EEG recording

The participants performed 192 trials of the CWST during the EEG recordings before and after the stimulation. Event-related EEG was acquired at a sampling rate of 1000 Hz and with DC (0 Hz) included with a NeuroConn NeuroPrax EEG device (NeuroConn, Illmenau, Germany).

No bandpass or notch filter was applied during recording. The reference was placed at the right mastoid but the EEG activity was later rereferenced to common average. 28 Ag-AgCl electrodes were positioned at Fp1, Fp2, F7, F3, F4, F8, FC5, FC1, FC2, FC6, T3, C3, Cz, C4, T4, CP5, CP1, CP2, CP6, T5, P3, Pz, P4, T6, O1, O2. Impedances were kept below 20 kΩ. Two EOG channels were used to send electrical trigger inputs from the presentation software PsychoPy and demarcate fixation and trial periods. The data were epoched between 1 s before and 1.7 s after stimulus presentation. Epochs of error trials and of post-error trials were removed. The epochs were demeaned over the complete duration and detrended. Epochs with high variance or high kurtosis were removed automatically before electrical and muscular artifact-containing epochs were eliminated manually. Eye blinks and lateral eye movements were eliminated using independent component analysis (Jung et al., 1998). The EEG data preprocessing was done using the FieldTrip toolbox (Oostenveld et al.,2011).

3.3.6 Analysis

All analyses were conducted in the R software (R Core Team,2018) if not stated otherwise.

3.3.6.1 Sleep and arousal At the beginning and end of each experimental session the partici-pants self-reported their arousal on a scale from one (tired) to ten (completely awake). Similarly, they reported sleep quality in the prior night on a scale from 1 (bad) to 5 (good). Higher arousal levels increase error rates in incongruent trials (Pallak et al., 1975), while sleep deprivation generally increases RT without changing interference or facilitation (Cain et al.,2011). Both in-dicators were individually compared across stimulation conditions employing a non-parametric paired sample Kruskal-Wallis test.

3.3.6.2 Generalized linear mixed models for behavioral data Generalized linear mixed models (GLMM) are used in research designs in which not normally distributed data from mul-tiple non-independent data sources is analyzed (Breslow and Clayton, 1993). We analyzed all GLMM with the package lme41.1-15 in R (Bates et al.,2014). During response time tasks mul-tiple participants respond many times, creating datasets in which each participant has a unique data distribution. The RT are analyzed without averaging per participant, but acknowledging the individual participants as non-independent data sources, thus increasing the statistical power.

Additionally, RT distributions have a right skew as responses can be given until trial termination (1.5 s after stimulus presentation) and necessarily are of a positive value. An inverse Gaussian distribution was used to account for this distribution (Lo and Andrews, 2015). Participants and word-color per trial were included as random effects in all GLMM for behavioral data. Thus, individual differences in speed are accounted for the across-person variability.

For the GLMM of the phase during which transcranial stimulation was applied the categorical fixed factors congruency of current trial (CCT; factor levels: congruent, incongruent), congru-ency of previous trial (CPT; factor levels: congruent, incongruent) and stimulation (factor levels:

sham, 4 Hz tACS, 6 Hz tACS, tRNS) were sum-coded. For the fixed effect stimulation, sham stimulation was compared to each other stimulation. The main interaction and the triple interac-tion between CCT, CPT and stimulainterac-tions including all double interacinterac-tions were analyzed.

For the GLMM of the phases before and after which transcranial stimulation was applied also the categorial fixed factors CCT and stimulation were sum-coded together with time (factor levels: before stimulation, after stimulation). For the fixed effect stimulation, sham stimulation was compared to each other stimulation. We analyzed the main effects of all three factors, all double interactions and their triple interaction.

We report the Z-values and p-values of the effects via the Welch-Satterthwaite’s approximation method (Kuznetsova et al.,2017).

3.3.6.3 Time-frequency analysis Only 23 participants met the inclusion criterion of having at least 20 trials per condition and therefore were included in all analyses. Based on the observa-tion that non-phase locked theta power is predictive of behavioral outcomes (Cohen and Donner, 2013), we excluded theta power phase-locked to stimulus or response in the time-domain from our analysis.

The time-frequency power was calculated from 2 Hz to 30 Hz using a 5 cycle Morlet wavelet (gwdith = 2). The complete epoch was baseline normalized into normchange space against the mean value between -400 ms to -100 ms. As first step the averaged time-frequency power from all conditions and participants was plotted per electrode. Three electrodes (FC1, FC2, Cz) with strongest theta power changes over the midfrontal areas were selected for further analysis . The data of these three electrodes was averaged over all participants, times, trials and conditions.

As this grandaverage incorporates all data, it is orthogonal to any possible differences between conditions. The time-frequency window of interest (400 ms – 750 ms, 3.7 Hz – 6.6 Hz) is similarly reported in previous literature, and was chosen in accordance with a local maximum in the grandaveraged data (Hanslmayr et al., 2008). This narrow approach best serves to test the hypothesis that the clearly defined cognitive processes during Stroop task were changed by after-effects of transcranial stimulation.

Figure 10: Time-frequency data from the electrodes FC1, FC2 and Cz was averaged over congruency conditions, time points and participants. The left panel shows the topographical distribution of the local maximum in the ROI.

In the right panel the region of interest (ROI, red box) was determined by a local maximum in theta power that was not phase-locked to presentation of stimulus (dotted line). The region of interest is between 400 ms to 750 ms and 3.7 Hz to 6.6 Hz.

Statistical analysis of EEG The mean power value within this time-frequency window was extracted for every trial. The values were exported to R and entered into a 2 linear mixed model with three fixed factors (CCT, factor levels: congruent vs. incongruent; time, factor levels:

before stimulation, after stimulation; stimulation condition, factor levels: 4 Hz tACS, 6 Hz tACS, tRNS, sham). Assumptions of normality were tested both by plotting and by Shapiro-Wilk-tests. While the tests were more compatible with the time-frequency data not being normally distributed, the visual inspection of histograms and quantile-quantile plots confirmed that the data can be assumed to be distributed normally. We report the Z-values and p-values of the effects via the Welch-Satterthwaite’s approximation method (Kuznetsova et al.,2017).

3.3.6.4 Drift diffusion models for conflict tasks We used the drift diffusion model for con-flict tasks (DMC) to model the behavioral data (Ulrich et al., 2015). This model allows de-composing RT and accuracy of two-alternative forced choice tasks into several parameters that underlie the decision process. The accumulation of evidence begins with the first information that reaches the brain, and as soon as it reaches a certain threshold for one alternative, a decision is being made (for an introduction please consult (Ratcliff, 1978;Ratcliff and McKoon,2008).

Total RT is divided into the decision process (D) and the residual time (R), which includes the sensory processing of stimulus and response execution (Ulrich et al.,2015). DMC decomposes the D into several parameters by accounting for the RT and accuracy of both congruent and incongruent trials. For a response to occur the boundary (a) has to be crossed by the evidence accumulation. R is characterized by the nondecision (Ter) and the variability of Ter (s_r). A controlled process integrates task-relevant information whereas an automatic process integrates task-irrelevant information. The controlled process has a constant drift rate (μc), whereas the drift rate of the automatic process is changing over time. It’s best described by a gamma density function which decays over time after an early maximum. The underlying parameters amplitude (ζ), the time point of maximal amplitude (tmax) and the time at which 90 percent of the distri-bution has decayed (t₉₀;Ulrich et al.,2015). We fitted the model as has been described byLehr et al.(2019).

3.4 Results