Parietal rtms distorts the mental number line: Simulating spatial neglect in healthy subjects

Neuropsychologia 44 (2006) 860 868 Parietal rtms distorts the mental number line: Simulating spatial neglect in healthy subjects Silke M. Göbel a,b,, Marco Calabria c, Alessandro Farnè c,d, Yves Rossetti c,d,e a Department of Experimental Psychology, University of Oxford, South Parks Road, Oxford OX1 3UD, UK b Department of Psychology, University of York, York YO10 5DD, UK c Espace et Action, UMR-S 534 INSERM-UCBL, Institut National de la Santé etdelarecherchemédicale, Université Claude Bernard, 16 Avenue Lépine, 69676 Bron, France d Institut Fédératif des Neurosciences de Lyon (IFNL), Bron, France e Mouvement et Handicap, Hôpital Henry Gabrielle, Hospices Civils de Lyon et Université Claude Bernard, St Genis Laval, France Received 13 May 2005; received in revised form 14 September 2005; accepted 16 September 2005 Available online 2 November 2005 Abstract Patients with left-sided visuospatial neglect, typically after damage to the right parietal lobe, show a systematic bias towards larger numbers when asked to bisect a numerical interval. This has been taken as further evidence for a spatial representation of numbers, perhaps akin to a mental number line with smaller numbers represented to the left and larger numbers to the right. Previously, contralateral neglect-like symptoms in physical line bisection have been induced in healthy subjects with repetitive transcranial magnetic stimulation (rtms) over right posterior parietal lobe. Here we used rtms over parietal and occipital sites in healthy subjects to investigate spatial representations in a number bisection task. Subjects were asked to name the midpoint of numerical intervals without calculating. On control trials subjects behaviour was similar to performance reported in physical line bisection experiments. Subjects underestimated the midpoint of the numerical interval. Repetitive transcranial magnetic stimulation produced representational neglect-like symptoms in number bisection when applied over right posterior parietal cortex (right PPC). Repetitive TMS over right PPC shifted the perceived midpoint of the numerical interval significantly to the right while occipital TMS had no effect on bisection performance. Our study therefore provides further evidence that subjects use spatial representations, perhaps akin to a mental number line, in basic numerical processing tasks. Furthermore, we showed that the right posterior parietal cortex is crucially involved in spatial representation of numbers. 2005 Elsevier Ltd. All rights reserved. Keywords: Number bisection; Repetitive transcranial magnetic stimulation; Posterior parietal cortex; Unilateral neglect; Mental number line 1. Introduction Healthy subjects when asked to bisect a physical line tend to exhibit a small leftward bias, i.e. they normally bisect lines slightly to the left of the midpoint (pseudoneglect) (Jewell & McCourt, 2000). In contrast, neglect patients show a rightward bias in line bisection that might be due to neglecting part or most of the left side of the line (Halligan & Marshall, 1993). There are several means to alleviate unilateral neglect or to simulate neglect in healthy subjects such as short-term adaptation Corresponding author at: Department of Psychology, University of York, York YO10 5DD, UK. Tel.: +44 1865 271378; fax: +44 1865 310447. E-mail address: s.goebel@psychology.york.ac.uk (S.M. Göbel). to prisms (for a review see Rossetti & Rode, 2002). Fierro et al. (2000) showed that this rightward bias in line bisection could be induced in healthy subjects by transcranial magnetic stimulation (TMS) over right but not left posterior parietal cortex (PPC). Although the basic pathophysiological principles leading to spatial neglect are still an issue of lively debate (e.g. Halligan & Marshall, 1994; Karnath, 2001; Milner & Goodale, 1995), there is evidence that the most frequent anatomical correlate of visuospatial hemineglect in humans is damage to the inferior parietal lobule (Halligan, Fink, Marshall, & Vallar, 2003; Vallar & Perani, 1986). Neuroimaging and neurointerference data support the view that the right inferior parietal lobule is involved in spatial tasks such as line bisection (Bjoertomt, Cowey, & Walsh, 2002; Fink et al., 2000; Fink, Marshall, Weiss, & Zilles, 2001), visual search (Walsh, Ellison, Ashbridge, & Cowey, 1999) and 0028-3932/$ see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.neuropsychologia.2005.09.007

S.M. Göbel et al. / Neuropsychologia 44 (2006) 860 868 861 mental rotation (Harris & Miniussi, 2003). Some patients with unilateral neglect also show a spatial deficit for left-sided stimuli that extends to mental images (Bisiach & Luzatti, 1978; Bisiach & Vallar, 1988). Recently Zorzi, Priftis, and Umilta (2002) reported that neglect patients with right parietal lesions not only show a systematic bias when asked to bisect a line, but also when they were asked to bisect a numerical interval (see also Rossetti et al., 2004). Along with the importance of left PPC in calculation and number representation (Chochon, Cohen, van de Moortele, & Dehaene, 1999; Cipolotti & van Harskamp, 2001; Dehaene, 2000; Dehaene, Piazza, Pinel, & Cohen, 2003; Göbel, Walsh, & Rushworth, 2001; Hecaen, Angelergues, & Houllier, 1961) these findings suggest a role for the right PPC in spatial number representation, perhaps akin to a mental number line. Galton (1880) was the first to report what he called mental number forms, highly individualistic associations of numbers with a mental image of numbers represented in space, mostly along a line, a mental number line. Mental number lines have also been described more recently (Seron, Pesenti, Noel, Deloche, & Cornet, 1992) and it has been suggested that explicit automatic mental number lines could be a specific form of synaesthesia (Hubbard, Piazza, Pinnel, & Dehaene, 2005). However, support for the number line model of number representation (Restle, 1970) does not just come from the selective group of subjects with explicit mental number lines but also stems from associations between number size and spatial response codes found in subjects who do not possess explicit mental number lines. Several studies have proposed a link between number size and spatial response codes and provide support for a canonical orientation of the mental number line (i.e. smaller numbers represented to the left side of space and larger numbers to the right side of space). Subjects performing a parity judgement task, for example, are faster to respond with their left hand to smaller numbers and with their right hand to larger numbers (the spatial numerical response code or SNARC effect, Dehaene, Bossini, & Giraux, 1993). Similar effects of task-irrelevant number size on spatial responses have been reported, for example for pointing (Fischer, 2003) oreyemovement responses (Bächtold, Baumüller, & Brugger, 1998; Fischer, Warlop, Hill, & Fias, 2004) to the left or the right side of space, bisecting digits strings (Fischer, 2001) and orienting spatial attention (Fischer, Castel, Dodd, & Pratt, 2003). Disturbances in number processing and calculation have been commonly reported after damage to the inferior parietal lobes (Cipolotti & van Harskamp, 2001; Dehaene, 2000; Hecaen et al., 1961). Acalculia, difficulty in calculation, is mostly associated with lesions in the left hemisphere (Grafman, Passafiume, Faglioni, & Boller, 1982). However, recent imaging studies suggest that areas in left and right intraparietal sulcus (IPS) are active during number processing (Chochon et al., 1999; Eger, Sterzer, Russ, Giraud, & Kleinschmidt, 2003; Pinel, Piazza, Le Bihan, & Dehaene, 2004; Rickard et al., 2000). Dehaene et al. (2003), in the latest version of the triple-code model of number processing, suggest that a non-verbal representation of numerical quantity perhaps analogous to a number line is present in the horizontal segment of the intraparietal sulcus of both hemispheres. Thus, hemispheric dominance for basic number processing is less clear than for spatial cognition. Few acalculic patients with left parietal lesions have been reported who were impaired in basic number processing tasks such as number comparison or number bisection (Cipolotti & van Harskamp, 2001; Lemer, Dehaene, Spelke, & Cohen, 2003). However, most neglect patients with right parietal lesions tested on number bisection show an impairment on these tasks (Rossetti et al., 2004; Vuilleumier & Rafal, 1999; Zorzi et al., 2002). Interestingly, one of the few acalculic patients in the literature who failed at number bisection (patient MAR, Dehaene & Cohen, 1997) had a lesion in the right parietal lobe, but was left-handed. The aim of the present study was to explore the role of both posterior parietal cortices in spatial number representation by using repetitive transcranial magnetic stimulation. In particular we aimed to test the prediction that the right posterior parietal cortex in healthy subjects to be involved in spatial representation of numbers as assessed by number bisection. 2. Methods 2.1. Subjects Twenty-eight healthy volunteers, aged 19 41 years, with English as their mother tongue were tested (12 female and 16 male, all right-handed). All subjects were checked for TMS exclusion criteria and gave their informed written consent before participating. The procedure was approved by the Ethics Committee of the University of Oxford (OxREC number C02.092). Subjects were over 18 years of age, either held or were studying for a university degree, had normal or corrected to normal visual acuity and were free of any neurological condition. They were reimbursed for travel expenses and time taken to participate in the study. 2.2. Stimuli and apparatus Subjects were presented aurally with 60 different pairs of three-digit numbers in ascending order from 117 166 to 959 984. Each pair of three-digit numbers was in the same hundreds. Numerical distance between the numbers of each pair was either 16, 25, 36, 49 or 64. Each pair of numbers was recorded as one single sound file before the experiment and was spoken by a male British voice. An example for one such single sound file is 758 783 (see Fig. 1). The recorded numbers were then manipulated with the help of a sound programme (CoolEditPro) so that the entire presentation of each sound file took 3500 ms with 500 ms separating the first three-digit number (e.g. 758) from the second three-digit number (e.g. 783). For generating the magnetic pulses we used a Magstim Super Rapid stimulator (The Magstim Company Limited, Whitland, UK) with a 70 mm figure of eight coil. Magnetic stimulus intensity was between 55 and 70% of the maximum stimulator output. The intensity of the magnetic stimulation was set separately for each individual at 10% above their active motor threshold. Motor threshold was defined as minimum percentage of the stimulator output that evoked a visually detectable twitch in the contralateral hand when contracted (Pridmore et al., 1998). Frequency, intensity and duration of rtms were in accordance with the safety guidelines suggested by Wassermann (1998). 2.3. Procedure Subjects sat in front of two loudspeakers and were blindfolded for the duration of the experiment. Subjects had to estimate and name the number that lay in the middle of the interval described by the two numbers. Instructions provided to the subject emphasised that they should perform the task without calculating and answer as quickly as possible. Their verbal response and reaction times (RT) were recorded. RT was calculated with respect to the subjects response onset.

862 S.M. Göbel et al. / Neuropsychologia 44 (2006) 860 868 Fig. 1. In each trial subjects heard a male voice naming two three-digit numbers. These two three-digit numbers were separated by a silence lasting 500 ms. The total duration of the utterance of the two three-digit numbers was 3500 ms. Subjects were asked to name the numerical midpoint of the interval described by the two three-digit numbers without calculating. The intertrial interval lasted 3000 ms. Subjects responded towards the end of the intertrial interval. On 50% of the trials immediately after the end of the utterance rtms was applied at 5 Hz for 1000 ms over parietal or occipital stimulation sites. Each block consisted of 120 trials, preceded by an initial training block of five non-tms trials. The order of the sound files was pseudorandom within each block. The intertrial interval was 3 s. On 60 trials in each experimental block rtms was applied over the subject s scalp at 5 Hz. The rtms stimulation started immediately after the end of the sound file and lasted for 1000 ms (see Fig. 1). These TMS parameters were chosen, because pilot studies showed that subjects responses in our task occur mainly between 2000 and 3000 ms after the end of the sound file. Previously we used a slightly different rtms protocol (500 ms of 10 Hz rtms), but this was in number comparison tasks in which subjects gave responses within 500 ms of stimulus presentation (Göbel et al., 2001). For the current experiment we decided to use 1000 ms of rtms in order to have a longer time window of possible rtms interference. We lowered the frequency of rtms to 5 Hz to be able to have a sufficient number of TMS trials while being in line with safety regulations. The rtms trials occurred pseudorandomly with the constraint that at the end of a block each sound file had been presented twice, once with TMS and once without TMS. Fourteen subjects (six female, eight male; aged 19 29 years, mean age 22 years) completed two experimental blocks (experiment 1). In one block they received stimulation over the left angular gyrus/adjacent posterior part of the intraparietal sulcus (pipl + S), in the other block TMS was applied over their right pipl + S. The order of stimulated hemispheres was counter-balanced across subjects. The remaining 14 subjects (six female, eight male; aged 19 41 years, mean age 27 years) were stimulated over the occipital cortex (experiment 2; OCC). A central occipital cortex site was chosen as control site for several reasons. First, we decided to stimulate over the occipital cortex because Bjoertomt et al. (2002) have successfully used the occipital cortex as control site before in a line bisection task. Secondly, we only stimulated centrally and not over left and right occipital cortex, because there is no evidence that the lateralised noise of the discharge of the TMS coils may result in measurable attentional biases in bisection tasks (Bjoertomt et al., 2002; Fierro et al., 2000). 2.4. Localisation of TMS sites High-resolution T1-weighted anatomical scans from a 3 T Varian INOVA MRI system (1.5 mm thick axial slices with 1 mm 1 mm in plane resolution) were obtained of the subjects brains. The pipl + S site was first established for each subject separately for each hemisphere by using a visual search task (for details see Ashbridge, Walsh, & Cowey, 1997; Göbel et al., 2001). The number bisection task was then carried out while rtms was delivered at the site that showed disruptive effects for the visual search task (see Fig. 2A, B, D and E). The location of the pipl + S site was confirmed by MRI scan using a method of the frameless stereotaxy. A Polaris (Northern Digital, Ontario, Canada) infra-red tracking device was used to measure the position of the subject s head and Brainsight software (Rogue Research, Montreal, Canada) was used to co-register the subject s head with the subject s MRI scan. The coil was placed between the posterior superior temporal sulcus and the intraparietal sulcus, and thus over the same brain regions as previously stimulated (see Ashbridge et al., 1997; Göbel et al., 2001; Rushworth, Ellison, & Walsh, 2001). The occipital site (OCC) was established for each subject by using the 10 20 electrode system (AEEGS, 1991). Transcranial magnetic stimulation was applied at the site that was 10% of the inion nasion distance (about 3.0 3.6 cm) above inion. The location of the occipital site was then confirmed by frameless stereotaxy (see Fig. 2C and F). 2.5. Data analysis Bisection errors were calculated by subtracting the arithmetical midpoint from the subjective midpoint that was given by the subjects. Negative bisection errors therefore mean that subjects perceived the midpoint to be smaller than the arithmetical midpoint and positive bisection errors result when subjects perceived the midpoint to be larger than the arithmetical midpoint. Median bisection errors and reaction times were analysed separately, because there was no significant correlation between reaction times and bisection errors (r = 0.13, p = 0.43). First, we analysed only the data from trials without TMS. Two separate repeated-measures one-way ANOVAs were carried out on reaction times/bisection errors with interval size (16, 25, 36, 49, and 64) as a withinsubject factor and with session (left IPL + S, right IPL + S, OCC) as a betweensubject factor. There were no significant differences between the groups (for RT: F(8, 74) = 1.62, p = 0.13; for bisection error: F(8, 74) = 0.48, p = 0.86). To analyse the effect of TMS, we ran separate analyses for experiments 1 and 2. As the TMS effect in general did not vary for the different numerical intervals, we did not include interval size as a factor in these analyses. The effect of parietal TMS was analysed by two separate repeated-measures two-way ANOVAs on reaction times/bisection errors with trial type (control trials, trials with TMS) and hemisphere (left parietal, right parietal) as within-subject factors and order (left parietal first, right parietal first) as a between-subject factor. We followed up

S.M. Göbel et al. / Neuropsychologia 44 (2006) 860 868 863 Fig. 2. TMS sites over right posterior IPS + L (A and D), left posterior IPS + L (B and E) and occipital lobe (C and F). The top row of images show axial views of an average MRI scan derived from several subjects after transformation to a standard template. Circles indicate the points where TMS was directed. Mean co-ordinates are indicated by crosshairs (right posterior IPS + L: x = 38, y = 65, z = 48; left posterior IPS + L: x = 34, y = 62, z = 50, occipital lobe: x = 1, y = 98, z = 18). The bottom row of images shows approximately axial views of a single subject s MRI scan. The MRI scan was co-registered with visible landmarks on the subject s head so that the position of the TMS coil could be measured with respect to the subject s brain during the experiment. Crosses indicate the position of the TMS coil at which rtms was administered. these analyses by separate one-way ANOVAs on reaction times/bisection errors with trial type (control trials, trials with TMS) as a within-subject factor. The effect of occipital TMS was assessed by two separate one-way ANOVAs on reaction times/bisection errors with trial type (control trials, trials with TMS) as within-subject factor. 3. Results 3.1. Behavioural results Subjects took on average 2737 ms before they responded. The larger the numerical interval the longer were their reaction times (F(4, 36) = 5.33, p = 0.002, see Fig. 3A). On average subjects underestimated the midpoint of the numerical interval by half a digit ( 0.49). However, the size of the numerical interval affected the bisection error significantly (F(4, 36) = 3.26, p = 0.02, see Fig. 3B). While subjects underestimated the midpoint for intervals 16, 25, 36 and 49, subjects overestimated the midpoint of largest interval (64) by 0.54 digits. 3.2. Parietal TMS Interestingly, parietal TMS did not affect RTs (F(1, 13) = 2.07, p = 0.18; see Fig. 4). However, parietal stimulation significantly shifted the perceived midpoint (F(1, 13) = 5.94, p = 0.03; see Fig. 5). When subjects were stimulated over right parietal cortex the negativity of the average bisection error decreased significantly (from 0.52 to 0.13; F(1, 13) = 4.52, p = 0.05). Transcranial magnetic stimulation over left parietal cortex also shifted the bisection error (from 0.48 to 0.25), but this effect was statistically not significant (F(1, 13) = 2.28, p = 0.16). All effects and interactions of order were nonsignificant. 3.3. Occipital TMS When TMS was applied over the occipital cortex reaction times decreased significantly from 2970 to 2814 ms (F(1,

864 S.M. Göbel et al. / Neuropsychologia 44 (2006) 860 868 Fig. 3. (A) Reaction times (RTs) on control trials: subjects took longer to respond the larger the numerical interval. (B) Number bisection errors on control trials: subjects underestimated the midpoint for smaller numerical intervals. 4. Discussion Fig. 4. rtms effect on reaction times: reaction times on controls trials (in black) were not significantly different from reaction times for TMS trials (in grey) when rtms was applied over the parietal sites. TMS, however, significantly decreased reaction times when applied over the occipital site. 13) = 5.28, p = 0.04, see Fig. 4). In contrast, there was no significant effect of TMS on the bisection error (F(1, 13) = 0.53, p = 0.48; see Fig. 5) when TMS was applied over the occipital cortex. Our study provides further evidence that the posterior parietal lobe is involved in spatial number representation. We showed a significant shift of bisection errors towards the right side of space for magnetic stimulation when TMS was applied over the right posterior parietal cortex. This study presents converging evidence to number bisection studies on patients (Rossetti et al., 2004; Zorzi et al., 2002) showing that patients with right parietal damage and neglect misjudge the midpoint of a numerical interval and to findings from TMS studies of line bisection (Bjoertomt et al., 2002; Fierro, Brighina, Piazza, Oliveri, & Bisiach, 2001). Fierro et al. (2001) showed that stimulating normal subjects over right posterior parietal lobule leads to a shift in bisection errors towards the right for line bisection. These findings suggest that transcranial magnetic stimulation over the right parietal cortex is altering a representation of numbers that is likely to follow a spatial format. As it has been reported that TMS applied to this area is capable of inducing a right-sided bias for physical line bisection (Bjoertomt et al., 2002; Fierro et al., 2001) it is probably the left side of that spatial representation of numbers Fig. 5. rtms effect on number bisection errors: on control trials (in grey) subjects underestimated the midpoint of the numerical interval. On trials with repetitive TMS (in black), subjects showed a significant shift in midpoint estimation towards the right for parietal rtms (experiment 1). Occipital rtms (experiment 2), however, had no effect on number bisection errors.

S.M. Göbel et al. / Neuropsychologia 44 (2006) 860 868 865 that is also altered by TMS in the present study. In our study we also found behavioural evidence that subjects performed number bisection analogous to line bisection, with smaller numbers to the left and larger numbers towards the right side of a mental number line. On average subjects underestimated the midpoint of the numerical interval. This is in line with results from an earlier study of number bisection (Calabria, Michel, Jacquin- Courtois, Göbel, & Rossetti, 2004) and is similar to findings in physical line bisection. Although this has remained a matter of debate for years, it seems reasonable to admit that when healthy subjects are tested on line bisection tasks they tend to show a slight but significant tendency to overestimate the length of the left side of the line relative to its right side, i.e. they put the midpoint of the physical line to the left of the correct midpoint (Jewell & McCourt, 2000). This has been termed pseudoneglect. Furthermore, Werth and Poppel (1988) showed that in imagined lines the direction of pseudoneglect in healthy subjects depends on the length of the line with leftward errors for short lines and rightward errors for long lines (it is however unclear whether there is a reliable effect of line length in physical line bisection in normals, see Halligan & Marshall, 1988; McCourt & Jewell, 1999). In our experiment it did not only take subjects longer to respond for larger numerical intervals (as reported before, e.g. Nuerk, Geppert, van Herten, & Willmes, 2002), but the bisection error changed significantly with the size of the numerical interval. On average subjects showed a bias towards the left side for shorter numerical lines and a bias towards the right side for the longest interval which is analogous to Werth and Poppel s findings. Hence, our behavioural data suggest that subjects solved the number bisection task in a manner analogous to line bisection and employed a spatial number representation. Alternatively both biases may be a result of a disturbance of a common magnitude processor or mechanism (Walsh, 2003). In addition, the fact that this tendency is found for every interval as in another study (Calabria et al., 2004) suggests that number bisection may be more sensitive than line bisection (see also Rossetti et al., 2004). Repetitive transcranial magnetic stimulation had a significant effect on bisection errors when applied over the right posterior parietal site, but not when applied over the occipital site, thus showing an involvement of the posterior parietal lobe in estimating the midpoint of a numerical interval. The posterior parietal cortex has been shown to be involved in various cognitive tasks (Simon, Mangin, Cohen, Le Bihan, & Dehaene, 2002; Walsh, 2003) including number processing (Chochon et al., 1999; Dehaene, Spelke, Pinel, Stanescu, & Tsivkin, 1999; Gruber, Indefrey, Steinmetz, & Kleinschmidt, 2001) and physical line bisection (Bjoertomt et al., 2002; Fierro et al., 2001; Fink et al., 2000, 2001). Basic number processing tasks such as number comparison activate the intraparietal sulcus bilaterally (Eger et al., 2003; Fias, Lammertyn, Reynvoet, Dupont, & Orban, 2003; Pinel et al., 2004). When the posterior parietal lobe is damaged, subjects are impaired on various cognitive tasks including calculation (Cipolotti & van Harskamp, 2001; Grafman et al., 1982) and spatial cognition (Driver & Mattingley, 1998; Halligan & Marshall, 1993; Halligan et al., 2003). Neuroimaging studies, however, also suggest an involvement of the posterior parietal cortex in stimulus-response processing (Bunge, Hazeltine, Scanlon, Rosen, & Gabrieli, 2002; Rushworth, Johansen-Berg, Göbel, & Devlin, 2003; Sawamura, Shima, & Tanji, 2002) and verbal short-term memory (Paulesu, Frith, & Frackowiak, 1993; Price, 1998). The significant shift in bisection errors on trials with TMS over the right parietal site in our study, however, is unlikely to be due to impairments in stimulus-response processing or verbal short-term memory. Neither impairments in stimulus-response processing nor in verbal short-term memory predict a directional shift in number bisection errors. In both cases, however, an increase in reaction times would be predicted, but repetitive transcranial magnetic stimulation over the parietal sites in our study had no significant effect on reaction times. The TMS effect was specific to a spatial measure, the bisection error. Transcranial magnetic stimulation over the occipital site, however, significantly decreased reaction times. This is a common finding for magnetic stimulation over task-irrelevant sites (Walsh & Pascual-Leone, 2003) and is probably due to the loud click of the coil when the magnetic pulse is discharged and to the concurrent tactile stimulation of the skull (intersensory facilitation, Hershenon, 1962). In our study we found a significant shift of bisection errors towards the right side of space for magnetic stimulation when TMS was applied over the right posterior parietal cortex. However, it could be argued that in order to solve the task, subjects had to estimate the midpoint of the numerical interval and that magnetic stimulation impaired estimation rather than a spatial number representation. The debate about whether there are separate brain systems for estimation and exact calculation is by no means decided (Cipolotti & van Harskamp, 2001; Dehaene et al., 2003; Lemer et al., 2003), and indeed estimation and approximation have been related to activity in the right posterior parietal cortex and IPS (Dehaene et al., 1999; Stanescu-Cosson et al., 2000). Furthermore, patients with left hemisphere damage (Dehaene & Cohen, 1991) have been reported who, although inefficient and inaccurate at calculation, could still approximate answers. Therefore, one could argue that right parietal TMS in our study interfered with the subjects ability to estimate a numerical answer, and not with a spatial number representation. Vuilleumier, Ortigue, and Brugger (2004) reported that neglect patients when asked to judge whether a single number was smaller or larger than 5 were selectively slower to respond to 4 and when asked to compare numbers to 7 they were selectively slower to respond to 6. This result cannot be explained by an impairment in estimation. Furthermore, this finding is specific to patients with neglect, thus strongly arguing for a spatial representation of numbers in the right parietal lobe. More evidence for an underlying spatial deficit causing shifts in number bisection stems from prism adaptation studies. Rossetti et al. (1998) showed that neglect patients improve their performance in several neuropsychological tests after prism adaptation. Further studies have confirmed and extended this results ranging from line bisection (e.g. Farné, Rossetti, Toniolo, & Ladavas, 2002) to mental imagery (Rode, Rossetti, & Biosson, 2001). Mental number bisection can also be improved following prism adaptation. Neglect patients in contrast to controls

866 S.M. Göbel et al. / Neuropsychologia 44 (2006) 860 868 systematically overestimate the midpoint of the numerical interval, but this symptom improved markedly after prism exposure (Rossetti et al., 2004). Fewer studies have investigated cognitive effects of prism adaptation in healthy individuals (Berberovic & Mattingley, 2003; Colent, Pisella, & Rossetti, 2000; Girardi, McIntosh, Michel, Vallar, & Rossetti, 2004; Michel et al., 2003a; Michel, Rossetti, Rode, & Tilikete, 2003b). Subjects performance on line bisection tasks after exposure to left-deviating prisms was very similar to neglect patients, and the same has recently been shown for number bisection. Calabria et al. (2004) showed that exposure to left-deviating prisms in normal subjects leads to a significant shift in number bisection towards the right side of space. We therefore suggest that magnetic stimulation over right posterior parietal cortex in our experiment led to an impairment of the left side of a spatial number representation, thus leading to a systematic shift in midpoint estimation towards the right side. We did not expect TMS over left parietal cortex to have an effect on number bisection. However, in our data there is a trend for a TMS effect over left parietal cortex. Although spatial neglect has been mainly reported after right hemisphere lesions, there have been studies showing that left posterior parietal impairments can result in visuospatial impairments, typically in the right side of space (Eglin, Robertson, & Knight, 1991). In a previous study we showed that rtms over left posterior PPC impaired performance in a number comparison task especially for numbers greater than (and in spatial terms on the right of) a reference number (Göbel et al., 2001). Therefore one might have predicted that TMS over the left posterior parietal cortex shifted the midpoint estimation towards the left. But this is not what we found. Although the effect on its own is non-significant there is a surprising trend for a midpoint shift to the right, like for the right posterior parietal cortex. Interestingly, the same general tendency has been reported in studies using prism adaptation. Prism adaptation to the right is significantly efficient in patients while left-shifting prisms most often produce non-significant effects. Furthermore, the reverse is true for healthy subjects in which significant effects are found with left-shifting prisms and non-significant trends with right-shifting prisms (Colent et al., 2000). We suggest that this finding might be explained in a framework described by Berberovic and Mattingley (2003) in which a hemispheric asymmetry in the processing of spatial errors for peripersonal and extrapersonal space is proposed. They tested healthy subjects before and after prism adaptation in visual midpoint judgements. As in previous studies, there was a significant rightward shift in visual midpoint judgements after adaptation to left-deviating prisms in peripersonal and extrapersonal space. But they also found a significant rightward shift after adaptation to right-deviating prisms, which was specific for extrapersonal space. This finding is analogous to our TMS effect over left posterior parietal cortex on number bisection. Much more research certainly is needed at this early stage, but we would like to speculate that the directional TMS trend over left posterior parietal cortex might be an indication that most people represent numbers in extrapersonal space. This hypothesis can be tested, for example by assessing number bisection errors before and after prism adaptation to right-deviating prisms. Assuming that Berberovic and Mattingley (2003) framework applies and mental number lines are represented in extrapersonal space, we predict that adaptation to right-deviating prisms in normal subjects will also result in a shift of the perceived midpoint towards the right. In conclusion, our study provides evidence that subjects use spatial representations, perhaps akin to a mental number line with smaller numbers to the left side of space and larger numbers to the right side of space, in basic numerical processing tasks such as number bisection. Furthermore, we showed that the right posterior parietal cortex is crucially involved in spatial representation of numbers. Acknowledgements This work was supported by the Leverhulme Trust and the Medical Research Council. SG was a Junior Research Fellow at Jesus College, Oxford. We also thank Peter Hobden for his assistance with the MRI scans. References AEEGS. (1991). 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