Common substrate for mental arithmetic and finger representation in the parietal cortex
Michael Andres1,2,3, Nicolas Michaux1,2, and Mauro Pesenti1,2
1 Institut de Recherche en Sciences Psychologiques, Université catholique de Louvain, Place
Cardinal Mercier 10, 1348 Louvain-la-Neuve, Belgium
2 Institute of Neuroscience, Université catholique de Louvain, Avenue Hippocrate 10, 1200
3 Department of Experimental Psychology, Ghent University, Henri Dunantlaan 2, 9000 Gent,
Running title : Neural representation of numbers and fingers
Address correspondence to M. Andres, Department of Experimental Psychology, Ghent
University, Henri Dunantlaan 2, 9000 Gent, Belgium; e-mail: firstname.lastname@example.org
The history of mathematics provides several examples of the use of fingers to count or
calculate. These observations converge with developmental data showing that fingers play a
critical role in the acquisition of arithmetic knowledge. Further studies evidenced specific
interference of finger movements with arithmetic problem solving in adults, raising the
question of whether or not finger and number manipulations rely on common brain areas. In
the present study, functional magnetic resonance imaging (fMRI) was used to investigate the
possible overlap between the brain areas involved in mental arithmetic and those involved in
finger discrimination. Solving subtraction and multiplication problems was found to increase
activity bilaterally in the horizontal part of the intraparietal sulcus (hIPS) and in the posterior
part of the superior parietal lobule (PSPL). Finger discrimination was associated with increased
activity in a bilateral occipito-parieto-precentral network extending from the extrastriate body
area to the primary somatosensory and motor cortices. A conjunction analysis showed
common areas for mental arithmetic and finger representation in the hIPS and PSPL bilaterally.
Voxelwise correlations further showed that finger discrimination and mental arithmetic induce
a similar pattern of activity within the parietal areas only. Pattern similarity was more
important for the left than for the right hIPS and for subtraction than for multiplication. These
findings provide the first evidence that the brain circuits involved in finger representation also
underlie arithmetic operations in adults.
Keywords : counting, memory retrieval, calculation, embodied cognition
The use of fingers to count objects or calculate goes back to the Ancient Times (e.g.,
Cicero, Epistole ad Atticum, V, 21, 13, 106-43 BCN) and is further illustrated in famous
counting systems (e.g., Beda Venerabilis, De temporum ratione, 672-735 ACN) commonly
used across Europe in the Middle Ages (Butterworth, 1999; Williams & Williams, 1995). The
success of these counting systems across times and cultures is likely to result from their
capacity to pass the bottleneck of pre-existing representations in the brain of each individual
(De Cruz, 2006). In this view, fingers constitute a useful means for acquiring and transmitting
arithmetic knowledge because they provide a physical counterpart for mental operations and
they rely on pre-existing representations in the sensorimotor system. Several developmental
studies have confirmed the intimate relationship between numbers and fingers. Children’s
score in finger discrimination tests is the best predictor of their later arithmetical skills (Noël,
2005) and finger counting proved to be very important while learning to add or subtract
numbers (Domahs et al., 2008; Costa et al., 2012). In adults, behavioural studies reported
faster numerical judgements when target numbers were primed by finger configurations
congruent with the finger-counting habits of the participants (Di Luca et al., 2006; Di Luca et
al., 2010; Badets et al., 2010). A trace of finger-counting habits was also found in
electrophysiological studies showing increased corticospinal excitability (CSE) in hand muscles
during various numerical tasks (Andres et al., 2007; Sato et al., 2007).
There is now a large agreement that the parietal cortex plays an important role in mental
calculation, as shown by numerous neuropsychological (e.g., Takayama et al., 1994) and brain
imaging studies (for a recent meta-analysis, see Arsalidou & Taylor, 2011). Several studies
showed that arithmetic factors, such as problem size (Stanescu-Cosson et al., 2000; De Smedt
et al., 2011), number of operands (Menon et al., 2000) and strategy (Delazer et al., 2003,
2005; Grabner et al., 2009), influence the blood-oxygen level-dependent (BOLD) signal in the
horizontal part of the intraparietal sulcus (hIPS) and in the posterior superior parietal lobule
(PSPL), a region extending from the posterior segment of the IPS to the precuneus. In contrast
to subtraction and addition that may require calculation procedures, the answers of
multiplication problems are generally retrieved directly from long-term memory (Campbell,
1987; Galfano et al., 2003; LeFevre et al., 1996), with the contribution of the middle and
superior temporal gyrii (MTG and STG; Lampl et al., 1994; Prado et al., 2011; Sandrini et al.,
2003; Zhou et al., 2007) and/or the angular gyrus (ANG; Delazer et al., 2003; Grabner et al.,
2009; Grabner et al., 2011). Recent evidence from fMRI-guided TMS studies showed that the
integrity of the hIPS is required to perform both subtraction and multiplication problems,
challenging the view that the brain networks underlying these operations are entirely
separated (Andres et al., 2011; Sallilas et al., 2011). Finally, mental arithmetic has been
shown to recruit several areas in the frontal lobe (Arsalidou & Taylor, 2011), among which
areas in the ventral and dorsal parts of the premotor cortex (Pesenti et al., 2001; Piazza et al.,
2006). Interestingly, the parietal and frontal areas activated during mental arithmetic are very
close to those underlying finger representation (Harrington et al., 2000; Haaland et al., 2004;
Pelgrims et al., 2009, 2011). However, so far, this apparent anatomical similarity only stems
from indirect comparisons of results coming from different studies.
In the present study, we used fMRI to measure the BOLD signal in the brain of healthy
adults who had to discriminate finger positions or to solve subtraction and multiplication
problems. We chose these arithmetic operations because dual-task experiments showed that
subtraction is slowed down by concurrent finger movements, whereas multiplication remains
unaffected, even after matching problems for response speed and accuracy (Michaux et al.,
submitted). This difference was attributed to the fact that multiplication is less sensitive to
finger interference because answers can be retrieved from long-term memory without
computation. Indeed, in children, single-digit multiplication problems are mostly solved by
memory retrieval from the fourth grade (Cooney et al., 1988), whereas subtraction often
involve computational strategies with a great emphasis on finger-based calculation procedures
in the early stages of acquisition (Fuson, 1988). Adults report almost exclusive reliance on
retrieval for multiplication (i.e., 95% for the problems used in the present study), whereas this
strategy is much less used for subtraction (i.e., 42% for the problems used in the present
study; Campbell & Xue, 2001). It is unclear, however, whether the predicted overlap between
the brain circuits underlying finger discrimination and those involved in mental arithmetic will
differ between operations. Although several brain imaging results demonstrated a specific
involvement of the STG and/or ANG in arithmetic operations solved by memory retrieval,
recent evidence suggests that subtraction and multiplication also recruit common areas in the
parietal and frontal cortex. In order to explore the similarity between the pattern of activity
observed during finger discrimination and that observed during each arithmetic operation, we
computed voxelwise correlations between tasks in the parietal and frontal areas showing
2. Material and methods
Eighteen right-handed French-speaking males (mean ± S.D.: 21.3 ± 2.5 years) gave
their informed consent to participate to this study. They had no history of neurological or
psychiatric disorders, had normal or corrected-to-normal vision, and they were unaware of the
purpose of the study. The experiment was non-invasive and was performed in accordance with
the ethical standards laid down in the 1964 Helsinki Declaration. The experimental protocol
was approved by the Biomedical Ethical Committee of the Université catholique de Louvain.
2.2. Tasks and stimuli
The three experimental tasks were matched with specific control tasks in terms of visual
display and response requirements (see Figure 1). In the finger discrimination task (adapted
from Kinsbourne and Warrington, 1962), the participants held a wooden block of irregular
shape in each hand, with half of the fingers flexed in the holes and the other half extended
over the bumps of the blocks; the thumb was positioned on the lateral face of the block to
allow a stable grip (Figure 1A). In each trial, the palm view of a left or right hand was
displayed on the screen in black on a white background. During the experimental blocks, one
finger was red and the participants were instructed to answer aloud “yes” if their
corresponding finger was flexed into a hole of the wooden block and “no” if it was extended
over a bump, without moving or looking at their fingers (Figure 1B). All fingers but the thumb
were tested in each experimental block, using a pseudo-random order, so that the same finger
was not coloured in red in two consecutive trials. In the control task, all fingers on the drawing
had the same colour, either black or red, and the participants had to decide whether it was red
by answering aloud “yes” or “no” (Figure 1C). Different wooden blocks were placed in the left
and right hands at the beginning of each run in order to prevent the participants from relying
on learned associations between finger names and expected answers. The left and right hands
were tested in separate series of trials to avoid confusion between finger discrimination and
left-right orientation during the task. During the arithmetic tasks, one Arabic digit ranging from
3 to 9 was displayed on the screen and the participants had to subtract it from 11 or 13, or to
multiply it by 3 or 4, depending on the run (Figure 1C); the control task required reading
single uppercase letters (C, D, F, G, H, J). The wooden blocks were removed from the hands of
participants during the arithmetic tasks. In total, the participants performed 14 trials for each
finger of the two hands, 12 trials for each digit (or letter) in each arithmetic (or reading) task,
except for 3 and 4 (or C and D) that were presented 6 times in each arithmetic (or reading)
The participants practiced all tasks outside the magnet room in order to get familiar with
the instructions and response requirements. In particular, they were trained to produce audible
responses while keeping bucco-laryngo-facial movements to a minimum. In the magnet room,
the participants were lying in the scanner with both arms resting along the body, palms up,
and viewed the stimuli projected on a screen, in the rear of the scanner, via a tilted mirror
mounted on the head coil. Each experimental task and its control were tested twice in 6 runs
counterbalanced across participants. We used a block-design paradigm with short series of
17500 ms, interleaved with 10000 ms fixation periods, to optimize the signal-to-noise ratio
while controlling for speech-related head motion artefacts (Birn et al., 2004). Each run
consisted of 12 series alternating between an experimental task and its control. Each series
involved 5 trials where hand drawings or digits/letters were displayed for 150 ms with a 3500-
ms intertrial interval. The participants were reminded of the instructions at the beginning of
each run. Stimulus display was controlled by E-prime 2.0 (Psychology Software Tools,
Pittsburgh, USA) and the verbal responses were recorded by a digital recorder (for more
details about this procedure, see Andres et al., 2011).
2.4. Imaging protocol
For each participant, a high-resolution anatomical image was first acquired with a 3.0
Tesla magnetic resonance imager and an 8-channel phased array head coil (Achieva, Philips
Medical Systems, Andover, MA, USA) using a T1-weighted 3D turbo fast field-echo sequence
with an inversion recovery prepulse (TE = 4.6 ms, TR = 9.1 ms, Flip angle = 8°, Field of view
= 220 x 197 mm, 150 contiguous axial slices of 1 mm, voxel size = 0.81 x 0.95 x 1 mm,
SENSE factor = 1.4). Functional images were then acquired as series of blood-oxygen-
sensitive T2*-weighted echo-planar image volumes (GRE-EPI). Each run consisted of 132
volumes and was preceded by 4 dummy scans to allow for magnetic saturation effects.
Acquisition parameters were: TE = 50 ms, TR = 2500 ms, Flip angle = 90°, FOV = 220 x 220
mm, 36 slices acquired in an ascending interleaved sequence, slice thickness = 3.5 mm with
no interslice gap, SENSE factor (parallel imaging) = 2.5.
2.5. Data analysis
A first analysis of variance (ANOVA) was performed on error rates and median response
latencies (RLs) of correct trials with TASK (subtraction, multiplication vs. finger) as within-
subject factor. A second ANOVA was performed on the median RLs in the finger discrimination
task with HAND SIDE (left vs. right) and FINGERS (index, middle, ring vs. pinkie) as within-subject
factors. This ANOVA was not conducted on error rates due to empty cells. Paired t-tests were
used for post-hoc comparisons (p<.05, Bonferroni adjustment for multiple comparisons).
Average RLs are reported with standard errors (S.E.) corrected for within-subject designs
(Loftus & Masson, 1994).
The functional data were processed and analyzed using Statistical Parametric Mapping
(SPM5, Welcome Department of Cognitive Neurology, London, UK,
http://www.fil.ion.ucl.ac.uk/spm). The functional images were (1) corrected for slice
acquisition delays, (2) re-aligned to the first scan of the first run (closest to the anatomical
scan) to correct for within- and between-run motion, (3) coregistered with the anatomical
image, (4) normalized to the MNI template using an affine fourth degree ß-spline interpolation
transformation and a voxel size of 2x2x2 mm3 after the skull and bones had been removed
with a mask based on the individual anatomical images, and (5) spatially smoothed using a 8-
mm FWHM Gaussian kernel. Condition-related BOLD signal changes were estimated for each
participant by a general linear model in which the responses evoked by each condition were
modelled by a standard hemodynamic response function. The contrasts of interest were
computed at the individual level to identify the cerebral areas significantly activated by
subtraction or multiplication. The significant cerebral activations for the critical contrasts
(finger discrimination minus colour judgement; subtraction minus letter reading; multiplication
minus letter reading; multiplication minus subtraction; subtraction minus multiplication) were
examined at the group level in random-effect analyses with the statistical threshold set at
p<0.05 corrected for the false discovery rate (pFDR). In order to reveal the brain areas
commonly activated in finger and arithmetic tasks, the contrasts computed at the group level
were entered in a conjunction analysis using the minimum statistic (MS) compared to the
conjunction null (CN; Nichols et al., 2005).
Voxelwise correlations were then computed between task-related changes of the BOLD
signal in the areas revealed by the conjunction analysis. If two tasks recruit the same neuronal
populations, a positive correlation is expected because the pattern of voxels showing low and
high activity increases should be similar for both tasks; dissimilar patterns of peak voxels
between tasks should be reflected by a null or negative correlation (Dormal et al., 2011;
Downing et al., 2007; Peelen et al., 2006; Peelen et al., 2007; Peelen & Downing, 2007). The
clusters revealed by the conjunction analysis were intersected with a 5-mm-radius sphere
centred on peak voxels, using the MarsBAR toolbox (http://marsbar.sourceforge.net; Brett et
al., 2002), and t-values were extracted for each contrast and each participant from a set of
normalized but unsmoothed data (multiplication minus letter reading, subtraction minus letter
reading, finger discrimination minus colour judgement). Pearson coefficients were used to
estimate, in each participant, a voxelwise correlation between the t-values of each contrast. As
a control, we also measured voxelwise correlations between tasks in 5-mm spheres centred on
the peak voxel in the left and right extrastriate body areas (EBA), which were activated during
finger discrimination but not during mental arithmetic.
3.1. Behavioural results
The error rates did not differ between subtraction (mean ± S.E.: 3.5 ± 1.1 %),
multiplication (3.9 ± 0.5 %) and finger discrimination (3.3 ± 0.6 %; F<1). A significant effect
of TASK was found on RLs (F(2,34)=14.84, p<.001), showing that performance was slower in
the subtraction task (905 ± 23 ms) than in the multiplication (792 ± 24 ms, t(17)=3.20,
p<.016) and finger discrimination tasks (695 ± 20 ms, t(17)=5.02, p<.001; Figure 2A). In the
finger discrimination task, a main effect of FINGER (F(3,51)=7.55, p<.001) was found, with
slower responses for the middle finger (746 ± 13 ms) when compared to the index (683 ± 11
ms, t(17)=3.77, p<.01) and the pinkie (661 ± 9 ms, t(17)=4.29, p<.01), and for the ring
finger (721 ± 14 ms) when compared to the pinkie (t(17)=3.69, p<.01). Performance was as
fast and accurate for the left (701 ± 8.3 ms and 2.1 ± 0.6 %) and right hands (705 ± 8.3 ms
and 4.6 ± 1.2 %; F<1).
3.2. fMRI results
The contrast between mental arithmetic and letter reading showed bilateral activations in
the hIPS, in the PSPL, and right-sided activations in the orbital part of the inferior frontal gyrus
(IFG; Figure 2B and Table 1). The direct contrast between multiplication and subtraction
revealed further activations in the left and right superior temporal gyrus (STG). No area was
significantly more activated during subtraction than multiplication. The contrast between finger
discrimination and colour judgement showed a bilateral occipito-parieto-precentral network
(Figure 2C and Table 1). Increased activity was observed bilaterally in the EBA, the hIPS, the
PSPL and the frontal eye fields (FEF). Clusters of activation were also found in the left inferior
precentral sulcus (PrCS), the right IFG and the right middle frontal gyrus (MFG). The direct
contrasts between the left and right hands, and vice-versa, revealed additional activations in
the contralateral somatosensory (S1) and motor cortices (M1).
The conjunction analysis showed common activations for finger discrimination,
subtraction and multiplication in the hIPS and PSPL, bilaterally, and in the right IFG (Figure
2D). In order to investigate further the functional overlap between finger discrimination and
each arithmetic task, we measured voxelwise correlations in each area identified in the
conjunction analysis. In the hIPS and PSPL, positive correlations were found between the
activation patterns elicited by finger discrimination and each arithmetic task (all r ranging
between .3 and .6; all p<.002; Table 2). Voxelwise correlations between task-related patterns
in the EBA, chosen as a control site because of its specific contribution to finger discrimination,
showed only weak and nonsignificant correlations (all r between -.08 and .2, all p>.08). In the
left hemisphere, correlations between finger- and arithmetic-related patterns were significantly
larger in the hIPS and PSPL than in the EBA (all p<.002; Table 2). In the right hemisphere, a
significant difference was observed between the PSPL and the EBA (all p<.007) but not
between the hIPS and the EBA (all p>.08). An ANOVA with HEMISPHERE (left vs. right), AREA
(hIPS vs. PSPL) and CORRELATION (finger-subtraction vs. finger-multiplication) as within-subject
factors revealed a main effect of AREA (F(1,17)=8.34, p<.01), with larger correlations in the
PSPL than in the hIPS, and an interaction between AREA and HEMISPHERE (F(1,17)=5.49,
p<.032), evidencing higher similarity between activation patterns in the left than in the right
hIPS (Table 2). Results also showed a main effect of CORRELATION (F(1,17)=8.23, p<.001),
indicating that the activation pattern observed during finger discrimination was more similar to
the one observed during subtraction than during multiplication across all parietal areas. Finally,
correlations between activation patterns in the right IFG (finger-subtraction: r=.21 ± .07;
finger-multiplication : r=.22 ± .08) did not differ significantly from the correlations measured
for the right EBA, chosen as a control site (all p>.3).
The present study tested the hypothesis that the cerebral network involved in mental
arithmetic overlaps with the one involved in finger discrimination. To do so, whole brain
activity was measured while participants solved subtraction and multiplication problems or
performed a finger discrimination task. The behavioural results showed that subtraction was
performed more slowly than multiplication or finger discrimination, whereas the error rate was
equal in the three tasks. At the functional level, increased activity was found in the hIPS and
PSPL bilaterally during subtraction and multiplication, with additional activations in the left and
right STG during multiplication. This finding converges with recent fMRI and TMS results to
indicate that both operations require accessing number representations in the parietal cortex,
whereas perisylvian areas exclusively contribute to the memory retrieval of arithmetic
operations learned by repetition, such as multiplication (Andres et al., 2011; Prado et al.,
2011; Sallilas et al., 2011; Zhou et al., 2007). Finger discrimination increased activity in
sensorimotor areas containing a topographic representation of the body, such as the bilateral
EBA (Downing et al., 2007) and the contralateral M1 (Dechent et Frahm, 2003) and S1
(Schweizer et al., 2008). Several other areas along the IPS and the PrCS were activated during
finger discrimination, irrespective of the tested hand. This parieto-precentral network has been
repeatedly associated to the execution or mental imagery of hand and finger movements
(Harrington et al., 2000; Haaland et al., 2004; Pelgrims et al., 2009, 2011).
In the parietal cortices, the areas involved in mental arithmetic and finger discrimination
overlapped in the hIPS and PSPL of both hemispheres. In all areas but the right hIPS, the
patterns of activity observed during finger discrimination and arithmetic were highly
correlated, indicating that brain activity was distributed similarly across voxels during these
tasks. The AREA by HEMISPHERE interaction, evidencing larger between-task correlations for the
left than for the right hIPS, might reflect a left hIPS specialization for precise numerical
representations during the development of finger-counting abilities (Andres et al., 2005; 2008;
Piazza et al., 2007). Dual-task experiments showed that finger movements slow down
arithmetic operations solved by counting whereas operations solved by memory retrieval
remain unaffected (Imbo et al., 2011; Michaux et al., submitted). The multiplication and
subtraction problems used in the present study typically lead to a rate of memory retrieval of
respectively 95% and 42% in occidental cultures (Campbell & Xue, 2001). Our RL data confirm
that multiplication problems were solved through fast and automatic processes, such as
memory retrieval, whereas subtraction problems required more time-consuming computational
strategies. However, we found that both operations induced activation in the parietal areas
underlying finger discrimination. One possible interpretation is that the parietal cortex provides
a common medium to represent numbers and fingers but that the way this medium is
exploited differs between operations. In line with this, voxelwise correlations showed that the
pattern of activity induced by finger discrimination in the hIPS and PSPL was more similar to
the one observed during subtraction than during multiplication. The similarity of activation
patterns is not linked to a speed confound since the slowest (i.e., subtraction) and fastest (i.e.,
finger discrimination) tasks turned out to be more correlated with each other. We rather
suggest that the neural overlap between arithmetic operations and finger discrimination is
influenced by solving strategies, as suggested by our behavioural results and introspective
reports from previous studies (Campbell & Xue, 2001). Previous brain imaging results
corroborate the view that the solving of subtraction problems requires manipulating number
representations with the joint contribution of the hIPS and PSPL (Eger et al., 2003; Knops et
al., 2009a; Piazza et al., 2007; Prado et al., 2011). Although the presentation of simple
multiplication problems was also associated to increased activity in these parietal areas
(Andres et al., 2011; Rickard et al., 2000; Zago et al., 2001), it was shown that these
problems induce automatic activation of the answer in long-term memory with the potential
support of additional areas in the MTG and STG (Andres et al., 2011; Prado et al., 2011; Zhou
et al., 2007) and/or the ANG (Delazer et al., 2003; Grabner et al., 2009; Grabner et al., 2011;
Price & Ansari, 2011).
Because neural overlap was found in parietal areas whose contribution to finger
discrimination was not specific to the left or the right hand, it is reasonable to assume that this
overlap is not related to somatic representations. In the finger discrimination task, the absence
of visual feedback put strong demands on the ability to represent the relative position of the
fingers, as evidenced by increased RLs for the middle fingers that have more neighbours than
the others. The pattern of activation in this task was analogue to the one observed in the
contrast between complex and simple finger movements in other fMRI studies (Harrington et
al., 2000; Haaland et al., 2004). These studies showed that activity along the hIPS and PSPL
increased with the number of transitions between fingers, irrespective of hand laterality,
whereas M1 and S1 were activated in response to contralateral hand movements regardless of
finger transitions. Cell recordings in the monkey homologue of the hIPS showed that neuronal
activity in this area can predict a transition between two different movements, with
incremental increases reflecting the number of times a movement is repeated before a
transition (Sawamura et al., 2002). Altogether, these results suggest that the parietal network
underlying finger discrimination is endowed with suitable properties for keeping track of
incremental changes during arithmetic operations. The hIPS activation extends in areas whose
role in visuomotor functions, such as pointing or grasping, is well established both in human
and non-human primates (Binkofski et al., 1999; Simon et al., 2002). The same areas have
also been related to movement preparation and motor intention (Göbel et al., 2004;
Rushworth et al., 2003; Thoenissen et al., 2002). In contrast, the PSPL is known to interact
with the FEF to support eye movements and attention shifts (for a meta-analysis, see Grosbras
et al., 2005). The correlation between the pattern of activation observed in the PSPL during
finger discrimination and arithmetic could therefore indicate that the two tasks share common
resources for attention allocation over the mental representation of fingers and numbers. It
has been suggested that computing the result of an arithmetic problem is analogue to shifting
attention to the left or right side of a mental number line (Hubbard et al., 2005; Knops,
2009b). Indeed, a common neural code was found for leftward saccades and subtraction and
for rightward saccades and addition in the PSPL (Knops et al., 2009a). Although simple
multiplication problems are solved by memory retrieval, it is reasonable to assume that
visuospatial processes can help narrowing down the range of potential answers as they do for
addition and subtraction (Dehaene & Cohen, 1991). This view is indirectly supported by
developmental studies showing that children have intuitive knowledge of multiplication
operations before they get trained with these operations (McCrink and Spelke, 2010) and by
other brain imaging studies corroborating the increase of activity in the PSPL during basic
multiplication (Andres et al., 2011; Rickard et al., 2000). The FEF were not activated during
arithmetic tasks in our study but previous studies suggest that these areas also contribute to
represent numbers on a visuospatial medium (Knops et al., 2009a; Rusconi et al., 2011).
Further research is required, however, to determine the exact nature of the processes shared
by finger discrimination and mental arithmetic in the hIPS and PSPL.
Finally, a cluster of activation was found in the inferior part of the left PrCS during finger
discrimination but not during mental arithmetic, in contrast with several previous results
(Arsalidou & Taylor, 2011). Further studies are required to explain this discrepancy, for
example, by using a larger set of arithmetic problems. It is worth noting that activation in the
left PrCS might have been underestimated in the finger discrimination task as well, because
the colour judgement task, used as a reference, also involved finger drawings. The only
common focus of activation in the frontal lobe was located in the right IFG. It has been argued
that this area controls the search within working memory contents (Lepsien et al., 2005). A
previous study showed that this area was equally activated when numbers, syllables or
locations are manipulated vs. rehearsed in working memory (Zago et al., 2008). Our multi-
voxel pattern analysis suggests that numbers and fingers do not activate the same parts of the
IFG, meaning that the recruitment of this area is not completely independent of the contents
stored in working memory.
The present study adds further evidence to the view that finger representations might
offer a support for arithmetic operations. Results showed that finger discrimination and mental
arithmetic share common parietal and frontal areas in the adult brain. In contrast with the EBA
and S1/M1, these areas do not contribute to somatic representations, as evidenced by a
similar increase of activity while representing the left or right hand. Voxelwise correlations
were used to explore further the neural overlap between finger discrimination and arithmetic
tasks and similar patterns of activity were found in the hIPS and PSPL but not in the IFG.
Correlations were higher in the left than in the right hIPS and they were also influenced by
arithmetic operation. The parietal areas involved in finger discrimination seem more important
to index numerical changes during subtraction than during multiplication, presumably because
multiplication problems are mostly solved by memory retrieval with the support of additional
areas in the temporal cortex. Future research should clarify the nature of the neural
mechanisms shared by finger discrimination and mental arithmetic in the hIPS and PSPL with a
special emphasis on the respective contribution of motor and spatial processes.
This work was supported by grants from the Fonds National pour la Recherche Scientifique
(grant 1.B099.09, FRS-FNRS, Belgium), and the Fonds Spéciaux de Recherche of the
Université catholique de Louvain (grant FSR09-CWS/09.285). M.A. was a post-doctoral
researcher, N.M. is a research fellow and M.P. a research associate at the Fonds National pour
la Recherche Scientifique (FRS-FNRS, Belgium). We are grateful to Pierre Leclef for his
contribution to the acquisition of fMRI data, to Cécile Grandin for the medical supervision, to
the Radiodiagnosis Unit at the Cliniques Universitaires St. Luc (Brussels) for technical support
during fMRI testing, and to Manuela Piazza for her suggestions about data analysis.
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Figure 1. A. Photograph of the wooden blocks used in the finger discrimination task. During
the task, participants held a different block in each hand, palms up, with the thumb in a lateral
position. B. Illustration of the participant’s grip on the wooden block, with half of the fingers
placed over the bumps (upper position) and the others in the holes of the block (down
position). C. Time course of each experimental task and its reference. In arithmetic tasks, they
had to multiply the Arabic digit by 3 or 4, or to subtract it from 11 or 13. In the finger
discrimination task, the participants were instructed to decide whether the red finger was in a
down position by saying “yes” or “no”. Control tasks consisted in letter reading or colour
judgements (see Procedure for further details).
Figure 2. A. Mean RLs and S.E. as a function of task (S=soustraction, M=multiplication,
F=finger discrimination) and finger. B. Brain areas showing increased activity in mental
arithmetic tasks compared to letter reading (pFDR<.05). C. Brain regions showing increased
activity in finger discrimination compared to color judgements. D. Overlapping activations in
finger discrimination and arithmetic tasks. Diagrams represent the percent of signal change in
peak voxels (MNI coordinates) for each experimental task (black) and its reference (grey).
Table 1. Summary of the activations observed during subtraction, multiplication and finger
discrimination (pFDR<.05; minimum cluster size k = 100 voxels).
Contrast Brain area x y z T-value k
Arithmetic – Letter reading Left PSPL -28 -72 42 5.80 664
Left hIPS -32 -58 42 5.58
Right PSPL 32 -70 42 5.13 377
Right IFG 42 20 -2 4.80 282
Right hIPS 48 -40 48 4.06 200
Multiplication – Subtraction Left STG -60 -14 0 5.87 1616
Right STG 60 -2 -2 5.53 1047
Finger task – Color task Left PSPL -20 -68 62 11.61 5914
Left hIPS -38 -44 50 11.08
Left EBA -48 -68 -2 7.03
Right hIPS 44 -40 52 10.87 5966
Right PSPL 30 -72 40 9.16
Right EBA 54 -60 -8 7.06 335
Left FEF -28 -4 50 6.37 681
Right IFG 38 26 -4 6.35 534
Right FEF 26 -2 56 5.08 874
Right MFG 50 32 30 4.65 548
Left PrCS -46 4 34 3.97 283
Right Hand – Left Hand Left M1 / S1 -46 -22 62 7.39 895
Left Hand – Right Hand Right M1 / S1 42 -20 62 6.46 188
x, y, z = MNI stereotaxic coordinates of the peak voxels; k = cluster size (number of voxels); EBA =
extrastriate body area, FEF = frontal eye fields, hIPS = intraparietal sulcus (horizontal part), IFG =
inferior frontal gyrus (orbital part), M1 = primary motor cortex, MFG = middle frontal gyrus, PrCS = pre-
central sulcus (inferior part), PSPL = posterior superior parietal lobule, S1 = primary somatosensory
cortex, STG = superior temporal gyrus.
Table 2. Mean correlations (and S.E.) between the patterns of activation induced by finger
discrimination and mental arithmetic in the hIPS and the PSPL. Asterisks indicate a significant
difference when compared to the EBA taken as a control site for its specific contribution to
finger discrimination (* p<.001). Same abbreviations as in Table 1.
Finger and Subtraction Finger and Multiplication
Left hemisphere Right hemisphere Left hemisphere Right hemisphere
PSPL 0.59 ± 0.07 * 0.61 ± 0.06 * 0.44 ± 0.09 * 0.56 ± 0.07 *
hIPS 0.59 ± 0.08 * 0.41 ± 0.06 0.45 ± 0.01 * 0.31 ± 0.09
EBA 0.11 ± 0.10 0.22 ± 0.10 -0.08 ± 0.11 0.08 ± 0.10
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