Differential Contributions of the Left and Right Inferior Parietal ... · Arabic numerals, as...

Differential Contributions of the Left andRight Inferior Parietal Lobules to NumberProcessing

F ChochonINSERM U334 Orsay France

L CohenINSERM U334 Orsay and Hocircpital de la Salpecirctriegravere Paris France

P F van de Moortele and S DehaeneINSERM U334 Orsay France

Abstract

We measured cerebral activation with functional magneticresonance imaging at 3 Tesla while eight healthy volunteersperformed various number processing tasks known to be dis-sociable in brain-lesioned patients naming comparing multi-plying or subtracting single digits The results revealed theactivation of a circuit comprising bilateral intraparietal pre-frontal and anterior cingulate components The extension and

lateralization of this circuit was modulated by task demandsThe intraparietal and prefrontal activation was more importantin the right hemisphere during the comparison task and in theleft hemisphere during the multiplication task and was in-tensely bilateral during the subtraction task Thus partiallydistinct cerebral circuits with the dorsal parietal pathway un-derlie distinct arithmetic operations

INTRODUCTION

Previous neuropsychological and imaging work has em-phasized the crucial role of the left inferior parietallobule in number processing In brain-lesioned cases thisarea is the main lesion site causing acalculia a selectivedecit in arithmetic (Dehaene amp Cohen 1997 Gerst-mann 1940 Takayama Sugishita Akiguchi amp Kimura1994) Furthermore this region is activated when normalsubjects perform simple mental calculations such as sin-gle-digit multiplication (Dehaene et al 1996) approxi-mation (Dehaene Spelke Stanescu Pinel amp Tsivkin1999) or serial subtraction (Roland amp Friberg 1985Rueckert et al 1996) However those brain-imagingstudies have also repeatedly evidenced a concomitantactivation of the homologous inferior parietal region ofthe right hemisphere in the same tasks

The present brain-imaging study was designed tothrow some light on the respective contributions of theleft and right inferior parietal areas to number process-ing We postulated that different number-processingtasks are associated with distinct cerebral circuits and inparticular with distinct patterns of lateralization withinthe parietal lobe We selected tasks based on two criteriatheir frequent dissociation in single-case studies of pa-

tients with number-processing decits and the predic-tions that could be derived about them from currenttheories of number processing

Dissociations between Operations inBrain-Lesioned Patients

The main motivation for our study lies in the nding thatin many single-case studies of patients with number-processing decits different arithmetic operations suchas naming comparing multiplying and subtracting digitsare not equally impaired First digit naming is oftenselectively preserved in ldquoGerstmann syndromerdquo patientswith acalculia stemming from a left inferior parietallesion and who experience severe difculties in mentalarithmetic Such patients may fail to compute for in-stance 3 1 or 9 acute 8 yet experience no difculty inreading the numbers aloud (Dehaene amp Cohen 1997Takayama et al 1994) Conversely digit naming can beimpaired in patients who otherwise have no difculty inmental arithmetic (Cipolotti amp Butterworth 1995) in-cluding patients with pure alexia (Cohen amp Dehaene1995) This double dissociation has led to the suggestionthat naming a digit can occur without necessarily access-

copy 1999 Massachusetts Institute of Technology Journal of Cognitive Neuroscience 116 pp 617ndash630

ing its semantic code (Cipolotti amp Butterworth 1995Dehaene amp Cohen 1995)

Dissociations between arithmetic operations are alsoon record The most frequent dissociation is betweencomparison and calculation Severely aphasic and acalcu-lic patients with major left-hemispheric lesions even ifthey cannot name add subtract or multiply digits maystill decide which of two numbers is larger (Dehaene ampCohen 1991 Grafman Kampen Rosenberg Salazar ampBoller 1989) The hypothesis that number comparison issupported at least in part by right-hemispheric processesreceives support from studies of split-brain patientsWhen pairs of digits are ashed in the left visual eldtherefore contacting the right hemisphere only split-brain patients are generally unable to read them aloudor calculate with them Yet they can decide whether thetwo digits are identical or which of them is larger (Co-hen amp Dehaene 1996 Gazzaniga amp Hillyard 1971 Gaz-zaniga amp Smylie 1984 Seymour Reuter-Lorenz ampGazzaniga 1994) It is noteworthy that when digits areashed in their right hemield and hence to their lefthemisphere these patients can readily name compareor calculate with them Hence the ability to comparetwo numbers seems to be redundantly available to bothhemispheres whereas naming and calculating abilitiesseem to require a left-hemispheric contribution

Even two seemingly similar arithmetic operationssuch as subtraction and multiplication can be dissoci-ated There are several cases on record that have a selec-tive decit of addition and multiplication in the face ofrelatively spared subtraction (Dagenbach amp McCloskey1992 Lampl Eshel Gilad amp Sarova-Pinhas 1994 McNeilamp Warrington 1994 Pesenti Seron amp van der Linden1994) or the converse (Delazer amp Benke 1997) RecentlyDehaene and Cohen (1997) have reported a doubledissociation between parietal and subcortical acalculiaA patient with a left subcortical lesion suffered from aserious impairment of rote memory for multiplicationproblems whereas her performance in solving additionand subtraction problems was much better Converselyanother patient with an inferior parietal lesion andGerstmannrsquos syndrome failed to solve very simple addi-tion and subtraction problems whereas he performed

signicantly better when retrieving rote multiplicationfacts1

Although such cases clearly suggest that distinct arith-metic operations rely partly on dissociable brain circuitsthey provide little information about their anatomicallocalization Most of these studies were framed in acognitive neuropsychological perspective and did notspecically look for the anatomical substrates of thedecits Furthermore brain lesions are often too large toallow for precise anatomical inferences and there arestill too few cases in the literature to warrant a statisticalmeta-analysis of lesion localization At present the onlysolid anatomical conclusions that may be drawn fromthe neuropsychological litterature are that (1) the leftinferior parietal region is critical for most calculationdecits particularly subtraction although number nam-ing comparison and even multiplication may be rela-tively preserved and (2) the right parietal area isgenerally not associated with specic number-process-ing decits in clinical neuropsychological practice al-though impairments of number comparison (Rosselli ampArdila 1989) and of the comprehension of arithmeticrelations (Langdon amp Warrington 1997) have been re-ported in some group studies of patients with rightparietal lesions

A Model of Number Processing Circuits

A model of the functional and anatomical architectureof the number processing system the triple-code model(Dehaene 1992 Dehaene amp Cohen 1995) can partiallyexplain the occurrence of dissociations between opera-tions The model assumes that numbers can be repre-sented in the human brain in three distinct formats asArabic numerals as sequences of words and as analogi-cal representations of the corresponding numericalquantity (Figure 1) In the visual Arabic code numbersare encoded as strings of digits on an internal visuospa-tial scratchpad This representation putatively involvingthe left and right ventromesial occipito-temporal path-ways allows for the identication of Arabic numerals andsubserves multidigit operations and parity judgments Inthe verbal code numbers are encoded as syntactically

Figure 1 Schematic diagramof the architecture of the tri-ple-code model

618 Journal of Cognitive Neuroscience Volume 11 Number 6

organized sequences of words (eg twenty-four) Thisrepresentation supported by left perisylvian languageareas allows for the comprehension and production ofspoken numerals It is postulated to be the obligatoryentry code for accessing stored tables of rote arithmeticfacts encoded in the form of short sentences in verbalmemory (eg two times three six) Finally in the mag-nitude code numbers are represented as analogicalquantities on an oriented line Numerical relations suchas knowing that 9 is larger than 5 are then implicitlyrepresented by proximity relations on the number lineThus this semantic code putatively involving the leftand right inferior parietal lobules supports number com-parison and other semantic manipulations of numericalquantities

The model assumes that these three cardinal repre-sentations are linked by direct transcoding routes thatallow numbers to be rapidly translated internally to andfrom the different formats (see Figure 1) According tothis model two main routes are therefore available tosolve single-digit arithmetical problems presented in Ara-bic format First there is a direct route in which theinput numerals are converted into a verbal format andthen a rote verbal memory store is accessed for arithme-tic facts This route is typically used for overlearned factssuch as single-digit addition and multiplication problemsfor which a stored ldquotablerdquo is available The second routeis an indirect semantic route in which mental manipu-lations of numerical quantities are used to compute theresults This pathway is used whenever rote verbalknowledge of the answer is lacking most typically forsubtraction problems According to the model quantityprocessing relies on the inferior parietal cortex in con-nection with the left perisylvian language networkwhenever verbal output is required

Experimental Design

Based on the neuropsychological literature and the tri-ple-code model digit naming comparison multiplica-tion and subtraction were selected as contrastive tasksfor our brain-imaging experiments In all four tasks sin-gle digits between 1 and 9 were presented visually at arate of one every 2 sec In the naming task subjectsnamed the target digits In the comparison task they hadto compare the target digits to 5 responding with thewords ldquolargerrdquo or ldquosmallerrdquo In the multiplication tasksubjects multiplied the target digits by 3 Finally in thesubtraction task they subtracted the target digits from11

The control task was a simple letter-naming task Asingle letter from A to I was ashed with the same timingas the digit stimuli and subjects simply responded withthe letterrsquos name This task controlled for the visual andresponse requirements of the arithmetic tasks Contrast-ing the functional magnetic resonance imaging (fMRI)responses during arithmetic relative to control should

isolate the cerebral networks involved in the internaltransformation of numerical information

To avoid head movement in the fMRI scanner thesubjects were asked to utter the responses subvocally ldquointheir headrdquo which prevented us from measuring theirperformance To provide reference behavioral data aboutthe tasks eight additional subjects were asked to per-form the same tasks with overt responses outside thescanner while their response times were recorded witha voice key

Predictions for Brain Activity during Arithmetic

Three critical predictions of the triple-code model wereexamined in the fMRI results

1 Digit naming should involve a direct asemantictranscoding route from the visual number form to theleft-hemispheric verbal system without requiring accessto the quantity system Hence little or no activationshould be found in left and right parietal cortices duringdigit naming

2 Number comparison should activate a bilateral in-ferior parietal network The evidence for preserved num-ber comparison in the right hemisphere of split-brainpatients and in cases of large left-hemispheric lesionsleads us to predict a strong activation of the right inferiorparietal area during number comparison above and be-yond any left-hemispheric activation

3 Multiplication and subtraction should show par-tially different activation patterns Subtraction which isnot generally learned by rote verbal strategies and canbe selectively impaired following inferior parietal lesionsshould yield greater activation of the quantity systemthan multiplication Conversely multiplication which isgenerally stored in rote verbal memory should involveleft-hemispheric language areas and should be muchmore strongly lateralized to the left hemisphere thansubtraction

RESULTS

Behavioral Findings

Subjects tested outside the fMRI scanner made 02 and07 errors in the letter and digit naming tasks respec-tively 09 errors in the comparison task and 2 errorsin the multiplication and subtraction tasks Only 10 cor-rect trials out of 2240 trials yielded response latencieslonger than 2 sec (all in the 2- to 3-sec range 3 trials inmultiplication and 7 in subtraction) Thus all ve experi-mental tasks were performed with high accuracy withinthe time limits imposed by the fMRI procedure (onestimulus every 2 sec)

Mean naming latencies were computed on the basisof correct trials excluding ve additional trials on whichthe response failed to trigger the voice key Letter- anddigit-naming latencies did not differ (mean = 455 msec

Chochon et al 619

and 451 msec respectively F(1 7) lt 1) Both namingtasks were faster than digit comparison (mean = 540msec Fs(1 7) gt 23 Ps lt 0002) Comparison was fasterthan multiplication (mean = 807 msec F(1 7) = 155P = 00056) which itself was faster than subtraction(mean = 919 msec F(1 7) = 673 P = 0036)

Brain-Imaging Findings

We rst determined which areas are involved in all fournumber processing tasks relative to the control task ofletter naming Activation peaks together with their Zscore their Talairach coordinates and the correspondingBrodmannrsquos areas (BAs) are listed in the Tables 1 and 2A distributed bilateral parietal frontal and anterior cin-gulate network was activated In the parietal lobe acti-vation was concentrated along the banks of theintraparietal sulcus extending inferiorily into the supe-rior part of the inferior parietal lobule (BA 3940) andanteriorily in the depth of the postcentral sulcus Theother active areas were the anterior cingulate gyrus (BA32) the bilateral frontal lobes including the inferiorgyrus (BA 4445) the middle dorsolateral gyrus (BA946) and the right superior gyrus (BA 68) as well asthe left precentral gyrus (BA 6) and the mesial frontalgyrus (supplementary motor area or SMA and BA 811)

Figure 2 demonstrates the range of interindividualvariation for this contrast (number processing versusletter naming) Five subjects showed a clearly bilateralpattern of activation in the inferior parietal lobe

whereas three subjects showed signicant activationonly in the left intraparietal region Nevertheless in allcases the activation during number processing followedthe banks of the middle sectors of the intraparietalsulcus often extending anteriorily into the depth of thepostcentral sulcus particularly in the right hemisphere

We then analyzed separately the four contrasts denedby each numerical task versus control (see Figure 3 andTables 1 and 2) During digit naming versus control onlythe right inferior frontal gyrus and the right mesial fron-tal gyrus were weakly activated During digit comparisonversus control a parieto-fronto-cingular network wasagain detected The activated areas were in the rightparietal lobe the postcentral gyrus andor sulcus andthe intraparietal sulcus In the left parietal lobe theintraparietal sulcus and the superior part of the inferiorparietal lobule were activated The activated frontal areasconsisted of the left inferior frontal gyrus the left mesialfrontal gyrus the left precentral gyrus the right inferiorfrontal gyrus and the right precentral gyrus The anteriorcingulate gyrus and the right putamen were also acti-vated

During multiplication versus control a network simi-lar to the one observed during number comparison wasactivated However although activation remained bilat-eral there was now a clear predominance in the lefthemisphere (see Tables 1 and 2) The active parietal areaswere both intraparietal sulci the right postcentral gyrusandor sulcus and the superior part of the left inferiorparietal lobule The anterior cingulate gyrus was also

Table 1 Coordinates and Z Scores of Signicant Activation Peaks in the Parietal Lobe

Contrast

Brain Area

Coordinatesin Talairach

SpaceAll Tasks

vs ControlDigit Naming

vs ControlComparisonvs Control

Multiplicationvs Control

Subtraction vs Control

R postcentral sulcusanterior intraparie-tal sulcus

42 30 45 821(4 S)

638(3 S)

601(3 S)

797(3 S)

R intraparietal sulcus(middle part)

42 39 39 764(4 S)

737(5 S)


39 42 42 770(5 S)

489(3 S)

575(2 S)

764(6 S)

R intraparietal sulcus(posterior part)

33 48 45 764(6 S)

550(5 S)

481(2 S)

738(3 S)

L intraparietal sulcus(middle part)

45 42 39 833(6 S)

469(2 S)

733(3 S)

793(8 S)

L intraparietal sulcus(posterior part)

39 54 48 795(8 S)

535(5 S)

753(5 S)

783(7 S)


27 66 42 818(7 S)

469(2 S)

717(4 S)

793(7 S)

Note The number of subjects showing a signicant activation in this anatomical area appears in parentheses


activated In the frontal lobe both inferior frontal gyriwere activated together with both dorsolateral frontalgyri and the right superior frontal gyrus The individualanalysis also detected activation in the mesial frontalcortex in ve subjects although this localization did notappear in the group analysis

In subtraction versus control the same parieto-fronto-cingular network was now greatly activated equally inboth hemispheres Areas of activation encompassed bothintraparietal sulci the superior part of both inferior pa-rietal gyri and the right postcentral sulcus The leftpostcentral sulcus was also activated in ve subjectsalthough not in the group analysis In the frontal lobeboth inferior frontal gyri were activated together withthe dorsolateral frontal gyri the left precentral gyrus andthe right superior frontal gyrus The mesial frontal gyriwere also activated in ve subjects as in the multiplica-tion task Finally the anterior cingulate gyrus alsoshowed activation To determine which of these activa-tion patterns were signicantly different across tasks wethen directly contrasted the numerical tasks with oneanother (see Methods) Although all 12 pairs of suchcomparisons were analyzed the results turned out to berelatively simple because the occurrence of additional

activation followed a strictly hierarchical pattern Thefour numerical tasks could be placed in the order Nam-ing lt Comparison lt Multiplication lt Subtraction Therenever was a signicant activation in any brain regionwhen a given task was contrasted with a task higher inthe hierarchy We therefore only report the six compari-sons in which a signicant difference was found (seeFigure 4 and Table 3)

During comparison versus digit naming activationwas detected only in the right postcentral sulcus At thenext level in the hierarchy for multiplication versus digitnaming activation largely predominated in the left hemi-sphere in the left precentral gyrus and sulcus and alongall of the left intraparietal sulcus The only right-hemi-spheric activation was in the postcentral sulcus Whenmultiplication was contrasted to comparison howeveronly the left intraparietal activation remained signicantFinally for subtraction versus digit naming the samefronto-cingulo-parietal network described in subtractionversus letter naming was activated in both hemispheresalthough with a lower intensity When subtraction wascontrasted with comparison the same network wasagain bilaterally activated with the sole exception of theabsence of activation in the right postcentral sulcus

Table 2 Coordinates and Z Scores of Signicant Activation Peaks Outside the Parietal Lobe

Contrast

Brain Area


SpaceAll Tasks





R superior frontal gyrus BA 68 24 9 48 779(4 S)

512(2 S)

766(2 S)

R dorsolateral frontal gyrus BA946

42 45 18 658(5 S)

466(3 S)

732(6 S)

R inferior frontal gyrus BA4447

36 27 6 742(5 S)

462(2 S)

558(2 S)

419(2 S)

769(6 S)

R precentral gyrus BA 6 51 3 36 486(3 S)

R putamen 22 18 4 355

L dorsolateral frontal gyrus BA946

30 6 51 771(6 S)

541(4 S)

731(6 S)

L inferior frontal gyrus BA4447

36 27 3 768(7 S)

532(3 S)

495(4 S)

760(5 S)

L precentral gyrus BA 6 -42 3 51 750(4 S)

574(3 S)

722(4 S)

Mesial frontal gyrusSMA BA6811

12 33 30 536(2 S)

401(3 S)

Anterior cingulate gyrus BA 32 12 18 36 724(4 S)

526(3 S)

511(3 S)

747(4 S)

Note The number of subjects showing a signicant activation in this anatomical area appears in parentheses Anatomical labels should be inter-preted cautiously because they were obtained by reporting the group activation peaks on the Talairach atlas BA is the approximate Brod-mannrsquos area

Chochon et al 621

Figure 2 Individual analysisof the eight subjects duringall four number processingtasks versus control at p =0001 corrected at 01 The in-dividual anatomical images ofall the subjects have been nor-malized For each image thesubjectrsquos sex (m or f) and ageas well as the axial coordinateof the slice (z) are provided

Figure 3 Group analysis ofthe comparison multiplica-tion and subtraction tasks ver-sus their control at p = 0001corrected at 005 Z gives theTalairach coordinate of theslices


When subtraction was contrasted with multiplicationconversely the parietal activation was now restricted tothe right hemisphere in the right anterior intraparie-talpostcentral region In the frontal lobe both inferiorgyri were activated together with the right dorsolateralgyrus

DISCUSSION

We begin by briey summarizing the results A distrib-uted network of brain regions including parietal frontaland anterior cingulate areas was engaged during numberprocessing However there were important differencesas a function of task demands First the parieto-fronto-cingular network was only activated when subjects wereengaged in active number manipulations tasks (compari-son multiplication or subtraction) but not in simpledigit naming relative to the letter-naming control Sec-ond although the circuit was already engaged bilaterallyduring the number comparison task relative to controlthe four numerical tasks could be ordered hierarchicallyin the order Naming lt Comparison lt Multiplication ltSubtraction so each higher-level task added a specicactivation to the immediately lower task Relative to digitnaming comparison only activated the depth of the rightpostcentral sulcus Relative to comparison multiplica-tion caused a strong additional left intraparietal acti-vation Finally relative to multiplication subtractionyielded greater right postcentral and bilateral prefrontalactivation

A Parieto-Fronto-Cingular Network for NumberProcessing

The network of areas active during number processingincluded parietal frontal and anterior cingulate compo-nents In the parietal lobe activation was concentratedalong the banks of the intraparietal sulcus as well in thedepth of the postcentral gyrus In the frontal lobe theactive areas were distributed in the inferior (BA 4445)dorsolateral (BA 469) and superior (BA 68) frontal gyrias well as the SMA and premotor cortex Anatomicallythese areas constitute a well-described network that isactive in different cognitive tasks involving workingmemory and visuospatial attention (Corbetta MiezinSchulman amp Petersen 1993 Goldman-Rakic 1984 Nobreet al 1997) On the basis of anatomical tracing lesionand single-cell recording studies Goldman-Rakic (1988)has proposed that different cognitive functions may becontrolled within parallel distributed neural systemslinking posterior parietal prefrontal and anterior cingu-late cortices and related subcortical structures Our re-sults suggest that in humans the internal manipulationof numbers is realized in such a circuit in close anatomi-cal connection with the dorsal parietal pathway

Part of the activations we observed especially in theprefrontal and anterior cingulate cortex are undoubt-edly related to nonnumerical factors such as workingmemory and executive attention Our numerical taskswere initially designed to require minimal contributionsfrom working memory and strategical processes On

Figure 4 Comparisonsacross the four numericaltasks The glass-brain viewsshowed the active areas forcontrasts comparing any twonumerical tasks (p lt 0001corrected p lt 005) Contrastswere masked by the corre-sponding contrast of the toptask relative to the letter-nam-ing control (p lt 0001) to fo-cus only on activations andcancel out deactivations rela-tive to control Six contrastsshowed signicant effectswhereas the six contrasts inthe opposite directionshowed no signicantdifference

Chochon et al 623

Table 3 Coordinates and Z Scores of Signicant Activation Peaks When Numerical Tasks Were Contrasted

Brain Area and Approximate Brodmannrsquos Area Z Score Coordinates

Comparison vs Digit Naming

R postcentral sulcus 465 42 24 45

Multiplication vs Digit Naming

L precentral gyrus BA 6 535 51 3 39

L intraparietal sulcus (posterior part) 487 30 72 33

L intraparietal sulcus (anterior part) 463 45 36 36


Multiplication vs Comparison


Subtraction vs Digit Naming


R inferior frontal gyrus BA 4445 693 48 18 15


R postcentral sulcusanterior intraparietal sulcus 670 42 30 45


L frontal dorsolateral gyrus BA 46 661 48 33 21

R dorsolateral gyrus BA 946 657 4242 21

L intraparietal sulcus (middle part) 633 51 42 42

R anterior cingulate gyrus BA 32 620 6 21 33

L inferior frontal gyrus BA 45 619 39 24 3


Subtraction vs Comparison

R intraparietal sulcus (posterior part) 615 27 63 30

R intraparietal sulcus (middle part) 606 27 39 33


L dorsolateral gyrus BA 46 531 51 36 18


R dorsolateral gyrus BA 10 494 24 42 3








Subtraction vs Multiplication






each trial only a single digit was presented and a singleinternal operation was required Yet in retrospect thereare several ways in which working memory might havebeen involved First the target digits were ashed foronly 200 msec after which they had to be kept in mindSecond subjects were asked to keep in mind the secondoperand of each operation (3 for multiplication 5 forcomparison and 11 for subtraction) Third subjects re-ported a posteriori that the pace of the task implied thatfor the most difcult multiplication and subtraction tri-als on some trials they had not fully completed process-ing before the next target appeared therefore theyoccasionally had to monitor two items in memoryFourth subjects also reported that on multiplication andsubtraction trials they often did not retrieve the resultof say 11 8 from memory Rather they claimed toresort to simple strategies such as knowledge of sumstotaling 10 (eg 11 = 10 + 1 = (8 + 2) + 1 hence 11 8 = 2 + 1 = 3) Psychological research has indicated thateven simple problems may require a strategical se-quence of steps and hence the storage of intermediateresults (LeFevre et al 1996) Thus working memoryrequirements may explain our observation of a strongactivation in prefrontal cortex during simple calcula-tion and also explain why this activation becamemore intense as the task increased in difculty fromdigit naming to comparison multiplication and subtrac-tion

It seems unlikely however that working memory andattentional factors entirely explain the parietal lobe re-sults First although the amount of activation was gener-ally correlated with task difculty as measured byreaction time and error rate a single task-difculty factorcannot explain the specic nonlinear manner in whichthe left and right parietal activations emerged (rightparietal activation in the comparison task then left inthe multiplication task see Figure 4) Second it is hard tosee how our results could have been contaminated by anartifactual activation of the visuospatial attentional sys-tem Our stimuli consisted of a single target digit (or asingle letter in the control task) appearing at the center ofthe screen for 200 msec Hence there was no necessityfor overt or covert spatial movement of gaze or attentionFurthermore even if attention was required for instancein the temporal domain to focus on the precise momentof appearance of the stimuli there should be no differ-ence with the control task of digit naming in that respect

We envisage two alternative explanations for thestrong parietal involvement in number processing Firstit may reect the activation of a number-processing areaanatomically close to but separate from the cerebralareas for visuospatial attention Highly selective decitsfor numbers can occur following an inferior parietallesion of the dominant hemisphere (Dehaene amp Cohen1997 Warrington 1982) Although parietal acalculia isfrequently associated with agraphia nger agnosia andleft-right confusion in a tetrad of symptoms called

Gerstmannrsquos syndrome (Gerstmann 1940) these decitsare dissociable (Benton 1992) suggesting that knowl-edge of numbers may occupy its own specic corticalterritory Indeed Dehaene and Cohen (1997) have sug-gested that acalculia in Gerstmannrsquos syndrome is bestdescribed as a category-specic decit for numbers simi-lar to the specic loss of knowledge that can occur forother categories of words such as animals body partstools or fruits and vegetables (Warrington amp McCarthy1987 Warrington amp Shallice 1984) Patient MAR (De-haene amp Cohen 1997) could still read and write Arabicnumerals but failed in tasks tapping elementary knowl-edge of numerical quantities such as computing 3 1 ordeciding which number falls between 2 and 4 (althoughhe could decide which letter falls between B and D orwhich month falls between February and April) Suchevidence together with data showing that infants andanimals possess elementary numerical abilities and thatearly brain damage can result in a selective inability forarithmetic has been taken to suggest that ldquonumbersenserdquo is a biologically determined ability of the humanwith a long evolutionary history and a specic cerebralsubstrate (Dehaene 1997) According to this workinghypothesis the intraparietal activation might reect thecerebral localization of a category-specic internal rep-resentation of numbers

An alternative explanation is that the internal manipu-lation of numbers draws on visuospatial resources thatare also recruited for genuinely spatial tasks Experi-ments with normal subjects have revealed an intimatelink between numbers and space Whenever subjectsprocess numbers they respond faster on the right-handside for larger numbers and on the left-hand side forsmaller numbers thus revealing an automatic spatial-numerical association or SNARC effect (Dehaene Boss-ini amp Giraux 1993) Numbers seem to be representedinternally in a spatially extended way and the metaphorof a number line (Restle 1970) has been proposed forthe internal representation of numerical quantities (De-haene 1992 Gallistel amp Gelman 1992) Indeed a smallfraction of normal subjects have the subjective experi-ence of seeing a number line extended in two- or three-dimensional space often with rich details and colors(Galton 1880 Seron Pesenti Noeumll Deloche amp Cornet1992) Spalding and Zangwill (1950) reported the caseof a patient who claimed to have suddenly lost such avisual image of numbers and who experienced difcul-ties in calculating and in orienting in space following alesion in the left parieto-occipital area Restle (1970)suggested that subjects calculate by mentally movingalong an oriented number line for instance shifting at-tention one step to the left of 3 to compute 3 1 Theuse of such spatial strategies for mental arithmetic mightexplain the activation of areas traditionally attributed tovisuospatial attention during internal number processingtasks with no overt or covert attention-orienting compo-nents

Chochon et al 625

Dissociations between Numerical Operations

In this section we confront the results to our initialtheoretical predictions about the dissociations betweennaming comparing multiplying and subtracting num-bers

An Asemantic Route for Number Naming

A rst prediction was that the naming task would fail tostrongly activate parietal areas associated with the se-mantic processing of numbers because a direct aseman-tic transcoding route is available for digit naming Thisprediction was largely validated Contrasting digit nam-ing with letter naming revealed no activation of theparietal lobe at a conventional level of signicance2 Theonly activations were located in the right inferior frontaland right mesial frontal gyri This suggests a greater rightfrontal contribution to number production than to letterproduction a nding that may be related to the occa-sional dissociation of number production from the pro-duction of other words in either the spoken (CohenVerstichel amp Dehaene 1998) or the written modality(Anderson Damasio amp Damasio 1990)

Number Comparison and the Right Parietal Lobe

A second prediction derived from the triple-code modelof number processing was that number comparisonshould activate the left and right inferior parietal lobuleswhich are hypothesized to support a semantic repre-sentation of numerical quantities Based on evidencefrom split-brain patients and those with major left-hemi-sphere lesions we predicted that the right parietallobule would play an important role in number compari-son The results conrmed this prediction Both parietallobes were activated with a slight predominance for theright hemisphere The right postcentral sulcus in particu-lar was strongly solicited and was the only region to beactivated during comparison relative to digit namingThis right-hemispheric predominance for number com-parison ts well with the results of a recent event-relatedpotential (ERP) study (Dehaene 1996) In a task identicalto the present one (comparison with a xed standard of5) a right-lateralized parieto-occipito-temporal ERP com-ponent was shown to be signicantly affected by thedistance between the target numbers and 5 but not bythe notation used for the numbers (spelled-out numeralsor Arabic digits) or by the hand used for respondingDipole modeling showed that this distance electricaleffect which indexes the critical step of quantity com-parison in this task was consistent with a bilateral gen-erator located deep in the left and right inferior parietalareas with a stronger activity in the right hemisphere

More surprising is the activation of the frontal cortexanterior cingulate and right putamen during number

comparison relative to letter naming These areas werenot predicted by available models of number processingAs noted above they might be related to processes notspecic to numbers but inherent to the comparison tasksuch as working memory for the reference numberresponse decision execution or inhibition of digit nam-ing and calculation In an ERP study of number compari-son Dehaene et al (1996) have reported an activation ofthe anterior cingulate cortex related to error monitoringand correction which may have contributed to the pre-sent task

Multiplication versus Subtraction

Our third prediction was that multiplication and subtrac-tion although supercially similar would yield differentactivation patterns with a greater bilateral inferior parie-tal involvement during subtraction and a strict left-hemi-spheric lateralization with activation of perisylvianlanguage areas during multiplication This prediction wasonly partially supported by the data Certainly subtrac-tion entailed a considerable bilateral activation of theintraparietal sulcus particularly relative to number com-parison (Figure 4) Furthermore activation was highlyleft-lateralized during multiplication being conned tothe left intraparietal area during multiplication relativeto comparison However the direct contrast betweenmultiplication and subtraction revealing only a few dif-ferences Several prefrontal areas and the right postcen-tral region were signicantly more active duringsubtraction whereas no area was signicantly more ac-tive during multiplication The predicted activation oflanguage areas during multiplication was remarkably ab-sent3 One possibility is that these areas were alreadypresent in all control conditions (because subjects al-ways had to name the result) and were therefore can-celed out in all contrasts Indeed exact resolution ofaddition problems strongly activated the left inferiorfrontal region and the left angular gyrus among otherareas in a recent study in which the control task in-volved the presentation of letters but did not requirenaming (Dehaene et al 1999)

The association of multiplication with the left intra-parietal area although not predicted by our theoreticalframework is clearly compatible with previous ndingsWith positron emission tomography (PET) Dehaene etal (1996) reported bilateral inferior parietal activationwith a left lateralization during a multiplication taskWith ERPs Kiefer and Dehaene (1997) also found leftlateralized inferior parietal activity during both simpleand complex multiplication facts with a tendency for alater bilateral activation for complex multiplication factsonly These observations must be reconciled with theobservation that parietal lesions that affect number com-prehension may leave multiplication retrieval partiallyintact (Dehaene amp Cohen 1997 Delazer amp Benke 1997)


A plausible explanation is that the robust parietal activa-tion during multiplication reects quantity-based proc-esses that are useful to normal subjects but are notstrictly needed for the task When solving even simplemultiplication problems normal subjects often use acombination of direct retrieval and quantity-based strate-gies (Campbell 1994 LeFevre et al 1996) For instancethe order of the operands may be reversed (3 acute 8 = 8 acute3 = 24) or the problem may be decomposed into simplerfacts (3 acute 5 = 5 + 5 + 5 = 15) Such ldquosemantic elabora-tionrdquo strategies require an understanding of the quanti-ties involved in the original problem which would beexpected to result in inferior parietal activation (De-haene amp Cohen 1995) Given the replicability of thisactivation the triple-code model should acknowledgethat the semantic representation of numerical quantitiesmakes an important although perhaps optional contri-bution to the retrieval of arithmetic facts

CONCLUSION

The present results establish both the existence of aparieto-fronto-cingulate network active during variousmental arithmetic tasks and its variable involvement asa function of task demands The left and right parietalregions although they both contribute to mental arith-metic may not be functionally equivalent At present weonly have little cues about what these functions may beIt is noteworthy however that a task calling only for theinternal manipulation of numerical quantity numbercomparison was found to rely more on the right parietallobule whereas a task presumably requiring access toverbal memory was more strongly associated with theleft parietal lobule Our working hypothesis which wewould like to tentatively propose in this conclusion isthat although both parietal areas are involved in manipu-lating quantity information only the left parietal regionprovides the interconnection of the quantity repre-sentation with the linguistic code Indeed this is a directconsequence of the triple-code model in which the leftinferior parietal region provides the only direct connec-tion between the left verbal system and the right parietalquantity system (Figure 1) During multiplication the leftparietal region would be strongly activated because sub-jects use the quantity representation to monitor theplausibility of the results they have obtained throughverbal computations as suggested above During com-parison the right parietal region would sufce becausecomparison involves accessing the quantity system fromthe Arabic notation but does not require any translationbetween the verbal and quantity formats During subtrac-tion nally both the left and the right parietal lobuleswould be active because subtraction requires both inter-nal quantity manipulations and naming of the resultingquantity The pivotal role of the left parietal region would

also explain why left but not right inferior parietallesions yield strong impairments of calculation

METHOD

Subjects

Eight right-handed subjects (four women and four men)aged between 20 and 30 years participated in the imag-ing study All were drug free had no neurological orpsychiatric history and had normal anatomical magneticresonance images All gave their written informed con-sent The experiment was approved by the Ethical Com-mittee of the Hocircpital de Bicecirctre Paris

Stimuli

In the imager visual stimuli were projected on a translu-cent screen placed at the subjectrsquos head Stimuli weredisplayed using an active-matrix video projector con-trolled by a PC computer running the EXPE5 softwarefor millisecond timing (Pallier Dupoux amp Jeannin 1997)Subjects wore a head-mounted mirror that allowed themto see the stimuli in their normal upright position Thesame stimuli were used for the four numerical tasks(naming comparison multiplication and subtraction)Random digits between 1 and 9 excluding digit 5 wereashed for 200 msec at a rate of one every 2 sec Forthe control task random letters between A and I exclud-ing letter E were ashed using the same parameters ofduration and rate Letters and digits were presented inalternating blocks of 18 trials (36 sec) each

Tasks

To prevent head movements subjects were told to per-form all the tasks mentally without overt vocalizationDuring letter blocks they named the letters mentallyDuring the digit blocks they performed one of thefollowing four numerical tasks In the naming task sub-jects had to name the target digit In the comparison tasksubjects were instructed to compare the target digit tothe standard number 5 mentally saying ldquolargerrdquo orldquosmallerrdquo In the multiplication task subjects had to mul-tiply the target digit by 3 and then to name the resultmentally In the subtraction task subjects had to subtractthe target digit from 11 and to name the result mentallyFor each task the paradigm consisted in three experi-mental blocks alternating with three control blocksThus each experiment included four runs of 336 sec(ie one run for each experimental task)

Data Acquisition

All experiments were performed on a 3-T whole-bodysystem (Bruker Germany) equipped with a quadrature

Chochon et al 627

birdcage radio frequency (RF) coil and a head-gradientcoil insert designed for echoplanar imaging Foam pad-ding was used to limit head motion within the coilFunctional images were obtained with a T2-weightedgradient echo echo planar imaging sequence (TR = 6000msec TE = 40 msec FOV = 220 acute 220 mm2 matrix =64 acute 64) using blood oxygen level-dependent contrastEighteen 5-mm-thick axial slices covering most of thebrain were acquired every 6 sec Thirty-nine images eachconsisting of 18 slices were collected consecutively foreach task The rst three images were not included inthe analysis Functional images were reconstructed andanalyzed off-line High-resolution images (3-D gradient-echo inversion-recovery sequence TI = 700 msec TR =1600 msec FOV = 192 256 acute 256 mm3 matrix = 256 acute128 acute 256 slice thickness = 1 mm along head-foot axis)were also acquired for anatomical localization

Data Analysis

All subsequent data analyses were performed with Sta-tistical Parametric Mapping version 96 (SPM96) To cor-rect for motion the scans from each subject wererealigned using the last image as a reference (the imagewhose acquisition time is nearest to that of anatomicalimages) For each subject anatomical images were trans-formed stereotactically to Talairach coordinates using thestandard template of the Montreal Neurological InstituteThe functional scans were then normalized using thesame transformation Functional images were smoothedwith a Gaussian spatial lter of 5 mm The resultingimages had cubic voxels of 3 acute 3 acute 3 mm3 and the nalimage resolution was 73 acute 73 acute 72 mm3 The anatomi-cal images had cubic voxels of 2 acute 2 acute 2 mm3

Each block of activation was modeled by two tempo-ral basis functions the rst one for the early componentof the activation and the second one for the later com-ponent We used a high-pass lter set at 120 sec roughlytwice the period of the paradigm Individual data wereanalyzed using a randomized block design with globalbrain activity as a covariate of noninterest After statisti-cal analysis and for each subject the activation mapswere superimposed on individual anatomical images forlocalization purposes with the support of their Talairachcoordinates

For the group analysis we used a voxelwise sig-nicance threshold of 0001 corrected to p lt 005 formultiple comparisons by the standard procedure ofSPM96 With the particular statistical parameters of ourimages this corresponded to reporting only clusterswith more than 16 neighboring voxels each active atp lt 0001 To identify active areas we rst examined acontrast comparing the main effect of the four numericaltasks relative to the letter-naming control Then we ex-amined the four contrasts digit naming gt control com-parison gt control multiplication gt control and

subtraction gt control to identify the areas involved ineach numerical task Finally we also analyzed the 12contrasts corresponding to all possible comparisons be-tween two numerical tasks Because each numerical taskwas acquired in a distinct block these between-taskcontrasts were framed as interaction terms in SPM96 Forinstance to compare multiplication with subtraction weused the following interaction term (multiplication itsletter-naming control) (subtraction its letter-namingcontrol) We masked these contrasts with the originalcontrast of the appropriate task relative to control Forinstance the above contrast for multiplication gt subtrac-tion was masked by the original contrast multiplica-tion gt letter-naming control (at p lt 0001) This ensuredthat we looked only at areas that showed signicantdifferences across tasks and were active relative to con-trol Signicant differences that were due to a greaterdeactivation in one task relative to the other whoseinterpretation is difcult were canceled out by this pro-cedure

The same statistical analysis was applied separately toeach individual subject Because of the smaller numberof degrees of freedom a voxelwise signicance thresh-old of 0001 corrected to p lt 01 was then used Detailsof the individual analyses are available from the authorsHere we only report for each signicant effect in thegroup analysis the number of subjects who showed thateffect in the same anatomical area in the individualanalysis

Behavioral Control Study

Eight additional subjects were run in a behavioral con-trol study The same stimuli were presented on a standardPC monitor in ve blocks of 56 trials each correspond-ing to the ve tasks (letter naming digit naming com-parison multiplication and subtraction) Subjects spoketheir responses aloud in a voice-activated relay Vocalreaction times were measured to the closest millisecondand responses were recorded for subsequent scoring oferrors Each trial consisted of an initial 2000-msec blankscreen The stimulus was then ashed for 200 msec Thesubjectrsquos vocal response triggered the next trial The vetasks were presented in random order

Acknowledgments

This work was supported by INSERM the Groupement drsquoIn-teacuterecirct Scientique (GIS) ldquoSciences de la Cognitionrdquo and theFondation pour la Recherche Meacutedicale (FRM) We thankE Giacomini D Le Bihan G Le Clecrsquoh S Leheacutericy and J BPoline for their technical and statistical help

Reprint requests should be sent to Stanislas Dehaene INSERMU334 Service Hospitalier Freacutedeacuteric Joliot CEADSV 4 place duGeacuteneacuteral Leclerc 91401 Orsay Cedex France or via e-maildehaeneshfjceafr


Notes

1 This patient MAR was unusual in that he showedGerstmannrsquos syndrome following a right inferior parietal le-sion The patient was left-handed however and might have hadan unusual lateralization pattern More recently the dissocia-tion between severely impaired subtraction and relatively morepreserved multiplication was replicated in several cases ofacalculia and Gerstmannrsquos syndrome stemming from a classicalleft inferior parietal lesion (Delazer amp Benke 1997 L Cohenand S Dehaene 1997 unpublished observations)2 In various chronometric tasks including naming the merepresentation of a digit on a screen sufces to induce a quan-tity-based interference in response times (Brysbaert 1995 De-haene amp Akhavein 1995 Dehaene et al 1998 LeFevre Bisanzamp Mrkonjic 1988) Thus one might have expected an automaticactivation of the parietal quantity system during naming evenif it was not strictly required for the task We therefore reex-amined the presence of subthreshold parietal activation duringthe naming task at a lower level of signicance We rst usedthe data from the subtraction condition to identify seven activevoxels related to number processing in the inferior parietallobules (at the conventional level of signicance p lt 0001corrected for multiple comparisons to p lt 005) We then askedwhether these voxels showed a signicance difference in thecontrast of naming versus control now at the lower sig-nicance of p lt 005 This was indeed the case All sevenparietal activation peaks listed in Table 1 showed a small in-crease in activation during digit naming as compared to letternaming signicant at p lt 005 In fact two major clusters of104 and 71 voxels respectively were activated at p lt 005 inthe left and right intraparietalpostcentral area during digitnaming compared to letter naming3 The left basal ganglia have been tentatively implicated inthe retrieval of rote multiplication facts (Dehaene amp Cohen1995) Here we did not nd left subcortical involvement inmultiplication with standard statistical thresholds Becausethose thresholds required at least 16 contiguous voxels (432mm3) each with p lt 0001 for a cluster of active voxels to beconsidered signicant we also reexamined subcortical activitywithout imposing a minimum cluster size but with a stringentvoxelwise threshold of p lt 00001 Although no activation wasfound in subtraction versus letter naming we did nd a singlesubcortical activation in the head of the left caudate nucleus( 18 8 22 Z = 390 5 voxels) in multiplication versus letternaming This activation although still present in multiplicationversus digit naming was not present when multiplication wascontrasted with either comparison or subtraction even at p lt005 Thus the evidence for a specic role of the left basalganglia in multiplication remained weak at best

REFERENCES

Anderson S W Damasio A R amp Damasio H (1990) Trou-bled letters but not numbers Domain specic cognitiveimpairments following focal damage in frontal cortexBrain 113 749ndash766

Benton A L (1992) Gerstmannrsquos syndrome Archives of Neu-rology 49 445ndash447

Brysbaert M (1995) Arabic number reading On the natureof the numerical scale and the origin of phonological re-coding Journal of Experimental Psychology General124 434ndash452

Campbell J I D (1994) Architectures for numerical cogni-tion Cognition 53 1ndash44

Cipolotti L amp Butterworth B (1995) Toward a multiroutemodel of number processing Impaired number transcod-

ing with preserved calculation skills Journal of Experi-mental Psychology General 124 375ndash390

Cohen L amp Dehaene S (1995) Number processing in purealexia The effect of hemispheric asymmetries and task de-mands NeuroCase 1 121ndash137

Cohen L amp Dehaene S (1996) Cerebral networks for num-ber processing Evidence from a case of posterior callosallesion NeuroCase 2 155ndash174

Cohen L Verstichel P amp Dehaene S (1998) Neologistic jar-gon sparing numbers A category-specic phonological im-pairment Cognitive Neuropsychology 14 1029ndash1061

Corbetta M Miezin F M Schulman G L amp Petersen S E(1993) A PET study of visuospatial attention Journal ofNeuroscience 13 1202ndash1226

Dagenbach D amp McCloskey M (1992) The organization ofarithmetic facts in memory Evidence from a brain-dam-aged patient Brain and Cognition 20 345ndash366

Dehaene S (1992) Varieties of numerical abilities Cogni-tion 44 1ndash42

Dehaene S (1996) The organization of brain activations innumber comparison Event-related potentials and the addi-tive-factors methods Journal of Cognitive Neuroscience8 47ndash68

Dehaene S (1997) The number sense New York OxfordUniversity Press

Dehaene S amp Akhavein R (1995) Attention automaticityand levels of representation in number processing Jour-nal of Experimental Psychology Learning Memory andCognition 21 314ndash326

Dehaene S Bossini S amp Giraux P (1993) The mental repre-sentation of parity and numerical magnitude Journal ofExperimental Psychology General 122 371ndash396

Dehaene S amp Cohen L (1991) Two mental calculation sys-tems A case study of severe acalculia with preserved ap-proximation Neuropsychologia 29 1045ndash1074

Dehaene S amp Cohen L (1995) Towards an anatomical andfunctional model of number processing MathematicalCognition 1 83ndash120

Dehaene S amp Cohen L (1997) Cerebral pathways for calcu-lation Double dissociation between rote verbal and quanti-tative knowledge of arithmetic Cortex 33 219ndash250

Dehaene S Naccache L Le Clecrsquoh G Koechlin E MuellerM Dehaene-Lambertz G van de Moortele P F amp Le Bi-han D (1998) Imaging unconscious semantic priming Na-ture 395 597ndash600

Dehaene S Spelke E Stanescu R Pinel P amp Tsivkin S(1999) Sources of mathematical thinking Behavioral andbrain-imaging evidence Science 284 970ndash974

Dehaene S Tzourio N Frak V Raynaud L Cohen LMehler J amp Mazoyer B (1996) Cerebral activations dur-ing number multiplication and comparison A PET studyNeuropsychologia 34 1097ndash1106

Delazer M amp Benke T (1997) Arithmetic facts withoutmeaning Cortex 33 697ndash710

Gallistel C R amp Gelman R (1992) Preverbal and verbalcounting and computation Cognition 44 43ndash74

Galton F (1880) Visualized numerals Nature 21 252ndash256Gazzaniga M S amp Hillyard S A (1971) Language and

speech capacity of the right hemisphere Neuropsycholo-gia 9 273ndash280

Gazzaniga M S amp Smylie C E (1984) Dissociation of lan-guage and cognition A psychological prole of two discon-nected right hemispheres Brain 107 145ndash153

Gerstmann J (1940) Syndrome of nger agnosia disorienta-tion for right and left agraphia and acalculia Archives ofNeurology and Psychiatry 44 398ndash408

Goldman-Rakic P S (1984) Modular organization of prefron-tal cortex Trends in Neuroscience 7 419ndash424

Chochon et al 629

Goldman-Rakic P S (1988) Topography of cognition Paralleldistributed networks in primate association cortex An-nual Review of Neuroscience 11 137ndash156

Grafman J Kampen D Rosenberg J Salazar A amp Boller F(1989) Calculation abilities in a patient with a virtual lefthemispherectomy Behavioral Neurology 2 183ndash194

Kiefer M amp Dehaene S (1997) The time course of parietalactivation in single-digit multiplication Evidence fromevent-related potentials Mathematical Cognition 3 1ndash30

Lampl Y Eshel Y Gilad R amp Sarova-Pinhas I (1994) Selec-tive acalculia with sparing of the subtraction process in apatient with left parietotemporal hemorrhage Neurology44 1759ndash1761

Langdon D W amp Warrington E K (1997) The abstraction ofnumerical relations A role for the right hemisphere inarithmetic Journal of the International Neuropsychologi-cal Society 3 260ndash268

LeFevre J A Bisanz J Daley K E Buffone L Greenbaum SL amp Sadesky G S (1996) Multiple routes to solution ofsingle-digit multiplication problems Journal of Experimen-tal Psychology General 125 284ndash306

LeFevre J Bisanz J amp Mrkonjic L (1988) Cognitive arithme-tic Evidence for obligatory activation of arithmetic factsMemory amp Cognition 16 45ndash53

McNeil J E amp Warrington E K (1994) A dissociation be-tween addition and subtraction within written calculationNeuropsychologia 32 717ndash728

Nobre A C Sebestyen G N Gitelman D R MesulamM M Frackowiak R S J amp Frith C D (1997) Functionallocalization of the system for visuospatial attention usingpositron emission tomography Brain 120 515ndash533

Pallier C Dupoux E amp Jeannin X (1997) EXPE5 An ex-pandable programming language for on-line psychologicalexperiments Behavior Research Methods Instrumentsand Computers 29 322ndash327

Pesenti M Seron X amp van der Linden M (1994) Selective

impairment as evidence for mental organization of arith-metical facts BB a case of preserved subtraction Cortex30 661ndash671

Restle F (1970) Speed of adding and comparing numbersJournal of Experimental Psychology 91 191ndash205

Roland P E amp Friberg L (1985) Localization of cortical ar-eas activated by thinking Journal of Neurophysiology 531219ndash1243

Rosselli M amp Ardila A (1989) Calculation decits in pa-tients with right and left hemisphere damage Neuropsy-chologia 27 607ndash617

Rueckert L Lange N Partiot A Appollonio I Litvar ILe Bihan D amp Grafman J (1996) Visualizing cortical acti-vation during mental calculation with functional MRINeuroimage 3 97ndash103

Seron X Pesenti M Noeumll M P Deloche G amp Cornet J-A(1992) Images of numbers or when 98 is upper left and 6sky blue Cognition 44 159ndash196

Seymour S E Reuter-Lorenz P A amp Gazzaniga M S (1994)The disconnection syndrome Basic ndings reafrmedBrain 117 105ndash115

Spalding J M K amp Zangwill O L (1950) Disturbance ofnumber-form in a case of brain injury Journal of Neurol-ogy 13 24ndash29

Takayama Y Sugishita M Akiguchi I amp Kimura J (1994)Isolated acalculia due to left parietal lesion Archives ofNeurology 51 286ndash291

Warrington E K (1982) The fractionation of arithmeticalskills A single case study Quarterly Journal of Experimen-tal Psychology 34A 31ndash51

Warrington E K amp McCarthy R (1987) Categories of knowl-edge Further fractionation and an attempted integrationBrain 110 1273ndash1296

Warrington E K amp Shallice T (1984) Category-specic se-mantic impairments Brain 107 829ndash854


ing its semantic code (Cipolotti amp Butterworth 1995Dehaene amp Cohen 1995)

Dissociations between arithmetic operations are alsoon record The most frequent dissociation is betweencomparison and calculation Severely aphasic and acalcu-lic patients with major left-hemispheric lesions even ifthey cannot name add subtract or multiply digits maystill decide which of two numbers is larger (Dehaene ampCohen 1991 Grafman Kampen Rosenberg Salazar ampBoller 1989) The hypothesis that number comparison issupported at least in part by right-hemispheric processesreceives support from studies of split-brain patientsWhen pairs of digits are ashed in the left visual eldtherefore contacting the right hemisphere only split-brain patients are generally unable to read them aloudor calculate with them Yet they can decide whether thetwo digits are identical or which of them is larger (Co-hen amp Dehaene 1996 Gazzaniga amp Hillyard 1971 Gaz-zaniga amp Smylie 1984 Seymour Reuter-Lorenz ampGazzaniga 1994) It is noteworthy that when digits areashed in their right hemield and hence to their lefthemisphere these patients can readily name compareor calculate with them Hence the ability to comparetwo numbers seems to be redundantly available to bothhemispheres whereas naming and calculating abilitiesseem to require a left-hemispheric contribution

Even two seemingly similar arithmetic operationssuch as subtraction and multiplication can be dissoci-ated There are several cases on record that have a selec-tive decit of addition and multiplication in the face ofrelatively spared subtraction (Dagenbach amp McCloskey1992 Lampl Eshel Gilad amp Sarova-Pinhas 1994 McNeilamp Warrington 1994 Pesenti Seron amp van der Linden1994) or the converse (Delazer amp Benke 1997) RecentlyDehaene and Cohen (1997) have reported a doubledissociation between parietal and subcortical acalculiaA patient with a left subcortical lesion suffered from aserious impairment of rote memory for multiplicationproblems whereas her performance in solving additionand subtraction problems was much better Converselyanother patient with an inferior parietal lesion andGerstmannrsquos syndrome failed to solve very simple addi-tion and subtraction problems whereas he performed

signicantly better when retrieving rote multiplicationfacts1

Although such cases clearly suggest that distinct arith-metic operations rely partly on dissociable brain circuitsthey provide little information about their anatomicallocalization Most of these studies were framed in acognitive neuropsychological perspective and did notspecically look for the anatomical substrates of thedecits Furthermore brain lesions are often too large toallow for precise anatomical inferences and there arestill too few cases in the literature to warrant a statisticalmeta-analysis of lesion localization At present the onlysolid anatomical conclusions that may be drawn fromthe neuropsychological litterature are that (1) the leftinferior parietal region is critical for most calculationdecits particularly subtraction although number nam-ing comparison and even multiplication may be rela-tively preserved and (2) the right parietal area isgenerally not associated with specic number-process-ing decits in clinical neuropsychological practice al-though impairments of number comparison (Rosselli ampArdila 1989) and of the comprehension of arithmeticrelations (Langdon amp Warrington 1997) have been re-ported in some group studies of patients with rightparietal lesions

A Model of Number Processing Circuits

A model of the functional and anatomical architectureof the number processing system the triple-code model(Dehaene 1992 Dehaene amp Cohen 1995) can partiallyexplain the occurrence of dissociations between opera-tions The model assumes that numbers can be repre-sented in the human brain in three distinct formats asArabic numerals as sequences of words and as analogi-cal representations of the corresponding numericalquantity (Figure 1) In the visual Arabic code numbersare encoded as strings of digits on an internal visuospa-tial scratchpad This representation putatively involvingthe left and right ventromesial occipito-temporal path-ways allows for the identication of Arabic numerals andsubserves multidigit operations and parity judgments Inthe verbal code numbers are encoded as syntactically

Figure 1 Schematic diagramof the architecture of the tri-ple-code model




Experimental Design










RESULTS

Behavioral Findings



Chochon et al 619









Contrast

Brain Area


SpaceAll Tasks






42 30 45 821(4 S)

638(3 S)

601(3 S)

797(3 S)


42 39 39 764(4 S)

737(5 S)


39 42 42 770(5 S)

489(3 S)

575(2 S)

764(6 S)


33 48 45 764(6 S)

550(5 S)

481(2 S)

738(3 S)


45 42 39 833(6 S)

469(2 S)

733(3 S)

793(8 S)


39 54 48 795(8 S)

535(5 S)

753(5 S)

783(7 S)


27 66 42 818(7 S)

469(2 S)

717(4 S)

793(7 S)








Contrast

Brain Area


SpaceAll Tasks






512(2 S)

766(2 S)


42 45 18 658(5 S)

466(3 S)

732(6 S)


36 27 6 742(5 S)

462(2 S)

558(2 S)

419(2 S)

769(6 S)


R putamen 22 18 4 355


30 6 51 771(6 S)

541(4 S)

731(6 S)


36 27 3 768(7 S)

532(3 S)

495(4 S)

760(5 S)


574(3 S)

722(4 S)


12 33 30 536(2 S)

401(3 S)


526(3 S)

511(3 S)

747(4 S)


Chochon et al 621





DISCUSSION






Chochon et al 623

















































Chochon et al 625














CONCLUSION



METHOD

Subjects


Stimuli


Tasks


Data Acquisition


Chochon et al 627


Data Analysis








Acknowledgments




Notes


REFERENCES






























Chochon et al 629



























Experimental Design










RESULTS

Behavioral Findings



Chochon et al 619









Contrast

Brain Area


SpaceAll Tasks






42 30 45 821(4 S)

638(3 S)

601(3 S)

797(3 S)


42 39 39 764(4 S)

737(5 S)


39 42 42 770(5 S)

489(3 S)

575(2 S)

764(6 S)


33 48 45 764(6 S)

550(5 S)

481(2 S)

738(3 S)


45 42 39 833(6 S)

469(2 S)

733(3 S)

793(8 S)


39 54 48 795(8 S)

535(5 S)

753(5 S)

783(7 S)


27 66 42 818(7 S)

469(2 S)

717(4 S)

793(7 S)








Contrast

Brain Area


SpaceAll Tasks






512(2 S)

766(2 S)


42 45 18 658(5 S)

466(3 S)

732(6 S)


36 27 6 742(5 S)

462(2 S)

558(2 S)

419(2 S)

769(6 S)


R putamen 22 18 4 355


30 6 51 771(6 S)

541(4 S)

731(6 S)


36 27 3 768(7 S)

532(3 S)

495(4 S)

760(5 S)


574(3 S)

722(4 S)


12 33 30 536(2 S)

401(3 S)


526(3 S)

511(3 S)

747(4 S)


Chochon et al 621





DISCUSSION






Chochon et al 623

















































Chochon et al 625














CONCLUSION



METHOD

Subjects


Stimuli


Tasks


Data Acquisition


Chochon et al 627


Data Analysis








Acknowledgments




Notes


REFERENCES






























Chochon et al 629

































Contrast

Brain Area


SpaceAll Tasks






42 30 45 821(4 S)

638(3 S)

601(3 S)

797(3 S)


42 39 39 764(4 S)

737(5 S)


39 42 42 770(5 S)

489(3 S)

575(2 S)

764(6 S)


33 48 45 764(6 S)

550(5 S)

481(2 S)

738(3 S)


45 42 39 833(6 S)

469(2 S)

733(3 S)

793(8 S)


39 54 48 795(8 S)

535(5 S)

753(5 S)

783(7 S)


27 66 42 818(7 S)

469(2 S)

717(4 S)

793(7 S)








Contrast

Brain Area


SpaceAll Tasks






512(2 S)

766(2 S)


42 45 18 658(5 S)

466(3 S)

732(6 S)


36 27 6 742(5 S)

462(2 S)

558(2 S)

419(2 S)

769(6 S)


R putamen 22 18 4 355


30 6 51 771(6 S)

541(4 S)

731(6 S)


36 27 3 768(7 S)

532(3 S)

495(4 S)

760(5 S)


574(3 S)

722(4 S)


12 33 30 536(2 S)

401(3 S)


526(3 S)

511(3 S)

747(4 S)


Chochon et al 621





DISCUSSION






Chochon et al 623

















































Chochon et al 625














CONCLUSION



METHOD

Subjects


Stimuli


Tasks


Data Acquisition


Chochon et al 627


Data Analysis








Acknowledgments




Notes


REFERENCES






























Chochon et al 629






























Contrast

Brain Area


SpaceAll Tasks






512(2 S)

766(2 S)


42 45 18 658(5 S)

466(3 S)

732(6 S)


36 27 6 742(5 S)

462(2 S)

558(2 S)

419(2 S)

769(6 S)


R putamen 22 18 4 355


30 6 51 771(6 S)

541(4 S)

731(6 S)


36 27 3 768(7 S)

532(3 S)

495(4 S)

760(5 S)


574(3 S)

722(4 S)


12 33 30 536(2 S)

401(3 S)


526(3 S)

511(3 S)

747(4 S)


Chochon et al 621





DISCUSSION






Chochon et al 623

















































Chochon et al 625














CONCLUSION



METHOD

Subjects


Stimuli


Tasks


Data Acquisition


Chochon et al 627


Data Analysis








Acknowledgments




Notes


REFERENCES






























Chochon et al 629





























DISCUSSION






Chochon et al 623

















































Chochon et al 625














CONCLUSION



METHOD

Subjects


Stimuli


Tasks


Data Acquisition


Chochon et al 627


Data Analysis








Acknowledgments




Notes


REFERENCES






























Chochon et al 629


























DISCUSSION






Chochon et al 623

















































Chochon et al 625














CONCLUSION



METHOD

Subjects


Stimuli


Tasks


Data Acquisition


Chochon et al 627


Data Analysis








Acknowledgments




Notes


REFERENCES






























Chochon et al 629









































































Chochon et al 625














CONCLUSION



METHOD

Subjects


Stimuli


Tasks


Data Acquisition


Chochon et al 627


Data Analysis








Acknowledgments




Notes


REFERENCES






























Chochon et al 629






























Chochon et al 625














CONCLUSION



METHOD

Subjects


Stimuli


Tasks


Data Acquisition


Chochon et al 627


Data Analysis








Acknowledgments




Notes


REFERENCES






























Chochon et al 629






































CONCLUSION



METHOD

Subjects


Stimuli


Tasks


Data Acquisition


Chochon et al 627


Data Analysis








Acknowledgments




Notes


REFERENCES






























Chochon et al 629


























CONCLUSION



METHOD

Subjects


Stimuli


Tasks


Data Acquisition


Chochon et al 627


Data Analysis








Acknowledgments




Notes


REFERENCES






























Chochon et al 629


























Data Analysis








Acknowledgments




Notes


REFERENCES






























Chochon et al 629

























Notes


REFERENCES






























Chochon et al 629

















































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