Individualized Closed-Loop Acoustic Stimulation Suggests an Alpha Phase Dependence of Sound Evoked and Induced Brain Activity Measured with EEG Recordings

Ethics statement and participants

All subjects in this study gave written informed consent for participation and to share their deidentified data with Elemind Technologies according to our protocol approved by the University of Connecticut Institutional Review Board. Subjects were compensated at an approved hourly rate for participating in the experiment. Data for three out of 22 subjects total was not included in the present study due to incomplete datasets across conditions or extensive signal artifacts. A total of nineteen young adults (9 females, 10 males) ages 18–32 [mean ± SD = 24.47 (±5.8)] participated in this study. All participants had normal or corrected-to-normal vision and intact hearing ability with clear ear canals and no history of neurological disorders and confirmed they were not taking medications. A subset of data presented here appears in a preprint report (Bressler et al., 2023) and the mean ERP-P1 latency from this subset was used in a separate study to set fixed alpha phases (Bressler et al., 2023).

EEG recording task paradigms

EEG recording paradigms were designed to test the hypothesis that sound played phase locked to frontal (Fpz) individually tailored trough or peak alpha phases have distinct effects on auditory ERP and alpha oscillations. Primate frontal and auditory cortices both have short latency auditory evoked responses, as demonstrated with intracranial recordings by our group (Marrouch et al., 2020) and others (Howard et al., 2000; Happel et al., 2010; Haegens et al., 2015; Komatsu et al., 2015; Kajikawa et al., 2017). Moreover, frontal and auditory cortices are known to generate alpha oscillations under a variety task conditions (Haegens et al., 2015; de Pesters et al., 2016; Lakatos et al., 2016; Bonnefond et al., 2017; Billig et al., 2019). Robust frontal alpha oscillations are observed with eyes closed and localized to superficial radial dipole layers with more robust signals measured with EEG, as compared with MEG (Srinivasan et al., 2006). Thus, we tested feasibility to play sounds phase locked to alpha measured with frontal (Fpz) EEG electrodes, as illustrated (Fig. 1). In addition, we recorded from a prefrontal (Fz) location and referenced both electrodes to the left mastoid (M1). All EEG recordings were carried out inside a sound isolation room while subjects participated in three task paradigms (Fig. 1). For the “baseline eyes closed task,” participants closed their eyes and sat quietly while EEG was recorded for an average of 2.36 (0.32 s) following a 60 s baseline in order to quantify their IAF, as detailed below (Figs. 1A, 2A). In the second “random phase eyes open task,” participants watched a silent cartoon video in a relaxed sitting position and were instructed to ignore sounds (Fig. 1B), as in prior auditory evoked response studies (Choi et al., 2013; Prakash et al., 2016). Prior studies found alpha levels are reduced with eyes open which is hypothesized to be due to increased allocation of attention to auditory sensory input (Clements et al., 2022). Likewise, here the “random phase eyes open task” resulted in reduced prestimulus alpha power levels which allowed us to measure the auditory ERP component latencies independent of ongoing alpha (detailed below). Data from these first two tasks was used to estimate the individually tailored alpha trough and peak phases aligning the sound evoked positive, P1, response to the following peak and trough phases, respectively (Figs. 1D,E, 3). The third, “trough and peak phase task,” was designed to keep subjects alert, while ignoring sounds with the goal of promoting high prestimulus alpha power levels. This task consisted of two back-to-back 15 min sessions where participants were instructed to ignore auditory stimuli while they carried out “mental arithmetic” (Palva et al., 2005), while sitting in a relaxed position with eyes closed. The “mental arithmetic” was to rehearse a newly assigned 11 by 1 (double digit) multiplication table on which they were quizzed following the session. For example, the number 13 multiplied by each number in the series spanning from 10 to 21. Following each 15 min session, subjects verbally reported the 11 multiplications and no quantitative analysis was performed. Post hoc alpha power analyses detailed below confirmed that prestimulus alpha power was high in the “trough and peak phase task” used to quantify phase-dependent differences (Fig. 4). The auditory ERP latencies and amplitudes were compared across random, trough, and peak phases, as detailed below (Figs. 5, 6; Table 1).

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Figure 1.

EEG recording and task conditions used to determine and test brain responses to individualized alpha phases. A–C, Scalp EEG was recorded while subjects participated in three separate task paradigms. There were two recording locations including frontal (Fpz) and prefrontal (Fz) locations referenced to the left mastoid (M1). A, Ai, The first task is the “baseline eyes closed” task where no sounds are played as EEG data was collected for a total duration of 2 min in all subjects. Aii, EEG recording of alpha band activity in the same time window for frontal (Fpz) and prefrontal (Fz) recording locations in the example subject (Sub 136). B, Bi, For the “random phase eyes open task,” after a 30 s baseline, pink-noise sounds are delivered phase locked to random alpha phases with an average ISI of 927 ms for a total of 15 min (aka 900 s). Bii, Average auditory ERP obtained at frontal (Fpz, top) and prefrontal (Fz, bottom) locations for an example subject (Sub 136). C, Ci, For the “trough and peak phase task,” after a 30 s baseline, pink-noise sounds are delivered phase locked to random alpha phases with an average ISI of 1,636 for a total of 15 min (aka 900 s). Ciii, Average auditory ERP for peak and trough phase-locked sounds at frontal (Fpz, top) and prefrontal (Fz, bottom) locations. D, E, Schematic illustration of how the individualized alpha peak and trough phases are estimated for an example subject (Sub 136). Here and elsewhere, the solid line denotes the mean and the light shaded area the standard error of the mean (SEM).

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Figure 2.

Estimation of IAF. A, B, Multitaper time-frequency power spectrograms for the example subject (Sub 136) measured at the frontal (A, Fpz) and prefrontal (B, Fz) locations. Ai, Bi, Detrended spectral density plots used to find the frequency with maximum power as an estimate of IAF for an example subject (Sub 136). Red dot indicates the location of the power maximum in each plot. C, D, The population average of multitaper time-frequency power spectrograms (n = 19) for the frontal (C, Fpz) and prefrontal (D, Fz) locations. Ci, Di, Corresponding population average detrended PSD plots for frontal (Ci) and prefrontal (Di) locations. As the power tends to be lower for people with higher frequency IAF, the population average spectrogram yields IAFs of 9.6 and 9.67 Hz at frontal (Fpz) and prefrontal (Fz) locations, whereas the average of individual IAFs is closer to 10 Hz (see text).

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Figure 3.

Individualized trough and peak sound onset phases align auditory evoked P1 potentials with poststimulus peak and trough phases with minimal phase-locking error. A, As illustrated for trough phase, the target phases vary systematically with the ERP-P1 latency and IAF (lines Hz) across subjects (n = 19). B–H, Radial plots of individual subject phases (thin lines, circles), population means (thick line), and standard deviations (circular arc). B, C, Radial plots show the opposing distributions of target trough and peak phases which have means (standard deviations) of 127° (44°) and 307° (44°), respectively. This corresponds to opposing (180° shifted) alpha phases. In A–C, the orange filled circles denote the individualized phases for Subject 136 who has an IAF of 11.9 Hz (as in Figs. 1 and 2). In A–C, the pink filled circles show a hypothetical subject with an IAF of 10 Hz and an ERP-P1 latency of 50 ms for reference. D, E, Radial plots show the distribution of actual trough and peak phases which have means (standard deviations) of 127 (−64) and 308 (−68.85) angular degrees, respectively. This corresponds to opposing (181° shifted) alpha phases. The target (B, C) and actual (D, E) phase-locked phases are not significantly different at the frontal (Fpz) location (Watson's U2 test: trough U = 0.002 and p = 0.350; peak U = 0.005, p = 0.300). F, G, At frontal (Fpz) locations, with frontal trough and peak phase-locked sounds, the auditory evoked P1 potentials occur at 337° (38°) and 166° (53°), respectively. Thus, the P1 potentials arrive in opposing (171° shifted) phases with trough and peak sound onsets at Fpz. H, I, At prefrontal (Fz) locations, with frontal trough and peak phase-locked sounds, the auditory evoked P1 potentials occur at 318° (39°) and 137° (42°), respectively. Thus, the P1 potentials arrive in opposing (181° shifted) phases with trough and peak sound onsets at Fz. J, K, The mean actual phases achieved with real-time ecHT phase-locking are close to the target phase. J, The PLV is 0.92(0.02) and the phase-locking error relative to target phase is −9° (5) with the ecHT causal filter signal processing. K, The mean PLV is 0.68 (0.12) and the PE is −13.04° (32) with standard Hilbert transform (sHT) causal filter signal processing. The length of the mean vector denotes the mean, with the arc corresponding to the standard deviation in PEs across participants. Radial histogram phase analysis and radial plots are based on a cosine function estimate of the alpha oscillations and using a bin size of 20°. Data include n = 19 subjects and additional pink dot is a reference point.

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Figure 4.

High prestimulus alpha levels with “trough and peak phase task” assure potential to phase lock to alpha. A–D, EEG data obtained during the “trough and peak phase task” condition, yields high alpha levels at −500 ms (A, C) versus −700 ms (B, D) prior to sound stimulus onset at frontal (Fpz) and prefrontal (Fz) locations. Alpha levels are highest in the −500 ms time window before sound onsets (A, B). Permutation testing with post hoc cluster analyses confirms that prestimulus alpha power does not vary with trough versus peak phase (p > 0.05). Beta is significantly greater for peak versus trough phases at the frontal (Fpz, A, C) location in the −500 and −700 ms prestimulus windows with p = 0.011 and p = 0.008, respectively. Gamma is significantly greater for peak versus trough at frontal (Fpz, C) locations and greater for trough versus peak at prefrontal (Fz, B) locations with p = 0.0101 and p = 0.020, respectively. E, F, Prestimulus alpha levels are also high with a second analysis that optimizes quantification of power spectral frequencies that are time locked and phase locked to sound onsets in the prestimulus time window (−700 ms) at both locations (Fpz, Fz). In addition, this approach finds high delta band power in the prestimulus time window likely due to the slow quasi periodic ISIs used for playing phase-locked sounds. Permutation testing finds no differences in delta or alpha power levels across phase-locked conditions. G–K, Data obtained during the “random phase task” condition, standard non-normalized PSD analysis confirms that alpha power is at low levels at −500 ms (G, J) and −700 ms (H, K) prior to sound stimulus onset at frontal (Fpz) and prefrontal (Fz) locations. I, L, With the “random phase task” condition, alpha power also is low in the prestimulus time window (−700 ms) using the second method of analysis as in E and F panels.

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Figure 5.

Amplitudes of the average auditory ERP components vary with individualized alpha phase, but prestimulus alpha levels do not. A, B, The pink-noise auditory ERP response acquired during the “random phase eyes open task” and averaged across all subjects (n = 19) for frontal (Fpz, A) and prefrontal (Fz, B) locations. C, D, Phase-dependent differences are observed across five components (Pa, P1, N1, P2, N2) of the subject averaged auditory ERP at frontal (Fpz, C) and prefrontal (Fz, D) locations. Pa and N2 potentials are smaller for the trough (blue) versus peak (red) phase condition. In contrast, P1, N1, and P2 components are all larger for the trough (blue) versus peak (red) condition. C, D, Bottom, Permutation tests followed by cluster analysis (Materials and Methods) confirms significant phase-dependent differences across all five ERP components. For frontal (Fpz, C) location, the maximum p values for Pa, P1, N1, P2, and N2 are 0.0003, 0.0021, 0.0010, 0.0006, and 0.0134 at 16, 60, 102, 160, and 257 ms time points, respectively. For prefrontal (Fz, D) location, the maximum p values for Pa, P1, N1, P2, and N2 are 0.0002, 0.0026, 0.0040, 0.0008, and 0.0101 at 16, 62, 104, 158, and 260 ms time points, respectively. Shaded boxed areas correspond to the temporal windows used to compare ERP components here and for data shown in Figure 6 used to run additional pairwise t tests (Table 1).

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Figure 6.

Auditory ERP component latencies are consistent across phase conditions but amplitudes vary with peak versus trough. A, B, No significant differences are observed for ERP component latencies (Pa, P1, N1, P2, and N2) for trough (blue), peak (red), and random (gray) phase conditions at frontal (A, Fpz) or prefrontal (B, Fz) locations. Multiway ANOVA of ERP latency finds significant differences across electrodes (F_(1,144) = 10.08; p = 0.002), but no main effect of condition (F_(2,72) = 2.05; p = 0.130). C, D, Multiway ANOVA of ERP amplitude finds significant differences across electrodes [Fpz vs Fz; (F_(1,144) = 22.88; p = 0.0000023) and trough, peak, and random phase conditions (F_(2,72) = 27.86; p = 0.0000000000033). Notably, the early Pa component is smaller amplitude for trough versus peak conditions, whereas the P1 and N1 components are larger for trough versus peak phase condition. See Table 1 for full statistical comparisons of trough versus peak phase condition effects on latency and amplitude. For above figures, means (horizontal lines), individual values (colored dots), and distribution (half-violin) plots are shown for each measure. Light gray lines show within subject measures across phase conditions.

Sound design

All EEG recording and sound presentations were carried out inside an electrically shielded, sound-attenuating chamber while participants sat upright on a firm padded chair with their head against a head rest. Based on prior work, sounds were designed to be short duration with a high maximal sound level in order to evoke large and short latency P1 and N1 components of the auditory ERP response and to be challenging to ignore (Picton et al., 1974; Schadow et al., 2007; Thaerig et al., 2008; Prakash et al., 2016; Fujita et al., 2022). Binaurally presented sounds were short duration (12 ms), loud (85 dB maximum sound level in both ears), broad spectral band pink-noise sound pulses. Pink-noise sound pulses were shaped with a basis-spline function to create smooth onsets and offsets with minimal spectral splatter artifacts, as detailed in our prior report (Lee et al., 2016). In the “random phase eyes open task,” sound pulses were delivered at randomly ordered alpha phases separated by an interstimulus interval (ISI) which ranged from 878 to 1,634 ms (1 ms increments) with a mean ISI of 0.927 s (0.171 s) corresponding to a stimulus rate of ∼1 Hz (Fig. 1B,Bi). In the “trough and peak phase task,” ISI ranged from 1,628 to 1,650 ms (10 ms increments) with a mean of 1.636 s (0.055 s) corresponding to a stimulus rate of 0.611 Hz (Fig. 1C,Ci). In both tasks, the auditory stimulus interval was designed to minimize adaptation and variation in amplitudes and latencies of the P1 component (Dolu et al., 2001). A Wald–Wolfowitz test for random sequences with Benjamini–Hochberg post hoc correction for multiple comparisons confirmed that sounds were delivered with randomly interleaved phases in both tasks (Magel and Wibowo, 1997). Pink-noise sounds were delivered through calibrated Etymotic earphones (ER4 microPro) with disposable clean tips. Timing of sound delivery was controlled by a custom research-grade brain–computer interface device by Elemind Technologies which recorded EEG to track instantaneous target alpha phase and deliver phase-locked sounds.

Closed-loop phase-locking approach

For closed-loop phase-locking to alpha oscillations in the EEG, we used a research device (Elemind Technologies) that implements a novel ecHT algorithm to estimate the instantaneous alpha phase and play sounds phase locked in real time. In post hoc analysis, when a complete time course of EEG data is available, prior studies typically have used the standard Hilbert transform with acausal filtering. However, the standard Hilbert transform generates Gibbs distortion errors when reading out instantaneous phase in real time, as detailed previously (Schreglmann et al., 2021). These Gibbs distortion errors have been attributed to nonuniform convergence of the discrete Fourier transform (DFT) at the discontinuity between the beginning and endpoints of the calculated analytic signal. In contrast, the ecHT algorithm implements a causal bandpass filter centered around the frequency band of interest leading to a reduced contribution of off-frequency DFT coefficients. Prior studies have demonstrated that the ecHT algorithm mitigates the endpoint Gibbs distortion errors and allows for the high quality estimation of sample-by-sample oscillatory phase and amplitude in real time (Schreglmann et al., 2021). Data analyses and simulations implementing the ecHT algorithm found the Gibbs distortion errors were minimized provided the parameters of the bandpass filter were properly tuned to match the narrowband signal of interest (Schreglmann et al., 2021; Bressler et al., 2023). For detailed descriptions of how the ecHT algorithm works, please refer to this prior work (Schreglmann et al., 2021; Bressler et al., 2023).

Data acquisition

Following scalp measurements to determine 10/20 EEG electrode locations, adhesive disposable Ag/Ag-Cl electrodes (Vermed) were placed at scalp locations corresponding to Fpz and Fz for positive leads and left mastoid for reference (Fig. 1). A ground electrode was placed at the left frontal position (F1). Unprocessed “raw” EEG signals were collected via the Elemind Technologies “ecHT” research device which tracked instantaneous alpha phase in real time and delivered pink-noise sound pulses at target alpha phases. The Fourier and ecHT signal processing and phase-locking that were implemented here through an ecHT research device were detailed previously (Schreglmann et al., 2021). Experimental input parameters including the IAF and target trough and peak phases, pink-noise sound pulse duration, decibel level, jittered stimulus intervals, baseline and total recording durations were set using LabVIEW scripts (National Instruments) and loaded on the device through a Dell computer interface.

EEG preprocessing

All analyses were conducted in MATLAB (version 2023b). Additionally, the Chronux, Signal Processing, and Circular Statistics toolboxes (versions 2.12, 9.2, and 1.21, respectively) were used. Prior to all analyses, an acausal bandpass filter from 0.2 to 70 Hz was applied to the EEG which was recorded with a sampling frequency of 501 Hz. Data were epoched from −0.25 to 0.5 s relative to the onset of the stimulus presentation for presentation of evoked response oscillations (EROs), but from −0.25 to 0.9 s for broad- and narrowband power analyses in all tasks including sounds. Trials with gross artifact magnitudes squared exceeding 100 µV² such as eyeblinks were removed.

Spectral time-frequency analyses

For time-frequency signal analyses, we used Fourier decomposition with Hilbert or wavelet transforms which can generate comparable time and frequency resolution (Bruns, 2004). For IAF estimates detailed below, signals were processed with the multitaper Hilbert transform to generate time-frequency spectrograms (Fig. 2), which optimize spectral frequency resolution (Prerau et al., 2017). Multitaper spectrograms were generated using a Fourier transform and 4 temporal filters (tapers) with a 6 s sliding analysis window and step size of 150 ms (Prerau et al., 2017). To calculate post hoc phase-locking value (PLV) and phase error (PE; detailed below), we filtered individual trial data with a bandpass causal filter centered around IAF (±25%) followed by an ecHT transform implemented on the device (Fig. 3J). For comparison, the PLV and PE also were calculated using a standard Hilbert transform applied to the recorded data filtered with the same bandpass causal filter (Fig. 3K). To compute the instantaneous alpha frequency, we used the same bandpass causal filter centered at IAF followed by the endpoint corrected or standard Hilbert transform (detailed below). All remaining spectral time-frequency analyses were carried out using the Morlet wavelet transformation which enables high resolution in both frequency and time domains (Cohen 2019). Stimulus-related changes in frequency and power over time using the Morlet wavelet transform to generate broadband time-frequency power spectrograms (Figs. 8, 9) and alpha band time-power plots (Fig. 10). The Morlet wavelet transform was used for spectral decomposition as follows:φ=e−i2πft⋅e((−t2)/(2σ)2). (1)

Here, “i” represents the complex variable, “f” is the center frequency, and “σ” is the time bandwidth of the wavelet. Wavelets were produced using 140 linearly spaced center frequencies f ranging from 1 to 70 Hz. Cycles (c) were linearly spaced from 5 to 12 with each center frequency, with the time bandwidth σ being the following:σ=c2πf. (2)Signal envelopes were extracted by taking the absolute value of the wavelet transformed signals, whereas power was considered the magnitude squared. Phase values in radians were extracted using the MATLAB function called “angle”.

IAF estimates

To estimate phases for delivering phase-locked sounds, we estimated each subjects IAF which is known to vary across individual adult subjects IAF (Haegens et al., 2014; Zibrandtsen and Kjaer 2020). The 1/f aperiodic component of the corresponding power spectral density (PSD) plot was fitted with a third-order polynomial and subtracted to determine the frequency with maximum power or IAF (Fig. 2). The MATLAB “findpeaks” function was used to the frequency with maximum power or IAF after specifying a range of 7.5–16 Hz (Fig. 2, dots).

Calculating individualized target phase

Based on the physiology, we hypothesized that playing sounds at the trough or peak alpha phases which account for individual variations in alpha frequency and P1 latency would have distinct effects on auditory evoked brain responses (Fig. 1D,E). The auditory P1 potential latencies are known to vary across subjects (Prakash et al., 2016); hence, our target phases accounted for individual differences in P1 latency, as in prior studies in the visual system (Alexander et al., 2020). After measuring each subject's IAF (Fig. 2), we simulated the pre- and poststimulus alpha oscillations based on actual prestimulus alpha (Fig. 1D,E). To estimate the individualized trough onset phase, the P1_latency was multiplied by the IAF and converted to degrees as shown in Equation 3. The individualized peak phase was calculated with the same equation. All phase analysis and radial plots were based on a cosine function.Onset∠∘=−360∘×P1latency×IAF. (3)

Quantifying the alpha phase stationarity in prestimulus and poststimulus time window

As detailed above, we estimated target trough and peak phases for playing phase-locked sounds with the goal of optimizing the temporal overlap between the early auditory evoked P1 potential and the following peak and trough alpha phases, respectively. This assumes that alpha phase will remain unperturbed and stationary in the half-cycle preceding and following the phase-locked sound onset. To quantify this potential stationarity of alpha half-cycle phase, we ran a phase correlation analysis. A causal ecHT filtered EEG signal was used to quantify each individual subjects' alpha phase, as causal filters produce fewer temporal distortions for estimating prestimulus and poststimulus alpha phase (Ronconi et al., 2017). Circular correlations were estimated using the circ_corrcc function from the Circular Statistics Toolbox in MATLAB. Circular correlations were first Fisher z-transformed, and the absolute value was taken such that correlations ranged from [0 1]. With this approach, we find the alpha phase cycle preceding and following phase-locked sound onset was highly (r = 0.99 or 99%) correlated for trough and peak phase-locked sounds, supporting the idea that alpha phase remained stationary in the early time window preceding and following sound onset (see Results). As detailed below, we observed changes (nonstationarity) of alpha oscillation amplitude and frequency in later time windows following onset of the P1 potential and the first poststimulus half-cycle of alpha.

Quantifying P1-alpha phase alignment

One goal of this study was to determine whether the auditory P1 evoked potential was temporally aligned to the alpha half-phase following the phase-locked sound onset. To address this, the P1 latency was measured with standard procedures, as detailed below. As in the above analysis, we estimated each individual subjects' prestimulus and poststimulus alpha phases using a causal ecHT transform which yielded low PE (Fig. 3J). With this approach, we confirm the actual (Fig. 2D,E) trough and peak phases for playing phase-locked sounds were close to the target phases (Fig. 3B,C). Accordingly, sound onsets for trough and peak phases preceded the true trough (180°) and peak (360°/0°) phases by 53° and 52°, respectively. Next, for each individual subject, we determined the poststimulus alpha phase corresponding to the time of their individual P1 potential latency. We confirmed that trough and peak phase-locked sounds evoked an average P1 latency that preceded the true maximum peak (360°/0°) and trough (180°) phases by 23° and 14°, respectively (Fig. 4F,G, thick blue line). Thus, frontal alpha trough and peak phase-locked sounds generated P1 potentials that preceded the following individualized peak and trough phases by 18° (∼5 ms) on average. When sounds were played phase locked to frontal (Fpz) trough and peak phases, the P1 potential at the prefrontal location (Fz) preceded the true maximum peak and trough phases by 42° and 43° (∼12 ms), respectively, on average (Fig. 4H,I). Using a Watsons U2 test along with the causal ecHT signal filtering, we found this P1-phase alignment was not significantly different between electrodes (trough U2 = 0.384, p = 0.084; peak U2 = 0.368, p = 0.086). Thus, even though our closed-loop phase-locking targeted the more frontal (Fpz) location, a similar P1-alpha phase relationship was observed at the prefrontal location (Fz). For comparison, the P1-phase alignment also was determined for signals filtered with an acausal standard Hilbert Transform. With acausal filtering of frontal (Fpz) signals, the trough and peak phase-locked sounds were delivered at 126° (55°) and 308° (44°), respectively. With acausal filtering, for trough and peak phase-locked sounds, the P1 latencies on average coincided with poststimulus phases of 356° (39°) and 33° (75°), respectively. This inconsistent P1-phase alignment for signals filtered with an acausal standard Hilbert transform presumably reflects the temporal integration across prestimulus and poststimulus time windows on the order of 200 ms with acausal filters, as shown previously (Ronconi et al., 2017).

PLV and PE analysis

The PLV was computed for each subject and averaged to estimate the trial-by-trial probability that the actual phase was the same as the target phase (Fig. 3J,K). The PLV corresponds to the absolute value of the mean phase difference (Δθi(t)) between target and actual phase at time (t) expressed as a complex phase vector (Eq. 4; n = number of trials), as detailed previously (Lachaux et al., 1999; Aydore et al., 2013). The PLV ranges from 0 to 1, with a value of 1 indicating a 100% correspondence between target and actual phase across all stimulus trials. Additionally, the PE was computed to estimate the mean difference between actual versus target phase in degrees angle (Fig. 3J,K). The PE therefore indexes how far off the target phase-locking was on average. To compute PLV and PE, data was preprocessed using the endpoint corrected (ecHT) or a standard Hilbert (sHT) transform coupled with a causal filter. For the real-time automated phase calculation, the ecHT was coupled with an alpha band delimited causal filter that requires no information about the signal in the future from the time point the phase is calculated. For comparison, we use a standard Hilbert transform with causal filters. In all cases, the filters were band delimited based on each subject's IAF with the same narrowband delimitation (±25%) used during real-time phase tracking. Group statistics are obtained by evaluating the mean and standard error across participants.PLV=|1N∑n=1NeiΔθi(t)|. (4)

ERP analyses

To determine if there were alpha phase-dependent effects on the auditory ERP, we measured and compared auditory ERP amplitudes and latencies across task conditions (Figs. 5, 6; Table 1). For each subject, the auditory ERP was generated by smoothing the EEG signal with a fourth-order bandpass filter within the broad frequency range of 2–34 Hz, followed by averaging across trials. Smoothing using the bandpass filter was utilized for both visualization and subsequent analyses. ERP components were extracted using the MATLAB “findpeaks” function to locate maxima within time windows corresponding to each component. Consistent with prior work, auditory ERP component amplitudes and latencies were measured within the following time windows (Fig. 5, Table 1): Pa (1–45 ms), P1 (45–80 ms), N1 (80–150 ms), P2 (150–220 ms), and N2 (220–400 ms; Knight et al., 1999; Kisley et al., 2001; Eggermont and Ponton, 2002; Prakash et al., 2016). Grand average ERPs correspond to the arithmetic mean across subjects (Figs. 5, 6). As reported, we found minimal (<2 ms) and insignificant individual subject differences in the mean P1 latencies during the Random Phase Task versus the trough (mean difference = 1.11 ± 8.42 ms; t test p = 0.584) or peak (mean difference = 0.50 ± 11.56 ms; t test p = 0.865) phase-locked conditions at frontal (Fpz) locations. This mean difference across individual subjects was similar to the population mean differences which were statistically insignificant, as shown in Table 1. Thus, the P1 latency appears to be consistent across task conditions when examined on an individual basis and across the population. In the Results section, we report how auditory ERP component amplitudes vary with individualized trough and peak alpha phase at sound onset.

EROs

EROs were quantified using the same basic approach used for analyzing the auditory ERPs; however, the Morlet wavelet transformation was performed to isolate specific frequency ranges of interest. For example, alpha EROs were calculated by taking the average across trials for each participant at the wavelet corresponding to that subject's measured IAF, with the grand average alpha ERO being the mean across participants (Fig. 7).

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Figure 7.

Phase dependence and electrode differences for the alpha auditory ERO. A–D, The alpha band delimited ERO varies across trough (A, B, blue lines) and peak (C, D, red lines) phase conditions at frontal (A, C, Fpz) and prefrontal (B, D, Fz) locations. A, B, For trough phase condition, alpha oscillations remain high magnitude following sound onset (t = 0) at both locations. C, D, For peak phase condition, alpha oscillations are reduced following sound onset at both locations. E, F, The population average alpha ERO envelope is significantly higher for trough versus peak phase conditions at both locations. For Morlet wavelet transformed data shown here, permutation tests find significant differences in the early time window (50–250 ms) at both locations. For frontal (E, Fpz) and prefrontal (F, Fz) locations, the maximum difference is observed at 92 ms (p = 0052) and at 111 ms (p = 0.0087), respectively (bottom, p value distribution). Similar results are observed with a standard Hilbert transform (data not shown) with a p < 0.004, for the 50–250 ms time window at both locations (Methods). G, H, The phase-dependent difference (trough minus peak) is larger for the prefrontal (H, Fz) versus frontal (G, Fpz) locations. I, J, ERO envelopes are larger for the prefrontal location for both trough (I, Fz, dark blue line) and peak (J, Fz, dark red line) phase conditions. Permutation tests find differences by location are significant in the early time window before 250 ms (bottom, p value distribution). All plots here use the Morlet wavelet transform for spectral time-frequency analysis. Dark lines correspond to the means and light shaded areas the standard errors. The same phase-dependent effects were similarly significant (p < 0.001, for 50–250 ms) over the early poststimulation time window when analyzed with a standard Hilbert transform.

Stimulus evoked and induced effects

We visualized broadband (Figs. 8, 9) and quantified narrowband (Figs. 10, 11) evoked and induced responses to assess effects with higher and lower temporal coherence across trials, respectively (Helfrich et al., 2019). Evoked and induced responses were indexed here with intertrial phase clustering (ITPC), evoked power, total power, and induced power metrics, as described previously (David et al., 2006; Helfrich et al., 2019).

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Figure 8.

Broadband time-frequency plots illustrate phase-dependent differences in evoked and induced responses at the frontal (Fpz) location. A, B, E, F, Alpha ITPC and evoked power in the alpha range (dotted lines, 8–12 Hz) changes poststimulation (time = 0) in a phase-dependent manner with trough (A, B) versus peak (E, F) phase conditions. Independent of alpha phase, there is a time delayed peak in lower gamma frequency (35–60 Hz) range that coincides with the auditory ERP and a drop in alpha power relative to prestimulus baseline (0 to −200 ms). A, B, With trough phase condition, alpha power remains elevated within a narrow frequency band (arrow, alpha) poststimulation (arrow, alpha). E, F, With peak phase condition, alpha power and frequency (arrow, alpha) both decrease more so than with the trough phase condition. C, G, Baseline normalized Total Power also changes in a phase-dependent manner following sound onset. C, For trough phase, total power in the alpha range (dotted lines) increases (red, positive dB) and then decreases (green-blue, negative dB) in the early (0–300 ms) and late (>300 ms) time windows following sound onset, respectively. G, For peak phase, total power in the alpha range decreases (green-blue) and increases (yellow-green) in the early (0–300 ms) and late (>300 ms) time windows, respectively. D, H, Phase-dependent differences in the baseline normalized induced power are evident as a larger alpha desynchronization (aka power decrease, dark blue) in the late (>300 ms) time window for trough (D) versus peak (H) phase conditions.

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Figure 9.

Broadband time-frequency plots illustrate phase-dependent differences in evoked and induced responses at the prefrontal (Fz) location. A, B, E, F, Alpha ITPC and evoked power in the alpha range (dotted lines, 8–12 Hz) changes poststimulation (time = 0) in a phase-dependent manner with trough (A, B) versus peak (E, F) phase conditions. Independent of alpha phase, there is a time delayed peak in lower gamma frequency (35–60 Hz) range that coincides with the auditory ERP and a drop in alpha power relative to prestimulus baseline (0 to −200 ms). A, B, With trough phase condition, alpha power remains elevated within a narrow frequency band (arrow, alpha) poststimulation (arrow, alpha). E, F, With peak phase condition, alpha power and frequency (arrow, alpha) both decrease more so than with the trough phase condition. C, G, Baseline normalized total power also changes in a phase-dependent manner following sound onset. C, For trough phase, total power in the alpha range (dotted lines) increases (red, positive dB) and then decreases (yellow-green-blue, negative dB) in the early (0 to 300 ms) and late (>300 ms) time windows following sound onset, respectively. G, For peak phase, total power in the alpha range decreases (green-blue) and then increases (yellow) in the early (0–300 ms) and late (>300 ms) time windows, respectively. D, H, Phase-dependent differences in the baseline normalized induced power are evident as a larger alpha desynchronization (aka power decrease, dark blue) in the late (>300 ms) time window for trough (D) versus peak (H) phase conditions.

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Figure 10.

Alpha band delimited evoked and induced responses vary distinctly across individualized trough and peak alpha phase conditions. A, B, E, F, The evoked alpha phase coherence (ITPC, A, E) and evoked alpha power (B, F) are both markedly higher for the individualized trough (blue lines) versus peak (red lines) phase conditions in the early (0 to 300 ms) time window at both locations (Fpz, Fz). A, Bottom, Permutation testing with post hoc cluster analyses finds evoked alpha phase coherence (ITPC) and power are significantly higher for trough versus peak phase-locked sounds in the early (0–300 ms) and late (>300 ms) poststimulus time windows at both locations. C, G, Trough (blue lines) and peak (red lines) phase conditions generate opposing phase-dependent effects in early and late time windows for the baseline normalized alpha total power. C, G, Bottom, Permutation testing with post hoc cluster analyses finds total power is significantly higher for trough versus peak phase conditions in the early time for both locations. Only the frontal (Fpz, C) location has significant phase-dependent differences in the later time window for total power. D, H, Alpha desynchronization or decrease in induced alpha power is larger for trough versus peak phase conditions in the later time window at frontal locations (D). D, H, Bottom, Permutation testing finds phase-dependent alpha desynchronization in the late time window is significant at frontal locations only.

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Figure 11.

Phase-dependent change in evoked instantaneous alpha frequency across individualized trough and peak alpha phase conditions. A, B, Top, Standard Hilbert transform with causal filters used to analyze the instantaneous alpha frequency (Materials and Methods). With standard analysis, there are two apparent phase-dependent early responses labeled, E1 (<100 ms) and Early (<300 ms). A, B, Bottom, Permutation testing finds significant sustained alpha frequency changes with p value ≤0.04 during the Early time window (170–190 ms) at frontal (Fpz) location and the Early time window (160–225 ms) at the prefrontal (Fz) location. C, D, Top, ecHT with causal filters used to analyze the instantaneous alpha frequency (Materials and Methods). With ecHT analysis, there are two significant phase-dependent early responses labeled, E1 (<100 ms) and Early (<200 ms). C, D, Bottom, Permutation testing finds a continuous block of significant phase-dependent difference in frequency sliding with p values ≤0.01 in two time windows (E1 < 100 ms, Early <200 ms) at frontal (Fpz) location, and p values ≤0.0001 in the two time windows (E1 < 100 ms, Early <200 ms) at the prefrontal (Fz) location. There are additional less sustained alpha frequency changes indicated in the p value distributions. For both analyses, these phase-dependent changes in alpha frequency are more prominent at the prefrontal (Fz) versus frontal (Fpz) location. Exact p values indicated by p value distribution plots.

ITPC

The ITPC assesses the temporal precision and cross-trial phase coherence of evoked responses. The auditory evoked ITPC was calculated as described previously (Tallon-Baudry et al., 1996; Cohen, 2014a). Instantaneous ITPC is treated as the absolute value of the averaged phase values across trials at each time point:ITPC=|1N∑n=1Neiθi|, (5)where θi is the respective single-trial phase angle for the corresponding complex signal φi . For group-level statistics, subject-specific ITPC values were Fischer z-transformed before averaging and followed with nonparametric estimation of standard error.

The ITPC and evoked power assess the temporal precision of response phase and magnitude, respectively. The total power assesses the baseline normalized magnitude of the combined evoked and induced responses. Finally, the induced responses are estimated by subtracting the average evoked response from the total power, reflecting time-locked but nonphase-locked responses.

Evoked alpha frequency change

To quantify phase-dependent differences in the evoked alpha frequency that were evident in broadband time-frequency spectrograms (Figs. 8A,B, 9A,B), we computed the instantaneous alpha frequency using an approach similar to those described previously (Cohen 2014b; Vázquez-Marrufo et al., 2019); however, here we employed the bandpass IAF (±25%) causal filter prior to applying the Hilbert transform to minimize smearing backward time. Following the Hilbert transform, the instantaneous frequency was calculated as the mathematical derivative of the phase of the EEG signal, which is then multiplied by the sampling rate over 2π. Additionally, the ecHT is known to significantly attenuate the Gibbs phenomena typically introduced during bandpass filtering (Schreglmann et al., 2021; Hebron et al., 2022; Bressler et al., 2023). Therefore, we corroborate instantaneous frequency analyses using causal plateau filters with an implementation via the ecHT.

Task differences in prestimulus alpha power

Prior studies found that prestimulus alpha power levels must be high in order to see average or phase-dependent effects on the sensory ERP and alpha oscillations (Mathewson et al. 2011; Iemi et al., 2019). Hence, we aimed to confirm that our “trough and peak phase task” which used slow sound stimulation rates (0.611 Hz) resulted in high prestimulus alpha power levels, as observed in prior studies (Henry and Obleser 2012; Iemi et al., 2019; Cabral-Calderin and Henry, 2022). Here we examined the power (Fig. 4) in the prestimulus window using two methods and two time windows. For the first approach (Fig. 4A–D), we calculated prestimulus PSD using the FOOOF method during the prestimulus window (Iemi et al., 2019; Donoghue et al., 2020). Specifically, we confirm high alpha power during two, prestimulus windows of −0.5 s and −0.7 s (−500 ms and −700 ms) for the trough and peak phase conditions at frontal (Fig. 4A,B) and prefrontal (Fig. 4B,D) locations. For the second approach (Fig. 4E,F), we estimated the evoked power spectrum using a second approach (Cabral-Calderin and Henry, 2022). In this approach, the fast Fourier transform is taken of the average evoked activity across trials for each participant–electrode–condition interaction. When prestimulus activity is averaged before performing the FFT, oscillatory activity that is not time locked or phase locked to the stimulus onset in the prestimulus time window is averaged out. Hence, this procedure highlights signals which maintain consistent trial-by-trial time and phase alignment to sound onset. With the first approach, we observed high power levels in the alpha frequency range at both locations (Fig. 4A–D), and with the second approach, we observe high power levels in the delta and alpha frequency ranges at both locations (Fig. 4E,F). We used these same signal processing methods to quantify delta and alpha power prior to sound onset in the “random phase eyes open task” (Fig. 4G–L). In this task, we found low prestimulus alpha power levels as intended to measure auditory evoked potential latencies and amplitudes independent of alpha. Notably, we did not see high levels of phase coherence (ITPC) for delta oscillations in the prestimulus time window, as suggested in prior studies using different forms of analyses (Henry and Obleser 2012; Zoefel and Heil, 2013); however, we do see high delta power (Fig. 4E–L).

Total and evoked power

As outlined in previous literature, total power quantifies the combined phase-locked and nonphase-locked activity, whereas evoked power quantifies only the phase-locked activity (David et al., 2006). Broad and narrow alpha band analyses were run using the same approach (Figs. 8–10, respectively). After calculation, the baseline power in the prestimulus period (−250 −50 ms) was subtracted from the total power (aka baseline normalized). Total power was quantified for each subject by taking the average magnitude squared across all trial-time-frequency points as follows:TotalPower=1n∑i=0n|φi|2, (6)where φi is taken as the instantaneous trial-time-frequency point. Similarly, evoked power is taken as the corresponding power to the averaged signal as follows:EvokedPower=|1n∑i=0nφi|2. (7)

Induced power

Induced power was quantified to estimate transient, time-locked but nonphase-locked activity. Unlike the evoked power or total power, to compute the induced power, we subtracted the ERP. Negative and positive changes in induced power, as calculated here, have been referred to as event-related desynchronization and event-related synchronization, respectively (Iemi et al., 2019). Here, we defined induced power as the average magnitude squared, frequency-specific activity after subtracting each subject's evoked activity from each trial and subsequently performing the complex Morlet wavelet transform as described above (φı^) :InducedPower=1n∑ı^=0n|(φı^)|2. (8)The alpha band delimited induced power (Fig. 10) was derived identically to the broadband metric of induced power but within the IAF band used throughout the study. After calculation, the baseline power in the prestimulus period (−250 to −50 ms) was subtracted from the induced power (aka baseline normalized) to allow direct comparisons to the total power.

Statistical procedures

Nonparametric permutation testing was carried out to determine statistical differences in magnitudes of the ERP components, alpha ERO envelopes, alpha ITPC, evoked power, total power, and induced power (Maris and Oostenveld 2007; Cohen, 2014a). In brief, subject-specific trial-condition averages were taken. After which, for one thousand iterations, condition mean labels are swapped randomly, and the group average for the shuffled conditions were calculated. We then z-score our true mean differences relative to the resulting distribution and further estimate our permutation p values for each time point. Cluster-based correction is performed by taking from each permutation iteration the largest cluster of test statistics above our voxel significance threshold (p < 0.05). From which, our corrected cluster threshold is taken as the 95th percentile of the maximum cluster sizes over each permutation, and significant clusters are taken as those above said threshold. Unless otherwise noted, all variances reported in parentheses are the standard error of the mean (SEM).

For parametric analyses of ERP component latencies and amplitudes, two procedures were used. First, a multiway analysis of variance (MANOVA) was performed to investigate fixed effects of condition, electrode, and component on ERP component latency and amplitude. Given that the optimal phase of stimulation for both trough and peak phase conditions was estimated using P1 latency as determined by random-phase acoustic stimulation, we ran a MANOVA to examine the five component latencies across random, trough, and peak conditions. Second, in addition to permutation testing, we delineated trough versus peak phase-dependent differences in the five ERP component latencies and amplitudes and ran paired t tests followed by a Benjamini–Hochberg correction for multiple comparisons. Throughout the manuscript, standard deviations are reported in parenthesis.

Finally, statistical comparisons of circular data are performed primarily with two tests: Rayleigh's and Watson's U2. Rayleigh's test assesses the significance of nonuniformity of circular data, whereas Watsons U2 evaluates the significance of differences between two samples of circular data (Mégevand, 2017; Philipp Berens, 2024).

Data and code availability

All code for all analyses are available here: https://github.com/readlabuser/Individualized-closed-loop-sensory-stimulation-reveals-alpha-phase-dependence.