Using one-size-fits-all montages for tACS can lead to high inter-individual variability in terms of the induced electric field and the strength of tACS effects. Here, we go a step past the current literature by individualizing the tACS montages to target individually defined functional targets and compare their electric field properties relative to two different group montages previously used in the literature for targeting auditory regions (Figures 1–2; van Bree et al., 2021; Baltus et al., 2018).

Figure 1

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Figure 2

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Listeners participated in one magnetic resonance imaging (MRI) session where functional and structural MRI datasets were collected. During the functional runs, participants listened to a 2 Hz FM stimulus and detected silent gaps presented at different phase locations along the modulation cycle (Figure 1a, see Materials and methods). As expected, increased BOLD signal in auditory temporal areas, including bilateral Heschl’s gyri and superior temporal gyrus, was observed in response to the auditory stimulus (Figure 1b). Target regions of interest (ROI) were defined for each individual as the brain regions exhibiting the strongest response to the FM-stimulus (one per hemisphere, see Materials and methods, Figure 1c and e, Supplementary file 1a).

Using individual finite element method (FEM) head models (see Materials and methods) and the lead field-based constrained optimization approach implemented in SimNIBS (Saturnino et al., 2019), the individual electrode montage was optimized to focus the electric field as precisely as possible at the target ROI, with a field orientation matching an auditory dipole as estimated in a previous study targeting auditory regions (Baltus et al., 2018), and a desired field intensity of 0.09 V/m (Figure 1d–g, see Methods). The resulting individual montages varied across participants and could take on two out of seven different electrode positions for the left hemisphere: FC5, C1, C3, C5, T7, TP7, P7, and two out of nine different electrode positions for the right hemisphere: FC4, FC6, C2, C4, C6, T8, TP8, P8, and PO8. Despite some variability, the most common montages included the electrodes C5-TP7 and C6-TP8, with for example TP7 being used for 34 out of 39 participants (Figure 1f).

Electric field simulations were performed for each individual brain using the individually optimized montage (from now on referred to as individualized montage) with electrodes placed differently across participants, as well as two additional montages from the literature, with electrodes placed at the same positions across participants (Figure 2a, see Materials and methods): (1) same electrode shape and size as for the individualized montage but placed over FC5-TP7/P7 and FC6-TP8/P8 (referred to as standard montage in the rest of the document) as in Baltus et al., 2018, and a ring-electrode montage with center electrodes placed over T7 and T8 similar to the montage previously used by van Bree et al., 2021.

To compare between tACS montages in terms of their simulated electric field profiles, seven different dependent measures were computed for each participant and montage. Two measures referred to spatial targeting: (1) mean Euclidian distance between the center coordinates of the functional ROIs (one per hemisphere) and the center coordinates of the peak of the electric field in each hemisphere (where the peak is for the 99-percentile-thresholded E-field strength across all voxels for the given hemisphere) and (2) spatial Pearson correlation coefficient between the individual BOLD signal t-map and the electric field map. Four measures quantified the electric field (E-field) strength: (3) peak E-field strength for the whole brain (based on the 95-percentile-thresholded E-field map), (4) mean peak E-field strength in the functional ROIs (based on the 95-percentile-thresholded E-field from a 7 mm sphere around the center coordinates of the functional ROIs), (5) peak normal component of the E-field for the whole brain (95-percentile-thresholded), and (6) peak normal component of the E-field in the functional ROI (defined as in 4). The last measure quantified (7) E-field focality (cortical area in mm² with E-field strength higher than the 50th percentile). Repeated measures analysis of variance (rmANOVA) showed a significant effect of montage on all of the investigated measures (all F_(2,76) ≥ 9.938, p ≤ 1.5e-04, Figure 2b).

Regarding the spatial targeting of the functional ROI, the Euclidian distance between the E-field peaks and the target functional ROIs averaged across hemispheres was higher for the ring-electrode montage compared to both the individualized and the standard montages (all t₍₃₈₎ ≥ 4.986, p≤4.163e-05, Bonferroni corrected). Fisher-Z-transformed correlation values between the E-field map and the BOLD signal map were also higher for the ring-electrode montage compared to both individualized and standard montages (all t₍₃₈₎ ≥ 2.798, p ≤ 0.024, Bonferroni corrected). Thus, the ring-electrode montage produced electric fields that were better correlated with the functional activation maps across the entire brain than the other two montages, but peak electric field missed the mark. No significant difference between the standard and the individualized montage was observed either for the distance between the E-field and the functional map peaks or the E-field to BOLD correlation (all |t|₍₃₈₎ ≤ 2.047, p ≥ 0.143, Bonferroni corrected).

Regarding E-field strength, the standard montage induced higher electric field than the ring-electrode montage and the individualized montages for the whole brain and within the ROI; the same was true when considering only its normal component (all t₍₃₈₎ ≥ 2.568, p≤0.043, Bonferroni corrected, Figure 2b). The individualized montage showed stronger E-field and normal component of the E-field, for the whole brain and within the ROI, when compared to the ring-electrode montage (all t₍₃₈₎ ≥ 13.43, p ≤ 1.665e-15, Bonferroni corrected, Figure 2b). In terms of focality, the ring-electrode montage was the most focal of the three (all t₍₃₈₎ ≥ 8,098, p ≤ 2.54e-9, Bonferroni corrected, Figure 2b), followed by the individualized montage which was more focal than the standard (t₍₃₈₎ = 9.578, p = 3.349e-11, Bonferroni corrected, Figure 2b). Thus, each montage has its pros and cons, and the choice of montage will depend on which of these dependent measures is prioritized. The critical question then is which measure – or combination of measures – best predicts inter-individual variability in the magnitude of the tACS effect on behavior.

Before running any simulations, we had decided a priori to use only the individualized and standard montages for our main behavioral experiment (see below), motivated by the fact that the 4-electrode arrangement allows for directing the E-field in a desired orientation (Baltus et al., 2018). Targeting a specific field orientation would not be possible using the ring-electrode configuration from the ring-electrode montage. In addition, comparing between the simulated E-fields across montages showed that the ring-electrode montage with the specific location tested here might in fact not be optimal for modulating oscillatory activity during our auditory task, since the peak of the induced E-field was farther away from our target ROI and its strength was weaker compared to that simulated for the other two montages. As already described, we did not observe any difference between the individual and the group montages in terms of spatial overlap to our target ROI. While the electric field was strongest for the standard montage compared to the individualized montage, the latter induced a more focal field compared to the standard montage, therefore each montage could be good in different ways. In the behavioral experiments included in the rest of the Results section, only the individualized and the standard montage were used. The ring-electrode montage was not tested any further.

Across two different sessions, subjects listened to 2 Hz FM sounds and detected silent gaps presented at different phase locations on the FM modulation cycle. While performing the task, participants received either sham or verum tACS at 2 Hz (within participant) with either the individualized montage or the standard montage (between participants). During the verum tACS runs, the phase lag between the auditory stimulus and the tACS signal varied from trial to trial (Figure 3a). Participants missing one session (N = 5) were excluded at this stage. All further analysis is presented for 37 participants (individualized montage: N = 16, standard montage: N = 21).

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To evaluate the effect of the FM-stimulus phase on gap detection in the absence of tACS, gaps presented during the sham condition were binned according to the FM-stimulus phase into which the gap fell and the mean detection rate (hit rate) was computed for each bin (Figure 3b). The strength of the FM-stimulus-driven behavioral modulation (FM-amplitude) and the optimal FM-stimulus phase (FM-phase) for gap detection were estimated by fitting a cosine function to hit rates as a function of FM-stimulus phase (Cabral-Calderin and Henry, 2022). FM-amplitude was significantly higher than chance for 33/37 participants in session 1 and for 27/37 participants in session 2 (comparison between each participant’s FM-amplitude and its corresponding surrogate distribution, p < 0.05, Figure 3c). In addition, FM-phase was clustered across participants (Rayleigh test session 1: Z = 29.031, p = 1.806e-17; session 2: Z = 26.531, p = 2.12e-15). No significant difference between sessions was observed either for FM-amplitude (t₍₃₆₎ = 0.99, p = 0.329) or for FM-phase (inter session phase distance clustered around zero, V = 28.391, p = 2.045e-11). A significant correlation between sessions was observed for FM-amplitude (Pearson’s r = 0.516, p = 0.001). The latter replicates our previous finding that the FM-stimulus driven modulation of gap detection performance is reliable across time. We retained the FM-amplitude and FM-phase parameters as reliable signatures of behavioral entrainment to the FM-stimulus and asked whether and how these signatures are modulated by tACS.

First, we tested a strong version of a hypothesis about how tACS would affect behavior, which is that tACS would ‘overwrite’ neural entrainment to the FM stimulus. To do so, the phase lag between the FM-stimulus and tACS (Audio-tACS lag) was estimated for each trial. Gaps were grouped according to the FM-stimulus phase (9 bins) and the Audio-tACS lag (6 bins) and mean detection rates were computed for each FM-phase and Audio-tACS lag combination (Figure 3a–b; Figure 3—figure supplement 1). A cosine function was fitted to the mean detection rates as a function of FM-stimulus phase, separated by Audio-tACS lag, and the amplitude and optimal phase parameters where estimated, similar to the sham condition. We hypothesized that tACS would interact with the FM-stimulus-driven neural entrainment and as such the behavioral signatures of entrainment – FM-amplitude and FM-phase – would vary as a function of Audio-tACS lag. First, if tACS overwrites entrainment to the FM-stimulus, we expect tACS phase to be more critical for gap detection than the phase of the auditory stimulus. As such, we anticipated a change in the FM-stimulus optimal phase as a function of Audio-tACS lag. Contrary to our expectations, in both sessions, optimal FM-phase was clustered across participants for all lag conditions around the same phase angle (V test with mean phase across lags as mean direction, all V > 25.303, p < 2.016e-09 Figure 3d). The same was true when separating by tACS montage (all V > 11.729, p < 1.476e-04). To further test the relevance of tACS phase for gap detection, we performed three mixed effect logistic regression models where single-trial gap detection performance was predicted by the FM-stimulus phase (model 1), plus the tACS phase at gap onset (model 2) and their interaction terms (model 3). Sham trials were excluded from this analysis. Before fitting the models, phase values were linearized by computing their sine and cosines. The best model was the one including only FM-stimulus phase (Δ AICc relative to model 2 = 6.20, Supplementary file 1b). This result, together with the lack of tACS effect on FM-phase indicates that tACS does not overwrite neural entrainment to the FM stimulus.

Our second hypothesis was that tACS could modulate the strength of entrainment to the FM stimulus, and as such, we expected FM-amplitude to be sinusoidally modulated by Audio-tACS lags: highest FM-amplitude should be observed for the optimal Audio-tACS lag since tACS would be aiding entrainment to the stimulus (constructive interference). In contrast, FM-amplitude was expected to be the smallest for tACS anti-phase to optimal lag: anti-phase tACS would disrupt entrainment to the FM stimulus since the electrical signal and the auditory rhythms are working against each other (destructive interference).

We wanted to test the effect of tACS lag on the FM-amplitude at the group level. However, it is already known that the optimal tACS lag for auditory perception often shows high inter-individual variability (Riecke et al., 2015; Figure 3e; Figure 3—figure supplement 2), which can affect the estimation of group-level tACS effects. To prevent inter-individual variability in optimal tACS lag from affecting the estimation of tACS effects at the group level, (1) individual optimal tACS lag (tACS-phase) was estimated for each participant and session using a cosine fit (Methods, Figure 3e) and (2) tACS lags were realigned by making the optimal tACS-phase correspond to phase zero and wrapping the remaining phases accordingly before doing group statistics (Figure 4a). Data from the optimal tACS lag and its opposite lag (corresponding trough) were excluded to avoid any artificial bias in estimating tACS effects induced by the alignment procedure (Zoefel et al., 2019). Data from the two tACS lags on either side of the optimal lag were averaged and used as an estimate of the FM-driven modulation in the optimal half of the tACS cycle (tACS(+)). Similarly, data from the two tACS lags on either side of the trough were averaged and used as an estimate of the FM-driven modulation in the suboptimal half of the tACS cycle (tACS(-)). A schematic of the calculation for obtaining tACS(+) and tACS(-) is shown in Figure 4b. tACS effects were tested using a mixed ANOVA with the repeated measures tACS lag condition (sham, tACS(+), tACS(-)) and session (1 and 2) and the between factor montage (standard vs. individualized). In addition, we included all two- and three-way interactions. Note that we chose to adopt this realignment procedure as done in previous studies (Riecke et al., 2015), instead of using the amplitude of the second cosine fit, because we were interested in investigating whether tACS could aid or disturb behavioral entrainment to the FM stimulus relative to the sham condition.

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tACS did successfully modulate FM-stimulus driven behavioral entrainment (main effect of tACS lag condition: F_{(2, 70)} = 26.202, p = 3.203e-09, Figure 4c). Post-hoc t-tests showed that FM-driven modulation was higher for tACS(+) when compared to sham t₍₃₆₎ = 3.562, p = 0.003 and to tACS(-) (t₍₃₆₎ = 9.501, p < 0.001, all p-values are Bonferroni corrected, Figure 4c). In addition, FM-driven modulation was significant lower at tACS(-) when compared to sham (t₍₃₆₎ = –3.090, p = 0.012, Figure 4c). No significant effect of session (F_(1,35) = 0.083, p = 0.775), montage (F_(1,35) = 1.602, p = 0.214) or interactions (montage*session F_(1,35) < 0.001, p = 0.985; montage*tACS lag F_(2,70) = 0.282, p = 0.755; tACS lag*session F_(2,70) = 1.033, p = 0.361; tACS lag*montage*session F_(2,70) = 0.098, p = 0.907) were observed. In order to further investigate whether the observed tACS effect was significantly larger than chance and not an artifact of our analysis procedure (Zoefel et al., 2019), we created 1000 surrogate datasets per participant and session by permuting the tACS lag designation across trials. The same binning procedure, realignment, and cosine fits were applied to each surrogate dataset as for the original data. This yielded a surrogate distribution of tACS(+) and tACS(-) values for each participant and session. These values were averaged across sessions since the original analysis did not show a main effect of session. We then computed the difference between tACS(+) and sham, tACS(-) and sham, and tACS(+) and tACS(-), separately for the original and surrogate datasets. The obtained difference for the original data where then z-scored using the mean and standard deviation of the surrogate distribution. Note that in this case we used data of all 42 participants who had at least one valid session (37 participants with both sessions). Three one-sample t-tests were conducted to investigate whether the size of the tACS effect obtained in the original data was significantly larger than that obtained by chance (Figure 4d). This analysis showed that all z-scores were significantly higher than zero (all t₍₄₁₎ > 2.36, p < 0.05, all p-values corrected for multiple comparisons using the Holm-Bonferroni method). Thus, tACS modulated behavioral signatures of neural entrainment to auditory rhythms, and critically both amplified and attenuated entrainment relative to sham depending on the phase relationship between the electrical and auditory stimulation. Such effect was not different either between session or montage group.

So far, we have evaluated whether tACS at different phase lags modulates behavioral signatures of entrainment: FM-amplitude and FM-phase. At the group level, we observed no modulation of optimal FM-stimulus phase (FM-phase) but a significant effect of tACS-lag on the FM-stimulus driven behavioral modulation (FM-amplitude). Next, we asked how reliable tACS effects are over time both in terms of the strength of tACS effects and the optimal tACS lag. This is critical to quantify if we want to plan tACS interventions using data from different sessions. For example, if optimal tACS lag constitutes a stable individual trait measure, it could be estimated in one session and used for applying tACS in following sessions to maximize treatment benefits.

To have a global measure of the magnitude of the tACS effect at the individual level, for each participant and session, the FM-driven modulation amplitude from the tACS negative half (tACS(-)) was subtracted from that during the tACS positive half (tACS(+)). This value was then interpreted as the amplitude of the tACS-induced behavioral modulation (tACS-amplitude, see Materials and methods, Figure 5a). To evaluate the reliability of the tACS induced modulation, tACS-amplitude values were compared and correlated between sessions. While no significant difference was observed between sessions, tACS-amplitude estimates did not correlate between sessions (session 1 vs session 2, t₍₃₆₎ = 0.806, p = 0.426, Pearson’s r = –0.162, p = 0.337, Figure 5a), suggesting a lack of reliability of the strength of tACS effects over time. No significant inter-session correlation was observed also when separating by montage group (all |r| < 0.354, p > 0.179).

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Regarding optimal tACS-phase, as already mentioned in previous sections, we observed high inter-individual variability as the Rayleigh test did not indicate any significant deviation from uniformity in either session (session 1: Z = 0.931, p = 0.397; session 2: Z = 0.133, p = 0.877, Figure 5b). In addition, no significant correlation between sessions was observed (circular correlation, Rho = 0.237, p = 0.137). Moreover, the distribution of phase distances between sessions was not clustered around zero (V test with mean direction 0, V = 4.838, p = 0.130, Figure 5b). Same was true when separating by montage group (all Z < 3.780, p > 0.122, |r| < 0.245, p > 0.272). Thus, contrary to the reliability we observed for the optimal FM-phase for gap detection, optimal tACS-phase lags were not stable across sessions.

We anticipated that the lack of reliability of optimal tACS phase could be influenced by a poor estimation of each single-session optimal phase lag due to a low number of trials per condition (FM-stimulus phase x Audio-tACS lag). If so, we hypothesized that the estimation of tACS effects should be strengthened by pooling data across sessions, as this would increase number of trials by a factor of 2. In this case, we expect tACS-amplitude to be equal or higher when estimated with the pooled data than when estimated for each separate session. However, we observed that tACS-amplitude was smaller when calculated with the pooled data than when averaging the tACS-amplitude across sessions (t₍₃₆₎ = –2.452, p = 0.019, Figure 5c). We interpret the smaller tACS-amplitude as an indication of tACS effect cancellation due to inter-session variability. In other words, this result suggests that the lack of reliability in tACS-phase cannot be explained by the number of trials used for its estimation.

To better understand what factors might be influencing inter-session variability in tACS effects, we estimated multiple linear models predicting inter-session difference in tACS-amplitude (session 1- session 2) and absolute circular distance in tACS-phase between sessions from a different combinations of regressors: (1) age, (2) gender, (3) number of days passed between sessions, ΔDays, (4) absolute time of the day difference in minutes, ΔMinutes, (5) tACS-montage, and (6) inter-session difference in gap size threshold. The winning model (F-statistic vs. constant model: 5.72, p = 0.007, R² = 0.257, Supplementary file 1c) showed that inter-session difference in tACS-amplitude was significantly predicted by the number of days passed between sessions (ΔDays ß = –0.383, t = –2.55, p = 0.016) and the absolute time of the day difference (ΔMinutes ß = 0.350, t = 2.333, p = 0.026). The visualization of these effects suggested that, compared to the first session, tACS-amplitude decreased in session 2 for participants with longer intervals passed between sessions and for participants tested at the same time of the day (Figure 5—figure supplement 1). This model was selected because it had the smallest Akaike’s information criterion (corrected for small samples), AICc. Moreover, the likelihood ratio test showed no evidence for choosing the more complex unrestricted model (stat = 2.411, p = 0.121). Following the same selection criteria, the winning model predicting inter-session variability in tACS-phase, included only the factor gender (Supplementary file 1d). However, this model was not significant in and of itself when compared to a constant model (F-statistic vs. constant model: 3.05, p = 0.09, R² = 0.082). Therefore, contrary to tACS-amplitude, the lack of reliability in tACS-phase cannot be explained by the interval passed between sessions or time of the day, but rather may be a more fundamental feature of intra-individual variability that should potentially influence the design of tACS experiments, in particular when conducted across multiple sessions.

So far, our results demonstrate that FM-stimulus driven behavioral modulation of gap detection (FM-amplitude) was significantly affected by the phase lag between the FM-stimulus and the tACS signal (Audio-tACS lag). However, the strength of the tACS effect was variable across participants. A natural question for us was what factors predict individual variability in the magnitude of the tACS effect. Specifically, we sought to explain variability in tACS effects from nine different variables including the seven parameters describing the optimality of the E-field simulated for each participant (Figure 2b); the strength of the BOLD signal response in the ROI to the auditory stimulus and the FM-driven behavioral modulation during sham stimulation. tACS-amplitude estimates were averaged across sessions since session did not significantly affect FM-amplitude (Figure 5a). Participants missing the fMRI session were excluded and the analysis was performed with data from 34 participants (individualized montage N = 16, standard montage N = 18). Different linear models were fitted to the data aiming to predict tACS modulation strength (averaged tACS-amplitude) from different combinations of regressors (see Materials and methods). The winning model (F-statistic vs. constant model: 3.41, p = 0.016, R² = 0.378, Figure 6, Supplementary file 1e) included the main effects: normal E-field (ß = –0.112, t = –0.656, p = 0.517), E-field focality (ß = 0.369, t = 1.969, p = 0.059), average distance between the E-field peaks and the center of the target functional ROIs for each hemisphere (Dist2Peak; ß = –0.054, t = –0.328, p = 0.746), and the interaction terms: normal E-field: focality (ß = 0.735, t = 3.260, p = 0.003) and normal E-field:Dist2Peak (ß = 0.548, t = 2.804, p = 0.009). Note however that only the interaction terms were significant.

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Visualization of the interaction terms showed that tACS effects were positively predicted by the normal E-field for participants with more focal E-fields that were closer to the functional target ROIs (Figure 6). However, in participants where the induced E-field was less focal and farther from the functional target, the normal E-field negatively predicted tACS effects. The latter can be seen in the plots in Figure 6, where the adjusted tACS effects are shown as a function of the normal E-field at three different fixed values of focality (Figure 6a) and Dist2Peak (Figure 6b). Thus, when the electric field accurately reaches its intended target, high field strength increases behavioral consequences of tACS, but when the electric field misses its mark, high field strength is actually behaviorally detrimental.

When testing the effect of tACS on the amplitude of behavioral entrainment to the FM stimulus (FM-amplitude), we did not observe a significant effect of tACS montage (section tACS modulates the amplitude of the FM-stimulus driven behavioral entrainment). In other words, the specific tACS montage did not have a big impact on the size of the tACS effects overall (see Discussion). However, since testing the impact of individualizing the tACS montage on behavioral effects was one of the main aims of the current project, we nonetheless tried to investigate this further.

In the individualized montage group, we optimized each listener’s montage by taking into account individual anatomical and functional data. One possible consequence of such approach could be a lower inter-individual variability in tACS effects, rather than an overall increase in effect size. To test this hypothesis, participants were grouped according to the electrode montage and individual tACS-amplitude values (see previous section) were averaged across sessions. A variance test was performed on the average tACS-amplitude to test whether inter-individual variability was different between montage groups. For this analysis, all participants who completed both sessions were included (individualized N = 16, standard N = 21). No significant difference was observed in terms of the variance between groups (F_{(20, 15)} = 1.441, p = 0.475).

We then took a step back and compared the group variances separated by session, and by tACS condition (tACS(+), and tACS(-), Figure 4—figure supplement 1). Visual inspection of the plot suggested that inter-individual variability was smaller for the individualized montage group than for the standard montage group. To quantify this, we computed the coefficient of variation (cv) and interquartile range (iqr) for each group (session 1, individualized: tACS(+) cv = 0.3567, iqr = 0.1375, tACS(-) cv = 0.4848, iqr = 0.1480; standard: tACS(+) cv = 0.3757, iqr = 0.1684, tACS(-) cv = 0.4792, iqr = 0.1497; session 2, individualized: tACS(+) cv = 0.2531, iqr = 0.1086, tACS(-) cv = 0.2201, iqr = 0.0659; standard: tACS(+) cv = 0.3917, iqr = 0.1704, tACS(-) cv = 0.5174, iqr = 0.1736). However, the variance test was significant only for tACS(-) in session 2 (F _(20,15) = 4.31, p = 0.023, Bonferroni corrected for 4 comparisons). No significant differences in group variance were observed for the other conditions (all F_(20,15) < 1.924, p > 0.20, uncorrected). This result is suggestive, but larger sample sizes would be necessary to conduct a principled variance comparison between groups. At this stage, more evidence is needed to prove the superiority of individually optimized tACS montages for reducing inter-individual variability in tACS effects.

Participants detected near-threshold silent gaps embedded in a 2 Hz FM noise stimulus. Using this paradigm, it has been repeatedly shown that EEG activity entrains to the FM rhythm and that detection of silent gaps presented in the sound is modulated by the FM-stimulus phase into which the gap falls (Cabral-Calderin and Henry, 2022; Henry and Obleser, 2012; Henry et al., 2014; Bauer et al., 2018). Moreover, we have recently shown that both effects are reliable across participants and over time (Cabral-Calderin and Henry, 2022). Our first hypothesis was that tACS could overwrite neural entrainment to the FM stimulus (i.e. neural oscillations phase-lock to the tACS signal instead of the FM-stimulus) and as such, the optimal FM-stimulus phase would vary as a function of tACS lag. Contrary to our prediction, results showed that in both sessions, individual optimal FM phases for gap perception were always clustered around the same phase angle, regardless of the tACS lag. We hypothesize that a reason for this could be the already strong acoustic modulation of the stimuli that we used here, which had a modulation depth of 67% peak-to-center. Phasic effects of tACS on auditory perception have previously been shown mostly in the context of weakly modulated background sounds (Riecke et al., 2015) or for example when tACS was applied with the shape of an amplitude envelope that had been acoustically removed from a speech signal (Zoefel et al., 2018; Zoefel et al., 2020). We hypothesize that entrainment to the clear rhythm of the FM stimulus might have been too strong for tACS to overwrite. It has already been suggested, at least for tACS applied at frequencies matching the neural alpha band, that tACS is most effective at modulating oscillatory activity at the intended frequency when its power is not too high (Neuling et al., 2013). Along the same line, using single unit recordings it has recently been proposed that tACS competes with endogenous neural oscillations: tACS imposes its own rhythm on spiking activity when tACS strength is stronger than the endogenous oscillations but it decreases rhythmic spiking when tACS strength is weaker that the endogenous oscillations (Krause et al., 2022). Thus, we would predict that tACS may be more likely to shift the phase of neural entrainment when entrainment is weaker to start with, either because of weaker stimulus modulation or in listeners lacking young, healthy auditory systems (Rufener et al., 2016). Alternatively, our results could simply be interpreted as a clear superiority of the auditory stimulus for entrainment. In other words, sensory entrainment might just be stronger than tACS entrainment in this case where the stimulus rhythm was strong and salient. It would be interesting to further test whether this superiority of sensory entrainment applies to all sensory modalities or if there is a particular advantage for auditory stimuli when they compete with electrical stimulation. However, answering this question was beyond the scope of our study and needs further investigations with more appropriate paradigms.

Our second hypothesis was that, while tACS might not be able to overwrite entrainment to a strongly modulated FM stimulus in healthy young adults, it could still modulate the amplitude of the FM-driven entrainment. In other words, we anticipated that tACS would interfere with neural entrainment to the FM-stimulus depending on their relative phase lag: optimal tACS lag would aid neural entrainment (increase amplitude of FM-driven modulation) as in constructive interference, while the opposite lag would be detrimental (decrease amplitude of FM-driven modulation) since both the FM stimulus and the tACS signals would try to entrain neural activity with antiphase relationships, as in destructive interference. Our results showed that the amplitude of the FM-stimulus driven modulation (FM-amplitude) was sinusoidally modulated based on the relative phase between the stimulus rhythm and the electrical stimulation. Specifically, FM-amplitude was stronger for the phase lags around the realigned optimal tACS lag and weaker for the tACS lags opposite the optimal lag. The fact that FM-stimulus-driven modulation of gap performance was affected by tACS in a phase-specific manner implicitly suggests that neural entrainment to auditory stimuli is causally linked to auditory perception and that tACS is an effective tool for modulating both. Based on the association between neural entrainment and auditory perception (Peelle and Davis, 2012; Zion Golumbic et al., 2013; Horton et al., 2013; Doelling et al., 2014; Horton et al., 2014; Doelling and Poeppel, 2015; Nozaradan et al., 2016; Brodbeck et al., 2020), we anticipate that making entrainment stronger with tACS should lead to better cocktail party performance or better prediction/adaptation in a musical context.

Note that we did not control for the skin sensation induced by 2 Hz tACS in this experiment. Participants rated the strength of the perceived stimulation after each run. However, this information was used only to assess the safety and tolerability of the stimulation protocol. It is in principle possible that skin sensation would depend on tACS phase itself. However, in this study, we report effects that depend on the relationship between tACS-phase and FM-stimulus phase, which changed from trial to trial as the starting phase of the FM-stimulus was randomized across trials. We have no reason to expect the skin sensation to change with the tACS-audio lag and therefore do not consider this to be a confound in our data. We propose that by applying tACS at the right lag relative to auditory rhythms, we can aid how the brain synchronizes to the sounds and in turn modulate behavior. Since optimal tACS phase was variable across participants and sessions, this approach would require closed-loop protocols where the optimal tACS lag is estimated online (see next section). In addition, we anticipate that such an approach might work even better when entrainment to the auditory stimulus is not perfect, for example when the driving stimulus is weaker (weaker modulation) or masked by noise.

The reliability of tACS effects at the individual level is not fully understood. While inter-individual variability in response to electrical stimulation has been well documented (Kasten et al., 2019; Cabral-Calderin et al., 2016b; Zanto et al., 2021; Li et al., 2015), most studies test tACS in only one session, and when multiple sessions are conducted, a different tACS condition is implemented in each session (Cabral-Calderin et al., 2016b; Antal et al., 2008). Here, we tested participants under the same auditory and tACS conditions in two different sessions. This approach allowed us to test the stability of tACS effects across sessions. While no significant difference between sessions was observed for the amplitude of tACS effects (tACS-amplitude), tACS effects did not correlate between sessions. Moreover, no significant correlation was observed between optimal tACS phase lags (tACS-phase) across sessions, and the circular distance between sessions was not clustered.

In a previous study using stimuli with exactly the same parameters as in the current study, we showed neural entrainment to FM-sounds has a reliable phase lag over sessions (Cabral-Calderin and Henry, 2022), so any lack of reliability in optimal tACS lag cannot be explained by inconsistency in FM-stimulus-brain synchrony. One possible explanation for the lack of reliability of tACS effects could be differences in the placement of the tACS electrodes across sessions. We took special care to precisely and consistently place electrodes across sessions, thus we feel confident that our electrode placement did not significantly differ between sessions. Nevertheless, even subtle differences could induce changes in the precise angle of the current dipole induced in the auditory cortex or slightly affect the optimal spatial targeting of the field. Such subtle changes in electrode placement could lead to different frequency-tuned neurons receiving the strongest stimulation in every session. However, we encourage the reader to be careful with such interpretation. In this experiment, we used frequency modulated sounds. At the level of the auditory pathway, frequency modulation can be translated into amplitude-modulation of different frequency-tuned neurons: neuronal populations will be activated on and off depending on whether their preferred frequency is included in the FM stimulus. Within a given FM stimulus, different tACS lags will correspond to different center frequencies in the FM stimulus: highest current strength will correspond to a specific frequency. Note however that we randomized the stimulus center carrier frequency from trial to trial. Therefore, there is no one-to-one mapping between tACS phase and FM-stimulus carrier frequency. This idea would require further testing and systematic investigation into whether small changes in electrode placement changes optimal tACS lag and to what extent this is affected by the stimulus carrier frequency. We followed the standard procedure in the field for placing the tACS electrodes. If such subtle differences in electrode placement can already destroy inter-session reliability, there’s really no hope for any human to place them more precisely than that, so we will need to create new approaches in the field (e.g. similar to the neuronavigation systems used for TMS) to guarantee even more precise electrode placements than using the standard EEG 10–20 system. The idea that differences in optimal tACS lag can be explained by different frequency-tuned neurons being activated in each session relies on the spectral representation of FM sounds in the auditory pathway. However, neural processing of FM seems to involved not only frequency encoding but also direction and rate encoding: neurons selectively responding to FM direction or rate (Tabas and von Kriegstein, 2021). The latter makes the understanding of variability in optimal tACS phase even more complex. Interestingly, our results suggest that the inter-session interval and the difference in time of the day are two factors influencing the inter-session variability in the strength of tACS effects. Such finding suggests that inter-session variability in tACS effects cannot be exclusively explained but inconsistency in the electrode placement.

Several physiological factors could be behind the influence of inter-session intervals on inter-session reliability of tACS effects. For example, hormone changes in women related to the menstrual cycle have been shown to alter cortical excitability (Inghilleri et al., 2004). In the latter study, repetitive TMS had a facilitatory effects on motor evoked potentials on day 14 of the menstrual cycle but not on day 1. We did not control for the phase of the menstrual cycle of our female participants but our inter-session intervals suggest that female participants were at different phases in each session. However, if hormonal factors would explain the lack of inter-session reliability of tACS effects, we would expect male participants to be more reliable than female ones. However, we did not observe any effect of gender when investigating inter-session reliability in our models. Another factor to consider when interpreting inter-session variability of tACS effects is plasticity induced by the first session. In session 1, participants are less experienced with the task and as a result perceptual learning slopes might be bigger and differently interfere with tACS effects. In fact, within the same day, the effects of anodal transcranial direct current stimulation in a visual discrimination task seems to differ between blocks, being greatest at the beginning and not different from sham over time (Fertonani et al., 2011). In principle, adaptation to the electrical current in the auditory regions could change the weight of different input neuronal connections and as such change the optimal phase for tACS to affect neural entrainment to the auditory stimulus. Alternatively, another plausible explanation is that participants could have changed the strategy to perform the task in each session (Cabral-Calderin and Henry, 2022) leading to different cognitive processes being relevant in the different sessions and hence inducing more variable tACS effects.

The lack of test-retest reliability on tACS effects is an especially surprising result from the current study which requires further investigation. The implication of this result is it may not be possible to always estimate optimal tACS phase lag in a session using magneto- or electroencephalography and then apply it in a second session (van Bree et al., 2021), but closed-loop protocols where optimal tACS lag is constantly monitored during online tACS may be necessary. In a previous study (van Bree et al., 2021), the authors where able to predict optimal tACS phase for speech comprehension from EEG data. Note however, that this was possible only when the speech signal was presented after the tACS signal (no competition between the tACS and the sensory signal). In fact, when the auditory stimulus was presented during tACS, the authors showed no tACS-induced modulation of performance and optimal tACS phase could not be predicted from EEG data. Moreover, optimal tACS phase during stimulation did not correspond with estimated optimal phase in the post-stimulation period. Taken together, results from both studies suggest that optimal tACS phase might be stable only in the post-stimulation period, when tACS and the sensory signal do not compete with each other, and only endogenous “echoes” of entrained neural oscillations are expected to occur. In our paradigm, we only tested tACS effects while a strongly modulated FM stimulus at the tACS rate was presented. Competition between the electrical and acoustic signals for entrainment of endogenous oscillations, together with evoked responses to each signal modality and the electric signal per se (strong current vs. none) adds more variability in the optimal tACS phase. Other differences between the study designs include the sensory stimulus type (intelligible speech vs. FM sounds), which might involve different neural processes, and the tACS duration (burst of 3–6 s tACS with vs. 11 minutes tACS continuous with 20 s FM). Stability of tACS phases might depend as well on the stimulation length. In addition, in van Bree et al., 2021, tACS was applied only in one session. It remains to be seen whether optimal tACS phase for perception remains stable or if it changes over time due plasticity-induced changes as discussed above. In the latter case, optimal tACS phase would be predicted from EEG activity in the first tACS session but not in subsequent ones. In any case, the inconsistency of optimal tACS lags across sessions observed in our study suggests that individual variability in optimal tACS lags to modulate entrainment to rhythmic auditory stimuli does not arise exclusively from anatomical variability but other changes in functional brain activity might be important to consider. More research is needed to fully understand optimal tACS phases for perception.

Several studies have already shown that inter-individual variability in tACS effects can be partially explained by inter-individual variability in the strength of the simulated electric field as well as the spatial overlap between this and the targeted functional area (Kasten et al., 2019; Zanto et al., 2021; Preisig and Hervais-Adelman, 2022). Here, we used a model-comparison approach to determine the parameters that best explained individual variation in tACS effects; we started with E-field strength, E-field focality, the correspondence between the simulated E-field and the target functional regions (correlation between E-field map and BOLD map, Euclidian distance between E-field and BOLD peaks), baseline factors (FM-driven modulation amplitude at sham and the strength of the BOLD signal at the regions of interest) and the tACS montage. The best model showed that tACS effects were best explained by the interaction between the normal component of the E-field and the field focality, and the interaction between the normal E-field and the distance between the E-field peak and the peak of the functional activation map. The explanatory power of these interaction terms demonstrates that not only the field strength is important, but also how focal it is and how optimally it targets the intended brain region. For more focal electric fields targeting the correct brain regions, higher normal E-fields are beneficial. However, higher normal E-fields can be detrimental when the field is too broad and its peak farther away from the target ROI. This potentially relates to the fact that stronger electric fields will be applied to non-relevant brain areas with unintended consequences, potentially reducing the efficacy of tACS to modulate performance in the target task.

In the first part of this study, we simulated Electric field strength using 3 different tACS montages. The first two montages were taken from the literature (van Bree et al., 2021; Baltus et al., 2018) and were the same for all subjects, while the third montage was individually optimized to target individual functional ROIs using an fMRI-task localizer. Before running any simulations, we had already decided a priori to use only the individualized and standard montages for our main behavioral experiment, motivated by the fact that the 4 electrodes arrangement allows for directing the E-field in a desired orientation (Baltus et al., 2018). Directing the E-field in a desired orientation is not possible using the ring electrodes configuration. Ring-electrode montages will always have a focus on superficial brain areas under the center electrode, and the E-field direction in the focus will be normal to the brain surface. As already described, we did not observe any difference between the individual and the group montages in terms of spatial overlap to our target ROI. While the electric field was strongest for the standard montage compared to the individualized montage, the latter induced a more focal field compared to the standard montage, therefore each montage could be good in different ways.

By using the individualized montage, we aimed to go a step past previous studies, which have shown that inter-individual variability in the E-field predicts tACS effects. Here, we asked whether tACS effects could be strengthened if the montage is optimized to each participant’s anatomy and functional map, and if such approach would also reduce inter-individual variability. Compared to the standard montage, we did not observe any significant different between the overall tACS effects. We did observe a trend for decreased inter-individual variability for the individualized montage group, although this was only statistically significant for session 2 and for the amplitude of the FM-driven modulation at the non-optimal half of the tACS lags (tACS(-)).

Several points need to be considered when interpreting these results, (1) the standard montage was taken from a study where it was already optimized using anatomical and functional data from a single participant (Baltus et al., 2018). Therefore, our findings speak not to whether optimizing tACS montages is beneficial in general, but whether spatially optimizing the montage to each participant adds extra advantages. It could well be that the standard montage was already optimal for several participants with more standard brains. In fact, our individualized montage was spatially not so different from the standard one. (2) In the current experiment, we only tested healthy young participants. We anticipate that taking into account inter-individual anatomical and functional variability will be more relevant in clinical settings or in aging research, where such variability is more evident. (3) We did not optimize the tACS protocol in terms of the applied current strength. We used a fixed value because we were limited by the size of the electrodes, and going higher than that value would make it uncomfortable for the participant. Combining spatial optimization with current-strength optimization could lead to different outcomes than what we observed here. (4) The optimization procedure here was performed with the constraints of achieving the same E-field strength in both target ROIs, inducing a relatively balanced field in both hemispheres and allowing only for four electrodes, that is two per hemisphere. Different optimization results might be obtained when optimization for more stimulation channels and allowing for a quite liberal amount of total current.

As discussed above, our results showed that the strength of tACS effects was predicted by the interactions between the strength of the inward electric field with the field focality and the distance between the peak of the E-field and the target ROI. Since such information was not available beforehand, it was not considered in our optimization approach. Our montage was optimized to spatially overlap as much as possible with our functional target, which as expected turned out to be of relevance in the analysis. While we did not optimize for focality, the individualized montage was more focal than the standard montage, another factor contributing to tACS effects. However, we did not optimize for the strength of the inward electric field, since we were limited by how much current strength we could apply and aimed at inducing a symmetrical electric field in the brain. The standard montage in fact induced higher field strengths in the brain than our individualized montage. Future studies could try to systematically optimize for the 3 factors and test the impact of such procedures at the behavioral level. Our results suggest that in our current settings, although individualizing the tACS montage did not make a difference in terms of overall tACS effects, it could be a way to decrease inter-individual variability; given the highly variable nature of tACS effects in the literature, this may be desirable under some circumstances. However, our study was not designed to directly test the effect of tACS on sample variance, and more data would be needed to support this observation. To our knowledge, studies answering this question are missing in the tACS literature.

In summary, our results showed that while tACS did not affect the optimal FM-stimulus phase for gap detection, it did modulate the amplitude of the stimulus-induced behavioral modulation, a behavioral signature of the strength of neural entrainment. Both the optimal tACS lag and the amplitude of tACS effect were variable across participants and sessions, pointing towards the potential usefulness of closed-loop stimulation protocols, where optimal lags are evaluated online during stimulation. tACS effects were predicted by the interaction between the normal component of the E-field and the field focality and the interaction between the normal E-field and the distance between the peak of the E-field and the peak of the target ROI. These results suggest that the strength of the electric field is more beneficial when the E-field is closest to the target ROI and more focal, while stronger normal E-field in less focal and more distant E-fields can be detrimental. While no significant effect of tACS montage was observed in the overall tACS effects, the data hint at lower inter-individual variability in the group with the individualized montaged compared to the standard montage.

Our results advance our understanding of the use of tACS for modulating entrainment to auditory rhythms and put us a step forward on the way to personalized brain stimulation. Likewise, our study opens many questions for future research: (1) what other factors underlie the inter-session variability of tACS effects, (2) what factors determine the optimal tACS lag beyond brain anatomy, (3) how variable are optimal tACS lags within an individual depending on the sensory stimulation condition or targeted brain region, (4) what other factors should we consider when optimizing brain stimulation montages beyond spatial targeting, (5) what is the impact of our optimization approach when applying tACS in clinical or older populations? While future studies replicating our findings are needed, two specific recommendations for future research can be derived from our results: (1) Spatially optimizing the tACS montage can be used when aiming at decreasing inter-individual variability of tACS effects; (2) tACS montages should be optimized not only for the electric field strength, but for the strength of its normal component, the field focality and its spatial overlap with the target ROI.

Forty-two healthy participants took part in the study (18 females, mean age = 27.3; SD = 5.8). All participants took part in at least one tACS session and 39 participants took part in two tACS sessions separated by 3–301 days (median: 7 days). Variability in inter-session intervals was due to multiple lockdowns during the corona pandemic. Data from session one from one participant had to be excluded due to technical problems with the tACS signal recording. From the initial sample, three individuals did not participate in the fMRI session due to MRI contraindications (metal implants). All participants self-reported normal-hearing and normal or corrected-to-normal vision. At the time of the experiment no participant was taking medication for any neurological or psychiatric disorder.

Participants received financial compensation for their participation in the study. Written informed consent was obtained from all participants. The procedure was approved by the Ethics Council of the Max Planck Society (registration Saturnino et al., 2019_27) and in accordance with the declaration of Helsinki.

Auditory stimuli were generated by MATLAB software at a sampling rate of 44.1 kHz. Stimuli were 20 s long complex tones frequency modulated at a rate of 2 Hz and with a center-to-peak depth of 67% of the center frequency (Figure 1a). The center frequency for the complex carrier signals was randomly chosen for each stimulus within the range of 1000–1400 Hz. The complex carrier comprised 30 components sampled from a uniform distribution with a 500 Hz range. The amplitude of each component was scaled linearly based on its inverse distance from the center frequency; that is, the center frequency itself was the highest-amplitude component, and component amplitudes decreased with increasing distance from the center frequency. The onset phase of the stimulus was randomized from trial to trial, taking on one of eight values (0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, 7π/4), with the constraint that each trial would always start with a phase different from its predecessor. All stimuli were rms-amplitude normalized. Each 20 s stimulus contained 3–5 silent gaps (gap onset and offset were gated with 3 ms half-cosine ramps). Each gap was chosen to be centered in 1 of 9 equally spaced phase bins into which each single cycle of the frequency modulation was divided. No gaps were presented either in the first or the last second of the stimulus. A minimum of 1.5 s separated consecutive gaps.

The tACS sessions were conducted in an electrically shielded and acoustically isolated chamber and under normal-illumination conditions. Sound-level thresholds were determined for each participant according to the method of limits. All stimuli were then presented at 55 dB above the individual hearing threshold (55 dB sensation level, SL).

For each session, gap duration was individually adjusted to detection-threshold levels using an adaptive-tracking procedure comprising two interleaved staircases and a weighted up-down technique with custom weights as described in Cabral-Calderin and Henry, 2022. This resulted in gap durations ranging from 9 to 24ms across participants and sessions (session 1: mean = 16.805ms, SD = 3.558ms, range = 10–24ms; session 2: mean = 15.205, SD = 3.466, range = 9–22ms).

Before starting the main experiment, participants performed practice trials to make sure they understood the task. For the main experiment, listeners detected gaps embedded in the 20 s long FM stimuli. Listeners were instructed to respond as quickly as possible when they detected a gap via button-press. Participants performed five blocks, each comprising the same set of 32 stimuli (4 per starting phase) but in a different randomized order. Each stimulus included 3–5 gaps for a total of 136 gaps (13–16 per phase bin, mean ~15). The number of phase bins was chosen to balance having a good sampling resolution and a high number of trials per condition without making the task too long.

Unless otherwise specified, correlation analyses between linear variables were done using Pearson correlation coefficient. In case of circular data, circular–circular or circular–linear correlations were computed using the respective functions in the circular statistics toolbox for MATLAB (Berens, 2009). Differences between tACS montages in terms of the simulated electric fields were investigated using rmANOVAs. Post-hoc analyses were conducted using standard paired t-tests. Significant p-values were corrected using Bonferroni method.

Behavioral data generated and analyzed during this study are publicly shared in the OSF platform: https://osf.io/k5fwp/. Custom MATLAB scripts are made available via GitHub ( https://github.com/ycabralcalderin/Cabral-Calderin_et_al_eLife_2023/releases/tag/MATLAB_code_tACS_FMaudio_BehEntrainment copy archived at Cabral-Calderin, 2024).

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication. Open access funding provided by Max Planck Society.

We thank Hanna Kadel, Dominik Thiele, and Cornelius Abel for technical support. We thank the MRI core Unit of the Brain Imaging Center in Frankfurt for technical support setting up the MRI sequences. This work was supported by a European Research Council Starting Grant (BRAINSYNC) and a Max Planck Research Group granted to MJH. AT was supported by the Lundbeck foundation (grants R244-2017-196 and R313-2019-622).

Written informed consent was obtained from all participants. The procedure was approved by the Ethics Council of the Max Planck Society (registration No. 2019_27) and in accordance with the declaration of Helsinki.

1. Preprint posted: March 13, 2023
2. Sent for peer review: April 24, 2023
3. Reviewed Preprint version 1: July 21, 2023
4. Reviewed Preprint version 2: December 7, 2023
5. Version of Record published: January 30, 2024

You can cite all versions using the DOI https://doi.org/10.7554/eLife.87820. This DOI represents all versions, and will always resolve to the latest one.

© 2023, Cabral-Calderin et al.

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