fund fo Scientific Reseach (Belgium). We thank C. Gandin, L. Hemoye, and the Radiodiagnosis Unit at the Cliniques St. Luc (Bussels) fo thei suppot duing testing. REFERENCES Andes M, Davae M, Pesenti M, Olivie E, Seon X (2004): Numbe magnitude and gip apetue inteaction. NeuoRepot 15: Andes M, Osty DJ, Nicol F, Paus T (2008): Time couse of numbe magnitude intefeence duing gasping. 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