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 Brussels, Belgium

3

Department of Experimental Psychology, Ghent University, Henri Dunantlaan 2, 9000 Gent, Belgium

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: [email protected]

Abstract

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

1. Introduction 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 overlapping activations. 2. Material and methods 2.1. Participants 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) task. 2.3. Procedure 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 3500ms 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-oxygensensitive 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 withinsubject 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