Neuropsychologia 75 (2015) 565–576

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Dissociation between line bisection and mental-number-line bisection in healthy adults Francesca Rotondaro a,b,1, Sheila Merola a,b,1, Marilena Aiello c, Mario Pinto a,b, Fabrizio Doricchi a,b,n a

Dipartimento di Psicologia, Università “La Sapienza”, Roma, Italy Fondazione Santa Lucia IRCCS, Roma, Italy c Sissa – Cognitive Neuroscience Sector, Trieste, Italy b

art ic l e i nf o

a b s t r a c t

Article history: Received 2 March 2015 Received in revised form 13 July 2015 Accepted 14 July 2015 Available online 15 July 2015

Healthy adults bisect visual horizontal lines slightly to the left of their true center. This bias has been termed “pseudoneglect” and is considered to reflect right hemisphere dominance in the orienting of spatial attention. A previous investigation reported a positive correlation between pseudoneglect and a corresponding negative bias towards numbers lower than the true midpoint, i.e. supposedly to the left of the midpoint, during the mental bisection of number intervals that were defined by two visual arabic digits presented one to the left and one to the right of a horizontal line (Longo and Lourenco, 2007, Neuropsychologia, 45, 7, 1400–1407). Here, studying a sample of 60 healthy participants we verified whether this correlation still holds when the endpoints of number intervals are defined verbally, i.e. with no visual-spatial cues suggesting their left-to-right arrangement. Participants bisected horizontal lines (2 cm, 10 cm and 20 cm), short number intervals (3-, 5-, 7- and 9-unit) and large number intervals (16-, 24-, 32-, 40-, 48-, 56-, and 64-unit). Pseudoneglect was observed both in line and number interval bisection, confirming the results of Longo and Lourenco (2007). Nonetheless, the study of correlations between bisection biases averaged across different line and number intervals lengths and between all possible pairings of line and number interval lengths revealed no significant or systematic pattern. During line bisection pseudoneglect increased as a function of line length while with short number intervals pseudoneglect decreased and turned into an opposite positive bias as a function of interval length. With large number intervals no linear relationship was present between bisection bias and interval length and, as in Longo and Lourenco (2007), the higher was the starting point of the number interval the larger was pseudoneglect. These results show that verbally defined number intervals are not mentally inspected with the same mechanisms that are engaged by the bisection of horizontal visual lines. This suggests that number intervals are not inherently arranged along the mental equivalent of a left-to-right oriented horizontal line. This spatial representation seems rather adopted when, as in the case of the SNARC task, “left” vs. “right” codes must be used for the selection of responses associated with numbers or when, as in the case of Longo and Lourenco (2007), the numerical material to be processed is arranged in left-to-right order. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Line bisection Mental number line Numbers Spatial attention Spatial neglect Pseudoneglect

1. Introduction The discovery that in a task requiring the choice between a left and a right button press, left-to-right readers decide faster with the left button that a number is smaller than 5 (or that a number smaller than 5 is odd or even) and decide faster with the right button that a number is higher than 5 (or that a number higher n Corresponding author at: Dipartimento di Psicologia 39, Università degli Studi di Roma “La Sapienza”, Via dei Marsi 78, 00185 Roma, Italy. E-mail address: [email protected] (F. Doricchi). 1 These authors equally contributed to this work.

http://dx.doi.org/10.1016/j.neuropsychologia.2015.07.016 0028-3932/& 2015 Elsevier Ltd. All rights reserved.

than 5 is odd or even; Spatial-Numerical Association of Response Codes ¼SNARC; Dehaene et al., 1993), has led to the widespread assumption that number magnitudes have an inherent mental spatial representation that conforms to cultural reading styles, so that in western cultures smaller numbers are represented to the left or larger ones on a horizontal mental number line (MNL). The strength and reliability of the SNARC effect, has promoted the development of several lines of inquiry that exploit and explore the functional and anatomical links between the mechanisms underlying the representation of number magnitudes and those underlying the representation of space and the orienting of spatial attention. In the neuropsychological domain, it was suggested that

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right brain damaged patients (RBD) suffering defective attention for the left side of space, i.e. left spatial neglect, also suffer a similar deficit when they set mentally without formal calculation the midpoint of number intervals that are defined verbally by an examiner (Zorzi et al., 2002). A shift of the subjective midpoint of 5-, 7- and 9-unit number intervals toward numbers higher than the true midpoint (e.g. midpoint between 1 and 9¼ 7 instead of 5) was initially observed in a relatively small sample of neglect patients, just as if these patients were not paying attention to smaller numbers on the left side of number intervals. The phenomenological similarity between spatial and numerical impairments, was made even more captivating by the finding that a paradoxical bias toward numbers lower than the real midpoint, i.e. putatively to the left of the midpoint, was found in the mental bisection of short 3-unit number intervals, just like it is sometime found when neglect patients bisect very short visual horizontal lines (i.e. “cross-over" effect; Doricchi et al., 2005a). Nonetheless, in these initial observations the association between the bias in the mental bisection of number intervals and the bias in the bisection of horizontal visual lines was not empirically tested. Several studies have now investigated this issue and have clarified that the pathological bias in the bisection of number intervals is unrelated to the presence of a similar bias in the bisection of visual lines and is dissociated from the presence and severity of left side neglect in visual or imagery space (Rossetti et al., 2004; Doricchi et al., 2005b; 2009; Loetscher and Brugger, 2009; Loetscher et al., 2010; van Dijck et al., 2011a; 2011b; Rossetti et al., 2011; Aiello et al., 2012; 2013; Pia et al., 2012; Storer and Demeyere, 2014). More recently, in two independent investigations (both reported in Aiello et al. (2012)) it was rather found that RBD patients who suffer a pathological bisection bias toward numbers higher than the midpoint of number intervals also suffer an equivalent pathological bias when the same intervals are treated as time-intervals on a mental clock face, so that the spatial organization of intervals is reversed and higher time-numbers are represented on the left side, not right side, of the mental layout. These findings point at a dissociation between numerical and spatial-attentional biases and suggest that right brain damage disrupts the abstract representation of small numerical magnitudes, thus creating a corresponding bias toward larger magnitudes, independently from the mapping of small magnitudes on the left or the right side of a mental layout. Based on these findings, in the present study we wished to reinvestigate the functional association, or dissociation, between numerical and spatial biases by examining whether the error bias displayed by healthy participants in the bisection of visual horizontal lines is correlated with an equivalent bias in the mental bisection of number intervals whose endpoints are defined verbally. To this aim, we capitalized on the findings from a previous study by Longo and Lourenco (2007). These authors documented a significant correlation between the small leftward bias, termed “pseudoneglect”, that is typically observed in the line bisection performance of healthy adult participants (Jewell and McCourt, 2000) and a bias towards numbers smaller than the midpoint, i.e. putatively to the left of the midpoint, during the mental bisection of number intervals whose endpoints were presented visually, one to the left and one to the right of a short horizontal line. We hypothesized that if a left-to-right spatial arrangement is inherent to number magnitudes, then a correlation between the performance in the line and number interval bisection tasks should be found even when number intervals are defined verbally with no spatial cuing provided by the arrangement of interval endpoints to the left and to the right of a visual horizontal line. On the contrary, if the mental left-to-right arrangement of intervals is strategically triggered by the left-to-right visual spatial arrangement of numbers defining the interval endpoints, no equivalent correlation

should be found when number intervals are presented in a purely verbal manner.

2. Material and methods 2.1. Participants 60 healthy right-handed participants (40 females, 20 males, mean age¼ 21.9 y) were examined in the present investigation. Supplementary data gathered from a different sample of 31 participants to a previous study (Doricchi et al., 2009) were also included in the analyses of the “Line Bisection” task, the “Mental Bisection of Short Number Intervals” and in the study of the correlation between these two tasks (see below). The handedness of participants was assessed with the Italian adaptation (Salmaso and Longoni, 1985) of the Oldfield questionnaire (Oldfield, 1971). In this questionnaire a laterality quotient (LQ) equal to þ100 indicates complete right-hand dominance whereas an LQ of  100 indicates complete left-hand dominance. The LQ was þ 82.4 (s.d. ¼5.3) in the overall sample of 91 participants, þ89.6 (s.d. ¼10.6) in the sample 60 participants examined in the present investigation and þ93.1 (s.d. ¼ 10.4) in the sample of 31 participants gathered from our previous study (Doricchi et al., 2009). The LQ was comparable between the samples of 60 and 31 participants (t(1, 89) ¼ 1.5, p 4.05). 2.2. Tasks 2.2.1. “Line bisection” Participants marked with a fine line pencil the subjective center of horizontal lines that were individually printed at the center of a horizontally oriented A4 paper sheet. Lines were 2 cm, 10 cm or 20 cm long. Three trials per line length were administered. The sheet was presented at the center of a table, with its center aligned to the head-body mid-sagittal plane of participants. Individual bisection deviations from the objective center of lines were measured to the closest 0.5 mm. Rightward deviations from the objective line center were coded as positive ones and leftward deviations as negative ones. 2.2.2. “Mental Bisection of Short Number Intervals” In this task, participants were asked to speak out the midpoint of number intervals without making arithmetic calculations, thus providing an “approximate” bisection of intervals. In each trial two numbers defining the beginning and the end of 3-unit (e.g. 4–6), 5-unit (e.g. 3–7), 7-unit (e.g. 2–8) and 9-unit number intervals (e.g. 1–9) were presented through headphones. Intervals were taken from equivalent positions across the first three decades (e.g. 4-6, 14-16, 24-26; the complete list of intervals is reported in Supplementary Table 1). In the first part of the task, intervals were presented in ascending order (48 trials) and in the second part in descending order (48 trials). Bisection deviations toward numbers higher than the interval midpoint were scored as positive ones and deviations toward numbers lower than the midpoint as negative ones. 2.2.3. “Mental Bisection of Large Number Intervals” This task was performed only by the 60 participants to the present study and was equivalent to the preceding task, except from the length of number intervals. In analogy to the study by Longo and Lourenco (2007) larger 16-, 24-, 32-, 40-, 48-, 56-, and 64-unit intervals were presented. For each interval length, a pool of intervals was prepared taking as starting point of intervals different consecutive number positions over consecutive decades. The lower starting point of all intervals was 10 and the highest

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ending point was 89 (similar to intervals used in Longo and Lourenco, 2007). Using this method, a pool of sixty 16-unit, fifty 24-unit, forty 32 unit, forty 40-unit, thirty 48-unit, twenty 56-unit and ten 60-unit intervals was created (the pool of intervals is reported in Supplementary Table 2). Different random samples of six intervals per length were presented to each participant. In these samples each of the six 16-unit intervals started in a different decade among the first six decades; five out of the six 24-unit intervals started in one of the first five decades while the sixth interval had its starting point randomly positioned in one of these decades; four out of the six 32- and the six 40-unit intervals started in one of the first four decades while the two remaining intervals had their starting point randomly positioned in one of these decades; within the samples of 48-unit intervals, two intervals started in first, two in the second and two in the third decade; within the samples of 56-unit intervals three intervals started in the first and three in the second decade; within the sample of 64-unit intervals each of the six intervals started at different points in the first decade. Each interval was presented twice, once in ascending order (42 trials in total) and once in descending order (42 trials in total). As in the case of Short Number Intervals, bisection deviations toward numbers higher than the interval midpoint were scored as positive ones and deviations toward numbers lower than the midpoint as negative ones.

3. Procedure At variance with the study by Longo and Lourenco (2007) in which the bisections of line and number intervals were repeatedly alternated during a single experimental session, in the present investigations participants performed the line and number interval bisection tasks in three different sessions that were separated by a two/three days time interval. In the first session participants performed the “Line bisection” task, whereas during the second and third session they performed the two mental numerical tasks. Half of participants performed the “Mental Bisection of Short Number Intervals” during the second session and the “Mental Bisection of Large Number Intervals” during the third session. The other half of participants performed the two numerical tasks in reversed order. This procedure importantly reduces potential and spurious contamination between the strategies adopted in the performance of line and number interval bisections when these tasks are alternated in a single session. The possibility that any eventual lack of correlation between line and mental number interval bisection is crucially due the administration of these tasks in separate sessions/days seems limited by the results of a recent investigation (Göksun et al., 2013; see Section 5).

4. Results 4.1. “Line bisection” task Individual average bisection errors were entered in a Group of Participants (60, 31)  Line Length (2 cm, 10 cm, 20 cm) ANOVA. The main effect of Group was not significant [F(1,89) ¼0.16, p ¼.69, η²o .01]. Conversely, a significant Line Length effect was found [F(2,178) ¼8.3, p o.001, η² ¼.09]: this showed that the greater was line length the stronger was the error bias toward the left of the actual line center, i.e. pseudoneglect (2 cm¼  0.24 mm, s.d ¼0.49; 10 cm ¼  0.67 mm, s.d¼2.1; 20 cm ¼  1.38 mm, s.d.¼ 3.1; all planned comparisons of the means, p o0.01; Fig. 1A). The Group  Line Length interaction was not significant [F(2,178) ¼ 0.35, p ¼.70, η² o.01]. A series of t-tests showed that at all line length

Fig. 1. Line bisection task. (A) Mean bisection deviations from line midpoint (in mm with s.e.) reported as a function of line length in the overall group of participants (n¼91) and in the subgroups of participants to the present study (n¼60) and to a previous study (n¼ 31; Doricchi et al., 2009). Positive values indicate rightward shifts from true midpoint, negative values leftward shifts, i.e. pseudoneglect. (B) Mean percentage deviations (with s.e.) from line midpoint.

the error bias was significantly different from zero (2 cm: t(1,90) ¼  4.6; p o0.0001; 10 cm: t(1,90) ¼  3; p ¼0.003; 20 cm: t(1,90) ¼  4.1; po 0.0001). The average deviation across the different line lengths was 0.76 mm. All together, these results confirm previous observations on pseudoneglect by Longo and Lourenco (2007). Individual percentage deviations were analyzed through a Group of Participants (60, 31)  Line Length (2 cm, 10 cm, 20 cm) ANOVA. No Group effect was found [F(1,89) ¼0.11, p¼ .74, η² o.01] while a significant Line Length effect was present [F(2,178) ¼ 4.09, po .01, η² ¼.05]. Post-hoc comparisons showed that percentage deviation was significantly higher for 2 cm lines as compared to the other two line lengths (2 cm¼  1.23%; 10 cm¼  0. 67%; 20 cm¼  0.69%; all p o.02 Fig. 1B). The bisection biases and percentage deviations observed in our study are congruent with those reported in normative studies by Varnava and Halligan (2007; 140 healthy participants, 2 cm, 10 cm and 18 cm lines, five trials per line length) and Azouvi et al. (2002; 457 healthy participants, 5 cm and 20 cm lines, two trials per line length). 4.2. “Mental Bisection of Short Number Intervals” Individual average bisection errors were entered in a Group of Participant (60, 31)  Experimental Condition (Forward, Backward)  Number Interval Length (3-, 5-, 7- and 9-units) ANOVA. No significant main effect of Group [F(1,89) ¼ 2.1, p¼ .14, η² ¼.02] and no Group  Number Interval Length [F(3,267) ¼0.59, p ¼.62, η² o.01; Fig. 2A] or Group  Experimental Condition interaction [F(1,89) ¼0.15, p ¼.70, η² ¼ o .01] was found. A significant

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p¼ 0.6). The average bisection bias across the different interval length was equal to  0.016 units and was not different from zero (t(1,90) ¼ 0.94, p ¼0.3). Individual percentages of bisection error were entered in Group of Participants (60, 31)  Number Interval Length (3-, 5-, 7- and 9-units) ANOVA. A significant Number Interval Length effect was found [F(3,267) ¼192, p o.0001, η² ¼.68]. Post-hoc comparisons showed that the error increased in the 3- to 7-unit range and then decreased for 9-unit intervals (3-unit: 2.8% of error, 5-unit: 16.7% of error, 7-unit: 58.2% of error and 9-unit: 36.6% of error; all comparisons po .001; Fig. 2C). 4.2.1. Bisection bias as a function of the position of short number intervals along the mental number line To explore variations in the bisection bias as a function of the position occupied by an interval of a given length within a decade (e.g. 1–7, 2–8, 3–9; Number Interval Position Effect ¼NIPE; Doricchi et al., 2009), we entered individual bisection biases averaged across corresponding interval positions in the three decades considered in the test (e.g. 1–7, 11–17 and 21–27) in a series of oneway repeated measures ANOVA, one per each interval length. Nine-unit intervals were not considered because only one interval per decade was administered in this case. In these analyses we considered the overall group of 91 participants. The ANOVAs showed that the more intervals were positioned toward the end of the decade the more pseudoneglect increased (i.e. Interval position effect; 3-unit: F(1,6) ¼6.50; p o0.001; 5-unit intervals: F(1,4) ¼ 6.23; po 0.001; 7-unit: F(1,2) ¼56.48; po 0.001: Fig. 3). In the case of 7-unit intervals, a positive bias was found for intervals positioned at the beginning of the decade: this turned into a negative bias, i.e. pseudoneglect, for intervals positioned at the end of decades. A series of Interval Position  Decade ANOVAs showed no significant effect of Decade (all Fo 1), pointing out that the NIPE was recursively present across consecutive decades (Fig. 3). 4.3. “Mental Bisection of Large Number Intervals”

Fig. 2. Mental bisection of Short Number Intervals. (A) Mean deviation from interval midpoint (in units with s.e.) reported as a function of interval length (3-5-7 and 9 units) in the overall group of participants (n¼ 91) and in the subgroups of participants to the present study (n¼ 60) and to a previous study (n¼ 31; Doricchi et al., 2009). Positive values indicate a shift of the subjective midpoint towards numbers higher than the true interval midpoint, negative values towards numbers lower than the true midpoint, i.e. numerical pseudoneglect. (B) Mean percentages of bisection errors (with s.e.) reported as a function of interval length. (C) Mean deviation (in units with s.e.) from interval midpoint reported as a function of interval length (3-5-7 and 9 units) in the Forward (e.g. interval “1–9”) and Backward (e.g. interval “9–1”) experimental condition.

Experimental Condition effect [F(1,89) ¼4.6, p¼ .03, η²¼.05] showed that pseudoneglect was higher in the Backward than in the Forward condition (Forward¼ .02, Backward¼  .03 unit; Fig. 2C). A significant Number Interval Length effect [F(3,267) ¼10.16, p o.001, η²¼ .10] highlighted a bias toward numbers higher than the interval midpoint for 9-unit intervals and an opposite negative bias for 3- and 5- unit intervals. Planned comparisons showed that the bisection bias with 9 unit intervals was significantly different from biases observed at all other interval lengths (all p o0.03). A series of t-tests showed that the negative bisection bias observed for 3and 5-unit intervals was different from zero (3-unit: t(1,90) ¼  4.1, p o0.001; 5-unit: t(1,90) ¼  5.7, p o0.001) while the positive bias in 9-unit intervals was not different from zero (t(1,90) ¼ 1.4, p ¼0.1). No bisection bias was found with 7-unit intervals (t(1,90) ¼  0.44,

Individual average bisection errors were entered in an Experimental Condition (Forward, Backward)  Number Interval Length (16-, 24-, 32-, 40-, 48-, 56- and 64-units) ANOVA. A significant Number Interval Length effect was also found [F(6,354) ¼ 9.88, po .001, η² ¼.14]. This was qualified by planned comparisons showing that the null bisection bias observed for 64-units intervals was significantly different from the negative biases found at all other intervals lengths (all p o0.001; Fig. 4A). The Experimental Condition effect was significant [F(1,59) ¼12.80, p o.001, η²¼ .18] showing higher pseudoneglect in the Backward condition (Forward¼  .97 unit, Backward ¼  1.99; Fig. 4B). We also observed an Experimental Condition  Number Interval Length interaction [F(6,354) ¼2.96, p¼ .007, η² ¼.05] showing that the higher was the interval length the higher pseudoneglect in the Backward as compared to the Forward condition (40-unit: Forward ¼  1.88, Backward ¼  2.67; 48-unit: Forward¼  1.21, Backward ¼  2.92; 56-unit: Forward ¼  0.18, Backward¼  2.31 and 64-unit: Forward¼0.8, Backward ¼  0.5; all po .05). A series of t-tests showed that with the exception of 64-unit intervals, at all interval lengths the error bias was significantly different from zero (16-unit: t(1,59) ¼  7.4, p o0.0001; 24-unit: t(1,59) ¼  8.3257, p o0.0001; 32-unit: t(1,59) ¼  10.3, p o0.0001; 40-unit: t(1,59) ¼  8.9, p o0.0001; 48-unit: t(1,59) ¼ 6.2, po 0.0001; 56-unit: t(1,59) ¼  2.8, po 0.005; 64-unit: t(1,59) ¼0.34; p¼ n.s.). The average deviation across different interval lengths was equal to  1.49 units and was significantly different from zero (t(1,59) ¼ 6.5, po 0.001;) confirming the pseudoneglect observed by Longo and Lourenco (2007). The trend of the bisection bias as a function of interval length was closely similar to that previously

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Fig. 3. Mean deviation (in units with s.e.) in the mental bisection of 3-, 5- and 7- unit number intervals as a function of the interval position within decades. Positive values indicate a shift of the subjective midpoint towards numbers higher than the true interval midpoint, negative values towards numbers lower than the true midpoint. Graphs on the left side of the figure report the bisection error averaged across the three decades includes in the task. Graphs on the right side of the figure report the bisection error separately for each of the three decades included in the task.

reported by Göbel et al. (2006). Individual percentages of bisection error were entered in a Number Interval Length (16-, 24-, 32-, 40-, 48-, 56- and 64-units) one-way ANOVA. The Number Interval Length effect was significant [F(6,354) ¼ 44.9, po .0001, η² ¼.43]. Post-hoc tests showed that in the 16- to 32- unit interval range, bisection errors increased progressively as a function of interval length (16-unit: 76.6%, 24unit: 84.3%, 32-unit: 92.2%; all p o.001). This trend was not observed in the 48- to 64-unit range, where error was at ceiling (48unit: 93.7%, 56-unit: 93%, 64-unit: 92.9%; all p 4.52). Bisection

errors were less frequent for 40-unit intervals (64%) compared to all other interval lengths (all p o.001; Fig. 4C). This was probably due to the fact that the endpoints of 40-unit intervals have identical unit-digits (e.g. 42–82) so that the interval midpoint can be easily estimated by considering only 10-digits. 4.3.1. Bisection bias as a function of the position of large number intervals along the number line To investigate the relationship between the bisection bias and the position of number intervals in the numerical range

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4.4. Correlations between “line bisection” and the “Mental Bisection of Short Number Intervals”

Fig. 4. Mental bisection of Large Number Intervals. (A) Mean deviation from interval midpoint (in units with s.e.) reported as a function of interval length (16-2432-40-48-56 and 64 units). Positive values indicate a shift of the subjective midpoint towards numbers higher than the true interval midpoint, negative values towards numbers lower than the true midpoint, i.e. numerical pseudoneglect. (B) Mean percentages of bisection errors (with s.e.) reported as a function of interval length. (C) Mean deviation (in units with s.e.) from interval midpoint reported as a function of interval length in the Forward (e.g. interval “23–79 ”) and Backward (e.g. interval “79–23”) experimental condition.

considered in the present study, i.e. the MNL going from “10” to “89”, we evaluated the correlation between the bisection bias and the true numerical midpoint of the interval. While Longo and Lourenco (2007) investigated this correlation independently of interval length, here we adopted an analytical approach and investigated correlations separately for each interval length. For all interval lengths we found significant negative correlations (all Ro  0.38, all p o0.008; see Fig. 5), confirming a progressive increase of pseudoneglect as the midpoint of intervals moved toward higher number magnitudes. This increment was not found in 64-unit intervals: in this case no bisection bias was observed for intervals positioned at higher number magnitudes and no significant correlation was found between pseudoneglect and number interval position (R¼  0.35, P ¼0.32; Fig. 5).

Here we report the correlations calculated in the larger sample of 91 participants obtained by joining the 60 participants to the present study with that of 31 participants to a previous study (Doricchi et al., 2009). Correlations calculated in the smaller sample of the 60 participants to the present study are reported in Supplementary data. We initially explored the correlations among line bisection biases observed at each line length (i.e. 2, 10 and 20 cm) and bisection biases observed at each number interval length (3-, 5-, 7and 9-unit intervals). The r and p values of these correlations are reported in Table 1. Only one significant negative, rather than positive, correlation was found between the bisection of 10 cm lines and that of 7-unit intervals. When line bisection and number interval bisection biases were calculated independently of line and number interval lengths (as in Longo and Lourenco (2007)) no significant correlation was found (r ¼  0.16; p¼ 0.12). In a second step, we repeated the same analyses separately for ascending (i.e. Forward condition; e.g. 1–7) and descending (i.e. Backward condition; e.g. 7–1) number intervals. In the Forward condition significant negative correlations were found between 2 cm line and 5-unit intervals and between 2 cm lines and 7 unit intervals (see Supplementary Table 3). No correlation was found when line and number bisection biases when considered independently of line and interval length (r ¼ 0.16; p ¼0.11). In the Backward condition no significant correlation was found (see Supplementary Table 3; correlation between biases calculated independently of line and number interval length: r ¼  0.09; p¼ 0.38). In a third step, following the procedure used by Longo and Lourenco (2007), we repeated all previous correlation analyses separately in the subgroups of participants showing High vs. Low pseudoneglect in the bisection of visual lines. These two subgroups were created using as splitting reference the median of individual average line bisection biases calculated across all line lengths. The median was equal to  0.66 mm (s.d. ¼ 1.7). Forty-four participants were classified as High Pseudoneglect (average bisection bias ¼  2.1 mm, s.d.¼ 1.02 mm) and 46 as Low Pseudoneglect (average bisection bias ¼ 0.51 mm, s.d.¼ 1.1 mm). No significant correlation was found in both groups (Table 2) also when Forward and Backward conditions were considered separately (see Supplementary Tables 4 and 5). These results were also observed in the sample of 60 participants considered in the present study (see Supplementary Tables 6–10). Both in the sample of 91 and 60 participants no correlation resulted significant following Bonferroni correction for multiple comparisons. Finally, all these results remained unchanged when the same correlations were calculated using percentage deviations in line bisection instead of deviations measured in mm. 4.5. Correlation between “line bisection” and the “Mental bisection of Large number intervals” These correlations were calculated only in the sample of 60 participants to the present study, because no additional data from our previous study (Doricchi et al., 2009) were available for Large number intervals. The study of correlations among all the possible 21 pairings of line and number interval lengths highlighted negative correlations between 32, 56 and 64 units intervals and 2 cm lines and one positive correlation between 48 units intervals and 20 cm line between (Table 3). No other correlation was significant. No correlation was also found between bisection biases calculated independently of line and number interval length (Table 3). When the same analyses were repeated separately for Forward

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Fig. 5. Mean deviation (in units with s.e.) in the mental bisection of the “Large” number intervals reported as a function of the interval position within the numerical range considered in the study, i.e. 10 to 89. Positive values indicate a shift of the subjective midpoint towards numbers higher than the true interval midpoint, negative values towards numbers lower than the true midpoint, i.e. pseudoneglect. For each interval length, the value of the regression slope describing the trend of the bisection error bias as a function of interval position is reported at the top of each panel together with the level of probability indicating its difference from zero.

and Backward number interval bisections, in the Forward condition only one negative correlation was observed between 32-unit intervals and 2 cm lines while in the Backward conditions only two positive correlations were observed between 48-unit intervals and 10 cm and 20 cm lines (see Supplementary Table 11). No correlation was found between biases calculated independently of line and number interval length (see Supplementary Table 11). Using the same method adopted for short number intervals, we split the sample of 60 participants in the subgroups of participants showing High vs. Low pseudoneglect in the bisection of visual lines. The median bisection bias was equal to  0.77 mm. Thirty participants were classified as High pseudoneglect (average bisection bias ¼  2.081 mm, s.d. ¼ 1) and 30 as Low pseudoneglect

(average bisection bias ¼0.44 mm, s.d. ¼ 1.2). In High Pseudoneglect negative correlations were found between 32-unit intervals and 2 cm lines and between 16-unit intervals and 20 cm lines (Table 4). In Low Pseudoneglect a negative correlation was found between 56-unit intervals and 10 cm lines and a positive one between 32-unit intervals and 10 cm lines (Table 4). No correlation was found between biases calculated independently of line and number interval length (Table 4). In the Forward condition, High Pseudoneglect participants showed a negative correlation between 32-unit intervals and 2 cm lines while Low Pseudoneglect showed positive correlations between 16-unit intervals and 10 cm or 20 cm lines and between 32-unit intervals and 10 cm lines (see Supplementary Table 12). No correlation was found between

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Table 1 Correlations (Pearson's r with corresponding p values) between the bisection of “Short” number intervals and the bisection of 2 cm, 10 cm and 20 cm horizontal visual lines. Significant correlations are highlighted in bold character. Average correlation, i.e. independent of line and interval length, is reported at the bottom of the table. No correlation resulted significant following Bonferroni correction for multiple comparisons.

2 cm

Line length 10 cm

20 cm

3-unit

 0.06 p ¼0.55

0.09 p ¼ 0.39

 0.0003 p ¼0.99

5-unit

 0.09 p ¼0.38

 0.002 p ¼ 0.98

7-unit

 0.18 p ¼0.08

9-unit

 0.09 p ¼0.38

Interval length

Table 3 Correlations (Pearson's r with corresponding p values) between the bisection of “large” number intervals and the bisection of 2 cm, 10 cm and 20 cm horizontal visual lines. Significant correlations are highlighted in bold character. Average correlation, i.e. independent of line and interval length, is reported at the bottom of the table. No correlation resulted significant following Bonferroni correction for multiple comparisons.

2 cm

Line length 10 cm

20 cm

16-unit

0.11 p ¼0.39

0.21 p¼ 0.09

0.12 p¼ 0.34

 0.12 p ¼0.23

24-unit

 0.14 p ¼0.27

0.13 p¼ 0.29

0.16 p ¼0.21

 0.22 p ¼0.03

 0.14 p ¼ 0.16

32-unit

 0.30 p¼ 0.01

0.04 p¼ 0.72

0.01 p¼ 0.92

 0.05 p ¼ 0.59

 0.09 p ¼0.39

40-unit

 0.04 p ¼0.73

0.16 p ¼ 0.21

0.06 p¼ 0.63

48-unit

 0.02 p ¼0.83

0.22 p¼ 0.09

0.26 p ¼0.04

56-unit

 0.25 p¼ 0.04

 0.04 p¼ 0.72

 0.06 p ¼0.61

64-unit

 0.28 p¼ 0.02

 0.17 p¼ 0.18

 0.02 p¼ 0.84

Interval length

Average correlation: r ¼  0.16, p ¼ 0.12.

biases calculated independently of line and number interval length (Supplementary Table 12). In the Backward condition High Pseudoneglect showed a positive correlation between 56-unit intervals and 10 cm lines and a negative one between 16-unit intervals and 20 cm lines (see Supplementary Table 13). In the same condition, Low Pseudoneglect showed negative correlations between 24-unit intervals and 2 cm lines, 56-unit intervals and 10 cm lines, 64-unit intervals and 10 cm lines and positive correlations between 32unit intervals and 10 cm lines (Supplementary Table 13). No correlation was found between biases calculated independently of line and number interval length (Supplementary Table 13). As for the case of Short number intervals, no correlation resulted significant after Bonferroni correction for multiple comparisons. All these results remained unchanged when the same correlations were calculated using percentage deviations in line bisection instead of deviations measured in mm.

5. Discussion The line bisection task provides a measure of normal and pathological biases in the deployment of spatial attention along the horizontal space. Its performance is typically disrupted in RBD patients with left spatial neglect who show a pathological ipsilesional rightward bias in the bisection of long lines (i.e. length: 10

Average correlation: r¼ 0.05, p ¼0.66.

to 20 cm) and a paradoxical contralesional bias (i.e. “cross-over” effect) in the bisection of short lines (2 cm) when an additional contralateral primary visual field deficit, i.e. hemianopia, is associated with neglect (Doricchi et al., 2005a). In the same task, healthy humans show a consistent small deviation to the left of the true line midpoint, called “pseudoneglect”, which is considered to derive from the dominant lateralization of attentional and spatial functions in the right hemisphere. This interpretation is supported by a recent DTI study showing that in healthy humans the volume of white matter connections linking the parietal and frontal cortex in the right hemisphere, as compared with the left one, is positively correlated with the strength of pseudoneglect in line bisection (De Schotten et al., 2011). In the present study, in analogy with the results of the previous investigation by Longo and Lourenco (2007), we have observed significant “pseudoneglect” during line bisection in large samples of 60 and 90 healthy participants. Pseudoneglect was present at all line lengths (i.e. 2, 10 and 20 cm) and showed a linear increase as a

Table 2 Correlations (Pearson's r with corresponding p values) between the bisection of “Short” number intervals and the bisection of 2 cm, 10 cm and 20 cm horizontal visual lines in the groups of participants with High (2a) and Low (2b) pseudoneglect in the bisection of visual lines. Average correlations, i.e. independent of line and interval length, are reported at the bottom of the table. 2a: High pseudoneglect group

2b: Low pseudoneglect group

Interval length

2 cm

Line length 10 cm

20 cm

Interval length

2 cm

Line length 10 cm

20 cm

3-unit

 0.08 p ¼ 0.57

0.03 p ¼ 0.84

 0.01 p¼ 0.93

3-unit

 0.22 p ¼ 0.12

0.06 p ¼ 0.66

 0.16 p¼ 0.26

5-unit

0.14 p ¼ 0.33

0.18 p ¼ 0.22

0.009 p¼ 0.95

5-unit

 0.15 p ¼ 0.31

0.11 p ¼ 0.44

 0.04 p¼ 0.76

7-unit

 0.15 p ¼ 0.31

0.003 p ¼ 0.98

0.13 p¼ 0.38

7-unit

0.03 p ¼ 0.83

 0.20 p ¼ 0.17

 0.10 p¼ 0.49

9-unit

 0.19 p ¼ 0.20

0.09 p ¼ 0.53

0.08 p¼ 0.57

9-unit

0.17 p ¼ 0.24

0.04 p ¼ 0.74

 0.02 p¼ 0.86

(2a) Average correlation: r¼ 0.12, p ¼ 0.41; (2b) Average correlation: r¼  0.05, p ¼0.74.

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573

Table 4 Correlations (Pearson's r with corresponding p values) between the bisection of “Large” number intervals and the bisection of 2 cm, 10 cm and 20 cm horizontal visual lines in the groups of participants with High (4a) and Low (4b) pseudoneglect in the bisection of visual lines. Significant correlations are highlighted in bold character. Average correlation, i.e. independent of line and interval length, are reported at the bottom of the table. No correlation resulted significant following Bonferroni correction for multiple comparisons. 4a: High pseudoneglect

4b: Low pseudoneglect 2 cm

Line length 10 cm

20 cm

16-unit

0.07 p ¼ 0.69

 0.06 p ¼ 0.72

 0.43 p ¼ 0.01

24-unit

 0.15 p ¼ 0.40

0.27 p ¼0.14

32-unit

 0.46 p¼ 0.01

40-unit

48-unit

Interval length

56-unit 64-unit

2 cm

Line length 10 cm

20 cm

16-unit

 0.03 p ¼ 0.85

0.25 p ¼0.17

0.31 p ¼ 0.08

0.17 p ¼0.35

24-unit

 0.23 p ¼0.21

 0.03 p ¼ 0.84

0.14 p¼ 0.44

 0.11 p ¼ 0.53

0.19 p ¼ 0.29

32-unit

 0.12 p ¼ 0.50

0.44 p¼ 0.01

0.04 p ¼ 0.80

 0.18 p ¼ 0.34

0.07 p ¼ 0.68

 0.12 p ¼ 0.50

40-unit

 0.02 p ¼0.87

0.18 p ¼ 0.33

0.09 p¼ 0.61

 0.34 p ¼ 0.05  0.25 p ¼0.16  0.28 p ¼ 0.12

0.28 p ¼0.13 0.35 p ¼ 0.05 0.16 p ¼ 0.39

0.17 p ¼ 0.36 0.09 p ¼ 0.60 0.35 p ¼ 0.05

48-unit

0.19 p ¼ 0.29  0.23 p ¼0.21  0.14 p ¼ 0.43

0.001 p ¼ 0.99  0.41 p ¼0.02  0.32 p ¼ 0.08

0.31 p ¼ 0.09  0.12 p ¼0.51  0.06 p ¼ 0.75

Interval length

56-unit 64-unit

(4a) Average correlation: r¼ 0.19, p ¼0.30; (4b) Average correlation: r¼ 0.02, p ¼0.90.

function of increasing line length. Also in agreement with Longo and Lourenco (2007), we have found that during the mental bisection of Large number intervals (length ¼ 16- to 64-unit) healthy participants showed a clear average error bias in direction of numbers lower that the true interval midpoint, i.e. pseudoneglect (for the observation of numerical pseudoneglect in a slightly different bisection task see also Loftus et al., 2009). With Short number intervals the error bias averaged across all interval lengths was instead not different from zero. With both Short and Long number intervals the bisection bias was modulated both by the size of the number interval and, interval size being equal, by the magnitude of numbers defining the interval. Within the Short interval range (i.e. length ¼3- to 9-unit) a negative bisection bias was present with 3- and 5-unit intervals but, contrary to line bisection where the negative bias became more pronounced at longer line lengths, the bias disappeared in 7-unit intervals and turned into a positive bias with larger 9-unit intervals. In line with our previous findings, at each interval length the bisection bias was modulated by the position occupied by the interval within a decade (Number Interval Position Effect: NIPE; Doricchi et al., 2009). With 5- and 7- unit intervals the subjective midpoint was shifted towards numbers higher than the true midpoint for intervals at the beginning of decades and towards numbers lower than the midpoint for those at the end of decades. With 3-unit intervals no bias was found at the beginning of decades whereas the bias became more negative the more intervals were positioned at the end of decades. These modulations of the bisection bias were recursively present across consecutive decades (i.e. Number Interval Position Effect; Doricchi et al., 2009). Within the range of “Large” number intervals (i.e. length ¼ 16- to 64-unit), the variation of the bisection bias as a function of interval length was strikingly similar to that reported by Göbel et al. (2006) with 16-, 25-, 36-, 49- and 64-unit intervals: the bias was negative at shorter intervals and progressively turned into a positive bias at the largest 64-unit ones. Still in agreement with Longo and Lourenco (2007) at all number interval lengths, with the exception of 64-unit intervals, pseudoneglect augmented progressively as a function of the magnitude of numbers defining the interval. Plots of the error bias reported in Fig. 4 suggest that also in the case of Large number intervals some recursive modulation of the

bisection bias was present across consecutive decades although, probably due to the fact that each of these interval spanned across different decades (see Doricchi et al., 2009), this modulation was different from that observed in Short number intervals that were always included in a single decade. Crucially to the aim of the present study no significant correlation was found between individual bisection biases in the line and mental number interval bisection tasks. The lack of correlation was evident both when, in analogy with the study by Longo and Lourenco (2007), individual biases were averaged across different line and number interval lengths and when correlations were separately explored between different line and number interval lengths. In this latter case no systematic patterns of positive or negative correlations were found. No general correlations or systematic patterns of correlations between different line and number interval lengths were also found when the ascending (e.g. 1–9) or descending (e.g. 9–1) order of interval endpoints was taken into account. Finally, no significant correlations or pattern of correlations were found when data were analyzed separately in the subgroups of participants showing High and Low pseudoneglect in the bisection of visual lines. Consistent with the results of our study, Goksun et al. (2013) recently reported no correlation between the bisection biases observed in line bisection and in the mental bisection of short number intervals (i.e. 3-,5-,7- an 9-unit) in a large sample of 57 childrens (aged 7–9 years and 10–12 years), although clear pseudoneglect was observed in both tasks. It is important to note that in the study by Göksun et al. (2013), the line and number interval bisection task were administered during a single session lasting 30 min: this suggests that the absence of correlation between these tasks is not necessarily linked to their administration during separate experimental sessions (as was the case in our investigation). Some authors have described stronger pseudoneglect when lines are bisected with the non-dominant left hand (Beste et al., 2006; for review see Jewell and McCourt, 2000) and have proposed that this is due to the direct connection of the left hand with the spatially dominant right hemisphere (Beste et al., 2006). Based on this premise, one could argue that positive correlations between pseudoneglect in line and number interval bisection could be found in participants bisecting lines with the left hand. Though certainly deserving further investigation, this

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hypothesis is in part limited by evidence showing that stronger pseudoneglect for lines bisected with the left hand is not a homogeneous finding (see paragraph 1.3.4 in the review by Jewell and McCourt (2000)). The behavioral dissociation described in our study also combines with anatomical and fMRI findings showing an anatomical dissociation between structures implicated in line and mental number interval bisection. In fact, right hemisphere lesions most frequently associated to pathological ipsilesional bias in line bisection are located in the inferior parietal cortex and the underlying white matter (angular and supramarginal gyrus; Binder et al., 1992; Fink et al., 2000; Aiello et al., 2012) while those most frequently associated with number interval bisection bias are located, cortically and subcortically, in pre-frontal areas (Doricchi et al., 2005b, 2009; Aiello et al., 2012) corresponding to the pre-frontal number module localized in rhesus monkeys (Nieder et al., 2002). In addition to this, a recent high-resolution 7 T fMRI investigation documented no consistent relationship between numerosity coding and visuospatial responses in topographically organized representation of number magnitudes in the human parietal cortex (Harvey et al., 2013). All together the results of our study suggest that verbally defined number intervals are not mentally inspected and bisected through the same mechanisms engaged by the bisection of horizontal visual lines. These findings are at variance with those from the original study by Longo and Lourenco (2007) in which the endpoints of number intervals were visually presented one to the left and one to the right of a horizontal line and significant correlations between line and number interval bisection were found. This suggests (see also Nicholls et al., 2008) that the strategic adoption of a left-to-right mental organization of number magnitudes can be triggered by the left-to-right visual spatial arrangement of the numerical material to be processed. The same arrangement is evidently not automatically recovered and applied when, as in the case of the verbal version of number interval bisection task, an “approximate” number problem is formulated and responded-to verbally, therefore implying no perceptual left-toright organization of the numerical material to be processed or no left/right choice in the selection of the motor response to be associated with number magnitudes (as it happens in SNARC tasks; Dehaene et al., 1993). These conclusions are based on the contrasting results between the present investigation, which used a purely verbal-based numerical bisection task, and those reported by Longo and Lourenco (2007), that used a visual-spatial-based numerical interval bisection task. Testing further the reliability of this contrast in a study comparing the performance of visual-spatial-based vs. verbal-base bisections of the same number intervals within the same sample of healthy participants could strengthen the conclusion of the present study.

et al., 2012; 2013; Pia et al., 2012). This suggests that the mental bisection of number intervals is poorly and not systematically influenced by pathological biases of spatial attention. Nonetheless, and in contrast to this, studies that have investigated the performance of RBD patients with left spatial neglect in magnitude comparison-SNARC tasks requiring the association of left/right spatial response codes with number magnitudes have provided more homogenous results (Vuilleumier et al., 2004; van Dijck et al., 2011b; Zorzi et al., 2012; Masson et al., 2013). These show that patients with neglect have a clear RT asymmetry for numbers immediately adjacent to the numerical reference: RTs are faster for numbers higher than the reference (e.g. 6 when the reference is 5) and slower for numbers lower than the reference (e.g. 4 when the reference is 5, 6 when the reference is 7). This result suggests a pathological attentional bias with slowed processing of numbers located to the left of the numerical reference. We have recently emphasized (Aiello et al., 2012) that the dissociation between left spatial neglect and the bias in the verbal number interval bisection task and, conversely, the association between neglect and asymmetrical RTs performance in the SNARC task, points out that numbers are spatially coded from left-to-right when, as in the case of SNARC tasks, responses associated to numbers are selected on the basis of left vs. right spatial codes. The powerful influence of response related factors in setting the interaction between space and numbers is supported by ERPs studies showing that the SNARC effect arises during the selection of the left/right motor response, rather than at an early stage of perceptual or visual imagery processing (Keus and Schwarz, 2005; Gevers et al., 2006; Gut et al., 2012). In keeping with this observation, several recent investigations (Casarotti et al., 2007; Bonato et al., 2009; Ranzini et al., 2009; Jarick et al., 2009; Goffaux et al., 2012; van Dijck et al., 2014; Zanolie and Pecher, 2014; Fattorini et al., 2014) have showed that, contrary to the proposal advanced by Fischer et al. (2003), when no spatial code is used for the selection of the response the mere perception of numbers does not cause lateral shifts of attention. Nonetheless, available evidence suggests that at least two additional response-unrelated factors might play a role in the use of a left-to-right organized MNL. First, van Dijck et al. (2013, 2014) have demonstrated that when short arbitrary sequences of digits are temporarily kept in working memory, the ordinal position occupied by each digit in the sequence is coded according to left-to-right coordinates (see Doricchi et al. (2005a, 2005b), for the original suggestion of a working memory role in the pathological performance of RBD in the number interval bisection task). Second, a few studies have tested whether the explicit mental coding of number magnitudes (e.g. higher or lower than 5?) is sufficient to generate their left-toright representation. At the moment, these investigations have provided contrasting evidence with some authors reporting positive results in a small sample of participants (Casarotti et al., 2007) and others negative results (Zanolie and Pecher, 2014).

5.1. Factors determining the use of a left-to-right organized mental number line 6. Conclusions The combined evidence from the present study and from the study by Longo and Lourenco (2007) points out that the left-toright mental arrangement of number magnitudes importantly depends on the task at hand rather than being an inherent one. Neuropsychological investigations lend support to this conclusion. Studies that have examined the performance of RBD patients in the verbal number interval bisection task have failed to document a significant relationship between a pathological bisection bias toward numbers higher than the interval midpoint, i.e. supposedly to the right of the midpoint, and a similar pathological attentional bias in the line bisection task (Rossetti et al., 2004; Doricchi et al., 2005b; 2009; van Dijck et al., 2011b; Rossetti et al., 2011; Aiello

In the present study we have found that in healthy participants the spontaneous bias of spatial attention signaled by the error bias in the bisection of horizontal lines is unrelated and does not predict the direction of the error bias in the mental bisection of verbally defined number intervals along the so called “mental number line”. This dissociation is similar to that previously documented in RBD patients suffering left spatial neglect and pathological ipsilesional deviation in the bisection of visual lines (Rossetti et al., 2004; Doricchi et al., 2005b; 2009; Rossetti et al., 2011; van Dijck et al., 2011b; Aiello et al., 2012; 2013; Pia et al., 2012). This result provides further evidence challenging the notion

F. Rotondaro et al. / Neuropsychologia 75 (2015) 565–576

that the series of ascending integers has an inherent left-to-right spatial representation in the human brain. The same findings suggest that exploring the different factors that can trigger the left-to-right representation of numbers and defining their strength and reliability in different task contexts should be considered an important aim in future studies.

Acknowledgments This research was supported by grants from the University “La Sapienza” Rome (Ricerca Ateneo 2012) and the Fondazione Santa Lucia IRCCS(Ricerca Corrente 2013-14) – Rome to Fabrizio Doricchi.

Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.neuropsychologia. 2015.07.016.

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Dissociation between line bisection and mental-number-line bisection in healthy adults.

Healthy adults bisect visual horizontal lines slightly to the left of their true center. This bias has been termed "pseudoneglect" and is considered t...
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