Fig 1.
Experiment 1. (a) Participants listened to frequency-modulated (FM) auditory stimuli with varying modulation depths and were tasked with identifying silent gaps within stimuli. (b) Transcranial alternating current stimulation (tACS) was administered bilaterally targeting the auditory cortices using a multichannel system.
Concurrently, tACS-induced electrical signals were recorded via EEG for subsequent post hoc phase-lag analysis. The bottom brain maps depict the average estimated electric field distribution (E-field) of our stimulation montage across a cohort of 39 independent subjects (modified from [31], which was published under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited). (c) FM stimuli were initiated at random phases, producing variable phase lags in relation to the tACS signal. The trials were categorized into six phase-lag bins, constituting seven experimental tACS conditions: six specific phase lags and one sham condition. For visualization purposes, only 50 s of each stimulation condition is shown. The insets (transparent boxes at the beginning of each condition) show the same data zoomed into the first second to better observe phase lag differences. (d) Individual data showing hit rates as a function of the FM stimulus phase for each tACS condition when the FM stimulus was modulated at 11% (top) and 39% (bottom). Each column shows the data from a different participant. The color code is shown in (c). (e) Strength of behavioral entrainment to the FM stimulus (entAmp-FM) at each modulation depth. (f) Gap size threshold determined at the beginning of each session for each modulation depth. (g) Hit rate for each modulation depth. (h) Number of false alarms (FA) for each modulation depth across all stimulation conditions. (i) EntAmp-FM as a function of tACS lag for each modulation depth. Solid lines show the actual amplitude parameters obtained from the initial cosine fits of the data in (d), and dashed lines represent the second cosine fit to estimate the optimal tACS phase for modulating entrainment to the auditory stimulus. Each row represents a different participant, and the same three participants are shown for each modulation depth. (e–h) Each dot represents a single participant. Box plots show median (horizontal black lines), mean (black cross), 25th and 75th percentiles (box edges) and extreme datapoints not considered outliers (±2.7σ and 99.3 percentiles, whiskers). Red crosses represent outliers (more than 1.5 of the interquartile range away from the bottom or top of the box). *p = 0.05. Numerical data for panels d–i can be found in [32].
Fig 2.
Experiment 1, tACS effects. (a) Realignment procedure.
The optimal tACS lag (orange asterisk) was determined from the cosine function fitted to the entAmp-FM by tACS phase-lag data (dashed gray line). The phase bin closest to the optimal phase was identified (pink asterisk). This bin was set to zero phase and the remaining phases were wrapped around. The new realigned data is shown in blue. (b) EntAmp-FM as a function of tACS separated by modulation depth. The tACS lags correspond to the individually realigned lags; phase zero represents the individual optimal tACS lag estimated in (Fig 1I). EntAmp-FM values from the realigned peaks and troughs (semi-transparent) were excluded from further analyses. (c) Procedure for obtaining entAmp-FM at the optimal half-tACS cycle (tACS(+)) and its opposite (tACS(−)). (d) EntAmp-FM as a function of tACS separated by modulation depth. (e) Estimated marginal means, showing the main effects of the tACS condition and modulation depth (ModDepth). (f) EntAmp-FM differences between the three tACS conditions in (c) normalized (z-scores) to permuted distributions. (b, d, f) Each dot represents a single participant. Box plots show median (horizontal black lines), mean (black cross), 25th and 75th percentiles (box edges) and extreme datapoints not considered outliers (±2.7σ and 99.3 percentiles, whiskers). Red crosses represent outliers (more than 1.5 of the interquartile range away from the bottom or top of the box). *p = 0.05, **p < 0.001. Numerical data for panels b, d, and f can be found in [32].
Fig 3.
Experiment 2. (a) Participants listened to complex noise stimuli and were tasked with identifying silent gaps within them.
Concurrently, tACS was applied at one of four frequencies within the delta range. (b) Hit rates and mean reaction times as functions of tACS condition. (c) For each tACS frequency, gaps were grouped based on tACS phase. Cosine functions were fitted to the data to estimate the amplitude of behavioral entrainment to tACS. Gap detection performance at sham was used to establish a baseline level of rhythmic fluctuations. We assumed an oscillator that resets at each stimulus onset during sham. Gaps were grouped according to these hypothetical oscillators, and cosine functions were fitted to the resulting data. This was done for the four frequencies used for tACS stimulation. The amplitude parameter from these fits served as the baseline for analyzing tACS effects. In the figure, this is illustrated for the 2 Hz tACS condition. (d) Individual data showing hit rates as a function of tACS phase. The dashed lines indicate best-fit cosine functions. Each plot had a different participant. (e) Effect of tACS phase on gap detection performance. The plot shows the normalized values computed as (entAmp-tACS − baseline)/baseline, for each frequency. (f) Optimal tACS phase for gap detection (prefPhase-tACS) obtained from cosine fit. (b, d, e, f) Each dot represents a single participant. Box plots show median (horizontal black lines), mean (black cross), 25th and 75th percentiles (box edges) and extreme datapoints not considered outliers (±2.7σ and 99.3 percentiles, whiskers). Numerical data for panels b, d, and e can be found in [32].
Fig 4.
Experiment 2: Oscillator model.
(a) Model results for a 2 Hz ongoing oscillator at each tACS frequency, shown for three different k values– tACS strength relative to the ongoing oscillator amplitude. For illustration purposes, the tACS signal in the plots is phase-shifted by 180 degrees relative to the ongoing oscillation to better visualize entrainment. The percentage at the top of each plot represents the change in entrainment due to tACS − (entrainment amplitude during tACS − baseline)/baseline*100. The dashed line indicates the start of the stimulation at time = 10 s. (b) Output of the oscillator model showing the change in entrainment by tACS − (entrainment amplitude during tACS − baseline)/baseline*100 – as a function of the tACS amplitude relative to the baseline, and the frequency mismatch between the tACS frequency and the resonance frequency of the internal oscillator. (c) Individual data showing the correlation between the model output – change in entrainment relative to baseline – and the empirically observed amplitude of behavioral entrainment to tACS − (entAmp-tACS-baseline)/baseline – as a function of the model’s ongoing oscillator resonance frequency. The boxes at the top of each plot display the effect of tACS in Experiment 2 for each individual participant. Colored squares indicate positive (top) and negative (bottom) tACS effects relative to baseline. Red squares highlight participants with a tACS effect greater than 1, meaning entAmp-tACS is at least twice the baseline amplitude. RF: resonance frequency, red asterisks. (d) Predicted individual resonance frequencies. Each dot represents a single participant. (e) Dendrogram showing the clustering results. Each color represents a different cluster. (f) EntAmp-tACS values as a function of tACS frequency grouping participants based on their cluster identities in (e). Spread plots at the top show the predicted individual resonance frequencies for each participant in the cluster corresponding to the plots at the bottom. Each dot represents a single participant. Box plots show median (horizontal black lines), mean (black cross), 25th and 75th percentiles (box edges) and extreme datapoints not considered outliers (±2.7σ and 99.3 percentiles, whiskers). Numerical data for panels d and f can be found in [32].
Fig 5.
Experiment 3, EEG. (a) Cartoon depicting the stimulus design.
Participants listened to sounds modulated at different frequencies and detected gap periods presented in different phase bins of the modulation cycle. (b) EEG Amplitude spectra separated by FM frequency. The dashed vertical lines mark the FM frequency (in color) and first harmonic (black). Average group data are shown in blue, whereas individual data are shown in gray. (c) Resultant vector length spectra separated by the FM rate. The colors follow the same convention as in (b). (d) Normalized amplitude values quantifying neural entrainment to the FM stimulus separated by frequency. The amplitude values in (b) were normalized by dividing the amplitude of the EEG activity observed at each FM frequency during the presentation of the FM stimulus at a specific frequency by the mean amplitude recorded at that frequency when the FM stimulus was presented at all other frequencies. (e) Normalized resultant vector length as a function of FM frequency. Normalization was performed as described in (d). (f) Optimal FM frequency (rate) for neural entrainment (FM frequency with the highest normalized resultant vector length). (d–f) Each dot represents a single participant. (d–e) Box plots show the median (horizontal black lines), mean (black cross), 25th and 75th percentiles (box edges), and extreme data points not considered outliers (±2.7σ and 99.3 percentiles, whiskers). Red crosses represent outliers (more than 1.5 of the interquartile range away from the bottom or top of the box). Solid red lines display the best fit from the linear model, and dashed red lines show the 95% confidence intervals. Numerical data for panels d and e can be found in [32].
Fig 6.
(a) Individual data showing hit rate as a function of the FM stimulus phase separated by FM frequency. The dashed lines represent the cosine fits. Each plot had a different participant. (b) Gap size threshold as a function of FM frequency. These thresholds were determined using a staircase procedure at the beginning of each session. (c) Hit rate as a function of FM frequency. (d) Strength of behavioral entrainment to the FM stimulus (entAmp-FM) as a function of FM frequency. (e) Optimal FM phase of gap detection performance (prefPhase-FM) for each FM frequency. (f) Preferred FM rate for behavioral entrainment (FM frequency inducing the highest entAmp-FM in (d)). (b–f) Each dot represents a single participant. (b–d) Box plots show the median (horizontal black lines), mean (black cross), 25th and 75th percentiles (box edges), and extreme data points not considered outliers (±2.7σ and 99.3 percentiles, whiskers). Red crosses represent outliers (more than 1.5 times the interquartile range away from the bottom or top of the box). Solid red lines display best fit from the linear model and dashed red lines show the 95% confidence intervals. Numerical data for panels b–d can be found in [32].