Elsevier

Neuropsychologia

Volume 46, Issue 9, July 2008, Pages 2403-2414
Neuropsychologia

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

https://doi.org/10.1016/j.neuropsychologia.2008.03.001Get rights and content

Abstract

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.

Introduction

The possible roles of language and spatial functions in mathematical calculation remain a matter of debate in cognitive sciences (Brannon, 2005; Houdé & Tzourio-Mazoyer, 2003; Nieder, 2005). While recent cross-linguistic investigations demonstrated language effects on the development of basic calculation skills (Hodent, Bryant, & Houdé, 2005), studies with animals and preverbal 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 skills despite severely impaired language (Klessinger, Szczerbinski, & Varley, 2007; Rossor, Warrington, & Cipolotti, 1995; Varley, Klessinger, Romanowski, & Siegal, 2005). Finally, some brain-imaging studies have found evidence for the recruitment of left hemisphere perisylvian language areas during exact calculation (Cohen, Dehaene, Chochon, Lehéricy, & 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 (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, Baddeley, 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, Delazer et al., 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, Delazer et al., 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.

Section snippets

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.

Procedure and stimuli

The participants performed two types of tasks requesting WM components, namely maintenance and manipulation, using three types of material

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

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-temporo-parietal network of complex arithmetical processing tasks (Delazer et al., 2003, Delazer et al., 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

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 fronto-temporal system involved in the retrieval, selection, and association of symbolic information, and a right superior and posterior fronto-parietal system for spatial and attentional processes. In addition, our findings provide new information

Acknowledgements

The authors are grateful to P.-Y. Hervé, O. Houdé, B. Mazoyer, and E. Mellet for their stimulating discussions as well as to the two anonymous reviewers for their valuable comments.

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