Selective Modulation of Interhemispheric Functional Connectivity by HD-tACS Shapes Perception

40 Hz tACS Modulates Ambiguous Motion Perception

We assessed the mean duration of horizontal and vertical motion perception by means of a motion ratio (MR  =  time_horizontal/time_total) (Table S1) and found a nearly balanced distribution during sham (MR: 48.7%±1.9%, mean ± standard error of the mean [SEM]) (Figure 3A). Our results revealed a significant increase of perceived horizontal motion during in-phase stimulation (+1.4%±1.9%; change to common baseline) (Figure 3A, dashed line) as compared to anti-phase stimulation (−1.5%±1.5%; F_1,13 = 5.17, p<0.05, Cohen's d = 0.59; planned contrasts). This difference was not significant during the post condition (F_1,13 = 2.70, p = 0.12; d = 0.05) (Table S1). No significant results were found for the switch rate (reversals per minute) (Figure 3B; all p>0.1). Taken together, the behavioral results suggest that the targeted manipulation of the interhemispheric phase difference biased the conscious experience of apparent motion.

Phase- and Frequency-Specific Stimulation Effects on Interhemispheric Coherence

All analyses for the SAM were conducted without the gamma₁-range (spectral estimates in Figure 4A were obtained after spectral smoothing) to remove the 40 Hz stimulation artifacts. In order to assess whether stimulation selectively affected the gamma-band, grand average interhemispheric coherence values (Figure 4A) were submitted to a two-way repeated measures analysis of variance (RM-ANOVA) (session: sham, in-, and anti-phase stimulation; frequency: six bands). We report Greenhouse-Geisser corrected values in case of violation of sphericity. A significant interaction of session × frequency (F_1.72,22.38  = 20.5, p<0.005; session: F_1,13 = 40.7, p<0.005; frequency: F_1.56,20.22  = 52.3, p<0.005) indicated a frequency-specific modulation of interhemispheric coherence. Importantly, the increase in gamma-coherence during horizontal motion perception was present in both tACS conditions (Figure 4B; in-phase: +9.3%±3.7%; t₁₃ = −2.55, p<0.05; anti-phase: +31.7%±14.5%; t₁₃ = −2.18, p<0.05), without any changes in absolute gamma-band power (Figure 4C; in-phase: t₁₃ = −0.55, p = 0.59; anti-phase: t₁₃ = 1.20, p = 0.25). Importantly, a two-way RM-ANOVA with factors session (in- and anti-phase) and percept (vertical and horizontal) calculated on absolute coherence values (Figure 4A) indicated that the percept (F_1,13 = 8.86, p<0.05) related increase in gamma coherence was present in both sessions (F_1,13 = 52.69, p<0.005) and was not inflated when absolute coherence values were lower during anti-phase stimulation (interaction: F_1,13 = 0.81, p = 0.38).

In addition, source reconstruction revealed that gamma-band power was again confined to parieto-occipital areas and did not differ between different percepts or stimulation conditions (all p-values >0.05; cluster test) (Figure 4I).

Figure 4A indicated that the coherence modulation was confined to the gamma-band. Thus, we analyzed the gamma coherence change over the three conditions with cluster-based permutation statistics and found a significant difference between in- and anti-phase stimulation over stimulated parieto-occipital cortex (cluster test: p = 0.006) (Figure 4E), while no differences where present between both sham or post conditions (cluster tests: all p>0.05). The modulation at the channel pair of interest (Figure 2A) highlights the difference between the increase during in-phase stimulation (+0.07±0.02; change to common baseline) (Figure 4D, dashed line) and the decrease during anti-phase stimulation (−0.03±0.03; effect size: d = 1.00). This effect was not present between both sham or post conditions (sham: d = 0.39; post: d = −0.03).

Interestingly, the coherence modulation was strongest for subjects with an individual gamma coherence peak frequency close to 40 Hz (Figure 4G; cluster test: p = 0.049). The mean gamma peak frequency did not differ between sessions (t₁₃ = 0.17, p = 0.87; Peak_InPhase: 51.14 Hz±3.9 Hz; Peak_AntiPhase: 50.14 Hz±4.02 Hz). Importantly, the observed coherence effect was independent from any power changes (Figure 4H and 4I; all p-values >0.2). Taken together, these results indicate that 40 Hz tACS successfully modulated interhemispheric phase synchrony and behavioral outcome, depending on the chosen electrode montage and the subsequently induced phase shifts. The individual percept was influenced by (i) the absolute coherence values (Figure 4A and 4F) and (ii) the relative coherence difference between the vertical and the horizontal percept (Figures 2B, 2C, and 4B).

Outlasting Coherence Effects Are Related to Phase Differences of Stimulation

Entrainment would require that effects on the phase of the ongoing activity should outlast stimulation offset [23]. We found significantly modulated gamma coherence values after stimulation (sham, in-, anti-phase stimulation; RM-ANOVA: F_2,26 = 3.84, p<0.05) (Figure 5A). Specifically, we found a significant gamma-band coherence increase following in-phase stimulation (RS3) (Figure 5B) as compared to anti-phase stimulation (t₁₃ = 2.62, p<0.05; effect size: d = 0.67). We assessed the time course of gamma-band coherence across the six resting state intervals (time) with in- and anti-phase stimulation (session) with a two-way RM-ANOVA (Figure 5B), and found a significant interaction of session × time (F_3.13,40.65 = 3.08, p<0.05; session: F_1,13 = 3.73, p = 0.08; time: F_3.76,48.92 = 1.21, p = 0.32), indicating that coherence modulation did outlast stimulation offset. This effect was confined to the stimulated parieto-occipital cortical areas (cluster test: p = 0.039) (Figure 5B, inset). Importantly, the coherence modulation after stimulation (RS3) was independent from any changes in spectral gamma power (Figure 5D; t₁₃ = 0.07, p = 0.94). Additionally, we found a significant correlation between coherence modulation during stimulation and the outlasting changes after stimulation (cluster test: p = 0.026) (Figure 5C). These findings imply a direct relationship between effects during and after stimulation. Outlasting effects ceased after approximately 20 minutes (Figure 5B).

Electrophysiological Changes Index Behavioral Alterations

Our results indicate that the coherence change during stimulation was positively correlated with the altered MR (cluster test: p = 0.008) (Figure 4F), suggesting that increased interhemispheric coherence sustained the horizontal percept. Interestingly, the interhemispheric coherence and behavioral performance returned to baseline values before the post session (RS5) (Figures 3A and 5B). Those findings demonstrate that exogenously induced transient shifts in interhemispheric coherence selectively modulate perception of ambiguous motion.

Entrainment of Interhemispheric Phase Synchrony by tACS

We assessed the phase of the ongoing gamma-band activity during the zero crossing of the external sine wave (every 30 cycles) for four distinct frequency bands (δ, α, β_1/2, γ_2/3). For sham and post conditions, a dummy marker was inserted to mimic the tACS trigger events. We tested whether the distribution of instantaneous gamma-band phase angles was non-uniform with Rao's spacing test (Figure 6A) and assessed different distributions with Kuiper's tests. Based on a binomial distribution (p<0.0125; Bonferroni-corrected for four frequency bands), we assumed statistical significance at group level when >26 out of 28 comparisons were significant (Kuiper tests: p<0.0016 Bonferroni-corrected for 31 electrodes). The same analysis applied to the theta/delta, alpha, and beta-bands, indicated that the effect was most prominent in the gamma frequency range and to a lesser degree still present in the beta-band (Figure 6B).

The continuous visual stimulus presentation restrained us from an event-related analysis such as inter-trial coherence (ITC) and the removal of the γ₁-band impeded the analysis of a direct interaction between the ongoing activity and the externally applied sine wave. Thus, we analyzed the Shannon entropy across all spectral estimates as a surrogate marker for network dynamics and neuronal entrainment [24].

As shown previously [25],[26], tACS leads to more regular network dynamics and should therefore induce a subsequent entropy decrease. We found that the entropy was significantly reduced during stimulation as compared to sham over parieto-occipital electrodes (cluster test: p = 0.004) (Figure 6C). Entropy values returned to baseline during post (cluster test: p>0.05). We observed no differences between in- and anti-phase stimulation (cluster test: p>0.05). Figure 6D depicts the frequency-specific entropy decrease for both comparisons (stimulation/sham and post/sham), with a pronounced decrease in the beta-/gamma-range. These results demonstrated that the entropy decrease was stimulation-specific and indicated that tACS modulated network activity across several temporal scales (Figure 6D). Taken together, the biased phase relationship in gamma-band and more regular network dynamics strongly support entrainment as the putative mechanism of action of tACS [9].

Entrainment of Oscillatory Gamma-Band Signatures Modulates Alpha Power

The present findings demonstrate that 40 Hz tACS selectively modulates phase relationships in the gamma band (Figures 4A, 4D, 6A, and 6B), without any concurrent gamma power changes (Figure 4C, 4H, and 4I). In light of the entropy decrease across several temporal scales, we further evaluated their physiological interactions [27].

First, we analyzed the mean alpha power over time (8–12 Hz) (Figure 7A), revealing a prominent alpha decrease during the visual task as compared to fixation (t₁₃ = 28.6, p<0.0005; −73.5%±2.6%). We assessed the average alpha power by means of a three-way RM-ANOVA and found that alpha power was significantly modulated across conditions (sham/stimulation/post; F_1.57,20.44 = 8.13, p<0.005); however, no session (in-/anti-phase) or percept (horizontal/vertical) related effects were found (session: F_1,13 = 0.20, p = 0.67; percept: F_1,13 = 0.08, p = 0.79; all interactions: p>0.1). Secondly, we assessed the regional specificity of this power decrease and found a significant reduction over lateral parieto-occipital regions in the alpha range during tACS (cluster test: p = 0.014; Figure 7B; effect size: d = 1.45).

Given the physiological antagonistic role of alpha and gamma oscillations in the parieto-occipital cortex [27], we investigated cross-frequency interactions between alpha and gamma oscillations. Since no effects on the alpha phase coupling were observed (Figures 4A and 6B), we focused on envelope interactions. We calculated correlations (Pearson linear correlation and Fisher z-transformation) between the alpha-amplitude and the gamma₂-envelope (Figure 7C). We found a significant cluster when comparing sham and stimulation conditions over lateral parieto-occipital sensors (cluster test: p = 0.005; Figure 7D). No differences were present when sham and post conditions were compared (cluster test: p>0.05). In addition, we found no differences between in- and anti-phase stimulation (cluster test: p>0.05). These observations highlight the physiologic interaction between alpha and gamma oscillations: Entrainment of gamma oscillations promoted a secondary alpha power decrease through enhanced cross-frequency interactions as enforced by the external 40 Hz driving source.

Control Analyses

The phase-specific tACS effect on interhemispheric coherence was robust across several control analyses. First, magnitude squared coherence values can be affected by changes in amplitude correlation. Thus, we repeated all central analyses based on the phase-locking value [28], which is independent of the amplitude of a given signal. We confirmed the increase in gamma-band phase-locking during horizontal motion perception (116.3%±5.6%; t₁₃ = −2.93, p<0.05), as well as the phase-specific significant PLV modulation during stimulation (t₁₃ = 2.53, p<0.05; in-phase: 0.08±0.02, anti-phase: −0.01±0.04). Importantly, the PLV modulation after stimulation offset also confirmed all previous analyses (t₁₃ = 3.14, p<0.05; in-phase: 0.6%±0.3%, anti-phase: −1.1%±0.6%).

Second, EEG studies investigating gamma-band power can be contaminated by microsaccade artifacts [29]. We therefore analyzed eye-tracking data with respect to fixation and occurrence of microsaccades [30] to exclude potential confounds of eye movements on the observed coherence modulation. We found that subjects reliably fixated during both sessions and all conditions, independent of their percept (three-way RM-ANOVA: all factors and interactions p>0.05) (Figure S2). The influence of microsaccades was also assessed in a three-way ANOVA, indicating that the mean number of microsaccades per seconds did not vary between sessions, conditions, or percepts (three-way RM-ANOVA: all factors and interactions p>0.05) (Figure S3).

Long-Range Synchronization Mediates Cortical Information Flow

Cortical information flow between distant regions is dynamically established by selective phase synchronization [2],[6] and has been demonstrated for a variety of cognitive functions [3]. Especially, synchronization in the gamma-band has been suggested to constitute a fundamental mechanism for feature integration in the brain [1] and might facilitate the emergence of a stable percept of ambiguous stimuli [20],[31]. In particular, interhemispheric gamma-band coupling might play a crucial role for feature integration across both visual hemifields [7]. However, a number of pitfalls hamper the analysis of long-range synchronization in human EEG studies.

Especially, volume spread in the cortical tissue constitutes a severe constraint for the interpretation of human M/EEG data at sensor level [3]. Here, we utilized source reconstruction to highlight two distinct oscillatory gamma sources in the parieto-occipital cortex. The absence of any power differences between conditions or percepts reinforced our conclusion that interhemispheric coherence changes were a direct consequence of altered phase coupling and could not be attributed to differences in source configuration. Novel methods for coupling analysis at source level have successfully been introduced in the past [32]. However, these techniques ideally require the use of many more electrodes than employed in this study. Only relatively few electrodes have been utilized here, to avoid amplitude clipping of adjacent EEG electrodes during tACS, since stimulation currents exceed the usual recording range of EEG amplifiers by several orders of magnitude [9].

Previously, several connectivity measures have been introduced, which suppress coherent activity at 0° phase difference [33],[34], thus minimizing the effect of volume conduction at the expense of ignoring physiologic synchronized neuronal activity with 0° phase difference [35]. Here, we reconstructed oscillatory gamma power at source level to rule out that changes in oscillatory power may account for any of the observed coherence or phase-locking differences as observed at scalp level. We utilized sham stimulation as a baseline to control for these effects, since it is unlikely that volume conduction changes as a function of condition. Likewise, the vertical percept served as a baseline for the horizontal percept. Importantly, the directionality of behavioral and electrophysiological effects was directly related to opposite stimulation polarities. Hence, we assume that the key findings of this study were not affected by current methodological limitations.

Entrainment of Perceptually Relevant Brain Oscillations

Neocortical spike activity is directly controlled by weak electric fields generated by the cortex itself [36]. Recently, it has been shown that externally applied weak electric fields may mimic endogenous fields and therefore may modulate the temporal structure of large-scale neuronal networks [14],[25] and synchronize spiking activity [36] to different driving frequencies in a phase-specific manner [13].

Entrainment of perceptually relevant brain oscillations in humans has been demonstrated for repetitive transcranial magnetic stimulation (rTMS) [37] and tACS [9], but the exact mechanisms of action are still largely unknown. The direct interaction of a cortical oscillator and a rhythmic external source by synchronization has been suggested to constitute a key mechanism for entrainment [8]. Computational models indicated that the intrinsic network frequency is ideally suited to entrain the network [25]. Nonetheless, stimulation at adjacent frequencies with higher stimulation intensities can also entrain the network sufficiently [25],[26] and might explain the observed effects of the 40 Hz stimulation on the γ_2/3-range. Importantly, the strongest coherence modulation was observed in subjects with an intrinsic gamma peak frequency close to 40 Hz, emphasizing the need for frequency-matched stimulation protocols in future studies [38].

Previously, the assessment of neuronal activity during stimulation has been hampered by the difficulty to remove stimulation artifacts in concurrent EEG recordings. Recently, a novel approach for artifact rejection has been introduced to remove 10 Hz tACS artifacts [9]. However, its applicability is limited to lower stimulation frequencies, since the jitter in the exact tACS trigger location, caused by an internal-clock-mismatch between tACS and EEG devices, is amplified during 40 Hz tACS. Therefore, a notch-filter was applied to remove the stimulation artifact, a procedure that is commonly used for line noise removal [39]. Hence, we focused the analysis during stimulation on effects in adjacent frequency bands. Importantly, immediate stimulation effects on the phase of the ongoing activity were still present after stimulation offset, thus, making a successful gamma modulation with 40 Hz tACS highly likely. Current limitations concerning the artifact removal might be overcome with synchronized tACS-EEG systems and improved artifact rejection algorithms [9]. In addition, the combination of tACS with different imaging modalities, such as fMRI [40] or magnetoencephalography (MEG) [41] might extend our understanding of the physiological efficacy of tACS.

The modulation of long-range functional connectivity has been demonstrated for repetitive transcranial magnetic stimulation (rTMS) [42] and tACS [15]. However, none of the above studies presented conclusive behavioral and electrophysiological evidence for a successful modulation of perceptually relevant long-range synchronization.

The study by Strüber and colleagues [18] also employed the SAM paradigm. However, the authors found a divergent pattern of results. At the behavioral level, their results suggested that only anti-phasic stimulation at 40 Hz effectively modulated the conscious experience of apparent motion. Here we replicated the behavioral key finding, i.e., that anti-phase stimulation at 40 Hz introduces a bias to vertical motion. We extended the behavioral findings by demonstrating that a HD-tACS electrode montage may lead to a more focal in-phase stimulation (Figure S1), which biases the SAM perception to horizontal motion. In contrast, the in-phase montage used by Strüber and colleagues mainly targeted the occipital pole and resulted in no perceptual bias (Figure S1). Taken together, both studies suggest that 40 Hz tACS biases apparent motion perception, irrespective of SAM stimulus parameters or presentation (foveal or parafoveal) (Table S2) [43]. At the electrophysiological level, Strüber and coworkers reported that anti-phase stimulation resulted in increased interhemispheric coherence after stimulation, while we found the opposite pattern of results, i.e., in-phase stimulation enhanced synchronization, anti-phase stimulation impaired functional coupling. Strüber and colleagues had interpreted this apparent contradiction as functional decoupling, i.e., that two signals with opposite polarities still might be highly coherent as long as the phase shift remains constant. Given the differences in study design, stimulus presentation, and tACS settings (for a detailed overview please see Table S2), we assume that the divergent patterns might result from the fact that even slight variations in stimulation intensity or electrode montage might lead to opposite network effects [44]. In addition, divergent results might also be explained by the cortical network state dependence of tACS effects [14],[38]. These findings highlight the need for well-controlled tACS protocols, which should ideally be based on computational models and electric field predictions [25],[45].

In this study, we based our hypothesis on phase-specific electric field predictions (Figure S1) and subsequently presented evidence for the selective modulation of perceptually relevant interhemispheric gamma synchronization. Crucially, coherence effects, as induced during stimulation, outlasted the offset by approximately 20 minutes.

It has been argued that the low spatial specificity might constitute a severe limitation of tACS [46]. However, this characteristic might prove beneficial for the modulation of large-scale networks. Here we utilized bilateral 4×1 ring electrode montages [17] to selectively stimulate regions of extrastriate visual cortex involved in motion perception (Figure S1) [21],[47]. In the future, multi-channel stimulators and additional modeling work [16] will hopefully allow more focal stimulation settings.

Interestingly, we found that network dynamics across multiple temporal scales become more regular during external rhythmic stimulation. In particular, our results reveal that alpha power was selectively reduced after entrainment of gamma signatures. However, effects on phase coupling were mainly observed in the gamma-band. Our results support the idea that tACS effects on the phase of the ongoing activity are frequency-band specific [46], but ancillary effects might not be constrained to a single frequency-band [11]. At present, it remains unclear whether neuronal entrainment is the only mechanism contributing to the coherence effects or whether mechanisms of neural plasticity are equally important [48]. In absence of effects on alpha phase coupling, it is unlikely that entrainment induced the transient alpha power decrease. Our results rather imply that entrainment of gamma-band activity influenced the physiological antagonistic alpha-gamma interplay in the parieto-occipital cortex [27],[39]. Conversely, the alpha power decrease might serve as a surrogate marker for the selective entrainment of gamma band signatures, since this modulation resembles a physiologic antagonistic response to pronounced gamma band activity.

Physiological Efficacy of 40 Hz tACS

A number of recent studies have demonstrated that 40 Hz tACS modulates cognitive processing, e.g., enhances fluid intelligence [49], induces lucidity in dreams [50], or modulates the conscious experience of apparent motion [18]. So far, most studies utilized 40 Hz stimulation to entrain the gamma-band, even though some evidence suggested that 60 Hz tACS might be more effective than 40 Hz tACS [51]. However, results by Voss and colleagues [50] indicated that the efficacy of tACS at 25 Hz and 40 Hz might be similar. Currently, it is unclear whether there are distinct sub-bands within the gamma-band [52] and, furthermore, whether they can selectively be entrained with tACS. Previous tACS-EEG studies suggested very narrow-banded effects of tACS [9],[50], while our present results indicate that 40 Hz stimulation modulated the gamma-band in a broad frequency-range. Importantly, we found that the effects of 40 Hz tACS were mainly confined to the gamma-band, indicating that tACS operates within canonical frequency boundaries constituting the rhythmic brain architecture [53]. These findings imply that tACS might be a powerful tool to assess causal contributions of certain frequency-bands to distinct cognitive processes. Given that we observed clear cross-frequency interactions operating within physiologic boundaries, we urge caution when interpreting tACS effects in absence of electrophysiological recordings [54].

Interestingly, our data also indicated that subjects with a gamma coherence peak close to 40 Hz exhibited the strongest coherence modulation during 40 Hz tACS (Figure 4G). Thus, previously observed effects might be contorted due to a large intersubject variability. These findings further highlight the need for a rational design of tACS protocols [55].

The Role of Cortical Network States for Perception

Recently, it has become evident that cortical dynamics across multiple spatiotemporal scales influence conscious perception [3],[56]. Multi-stable phenomena have been related to changes in oscillatory activity in large-scale neuronal networks and might therefore reflect the periodical and constant reevaluation of sensory input [57]. Crucially, it has been shown that both, local ongoing activity [58] and interregional network activity [4], influence subsequent perception. Bistable perception is ideally suited to study underlying network activity, since identical sensory input can lead to distinct percepts, depending on the current network state [4].

Previously, perception of the SAM has been linked to different spectral features. In particular, it has been demonstrated that frontal gamma power increments [59] together with parieto-occipital alpha power decrements [60] precede a perceptual switch. Importantly, the subjects' perceptual bias was influenced by the level of interhemispheric gamma-band coherence (Figure 2C) [20] and the individual percept was enforced by selectively modulating coherence levels by tACS. Frontal gamma-band increments might trigger changes in parieto-occipital networks [61] and thereby influence perception. Our data suggest that the selective entrainment of interhemispheric gamma-band synchrony might mimic the physiologic mechanism of top-down controlled percept reversals. A similar mechanism has previously been demonstrated for bottom-up processes with lower level neuron populations entraining rhythmic patterns in higher cortical areas in a feed-forward fashion [62].

Complementary coupling analyses in source space employing human M/EEG [3] will be necessary to determine whether top-down control of the SAM is associated with the selective entrainment of interhemispheric phase synchrony.

Interestingly, decreased parieto-occipital alpha activity has been linked to a destabilization of the SAM [60]. In our study, we found a decrease in alpha activity in response to the entrainment of physiologic gamma-band signatures, however, without any accompanying switch rate changes (Figure 3B). This observation indicates that the alpha decrease might actually reflect a secondary process in response to the gamma mediated perceptual reversals, thus, highlighting the antagonistic role of alpha and gamma oscillations [27].

Taken together, our findings strongly support the idea that neuronal interactions across different cortical regions are encoded at multiple temporal scales [56] by selective synchronization between task-relevant areas [3].

Confounds and Limitations

tACS studies have a seemingly endless search space: Electrode placement, stimulation frequency, intensity, and duration are obvious concerns. Here we based our hypothesis on two recent SAM studies [18],[20] and subsequently reproduced their main findings. We documented the electrophysiological signatures of SAM perception in absence (Figure 2A–2C) and in presence of tACS (Figure 4A and 4B). However, a number of limitations do apply. (i) We only applied tACS for 20 minutes, since it had previously been shown that 20 minutes of 40 Hz tACS effectively modulated apparent motion perception [18]. While 20 minutes of stimulation are well within current safety limits [63], it is unclear how stimulation duration impacts the behavioral and electrophysiological outcome. (ii) Furthermore, our results suggest that stimulation at individual peak frequencies might actually be more efficient (Figure 4G) than using a fixed stimulation frequency. (iii) Another limitation is the preceding sham session. In accordance with previous results [9],[38], we observed outlasting stimulation effects for approximately 20–30 minutes, which impede an inverse procedure. Here we utilized a post condition to validate the sham condition and to control for outlasting behavioral and electrophysiological effects. Throughout the study we did not find any differences between sham and post conditions. Furthermore, the counter-balanced within-subject design in two sessions allowed us to study directionality effects, thus, minimizing concerns that the subjects could distinguish between real and sham stimulation. In fact, it was impossible for subjects to distinguish in- and anti-phase stimulation. (iv) Another clear restriction is the unbalanced electric field distribution (Figure S1). While our in-phase stimulation was very focal, the anti-phase montage led to a more distributed electric field. However, in contrast to the study by Strüber and colleagues [18], both montages targeted the extrastriate visual cortex and modulated the behavioral outcome. We believe that multi-channel stimulators and optimized electric field models will improve the focality of tACS in the future. We expect that a rational design of tACS experiments using frequency-matched and neuro-navigated protocols will improve the efficacy in human tACS studies [55].

So far, the basic physiological principles behind the efficacy of tACS are still largely unknown [46]. Further work in human, animal, and modeling studies will hopefully advance our understanding of tACS and its interactions with neuronal circuits. In the future, complementary modeling approaches may guide individually tailored stimulation protocols and electrode features to overcome current limitations, such as the unclear electric field distribution in the head, the cortical state dependence, and the high intersubject variability.

Participants

In accordance with previous studies [18],[20], 14 healthy volunteers (eight females, six males, mean age: 27.5±6.7 years) were recruited from the University Medical Center in Hamburg, Germany, including two of the authors (RFH, HK). All participants (including participating authors) were blinded towards the stimulation sequence. All subjects were right-handed, reported no history of neurological or psychiatric disease, and were medication-free during the experiments. They all had normal or corrected-to-normal vision. All participants gave written informed consent according to the local ethics committee and the Declaration of Helsinki. This study has been approved by the local Ethics Committee of the Medical Association in Hamburg, Germany (IRB number: PV4335).

Stimuli and Procedure

The SAM (Figure 1A) was generated with the Psychophysics Toolbox [67] implemented in MatLab (The MathWorks Inc.) and presented on a BenQ XL2420T screen (1,920×1,080, 120 Hz). The display was 60 cm away from the participants. The horizontal dot distance was 5.1°, the vertical 6.9° at a constant dot size of 0.35°. We introduced a shorter horizontal than vertical distance to compensate the vertical bias of equidistant SAMs [19]. Every trial of continuous visual stimulation lasted 1 minute. Participants reported their percept by pressing two different buttons with their right hand. All volunteers participated in two sessions of the experiment carried out within 1 week. After preparation of the tACS and EEG electrodes (see below), participants completed a training session with ambiguous and non-ambiguous trials to familiarize volunteers with the stimulus and to ensure that all participants could reliably track their percepts. On both days all participants completed ten trials during sham, 20 trials during stimulation (in- or anti-phasic tACS), and ten trials during the post condition. Whether participants were stimulated with in- or anti-phase stimulation on the first day was counterbalanced across subjects (Figure 1B, the participating experimenters were blinded whether they received in- or anti-phasic stimulation). A sham condition always preceded electrical stimulation to avoid carry-over effects [38]. Altogether, six resting state epochs, 3 minutes each, were recorded during stable fixation of a central dot to assess outlasting changes.

Data Acquisition

Data Analysis

EEG data

Data analysis was performed using MatLab (The MathWorks Inc), EEGLab) [69], FieldTrip [70], and customized MatLab code. All preprocessing steps were performed with EEGLab. The recorded EEG was filtered between 1 Hz and 100 Hz using two-pass finite element response filters (eegfilt.m function) as implemented in EEGLab and down-sampled to 1,000 Hz. For the analysis of the SAM data, a higher (>6th) order two-pass butterworth notch filter in the range from 35 to 45 Hz was applied to the sham, stimulation, and post measurements to remove the stimulation artifact and to keep results comparable across all conditions. Forward and backward filtering was performed to avoid phase distortions. Note, that sham and post conditions were also analyzed without the notch-filter for Figure 2. Then the data was segmented into 3,000 ms epochs, starting 500 ms after an indicated perceptual switch. Epochs containing excessive noise, saccades, or muscle artifacts were removed after visual inspection. Data acquired during resting states was split into 1-second segments. Segments containing artifacts were excluded after visual inspection.

Spectral estimates for SAM and resting state data were computed by means of a sliding Hanning window (1–35 Hz, 1 Hz steps, 500 ms window) and a multi-taper approach [71]; (36–100 Hz, 1 Hz steps, 250 ms window length, ±10 Hz frequency smoothing, SAM: 59 slepian tapers, resting state [RS]: 19 slepian tapers). Slow frequencies (delta/theta) were pooled and treated as one frequency band given that (a) delta-band activity is likely confounded by the stimulus presentation rate (visual tokens alternated every 250 ms and (b) a recent study already demonstrated that 6 Hz tACS did not impact apparent motion perception [18]. Coherence estimates were calculated for 13 interhemispheric channel pairs (inset Figure 2A) in 1 Hz steps and then averaged across the frequency bands of interest. The increase in interhemispheric coherence was quantified as the relative coherence increase for horizontal over vertical motion perception, since the vertical percept serves as a rigorous baseline that controls for effects such as volume conduction or reference electrode position [20]. The number of data segments per subject was balanced across conditions and percepts to avoid a sample size bias.

Cortical sources of gamma-band activity were reconstructed with a linear beamforming approach [32] as implemented in FieldTrip. A volume conduction model was derived from the MNI template brain, resulting in a three-shell model. The leadfield matrix was calculated using the boundary element method. The source activity at each grid point was estimated by constructing a spatial filter using the leadfield at a given point and the cross-spectral density matrix. For each participant and condition, the cross-spectral density matrix was calculated between all 31 EEG channels, separately for the RS (baseline) and the respective conditions and percepts. Differences were assessed by cluster-based permutation statistics [72].

In order to assess whether network activity was more regular during stimulation, we calculated the Shannon entropy at every channel for every condition on normalized spectral estimates S_x, i.e., for each frequency the spectra were divided by the sum of all estimates across channel and these quantities were formally treated like probabilities. The entropy H(X) was calculated for four frequency-bands of interest f (δ, α, β_1/2, γ_2/3) at every given channel x as:

Cross frequency interactions between alpha and gamma were assessed for every channel, condition, and subject separately. In order to calculate the amplitude-envelope-correlation between both, we first band-pass filtered every trial in the alpha and the gamma₂ range (Figure 7C), similar to the approach, which had been introduced and validated by Voytek and colleagues [39] for 1,000 ms data segments. We also utilized a two-way, zero phase-lag, finite impulse response filter (eegfilt.m function in EEGLab toolbox [69]) to prevent phase distortion. Then Hilbert's transform was applied to extract the amplitude of the alpha (Aα) and the gamma (Aγ) oscillation. Then a second Hilbert transform was used to extract the envelope (Eγ) of the band-pass (8–12 Hz) filtered gamma amplitude. Amplitude-envelope-correlations between Aα and Eγ were calculated for every trial separately. Subsequently, correlation values were Fisher-Z-transformed and averaged.

The instantaneous phase of the ongoing activity was also derived from the Hilbert transformation, after band-pass filtering the signal in different frequency bands as outlined above, and subsequently used for circular statistics.

Statistical analyses

In accordance with previous reports [18],[20], we focused our analysis on the electrode pair of interest (Figure 2A, red in inset). If not stated otherwise, we used repeated measures analyses of variance (RM-ANOVAs) with post hoc planned contrasts according to our hypothesis. Data were tested for normality with Lilliefors test and for sphericity with Mauchly's test. Where applicable, Greenhouse-Geisser correction was applied and corrected p-values and degrees of freedom are reported. Effect size was quantified by means of Cohen's d. All values reported are mean ± SEM. We confirmed the regional specificity of the observed effects with permutation statistics as implemented in Fieldtrip (Monte Carlo method; 1,000 iterations; p<0.05). The cluster approach corrects for the multiple comparison problem [72]. Dependent samples t-tests were computed at each sensor pair and for each frequency. Clusters were obtained by summing up t-values, which were adjacent in space and frequency below a cluster alpha level of 5%. A permutation distribution was computed by randomly switching condition labels within subjects in each of 1,000 iterations. The permutation p-value was obtained by comparing the cluster statistic to the random permutation distribution. The observed clusters were considered independently significant when the sum of t-values exceeded 95% of the permutated distribution. Circular statistics were calculated with the CircStat toolbox for MatLab [73]. We utilized Rao's spacing test to assess the non-uniform distribution of instantaneous phase angles, which is advantageous for assessment of multimodal non-uniform distributed data, in order to account for the procedure with two sessions. Differences in non-uniform circular distribution between conditions were assessed with Kuiper's tests.

Cluster-based permuted correlation analyses: In order to link the coherence modulation during stimulation to (i) the change in behavior and (ii) the outlasting coherence effects, we implemented a data-driven cluster-based permutation test based on Pearson's linear correlation coefficient. We calculated a baseline corrected composite measure of the behavioral MR by means of a motion index: MI  =  (MR_InPhase − MR_ShamIn) − (MR_AntiPhase − MR_ShamAnti), resulting in a single value per subject. During each iteration of the permutation test, we compared the coherence difference ΔCoh  =  Coh_InPhase − Coh_AntiPhase to the difference between both sham conditions and calculated a correlation value per channel pair. We utilized the Monte Carlo method for cluster tests as implemented in Fieldtrip. Therefore, we transformed the resulting correlation coefficients (r-values) into t-values using the following formula (n =  number of subjects):

Then clusters were formed based on combining adjacent sensors with p-values below a cluster alpha of 20% and summing up t-values. A permuted distribution was computed randomly switching condition labels within subjects in each of 1,000 iterations. On every iteration, clusters were again formed based on combining neighboring channels with t-values below the cluster alpha. The sum of t-values from the largest cluster was added to a permutation distribution. Finally, only clusters spanning at least two adjacent channels with a p<0.05 tested against the permutation distribution were considered significant. The same approach was used to compare the coherence modulation in the gamma-band after stimulation offset. However, here we calculated a coherence modulation index per channel pair after stimulation offset, resulting in a channel pair × subject matrix that was used for the correlation analysis. Hence, correlation values were not computed across different channel pairs.