High‐definition turns timing‐dependent: Different behavioural consequences during and following cathodal high‐definition transcranial direct current stimulation (HD tDCS) in a magnitude classification task

Neuromodulation with transcranial direct current stimulation (tDCS) can transiently alter neural activity, but its spatial precision is low. High‐definition (HD) tDCS was introduced to increase spatial precision by placing additional electrodes over the scalp. Initial evaluations of HD tDCS indicated polarity‐specific neurophysiological effects—similar to conventional tDCS albeit with greater spatial precision. Here, we compared the effects of cathodal tDCS or HD tDCS in a 4 × 1 configuration over prefrontal cortex (PFC) regions on behavioural outcomes in a magnitude classification task. We report results on overall performance, on the numerical distance effect as a measure of numerical processing, and on the spatial‐numerical associations of response codes (SNARC) effect, which was previously affected by prefrontal tDCS. Healthy volunteers (n = 68) received sham or cathodal HD tDCS at 1 mA over the left dorsolateral prefrontal cortex (DLPFC) or the left inferior frontal gyrus (IFG). Results were compared to an identical protocol with conventional cathodal tDCS to the left PFC versus sham (n = 64). Mixed effects models showed performance gains relative to sham tDCS in all conditions after tDCS (i.e. ‘offline’), whereas montages over PFC and DLPFC already showed performance gains during tDCS (i.e. ‘online’). In contrast to conventional tDCS, HD tDCS did not reduce the SNARC effect. Neither condition affected numerical processing, as expected. The results suggest that HD tDCS with cathodal polarity might require further adjustments (i.e. regarding tDCS intensity) for effective modulations of cognitive‐behavioural performance, which could be achieved by individualised current density in electric field modelling.


| INTRODUCTION
Neuromodulation with transcranial direct current stimulation (tDCS) is a non-invasive and prevailing tool to study human cognition and brain function (Polanía et al., 2018).Dependent on the polarity, tDCS yields neurophysiological effects in the cortex that are subsequently taken to modulate behaviour.Specifically, an electric field underlying the tDCS electrode can slightly depolarise or hyperpolarise perpendicular neuron soma depending on their orientation and the injected current's direction.As a result, increases and decreases in cortical excitability can be measured during and following anodal and cathodal tDCS, respectively (Jamil et al., 2017;Nitsche & Paulus, 2000).Beyond such polarity-dependent excitability changes, more diverse responses in associative cortical regions such as the prefrontal cortex (PFC) characterise the effects of tDCS, with additional neuroplastic processes exceeding the duration of tDCS and resulting in complex and nonlinear after effects.
In conventional tDCS, spatial precision is limited by relatively large electrode pads and diffuse electric fields.Recently, high-definition (HD) tDCS was introduced to increase the spatial focality of stimulation (Datta et al., 2009).By using a 4 Â 1 grid of small electrodes, the shape of the injected electric field is more focal underlying an active central electrode, whereas the four returning electrodes are less likely to induce opposite polarisation because of their shared current intensity.Indeed, electric field models and neurophysiological recordings confirmed a more precise and longer-lasting modulation of neurophysiological effects such as excitability changes, respectively (Kuo et al., 2013).First, their modelling indicated a higher concentration of the peak electric field of HD tDCS at the primary motor cortex, compared to conventional tDCS at the same intensity.Second, their recordings of motor-evoked potentials confirmed polarity-specific excitability changes by HD tDCS and even documented longer-lasting effects relative to conventional tDCS of the same intensity (Kuo et al., 2013).
However, the behavioural consequences of HD tDCS are less well understood.This pertains particularly to cathodal stimulation, which could be more susceptible to nonlinear influences (Batsikadze et al., 2013;Ostrowski et al., 2022).Specifically, both at the neurophysiological and behavioural level, cathodal stimulation effects were shown to be sensitive to current intensity and to possibly vanish if too low or too high intensities were applied (Batsikadze et al., 2013;Ostrowski et al., 2022); a similar nonlinear relationship was recently demonstrated in decreased and increased muscle strength following 1-1.5 and 2 mA cathodal tDCS, respectively (Vimolratana et al., 2023).Such a parametric window of cathodal tDCS effectivity could depend on the exact definition of current intensity at the electrode interface, or on the current density, which describes the actual electric field strength in a region of interest.Switching from regular to HD tDCS, however, by definition, will generate a different current density distribution even in the cortical regions directly situated under the target electrode.Even when selecting the identical current intensity, different current densities may emerge in a region of interest.Thus, results from conventional cathodal tDCS may not always be immediately transferable to HD tDCS.
At the same time, given its higher spatial precision, HD tDCS should enable to differentiate functional contributions of anatomically close regions.As such, for example, a study on response inhibition reported different modulations of reaction time (RT) by stimulation of the right inferior frontal gyrus (IFG) and dorsolateral prefrontal cortex (DLPFC) (Hogeveen et al., 2016).Thus, the better spatial resolution offered by HD tDCS is very appealing to cognitive neuroscience research.
Using conventional cathodal tDCS, we have repeatedly observed reductions in the spatial-numerical associations of response codes (SNARC) effect, a behavioural index of implicit numerical cognition (Schroeder et al., 2016(Schroeder et al., , 2017a)).Briefly, the SNARC effect emerges for directional responses (such as left-hand or right-hand key presses) to the presentation of stimuli with numerical magnitude (such as digits larger or smaller than a referent, typically the digit five).In a congruent block of a magnitude classification task, left-hand (right-hand) key presses are required to classify small digits (large digits), and RTs are typically faster in this congruent block than in the incongruent block with the reversed response mapping (Cipora et al., 2018;Dehaene et al., 1993).Moreover, the magnitude classification task also yields another interesting index of numerical processing in the numerical distance effect (Moyer & Landauer, 1967): Irrespective of the SNARC effect, RTs are slower if the arithmetic differences between stimulus digit and referent are smaller.Finally, overall RT in the task indicates general performance.To sum up, the magnitude classification task reveals three markers of behaviour in the SNARC effect, the numerical distance effect and the overall performance.
Regarding the SNARC effect, recent theoretical considerations emphasised a possibly critical role of verbal-linguistic processing at its basis (Gevers et al., 2010;Nuerk et al., 2004;Proctor & Cho, 2006;Schroeder et al., 2017b).Instead of assuming a mental number line representation, the linguistic markedness account explains RT differences in the SNARC effect by structural overlaps in stimulus and response codes, that is, a faster RT for unmarked response (e.g.right) and stimulus dimensions (e.g.large).The theory can also account for other circumstances of classification, such as parity judgment tasks.To further corroborate the account with neural data, however, a higher spatial precision of tDCS would be theoretically interesting.In our previous studies with conventional tDCS (Schroeder et al., 2016(Schroeder et al., , 2017a)), relatively large electrode pads were used that simultaneously targeted structures across the left PFC including the DLPFC and also the left IFG.Therefore, results from HD tDCS targeting the left IFG versus the left DLPFC might elucidate this research question.
Accordingly, the present study had the following aims.We attempted to compare cathodal tDCS with conventional and HD placements of the same current intensity at 1 mA.Furthermore, we aimed to investigate the specific contribution of the left IFG against the left DLPFC in a magnitude classification task by using focal HD tDCS.Given the broad involvement of the PFC in cognitive functioning, overall performance gains were possible.Numerical processing and the numerical distance effect in particular, however, should be hosted in parietal regions (Cohen Kadosh et al., 2008;Hubbard et al., 2005) and thus likely not susceptible to prefrontal tDCS.Accordingly, we did not expect that prefrontal tDCS modulated the numerical distance effect, similar to previous studies with cathodal tDCS (Farshad et al., 2024;Schroeder et al., 2016Schroeder et al., , 2017a)).Most critically, in order to support a verbal account of the SNARC effect, we expected that HD tDCS of the IFG, but not of the DLPFC, should yield a reduction relative to sham, similar to conventional tDCS.Finally, we also explored timedependent stimulation effects.Given that excitability changes following HD tDCS were longer lasting in motor-evoked potentials (Kuo et al., 2013), we hypothesised that HD tDCS could have stronger effects after stimulation (i.e.offline) than during stimulation (i.e.online) compared to conventional tDCS.We did not expect modulations of the numerical distance effect by any of our conditions.

| Participants
The study included a total of 132 healthy right-handed participants; 68 of those participants were randomly assigned to one of three HD tDCS conditions (left IFG, left DLPFC, sham).The remaining 64 participants received conventional tDCS (left PFC, sham) and were drawn from a larger study for re-analysis (Schroeder et al., 2020).Exclusion criteria for all participants were age below 18 years or above 45 years, left-handedness (according to the Edinburgh Handedness Inventory; Oldfield, 1971), previous or current neurological or psychological disorder, relevant medication or recreational substances, metal implants (or other implants, i.e. a pacemaker), pregnancy or epilepsy.The groups did not differ with respect to relevant demographic variables and were primarily well-educated university students (see Table 1).
Sample size was originally determined by a-priori power analysis.In the magnitude classification task, cathodal tDCS to the left PFC had a moderate effect size of Cohen's d = .62(Schroeder et al., 2016).To conceptually replicate the tDCS effect in the magnitude classification task, 30 participants were required.However, we deviated in two aspects from the sample size estimation.First, fewer participants were available in the HD tDCS conditions because of difficulties with the Covid-19 pandemic.Second, we analysed behavioural data at the trial level with mixed effects modelling to accommodate and improve statistical power.
The study was approved by the ethics committee of the local university (No of approval: 577/2018BO2) and informed consent was collected prior to participation.A single experiment lasted approximately 2 h, and the participants were reimbursed with monetary compensation or course credits.

| Study design
This study was a double-blind baseline-controlled mixedsubjects design (see Figure 1).The participants performed the magnitude classification task and another RT task reported elsewhere (Schroeder et al., 2022).They repeated each task three times: Before (HD-)tDCS (baseline), during real or sham tDCS (i.e.'online') and after real or sham tDCS (i.e.'offline').Data from conventional tDCS (active and sham) of the left PFC were pooled from another study with the identical design for comparison (Farshad et al., 2024).

| Stimulation protocols for tDCS and HD tDCS
A battery-powered multi-channel stimulator (Starstim tCS ® 5G, Neuroelectrics Barcelona S.L., Barcelona, Spain) was used to deliver tDCS or HD tDCS.For conventional tDCS, two circular rubber electrocdes (2.3-cm radius) were positioned over F3 and at the right upper arm.For HD tDCS, we prepared five circular rubber electrodes (1-cm radius) covered with adhesive conductive paste (Ten20 ® , Weaver and Co, USA).Electrodes were attached according to the international 10-20 EEG System in a focal 4 Â 1 configuration (Figure 2), with the cathode defined as central target electrode for cathodal stimulation (Datta et al., 2009;Guo et al., 2018).Electrode positions were selected according to previous studies and for maximum current density in the target regions (see Figure 3): In the DLPFC group, the cathode was attached over the left DLPFC (F3), surrounded by four anodes (Fp1, Fz, C3 and F7).In the IFG group, the cathode was attached over the left IFG (FC5), surrounded by four anodes (AF7, F1, CP1 and TP7).
Electrodes were attached to subjects' heads and encased within a neoprene cap prior to the baseline measurement.We used a cathodal current of 1 mA, and the four surrounding electrodes returned each .25 mA of the current.Previous polarity-specific studies have shown cognitive effects of cathodal tDCS at that intensity in conventional (Schroeder et al., 2018;Wolkenstein et al., 2014) and in HD configurations (Guo et al., 2018).Stimulation lasted for 30 min and was faded in and out with a 10 s ramp and an idle time of 5 min.In the sham group, stimulation lasted for only 30 s at the beginning and end of stimulation, in order to elicit comparable sensations; electrode placements were as in the PFC, DLPFC or IFG group with random assignment.
Given that HD tDCS led to longer-lasting excitability changes (Kuo et al., 2013), we recorded performance both during and following stimulation.
Adverse effects of tDCS were assessed after the offline measurements according to the most frequent sensations reported after tDCS (Brunoni et al., 2011).This was a double-blind study, and blinding efficacy was assessed after the end of the measurement.

| Magnitude classification task
The task was conducted on a 22-in.monitor with a viewing distance of approximately 60-70 cm.The task was programmed in PsychoPy version 3.2.4.(Peirce, 2007).The magnitude classification task was also described elsewhere (Schroeder et al., 2020).Briefly, the participants are repeatedly presented with a single-digit number (1-9 except 5) in the centre of the screen.To increase the SNARC effect, all participants started with the congruent response mapping (small-left, large-right) and performed five blocks of 40 trials each with randomised order of stimulus presentations.Next, they performed five blocks of 40 trials with the incongruent response mapping function of distance from the referent (e.g.distance = j5 À target digitj) as primary outcome in the numerical distance effect, with the highest RTs for the smallest numerical distances.Overall RT across stimuli and blocks was considered a general measure of performance.

| Statistical analysis
We conducted all analyses using R version 4.0.3(R Core Team, 2020).We fitted linear mixed models using the lmer() function of the lme4 package (Bates et al., 2014) at the trial level.To accommodate for repeated measures, we added a random effect for participant and a random effect for trial number nested in participant.Trial number was also included as a fixed effect in the model to encounter ongoing RT improvements because of practice with the task.
As fixed effects, we included Congruency (SNARC congruent vs. incongruent), Time (baseline, during tDCS and after tDCS) and Group (HD-DLPFC, HD-IFG, PFC and sham) and all interactions.Regarding our hypotheses, we were particularly interested in the three-way interaction, indicating a modulation of the SNARC effect, and in the two-way interaction of Time Â Group, indicating global performance.For a control analysis on the numerical distance effect, we replaced the fixed effect Congruency with the factor Distance (1, 2, 3, 4).We used REML and selected Nelder-Mead parameter optimisation.For interpretation, type-III analyses of variance with Wald chi-square test were extracted from mixed models using the package car (Fox & Weisberg, 2018).
Prior to analyses, we investigated individual outliers in the behavioural data according to the suggestions of Leys et al. ( 2013) using median-absolute deviation.Out of all trials, 7.37% were detected as outliers and removed from analyses.There was no indication of erroneous performance at the global or participant level.
Data and scripts are shared on the open-science framework: https://osf.io/fkupm/.
Group (left PFC, HD DLPFC, HD IFG and sham) are reported in Table 2. Overall, the mean RT of participants in the congruent block (M = 447 ms, SD = 74) was lower than the mean RT in the incongruent condition (M = 460 ms, SD = 86), indicating a regular SNARC effect.The respective fixed effect of congruency was statistically significant, χ 2 (1) = 330.42,p < .001.
Importantly, the model returned a significant threeway interaction of Congruency Â Group Â Time, χ 2 (6) = 59.12, p < .001.This indicated that the SNARC effect was differently modulated throughout the experiment across tDCS conditions.Follow-up model comparisons with sham tDCS showed that only conventional tDCS led to a reduction of the SNARC effect during and following stimulation, χ 2 (2) = 52.27,p < .001,see Figure 2b.
In contrast, HD tDCS of IFG or DLPFC did not significantly affect the SNARC effect: Within both models, the three-way interaction was statistically not significant, χ 2 (2) < 3.20, p > .202,suggesting comparable changes in the SNARC effect relative to sham.Additional regression coefficient analyses hinted at mean RT as a moderator of the difference between the HD versus conventional DLPFC tDCS, but not of the difference between all other configurations, see supporting information.
However, within the HD tDCS groups, there were significant two-way interactions of tDCS Â Time for comparing IFG with sham tDCS, χ 2 (2) = 13.79,p = .001,and for comparing DLPFC with sham tDCS, χ 2 (2) = 18.41, p < .001.Mean performance improvements across all groups are displayed in Figure 3a and Table 3. Relative to sham tDCS, performance gains were pronounced during both (HD) tDCS conditions across DLPFC (i.e.'online'), whereas performance gains were pronounced in all tDCS and sham conditions after tDCS (i.e.'offline').In direct comparison of the two HD tDCS conditions, this led to a significantly delayed improvement across time in the group receiving tDCS to the IFG, χ 2 (2) = 17.25, p < .001.

| Numerical distance effect
The mixed models on the numerical distance effect revealed the main effect of Distance, χ 2 = 1149.29,p < .001,indicating slower responses for digits closer to the referent (see Figure 3c).There was no modulation of Distance by tDCS Â Time, χ 2 (6) = 5.85, p = .439.There was, however, a significant practice effect with shorter numerical distance effects following baseline, χ 2 (2) = 11.65,p = .003.Moreover, differential performance gains were reproduced in this analysis by a significant two-way interaction of tDCS Â Time, χ 2 (6) = 17.58, p = .007,see previous section.

| ROI analyses
To better understand the difference between conditions-particularly between conventional and HD tDCS of the same brain region-we ran electric field computational models and extracted calculated current density at the possible regions of interest (ROIs).Specifically, we extracted current density of the electric fields for two target ROIs (left IFG and left DLPFC) and three control ROIs (primary motor cortex, right IFG and right DLPFC) from all three tDCS protocols using a default sphere of 10 mm.Analyses were performed using SimNIBS software and the Ernie standard head model (Thielscher et al., 2015).Weighted averages and their variances are displayed in Figure 3.

| Adverse effects and blinding
There were no serious adverse events.Mean adverse sensations are reported in Note: DLPFC = dorsolateral prefrontal cortex, HD = high-definition, IFG = inferior frontal gyrus, PFC = prefrontal cortex, RT = reaction time, SNARC = spatial numerical associations of response codes, tDCS = transcranial direct current stimulation.

| DISCUSSION
In this study, we evaluated cathodal tDCS with conventional or a more focal high-definition electrode placement (i.e.HD tDCS) during a magnitude classification task.Overall, RT decreased during and following stimulation and exceeded typical practice effects during sham.However, only in the conventional tDCS condition, decrease in overall RT was accompanied by a reduction of the SNARC effect.In contrast, numerical processing was not affected by neither tDCS condition, and regular numerical distance effects were observed throughout.Together, the results indicate that behavioural outcomes from cathodal HD tDCS differ in critical ways from conventional tDCS.Technical parameters such as the stimulation intensity, duration, and the task were identical across groups.However, it should be noted that current density differed according to the modelling and was 15-25% less dense at both coordinates underlying HD tDCS, compared to conventional tDCS.Particularly in cathodal tDCS with possible nonlinear effects at different stimulation doses (Batsikadze et al., 2013;Jacobson et al., 2012), it is possible that electric field density affects behavioural outcomes.
Computational models of the electric field density with a standard anatomical model confirmed the focal specificity of the two HD configurations (Figure 3).Interestingly, however, the magnitude of electric fields was weaker in both regions of interest for HD tDCS.Accordingly, to achieve the same current density, a higher intensity may be needed.This observation dovetails with a previous meta-analytic observation that inhibitory effects of cathodal HD tDCS may emerge at 1.5 mA but either at 1 or 2 mA (Ostrowski et al., 2022).This is also consistent with neurophysiological models of conventional cathodal tDCS which showed best effectivity at 1 mA but not 2 mA (Batsikadze et al., 2013).However, the observation deviates from neurophysiological data of HD tDCS that showed comparable excitability reductions during and following 2 mA conventional and HD tDCS (Kuo et al., 2013).Interestingly, excitability increases were not replicated in elderly patients of 65 years and older, indicating age-dependent dose-response effects (Ghasemian- Note: We reported results of analysis of variance and a Bayesian linear model, yielding quantitative evidence for either the alternative hypothesis (BF > 1) or for the null hypothesis (BF < 1).BF between 3 and 1/3 is considered anecdotal evidence, whereas a BF between 1/3 and 1/10 indicates moderate for the null and a BF of 1/10 and smaller indicates strong evidence for the null hypothesis of no differences between the groups (Jeffreys, 1961).All side effect questions were answered on a 5-point Likert scale from (1 = not at all to 5 = very much).BF = Bayes factor, DLPFC = dorsolateral prefrontal cortex, HD = high definition, IFG = inferior frontal gyrus, PFC, prefrontal cortex.Shirvan et al., 2022).Thus, before deciding on current intensity in future studies with cathodal HD tDCS, an informed estimate of the required current density in the ROI should be collected; for the SNARC effect, the present observations suggest that .14V/m in the PFC or .15V/m in the IFG would be required.Future studies with cathodal HD tDCS should therefore consider an intensity of 1.5 mA.Given structural differences in brain anatomy, individual electric field modelling should be considered to support this possible explanation with empirical data and to provide adequate individual models for tDCS parameter selection.It is possible that the presented computational model of conventional tDCS overestimated electric field magnitude, because we were only able to approximate the extracephalic position of the return anode.While diffuse current flow through the brain stem is expected in this montage, a previous study also observed reduced excitability changes with increased electrode distance (Moliadze et al., 2010).It is an outstanding empirical question how electric field density and electrode distance correlate, and individual modelling may be helpful for future studies to address this question.
Different effects of HD and conventional cathodal tDCS at identical intensity could be explained by differences in current density.However, other plausible explanations can be considered as well.Considering that cortical folding differs between individuals, a more diffuse electric field induced by conventional tDCS could have a higher probability of affecting the exact right brain region across more individuals.Such a diffuse individualdifferences account could be of clinical interest, yet disappointing from a neuroscientific perspective.To increase spatial targeting, further steps may be required and two approaches could be administered in the future.First, including neurophysiological correlates during stimulation can unravel the more immediate consequences of tDCS (Polanía et al., 2018).Second, consideration of individual brain anatomy can increase spatial precision of tDCS.For instance, anatomical images could guide electrode placement in neuronavigated tDCS or enable post-hoc parametric validation of underyling neurophysiological assumptions (e.g.Soleimani et al., 2021).
The magnitude classification task used in our study is a good measure of cathodal tDCS behavioural outcomes, given an increasing set of existing studies (Di Rosa et al., 2017;Schroeder et al., 2016).Furthermore, the task enables differential views into cognitive processing of different indices, namely the SNARC effect, numerical distance and overall performance.An interesting finding was the immediate performance gain during DLPFC stimulation, but delayed performance gain following IFG stimulation, relative to sham.This finding could reflect the diverse involvement and wide-spread connectivity of DLPFC in cognitive functioning (e.g.Jung et al., 2022) but a slightly more specific role of the left IFG in language-related processes and secondary co-activation of adjacent brain areas (Poldrack et al., 1999;Tyler et al., 2011).Because the mechanisms underlying after effects of tDCS are poorly understood to date (Korai et al., 2021;Liu et al., 2018), future research can investigate a potential delayed versus immediate modulation in connected brain networks.
A limitation of the study is the unequal group sizes, which was a result of the SARS-Coronovirus-2 pandemic.Participation in the HD tDCS groups was interrupted by the pandemic, whereas participants in the conventional tDCS experiment were required to wear masks throughout.Because the tDCS results did not differ from prepandemic studies (Schroeder et al., 2016(Schroeder et al., , 2017a)), we assumed comparability between the groups.Still, group sizes were sufficient to detect the reported differences with sham tDCS.Second, considering the intensity of the electric field for HD tDCS, we could not interpret the results regarding a more specific role of IFG or DLPFC for the SNARC effect.At the same time, almost identical tDCS effects in the left and right frontal cortex in another recent study question the assumption that verbal regions are most critical for the emergence of the SNARC (Farshad et al., 2024).Another limitation of the study are differences in baseline performance across groups, although a relatively homogeneous sample was recruited.Performance at baseline was included in our statistical models that quantified tDCS-related outcomes as the interaction of Group Â Time; moreover, we performed responder and non-responder analyses relative to sham tDCS (see supporting information).Performance at baseline may have influenced the susceptibility of participants to cathodal tDCS in the present study.At least, baseline differences seemed unrelated to pre-pandemic study participation.Regarding timing, although results descriptively suggested that overall speed improvements followed HD IFG but were immediately active during PFC and HD DLPFC tDCS (see also Figure S2), respective post-hoc tests were not conclusive.Unfortunately, we also encountered baseline differences between the groups (see Figure 2b) which could favour a reduction of the SNARC effect during conventional tDCS but not an overall improvement in RT.Finally, HD tDCS of both regions elicited stronger itching/tingling sensations in this study than conventional tDCS at the same intensity.
To conclude, the study showed critical differences in the effects of cathodal HD versus conventional tDCS, even with the same intensity and target placement.Accordingly, we could not corroborate differences between the left DLPFC and IFG regarding a modulation of the SNARC effect.Future studies should consider electric field density, ideally from individual modelling, when determining stimulation parameters.
T A B L E 1 Number of participants each gender (% female) and mean age (SD) dependent on tDCS group.PFC (N = 31)For reasons unrelated to the present study goal, we also assessed trait math anxiety and eating-related questionnaires (e.g.seeSchroeder et al., 2022).DLPFC = dorsolateral prefrontal cortex, HD = high-definition, IFG = inferior frontal gyrus, PFC = prefrontal cortex, tDCS = transcranial direct current stimulation.F I G U R E 1 Outline of the main experimental procedure.DLPFC = dorsolateral prefrontal cortex, HD = high-definition, IFG = inferior frontal gyrus, PFC = prefrontal cortex, RT = reaction time, SNARC = spatial numerical associations of response codes, tDCS = transcranial direct current stimulation.

(
small-right, large-left).Trials had a short fixation symbol (#; 250 ms), and incorrect or late responses (> 2 s) triggered immediate feedback in form of the German words 'Fehler' (Eng.'error') or 'Bitte schneller antworten!' (Eng.'Please respond faster!') for 500 ms.Between trials there was a blank jittered inter-trial-interval of 300-600 ms.We considered the RT difference between the congruent and incongruent block as primary outcome in the SNARC effect.Furthermore, we considered RT as a F I G U R E 2 Trajectory of behavioural outcomes before (baseline), during and after tDCS.(a) Total performance gains, (b) the trajectory of the SNARC effect and (c) the numerical distance effect.DLPFC = dorsolateral prefrontal cortex, HD = high-definition, IFG = inferior frontal gyrus, PFC = prefrontal cortex, RT = reaction time, SNARC = spatial numerical associations of response codes, tDCS = transcranial direct current stimulation.

F
I G U R E 3 Mean electric field (V/m) in target region by HD tDCS protocol, based on a standard head model.MNI coordinates were taken from Zhang et al. (

Table 4 .
Itching/tingling was higher in both groups receiving HD tDCS, F(3, 124)T A B L E 2 Mean RTs and standard deviation in the SNARC-congruent and incongruent blocks, disentangled per group and time.