Participants

Twelve children with MLD aged 8.5–10.9 (mean ± one standard error of the mean: 113.8 ± 7.3 months) without other neurological or psychiatric illness participated in this study. Children were selected from the same school, which was the only school that agreed to participate in our research at this stage given the lack of any records on the use and safety of tRNS for paediatric population. Children were diagnosed as having specific MLD by Fairley House School (London), a specialised school for children with specific learning needs. We trained children in the same room to control for any variance attributed to different learning environments. They were pseudo-randomly assigned to sham and active tRNS groups (Table 1). We obtained informed consent from parents/guardians, and children gave their assent to participate in this study. This study received ethical approval from the National Research Ethics Service Committee South Central-Hampshire B (11/SC/0401). All methods were performed in accordance with the approved guidelines and regulations.

Cognitive training

Children moved their bodies from side-to-side to map numbers on a virtual number line ﻿presented on an interactive whiteboard. They registered their responses by raising both hands in front of a time-of-flight camera (KinectTM) that detected body movements (Fig. 1a). Our training integrates bodily movements, as spatial-numerical and embodied learning have been suggested to promote better training effects in children than training without embodiment19,20,21. The game was adaptive, and challenged children with a range of difficulty levels depending on their performance. It featured number mapping of a range of difficulty levels (defined by the range of the number line; 0–5, 0–10, 0–50, 0–100, 0–500, 0–1000, and 0–1500) and a range of precision levels (7%, 6%, 5% and 4%) within each difficulty level. Three consecutive correct answers promoted the next trial to a more difficult level/precision level, while three consecutive incorrect answers demoted the next trial to an easier level/precision level (Fig. 1b). This game yielded three main measures: accuracy (precision of number mapping), response times (RT) and the level of each trial attempted. Children were instructed to move their body from side-to-side to locate the position of the number prompted on the center of the screen above the virtual number line, and to raise both their hands to register their answer. They were asked to respond as quickly and as accurately as they could for each trial. As the game included 7 difficulty levels and 4 precision levels, there were 28 levels in total. Children trained on this game for 9 days, 20 minutes each at school for 2 days per week, over the course of 5 weeks.

Transcranial random noise stimulation (tRNS)

Children in the active tRNS group received 0.75 mA of tRNS (0.1–500 Hz) to their bilateral dorsolateral prefrontal cortices (dlPFCs) via two saline-soaked, 25 cm2 circular sponges, attached under designated electrode positions (F3, F4) of a wireless tRNS cap that followed the International 10–20 system (Neuroelectrics Inc., Barcelona). The dlPFC was chosen, as the bilateral dlPFCs have been implicated in numerical processing in children22, and tRNS to the dlPFC during arithmetic training has shown promising results in healthy adults9, 15. TRNS was applied for 20 minutes per session as in previous tRNS protocols9, 15 and studies on paediatrics using another form of tES, transcranial direct current stimulation (tDCS)23, 24. We ran our study for 5 weeks in total, having considered the practical limitations of collecting data from school; term time, school timetable, and commitment from teachers to accommodate our study requirements (children catching up with lessons after taking part in our training). A light, battery-operated device attached to the back of the child-sized cap delivered electrical current for 20 minutes throughout each training session. As there were no prior studies using tRNS in children, we followed the recommendation of applying at least half of that administered to adults25; we applied 75% of 1mA9, 13, 26, shown to be well tolerated in adults without adverse effects. This dosage is estimated to equal that of 1 to 1.5 mA in adults, based on previous modeling of tDCS25. This decision was made after considering the parameters that would influence current distribution and density at the site of stimulation such as thinner scalp, less cerebrospinal fluid, and smaller head size of the paediatric population27, 28. A similar dosage using tDCS was well tolerated by children, and was not associated with adverse effects29. Despite stronger results with stimulation on consecutive days shown in a previous study on adults30, stimulation was applied during training twice a week, as a cautious approach to prevent and minimise any potential adverse effect of tRNS on paediatric population11, which are unknown at this stage. Children in the control group who did not received tRNS (no stimulation at all) wore the wireless cap to control for any placebo effects associated with wearing the tRNS cap. All children were blinded to their stimulation condition.

Mathematical assessment

Children’s mathematical performance were assessed using MALT, a standardized diagnostic tool calibrated to the UK National Curriculum levels31. MALT is commonly used by schools to monitor the performance of their students. Children were given 45 minutes to solve as many mathematical problems as they could, using pencil and paper. MALT was administered before and immediately after the 9 days of training.

Working memory

Given the link between mathematical achievement and working memory32 and findings of a previous study using tDCS33, we assessed children’s verbal and visuospatial working memory capacity using digit span and Corsi blocks respectively. We also examined performance on these indices to monitor for any changes associated with training effects, as well as any potential cognitive side effects linked with stimulation34, 35. In the digit span task, children listened to a series of digits read aloud by the experimenter and were asked to repeat the sequence. The first trial consisted of 2 digits, and the span increased by one digit with every 2 trials. In the Corsi blocks task, children observed the experimenter tapped a sequence on a series of blocks, and were asked to repeat the tapped sequence. Similar to the digit span task, the first sequence consisted of 2 blocks, and the tap sequence increased by one block with every 2 trials. Each task was terminated by 2 consecutive incorrect trials. The standard score of each task was the maximum number of items recalled in 2 consecutive spans.

Statistical analysis

In the main text, we report the results based on linear mixed effects models, which accounts for within-subject correlations more optimally compared to Analysis of Variance (ANOVA) i. For the interested reader, we also report the results of ANOVA and Bayesian analysis in the Supplementary Information, which show converging results. Due to our limited sample size however, we recommend these inferential statistics to be interpreted carefully.

Video game

Number line ranges increased as a function of Levels (e.g., Level 1: 0–5, Level 2: 0–10, Level 3: 0–50 etc.). To allow for comparison across Levels, we standardised accuracy responses across all Levels [Absolute deviation from Target/Number range*100], in line with previous studies17. We log-transformed (natural log) these scores twice to achieve a normal distribution of the residuals in mixed effects model analysis. For the ANOVA analysis in the Supplementary Information, these scores were log-transformed only once.

Transfer effects

As a measure of the accuracy of training performance, we used the normalised absolute percentage error as specified by the equation in the previous paragraph. We calculated the rate of gain in these accuracy values over the 9 days for each subject according to the following equation: [(Day 9–Day 1)/Day 1] and correlated it with children’s rate of improvement in MALT measures using the following equation: [(Post-training score − Pre-training score)/Pre-training score]*100.

Accuracy, Overall Levels and Response Times (RT)

We used R (R Core Team, 2016) and nlme 36 to perform a linear mixed effect analysis with maximised log-likelihood on the accuracy, overall levels and mean RT. The limits of the 95% of the bootstrapped distribution (R = 10,000) of beta coefficients were obtained using the package boot 37 [bootstrapped percentile interval, BPI). We set Group, Day (as continuous variable) and the interaction Group x Day as fixed effects and random intercepts for participants.

The effect of training on mathematics assessment

We then used regression analysis to examine how Group (tRNS vs. sham) affected the transfer from training to mathematics performance. This analysis was performed using Amos 22 (Arbuckle, 2013) using the maximum likelihood estimator.

Children’s experience of tRNS

Children were given a questionnaire at the end of training (9th Day), in which they were asked the following questions:

1. Did you receive brain stimulation? (A. During all sessions; B. Sometimes; or C. Not at all). 2. Do you think wearing the cap helps you to do well in maths? (A. Yes; B. Maybe; or C. Not at all). Why? 3. How did you feel when you wore the hat? (Open-ended question). 4. Did you feel uncomfortable wearing the hat? (A. Yes; B. Sometimes; or C. Not at all). 5. If the hat can help you with maths, will you wear it? (A. Yes; B. Maybe or C. Not at all).

Long-term effects

To assess for any long-term effects of tRNS, a one-off assessment of performance on the training and MALT was conducted without tRNS four months later (see Supplementary Results).