᭜HumanBrainMapping16:119–130(2002)᭜ DOI10.1002/hbm.10035 PrefrontalCortexInvolvementinProcessing IncorrectArithmeticEquations:EvidenceFrom Event-RelatedfMRI VinodMenon,1–3* KatherineMackenzie,1 SusanMichelleRivera,1 and AllanLeonardReiss1–3 1DepartmentofPsychiatryandBehavioralSciences,StanfordUniversitySchoolofMedicine, Stanford,California 2PrograminNeuroscience,StanfordUniversitySchoolofMedicine,Stanford,California 3StanfordBrainResearchCenter,StanfordUniversitySchoolofMedicine,Stanford,California

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Abstract:Themainaimofthisstudywastoinvestigatethedifferentialprocessingofcorrectandincorrect equationstogainfurtherinsightintotheneuralprocessesinvolvedinarithmeticreasoning.Electrophysio- logicalstudiesinhumanshavedemonstratedthatprocessingincorrectarithmeticequations(e.g.,2ϩ2ϭ5) elicitsaprominentevent-relatedpotential(ERP)comparedtoprocessingcorrectequations(e.g.,2ϩ2ϭ4).In thepresentstudy,weinvestigatedtheneuralsubstratesofthisprocessusingevent-relatedfunctionalmagnetic resonanceimaging(fMRI).Subjectswerepresentedwitharithmeticequationsandaskedtoindicatewhether thesolutiondisplayedwascorrectorincorrect.Wefoundgreateractivationtoincorrect,comparedtocorrect equations,intheleftdorsolateralprefrontalcortex(DLPFC,BA46)andtheleftventrolateralprefrontalcortex (VLPFC,BA47).Ourresultsprovidethefirstbrainimagingevidencefordifferentialprocessingofincorrectvs. correctequations.Theprefrontalcortexactivationobservedinprocessingincorrectequationsoverlapswith brainareasknowntobeinvolvedinworkingmemoryandinterferenceprocessing.TheDLPFCregion differentiallyactivatedbyincorrectequationswasalsoinvolvedinoverallarithmeticprocessing,whereasthe VLPFCwasactivatedonlyduringthedifferentialprocessingofincorrectequations.Differentialresponseto correctandincorrectarithmeticequationswasnotobservedinparietalcortexregionssuchastheangular gyrusandintra-parietalsulcus,whichareknowntoplayaspecificroleinperformingarithmeticcomputations. Thepatternofbrainresponseobservedisconsistentwiththehypothesisthatprocessingincorrectequations involvesdetectionofanincorrectanswerandresolutionoftheinterferencebetweentheinternallycomputed andexternallypresentedincorrectanswer.Morespecifically,greateractivationduringprocessingofincorrect equationsappearstoreflectadditionaloperationsinvolvedinmaintainingtheresultsinworkingmemory, whilesubjectsattempttoresolvetheconflictandselectaresponse.Thesefindingsallowustofurtherdelineate anddissociatethecontributionsofprefrontalandparietalcorticestoarithmeticreasoning.Hum.BrainMapping 16:119–130,2002. ©2002Wiley-Liss,Inc.

Keywords:arithmetic;N400;prefrontalcortex;angulargyrus;fMRI;interference;Stroop

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INTRODUCTION

Arithmeticreasoningisauniquelyhumanskillthat weutilizenearlyeveryday.Brainimagingstudies Contractgrantsponsor:NIH;Contractgrantnumber:HD40761, MH50047,MH01142,HD31715. haveidentifiedadistributednetworkinvolvedin *Correspondenceto:V.Menon,PhD,DepartmentofPsychiatry& arithmeticreasoningincludingthelateralandventral BehavioralSciences,StanfordUniversitySchoolofMedicine,401 prefrontalcortex,andposteriorparietallobe,aswell QuarryRoad,Stanford,CA94305-5719.E-mail:[email protected] assubcorticalregionsincludingthecaudatenucleus Receivedforpublication22March2001;accepted30January2002 andcerebellum[Burbaudetal.,1995;Dehaeneetal.,

PublishedonlinexxMonth2002 ©2002Wiley-Liss,Inc. ᭜ Menon et al. ᭜

1999; Menon et al., 2000b]. Isolating the processes scalp topography of the arithmetic N400 is, however, involved in arithmetic reasoning, and their neural fairly diffuse, making it difficult to identify specific bases, however, presents a considerable challenge. In- areas involved in the differential processing of vestigations of the psychological and neural bases of incorrect arithmetic equations. arithmetic reasoning are frequently based on verifica- In a previous study we used functional magnetic tion tasks in which subjects are presented with an resonance imaging (fMRI) to examine which brain equation of the form, “2 ϩ 3 ϭ 5”, and are asked to areas contribute uniquely to numeric computation make a decision regarding whether the presented an- [Menon et al., 2000b]. We used a classic arithmetic swer is correct or incorrect [Allen et al., 1997; Menon et verification task involving simple addition and sub- al., 2000a, b; Rickard et al., 2000]. A key aspect of this traction; task difficulty was manipulated by varying type of arithmetic reasoning is the ability to distin- the number of operands (“3 ϩ 5 ϭ 8” or “3 ϩ 5 Ϫ 1 guish between incorrect and correct arithmetic equa- ϭ 6). Brain activation to incorrect and correct equa- tions. In this study we examine differences in the way tions (e.g., ”3 ϩ 5 ϭ 8“ or ”2 ϩ 3 ϭ 6) was combined the brain processes incorrect and correct equations. and analyzed together to examine activation resulting Analyses of brain imaging data from verification from general arithmetic processing. The results of this tasks have generally focused on processing both cor- study showed that the contribution of the parietal and rect (e.g., 2 ϩ 2 ϭ 4) and incorrect (e.g., 2 ϩ 2 ϭ 5) prefrontal cortices during general arithmetic process- equations. Typically, brain activation during the pro- ing tasks could be dissociated from each other. The cessing of these equations is averaged and compared angular , in particular, appears to be specifically to a control condition involving non-arithmetic oper- involved in arithmetic computation independent of ations [Menon et al., 2000a,b; Rickard et al., 2000]. other processing demands [Menon et al., 2000b]. The Although several common operations are involved in , on the other hand, appears to be processing correct and incorrect equations, recent be- involved in supporting processes necessary for arith- havioral and electrophysiological evidence indicates metic reasoning, such as maintaining digits in work- that the brain processes these two types of arithmetic ing memory [Harmony et al., 1999; Kazui et al., 2000] equations differently [Niedeggen and Rosler, 1999; and rapid processing of arithmetic stimuli [Menon et Niedeggen et al., 1999; Zbrodoff and Logan, 2000]. The al., 2000b]. Accordingly, although lesions of the pre- main aim of this study was to investigate the differ- frontal cortex can result in poorer overall performance ential processing of correct and incorrect equations to on arithmetic tasks [Fasotti et al., 1992; Lucchelli and gain further insight into the neural processes involved De Renzi, 1993; Luria, 1966], lesions in the angular in arithmetic reasoning. gyrus produce more profound and specificdeficits in Research related to the processing of correct and the ability to perform arithmetic computations [Kahn incorrect arithmetic equations has been limited to a and Whitaker, 1991; Levin, 1993; Takayama et al., few studies. The strongest behavioral evidence for 1994]. Given that electrophysiological evidence sug- differential processing of correct and incorrect arith- gests that the brain processes incorrect and correct metic equations comes from a recent study by Zbrod- equations differently, we used event-related fMRI off and Logan [2000] which found that it took partic- analyses [Burock et al., 1998; Dale, 1999; Menon et al., ipants, on average, 56 msec longer to produce the 1997b; Rosen et al., 1998] to examine differences in correct solution for equations displayed with incor- brain activation during the processing of these two rect, compared to correct, solutions. Zbrodoff and Lo- types of equations. gan have described this process as an arithmetic Subjects were presented with arithmetic equations Stroop effect, in which the presentation of an incorrect involving simple addition or subtraction. Brain activa- answer interferes with the subject’s ability to produce tion occurring during the presentation of correct equa- the correct answer. Two event-related potential (ERP) tions (e.g., 5 ϩ 3 ϭ 8, or 5 ϩ 3 Ϫ 1 ϭ 7) was compared studies from Neideggen et al. [1999] have provided to that occurring during the presentation of incorrect more direct evidence that incorrect equations are pro- equations (e.g., 5 ϩ 2 ϭ 8, or 5 ϩ 2 Ϫ 1 ϭ 5). Subjects cessed differently from correct equations [Niedeggen were asked to indicate whether or not the solution and Rosler, 1999]. These studies have shown that dur- displayed was correct. We hypothesized that process- ing arithmetic verification tasks, processing of incor- ing incorrect, compared to correct, equations would rect, compared to correct, equations evokes a large involve the recruitment of additional cognitive re- negative brain potential, peaking between 300 and 500 sources and this would in turn result in greater acti- msec after presentation of the equation. This ERP com- vation in specific brain regions. Further, if the process- ponent has been termed the arithmetic N400. The ing of incorrect equations involves increased

᭜ 120 ᭜ ᭜ PFC and Incorrect Arithmetic Equations: An fMRI Study ᭜ calculation load, differential activation would primar- alternating experimental and control epochs was used ily be observed in the angular gyrus of the parietal in this study. In both epochs, numbers between 1 and cortex [Menon et al., 2000b]. On the other hand, if 9 were presented visually for 5,250 msec, with an ISI of processing incorrect equations was more closely re- 750 msec. The experiment began with a 30-sec rest lated to resolving an interference between the pre- epoch followed by six alternating 30-sec epochs of sented and computed answers, or keeping digits in “easy” (2-operand equation) experimental trials and working memory, activation would primarily be ob- control trials. These six “easy” epochs were followed served in prefrontal cortex regions known to support by a second 30-sec rest epoch. After this rest epoch, these functions. subjects were presented with six alternating 30-sec We also investigated the effect of increased level of epochs of “difficult” experimental (3-operand equa- arithmetic complexity on processing of incorrect, com- tion) and control trials. The experiment concluded pared to correct, equations by comparing brain acti- with a 30-sec rest epoch. During the rest condition, vation to 2- and 3- operand equations. The 3-operand subjects passively viewed a blank screen. The easy condition was more difficult due to the fact that sub- epochs were presented before the difficult epochs for jects were required to manipulate an additional oper- all subjects. The main reason for this aspect of the task and, and to switch between addition and subtraction design was that we wanted to use the same tasks in within the problem (e.g., 5 ϩ 2 Ϫ 1 ϭ 5). We hypoth- typically developing children as well as children and esized that, if subjects engaged in recalculation of the adults with difficulties in mathematical reasoning who equation during incorrect trials, greater activation of might have become anxious and frustrated if they the should be seen for 3-operand, com- performed the difficult epochs first [Rivera et al., 2000, pared to 2-operand, incorrect equations. If, however, 2001]. Although the experimental design is slightly the processing of incorrect arithmetic solutions in- less than optimal for the present study, we do not volves a more general process, such as detection of a believe that a significant confound from practice ef- discrepancy between correct and incorrect solutions fects would be present because the 2- and 3-operand and resolution of such an interference, we would not computations were extremely simple for most sub- expect differential activation for the two types of equa- jects. tion in the parietal cortex. A major strength of this The “easy” experimental epochs consisted of five, study is that a random effects model was used to 2-operand addition or subtraction problems (random- analyze event-related activation across 16 subjects. Us- ly intermixed) with either a correct (e.g., 1 ϩ 2 ϭ 3) or ing such a model ensured that only voxels consistently an incorrect resultant (e.g., 5 Ϫ 2 ϭ 4). The “difficult” activated across subjects, rather than within individ- experimental epochs consisted of five, 3-operand ad- ual subjects, would emerge as significant population dition and subtraction problems with either a correct activation [Holmes and Friston, 1998]. Findings from (e.g., 6 Ϫ 3 ϩ 5 ϭ 8) or an incorrect resultant (e.g., 6 the present study provide new information on a key ϩ 2 Ϫ 3 ϭ 4). The 3-operand equations each had one aspect of arithmetic reasoning and on the neural sub- addition and one subtraction operation. Subjects were strates of the arithmetic N400. asked to respond with a button press only if the an- swer to the equation was correct. A total of fifteen MATERIALS AND METHODS different equations for each experimental condition (“easy” or “difficult”) were displayed, six correct and Subjects nine incorrect (Table I). The incorrect resultant trials were either one more than the correct answer (e.g., 5 Sixteen healthy subjects (8 males and 8 females; ages ϩ 3 ϭ 9), or one less than the correct answer (e.g., 5 16–23) participated in this study after giving written ϩ 3 ϭ 7) so that subjects would tend to perform more informed consent, in accordance with the declaration exact, rather than approximate, numerical calcula- of Helsinki and the Stanford Human Subjects Com- tions. mittee. Before the experiment, subjects were assessed The “easy” control epoch consisted of a string of five using the Wechsler Adult Intelligence Scale (WAIS-III) digits (e.g., 1, 4, 0, 3, 5), subjects were asked to respond [Wechsler, 1991]. with a button press if “0” was one of the numbers displayed in the string. The “difficult” control epoch Experimental design consisted of a string of seven digits (e.g., 1, 4, 0, 2, 3, 6, 5); subjects were asked to respond with a button press A block fMRI experimental design (with event-re- if “0” was one of the numbers displayed in the string. lated data analyses, as described below), consisting of A total of 15 different strings were displayed for each

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TABLE I. Two- and three-operand arithmetic sagittal plane; 256 ϫ 192 matrix; acquired resolution equations used in the study ϭ 1.5 ϫ 0.9 ϫ 1.2 mm. The images were reconstructed as a 124 ϫ 256 ϫ 256 matrix with a 1.5 ϫ 0.9 ϫ 0.9 mm Two-operand equations Three-operand equations spatial resolution. 6 Ϫ 2 ϭ 40ϩ 0 ϩ 0 ϭ 0a The task was programmed using Psyscope [Cohen 2 ϩ 2 ϭ 33Ϫ 1 ϩ 5 ϭ 8 et al., 1993] on a Macintosh computer. Initiation of 3 ϩ 3 ϭ 62ϩ 2 ϩ 1 ϭ 5 scan and task was synchronized using TTL pulse de- 4 ϩ 4 ϭ 93Ϫ 3 ϩ 2 ϭ 3 livery to the scanner timing microprocessor board 5 ϩ 5 ϭ 95Ϫ 5 ϩ 4 ϭ 5 form CMU Button Box microprocessor (http://pop- 2 ϩ 1 ϭ 27Ϫ 5 ϩ 6 ϭ 8 py.psy.cmu.edu/psyscope) connected to the Macin- 3 ϩ 2 ϭ 69Ϫ 9 ϩ 8 ϭ 9 tosh. Stimuli were presented visually at the center of a ϩ ϭ Ϫ Ϫ ϭ 1 7 832 0 0 screen using a custom-built magnet compatible pro- ϩ ϭ ϩ Ϫ ϭ 5 4 943 1 7 jection system (Resonance Technology, CA). 1 ϩ 8 ϭ 81Ϫ 1 ϩ 0 ϭ 0 3 ϩ 1 ϭ 45Ϫ 3 ϩ 0 ϭ 2 4 ϩ 2 ϭ 57Ϫ 5 ϩ 2 ϭ 5 Image preprocessing 5 ϩ 3 ϭ 99Ϫ 7 ϩ 4 ϭ 7 ϩ ϭ ϩ Ϫ ϭ 4 3 608 5 3 Images were reconstructed, by inverse Fourier ϩ ϭ ϩ Ϫ ϭ 4 1 563 8 2 transform, for each of the 225 time points into 64 ϫ 64 ϫ ϫ ϫ a A simple equation containing zeros was presented to alert subjects 18 image matrices (voxel size: 3.75 3.75 7mm). to the transition to 3-operand equations. FMRI data were preprocessed using SPM (http:// www.fil.ion.ucl.ac.uk/som). Images were corrected for movement using least square minimization with- control condition (“easy” or “difficult”), 6 with “0” out higher-order corrections for spin history, and nor- and 9 without “0”. malized to stereotaxic Talairach coordinates [Talairach A single button press (rather than two different and Tournoux, 1988]. Images were then resampled button presses for correct and incorrect trials) was every 22 mm using sync interpolation and smoothed used because we wanted to use the same tasks in low witha4mmGaussian kernel to decrease spatial noise. functioning children, adolescents and adults (60 Ͻ IQ Ͻ 80), some of whom had difficulty switching be- tween responses. The number of responses was, how- Statistical analysis ever, counterbalanced between experimental and con- trol epochs. Although a block fMRI design was used in the present study, fMRI data were analyzed using event- fMRI Acquisition related methods. The aim of the analysis was to de- termine brain activation to incorrect, compared to cor- Images were acquired on a 1.5 T GE Signa scanner rect, equations. Statistical analysis was performed on with EchoSpeed gradients using a custom-built whole individual and group data using the general linear head coil that provides a 50% advantage in signal to model and the theory of Gaussian random fields as noise ratio over that of the standard GE coil [Hayes implemented in SPM99 [Friston et al., 1995]. This and Mathias, 1996]. A custom-built head holder was method takes advantage of multivariate regression used to prevent head movement. Eighteen axial slices analysis and corrects for temporal and spatial autocor- (6 mm thick, 1 mm skip) parallel to the anterior and relations in the fMRI data [Worsley and Friston, 1995]. posterior commissure covering the whole brain were Because incorrect and correct equations occurred imaged with a temporal resolution of 2 sec using a T2* randomly with respect to each other, activation to weighted gradient echo spiral pulse sequence (TR these events could be statistically separated. To do this ϭ 2,000 msec, TE ϭ 40 msec, flip angle ϭ 89° and 1 we first had to determine that brain activation to cor- interleave) [Glover and Lai, 1998]. The field of view rect and incorrect equations were not statistically cor- was 240 mm and the effective in-plane spatial resolu- related. Expected waveforms for events correspond- tion was 3.75 mm. To aid in localization of functional ing to correct and incorrect equations were computed data, a high resolution T1 weighted spoiled grass gra- after convolution with the hemodynamic response dient recalled (SPGR) 3D MRI sequence with the fol- function [Kruggel and von Cramon, 1999]. The corre- lowing parameters was used: TR ϭ 24 msec; TE ϭ 5 lation between these events was 0.05 for the 2-operand msec; flip angle ϭ 40°;24cmfield view, 124 slices in condition and 0.10 for the 3-operand condition, allow-

᭜ 122 ᭜ ᭜ PFC and Incorrect Arithmetic Equations: An fMRI Study ᭜ ing us to independently assess brain activation to cor- minus control (no zero-containing strings minus zero- rect and incorrect equations [Clark et al., 1998]. containing strings). Note that in this comparison, ac- A within-subjects procedure was used to model all tivation from control trials was subtracted out to elim- the effects of interest for each subject. Individual sub- inate the effect of response inhibition. The number of ject models were identical across subjects (i.e., a bal- trials that required subjects to withhold response was anced design was used). Confounding effects of fluc- identical during the arithmetic processing and the tuations in global mean were removed by propor- control conditions. Two additional analyses compared tional scaling where, for each time point, each voxel experimental and control epochs, irrespective of trial was scaled by the global mean at that time point. Low type. frequency noise was removed with a high pass filter (0.5 cycles/min) applied to the fMRI time series at Contrast 3 each voxel. A temporal smoothing function (Gaussian kernel corresponding to dispersion of 8 sec) was ap- The main effect of arithmetic processing was exam- plied to the fMRI time series to enhance the temporal ined with the following comparison: (3-operand ex- signal to noise ratio. We then defined the effects of perimental epochs) plus (2-operand experimental ep- interest for each subject with the relevant contrasts of ochs) minus (all control epochs). the parameter estimates. A random effects model [Holmes and Friston, 1998] Contrast 4 was then used to determine which brain regions show greater activation during the processing of incorrect, The main effect of task difficulty during arithmetic compared to correct, equations for the 2- and 3-oper- processing was examined with the following compar- and conditions. Group analysis was performed using ison: (3-operand experimental epochs) minus (2-oper- a two-stage hierarchical procedure. In the first step, and experimental epochs). Activation foci were super- contrast images corresponding to the difference be- imposed on high-resolution T1-weighted images and tween brain responses to correct and incorrect equa- their locations interpreted using known neuroana- tions were derived after adjusting for the hemody- tomical landmarks [Duvernoy et al., 1999; Mai et al., namic response. In the second step, these contrast 1997]. images were analyzed using a general linear model to determine voxel-wise t-statistics. A one-way t-test was then used to determine group activation for each con- Behavioral data analysis dition of interest. Finally, the t-statistics were normal- ized to Z scores, and significant clusters of activation Mean percentage of correct responses and false were determined using the joint expected probability alarms, and reaction time (RT) were computed and distribution of height and extent of Z scores [Poline et compared across the 2- and 3-operand experimental al., 1997], with height (Z Ͼ 2.33; P Ͻ 0.01) and extent and control conditions using a one-way ANOVA. threshold (P Ͻ 0.05). Contrast images were calculated using a within- RESULTS subject design for the following analyses. Behavioral Contrast 1 Mean accuracy (percentage of correct responses) The interaction between (i) processing incorrect vs. was 99.6% (SD ϭ 1.1%), 98.8% (SD ϭ 2.7%), and 96.7% correct arithmetic equations and (ii) number of oper- (SD ϭ 6.0%) for the control, and 2- and 3-operand ands was examined using the following comparison: experimental trials respectively. For 2-operand trials, (3-operand incorrect minus correct trials) minus (2- the false alarm rate (responding “true” to an incorrect operand incorrect minus correct trials). equation by making a button press) was 2.1% (SD ϭ 4.5%) and the miss rate (responding “false” to a Contrast 2 correct equation by withholding response) was 0%. For 3-operand trials, the false alarm rate was 4.2% (SD The main effect of processing incorrect vs. correct ϭ 6.9%) and the miss rate was 2.1% (SD ϭ 5.7%). arithmetic equations was examined using the follow- ANOVA of accuracy, false alarm rates, and misses ing comparison: (3-operand incorrect minus correct revealed no significant differences between 2- and trials) plus (2-operand incorrect minus correct trials) 3-operand trials (P Ͼ 0.05).

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TABLE II. Brain areas that showed significant activation during the processing of incorrect, compared to correct, equations

Corrected Number of voxels Talairach Brain area P-value in cluster Z max coordinates

Left dorsolateral prefrontal cortex (BA 9/46) 0.005 243 3.40 Ϫ46, 22, 24 Left ventrolateral prefrontal cortex (BA 47) 0.042 168 3.57 Ϫ46, 42, Ϫ6

Mean RT was 818.4 (SD ϭ 144.0 msec) for the con- Contrast 3 Compared to Contrast 2 trol trials, 1,233.8 msec (SD ϭ 224.9 msec) for 2-oper- and trials, 2,012.3 (SD ϭ 327.3 msec) for 3-operand Of the several brain regions that were activated trials, and. ANOVA on RTs revealed a significant during arithmetic processing (irrespective of trial main effect of condition (F[2,30] ϭ 169.94; P Ͻ 0.0000). type), only the left region RTs for 3-operand trials were significantly longer than showed overlapping activation during incorrect, com- RTs for 2-operand trials (t[15] ϭ 7.84; P Ͻ 0.000). pared to correct, arithmetic processing (Fig. 3).

Brain activation Contrast 4

Contrast 1 Although there were no differences between incor- rect and correct trials for 3-operand equations versus No significant difference in brain activation was incorrect and correct trials for 2-operand equations observed when incorrect versus correct trials in the (Contrast 1), a significant difference in activation be- 2-operand condition were subtracted from those in the tween processing of 3- and 2-operand equations was 3-operand condition. We therefore examined the main found in the right angular gyrus/intra-parietal effect of processing incorrect versus correct arithmetic (Fig. 4). equations by combining activation from the 2-operand and 3-operand conditions (Contrast 2 below). DISCUSSION

Contrast 2 This is the first brain imaging study to investigate brain areas involved in the differential processing of Significant brain activation to incorrect, compared incorrect and correct arithmetic equations. Using to correct, arithmetic equations was observed in the even-related fMRI analyses we found that processing left middle and inferior frontal gyri (Table II, Figs. 1 incorrect equations resulted in significantly greater and 2). activation than processing of correct equations in par-

Figure 1. Surface rendering of brain areas that showed significant activation 9/46 and 47). Results are from a random effects analysis of event- during the processing of incorrect, compared to correct, arith- related activation in 16 subjects; each activated cluster was signif- metic equations. Activation was limited to two clusters in the left icant after corrections for multiple spatial comparisons (P Ͻ 0.01). dorsolateral and ventrolateral prefrontal cortex (Brodmann areas

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Figure 2. Coronal sections showing activation dur- ing the processing of incorrect, com- pared to correct, arithmetic equations. Other details as in Figure 1. ticular brain regions. This result confirms findings marily encompassing the posterior dorsolateral pre- from electrophysiological studies, which have found frontal cortex (DLPFC; 9/46) and the that processing incorrect, compared to correct, equa- ventrolateral prefrontal cortex (VLPFC; Brodmann tions results in larger electrophysiological signals Area 47). It is unlikely that the prefrontal cortex acti- [Niedeggen et al., 1999]. Together, these studies pro- vation was due to the motor component of response vide new information about the spatial and temporal inhibition because the number of trials with response characteristics underlying the processing of incorrect inhibition demands was balanced across the experi- arithmetic equations. mental and control conditions. Rather, the activation Increased activation during processing of the incor- appears to be related to cognitive interference process- rect equations was restricted to the left lateral prefron- ing as discussed below. tal cortex, a region that several studies have impli- There are a number of cognitive processes that cated in arithmetic processing [Burbaud et al., 1995; might be invoked specifically by processing of incor- Fasotti et al., 1992; Luria, 1966; Menon et al., 2000b; rect, compared to correct, arithmetic equations. When Rueckert et al., 1996]. Activation foci were localized to presented with an equation, subjects must presumably middle and inferior frontal gyri (Figs. 1 and 2), pri- produce an answer through mental calculation, and

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Figure 3. Overlap between brain areas activated during: 1) the processing of incorrect, compared to correct, arithmetic equa- tions (shown in the yellow-red-black color scale), and 2) arithmetic processing (correct and incorrect equations com- pared to the control condition: shown in cyan). The left dorsolateral prefrontal cortex (DLPFC) in the middle frontal gy- rus showed an overlap in activation in the two analyses (circled in yellow). The left ventro-lateral prefrontal cortex (VLPFC) activation in the , on the other hand, was activated only during the differential processing of incorrect equations (circled in green). compare the result with the answer presented on the during arithmetic verification tasks. We would there- screen. Cognitive operations related to detecting the fore expect that activation observed during incorrect, incorrect solution, and resolving the resultant interfer- compared to correct, arithmetic processing would ence between the calculated and displayed results, overlap with brain areas that have previously been would then be evoked. Zbrodoff and Logan [2000] reported to be activated during proactive interference have examined the psychological processes underly- and conflict resolution. It is possible that subjects en- ing production during arithmetic processing tasks. Us- gage in a process of recalculating the answer for fur- ing a number of different manipulations, they provide ther verification when they realize that a discrepancy convincing evidence that when a false answer is pre- exists between the calculated answer and the one dis- sented, it interferes with production of solutions to played. In this case, additional neural activity related simple arithmetic equations (“the arithmetic Stroop to the recalculation process itself might be initiated. It effect”). Thus, interference detection and resolution is also possible that subjects made decisions about the should represent key operations involved in the dif- veracity of equations based on violation of parity ferential processing of incorrect arithmetic equations rules. For example, the sum of even numbers should

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Figure 3 (cont’d). be even. Research on parity has shown that partici- ipants are unaware of having used parity rules, sug- pants are able to more easily identify the solution as gesting that they used these rules in an automatic incorrect when a proposed solution to an equation fashion, as a form of tacit knowledge or skill [Krueger violates the rules of parity. Furthermore, most partic- and Hallford, 1984]. The important point here is that

Figure 4. Surface rendering of brain areas that showed significant activation during the processing of 3-operand, compared to 2-operand, arithmetic equations, irrespective of trial type. Activation was limited to the right angular gyrus/intra-parietal sulcus.

᭜ 127 ᭜ ᭜ Menon et al. ᭜ even if subjects detected an incorrect equation without In the present study, performance monitoring as well any real calculation, an interference process similar to as other operations such as response inhibition and the one discussed above would still be evoked. response competition were balanced between the ex- The pattern of brain response observed in this study perimental and control conditions. These factors may is consistent with the hypothesis that processing in- underlie lack of ACC activation specifically related to correct equations involves detection of an incorrect the processing of incorrect arithmetic equations. answer and resolution of the interference between the In contrast to the lateral prefrontal cortex, the pari- internally computed and externally presented incor- etal cortex was not differentially activated by incor- rect answer. Sub-regions of the DLPFC and the VLPFC rect, compared to correct, trials. Previous imaging cortex, that are differentially activated during the pro- studies have implicated both the prefrontal and pari- cessing of incorrect equations, have been shown to be etal cortices in arithmetic processing [Burbaud et al., very generally involved in interference resolution 1995; Dehaene et al., 1999; Menon et al., 2000a] and we [Jonides et al., 1998; Menon et al., 2001]. have recently proposed that the prefrontal cortex may Recent imaging studies have suggested that al- be more involved in retrieval of arithmetic facts, work- though the VLPFC is involved more in the organiza- ing memory, and other support processes, whereas tion of information in working memory, interference the posterior parietal cortex may be more involved in resolution and selective retrieval, the DLPFC is more the calculation process per se [Menon et al., 2000a]. In involved in maintenance and manipulation of infor- the present study, the parietal cortex was activated by mation held in working memory [Owen, 1997; Rowe both 3-operand and 2-operand trials (Fig. 3B); further- et al., 2000]. It is likely that activations in these regions more, the angular gyrus showed greater activation are closely related, because operations involving real- during 3-operand, compared to 2-operand, trials (Fig. time interference resolution would also require oblig- 4) [see also Menon et al., 2000b]. The lack of differen- atory access to the verbal rehearsal as well as the tial activation to incorrect trials in the parietal cortex, storage components of working memory. In other and particularly in the angular gyrus, suggests that words, greater activation during processing of incor- subjects were not recalculating the result to verify rect equations appears to reflect additional operations whether the solution displayed on the screen was involved in maintaining the results in working mem- incorrect. If subjects were recomputing the result, we ory, while subjects attempt to resolve the conflict and would have expected an increase in activation in the select a response. Thus, it is not surprising that the angular gyrus and other parietal lobe regions that are DLPFC and VLPFC regions activated in the present critically involved in arithmetic computations during study are consistently activated during verbal work- 3-operand equations, which require more computa- ing memory tasks and furthermore, show greater ac- tion than 2-operand equations. It is important to note tivation when interference processes related to work- that participants in this study performed both the 2- ing memory task performance must be resolved and 3-operand tasks with a high level of accuracy. In [D’Esposito et al., 1999; Jonides et al., 1998]. Further- the more difficult 3-operand task, the average accu- more, the DLPFC region differentially activated by racy was 98.7% and half of the subjects responded incorrect equations was also involved in overall arith- correctly to 100% of the trials. It is possible that if task metic processing (Fig. 3). On the other hand, the performance was less automatized and subjects per- VLPFC was activated only during the differential pro- formed these arithmetic tasks poorly, they might re- cessing of incorrect equations. These results provide compute the resultant during verification thereby en- evidence that the contribution of the DLPFC and gaging other brain areas including the angular gyrus VLPFC regions during the processing of incorrect in the parietal lobe. equations can be dissociated. We propose that the regions of DLPFC and VLPFC No activation was observed in the anterior cingulate activated in the present study may contribute signifi- cortex (ACC), a brain region thought to be involved in cantly to the scalp-recorded arithmetic N400 effect response selection, inhibition and competition [Carter [Niedeggen and Rosler, 1999]. It is nevertheless pos- et al., 2000; Menon et al., 2001]. The differential role of sible that there are sources not uncovered by the the DLPFC and ACC in interference processing re- present study. The scalp N400 elicited during arith- mains a topic of debate in the literature [Cohen et al., metic tasks used by Neideggen et al. [1999] had a 2000]. One recent study has suggested that the DLPFC diffuse topography over the centro-frontal as well as is more involved in implementation of cognitive con- parietal electrode locations. It is important to note that trol and the anterior is more involved the ERP studies have used more difficult multiplica- in performance monitoring [MacDonald et al., 2000]. tion tasks, compared to simple addition and subtrac-

᭜ 128 ᭜ ᭜ PFC and Incorrect Arithmetic Equations: An fMRI Study ᭜ tion tasks used in the present study. ERPs elicited in tremely rapid presentation rates using functional MRI. Neuro- posterior scalp regions during the more difficult mul- report 9:3735–3739. tiplication tasks may in fact reflect brain activation Carter CS, Macdonald AM, Botvinick M, Ross LL, Stenger VA, Noll D, Cohen JD (2000): Parsing executive processes: strategic vs. related to recomputation of the answer. To date there evaluative functions of the anterior cingulate cortex. Proc Natl have been no ERP studies of the arithmetic N400 using Acad Sci USA 97:1944–1948. the simple and relatively well automatized arithmetic Clark VP, Maisog JM, Haxby JV (1998): fMRI study of face percep- equations used in the present study. So far no source tion and memory using random stimulus sequences. 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