Auditory stimulus and tACS optimization pipeline.

a) Stimulus representation. A complex noise stimulus is frequency modulated at 2 Hz without any rhythmic modulation of its amplitude. Silent gaps are presented at different phase locations of the FM-stimulus modulation cycle. b) Group data showing the regions exhibiting higher BOLD signal during the FM- stimulus presentation compared to the implicit baseline, p(FWE) < 0.05. Distribution plots in the center show the beta estimates extracted for the whole cluster for each participant per hemisphere. Box plots show median (horizontal dashed lines), mean (black cross), 25th and 75th percentiles (box edges) and extreme datapoints not considered outliers (+/–2.7σ and 99.3 percentiles, whiskers). Each circle represents a single participant. c) Overlap of single-participant binary masks after thresholding the individual t-maps for the same contrast as shown in (b). d) Pipeline for optimizing the tACS electrode montage for each individual participant to target the individual functional targets. e) Target regions of interest used for the optimization step in SimNIBS. Individual dots represent the individual 3-mm-radius spheres around the center coordinates from the functional masks shown in (c). f) Electrodes included in the optimized montages across participants. g) Electric field (E) and electric field strength (normE) resulting from the optimized montage for one example participant. Only the left hemisphere is shown. Blue and red circles denote the resulting electrodes. Small red arrows on the inset show the target E-field orientation.

Electric field simulation results.

a) Group average maps showing the strength of the simulated electric field (E-field strength, right) and its normal component (normal E- field, middle), separated by montage: high-definition montage (HD), top; standard montage, middle, and individualized montage, bottom. Each montage is represented in the left subpanel. b) Plots showing the individual values for the seven E-field parameters estimated per montage and participant. Each dot represents a single participant. Box plots show median (dashed vertical lines), mean (cross in the middle of the box), 25th and 75th percentiles (box edges) and extreme datapoints not considered outliers (+/–2.7σ and 99.3 percentiles, whiskers). Red crosses represent outliers (more than 1.5 times the interquartile range away from the bottom or top of the box). Note that outliers were not excluded from analyses. *p < 0.05, **p < 0.001, Bonferroni corrected.

tACS effects and individual variability.

a) While performing the auditory task, participants received either sham (blue) or 2-Hz tACS stimulation. The phase lag between the FM stimulus (black) and the tACS signal varied from trial to trial and was grouped into six different phase-lag bins. Each color in the figure represents a different bin. Empty black circles in the circular plot on the left mark the phase in the center of each bin. b) Hit rates as a function of FM-stimulus phase separated by tACS condition for both sessions (S1 and S2) from 3 example participants. Colors follow the same coding as in (a). c) Amplitude of the FM-stimulus driven behavioral modulation (FM-amplitude) and optimal FM-stimulus phase (FM-phase) in the sham condition. Left top plot shows the FM-amplitude values from the sham condition. Vertical lines represent the mean 95 percentile from individual surrogate distribution, session 1 dashed line, session 2 solid line. Each dot represents a single participant. Box plots show median (dashed vertical lines), mean (cross in the middle of the box), 25th and 75th percentiles (box edges) and extreme datapoints not considered outliers (+/–2.7σ and 99.3 percentiles, whiskers). Crosses represent outliers (more than 1.5 times the interquartile range away from the bottom or top of the box). Scatter plot on the right top shows the FM-amplitude in session 2 (S2) as a function of FM-amplitude in session 1 (S1). Dashed line is the diagonal and the solid line the best-fit regression line. Circular plots in the bottom panel show the optimal FM- phase for each session and the circular distance between sessions. The black line is the resultant vector. d) Optimal FM-phase separated by tACS lag condition. Each plot shows a different phase lag according to the coordinates presented in top left legend. Color code also matches that from panel (a). For each plot, session 1 is presented in the corresponding color and session 2 in gray. The resultant vector is shown following the same convention. e) FM-amplitude as a function of tACS phase lag for 4 single-participant examples. Solid lines show true data and dashed lines the cosine fit. Only session one is shown.

Group level tACS results.

a) Amplitude of the FM-stimulus driven behavioral modulation (FM-amplitude) as a function of the realigned tACS lag conditions. Zero lag corresponds to each individual optimal tACS lag (based on a cosine fit). FM-amplitude for optimal lag and the opposite lag (marked with red x in the x-axis) were removed from further analyses and an estimate of FM-amplitude for the positive (tACS(+)) and negative tACS half cycles (tACS(-)) was obtained by averaging the individual FM-amplitude values from the two bins adjacent to the optimal lag (marked in pink in the x-axis) and its corresponding trough (marked in green in the x-axis), respectively. b) FM-amplitude values estimated for sham, tACS(+), and tACS(-), as described in (a), averaged over sessions. In all plots in the figure, each dot represents a single participant. Box plots show median (dashed vertical lines), mean (cross in the middle of the box), 25th and 75th percentiles (box edges) and extreme datapoints not considered outliers (+/–2.7σ and 99.3 percentiles, whiskers). Crosses represent outliers (more than 1.5 times the interquartile range away from the bottom or top of the box). S1: session 1, S2: session 2. *p = 0.05, **p

Effects of tACS on behavioral signatures of entrainment were not reliable over sessions.

a) Amplitude of the tACS effect (tACS-amplitude) for session 2 as a function of session 1. tACS-amplitude was computed as the difference between the FM-amplitude values at tACS (+) and tACS (-) in Fig. 4b. Dashed line is the diagonal and gray solid line represents the regression line. Each dot represents a participant b) Optimal tACS phase lag (tACS-phase) estimated from the cosine fits in (Fig. 3e). The first two circular plots show optimal tACS-phase for each session while the third one shows the circular distance between sessions. The black line is the resultant vector. c) The scatter plot shows the amplitude parameter obtained from fitting the cosine function to each session independently (as in b) and then averaged across sessions as a function of the fit amplitude obtained when fitting the cosine function to the data pooled across sessions. S1: session 1, S2: session 2.

Predicting tACS effects from electric field simulation.

a) Interaction between the normal E-field and the field focality. Scatter plot on the left shows tACS effects (tACS- amplitude) as a function of the normal E-field. Each dot represents a different subject. Dot color and size represent the normalized field focality in arbitrary units. Higher values correspond to more focal electric fields. Solid lines represent the predicted adjusted response for the tACS- amplitude as a function of the normal E-field for three fixed values of focality. The plot in the right shows the main effects (blue) of focality and normal E-field and the conditional effect of each predictor given a specific value of the other (red). Horizontal lines through the effect values indicate their 95% confidence intervals. b) Interaction between the normal E-field and the distance between the peak of the E-field and the target ROIs (Dist2Peak). Similar to (a), scatter plot on the left shows tACS-amplitude as a function of the normal E-field but dots color and size now represent the normalized Dist2Peak. Higher values correspond to shorter distance. Solid lines represent the predicted adjusted response for the tACS-amplitude as a function of the normal E-field for three fixed values of Dist2Peak. The plot in the right shows the main effects (blue) of Dist2Peak and normal E-field and the conditional effect of each predictor given a specific value of the other (red). Horizontal lines through the effect values indicate their 95% confidence intervals. Colors in the bottom for the Focality and Dist2Peak levels correspond to the same color code in the upper plots.