Citation Van Beek, L., Ghesquière, P., Lagae, L., De Smedt, B. (2015). Arithmetic difficulties in children with mild traumatic brain injury at the subacute stage of recovery. DMCN.

Archived version Author manuscript: the content is identical to the content of the published paper, but without the final typesetting by the publisher

Published version

Journal homepage http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1469-8749

Corresponding author contact

+32 (0)16 325705

Senior author contact Bert.DeSmedt@ppw.kuleuven.be+32 (0)16 325705

IR https://lirias.kuleuven.be

(article begins on next page)

1

Arithmetic difficulties in children with mild

traumatic brain injury at the subacute stage of

recovery

Leen Van Beeka, Pol Ghesquièrea, Bert De Smedta*$ & Lieven Lagaeb$

a Parenting and Special Education, Faculty of Psychology and Educational Sciences, University of Leuven, Belgiumb Department of Development and Regeneration, Biomedical sciences group, University of Leuven, Belgium

$ These authors should be considered as joint last authors.

* Correspondence concerning this article should be addressed to Bert De Smedt, Parenting and Special Education Research Unit, Leopold Vanderkelenstraat 32 – box 3765, B-3000 Leuven, BELGIUM, Phone: + 32 16 32 57 05, Email: Bert.DeSmedt@ppw.kuleuven.be

2

Abstract

AimArithmetic difficulties have been reported in pediatric mild traumatic brain injury (mTBI) but the electrophysiological abnormalities underlying these impairments remain unknown. We therefore used event-related potentials (ERP) to investigate brain functioning during arithmetic in children at the subacute phase following mTBI.

MethodParticipants were 16 pediatric mTBI patients at the subacute phase of recovery (10 boys; mean age 10y 8mo) and 16 well-matched controls (11 boys; mean age 10y 9mo). All children were asked to solve single-digit addition problems of small (sum ≤ 10) and large problem size (sum > 10) with simultaneous recording of ERPs.

ResultsChildren with mTBI performed significantly less accurately (mean 81 %) than controls (mean 91 %) on the large (p = .026) but not on the small problems (p = .171). We observed no group differences in the early ERP-components P1, N1, P2, and N2 (all ps ≥ .241), yet significant group differences (p = .019) emerged for the late positivity component LPC, for which patients (mean 8.35 µV) showed smaller mean amplitudes than controls (mean 12.95 µV).

InterpretationImmediately after the injury, arithmetic difficulties in children with mTBI are particularly pronounced on more complex arithmetical problems that are less automated. This is reflected in the ERP pattern with decreased LPC but normal N2 and early ERP-components.

Keywords: arithmetic difficulties, children, mild traumatic brain injury (mTBI), event-related potential (ERP), late positivity component (LPC)

Running title: Arithmetic difficulties in pediatric mTBI

What this paper adds: Children with mild TBI have difficulties with solving large arithmetic problems in the

subacute phase following their injury. Children with mild TBI showed normal early ERP-components and N2 during arithmetic

processing immediately after their injury, indicating no difficulties with encoding or retrieving the answer.

Children with mild TBI at the subacute stage of recovery showed a decreased late positivity component (LPC) during arithmetic processing, suggesting difficulties with calculating the answer.

3

Pediatric mild traumatic brain injury (mTBI) is known to produce cognitive problems (such as deficits in working memory) as well as academic difficulties (predominantly problems regarding arithmetic) at the subacute stage of the injury.1-3 These cognitive and arithmetic difficulties are subtle, even though they may influence daily activities or performance at school.4 Recently, neuroimaging, such as functional MRI, and electrophysiological techniques, such as event-related potentials (ERPs) have started to unravel the underlying neurophysiological bases of cognitive dysfunctions associated with mTBI. ERPs are an ideal method for monitoring the flow of information in the brain during the performance of a cognitive task, even in the case of subtle cognitive deficits that might not always be detected by means of standard clinical tests, such as arithmetic difficulties in mTBI. This approach has also an excellent temporal resolution, which gives researchers the ability to follow cognitive processes with milliseconds precision. To the best of our knowledge, no ERP study in arithmetic has been conducted in mTBI patients. Moreover, there have been no group studies in children with pediatric mTBI investigating the subacute stage of injury. We therefore used ERPs during an arithmetic task to refine our understanding of arithmetic difficulties in pediatric mTBI at the subacute stage of recovery (i.e. 4 weeks after injury).

Various studies have used ERPs to investigate cognitive functioning following mTBI in adults. ERPs are typically classified into two broad categories: exogenous and endogenous components. Early exogenous components, such as the visual P1 and N1, are known to reflect automated sensory processing (i.e. encoding of basic stimuli properties), while later endogenous ERP components, such as P3, are heavily influenced by higher order cognitive processes, such as working memory.5 Little is known about the effect of mTBI on the early exogenous components with only some preliminary data suggesting that mTBI might affect the speed of encoding.5 By contrast, most of the studies on mTBI have focused on the P3 component.5 The P3, which typically occurs about 300 to 800 ms post-stimulus, has been further divided into the P3a and P3b subcomponents.6 Specifically, the P3a has an anterior scalp distribution, is associated with shorter latencies and has been related to the orienting of attention. The P3b, on the other hand, has a posterior scalp distribution and has been associated with the allocation of attentional resources. Although conflicting results were obtained during previous ERP studies in adult mTBI, the majority of studies have reported reduced amplitudes or delayed latencies, with a reduced amplitude of P3b as most consistent finding, in mTBI patients when compared to healthy controls.5

ERP studies in pediatric mTBI are scarce. As far as we know, only two studies used ERPs in pediatric mTBI. Boutin and colleagues investigated in an 8-year-old girl the impact of a sport concussion with electrophysiology.7 This longitudinal case-study showed persistent electrophysiological deficits during the perception of gratings up to 1 year post-injury, although neuropsychological impairments as detected through clinical tests were normalized 22 weeks after injury. More recently, Baillargeon and colleagues studied P3a and P3b in 32 concussed 9 to 12-year-old children at the chronic stage of injury.8 They showed significantly lowered amplitude of the P3b but not P3a in concussed children. To the best of our knowledge, no group studies in pediatric mTBI at the subacute stage of recovery have been reported.

In the present study, we used a problem size effect paradigm to examine the electrophysiological correlates of arithmetic.9, 10 The problem size effect is a well-known phenomenon in the field of mathematical cognition, which indicates that reaction times and error rates are larger in arithmetic problems of a large size (e.g., 8 + 7) as compared to problems with a small size (e.g., 2 + 3). 11 The electrophysiological correlates of this problem size effect are well described in adults and they recently have been studied in children.10 These data revealed the existence of early exogeneous components P1, N1, P2 within the first 250 ms post-stimulus, yet these early components are not different between small and large problem sizes. After these early components, an anterior negativity occurs around 400 ms. This negativity is larger in large compared to small problems, which might reflect the use of more executive resources when solving large compared to small problems. Following this negativity around 400 ms, participants typically display a posterior late positive slow wave which has been referred to as the late positivity component (LPC) or P3b. The mean amplitude of this LPC increased with problem size and this increase has been explained by differences in frequency of exposure between small and large problems (i.e. small problems are processed more frequently than

4

large problems) together with the use of different strategies (i.e. automatized retrieval strategies for small problems versus slower procedural strategies for large problems). Against this background, Van Beek et al. suggested the ERPs of the problem size effect during arithmetic as a useful neural marker for detecting arithmetical impairments.10 To this end, the present study used the ERP problem size approach to investigate whether the electrophysiological brain signatures of the arithmetic problem size effect (i.e. N2 and LPC) differed between children with pediatric mTBI and healthy controls.

Method

PARTICIPANTS

Participant characteristics are displayed in Table 1. All pediatric mTBI patients had a pediatric Glasgow Coma Scale (GCS) of 13-15, and at least one of the following symptoms: (1) alteration in mental status at the time of injury (e.g., confusion, disorientation, dizziness); (2) loss of consciousness < 30 minutes, (3) post-traumatic amnesia < 24 hours; and/or (4) other neurological abnormalities that may or may not be transient (e.g., seizure or focal signs). Patients were recruited at hospitals in Leuven, Belgium and were tested between 6 and 30 days post-injury. All of them returned to school within one week post-injury. Control children, which were recruited from local schools, were matched in terms of age, sex, verbal ability, and premorbid mathematical abilities. All participants were native Dutch speakers and had normal or corrected-to-normal vision. None of the mTBI patients and controls had a history of previous TBI, neurologic problems, psychiatric disorders or diagnosis of learning difficulties.

The study was approved by the local Ethical Board and written informed consent according to the Declaration of Helsinki was obtained from the parents of each child and from children over age 8; assent was given by each participating child.

Table 1. Participant characteristics.

Pediatric mTBI patients ControlsN 16 16Age (years)

Mean (SD) 10y 8 mo (1y 6 mo) 10y 9 mo (1y 6 mo)Range 7y 1 mo-12y 10 mo 7y 3 mo-12y 8 mo

Sex, M/F 10/6 11/5Verbal abilitya 98 (12) 101 (14)Premorbid mathematical abilitiesb (pc)

Mean (SD) 71.24 (16.79) 81.06 (14.07)Range 40.00-94.50 45.00-97.00

a Verbal ability was assessed with the Vocabulary subtest of the Dutch Wechsler Intelligence Scale for Children, Third Edition, WISC-III-NL.12

b Premorbid mathematical ability was assessed with a curriculum-based standardized achievement test for mathematics.13 Percentile ranks were available for 28 of the 32 participants (12 mTBI patients, 16 controls) and dated from one month to one year before testing. As these data are measured at the ordinal level, we used Wilcoxon signed-ranks test to test for a difference between mTBI patients and controls. This difference was not significant (p = .307). It should be emphasized that none of the children had learning difficulties as indicated by the parents. Furthermore, all children had at least an average percentile rank (pc ≥ 40) on the standardized mathematical abilities test administered before the injury and participation in this study.

STIMULI AND EXPERIMENTAL PROCEDURE

The stimuli and experimental procedure were identical to Van Beek et al. 10 which investigated the ERP problem size in typically developing children. Single-digit addition problems (i.e. a + b) were presented on a screen using Presentation software (Neurobehavioral Systems, Inc., Albany, CA, USA). Twenty small (sums ≤ 10) and 20 large (sums > 10) problems were selected from all possible pairwise combinations of the digits between 2 and 9, with the exclusion of tie problems (e.g., 4 + 4)

5

and problems containing a 0 or 1 as operand or answer. Each problem was presented twice and the position of the largest addend was counterbalanced for both problem types. Numbers were presented in white against a black background with a visual angle of 2.01° vertically and 5.27° horizontally.

First, electrode placement and impedance calibration was done. Next, the experimental procedure was described to the child. The child had to mentally solve the problem and speak the solution into a voice-key. Both accuracy and speed were stressed. The child was instructed to avoid movements to reduce muscle artifacts in the EEG signal, and to look at the middle of the computer screen and maintain fixation to avoid unnecessary eye movements.

Each child started with one practice run consisting of 12 trials to ensure good understanding of the task and to avoid movements during the experimental task. Following the practice run, all participants performed 80 test trials, which were organized into 4 runs of 20 trials separated by rest periods. Each trial consisted of (1) a fixation cross in the center of the screen which remained visible for 500 ms, (2) the addition problem which was shown until response or for a maximum 10000 ms, and (3) a fixed interstimulus interval (ISI) of 1500 ms.

ELECTROPHYSIOLOGICAL RECORDING

Electrode placement was done according to the international 10-10 system14 using an EEG recording cap with Ag/AgCl sintered ring electrodes (Easy Cap). Thirty-one electrodes were placed at Fp1, Fp2, F3, F4, F7, F8, Fz, FC1, FC2, FC5, FC6, FT9, FT10, C3, C4, Cz, CP1, CP2, CP5, CP6, T3, T4, T5, T6, P3, P4, Pz, PO9, PO10, O1 and O2. Additional four electro-oculogram (EOG) electrodes were placed resulting in two EOG channels: horizontal EOG - two electrodes on the outer canthi of the eyes - and vertical EOG - two electrodes above and below one eye. EOG channels allowed us to detect both vertical and horizontal eye movements and effectively remove them from EEG recording during subsequent preprocessing of the signal. Two linked mastoid electrodes were used as a reference. EEG was sampled at a frequency of 1000 Hz with 12 bits A/D converter and amplified using a band-pass filter of 70 Hz. Registration of the digital EEG was made using the software program BrainRT (OSG, Belgium). The impedance of all electrodes was monitored for each subject prior to recording and was always kept below 5 kΩ.

DATA ANALYSIS

Behavioral data

Accuracy and mean reaction time for correctly solved trials were each analyzed using a two-way repeated measures analysis of variance (ANOVA), taking group (mTBI patients vs. controls) as between subject factor and problem size (small vs. large) as within-subject factor. Post-hoc comparisons were corrected using Bonferroni adjustments.

EEG analysis

Analysis of the electrophysiological responses was done in the same way as in.10 Data processing was performed offline using the EEGLAB v.10.2 toolbox (Matlab R2008a platform).15 Preprocessing consisted of data filtering with a 30 Hz digital low pass filter and removing eye and other movement artifacts with an algorithm based on the principle of Independent Component Analysis.16

Subsequently, the continuous EEG signal was divided into epochs including a 200 ms pre-stimulus baseline period and a 900 ms post-stimulus period. Next, epochs for every subject in each experimental condition were averaged, excluding incorrect trials and those with artifacts (i.e. voltage exceeded ± 120 µV in any electrode site).

ERPs were time-locked to the onset of the arithmetic problems and were quantified as peak amplitudes and latencies in the 100 - 150 (P1 component), 150 - 250 (N1 component), 150 - 350 (P2 component) and 250 - 500 (N2 component) milliseconds windows following the arithmetic stimuli. The late slow

6

wave, i.e. late positivity component (LPC) was defined as having a mean amplitude value in the 500-675 ms range. The time windows of the components were based on the grand mean waveforms and previous ERP research in arithmetic in children.10, 17-19

Based on the existing body of evidence 10, 17-19 and visual inspection, we selected for the analysis of the early P1 and N1 components a group of posterior electrodes including PO9, PO10, O1 and O2. For analysis of the P2 component, we selected the following centro-parietal electrode sites: C3, Cz, C4, CP5, CP1, CP2, CP6, P3, Pz, P4. The N2 component was subdivided into three subcomponents: an anterior N2 (also referred to as N2b) which was analyzed at the following anterior electrode sites: Fp1, Fp2, F7, F3, Fz, F4, F8, FC5, FC1, FC2, FC6, C3, Cz and C4; a centro-parietal N2 component (also referred to as semantic N400) which was analyzed at the following centro-parietal electrode sites: C3, Cz, C4, CP5, CP1, CP2, CP6, P3, Pz, P4; and a posterior N2 component (also referred to as N2c) which was analyzed at the following posterior electrode sites: P3, Pz, P4. Finally, the LPC was analyzed at the following posterior electrode sites: P3, Pz, P4, PO9, PO10, O1 and O2.

Peak latencies and peak amplitudes of the P1, N1, P2 and N2 and mean amplitudes of the LPC were analyzed using a three-way repeated measures ANOVA, taking group (mTBI patients vs. controls) as between subject factor and problem size (small vs. large) and electrode site as within-subject factors. Post-hoc comparisons were corrected using Bonferroni adjustments.

Results

BEHAVIORAL DATA

The scores on the arithmetic task are displayed in Fig. 1. Large problems were solved for 86.3% correctly, which is 8.2% less accurate than small problems (95% CI [5.1-11.6]; p < .001). The mTBI patients solved 87.5% of the arithmetic problems correctly, which is 6.7% less accurate than the controls (95% CI [1.6-11.2]; p =.015). The results also revealed an interaction between group and problem size (p = 0.044; see Fig. 2): the group effect was observed for large problems (95% CI 1.8-17.9]; p = .026), but not for small problems (95% CI -.2-5.0]; p = .171).

Small problems were solved in 1.6 seconds on average, which is 0.66 seconds (95% CI [.53-.80]; p < .001) faster than large problems, with no significant difference between groups (see Fig. 3).

EVENT-RELATED POTENTIALS

Early components P1, N1 and P2No significant differences between mTBI patients and controls were found in the early components P1, N1 and P2. More specifically, there were no significant main effects of group for P1 peak amplitude (p = .849), P1 peak latency (p = .494), N1 peak amplitude (p = .765) or N1 peak latency (p = .241). With regard to P2, there was neither a main effect of group for the peak amplitude (p =.249), nor for the peak latency (p = .682). There were no group differences in the N2b peak amplitude (p = .769) and latency (p = .723). The overall ANOVA for N400 peak amplitude (p = .473) and N400 latency (p = .719) revealed no main effect of group. Finally, there were no group differences for N2c peak amplitude (p = .446) and N2c latency (p = .567).

N2 componentNo significant group differences were found in the three subcomponents of the N2 (all ps ≥ .446).

LPC effectThe mean amplitude of the LPC differed significantly between groups (95% CI [0.885-8.306]; p = 0.019; see Fig.4 and Fig. 5). mTBI patients had significantly smaller mean amplitudes in the 500-625 ms range compared with controls, i.e. 8.35 μV (SD 1.40 μV) versus 12.95 μV (SD 1.20 μV). There was also a significant effect of problem size (95% CI [0.084-2.702]; p = 0.039; see Fig. 6):

7

small problems had smaller mean amplitudes in the 500-625 ms range compared with large problems, i.e. 9.96 μV (SD 1.05 μV) versus 11.35 μV (SD .99 μV). We also observed a significant main effect of electrode site (p < .001). The mean amplitudes in the 500-625 ms range were as follows: P4 (mean 19.74 μV; SD 1.33), Pz (mean 14.76 μV ; SD 1.21 μV), P3 (mean 13.04 μV; SD 1.33 μV), O2 (mean 10.75 μV; SD 1.06 μV), O1 (mean 10.15 μV; SD 1.42 μV), PO10 (mean 3.38 μV; SD .67 μV), and PO9 (mean 2.73 μV; SD .98 μV). Post-hoc comparisons revealed that these means were significantly different except for the differences between P3 and P4, P3 and O1, P3 and O2, PO9 and PO10, and, O1 and O2. There were no significant interaction effects.

Discussion

The aim of the present study was to investigate brain functioning during arithmetic in children with mTBI at the subacute stage of recovery. The behavioural results showed that both mTBI patients and controls had more difficulty in solving large arithmetic problems than small arithmetic problems. This might be explained by the fact that small arithmetic problems are typically solved by retrieving the answer from long-term memory, whereas large arithmetic problems are more often solved by using a procedural strategy, such as counting or decomposing.20 As children with mTBI performed more poorly on the large but not on the small addition problems, our results suggest that while automatized retrieval appears to be preserved after injury, children with mTBI might have difficulties in procedural problem solving, a strategy which generally requires more attentional and working memory resources.21 We additionally investigated whether these difficulties in procedural problem solving were also present at the individual level by determining how many children with mTBI performed abnormally low on this task. To determine abnormal performance, we used a two-step procedure as in Ramus et al. 22 and De Smedt et al.23. The threshold for abnormal performance was set at 1.65SD below the mean of the control group. Such value corresponds to the 5th percentile in a normal distribution. However, a control child might occasionally show abnormal performance which highly influences the control mean and SD and makes the criterion for abnormal performance much more stringent than intended. Therefore a two-step criterion was applied. First, the control mean and SD were calculated for each child and control children who showed abnormal performance were identified (n = 1). Second, we recomputed the control mean and SD when the abnormally performing control children (n = 1) were excluded. Subsequently, these values were used to identify patients who scored below 1.65SD. The results revealed that 5 out of 20 patients (= 25%) scored below 1.65 SD of the adjusted control group mean (compared to 1/20 (= 5%) of the control children). These five patients were considered to have abnormal performance on the procedural problem solving task.

Solving arithmetic problems typically consists of three parts: converting a stimulus into appropriate internal codes (or ‘encoding’), retrieving or calculating the answer, and reporting the answer.24 Based on our ERP results children with mTBI at the subacute phase of recovery seem to have no difficulties with encoding. Indeed, we observed no group differences in the early exogenous components P1, N1 and P2, which are thought to reflect low-level processing (i.e. stimulus identification). We also observed no differences in the N2 component. This component has been previously related to cognitive control, such as response inhibition (anterior N2b),25 sub processes in stimulus identification, such as attention to relevant stimulus features (posterior N2c),25 and semantic processing when solving arithmetic problems by means of retrieval (centro-parietal N400).26 By contrast, the mean amplitude of the LPC, which has been proposed to index the amount of attentional resources available for updating the information in working memory,6 was decreased. This might indicate that children with mTBI allocated fewer attentional resources when updating the contents of working memory during arithmetic processing.

The current ERP data in children with mTBI at the subacute phase of recovery point to difficulties in calculating the answer rather than difficulties in encoding or retrieval. Moreover, our ERP data suggest that not all attentional systems are impaired after mTBI. Specifically, automatic processes, such as orienting the attention during stimulus identification (i.e. N2b) seems to be preserved, whereas the allocation of attentional resources in service of working memory is impaired (i.e. LPC). These data are in line with Baillargeon et al. 8 who reported a reduction in the P3b amplitude, but no change in P3a, in

8

concussed children at the chronic stage of injury. Our data extend these findings by showing that a similar pattern is observed in pediatric mTBI at the subacute stage, during a different task.

Even though all children with mTBI were examined within 4 weeks of injury, there were differences between these children in the number of days after injury. Because these differences might have affected the findings of the current study, we investigated whether the number of days post-injury was associated with all behavioral and ERP measures that were collected. There were no associations between these latter measures and the number of days since injury. Therefore, our current findings are not affected by the number of days post-injury. The current behavioral data revealed group differences in solving large arithmetic problems, but not in solving small problems. However, it is important to keep in mind that our modest sample size might have limited statistical power to detect group differences with smaller effect sizes.

It is important to point out that we did not observe an interaction effect between group and problem size in our ERP data suggesting similar deficits in solving small and large arithmetic problems at the neural level. This might be explained by the fact that our behavioral task was not as sensitive as the ERPs to detect subtle cognitive deficits associated with mTBI at the subacute stage of recovery. Clinicians should therefore be aware that children with mTBI might have mild brain dysfunctions despite normal cognitive assessments immediately after their injury. Furthermore, future studies should investigate whether the same pattern is observed at a more chronic stage of recovery. There is evidence suggesting that behavioral impairments following mTBI do not manifest themselves immediately after the injury but become apparent later.27

AcknowledgementsThis study was supported by grant G.A113.11N of the Research Foundation Flanders (FWO). We thank the children and their families for their time and contribution to this study. We also thank Ivan Myatchin and Jan Vervisch for their technical assistance with the ERP design and data analysis.

9

References

1. Ewing-Cobbs L, Barnes M, Fletcher JM, Levin HS, Swank PR, Song J. Modeling of longitudinal academic achievement scores after pediatric traumatic brain injury. Developmental Neuropsychology. 2004;25(1-2):107-33.

2. Slater EJ, Kohr MA. Academic and intellectual functioning of adolescents with closed head injury. Journal of Adolescents Research. 1989;4(3):371-84.

3. Taylor HG, Yeates KO, Wade SL, Drotar D, Stancin T, Minich N. A prospective study of short- and long-term outcomes after traumatic brain injury in children: Behavior and achievement. Neuropsychology. 2002;16(1):15-27.

4. Moser RS, Schatz P. Enduring effects of concussion in youth athletes. Arch Clin Neuropsychol. 2002;17(1):91-100.

5. Broglio SP, Moore RD, Hillman CH. A history of sport-related concussion on event-related brain potential correlates of cognition. International Journal of Psychophysiology. 2011;82(1):16-23.

6. Polich J. Updating p300: An integrative theory of P3a and P3b. Clinical Neurophysiology. 2007;118(10):2128-48.

7. Boutin D, Lassonde M, Robert M, Vanassing P, Ellemberg D. Neurophysiological assessment prior to and following sports-related concussion during childhood: A case study. Neurocase. 2008;14(3):239-48.

8. Baillargeon A, Lassonde M, Leclerc S, Ellemberg D. Neuropsychological and neurophysiological assessment of sport concussion in children, adolescents and adults. Brain Injury. 2012;26(3):211-20.

9. Stanescu-Cosson R, Pinel P, van de Moortele PF, Le Bihan D, Cohen L, Dehaene S. Understanding dissociations in dyscalculia - A brain imaging study of the impact of number size on the cerebral networks for exact and approximate calculation. Brain. 2000;123:2240-55.

10. Van Beek L, Ghesquière P, De Smedt B, Lagae L. The arithmetic problem size effect in children: an event-related potential study. Frontiers in Human Neuroscience. 2014;8.

11. Zbrodoff NJ, Logan GD. What everyone finds: The problem size effect. In: Campbell JID, editor. Handbook of mathematical cognition. New York: Psychology Press; 2005. p. 331-45.

12. Kort W, Schittekatte M, Dekker PH, Verhaeghe P, Compaan EL, Bosmans M, et al. WISC-III NL Wechsler Intelligence Scale for Children. Derde Editie NL. Handleiding en Verantwoording. Amsterdam: Harcourt Test Publishers/Nederlands Instituut voor Psychologen; 2005.

13. Dudal P. Leerlingvolgsysteem: Wiskunde—Toetsen 1–2-3 Basisboek [Student monitoring system: Mathematics—Tests 1–2-3 manual]. Leuven, Belgium: Garant.; 2000.

14. Jurcak V, Tsuzuki D, Dan I. 10/20, 10/10, and 10/5 systems revisited: Their validity as relative head-surface-based positioning systems. NeuroImage. 2007;34(4):1600-11.

15. Delorme A, Makeig S. EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis. J Neurosci Methods. 2004;134(1):9-21.

16. Mennes M, Wouters H, Vanrumste B, Lagae L, Stiers P. Validation of ICA as a tool to remove eye movement artifacts from EEG/ERP. Psychophysiology. 2010;47(6):1142-50.

17. Prieto-Corona B, Rodriguez-Camacho M, Silva-Pereyra J, Marosi E, Fernandez T, Guerrero V. Event-related potentials findings differ between children and adults during arithmetic-fact retrieval. Neurosci Lett. 2010;468(3):220-4.

18. Xuan D, Wang SH, Yang YL, Meng P, Xu F, Yang W, et al. Age difference in numeral recognition and calculation: An event-related potential study. Child Neuropsychol. 2007;13(1):1-17.

19. Zhou XL, Booth JR, Lu JY, Zhao H, Butterworth B, Chen CS, et al. Age-Independent and Age-Dependent Neural Substrate for Single-Digit Multiplication and Addition Arithmetic Problems. Developmental Neuropsychology. 2011;36(3):338-52.

20. LeFevre JA, Bisanz J, Daley KE, Buffone L, Greenham SL, Sadesky GS. Multiple routes to solution of single-digit multiplication problems. Journal of Experimental Psychology-General. 1996;125(3):284-306.

10

21. Hubber PJ, Gilmore C, Cragg L. The roles of the central executive and visuospatial storage in mental arithmetic: A comparison across strategies. Q J Exp Psychol. 2014;67(5):936-54.

22. Ramus F, Rosen S, Dakin SC, Day BL, Castellote JM, White S, et al. Theories of developmental dyslexia: insights from a multiple case study of dyslexic adults. Brain. 2003;126:841-65.

23. De Smedt B, Reynvoet B, Swillen A, Verschaffel L, Boets B, Ghesquiere P. Basic number processing and difficulties in single-digit arithmetic: Evidence from Velo-Cardio-Facial Syndrome. Cortex. 2009;45(2):177-88.

24. Campbell JI, Epp LJ. Architectures for arithmetic. In: Campbell JID, editor. Handbook of Mathematical Cognition. New York: Psychology Press; 2005. p. 347-60.

25. Folstein JR, Van Petten C. Influence of cognitive control and mismatch on the N2 component of the ERP: A review. Psychophysiology. 2008;45(1):152-70.

26. Zhou X, Chen C, Dong Q, Zhang H, Zhou R, Zhao H, et al. Event-related potentials of single-digit addition, subtraction, and multiplication. Neuropsychologia. 2006;44(12):2500-7.

27. Loher S, Fatzer ST, Roebers CM. Executive functions after pediatric mild traumatic brain injury: a prospective short-term longitudinal study. Appl Neuropsychol-Child. 2014;3(2):103-14.

11

Tables

Table 1. Participant characteristics.

Pediatric mTBI patients ControlsN 16 16Age (years)

Mean (SD) 10y 8 mo (1y 6 mo) 10y 9 mo (1y 6 mo)Range 7y 1 mo-12y 10 mo 7y 3 mo-12y 8 mo

Sex, M/F 10/6 11/5Verbal abilitya 98 (12) 101 (14)Premorbid mathematical abilitiesb (pc)

Mean (SD) 71.24 (16.79) 81.06 (14.07)Range 40.00-94.50 45.00-97.00

a Verbal ability was assessed with the Vocabulary subtest of the Dutch Wechsler Intelligence Scale for Children, Third Edition, WISC-III-NL.12

b Premorbid mathematical ability was assessed with a curriculum-based standardized achievement test for mathematics.13 Percentile ranks were available for 28 of the 32 participants (12 mTBI patients, 16 controls) and dated from one month to one year before testing. As these data are measured at the ordinal level, we used Wilcoxon signed-ranks test to test for a difference between mTBI patients and controls. This difference was not significant (p = .307). It should be emphasized that none of the children had learning difficulties as indicated by the parents. Furthermore, all children had at least an average percentile rank (pc ≥ 40) on the standardized mathematical abilities test administered before the injury and participation in this study.

12

Figures

Fig. 1. Boxplots of accuracy and reaction time on the arithmetic task as function of problem size and group.

13

Fig. 2. Boxplots of problem size effect (PSE, large minus small) in accuracy for each group.

14

Fig. 3. Boxplots of problem size effect (PSE, large minus small) in reaction time for each group. There was an outlier in one of the control children. This was due to a large difference in reaction times for solving large and small problems, whereas the reaction times themselves were not outlying. We ran all analyses (group comparisons and correlations) with and without this outlier and our findings were the same.

15

Fig. 4. Boxplots of LPC for each group.

16

Fig. 5. The mean event-related potentials elicited by single-digit additions over representative electrode O2 (blue line = controls; red line = mTBI patients). A significant group effect can be observed in the mean amplitude of the LPC component.

17

Fig. 6. The mean event-related potentials elicited by single-digit additions over representative electrode Pz (blue line = large problems; red line = small problems). A significant problem size effect can be observed in the mean amplitude of the LPC component.

18