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  • All participants gave their written informed consent to take part in the study, in line with the Declaration of Helsinki, and the study was approved by the Ethics Committee of the Medical School of the University of Liège. Twenty-six right-handed native French-speaking young adults (15 women), with no diagnosed psychological or neurological disorders, were recruited from the university community. The study was approved by the Ethics Committee of the Faculty of Medicine of the University of Liège, and was performed in accordance with the ethical standards described in the Declaration of Helsinki (1964). All participants gave their written informed consent prior to their inclusion in the study. Age ranged from 18 to 28 years, with a mean of 20.9 years. Minimal number of years of education was 14. In a first fMRI session, the order STM and alphabetical order judgment conditions were administered, including also the luminance judgment control condition. For each STM trials, the encoding phase consisted of the presentation of a list of six letters (e.g., ‘D, C, I, F, J, A’) ordered horizontally (fixed duration: 2500 msec) (see also Figure 1). For the maintenance phase, a fixation cross was displayed for a variable duration (random Gaussian distribution centered on a mean duration of 4500±1500 msec). Finally, the retrieval phase consisted of an array of two probe stimuli ordered vertically, in order to eliminate the possibility that the task could be completed by mere visuo-spatial matching between the target and probe stimuli. Participants indicated within 3000 msec if order information for the two probe stimuli matched information in the memory list (by pressing the button under the middle finger for ‘yes’ and by pressing the button under the index for ‘no’). More specifically, participants judged whether the probe letter presented on the top of the screen had occurred in a more leftward position in the memory list than the probe letter presented on the bottom of the screen. The positional distance varied from 2 to 5, while keeping alphabetical distance constant (distance of 3). We used letters from A to I which were also the same letters used in the alphabetical order judgment task. In the alphabetical order judgment task, the participants saw two letters displayed vertically on the screen and they had to decide within 3000 msec whether they were displayed in correct alphabetical order. The participants responded by pressing the button under their index finger for ‘no’ responses and the button under their middle finger for ‘yes’ responses. The distances varied from 2 to 5 alphabetical positions. In order to favor automatic access to ordinal information, only the first nine letters of the alphabet were used. The number of distances was mainly determined by the STM task where we used a STM load of 6 items, which is known to challenge STM capacities without leading to floor effects [8], [27]. We did not assess distances of 1 position since several studies had observed a reverse distance effect for alphabetical order judgment [29], [30] as well as for order STM judgments especially for consecutive pairs in ascending order [9]. The luminance judgment control condition [24] consisted of the presentation of two identical letters (‘A’) displayed in white font on a black screen at identical or different luminance levels. The participants had to decide within 3000 msec whether luminance levels were the same or not by pressing the button under their index finger for ‘no’ and the button under their middle finger for ‘yes’. We manipulated two different luminance levels (close versus further apart) in the luminance baseline condition in order to control for general executive processes associated with comparison judgments for highly similar versus dissimilar stimuli in the tasks-of-interest, and hence to isolate neural substrates associated with ordinal judgments and comparison processes as specifically as possible. The photometric luminance difference between the two letters was either small (close distance = difference of 80 cd/m2 hue–saturation– brightness) or large (far distance = difference of 160 cd/m2 hue-saturation-brightness). In order to control for processes associated with basic letter processing in the STM task, the luminance judgment trials were furthermore preceded by the presentation of six identical letters (‘A’) organized horizontally and which the participants viewed passively (see Figure 1). Figure data removed from full text. Figure identifier and caption: 10.1371/journal.pone.0092049.g001 Experimental design and timing of the four tasks.For each condition, a negative probe trial is illustrated. Finally, the neural substrates associated with ordinal distance effects for numerical information were assessed in a second session, using a numerical order judgment task based on the seminal paradigm developed by Pinel et al. [21]. After a fixation cross (250 msec), participants were presented a number (e.g., ‘45’; duration 1000 msec) and had to judge whether the number comes before or after the numerical standard ‘65’; the same standard was used for all trials [21]. The participants pressed on the button under the index finger for before-standard responses, and on the button under the middle finger for after-standard responses. The distances between the probe and the standard ranged from 1–7 units [distances 1 (60–64 and 66–70), 2 (55–59 and 71–75), 3 (50–54 and 76–80), 4 (45–49 and 81–85), 5 (40–44 and 86–90), 6 (35–39 and 91–95), and 7 (30–34 and 96–99)]. Given the relative long duration of the tasks administered in the first session, they were always presented first, and the numerical task was always presented in the second session, in order to diminish fatigue effects and to increase task compliance. For the order STM and alphabetical judgment conditions there were 24 trials per ordinal distances. For the luminance judgment control condition, there were 20 trials by distance. For the numerical order judgment task there were 20 trials for distances 1 to 6 and 18 trials for the distance 7. For each condition and distance, there was an equal number of trials requiring a ‘yes’ or ‘no’ response. For each session and condition, the different trials were presented in pseudorandom order, with the restriction that 2 successive trials of the same distance and condition could not be separated by more than 5 trials of a different condition (i.e., by more than 65 s on average) in order to keep blood oxygen level dependent (BOLD) signals for same condition epochs away from the lowest frequencies in the time series. Before the start of a new trial, a cue informing about task condition appeared on the top of the screen during 1000 msec. The duration of the intertrial interval was variable (random Gaussian distribution centered on a mean duration of 2000±500 msec) and further varied as a function of the participants’ response times: the probe array disappeared immediately after a response was recorded. If the participant did not respond within 3000 msec, “no response” was recorded and the next trial began. Both response accuracy and response times were collected. Finally, a practice session outside the magnetic resonance environment, prior to the start of the experiment, familiarized the participants with the specific task requirements and included the administration of 10 practice trials. Data were acquired on a 3-Tesla scanner (Siemens, Allegra, Erlangen, Germany) using a T2*-sensitive gradient-echo EPI sequence (TR = 2040 msec, TE = 30 msec, field of view (FOV) = 192×192 mm2, 64×64 matrix, 3 mm in-plane resolution, 34 axial slices with 3 mm thickness, and 25% interslice gap to cover most of the brain. The 3 initial volumes were discarded to avoid T1 saturation effects. Field maps were generated from a double-echo gradient recalled sequence (TR = 517 msec, TE = 4.92 and 7.38 msec, FOV = 230×230 mm2, 64×64 matrix, 34 transverse slices with 3 mm thickness and 25% gap, flip angle = 90°, bandwidth = 260 Hz/pixel) and used to correct echo-planar images for geometric distortion due to field inhomogeneities. A high-resolution T1-weighted magnetization-prepared rapid gradient echo image was acquired for anatomical reference (TR = 1960 msec, TE = 4.4 msec, time to inversion = 1100 msec, FOV = 230×173 mm2, matrix size 256×192×176, voxel size 0.9×0.9×0.9 mm3). For the first session (STM, alphabetical and luminance judgment), between 1134 and 1272 functional volumes were obtained. For the second session (numerical order judgment), between 346 and 392 functional volumes were obtained. Head movement was minimized by restraining the subject's head using a vacuum cushion. Stimuli were displayed on a screen positioned at the rear of the scanner, which the subject could comfortably see through a mirror mounted on the standard head coil. Data were preprocessed and analyzed using SPM8 software (Wellcome Department of Imaging Neuroscience, www.fil.ion.ucl.ac.uk/spm) implemented in MATLAB (Mathworks, Natick, MA). EPI time series were corrected for motion and distortion using “Realign and Unwarp” [31] using the generated field map together with the Fieldmap toolbox [32] provided in SPM8. A mean realigned functional image was then calculated by averaging all the realigned and unwarped functional scans, and the structural T1 image was coregistered to this mean functional image (rigid body transformation optimized to maximize the normalized mutual information between the 2 images). The mapping from subject to Montreal Neurological Institute space was estimated from the structural image with the “unified segmentation” approach [33]. The warping parameters were then separately applied to the functional and structural images to produce normalized images of resolution 2×2×2 mm3 and 1×1×1 mm3, respectively. The scans were screened for motion artifacts and time series with movements exceeding 3 mm (translation) or 3° (rotation) were discarded; this resulted in the removal of the data of 2 participants not presented here. Finally, the warped functional images were spatially smoothed with a Gaussian kernel of 8 mm full-width at half maximum (FWHM). For each subject brain responses were estimated at each voxel, using a general linear model with epoch regressors and event-related regressors. For the order STM and luminance judgment conditions, regressors were defined to cover encoding, maintenance and retrieval phases. Encoding and maintenance phases were modeled via a single regressor due to the short duration of the encoding phase leading to high autocorrelation between these two phases. The encoding-maintenance regressor ranged from the onset of each trial until the onset of the probe display. On this basis, we obtained two linear contrasts corresponding to the encoding-maintenance phase of order STM and luminance judgment conditions. For the order STM retrieval stage, as well as the alphabetical ordinal judgment, the luminance judgment retrieval stage and the numerical order judgment conditions, the regressor ranged from the onset of the probe display to the participant’s response. In order to ensure minimal autocorrelation between the two phase-specific regressors, the encoding/maintenance regressors for luminance and order STM was further orthogonalized relative to the other two retrieval regressors [4], [5], [10], [27], [34]: Shared variance between retrieval and late encoding/maintenance phases was attributed to the retrieval regressor. On this basis, for each condition, one linear contrast was performed, one for the encoding/maintenance phase of order STM, one for the retrieval phase of order STM and one for the alphabetical order judgment; for each of these contrasts, the corresponding luminance baseline events were subtracted. After that, for each subject and each condition, a parametric design was defined in order to highlight voxels sensitive to ordinal distance effects. For the order STM retrieval phase, the ordinal letter judgment, the luminance judgment and the numerical order judgment tasks, the regressor ranged from the onset of the probe display to the participant’s response with a parametric modulation for each distance. For each parametric design, the model included a regressor looking at activation whose intensity was modulated linearly by numerical/positional/alphabetical/luminance distance, plus their time derivatives. This model was applied for each task condition resulting in one target contrast for each condition. These contrasts were then entered in second-level analyses, corresponding to random effects models. One-sample t-tests for each phase of the STM, as well as for the alphabetical order judgment and the numerical order judgment were used to identify cerebral correlates of each condition for the task-related and distance effects. Null conjunction analyses assessed the commonality of activation profiles associated with the parametric distance effects across the different tasks [35] by exclusively masking for activation due to the luminance distance effect condition but also the brain activation differences between the each condition. For each model, the design matrix also included the realignment parameters to account for any residual movement-related effect. A high-pass filter was implemented using a cutoff period of 128 sec in order to remove the low-frequency drifts from the time series. Serial autocorrelations were estimated with a restricted maximum likelihood algorithm with an autoregressive model of order 1 (+ white noise). The resulting set of voxel values constituted a map of t statistics [SPM(t)]. All contrast images were then smoothed again (6-mm FWHM Gaussian kernel) in order to reduce remaining noise due to intersubject differences in anatomical variability in the individual contrast images. Statistical inferences were performed at the voxel level at p<.05, with FWE- corrections for multiple comparisons across the entire brain volume, as well as using small volume corrections for a priori locations of interest [36]. A Priori Locations of Interest: Regions of interest concerned the anterior and posterior bilateral IPS, based on aforementioned studies associating the anterior part of the horizontal of the IPS to processing of ordinal information in STM and numerical processing tasks, and associating the posterior part of the IPS to attentional control processes. The small volume correction was computed on a 10 mm radius sphere around the averaged coordinates published for the corresponding location of interest namely bilateral anterior IPS (−42, −42, 40 and 44, −40, 44) [4], [5], [10], [24], [37] and bilateral posterior IPS (−26, −62, 46; 28, −58, 40) [27], [28].
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