How verbal and spatial manipulation networks contribute to calculation: An fMRI study

Neuropsychologia 46 (2008) 2403–2414

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Neuropsychologia journal homepage: www.elsevier.com/locate/neuropsychologia

How verbal and spatial manipulation networks contribute to calculation: An fMRI study ´ Turbelin, Fred ´ eric ´ Laure Zago ∗ , Laurent Petit, Marie-Renee Andersson, Mathieu Vigneau, Nathalie Tzourio-Mazoyer CI-NAPS UMR 6232, CNRS, CEA, Universit´e Caen Basse Normandie, Universit´e Paris Descartes, France

a r t i c l e

i n f o

Article history: Received 27 April 2007 Received in revised form 3 March 2008 Accepted 4 March 2008 Available online 18 March 2008 Keywords: Arithmetic processing Asymmetry Intraparietal sulcus Numbers Working memory Adults

a b s t r a c t The manipulation of numbers required during calculation is known to rely on working memory (WM) resources. Here, we investigated the respective contributions of verbal and/or spatial WM manipulation brain networks during the addition of four numbers performed by adults, using functional magnetic resonance imaging (fMRI). Both manipulation and maintenance tasks were proposed with syllables, locations, or two-digit numbers. As compared to their maintenance, numbers manipulation (addition) elicited increased activation within a widespread cortical network including inferior temporal, parietal, and prefrontal regions. Our results demonstrate that mastery of arithmetic calculation requires the cooperation of three WM manipulation systems: an executive manipulation system conjointly recruited by the three manipulation tasks, including the anterior cingulate cortex (ACC), the orbital part of the inferior frontal gyrus, and the caudate nuclei; a left-lateralized, language-related, inferior fronto-temporal system elicited by numbers and syllables manipulation tasks required for retrieval, selection, and association of symbolic information; and a right superior and posterior fronto-parietal system elicited by numbers and locations manipulation tasks for spatial WM and attentional processes. Our results provide new information that the anterior intraparietal sulcus (IPS) is involved in tasks requiring a magnitude processing with symbolic (numbers) and nonsymbolic (locations) stimuli. Furthermore, the specificity of arithmetic processing is mediated by a left-hemispheric specialization of the anterior and posterior parts of the IPS as compared to a spatial task involving magnitude processing with nonsymbolic material. © 2008 Elsevier Ltd. All rights reserved.

1. Introduction The possible roles of language and spatial functions in mathematical calculation remain a matter of debate in cognitive sciences (Brannon, 2005; Houde´ & Tzourio-Mazoyer, 2003; Nieder, 2005). While recent cross-linguistic investigations demonstrated language effects on the development of basic calculation skills ´ 2005), studies with animals and pre(Hodent, Bryant, & Houde, verbal human infants have demonstrated basic numerical and calculation abilities (Dehaene, Dehaene-Lambertz, & Cohen, 1998; Wynn, 1992), indicating the independence of basic number capacity from language. In the field of neuropsychology, although aphasia is often associated with impaired number and calculation ability (Delazer, Girelli, Semenza, & Denes, 1999), dissociations between language and mathematics have also been demonstrated with reports of preserved language skills despite impaired mathematical abilities (Butterworth, 1999), or preserved mathematical

∗ Corresponding author at: Centre Cyceron, Boulevard Becquerel, BP 5229, 14074 Caen Cedex, France. Tel.: +33 2 31470267; fax: +33 2 31470222. E-mail address: [email protected] (L. Zago). 0028-3932/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.neuropsychologia.2008.03.001

skills despite severely impaired language (Klessinger, Szczerbinski, & Varley, 2007; Rossor, Warrington, & Cipolotti, 1995; Varley, Klessinger, Romanowski, & Siegal, 2005). Finally, some brainimaging studies have found evidence for the recruitment of left hemisphere perisylvian language areas during exact calculation ´ (Cohen, Dehaene, Chochon, Lehericy, & Naccache, 2000; Dehaene, Spelke, Pinel, Stanescu, & Tsivkin, 1999); however, others have shown the involvement of a bilateral parietofrontal network and the bilateral inferior temporal gyri associated with visuospatial working memory (WM) and visual mental imagery during mental calculation (Delazer et al., 2005; Venkatraman, Ansari, & Chee, 2005; Zago et al., 2001). With regard to the relationship between numerical representation and spatial functions, psychophysical studies in healthy humans have suggested that number processing may operate on an analogical magnitude format that is spatially organized by numerical proximity (Dehaene, Bossini, & Giraud, 1993; Dehaene et al., 1998). Support for an intimate relationship between space and number has also been provided by brain-lesion studies. Patients with hemispatial neglect resulting from brain damage to the right hemisphere showed specific representational deficits in number processing that implicate a spatial representation

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(Vuilleumier, Ortigue, & Brugger, 2004; Zorzi, Priftis, & Umilta, 2002). Recent findings from functional neuroimaging (Chochon, Cohen, van de Moortele, & Dehaene, 1999; Gruber, Indefrey, Steinmetz, & Kleinschmidt, 2001; Pesenti, Thioux, Seron, & De Volder, 2000; Rueckert et al., 1996; Zago et al., 2001) showed that number processing is critically associated with neural circuits in parietal lobes. Remarkably, many parietal areas reportedly active during mental arithmetic (Menon, Rivera, White, Glover, & Reiss, 2000; Pesenti et al., 2000; Venkatraman et al., 2005; Zago et al., 2001) are known to be implicated in visuo-spatial functions (Culham & Kanwisher, 2001; Husain & Nachev, 2007), including attention (Corbetta, Kincade, & Shulman, 2002), spatial WM (LaBar, Gitelman, Parrish, & Mesulam, 1999), and mental rotation (Kosslyn, Digirolamo, Thompson, & Alpert, 1998). To clarify the organization of number-related processes in the parietal lobe, Dehaene and co-workers have proposed a tripartite organization (Dehaene, Piazza, Pinel, & Cohen, 2003). The bilateral horizontal segment of the intraparietal sulcus (hIPS) would be a plausible candidate for a nonverbal representation of numerical quantity, analogous to a spatial “number line”. A left angular gyrus area, in connection with other left-hemispheric perisylvian areas, would support the manipulation of numbers in verbal form. Finally, a bilateral posterior superior parietal lobule (PSPL) system is supposed to support attentional orienting along the mental number line. Together, these data clearly suggest the involvement of language and spatial processes during calculation, but their interactions and their neuroanatomical bases have not yet been directly addressed in neuroimaging studies. Mental calculation is a cognitive ability that requires considerable access to the WM system (Baddeley, 1992, 2003) to maintain and manipulate numbers on a short-term medium. While there is behavioural evidence for a main role of executive processes during calculation (for a review, DeStefano & Lefevre, 2004), how numbers are manipulated in WM during arithmetical tasks remains unresolved. Some studies have identified a role for phonological manipulation (De Rammelaere, Stuyven, & Vandierendonck, 2001; Lee & Kang, 2002; Logie, Gilhooly, & Wynn, 1994; Noel, Desert, Aubrun, & Seron, 2001), while others showed a role for visuo-spatial manipulation in calculation (Hayes, 1973; Heathcote, 1994; Lee & Kang, 2002). Brain-imaging studies of single- or multi-digit calculation in healthy adults and reporting activation within the lateral frontal cortex were usually linked to WM processes requirements. In particular, the left inferior frontal activation together with the left inferior parietal activation was related to phonological WM processes required during simple (Rickard et al., 2000) or complex (Delazer et al., 2003, 2005; Gruber et al., 2001) calculations, during the processing of incorrect equations (Menon, Mackenzie, Rivera, & Reiss, 2002), and when the arithmetical difficulty level increased (Kong et al., 2005). By contrast, superior frontal activation in association with posterior parietal activation was interpreted as reflecting the involvement of the spatial WM and attentional processes (Pesenti et al., 2001; Zago et al., 2001). However, these interpretations are still speculative because they have never been assessed by direct comparisons of numerical, verbal, and spatial WM networks within the same individuals. In the present study, we examined how verbal and spatial WM components interact during mathematical calculation. The first aim of our study was to elucidate among the numerical manipulation brain regions those that overlap with verbal or spatial WM manipulation networks, and to highlight those devoted to arithmetic processing. Numerical manipulation brain regions were assessed with a mental arithmetic task (addition of four two-digit numbers) while verbal and spatial WM manipulation networks were assessed with manipulation tasks using syllables and locations materials, respectively.

The second aim of the study was to characterize the relative roles of the left and right parietal areas in numerical cognition. The model of a tripartite organization of the parietal lobe during number processing (Dehaene et al., 2003) suggests that the bilateral hIPS would be the core system for magnitude processing. However, the left intraparietal sulcus (IPS) has been preferentially found activated during simple operations (Chochon et al., 1999; Cowell, Egan, Code, Harasty, & Watson, 2000; Pesenti et al., 2000; Zago et al., 2001), symbolic and nonsymbolic precise quantitative comparisons (Fias, Lammertyn, Reynvoet, Dupont, & Orban, 2003), and symbolic and nonsymbolic arithmetic processing (Venkatraman et al., 2005). By contrast, bilateral IPS activation has been found in subtraction problems (Chochon et al., 1999), approximation and estimation (Stanescu-Cosson et al., 2000), and complex calculation (Delazer et al., 2003, 2005; Zago et al., 2001). These findings suggest a different contribution of the left and the right hemispheres during number processing. For example, it has been recently shown in a split-brain patient that while the left hemisphere is specialized for calculation, the right hemisphere does have some capacity for approximating the solution in exact calculation (Funnell, Colvin, & Gazzaniga, 2007). This left-hemispheric specialization for calculation is confirmed by several brain-lesion studies that show that calculation deficits are more frequently observed after left than after right parietal lesions (Delazer & Benke, 1997; Mayer et al., 1999; Takayama, Sugishita, Akiguchi, & Kimura, 1994). By contrast, in unilateral spatially neglecting patients with right-hemispheric lesions, number comparison deficits have been demonstrated (Vuilleumier et al., 2004). Here, we suggest that the involvement of the left or right IPS could be modulated by the nature of the numerical task, with the left IPS being dominant for exact arithmetic abilities and during tasks requiring precise numerical coding, and the right (or bilateral) IPS being more important for numerical processing based on a spatial representation. We thus hypothesized that calculation would show overlapped activation with spatial WM tasks in the right IPS, and specific activation in the left side. Therefore, we examined the hemispheric functional asymmetry of the numerical manipulation brain regions and compared them to the hemispheric functional asymmetry of the spatial and verbal manipulation WM brain systems. 2. Materials and methods 2.1. Participants Fourteen healthy participants (eight women), ages between 20 and 27 years, gave informed written consent for this fMRI study. All were right-handed, as assessed by the Edinburgh questionnaire (Oldfield, 1971) and free from neurological disorder, and had a normal brain MRI. All procedures were approved by the local Ethics Committee for Biomedical Research. 2.2. Procedure and stimuli The participants performed two types of tasks requesting WM components, namely maintenance and manipulation, using three types of material such as syllables, locations, and numbers. The structure of the behavioural tasks is shown in Fig. 1. The experiment consisted of six runs (2 runs/material), counterbalanced across participants. Each run started with a 30-s fixation block followed by a random alternation of maintenance and manipulation tasks (5 trials/task/run) with a given material. A trial was composed of (1) a 6-s encoding period, (2) a 9-s delay period, (3) a 3-s response period, and (4) a variable inter-trial interval (ITI) (mean ITI: 12 s, range: 9–15 s). For each trial using syllables, participants viewed four syllables during the encoding period, each centered on the screen and serially displayed for 1.5 s. Then, during the delay period, a crosshair was presented centrally and, depending on its color, participants had to perform one of two tasks: If the crosshair was green, they had to actively maintain in memory the set of syllables (syllables maintenance). If the crosshair was red, they had to manipulate the set of syllables to constitute a word (syllables manipulation). At the time of the response period, in the case of a maintenance trial, a single test syllable appeared in the center of the screen, and participants were required to give a motor response with the right hand indicating whether or not that syllable matched one of the syllables presented at encoding. In the case of a manipulation trial, a single test word appeared and they had to indicate whether

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Fig. 1. Three types of runs were proposed depending on the material (syllables, locations, or numbers). Each trial was composed of an encoding period (6 s), a delay period (9 s), a response period (3 s), and a variable inter-trial interval (ITI: range 9–15 s). During the delay period, two types of tasks were randomly proposed, depending on crosshair color: if the crosshair was green, then the task was to maintain information in WM; if the crosshair was red, then the task was to manipulate information (generate a word from syllables; generate a mirror-reversed image of locations along the vertical axis; or add the numbers). the test word could be generated from the four syllables presented at encoding. For the maintenance trials, the four syllables could never make up a word, whereas for the manipulation trials, only one single concrete noun could be generated from the syllables. Word frequency was equated between trials [2.73 ± 0.04, Brulex database (Content, Mousty, & Radeau, 1990)]. Probes matched the targets in 50% of all trials in each of the experimental conditions described below. Non-matched syllables differed by one letter from the matched syllable, and non-matched words differed by one syllable from the matched word. For trials using locations, at encoding the participants viewed a square serially presented in four different locations in a 6 × 12 transparent matrix (5◦ × 15◦ of visual angle). During the delay period, if the crosshair was green, participants had to maintain the set of four locations (locations maintenance). If the crosshair was red, they had to generate a mirror-reversed image of each of the stored locations along a vertical axis (locations manipulation). During the response period, a single test location appeared in the case of a maintenance trial, and participants had to indicate whether that location matched one of the four presented at encoding. In the case of a manipulation trial, a single mirror-reversed image composed of four locations appeared, and they had to indicate whether this image matched the mirror-reversed image, generated from the four locations presented at encoding. For maintenance trials, a non-matched probe was moved to an adjacent location. For manipulation trials, the non-matched mirror-reversed image differed at two locations. For trials using numbers, four two-digit numbers were serially displayed at encoding. During the delay period, if the crosshair was green, participants had to maintain the set of numbers (numbers maintenance). If the crosshair was red, they were required to add the set of numbers (numbers manipulation). At the response period, a single test number appeared in case of a maintenance trial, and they had to indicate whether that number matched one of the four numbers presented at encoding. In case of a manipulation trial, participants had to indicate whether the presented number corresponded to the sum of the four numbers presented at encoding. For maintenance trials, non-matched probes differed at ±1, whereas for manipulation trials, non-matched sums differed at ±3. For each trial, presented numbers were between 01 and 34, with no ties (numbers with 0 and 5), no repetition of the same digit in the units and in the tens, and no repetition of the same digit in an operand. In addition, the sum of each addition was between 66 and 70 without carry. Before entering the MRI scanner, participants practiced the tasks with stimuli that were not used in the experiment.

2.3. Post-experimental debriefing At the end of the fMRI session, a careful debriefing of each participant was carried out using a questionnaire. They were asked to describe the strategies they used to perform the different tasks. 2.4. Prior experiment A prior experiment was done to verify whether the three manipulation tasks were matched for difficulty and whether 9 s was long enough to perform each task. Twenty other participants were seated in front of a computer monitor (mean age ± S.D. = 26.6 ± 4.0 y.o., range: 20–34 y.o., 7 women). The protocol was the same as in the fMRI experiment, except that during manipulation delays, the participant was asked to press a button and to give an oral answer at the moment of task completion. The results showed no significant difference in performance between numbers, syllables, and locations during the manipulation tasks (66.6 ± 9.4%; F(2–19) = 2.2, p > 0.05), and participants answered in 6.9 ± 1.8 s on average, with no difference between materials (F(2–19) = 2.4, p > 0.05), suggesting that the 9-s delay was long enough to perform the manipulation tasks. As expected, the maintenance tasks were better performed (88.8 ± 7.0%) than the manipulation tasks [F(2–19) = 71.0, p < 0.0001]. 2.5. Imaging and image analysis Imaging was performed on a GE Signa 1.5 T MRI scanner. Presentation of stimuli and acquisition of performance were controlled using the Superlab package (SuperLab Pro software, Cedrus Co.). Participants viewed a backlit projection within the magnet bore through a mirror mounted on the head coil. They were instructed to look directly at each item as it appeared and to avoid moving their eyes as soon as a crosshair appeared, namely, during the delay period and the ITI. Structural MRI protocols consisted of a localizer scan, a high-resolution T1-weighted scan (T1-MRI, FOV = 240 mm × 240 mm, sampling = 0.94 mm × 0.94 mm × 1.5 mm), and a proton-density/T2-weighted scan (PD-MRI/T2-MRI; axial acquisition; FOV = 240 mm, sampling = 0.94 mm × 0.94 mm × 5 mm; 21 slices). Functional images were acquired with an echo planar imaging (EPI) blood oxygen level-dependent (BOLD) sequence (110 EPI volumes; TR = 3000 ms, TE = 60 ms,

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FA = 90◦ , sampling = 3.75 mm × 3.75 mm × 5 mm; 21 slices) covering the same field of view as the T2-MRI acquisition. The first three EPI volumes of the functional acquisition were discarded, allowing for signal stabilization, and differences in slice acquisition timing were corrected using the SPM99b software package (Welcome Department of Cognitive Neurology, London, UK, http://www.fil.ion.ucl.ac.uk/spm). The fourth volume of the run was considered to be the reference functional volume (fMRI0 ). For registration of fMRI0 onto the stereotactic Montreal Neurological Institute (MNI) template, rigid (fMRI0 onto T2-MRI and PD-MRI onto T1-MRI) and nonlinear (T1-MRI onto the MNI template) registration matrices were computed and then combined. The registration of fMRI0 and T1-MRI volumes in the MNI space was thereafter visually checked with MPI Tool software (Max-Planck Institute for Neurological Research, Cologne, Germany) and manually adjusted when necessary. Each fMRI volume was registered onto the fMRI0 volume (SPM99b) and resampled in the MNI space with the registration parameters calculated in the first procedure. Finally, data were spatially smoothed with an 8-mm3 full-width half-maximum Gaussian kernel, leading to an image smoothness of 12 mm in the three directions. The analysis field of view (common to all participants) was defined between z = −30 mm and z = +72 mm of the MNI space. 2.6. Voxel-based whole-brain analysis The pre-processed functional MRI images were analyzed with SPM99b. The individual data were analyzed separately for each participant and the different runs of the same condition were concatenated. Because the present report concentrates on delay periods, we considered six delay periods (6 experimental conditions: 2 Tasks × 3 Materials). Each delay was modeled using a boxcar function of 9 s (duration of the delay) convolved with the canonical hemodynamic response function and its temporal derivative employed in SPM. Low-frequency confounds were excluded from the model with a high-pass filter (253 s). First-level contrast images for every participant were then used for random effect analysis to draw inferences about brain activation at the group level. All trials were included in the analysis. 2.6.1. Comparisons of interest We first reported the brain regions involved during the manipulation of each material by comparing the manipulation to the maintenance conditions for each material. We then highlighted the brain regions that were conjointly activated during the three manipulation tasks by using the conjunction of [Manipulation minus Maintenance] for syllables, numbers, and locations (Price & Friston, 1997). Numbers manipulation brain regions that showed overlap activation with syllables manipulation were highlighted with the average of [Manipulation minus Maintenance] for numbers and syllables, exclusively masked with locations manipulation (mask set at p < 0.001, uncorrected). The exclusive mask was used to cancel out activation that was also shared with locations manipulation. Numbers manipulation brain regions that showed overlap activation with locations manipulation were highlighted by the average of [Manipulation minus Maintenance] for numbers and locations, exclusively masked with syllables manipulation (mask set at p < 0.001, uncorrected). Finally, the between-task comparisons were also presented: ([Numbers Manipulation minus Maintenance] versus [Syllables Manipulation minus Maintenance]) and ([Numbers Manipulation minus Maintenance] versus [Locations Manipulation minus Maintenance]). The statistical threshold for each comparison was set at p < 0.05 at the cluster level (with a standard voxel-level cutoff of p < 0.001), whole-brain corrected for multiple comparisons. The conjunction analysis of [Manipulation minus Maintenance] for three materials was reported to be p < 0.05 at the voxel level, whole-brain corrected. Activation foci were superimposed on a high-resolution, MNI-TI-weighted image, and their locations assessed using in-house automatic anatomical labeling [AAL software (Tzourio-Mazoyer et al., 2002)]. 2.7. Functional asymmetry analysis This analysis was performed to identify whether 1/brain regions showing common activation between numbers and syllables manipulation and between numbers and locations manipulation elicit a common hemispheric asymmetry; 2/numbers manipulation task yields different hemispheric asymmetry when compared to syllables or locations manipulation conditions. First, voxel-by-voxel inter-hemispheric differences were assessed by subtracting BOLD values of one hemisphere from those of the other hemisphere, for each participant and under each condition. To do so, left/right flipped condition maps were subtracted from non-flipped condition maps, which resulted in individual asymmetry maps (Mazard, Laou, Joliot, & Mellet, 2005; Vigneau, Jobard, Mazoyer, & Tzourio-Mazoyer, 2005). These individual asymmetry maps were used to generate the following contrasts at the group-level: [Manipulation minus Maintenance] for numbers and syllables; [Manipulation minus Maintenance] for numbers and locations; [Numbers Manipulation minus Syllables Manipulation]; and [Numbers Manipulation minus Locations Manipulation]. The statistical threshold for each comparison was set at p < 0.05 at the cluster level (with a standard voxel-level cutoff of p < 0.001), whole-brain corrected for multiple comparisons.

3. Results 3.1. Behavioural results Repeated-measures ANOVA analyses were performed on error rates and correct response times (RTs). Both were carried out with Tasks (Maintenance and Manipulation) and Materials (Syllables, Numbers, Locations) as within-individual factors. Mean error rate was low (19.4 ± 16.2%, S.D.). The ANOVA performed on arcsine-transformed values revealed a main effect of Tasks [F(1–13) = 31.5; p < 0.01]. Participants made more errors in manipulation than maintenance (23.6 ± 16.2% versus 15.2 ± 15.3%) tasks. No main effect of Materials or Materials × Tasks interaction reached significance. The ANOVA performed on RTs showed main effects of Tasks [F(1–13) = 14.9, p < 0.01], and Materials [F(2–13) = 11.8, p < 0.01]. Participants answered faster to Maintenance (1359 ± 234 ms) than to Manipulation trials (1480 ± 300 ms), and for numbers (1288.2 ± 222.7 ms) than for syllables (1428.2 ± 189.6 ms; t(13) = −2.5, p = 0.02) or for locations (1542.7 ± 195.8 ms; t(13), p = 0.0001; no significant difference between syllables and locations, p > 0.05, all post hoc Bonferroni corrected t-tests). A significant Tasks × Materials interaction was observed [F(2–26) = 12.3, p < 0.01], due to the fact that the increase of RTs between maintenance and manipulation was not significant for numbers (Maintenance: 1233 ± 300 ms versus Manipulation: 1343 ± 214 ms; t(13) = 1.4, p > 0.1), but it was for syllables (1250 ± 204 ms versus 1605 ± 226 ms; t(13) = 6.4, p < 0.01) and for locations (1483 ± 235 versus 1602 ± 209; t(13) = −2.07, p < 0.05). 3.2. Introspective reports During the numbers manipulation task, all participants reported using both verbal (phonological manipulation) and spatial manipulations (visuo-spatial re-organization on a mental blackboard) of numbers to perform calculation. Moreover, half of the participants serially added the numbers while six others used a non-sequential procedure (i.e. adding numbers that can be easily added, and then the other numbers). One participant reported difficulty describing his strategy. For the manipulation of syllables, six participants indicated that they preferentially used a phonological manipulation of syllables to retrieve the word, while six others visually and spatially manipulated the syllables to find the word, and two others used both. During locations manipulation, most of the participants (10/14) reported using the successive mirroring of the locations based on the evaluation of a precise metric. The others formed a global shape that they mirrored afterwards. During the maintenance tasks, most of the participants (10/14) used the same strategy for maintaining numbers and syllables during delay, namely the phonological rehearsal. The four others used the visualization of the numbers and syllables, in addition to the verbal rehearsal. During locations maintenance, 8/14 indicated that they used a visuo-spatial rehearsal of each location, and four others formed a global pattern from the locations that was then maintained. Two others used a mixed strategy. Finally, none of our participants indicated that they manipulated information during the encoding period. Rather, they tried to concentrate, so as to correctly encode each item. 3.3. fMRI results 3.3.1. BOLD variations 3.3.1.1. Numbers manipulation brain regions. As shown in Fig. 2A, numbers manipulation (as compared to maintenance) showed increased activation within a large bilateral fronto-parietal network. It encompassed the posterior parts of the superior and middle

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Fig. 2. Group statistical parametric maps corresponding to: (A) [Numbers Manipulation minus Maintenance]. (B) Mean of [Numbers Manipulation minus Maintenance] + [Syllables Manipulation minus Maintenance] masked by locations manipulation (exclusive mask set at p < 0.001, uncorrected) is shown in red; the mean of [Numbers Manipulation minus Maintenance] + [Locations Manipulation minus Maintenance] masked by syllables manipulation (exclusive mask set at p < 0.001, uncorrected) is shown in blue; and the conjunction of [Manipulation minus Maintenance] for the three materials is shown in green. Plots illustrate the parameter estimates for the different conditions at specific coordinates given in Table 1. Activations are those exceeding a corrected threshold of p < 0.05, rendered onto a 3-D renderer and axial slices of the MNI standard brain (IFG: inferior frontal gyrus; ITG: inferior temporal gyrus; ACC: anterior cingulate cortex; IFG orb: inferior frontal gyrus orbital part).

frontal gyri, and the inferior frontal gyrus. In the parietal cortex, activation followed the IPS, from the supramarginal gyrus (SMG) to its posterior part close to the superior parietal gyrus. Another cluster of increased activation was found in the posterior part of the left inferior temporal gyrus (ITG). Higher BOLD activity was also found bilaterally in the anterior cingulate cortex (ACC), in the lower part of the inferior frontal gyrus (orbitary part, inferior frontal gyrus orbital (IFG orb)), and in the caudate nucleus (Table 1).

3.3.1.2. Syllables manipulation brain regions. Syllables manipulation as compared to maintenance showed increased activation bilaterally within the ACC and the IFG orb (Table 1).

3.3.1.3. Locations manipulation brain regions. Locations manipulation showed increased activation in the right ACC and the right caudate nucleus (Table 1).

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Table 1 MNI coordinates of activation peaks for the comparisons of interest Anatomical region

MNI coordinates (x, y, z)

Z score (voxel-level)

Nb voxels

[Numbers Manipulation − Maintenance] R anterior cingulate cortex L superior frontal sulcus L inferior frontal gyrus (op. part) L inferior frontal gyrus (tri. part) L inferior frontal gyrus (orb. part) R superior frontal sulcus R inferior frontal gyrus (op. part) R inferior frontal gyrus (tri. part) R inferior frontal gyrus (orb. part) R caudate L caudate L supramarginal gyrus/IPS L supramarginal gyrus L IPS (post. part) R IPS (post. part) R supramarginal gyrus/IPS L inferior temporal gyrus Cerebellum

10 −26 −46 −48 −30 36 54 48 38 12 −12 −48 −54 −26 32 44 −52 2

36 8 10 44 30 4 14 52 26 8 10 −38 −34 −66 −64 −42 −56 −74

28 54 22 18 −6 54 10 20 −2 0 4 42 46 46 48 42 −14 −16

6.1 4.8 6.0 5.1 5.1 4.2 4.4 4.2 5.7 5.9 5.0 6.3 6.0 5.2 5.2 4.8 5.4 5.1

5443 Lo Lo Lo Lo 351 199 171 606 2617 Lo 2453 Lo Lo 1092 Lo 107 353

[Syllables Manipulation − Maintenance] R anterior cingulate cortex L anterior cingulate cortex R inferior frontal gyrus (orb. part) L inferior frontal gyrus (orb. part)

10 −2 38 −30

36 34 26 28

28 32 −2 −6

4.3 3.7 4.1 3.8

735 Lo 181 93

10 12

36 8

30 −2

4.5 4.4

221 118

Conjunction of [Manipulation − Maintenance] for numbers, syllables, and locations R anterior cingulate cortex 10 36 L anterior cingulate cortex −6 40 R caudate 12 10 L caudate −10 6 R inferior frontal gyrus (orb. part) 38 26 L inferior frontal gyrus (orb. part) −34 28

28 20 0 0 −6 −6

Inf 6.1 6.8 5.5 6.4 5.4

827 Lo 143 37 213 38

[Numbers Manipulation − Maintenance] + [Syllables Manipulation − Maintenance] L inferior frontal gyrus −42 36 L inferior temporal gyrus −52 −56

6 −14

5.2 4.7

374 98

[Numbers Manipulation − Maintenance] + [Locations Manipulation − Maintenance] R middle frontal gyrus/superior frontal sulcus 36 12 L supramarginal gyrus −58 −26 L IPS (ant. part) −50 −40 R superior parietal gyrus (post. part) 34 −64 R IPS (ant. part) 46 −42

46 40 58 48 46

4.5 5.2 4.9 5.0 4.9

336 406 Lo 1283 Lo

[Numbers Manipulation − Maintenance] minus [Syllables Manipulation − Maintenance] L supramarginal gyrus/IPS (ant. part) −50 −40

44

3.9

172

[Locations Manipulation − Maintenance] R anterior cingulate cortex R caudate

Statistical threshold was set at p < 0.05, whole-brain cluster-level corrected, except for the conjunction analysis, which was set at p < 0.05, whole-brain voxel level (L: left; R: right; IPS: intraparietal sulcus; op.: opercular; tri.: triangular; orb.: orbitaris; post.: posterior; ant.: anterior).

3.3.1.4. Conjoint brain regions for manipulating numbers, syllables, and locations. The manipulation of the three materials (as compared to their respective maintenance tasks) showed increased conjoint bilateral activity within the ACC, IFG orb, and caudate nucleus (Fig. 2B, green). Histograms (green box) illustrate BOLD signal estimates at peak coordinates given in Table 1. 3.3.1.5. Common brain regions for manipulating numbers and syllables. Common increased BOLD activation for the manipulation of both numbers and syllables was found in the left inferior frontal gyrus (IFG) and the left ITG (Fig. 2B, red; Table 1). As shown in the histograms (Fig. 2B, red box), these two regions exhibited significantly higher activity during manipulation than maintenance of numbers and syllables but not for locations. 3.3.1.6. Common brain regions for manipulating numbers and locations. Common increased BOLD activation for the manipulation of numbers and locations was mainly observed in the right

hemisphere, including the right middle frontal gyrus extending to the superior frontal sulcus, and the superior and posterior parietal gyrus. Bilateral activation was detected in the upper part of the SMG, extending to the anterior part of the IPS (Fig. 2B, blue; Table 1). As shown in the histograms (blue box), these regions exhibited a similar profile with higher activity during manipulation than during maintenance for both locations and numbers but not for syllables. In addition, note that the level of BOLD signal was also increased during Locations maintenance. 3.3.1.7. Numbers manipulation versus syllables manipulation. Higher BOLD activity for numbers manipulation than syllables manipulation was found in the left SMG, extending to the anterior IPS (Table 1 ([Numbers Manipulation − Maintenance] minus [Syllables Manipulation − Maintenance]). The reverse comparison did not reveal any significant higher activation during syllables manipulation than numbers manipulation.

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3.3.1.8. Numbers manipulation versus locations manipulation. No significant higher BOLD activity was found for numbers manipulation as compared to locations manipulation tasks and for locations manipulation as compared to numbers manipulation. 3.3.2. Functional asymmetry analysis 3.3.2.1. Common asymmetric brain regions for manipulating numbers and syllables. Both the IFG and the ITG, which previously exhibited overlapped activation during both numbers and syllables manipulation tasks, showed a common leftward lateralization (Table 2). 3.3.2.2. Common asymmetric brain regions for manipulating numbers and locations. Within the regions that showed common BOLD variations for number and locations manipulation tasks, the middle/superior frontal gyri showed a significant common rightward asymmetry (Table 2). 3.3.2.3. Asymmetry differences in numbers manipulation versus syllables manipulation. This comparison did not elicit significant differences in functional asymmetry. 3.3.2.4. Asymmetry differences in numbers manipulation versus locations manipulation. Significant differences in asymmetry were detected in the left ITG, the left IFG and within two foci along the left IPS: one in the upper part of SMG, posterior to the postcentral sulcus and close to the anterior IPS (SMG/IPS), and the other in the posterior IPS (Table 2 and Fig. 3, left row). To specify these functional asymmetry differences, individual BOLD values were extracted for each condition (as compared to fixation) within both left and right sides within each region. A 2 × 2 × 3 repeated measure ANOVA was performed with Hemispheres (left [LH] versus right [RH]), Tasks (Maintenance versus Manipulation), and Materials (syllables, numbers or locations) as within-individual factors. As illustrated in the histograms (Fig. 3, right row), the interaction of Materials × Tasks × Hemispheres was significant within the four regions (ITG cluster -623 voxels[F(2–26) = 27.3, p < 0.0001]; IFG cluster -648 voxels- [F(2–26) = 18.9, p < 0.0001]; SMG/IPS cluster -142 voxels- [F(2–26) = 4.3, p < 0.02]; post IPS cluster -84 voxels- [F(2–26) = 6.2, p < 0.006]). We then defined a Functional Asymmetry Index (FAI) computed as the difference between BOLD values in the left and right sides for each task and each material, and compared FAIs with post hoc t-tests (Bonferroni for corrected multiple comparisons, p corr < 0.003). Within the ITG cluster, the numbers manipulation FAI (0.28 ± 0.11, S.D.) indicated a leftward asymmetry, which was due to a major decrease of BOLD signal in the RH. This numbers manipulation FAI was significantly different from the locations manipulation FAI (−0.03 ± 0.1; p < 0.0001), which indicated a bilateral hemispheric contribution. As evidenced in a previous comparison, the syllables manipulation FAI (0.23 ± 0.10) showed a leftward asymmetry similar to the one found for numbers manipulation (no difference between both, p = 0.1), and different from the locations manipulation FAI (p < 0.0001). The same effects were found for the maintenance tasks (Numbers FAI: 0.09 ± 0.07; Locations FAI: −0.01 ± 0.10, Syllables FAI: 0.14 ± 0.09). Note that the leftward asymmetry in numbers maintenance was due to larger decreases of BOLD signal in the RH than the LH. Within the IFG cluster, the numbers manipulation FAI (0.42 ± 0.15) showed a significant larger leftward asymmetry than for the locations manipulation FAI (0.05 ± 0.1, p < 0.0001), this latter eliciting a more bilateral hemispheric contribution. As for ITG, syllables manipulation (FAI: 0.30 ± 0.14) also showed a strong leftward asymmetry, which was however less important than the leftward asymmetry found for numbers (p = 0.001). The same effects were

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found for the maintenance tasks (Syllables FAI: 0.19 ± 0.12; Numbers FAI: 0.20 ± 0.12, no difference between both p = 0.9; Locations FAI: 0.06 ± 0.09, p’s < 0.0001). Within the SMG/IPS cluster, the numbers manipulation FAI (0.19 ± 0.19) indicated a leftward asymmetry while the locations manipulation FAI (−0.16 ± 0.28) showed a rightward asymmetry (p < 0.0001). The syllables manipulation task also showed a leftward asymmetry (FAI = 0.14 ± 0.12) similar to the one found in numbers manipulation (p = 0.3) and significantly different from the rightward asymmetry for locations manipulation (p < 0.0001). Note that the level of BOLD signal for the syllables manipulation condition was largely lower than for numbers or locations manipulation tasks. This indicates that this region was not preferentially recruited during syllables as compared to numbers or locations manipulation tasks. The same effects were found for the maintenance tasks (Syllables FAI: 0.16 ± 0.11; Numbers FAI: 0.09 ± 0.10, no difference between both p = 0.2; Locations FAI: −0.10 ± 0.15, p’s < 0.002). Within the post IPS cluster, the numbers manipulation FAI (0.36 ± 0.28) indicated a strong leftward asymmetry while the locations manipulation FAI (0.03 ± 0.22) showed a bilateral hemispheric contribution (p < 0.0001). The syllables manipulation task showed a leftward asymmetry (FAI: 0.21 ± 0.17), which was significantly close to be less important than the leftward asymmetry detected for numbers manipulation (p < 0.008) and significantly different from the bilateral hemispheric contribution during the locations manipulation task (p < 0.0009). For the maintenance tasks, the only significant difference was found between syllables maintenance FAI (0.22 ± 0.11) and locations maintenance FAI (0.008 ± 0.17, p < 0.0002). 4. Discussion The results of the present study show that manipulating four two-digit numbers to perform an addition, as compared to their simple maintenance, engaged the large-scale fronto-temporoparietal network of complex arithmetical processing tasks (Delazer et al., 2003, 2005; Zago et al., 2001). The main advance of the present study is that the experimental design allows disentangling, within these large-scale neural networks, the brain regions related to either verbal or spatial manipulation components, as well as those devoted to arithmetic processing. Although the three manipulation tasks were accurately performed, our results show that the participants answered as fast to evaluate whether the displayed sum was correct as to evaluate whether the displayed number matched one of the four memorized numbers. In other words, the increase of response time found between maintenance and manipulation response trials for syllables and locations was not observed for numbers. This behavioural interaction might indicate that the arithmetic task was easier than the other two manipulation tasks. However, in the present design, the response was recorded during the response period and corresponded to the evaluation (correct or incorrect) of one displayed response. We thus consider the behavioural response as an indirect measure of the cognitive activity (here, the manipulation of information in WM) occurring during the delay period. By contrast, results of the pilot experiment, during which participants orally gave their response as soon as they found it during the manipulation delays, showed no difference between the three manipulation tasks. 4.1. An executive brain network for manipulating numbers, syllables, and locations Our study provides evidence that calculation requires the involvement of an executive brain system, including the ACC, the

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Table 2 MNI coordinates of activation peaks showing a significant functional asymmetry Anatomical region

MNI coordinates (x, y, z)

Z score (voxel-level)

Nb voxels

[Numbers Manipulation − Maintenance] + [Syllables Manipulation − Maintenance] L inferior temporal gyrus −50 −54 L inferior frontal gyrus −40 34

−10 10

4.6 4.5

271 102

[Numbers Manipulation − Maintenance] + [Locations Manipulation − Maintenance] R middle frontal gyrus/superior frontal sulcus 36 20

42

4.2

117

−12 24 22 46 40

7.3 4.9 4.5 4.7 4.1

623 648 Lo 142 84

[Numbers Manipulation] − [Locations Manipulation] L inferior temporal gyrus L inferior frontal gyrus (op. part) L inferior frontal gyrus (tri. part) L supramarginal gyrus / IPS (ant. part) L IPS (post. part)

−52 −44 −52 −46 −28

−54 8 28 −34 −66

Statistical threshold was set at p < 0.05, whole-brain cluster-level corrected (Lo = local maximum within a larger activation cluster; L: left; R: right; IPS: intraparietal sulcus; post.: posterior; op.: opercular; tri.: triangular).

orbital part of the IFG, and the caudate nucleus. In addition, our findings demonstrate that this executive brain system is independent from the material to be manipulated because it was engaged during the manipulation of numbers, syllables, and locations. Each of these brain regions has been previously linked to executive processes, including the manipulation of information in WM, the focus of attention on the different items to be manipulated, and the monitoring and control of performance. All are clearly required during the manipulation tasks. In particular, ACC has been involved in cognitive control required by performance monitoring, error detection, and immediate re-adjustment (Ridderinkhof, Ullsperger, Crone, & Nieuwenhuis, 2004; Ullsperger & von Cramon, 2004). It is known to be sensitive to task difficulty (Barch et al., 1997) and engaged by mental effort (Botvinick, Cohen, & Carter, 2004), which is consistent with the lower performance during manipulation than maintenance tasks. The orbital part of the IFG has been engaged during tasks requiring the transformation of the identity or characteristics of stimuli in WM (Wager & Smith, 2003), as well as in tasks requiring the orientation of attention within the contents of WM (Lepsien, Griffin, Devlin, & Nobre, 2005), which facilitates the search within WM and enhances retrieval. In the present study, participants had to focus their attention on the different items being manipulated, to retrieve a word, to add the different numbers, or to build a mirror-reversed shape. Finally, the caudate nucleus has been shown to play a role in cognition and executive functions. In particular, neuroimaging studies have localized delay period activity in the caudate nucleus (Postle & D’Esposito, 1999a, 1999b), and it has been proposed that caudate activity mediates the sustained activity occurring within the frontal cortex during the delay period (Cohen et al., 1997; Goldman-Rakic, 1995). A recent study provided evidence for a specific increase of caudate activation during the process of manipulation (as compared to maintenance) of verbal information in WM (Lewis, Dove, Robbins, Barker, & Owen, 2004). As a whole, our results provide evidence that a network of frontal executive areas is engaged in WM manipulation independently of the type of material (verbal, spatial, or numerical). Here, we suggest that this neural network encompassing core frontal regions targeting particular executive processes may subtend the central executive component of the WM (Baddeley, 2003). 4.2. A left inferior fronto-temporal network for manipulating numbers and syllables In addition to identifying the executive brain system shared by the three manipulation tasks, our results indicate that syllables and

numbers manipulation tasks elicited increased activation within two left-hemispheric regions, namely the inferior frontal and temporal gyri. These two brain regions thus represent languagemediated processes that are involved during the manipulation of numbers and syllables as compared to their maintenance. The role of the left IFG in phonologic and semantic processing has been consistently demonstrated (Poldrack et al., 1999). In particular, the ventral part of the left IFG, corresponding to our activation, is involved in semantic retrieval (Vigneau et al., 2006) and the selection process required to resolve interference or competition between retrieved candidates (Badre, Poldrack, PareBlagoev, Insler, & Wagner, 2005). Here, both verbal and numerical manipulation tasks required the retrieval and selection of the appropriate candidate from the manipulation of semantic materials. Our findings are in line with those of work involving patients with frontal brain damage, which identified conjoint difficulty in retrieving arithmetic facts and words (Benton, 1987). In particular, it has been recently demonstrated using voxel-based lesion symptom mapping, that concomitant deficits in arithmetic and language comprehension were associated with the left IFG (Baldo & Dronkers, 2007). Common activation was also detected in the left ITG. This region is known to play a role during visual mental imagery tasks (Mellet, Tzourio, Denis, & Mazoyer, 1998b), and its left-sided activation has been related to mental imagery tasks that include semantic content or some lexico-semantic information (Mazard et al., 2005; Mellet et al., 2000). Within this context, our results demonstrate that the left ITG strongly responds during the mental manipulation of Arabic numbers and syllables, which probably reflects the engagement of mental imagery processes required by the manipulation of symbolic materials. Interestingly, it has been showed that the left inferior temporal region contained “modality-neutral” systems for mediating between conceptual knowledge and word retrieval (specifically activated during the naming of objects and tools), whatever the sensory modality (visual or auditory, Tranel, Grabowski, Lyon, & Damasio, 2005). Along the same lines as our results, it has been proposed that the posterior-inferior temporal region may be where visual (in our case, a visual mental image) and verbal representations of symbolic materials bind under the control of left inferior frontal semantic areas (Vigneau et al., 2005). A second goal of the present study was to explore the asymmetry of the cortical activations. Concerning the verbal and numerical materials, our results show that their manipulation produced a common leftward asymmetry. This obviously confirms the left-hemispheric specialization for language and calculation. Interestingly, the leftward asymmetry observed within the two regions did however reflect different hemispheric contributions. In the IFG cluster, the leftward asymmetry was due to a massive BOLD sig-

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Fig. 3. Inter-hemispheric differences for the comparison [Numbers Manipulation minus Locations Manipulation]. Activations are those exceeding a corrected threshold of p < 0.05 whole-brain cluster-level corrected and rendered onto axial slices of the MNI standard brain. Coordinates are given in Table 2. For each functional cluster, BOLD signal variations are extracted for both left and right hemispheres, for each condition and each material (IFG: inferior frontal gyrus, ITG: inferior temporal gyrus; SMG/IPS: supramarginal gyrus/intraparietal sulcus; post IPS: posterior part of intraparietal sulcus; L: left hemisphere; R: right hemisphere). Error bars denote standard error.

nal increase in the left side while the right side showed a small increase (see Fig. 3). In other words, the leftward asymmetry in the IFG reflected a predominant involvement of the left hemisphere. By contrast, the leftward asymmetry found in the ITG was due to both

a BOLD signal increase in the left side and a signal decrease in the right side. In that case, the leftward asymmetry may reflect a process of inter-hemispheric inhibition, from the left to the right ITG, through the corpus callosum, which has been shown to play a sig-

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nificant role in inter-hemispheric inhibition (Hamzei et al., 2002). Our data illustrate that the functional asymmetry is a process that operates through the dynamics of the interaction between left and right hemispheres. Interestingly, within the ITG cluster, while syllables maintenance showed the same BOLD profile as those of syllables maintenance and numbers manipulation (BOLD increase in the left and decrease in the right side), numbers maintenance demonstrated BOLD signal decreases, both in the left and right sides. Although the interpretation of these bilateral deactivations requires further investigations, it indicates that, in the present study, the ITG do not contribute to the maintenance of numbers while the left side clearly plays a role during the manipulation of symbolic materials. Overall, our findings provide evidence that, to some degree, calculation and language processes rely on common substrates, corresponding to a left-lateralized inferior fronto-temporal network dedicated to the retrieval, selection, and association of symbolic information. 4.3. A right superior and posterior fronto-parietal network for manipulating numbers and locations Regarding the manipulation of numerical and spatial materials, our data showed areas of overlapping activation within the right superior and posterior parietal cortex and the right middle frontal gyrus extending to the superior frontal gyrus. These regions have indeed been engaged in a variety of spatial functions including shifts of spatial attention (Beauchamp, Petit, Ellmore, Ingeholm, & Haxby, 2001; Behrmann, Geng, & Shomstein, 2004; Corbetta et al., 1998; Wojciulik & Kanwisher, 1999), spatial WM (Wager & Smith, 2003) and spatial mental imagery (Mellet, Petit, Denis, & Tzourio, 1998a). Furthermore, this right fronto-parietal activation observed here, together with the rightward asymmetry of the middle frontal/superior frontal region common to both numbers and locations manipulation tasks are consistent with neuroimaging studies of spatial selective attention that evidenced a right-hemisphere dominant network of frontal and parietal sites (for a review, Awh & Jonides, 2001). Finally, the locus of the posterior parietal activation in our study is consistent with the PSPL system supposed to orient the attention along the mental number line (Dehaene et al., 2003). Here, our data are in favour of an intimate relationship between numerical cognition and spatial attention (Hubbard, Piazza, Pinel, & Dehaene, 2005; Houde´ & Tzourio-Mazoyer, 2003), and indicate that this relationship concerns more specifically the right hemisphere. Overall, our findings demonstrate that calculation and spatial manipulation share common substrates, implemented in a right hemisphere fronto-parietal system underlying spatial attentional processes. 4.4. A bilateral anterior IPS magnitude system for manipulating numbers and locations Manipulating numbers and locations elicited overlapped activation in the SMG and adjoining anterior part of the IPS, bilaterally. This region, characterized as the core system for representing numerical magnitude (Dehaene et al., 2003), has also been involved in the comparison of size or numbers with symbolic materials such as letters, Arabic digits (Pinel, Piazza, Le Bihan, & Dehaene, 2004), or number words (Pinel et al., 1999; Pinel, Dehaene, Riviere, & LeBihan, 2001). The IPS appeared to be important in determining magnitude for different symbolic (numbers, letters) and nonsymbolic (angles, line) stimuli (Fias et al., 2003; Fulbright, Manson, Skudlarski, Lacadie, & Gore, 2003). The anterior IPS has been also found during the addition (Venkatraman et al., 2005) and the com-

parison (Ansari, Lyons, van Eimeren, & Xu, 2007) of symbolic (Arabic numerals) and nonsymbolic (dots) materials. Here, our findings provide new information that the bilateral activation in the anterior part of the IPS is attributed to a magnitude process, involved during an arithmetic calculation as well as during a spatial task that required the evaluation of distances to perform the mirroring of the locations. Thus, this bilateral anterior IPS activation is not number specific but rather reflects a magnitude process operating on symbolic (numbers) and nonsymbolic (locations) stimuli. This bilateral IPS involvement common to numbers and locations manipulation tasks could account for neuropsychological findings showing that patients with number-processing deficits after left or right parietal lesions often experience spatial deficits. One may note, however, that depending on the damaged hemisphere, the spatial deficits are of different types. Patients with left inferior parietal lesions who exhibit important deficits in calculation and number processing (Cipolotti, Butterworth, & Denes, 1991; Lemer, Dehaene, Spelke, & Cohen, 2003; van Harskamp, Rudge, & Cipolotti, 2002) often show left–right disorientation, finger agnosia, and agraphia (Delazer & Benke, 1997; Lemer et al., 2003; Mayer et al., 1999). In contrast, patients with unilateral spatial neglect after right parietal damage exhibit numerical disorders specifically affecting the spatial sphere, such as a distortion of the spatial representation of numbers without pronounced dyscalculia (Vuilleumier et al., 2004; Zorzi et al., 2002). This dissociation of deficits can be related to our results, which demonstrated within the IPS the existence of a hemispheric asymmetry in the manipulation of symbolic versus nonsymbolic stimuli. 4.5. A left-hemispheric specialization of the IPS for manipulating numbers The functional asymmetry analysis highlighted a different functional asymmetry between numbers and locations manipulation tasks within two regions along the IPS. Although activation was, on the whole, bilateral, a strong left-hemispheric asymmetry was found for manipulating numbers in both the SMG/IPS and post IPS regions while a right-hemispheric advantage was observed for manipulating locations within the SMG/IPS (see Fig. 3). A bilateral contribution was found for locations manipulation in the post IPS. Taken together, these results indicate that although both hemispheres have access to a magnitude representation, there is a differential contribution of homologous left and right areas, with a left-hemispheric dominance during the arithmetic processing of symbolic stimuli and a right-hemispheric dominance during the manipulation of nonsymbolic stimuli. A repetitive Transcranial Magnetic Stimulation (rTMS) study has demonstrated that stimulation over the anterior part of the left inferior parietal lobule induced deficits during the numerical comparison task of Arabic digits, whereas rTMS stimulation over the right side did not affect this task (Sandrini, Rossini, & Miniussi, 2004). In addition, rTMS stimulation over the left anterior IPS induced pronounced deficits during the processing of symbolic (Arabic numbers) and nonsymbolic (dots arrays) numerosities, whereas rTMS over the right side did not (Cappelletti, Barth, Fregni, Spelke, & Pascual-Leone, 2007). Furthermore, using the same technique over the left anterior IPS, Knops, Nuerk, Sparing, Foltys, & Willmes (2006) have shown that this region plays a functional role in number magnitude processing as well as in integrating unit-decade magnitude information of two-digit numbers (Knops et al., 2006). Taken together with our findings, the left-hemispheric specialization of the anterior IPS may reflect the exact magnitude processing of numbers mandatory for performing the arithmetical task, while the right-hemispheric dominance found for spatial manipulation might reflect the mag-

L. Zago et al. / Neuropsychologia 46 (2008) 2403–2414

nitude processing of non-numeric information during a spatial task. As concern the post IPS region, rTMS stimulation over the left posterior parietal cortex has been shown to elicit pronounced deficits during a number comparison task, whereas rTMS over the right side was found to be less disruptive. By contrast, whatever the side of the stimulation, deficits were found during a visuo-spatial search task (Gobel, Walsh, & Rushworth, 2001). This result is consistent with the bilateral posterior IPS activation that we observed for locations manipulation. Furthermore, rTMS stimulation on the right posterior parietal region produced deficits during a number bisection task (Gobel, Calabria, Farne, & Rossetti, 2006), suggesting that this region would be more linked to a spatial representation of numbers. Although the respective functional roles of the anterior and posterior parts of the IPS need to be further determined, our findings clearly demonstrate that the left-hemispheric functional contribution of the IPS would be a special feature of a mental calculation task that requires mastery of advanced arithmetical operations. 5. Conclusion Our study provides evidence that the mastery of arithmetic calculation requires the cooperation of three WM manipulation systems: a central executive system including the ACC, the orbital part of the IFG, and the caudate nucleus; a left inferior frontotemporal system involved in the retrieval, selection, and association of symbolic information, and a right superior and posterior frontoparietal system for spatial and attentional processes. In addition, our findings provide new information that, although calculation requires magnitude processing subtended by bilateral anterior IPS activation, the specificity of arithmetic processing is expressed by a left-hemispheric specialization of two intraparietal sites. Acknowledgements ´ O. Houde, ´ B. Mazoyer, The authors are grateful to P.-Y. Herve, and E. Mellet for their stimulating discussions as well as to the two anonymous reviewers for their valuable comments. References Ansari, D., Lyons, I. M., van Eimeren, L., & Xu, F. (2007). Linking visual attention and number processing in the brain: The role of the temporo-parietal junction in small and large symbolic and nonsymbolic number comparison. Journal of Cognitive Neuroscience, 19, 1845–1853. Awh, E., & Jonides, J. (2001). Overlapping mechanisms of attention and spatial working memory. Trends in Cognitive Sciences, 5, 119–126. Baddeley, A. D. (1992). Working memory. Science, 255, 556–559. Baddeley, A. D. (2003). Working memory: Looking back and looking forward. Nature Review Neuroscience, 4, 829–839. Badre, D., Poldrack, R. A., Pare-Blagoev, E. J., Insler, R. Z., & Wagner, A. D. (2005). Dissociable controlled retrieval and generalized selection mechanisms in ventrolateral prefrontal cortex. Neuron, 47, 907–918. Baldo, J. V., & Dronkers, N. F. (2007). Neural correlates of arithmetic and language comprehension: A common substrate? Neuropsychologia, 45, 229–235. Barch, D. M., Braver, T. S., Nystrom, L. E., Forman, S. D., Noll, D. C., & Cohen, J. D. (1997). Dissociating working memory from task difficulty in human prefrontal cortex. Neuropsychologia, 35, 1373–1380. Beauchamp, M. S., Petit, L., Ellmore, T. M., Ingeholm, J., & Haxby, J. V. (2001). A parametric fMRI study of overt and covert shifts of visuospatial attention. Neuroimage, 14, 310–321. Behrmann, M., Geng, J. J., & Shomstein, S. (2004). Parietal cortex and attention. Current Opinion in Neurobiology, 14, 212–217. Benton, A. L. (1987). Mathematical disability and the Gerstmann syndrome. In G. Deloche & X. Seron (Eds.), Mathematical disabilities: A cognitive neuropsychological perspective. New Jersey: Lawrence Erlbaum. Botvinick, M. M., Cohen, J. D., & Carter, C. S. (2004). Conflict monitoring and anterior cingulate cortex: An update. Trends in Cognitive Sciences, 8, 539–546. Brannon, E. M. (2005). The independence of language and mathematical reasoning. Proceedings of the National Academy of Sciences USA, 102(9), 3177–3178. Butterworth, B. (1999). The mathematical brain. London: Macmillan.

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