Regional specificity of cathodal transcranial direct current stimulation effects on spatial–numerical associations: Comparison of four stimulation sites

Neuromodulation with transcranial direct current stimulation (tDCS) is an increasingly popular research tool to experimentally manipulate cortical areas and probe their causal involvements in behavior, but its replicability and regional specificity are not clear. This registered report investigated cathodal tDCS effects on spatial–numerical associations (i.e., the SNARC effect), the numerical distance effect (NDE), and inhibitory control (i.e., stop‐signal reaction time; SSRT). Healthy adults (N = 160) were randomly assigned to one of five groups to receive sham tDCS or 1 mA cathodal tDCS to one of four stimulation sites (left/right prefrontal cortex [PFC], left/right posterior parietal cortex) with extracephalic return. We replicated that cathodal tDCS over the left PFC reduced the SNARC effect compared to sham tDCS and to tDCS over the left parietal cortex. However, neither NDE nor SSRT were modulated in the main analyses. Post hoc contrasts and exploratory analyses showed that cathodal tDCS over the right PFC had a time‐dependent effect by delayed practice‐related improvements in SSRT. Math anxiety moderated changes in the NDE in the groups receiving tDCS to the right parietal cortex. With few exceptions, the replicability and regional specificity of tDCS effects on behavior were weak and partially moderated by individual differences. Future research needs to characterize the parameter settings for effective neuromodulation.

. Results on the functional neuroanatomy of different controlled or implicit processes appear to corroborate this view at large (Aron et al., 2004;Garavan et al., 1999;Hubbard et al., 2005;Miller & Cohen, 2001;Stanley et al., 2008), but causal dissociations at the neural level were not yet tested in a single study design.The present registered report aims to investigate the regional specificity and distinctiveness of controlled and implicit aspects of cognition in behavioral indices with noninvasive brain stimulation.
Probing brain networks for their involvement in cognitive processes can amend to the notion of distinct systems by dissociating the involved brain regions.Particularly the causal contribution of brain regions to different facets of behavior can be studied by transiently modulating brain activity patterns with noninvasive brain stimulation (Polanía et al., 2012).When using transcranial direct current stimulation (tDCS), a weak direct current is sent through the scalp which would slightly depolarize or hyperpolarize most resting membrane thresholds in a targeted region, mostly dependent on electrode position and current direction (Fertonani & Miniussi, 2017;Nitsche & Paulus, 2000;Priori et al., 1998).
Accordingly, in neurocognitive investigations, hyperpolarizing cathodal tDCS to prefrontal regions can modulate certain cognitive processes, for example, to impair working memory processes (Wolkenstein et al., 2014;Zaehle et al., 2011) and reduce implicit associations (Schroeder et al., 2016(Schroeder et al., , 2018) ) or response inhibition (Friehs & Frings, 2019a;Hogeveen et al., 2016;Jacobson et al., 2011;Nieratschker et al., 2015).Thereby, this technology allows not only for a modulation of cognitive processing, but can provide a critical test for a theory that predicts united or divided systems which should respond to regional brain stimulation in ensemble or produce dissociable modulations, respectively.Vice versa, the demonstration of task-selective effects of tDCS configurations on theoretically distinct aspects of cognitive processing can causally bolster the regional specificity of targeted brain regions.

| Spatial-numerical associations and numerical distance
To examine and reliably measure implicit and explicit components of cognitive processing, specific indices in behavioral assessments can be used.Effects in numerical cognition reflect the implicit and explicit components of cognitive processing rather uniquely: Although symbolic magnitudes (i.e., single digits) allow for objective decisions based on clearly set mathematical rules, task-irrelevant spatial-numerical associations emerge implicitly and influence directional responses (Cipora et al., 2018).For instance, when asked to indicate parity or magnitude of a presented digit by a manual key press, left-hand responses are faster for small numbers and right-hand responses are faster for large numbers (Cipora, van Dijck, et al., 2019;Dehaene et al., 1993;Wood et al., 2008).Originally termed the "Spatial-Numerical Associations of Response Codes" (SNARC) effect, this behavioral signature is taken to reflect spontaneous encoding of biased task information in verbal working memory by most recent accounts (Abrahamse et al., 2016;Schroeder et al., 2017b;van Dijck & Fias, 2011).According to this theoretical consideration, the activation of an implicit bias should draw on verbal working memory processes corroborated by the left prefrontal cortex (PFC), which was confirmed by inhibitory cathodal tDCS to this region in four previous experiments (Schroeder et al., 2016(Schroeder et al., , 2017a(Schroeder et al., , 2018)).
Moreover, a different electrode setup targeting either left or right posterior parietal cortex (PPC) did not modulate the SNARC effect in the parity judgment task in a different study setup (Di Rosa et al., 2017).
In numerical cognition research, posterior parietal brain areas are established to subserve arithmetic and numerical magnitude processing, particularly including the (horizontal) intraparietal sulcus, angular gyrus, and posterior superior parietal lobe (Dehaene et al., 2003;Hubbard et al., 2005;Piazza et al., 2007;Sokolowski et al., 2017).Recent fMRI studies enabled the identification of frontoparietal arithmetic and number processing networks (Klein et al., 2016;Sokolowski et al., 2017).Both model and imaging results particularly showed activation patterns in left-hemispheric prefrontal clusters (BA 44,45,and 47) consistent with the notion of verbal processes (see also Dehaene et al., 2003).Also for spatial associations of numbers, frontal areas were outlined to contribute causally in brain-damaged patients (Doricchi et al., 2005) and following stimulation with repetitive transcranial magnetic stimulation (rTMS) (Rusconi et al., 2011(Rusconi et al., , 2013)).
At the same time, when the SNARC effect is measured with the magnitude classification task, another signature of numerical magnitude processing can be observed in the numerical distance effect (NDE) (Dehaene et al., 1990;Moyer & Landauer, 1967).Response latencies increase with decreasing numerical distance (i.e., the differences between numbers to be compared), irrespective of response hand (Dehaene et al., 1990;Moyer & Landauer, 1967).The NDE was not modulated by frontal tDCS in our previous results

Significance
This study was designed to replicate three neuromodulation results by systematically varying the electrode position.According to preregistered hypotheses, we applied neuromodulation with cathodal tDCS or with a placebo protocol over four distant brain regions.Only one of the measured tasks showed the expected neuromodulation effect.Moreover, very few of the planned contrasts between brain regions showed differences.We thus conclude that both the replicability and the regional accuracy of cathodal tDCS are weak.We also observed moderator effects of gender and anxiety, which is in line with a large variability of tDCS effects.(Schroeder et al., 2016), consistent with the view that numerical magnitude operations such as those implied in the NDE are bolstered by parietal regions (Piazza et al., 2007).Accordingly, the NDE was modulated by left cathodal parietal tDCS in a previous study (Li et al., 2015).On a more general level, different arithmetic indices such as distractor-distance, double-digit comparison or carry effects were malleable to parietal tDCS (Artemenko et al., 2015;Hauser et al., 2013;Klein et al., 2013;Schroeder, Dresler, et al., 2017) and to TMS (Cappelletti et al., 2007;Cohen Kadosh et al., 2007;Sandrini & Rusconi, 2009).

| Response inhibition
The intentional and controlled interruption of automatically triggered behaviors, eventually, is a key component of higher order executive functioning and deliberate cognitive processing.Response inhibition, more precisely, describes the deliberate interruption of predominant motor commands to inhibit already initiated or planned motor actions in favor of higher order goals (Logan et al., 1984;Verbruggen et al., 2019;Wessel & Aron, 2016).The stop-signal task (SST) is a well-established adaptive paradigm to assess response inhibition and requires participants to withhold responding following a variable stop-signal delay in a minority of stop trials (Verbruggen et al., 2019), and inhibitory control is particularly challenging in the presence of attractive rewards such as high-calorie food stimuli (Appelhans, 2009;Svaldi et al., 2015).Response inhibition is mainly corroborated by frontobasal brain networks including cortical hubs in the presupplementary motor area and right PFC 1 (Aron et al., 2004;Banich & Depue, 2015;Sharp et al., 2010).According to neuroimaging results, response stopping is enabled by a cascade of neural activity in right PFC, which is taken to inhibit subsequent motor actions through thalamic pathways upon signal change in the external environments (Banich & Depue, 2015;Garavan et al., 1999).Further activations in the left presupplementary motor area are taken to reflect response preparation (Nachev et al., 2005;Ray Li, 2006).Metaanalyses of inhibitory control confirmed the lateralization of neural activity in prefrontal and presupplementary motor areas, but they also revealed additional task-dependent activations in various areas such as the fusiform gyrus, precentral gyrus, and others (Simmonds et al., 2008;Zhang et al., 2017).
To date, various brain stimulation studies have already confirmed a causal link between response inhibition and the right PFC using TMS (Chambers et al., 2006) or tDCS (Friehs & Frings, 2019a;Hogeveen et al., 2016;Jacobson et al., 2011;Nieratschker et al., 2015).Regional specificity of response inhibition in the SST was already investigated with excitability-enhancing anodal tDCS in previous studies, which led to improved response inhibition (Hogeveen et al., 2016;Jacobson et al., 2011;Stramaccia et al., 2015).The present confirmatory research utilized cathodal tDCS, which led to impaired response inhibition when administered over right PFC, as indicated by longer stop-signal reaction time (SSRT) (Friehs & Frings, 2019a).Moreover, by collecting data from the SST along with the magnitude classification 2 task in one large study design, we expect to empirically outline the task selectivity of regional tDCS configurations.

| The present registered report
In this study, effects of left-and right-hemispheric cathodal tDCS to prefrontal and parietal regions on implicit spatial-numerical associations, NDE, and response inhibition are systematically investigated.
Although the previous tDCS studies in sum already demonstrated a convincing overall landscape regarding implicit and explicit behavioral indices in the respective tasks, a systematic comparison of different stimulation sites was not yet available.However, a single experimental study design is required to address remaining questions regarding the laterality and specificity of stimulation.Slight differences in stimulation protocols, tasks, and intraindividual differences may have influenced previous results; therefore, we assessed the same individuals before, during, and following tDCS with different target regions to (a) replicate the previous tDCS effects and (b) corroborate the assumed regional specificity in a single, comparable, and hypothesis-driven design.Stimulation effects are expected to be most pronounced underneath the target electrode, but tDCS is not very focal and can induce compensatory reactions in other brain regions as well (Fertonani & Miniussi, 2017;Schroeder & Plewnia, 2016); thus, the conclusiveness of tDCS results can be enhanced by including control tasks and stimulating control regions (Polanía et al., 2018).In the present design, we expected our behavioral measures to serve as mutual control tasks, for example, NDEs, but not implicit spatial-numerical associations or response inhibition should be affected by parietal tDCS and vice versa for prefrontal tDCS.
Finally, it is important to consider that the robustness of tDCS effects in general have been questioned in the more recent past (Horvath et al., 2015).This is a particular challenge for tDCS research because many technical parameters (e.g., position of target and return electrodes, intensity, current density) and behavioral parameters (e.g., instruction, task, and outcome) have to be considered and vary tremendously across studies.To further the understanding of stimulation effects, conceptual replications of previous results are required and registered reports can enhance the rigor of the scientific method and avoid Type II error inflation in confirmatory research by requiring a high-quality hypothesis-driven research design, high statistical power, peer review prior to data collection, and outcome-neutral publication of study results (Nosek et al., 2015;Prager et al., 2019).
Timing of stimulation is a further critical factor.Because the sensations induced by tDCS usually diminish to a negligible degree after the first minutes, performance can be assessed in parallel to neuromodulation (e.g., while resting membrane potential thresholds are shifted; online) or in a time window up to 1 h after stimulation (e.g., while neuroplastic after effects of tDCS are still present; offline) (Jamil et al., 2017;Nitsche & Paulus, 2000).Behaviorally, some studies reported superiority of offline effects (Friehs & Frings, 2019b;Jacobson et al., 2012), while others claim functional targeting due to concurrent task-related brain activity which interacts with a superimposed electric field (Bikson & Rahman, 2013).In any case, behavior (or rest) during tDCS influences both online and offline effects (Gill et al., 2015;Horvath et al., 2014).
To summarize, this registered report investigates the replicability and the regional specificity of cathodal tDCS effects on implicit and controlled facets of cognition.Thereby, three prominent behavioral indices were collected before, during, and following active or sham tDCS to systematically map implicit spatial-numerical associations, number magnitude processing in the NDE, and inhibitory control in the SST across the cortex.We used a mixed design with the within-subjects factor time (baseline, tDCS, post-tDCS) and the between-subjects factor stimulation site (left PFC, right PFC, left PPC, right PPC; see Figure 1) at an intensity of 1 mA cathodal tDCS, returned at the respective contralateral upper arm.An additional fifth group received sham tDCS to control for possible expectation effects.The confirmatory primary (a) and secondary (b) hypotheses are: 1. Cathodal tDCS to the left PFC will decrease spatial-numerical associations (a), the other stimulation conditions (right PFC, left + right PPC) will not have an effect (b).

| Statistical power analysis and sample size estimation
For the three primary hypotheses, we performed separate power analyses for a priori sample size estimation to attain a high power of 1 − β = .9at α = .05.A direct paired t test (baseline vs. active tDCS, one-tailed) of the respective behavioral index (SNARC effect, SSRT, NDE) in the relevant group was performed.The direction of anticipated effects is explicated in the hypotheses.As effect sizes are usually overestimated in the literature, we corrected effect sizes by −10% and entered the resulting values into G*Power (Faul et al., 2007).

| Power to replicate cathodal tDCS effects (primary hypotheses)
SNARC effect: In the magnitude classification task, cathodal tDCS to the left (PFC) had a moderate-strong effect size of Cohen's d = .62(Schroeder et al., 2016).To conceptually replicate the tDCS effect in the magnitude classification task, with the bias-corrected effect size, a sample of minimum N = 30 participants was required.NDE: In the magnitude classification task, cathodal tDCS to the left PPC had moderate-strong effect size of Cohen's d = .61(Li et al., 2015).To conceptually replicate this effect, a sample of minimum N = 31 participants was required.
Note that the two other cathodal tDCS studies with the SST used a F I G U R E 1 Electric field modeling of four tDCS configurations targeting left/right PFC/PPC (target cathode position in left panel, return anode position is the respective contralateral upper arm).Current density distributions (right panel) are calculated for stimulation with 1 mA using SimNIBS toolbox (Thielscher et al., 2015).cortical return anode (Jacobson et al., 2011;Stramaccia et al., 2015), but the electrode configuration used in Friehs and Frings (2019a) comes closest to our study despite a pure offline design.To conceptually replicate this effect, a sample of minimum N = 23 participants was required.
Finally, for detection of a within-between interaction term considering the factors group (active, sham) and three-levels of tDCS (baseline, tDCS, post-tDCS), and assuming medium-sized effects (f = .25) 3and a medium-sized correlation between measures (r = .5),a total of N = 36 participants (i.e., 18 per group) was suggested.
2.1.2| Power to investigate regional specificity (secondary hypotheses) The regional specificity of the three investigated tDCS modulations mentioned earlier are investigated by comparing results across electrode configurations.For the three secondary hypotheses regarding regional specificity, the interaction terms between tDCS site (between-subjects) and tDCS effect (within-subjects, three levels: baseline, tDCS, post-tDCS) were evaluated.Assuming medium-sized effects (f = .25) 3and a medium-sized correlation between measures (r = .5),with power and significance level held constant, a total of N = 52 participants (i.e., 13 per group) was suggested by power analysis.

| Participants
According to the highest sample size estimate revealed by the power analyses and the requirements for counterbalancing, we planned to test a minimum sample of N = 32 participants for each group, yielding a total of 160 participants who were randomly assigned to one of the four tDCS groups or to the sham tDCS group (see Table S1).One participant was erroneously assigned to the sham protocol instead of the left PFC group; this was noticed after data analysis.We recruited healthy and German-speaking volunteers from the student and general population.In total, 47 male participants and 113 female participants were randomized to the groups stratified by sex to consider sex influences in exploratory analyses, as recommended by the journal policy.All participants had corrected-to-normal or normal vision, were right-handed according to the Edinburgh Handedness Inventory (Oldfield, 1971), and did not meet any exclusion criteria.Age was restricted to minimum 18 and maximum 40 years because stimulation effects and SNARC effect can vary with age (Laakso et al., 2015;Ninaus et al., 2017).To comply with contraindications and safety recommendations for tDCS (Bikson et al., 2016), we applied the following self-reported exclusion criteria: neurological or current mental disorders, current medication with CNS-acting or recreational substances, nicotine addiction (i.e., consumption of more than six cigarettes/week), metal implants, pregnancy, epilepsy, pacemakers.
The study is in agreement with the Declaration of Helsinki and was approved by the ethical committee of the University Hospital Tübingen (ID of approval: 577/2018BO2).Participants signed an informed consent and received monetary compensation or student credit compensation for attending the experiment.

| tDCS
A CE-certified battery-powered multichannel device (StarStim8, Neuroelectrics, Spain) was used to generate and deliver tDCS through a pair of identical circular rubber electrodes (diameter: 4 cm) covered with adhesive gel (Ten20® conductive paste, Weaver and Co., USA).
Stimulation lasted 30 min (including a 5-min pretask idle time) with a current of 1 mA (current density: .079mA/cm 2 , see Figure 1 for current density distribution), which is well within evidence-based safety limits for tDCS (Bikson et al., 2016).Stimulation was faded in and out with a 10-s ramp.In case of sham tDCS, an identical configuration was prepared, but stimulation lasted only 30 s with additional rampup and -down phases in the beginning and the end of the stimulation period.Thus, sham tDCS was anticipated to elicit sensations comparable to real tDCS without producing excitability changes (Ambrus et al., 2012;Friehs et al., 2019;Gandiga et al., 2006), which additionally was critically assessed in adverse sensations questionnaires (Brunoni et al., 2011).Position of the target cathode depended on randomized group assignment to the experimental groups (F3 = left PFC, F4 = right PFC, P3 = left PPC, P4 = right PPC, according to the international 10-20 EEG system of electrode placement; Figure 1).
An additional sham group was recruited who received sham tDCS in any of the four electrode configurations.Participants who received sham stimulation were later collapsed to a single sham tDCS group (n = 32) as different sham configurations were not expected to produce differential effects.The return electrode (anode) was placed extracranially on the contralateral upper arm (M.deltoideus) to avoid an opposite polarization in another brain area (Friehs & Frings, 2019a;Schroeder et al., 2016).For the online assessment, both tasks were performed concurrent to active tDCS.Moreover, a prestimulation assessment in both tasks was collected after electrodes were fixed, but stimulation had not yet been initiated, as well as a poststimulation offline assessment.All electrodes were held in place after mounting using neoprene caps.
Table 1 presents stimulation parameters of the previous cathodal tDCS studies on the SST, NDE, and SNARC effect, which highlights several differences regarding intensity, electrode size and positioning, and current density.Due to the technical differences, this registered report cannot be considered a direct replication of the previous studies, but we optimized the stimulation parameters for replicability and comparability across our groups.

| Procedure and experimental task
The general procedure was identical for all participants except that tDCS electrodes were fixed to different regions depending on randomized group assignment.Figure 2 displays the overall timeline and study design.After giving consent and filling out questionnaires specified in the next section, electrodes were positioned and the impedance threshold was tested (<10 kΩ).Participants then subsequently performed practice trials and the baseline assessment of the magnitude classification and the SST before tDCS, concurrent to tDCS, and after tDCS.Assessments were interspersed with an idle time of 5 min (Wolkenstein et al., 2014).
Throughout the session, participants were seated comfortably in front of a 19-inch LCD monitor with 60 cm distance to the screen in a dimly lit room and adhered to the task instructions implemented in PsychoPy (Peirce et al., 2019).In both tasks, participants responded by pressing two keys on a standard QWERTZ keyboard placed in front of the monitor according to predefined stimulus-response mappings with their left or right index fingers (interkey distance 11.6 cm).Both tasks were preceded by 20 (or more) practice trials before the first baseline run to ensure that participants understood the tasks (i.e., the practice trials were repeated until participants reached 90% accuracy).The order of magnitude classification and SST was counterbalanced across participants within groups, but held constant within a session.
The magnitude classification task required participants to respond with a left (right) hand key press to small (large; referent: 5) singledigit numbers (i.e., 1-9 except 5).All numbers were presented 25 times in randomized order in each response mapping, resulting in 400 trials (10 blocks of 40 trials), which is in line with recommendations from simulations (Cipora & Wood, 2017).Throughout half of the task, the response mapping was reversed; for larger behavioral effects, all participants began with a congruent block (smaller than 5-left key, larger than 5-right key).Trials began with a short fixation F I G U R E 2 Procedure and study design.The spatial-numerical association of response codes (SNARC) effect and NDE was measured in the magnitude classification task and the stop-signal reaction time (SSRT) (this was corrected relative to the stage I submission, inside the figure and title, order of tasks was changed to SNARC, NDE, and SSRT) was measured in the stop-signal task (SST).The order of magnitude classification and SST were counterbalanced across participants during baseline, tDCS, and post-tDCS.Target electrode position of tDCS was randomly assigned to one of five groups, which were hypothesized to modulate specific behavioral indices (line and box formatting).
TA B L E 1 Overview of stimulation parameters in this study and previous studies using cathodal tDCS on SNARC effect, numerical distance effect (NDE), and stop-signal reaction time (SSRT).a

Study
Behavioral effect tDCS intensity (mA) Note: Target electrode positions according to 10-20 international system of electrode placement.
Abbreviations: NDE, numerical distance effect; SNARC, spatial-numerical association of response codes; SO, supraorbital region; SST, stop-signal task. a This was corrected relative to the stage I submission, we reordered the rows of the table for a consistent presentation.
symbol (#; 250 ms) which was followed by a centrally presented digit.
In line with previous research using the magnitude classification task (Cipora, Soltanlou, et al., 2019;Cutini et al., 2019;Schroeder et al., 2016;Wood et al., 2008), responses were defined as congruent (incongruent) if a left (right) response was given to a digit <5, and vice versa for digits >5 (Di Rosa et al., 2017).Numerical distance (to 5) was considered small for digits 3, 4, 6, and 7, and large for digits 1, 2, 8, and 9. Since we were interested in predefined conditions of the task, and to allow for identical analyses across the tasks, SNARC and NDEs were computed according to these definitions.
The SST was implemented according to the recommendations of the recent consensus paper (Verbruggen et al., 2019) and closely resembling previous studies (Svaldi et al., 2014;Verbruggen et al., 2008).All trials began with a central fixation dot (250 ms) which In both tasks, block-based feedback was provided to reiterate the task instructions, response mappings, and to inform participants about their mean RT and accuracy/number of go omissions and stop probability in the SST (which should be close to 50%).Self-paced breaks allowed for rest between all blocks.The sequence of all trials was fully randomized.
Originally, testing was anticipated to commence after critical re-

| Questionnaire data
Questionnaires were completed in all sessions before and after the stimulation to assess mood changes and adverse effects of tDCS (Brunoni et al., 2011).Participants were asked for various state ratings (current level of motivation, mood, hunger) to separate the experimental assessments and to explore possible side effects and moderators of tDCS, which are reported in the supplementary materials (Tables S2 and S3).After all assessments, we asked participants to rate common side effects of tDCS stimulation on a 5-point Likert-like scale.The rating included the most frequent adverse effects of tDCS: Tingling at the site of the electrode, tingling elsewhere, exhaustion, itching, headache, nausea, and an open category for other sensations (Brunoni et al., 2011).Across groups, adverse sensations should be equal to rule out the possible expectation effects.
Individual differences can influence brain stimulation effects and particularly math anxiety previously moderated the effects of tDCS on performance in tasks with numerical stimuli (Sarkar et al., 2014).
For investigation of the influence of individual differences on brain stimulation, we assessed math anxiety using the Abbreviated Math Anxiety Scale (AMAS) (Hopko et al., 2003).
For other unrelated analyses of the influences of individual differences (Fairburn et al., 2008), some further questionnaires were used to characterize the recruited sample (see Table S1) and further analyses of these questionnaires were not part of the registered report.Proposed analyses focused on correct response times (RTs), because accuracy rates were not affected in the previous tDCS studies on the SST and magnitude classification task (Friehs & Frings, 2019a;Li et al., 2015;Schroeder et al., 2016).This statement refers to the exact tasks under study and does not generalize to other behavioral measures; indeed, many other studies showed effects of cathodal tDCS on error rates (Frings et al., 2018;Wolkenstein et al., 2014) and accuracy appeared to be particularly sensitive for tDCS effects on working memory (Brunoni & Vanderhasselt, 2014;Friehs & Frings, 2019b;Hill et al., 2016).Recordings from the tDCS device were inspected to confirm the continuous delivery of current during the tasks for all participants.

|
For the magnitude classification task, outlier trials with RTs differing more than 2.5 standard deviations from the corresponding cell mean within participants (i.e., congruent, incongruent, low numerical distance, high numerical distance) were omitted (2.49% of all trials were rejected).For each participant and assessment (baseline, tDCS, post-tDCS), the script first calculated mean RTs for incongruent and congruent trials (SNARC effect) and for small and large numerical distance (NDE) and then calculated the RT difference between these two conditions.As outcome-neutral criteria independent of tDCS condition, the significance of the difference between congruent and incongruent trials (small and large numerical distance trials) in the baseline condition confirmed the presence of a SNARC effect (M = 19 ms) and a NDE effect (M = 27 ms) in the recruited sample.
For the SST, data were analyzed according to the proposal by Verbruggen et al. (2019), who extensively investigated the optimal and most reliable method for estimating response inhibition capabilities in this task.First, participants were rejected if their mean RT in go trials was shorter 4 than the mean RT in stop trials (n = 2) (Verbruggen et al., 2019).Next, the precision of the tracking algorithm was confirmed by comparing the mean resulting probability of stopping to P(stop) = 50% and participants were rejected if P(stop) was lower than 25% (n = 2) or higher than 75% (n = 9).In sum, preconditions were met for 92.5% of all participants (remaining n = 148).If the preconditions are met, the SSRT as the indirect indicator of response inhibition can be estimated by using the integration method with replacement of omission errors.The integration method is based on the race model of go and stop processes and SSRT re- Finally, questionnaire data (adverse effects and blinding efficacy) were aggregated accordingly and differences between stimulation groups were controlled for in a separate mixed effects model (between-subjects factor group).Because the tDCS intensity and total current delivery was identical in the active tDCS groups, we expected no statistically significant differences in these questionnaire ratings.We also expected no differences in the adverse sensations questionnaire from the sham tDCS group and the statistical test of the ratings confirmed the validity of the sham control.To quantify whether results favored the null hypothesis, Bayesian comparison to the null model were run as well (see section "performed analyses" for interpretation of Bayes factors).

| Performed analyses
We performed mixed effects modeling and Bayesian quantification of effects using lme4 and lmerTest packages for inferential statistics and the Bayes factors package for Bayesian tests in R 3.5 (Bates et al., 2014;Kuznetsova et al., 2017;Rouder et al., 2009).To investigate the directional primary hypotheses (1-3a.),we tested predefined paired contrasts (i.e., baseline vs. tDCS, baseline vs. post-tDCS) within the specific groups (i.e., group "left PFC" for spatial-numerical associations, "right PFC" for SSRT, "left PPC" for NDE).For unpaired contrasts the Welch corrected degrees of freedom were reported.
Moreover, the comparison to the sham tDCS group was tested in the two-way interaction between the fixed effects time (pre, dur- Considering the hypotheses, the predefined contrasts were as follows: 1. Cathodal tDCS to the left PFC will decrease spatial-numerical According to Cohen (1988), effect sizes are considered "small" for d ≥ .2/ 2 p ≥ .01,"medium" for d ≥ .5/ 2 p ≥ .09,and "large" for d ≥ .7/ 2 p ≥ .25.According to Jeffreys (1961), a BF 10 > 1 indicates anecdotal evidence for H 1 , BF 10 > 3 indicates moderate evidence for H 1 , and BF 10 > 10 indicates strong evidence for H 1 .Vice versa, a BF 10 < 1 indicates anecdotal evidence for H 0 , BF 10 < .33 indicates moderate evidence for H 0 , and BF 10 < .1 indicates strong evidence for H 0 .

| Influence of math anxiety and gender:
Planned exploratory extended models Since individual differences can influence brain stimulation effects and particularly math anxiety previously moderated the effects of tDCS on performance (Sarkar et al., 2014), we compared the full mixed effects models (i.e., 1-3b) with extended models including additional predictors.Main effects and interaction terms were entered simultaneously and separate model comparisons were performed for gender and math anxiety.We considered this an exploratory registered analysis which may explain further variance in the tDCS response.

| SNARC effect and cathodal tDCS of the left PFC (H1a)
To assess stimulation effects on the SNARC effect, within the linear mixed model specified earlier, we tested the two-way interaction of time (baseline, tDCS, post-tDCS) × group (left PFC, sham).

| Exploratory analysis
Given the results, we also explored post hoc whether there was a significant increase of the SNARC effect in the sham group (Figure 3a), which could indicate regression to the mean in the absence of a real tDCS effect.However, the SNARC effect did not significantly increase from baseline to tDCS (t(32) = −1.34,p = .189,d = −.23,BF 10 = .42)and also not from baseline to post-tDCS (t(32) = −.93,p = .362,d = −.16,BF 10 = .27).
Within the left PPC group, the NDE significantly decreased

| Exploratory analysis
Given the results, we also explored post hoc whether there was a significant decrease of NDE in the sham group, which could indicate a general practice effect (Figure 4).Indeed, NDE significantly decreased from baseline to tDCS (t(32) = 2.43, p = .021,d = .42,BF 10 = 1.85) but it did not significantly decrease from baseline to post-tDCS (t(32) = 1.89, p = .068,d = .33,BF 10 = .90).Thus, the pattern was comparable to the reduction of NDE in the active tDCS group.

| NDE and comparison of tDCS stimulation sites (H2b)
To assess regional specificity, we tested the two-way interaction of time (baseline, tDCS, post-tDCS) × group (left PFC, right PFC, left PPC, right PPC).Neither the expected interaction of group and time TA B L E 2 Targeted contrasts of baseline-adjusted group comparisons during tDCS and post-tDCS.As preregistered, we also report baseline-adjusted group comparisons of the left PPC versus the remaining groups (sham, left PFC, right PFC, right PPC).Both during and post-tDCS, there were no significant group differences after Holm correction (see Table 2).

| Exploratory analysis
Given the results, we also explored post hoc whether there was a significant decrease of SSRT in the sham group (Figure 5a).SSRT did significantly decrease from baseline to tDCS (t(30) = 3.85, p = .001,d = .69,BF 10 = 52.9),but not from baseline to post-tDCS (t(30) = 1.78, p = .085,d = .32,BF 10 = .77).A significant time effect for the sham group from baseline to tDCS without any stimulation could indicate a practice effect.Interestingly, this improvement in SSRT was present earlier ("during tDCS") compared to the active tDCS group, who improved later ("post-tDCS").
To clarify the diverging SSRT changes within groups, we performed another exploratory analysis with baselineadjusted SSRT changes.We tested the two-way interaction of time (baseline-adjusted comparisons during tDCS and post-tDCS) × group (right PFC, sham).In this analysis, the interaction of time and group was significant, with anecdotal evidence for the null hypothesis (F(1, 60) = 6.11, p = .016,BF 10 = .33).The result reflects the emergence of an earlier reduction of SSRT in the sham group compared to right PFC tDCS.Neither the main effect of time (F(1, 60) = .01,p = .903,BF 10 = .15)nor the main effect of group (F(1, 60) = .56,p = .453,BF 10 = .61)were statistically significant.

| Influence of math anxiety and gender
To assess the individual differences in brain stimulation effects, main effects and interaction terms of math anxiety and gender were compared and reported according to full mixed effects models.Data on math anxiety were available from 159 participants.

| SNARC effect
To assess the gender differences in brain stimulation effects on the SNARC effect, we tested the three-way interaction of gender (male, female) × time (baseline, tDCS, post-tDCS) × group (left PFC, right PFC, left PPC, right PPC).
However, a significant interaction of gender × time was found (F(2, 238) = 3.27, p = .039,BF 10 = .94).The three-way interaction of gender × group × time was not statistically significant (F(6, 238) = .44,p = .849,BF 10 = .06).Follow-up tests showed that NDE changes over time were contained in both female participants (F(2,178) = 5.01, p = .007,BF 10 = 3.47) and male participants (F(2, F I G U R E 6 Individual differences in math anxiety moderating changes in NDE in milliseconds (ms) between groups (left PFC, right PFC, left PPC, right PPC, sham) and measurement time points (a) (baseline vs. tDCS) and (b) (baseline vs. post-tDCS).Each black dot represents a distinct participant per group, showing the relationship between math anxiety and numerical distance effect from baseline to tDCS/baseline to post-tDCS.The gray shaded area represents the confidence intervals around the smoothed regression lines (in blue).72) = 10.1, p < .001,BF 10 = 186), but changes were more pronounced in male participants (see Table S5).

| DISCUSS ION
We obtained mixed positive and negative results regarding the replicability and regional specificity of cathodal tDCS effects on three distinct aspects of cognitive performance.In this registered report, we replicated that cathodal tDCS over the left PFC reduced the SNARC effect compared to sham tDCS and compared to tDCS over the left parietal cortex.The results also suggested that cathodal tDCS over the right PFC delayed practice-related SSRT improvements, albeit in a secondary exploratory analysis.The results, however, did not support cathodal tDCS effects over left parietal cortex on NDEs.
Furthermore, there was no further evidence for regional specificity of stimulation effects.
Moderator analyses of individual differences (math anxiety and gender) did not provide evidence for attenuation of tDCS effects on cognitive functions in general.However, in individuals with high math anxiety, larger reductions in the NDE were observed in the group receiving tDCS of the right PPC, whereas no such effect was observed in the sham and other groups.The details of the results are discussed separately for each task in the following sections.

| Stimulation effects in the left PFC on the SNARC effect
There were significant differences between the left PFC group and the sham group, as was expected in the preregistered hypothesis.
Within the left PFC group, the SNARC effect decreased significantly from baseline to tDCS and from baseline to post-tDCS.Within the sham group, the SNARC effect did not decrease.Given the baseline differences (see Figure 3), we also examined whether there was a significant increase in the SNARC effect in the sham group, which might indicate regression to the mean, as very low scores at the beginning of a repeated measure would tend to approach the mean (Masina et al., 2021).Notably though, the SNARC effect did not significantly increase.
The observed interaction between group and time is consistent with previously reported cathodal tDCS effects on the SNARC effect in the left PFC (Schroeder et al., 2016).A possible explanation for these neuromodulation results is the dependence of the SNARC effect on working memory functions which are hosted in the PFC (Arsalidou & Taylor, 2011;Baddeley, 2000;D'Esposito & Postle, 2015).This is consistent with the flexible assignments of spatial codes to numbers in working memory (Abrahamse et al., 2016;van Dijck et al., 2009;van Dijck & Fias, 2011), which indicated that numbers can be associated  with different spatial codes based on working memory information (Abrahamse et al., 2016;Fischer et al., 2010;van Dijck et al., 2009;van Dijck & Fias, 2011;Zhang et al., 2022).
Consistent with a previous study by Schroeder et al. (2016), our results showed that reducing PFC activity by cathodal tDCS can reduce automatic implicit associations.However, the evidence for regional specificity for this effect was limited.On one hand, planned post hoc contrasts significantly differentiated left PFC and left PPC and descriptively the largest difference occurred between the left PFC and the sham control condition.These findings could indicate a special role of the left hemisphere for the SNARC effect and confirm that the cognitive mechanism of the SNARC effect depends on PFC function.In contrast, stimulation of the (left) parietal cortex did not change the SNARC effect not only in our study, but also in previous tDCS experiments (Di Rosa et al., 2017).We, therefore, are inclined to conclude that the SNARC effect depends on the PFC rather than the PPC.Theoretically, a neurofunctional origin of the SNARC effect in prefrontal regions is consistent with a working memory account of the SNARC effect (Schroeder et al., 2016;van Dijck & Fias, 2011).
On the other hand, the current state of the results raises the question of the distinct effects of cathodal tDCS on the SNARC effect, that is, its regional specificity, as most stimulation configurations somewhat led to similar reductions.These present results underline the weak spatial resolution of tDCS and weak discrimination of different regions.To have a better spatial resolution, TMS can be used (e.g., Rusconi et al., 2011).For example, Rusconi et al. (2011) showed that the right frontal regions, in particular the right frontal eye field and the right inferior frontal gyrus, were also differentially involved in SNARC effect (Rusconi et al., 2011).Alternatively, inferences about regional specificity can be strengthened by combining tDCS with neuroimaging such as functional near-infrared spectroscopy (Cutini et al., 2014).
Alternatively, another possibility is that the neurocognitive mechanism underlying the SNARC effect is represented bilaterally.
A possible stimulation protocol to investigate this further could be bicephalic cathodal tDCS: For example, Klein et al. (2013) used bicephalic cathodal tDCS by stimulating the bilateral intraparietal cortices to modulate numerical processing.They reported that bilateral parietal cathodal tDCS could inhibit the processing of number magnitude information.Considering that the results of Klein et al. (2013) support the idea that magnitude information is represented bilaterally in the intraparietal cortices, it is of interest that this has also been reported in fMRI (Arsalidou & Taylor, 2011).Therefore and relevant to our study, as working memory is also coordinated across multiple brain networks (Pupíková et al., 2022), the SNARC effect in the left PFC could be linked to the contralateral hemisphere.As a result, one could speculate that simultaneous bilateral cathodal tDCS of left and right PFC could induce stronger reductions in the SNARC effect.Accordingly, in this study, unilateral left and right PFC tDCS led to comparable reductions of the SNARC effect, providing no support for an assumed left lateralization.At the same time, a recent model on the SNARC effect proposes a mixture of influences, sometimes acting in opposite directions, might lead to the behaviorally observed SNARC effect, which may explain the obscured regional specificity of the SNARC (Cipora et al., 2020).

| No stimulation effects of the NDE
In contrast to the SNARC effect, which associates numerical magnitude with spatial directions, numerical magnitude processing itself is more established to recruit parietal regions such as the horizontal segment of the intraparietal sulcus, the angular gyrus, and the posterior superior parietal lobe (Arsalidou & Taylor, 2011;Cutini et al., 2014;Dehaene et al., 2003).As previously suggested, the bilateral left and right PPC support number magnitude processing (Dehaene et al., 2003;Li et al., 2015).The efficacy of cathodal stimulation of the left versus right PPC on numerical processing was investigated in this study in the NDE.
There was no evidence for stimulation effects for the left or right parietal cortex.Instead, NDE decreased to similar extent in all groups, pointing at a general practice effect rather than a stimulation-induced effect (Sandrini et al., 2012).
Our null finding on the NDE is inconsistent with previous evidence from bipolar tDCS (Li et al., 2015) and TMS (Cappelletti et al., 2007).Previously, Li et al. (2015) observed a modulation of numerical distance by bipolar tDCS (i.e., tDCS of both parietal regions, cathode over the left PPC) and showed slower responses to pairs that were numerically in close distance.Thus, they applied a different tDCS configuration, namely a bipolar design with distinct cortical lateralization.Furthermore, it should be noted that a more difficult number comparison task was used in their study.Similarly, an effect of bicephalic parietal tDCS on numerical distractordistance effect was observed in more challenging multidigit addition (Klein et al., 2016).In a follow-up study (Artemenko et al., 2015) with the same task and unilateral instead of bilateral parietal stimulation, the authors did not find modulations of the distance effect.Taken together, number magnitude processing might be rather bilaterally represented in the parietal cortex and thus unilateral stimulation does not sufficiently impact on it.
Moreover, also the difficulty of number classification versus number comparison tasks with single-or multidigit stimuli might contribute to a higher sensitivity of NDE to tDCS, especially considering the robustness of the NDE in general (Hohol et al., 2020).
Consistent with this view, cathodal tDCS previously improved cognitive performance in high-load cognitive functions only (Weiss & Lavidor, 2012).Moreover, Schroeder et al. (2017a) reported that the tDCS effect was only effective when classifying digit magnitudes, but not when classifying digit font colors.Additionally, the reduction in high attentional load in bilateral tDCS was independent of the direction of polarity (Roe et al., 2016).Finally, also the weak spatial resolution of tDCS should be considered.Using inhibitory rTMS instead, Cappelletti et al. (2007) found a stronger effect of numerical distance after inhibitory rTMS at the left intraparietal sulcus.
To summarize, we outlined two methodological differences that can explain our results.Given that unilateral tDCS showed no effect of tDCS, bipolar stimulation might be required, possibly due to the bilateral representation of numerical processing.Second, task difficulty with a fixed versus variable referent number and single-versus multidigit numbers may be relevant to determine stimulation efficacy.Furthermore, as there were no distinct cathodal tDCS effects on the NDE in the left parietal cortex, and no effects of the stimulation configurations were found in other brain regions, providing no evidence for regional specificity in the stimulation effect.2023) also showed that 1 and 1.5 mA cathodal tDCS decreased muscle strength, while 2 mA tended to increase strength in certain muscles.Although we applied a relatively low intensity of 1 mA in this study, it is possible that the induced electric field may have already exceeded the effective dose-response in some individuals, contributing to some of the observed null findings.Overall, the relationship between the applied dose of tDCS (current strength, duration, electrode placement) and its effects on brain function is not well established, especially regarding cognitive behavioral outcomes.

| Possibly time-dependent stimulation effects on SSRT
The current study did not replicate the effects of cathodal tDCS over the right PFC on inhibitory control.Across three repetitions of the task during one session, participants improved in their inhibitory control, indicated by shorter SSRT, likely through practice.Such practice effects were already observed in the SST (Ditye et al., 2012) and in other domains (Sandrini et al., 2012).However, we also noted that SSRT improvements showed some differences across online and offline tDCS and corroborated these observations in exploratory analyses: In the sham condition, improvement was immediate during tDCS (t2), whereas in the cathodal tDCS condition, improvement was delayed and emerged post-tDCS (t3).
Accordingly, in comparison to the observation of increased SSRT following cathodal tDCS (Friehs & Frings, 2019a), the present results might indicate that an improvement in SSRT due to practice was delayed due to cathodal tDCS in our study.This interpretation is also in line with a recent study that showed immediate effects of anodal tDCS on inhibitory control in restrained eaters only in the first block of an SST (Schroeder et al., 2022).Given the importance of inhibitory control in everyday life, this function might quickly re-establish following an initial reaction due to external neuromodulation.Therefore, we would argue that the effects of tDCS could depend on prior task performance/brain state.However, this interpretation should be considered preliminary and requires further confirmatory research.
Exploratory group comparisons were also conducted following the unexpected differential SSRT changes for stimulation of parietal regions in comparison to sham tDCS.There was a significant difference between the left PPC and sham tDCS, and between the right PPC group and sham tDCS, like the initial delayed improvement in the right PFC group.While this was not initially addressed in our planned analysis, reconsidering the neurophysiological underpinnings of inhibitory control (Chambers et al., 2023;Schroeder et al., 2020) provides implications for interpreting this additional result.Accordingly, with the present parameters it is possible that by cathodal tDCS in this study (cf. Figure 1) regional specificity was not achieved and instead, stimulation of the larger inhibitory control network might have induced similar delays of improvements.Precisely, in the PPC conditions, other hubs of the inhibitory control network such as motor regions (e.g., presupplementary motor area) and the inferior parietal lobe might have been modulated (Aron, 2011;Swann et al., 2012).However, different results were obtained by anodal tDCS of the right IPL and IFG in a related study, showing no modulation of SSRT by anodal stimulation of IPL (Cai et al., 2016).Further confirmatory research is needed to clarify these conflicting results and their possible polarity dependence.To summarize, we observed practice-related improvements and suspect tDCS-related improvement delays in SSRT by stimulation of the right PFC.Considering also the immediate, but not prolonged effects of anodal tDCS on SSRT in previous studies, the time-dependent effects of tDCS on inhibitory control may depend on the previous brain state.Given the unexpected SSRT changes with stimulation of parietal regions compared to sham, a reconsideration of the neurophysiological basis of inhibitory control provides implications for the interpretation that regional specificity was not achieved by cathodal tDCS in this study and that, instead, stimulation of the larger inhibitory control network may have induced similar improvements in various regions.

| Influence of trait math anxiety
As stimulation effects might depend on individual differences such as math anxiety (Cohen Kadosh et al., 2007;Sarkar et al., 2014), we observed in this study that individual differences in math anxiety moderated only the effects of brain stimulation on the NDE.Individuals with high math anxiety showed a greater reduction over time in the NDE when stimulated at the right PPC, whereas no such effect was observed in the sham and other groups.Accordingly, our results extent previous observations of trait-specific tDCS effects (Xiang et al., 2021) in which individuals with low trait anxiety had a stronger behavioral response to tDCS than individuals with high trait anxiety.In individuals with high mathematics anxiety, however, tDCS improved reaction times and stress (Sarkar et al., 2014).Thus, greater anxiety can also lead to larger effects of cathodal tDCS.While this observation adds to accumulation evidence of psychological states as moderators of tDCS, the specificity of this finding in the present case to the right PPC is puzzling and unexpected.However, the small Bayes factor provides anecdotal evidence in the favor of alternative hypothesis.Thus, further research into the moderating effects of anxiety in neurostimulation studies may resolve and further explain its influence.

| Influence of gender
Recruitment was stratified by gender and systematically analyzed (cf.Wierenga et al., 2023 preprint).The analyses showed a moderated influence of gender with larger SNARC effects in males than in females, and with larger changes in NDE in males.This observation was somewhat surprising, given that most previous large-scale studies showed equivalent SNARC effect across gender (Cipora, Soltanlou, et al., 2019;Cipora, van Dijck, et al., 2019 preprint;but see Bull et al., 2013).Regarding SSRT, a significant interaction of gender and time indicated that SSRT improvements over time were contained in females, whereas males showed no practice-related improvement.
As individual differences were not the primary goal of this study, though gender assignment to groups was stratified, the subgroup sizes in these analyses were small and further, targeted investigation is warranted.However, crucial factors were controlled in our study (such as age, handedness, healthy population, and other parameters that could influence stimulation, such as nicotine, psychological, and neurological disorders) (Rudroff et al., 2020).
Future research should continue to consider individual differences, including anxiety, the role of menstrual cycle (Dubol et al., 2021), and particularly include differences in neuroanatomy or neural effects of tDCS, if possible.

| Limitations
The major limitation in our study was the difference between groups at baseline in SNARC effect, which appeared despite tions, including the brain stem.In addition, for this study, power analyses were conducted based relatively moderate-to-high effect sizes reported in the literature; it is important to highlight that this may not reflect the overall smaller effect sizes of tDCS in meta-analyses (Jacobson et al., 2012;Schroeder et al., 2020).
Accordingly, a sample size of 32 participants per group is still relatively small for a between-subject tDCS design, as pointed out by the reviewers.

| CON CLUS ION
In conclusion, the findings of the current registered report show that: (i) the regional specificity of cathodal tDCS effects on cognitive performance was weak, with few distinctions between stimulation sites, 2. Cathodal tDCS to the left PPC will decrease the NDE (a), but the other stimulation conditions (left + right PFC, right PPC) will not have an effect (b).
3. Cathodal tDCS to the right PFC will decrease response inhibition (a), but the other stimulation conditions (left PFC, left + right PPC) will not have an effect (b).
followed by the subsequent attractive stimulus in either the left or right box for maximum 2 s.The majority of trials (75%) consisted of a go-task (left or right-hand key press according to the presentation of a stimulus picture in one of two horizontally arranged boxes while the other box remained empty).The remaining trials (25%) amended a stop signal (a blue frame surrounding the target box) after a variable delay (stop-signal delay, SSD) which was initially set to 250 ms and continuously adjusted by ±50 ms after correct/incorrect inhibition in stop trials (SSD boundary minimum: 50 ms; maximum: 900 ms; staircase adaptation).Thus, the overall probability of correct responding in stop trials should be ~50%.Participants were instructed to select the side on which the picture had appeared as quickly as possible and not wait for the stop signal to occur.A jittered intertrial interval of 300-600 ms separated trials.Incorrect or late responses (>2 s in go trials) elicited immediate feedback in form of the German words "Fehler" (Eng."error") or "Bitte schneller antworten!"(Eng."please respond faster!") for 500 ms.Participants completed 4 blocks of 64 trials, thus a total of 64 stop trials and 192 go trials were analyzed for each assessment.
visions of the preregistered stage I review and following in-principle acceptance in January 2020 and to complete in October 2020.Analysis and preparation of the final manuscript was expected to finalize in December 2020, with an anticipated resubmission date on February 1, 2021.The actual data collection was delayed by the onset of the Covid 19 pandemic in March 2020, before any experiments had been performed.Despite the following coronavirus waves and corresponding lockdown periods in Germany from 2020 to 2022, data collection could be completed by the end of May 2022.Due to the hygiene protocol at our university, participants had to wear a mask throughout the session.Link to the approved stage I protocol: https:// doi.org/ 10. 1002/ jnr.24559 .
Data treatment and proposed analyses 2.6.1 | Data treatment New participants were recruited in cases of technical problems (e.g., failure to achieve electrode impedance threshold, automatic abortion of stimulation for unexpected sudden movements, and impedance increases [n = 13]; objective documentation of continuous stimulation and resistance was granted by stimulator recordings) or erroneous performance in any of the tasks (defined as overall response latencies or overall accuracies deviating more than 3 standard deviations from the mean of the overall sample or at chance level in either baseline or tDCS assessment).Moreover, data were rejected and replaced if more than 20% of the trials were missing in any task in either assessment (n = 0).
the point at which the stop process finishes by considering and integrating the individual RT distribution according to the stopping probability.SSRT is estimated as the difference between the nth go RT (with n = total number of go-trials × P(stop) according to the individual stopping probability) and the mean stop-signal delay (seeVerbruggen et al., 2019).For example, if an individual's stopping probability was .40, the .40× 192 = 76th fastest go RT were used from the individual's distribution of all go trials.Premature responses on unsuccessful stop trials and choice errors were included when calculating the mean SSD and the nth RT, respectively, because this version of the integration method produced the most reliable and least biased estimates of SSRT(Verbruggen et al., 2019).For the same reason, omitted responses were replaced with the maximum RT in order to compensate for the lacking RT in the determination of nth fastest go RT(Verbruggen et al., 2019).As higher SSRT values indicate worse response inhibition, we expected an increase in SSRT during cathodal tDCS to the right PFC to indicate impaired response inhibition.
ing, post) and group (active, sham).Participants were entered as random effect.The secondary hypotheses (1-3b.)were substantiated by the interaction between the fixed effects time (pre, during, post) and target electrode position (left PFC, right PFC, left PPC, right PPC).Participants were entered as random effect.Simple contrasts of baseline-adjusted values (tDCS, post-tDCS) were performed with the specific reference group according to the hypotheses (see below).Bonferroni-Holm correction was applied to control for multiple comparisons.For Bayes factor calculation, we omitted the interaction term of interest in a comparison to the full model by calling the lmBF() function.

F
I G U R E 3 (a) Mean SNARC effect in milliseconds (ms) ± standard deviation as a function of stimulation condition (left PFC vs. sham) and time (baseline, tDCS, post-tDCS).(b) Mean change in SNARC effect (in ms) as a function of stimulation condition (left PFC, right PFC, left PPC, right PPC, sham) and measurement time points (tDCS vs. baseline) and (post-tDCS vs. baseline).

F
I G U R E 4 Mean NDE in milliseconds (ms) ± standard deviation as a function of stimulation condition (left PPC vs. sham) and time (baseline, tDCS, post-tDCS).
cally significant (F(6, 238) = 3.37, p = .003,BF 10 = 8.21), driven by a larger SNARC effect for females in right PFC during tDCS (M = 18.2 ms, SD = 20.1 ms) than for males in right PFC during tDCS (M = 14.1 ms, SD = 28.5 ms), and a larger SNARC effect for females in right PFC post-tDCS (M = 19.8ms, SD = 20.3ms) than for males in right PFC post-tDCS (M = 11.1 ms, SD = 20.3ms) with different spatial codes based on their position in a maintained working memory sequence.Precisely, in their experimental settings, left hand responses were faster than right hand responses to numbers at the beginning of a verbal working memory sequence, suggesting that numbers can be flexibly associated and even reversed TA B L E 3 Mean (SD) adverse sensations between tDCS conditions.
randomization and strict consideration of possible moderator variables.Moreover, most stimulation configurations resulted in similar effects, which could be attributed to the low distinct effect of tDCS and the weak spatial resolution.Given that we tested unilateral tDCS, the present results might not generalize to bipolar or bicephalic stimulation configurations.For tasks that might be coordinated bilaterally, bicephalic tDCS might provide an interesting option to modulate the SNARC effect and other, possibly bilaterally represented cognitive functions.Furthermore, there are additional task parameters (e.g., difficulty, number of trials) that could influence the efficacy of tDCS.It should be noted that all data were collected during the Covid-19 pandemic.Due to official regulations, all participants wore mouth and nose protection throughout the session, which may have affected their performance to some extent.Another possible limitation of the study is the relatively diffuse current flow of tDCS.Although the placement of the anode on the participant's contralateral upper arm in our design avoided a dense anodal electric field in another brain region, this placement also induced relatively broad and diffuse current flow in all condi-

(
ii) individual differences can moderate and conceal tDCS effects, for example, gender and trait math anxiety, (iii) with the right technical, task, and population parameter settings (e.g., regarding electrode montage, task difficulty, and gender), replicable tDCS effects might be possible.D ECL A R ATI O N O F TR A N S PA R EN C YThe authors, reviewers, and editors affirm that in accordance with the policies set by the Journal of Neuroscience Research, this manuscript presents an accurate and transparent account of the study being reported and that all critical details describing the methods and results are present.AUTH O R CO NTR I B UTI O N SConceptualization: P.S., C.A., K.C., and J.S. Data curation: M.F., P.S. Methodology: M.F., P.S., C.A., K.C., and J.S. Investigation: M.F., P.S., and J.S. Formal analysis: M. F., P.S., C.A., and K.C. Writing -original draft: M.F. and P.S. Writing -review and editing: M.F., P.S., C.A., K.A., and J.S. Project administration: M.F., P.S., and J.S. Visualization: M.F. and P.S. Supervision: P.S. and J.S. Funding acquisition: P.S.ACK N OWLED G M ENTSThis research is enabled by a grant from the German Research Foundation/Deutsche Forschungsgemeinschaft awarded to PhilippS U PP O RTI N G I N FO R M ATI O NAdditional supporting information can be found online in the Supporting Information section at the end of this article.Data S1.Transparent Peer Review Report

Task Reference Contrast During tDCS Post-tDCS Test statistic p p cor d BF 10 Test statistic p p cor d BF 10 SNARC
*p < .05.

TABLE S2 .
Effect of tDCS on current level of motivation, mood, and hunger.

TABLE S3 .
Moderator analysis of tDCS by current level of motivation, mood, and hunger.

TABLE S4 .
Gender differences in brain stimulation effects on the SNARC effect.

TABLE S5 .
Gender differences in brain stimulation effects on the NDE.

TABLE S6 .
Gender differences in brain stimulation effects on the SSRT.