Enhancement of sleep slow wave activity using transcranial electrical stimulation with temporal interference: an interim analysis of the STRENGTHEN study

Study design

Data used in this study were acquired as part of the STRENGTHEN clinical trial (ClinicalTrials.gov, NCT06267521, registration date: 02/12/2024), a single-blind, longitudinal study aimed at enhancing cognitive flexibility and emotion regulation. The study design includes TES-TI delivered during sleep in the lab as well as brief, daily meditation training (Fig. 1A). Healthy participants (ages 18–50) were assigned in parallel to 1 of 4 groups: (Group 1) TES^15 kHz (0 Hz difference frequency) 2 nights per week and meditation; (Group 2) TES^15 kHz-TI^1 Hz (1 Hz difference frequency) 2 nights per week and sham meditation; (Group 3) TES^15 kHz-TI^1 Hz 1 night per week and meditation; (Group 4) TES^15 kHz-TI^1 Hz 2 nights per week and meditation (Fig. 1B). For all participants, interventions during sleep in the lab occurred over four consecutive weeks. Participants were assigned to their treatment group following pre-intervention baseline assessment, with efforts made during non-random allocation to ensure group equivalence on key demographic variables, particularly age and sex. This matching approach mitigated potential confounds related to sex and age-based differences in sleep. Participants were blinded to their experimental group, i.e., they did not know whether they were receiving TES^15 kHz (Group 1) or TES^15 kHz-TI^1 Hz (Groups 2, 3, and 4). Participants were reimbursed for their study participation. Neither participants nor the public were involved in the design, conduct, or reporting of this trial. All aspects of the study were approved by the University of Wisconsin-Madison Institutional Review Board.

The current study reflects a mechanistic sub-study within the broader STRENGTHEN trial; it is an interim analysis that focuses on the effects of TES^15 kHz-TI^1 Hz during NREM sleep using data collected from the first five cohorts of the STRENGTHEN trial (from February 19, 2024, to December 31, 2024). Each cohort contained approximately 5–6 participants who, for logistical reasons, went through the various phases of the study as a group. The analyses presented here were not pre-specified in the formal clinical trial registration; however, they were part of the planned exploratory aims within the Institutional Review Board-approved protocol and were designed prior to data collection from the analyzed cohorts. Primary and secondary endpoints of the trial related to cognitive flexibility and emotion regulation will be the focus of later work; as such, data from post-intervention follow-up periods were not included in the current work. The analyses performed here were initiated after interim inspection of the data showed large effect sizes. To maximize statistical power, the current study used data from the first five cohorts to examine the effects of TES^15 kHz-TI^1 Hz on NREM sleep (N = 21, 1 Hz, targeting left ventromedial prefrontal cortex during NREM sleep episodes in the first half of the night) by comparing the baseline night with the first and last intervention nights regardless of the group. A comparison between TES^15 kHz-TI^1 Hz and TES^15 kHz (i.e., directly assessing the potential effects of amplitude modulation) was also performed utilizing Group 1 participants from the first five cohorts (N = 7). More detailed information about statistical power and participant grouping can be found in the “Statistics and reproducibility” section. Another goal of the STRENGTHEN clinical trial, to be reported in a subsequent publication, was the assessment of TES^15 kHz-TI^6 Hz (6 Hz, targeting retrosplenial cortex) during REM sleep episodes later in the night.

Participants

In total, twenty-eight participants (30.5 ± 9.9 years, 61.0% (N = 17) female, N = 21 TES^15 kHz-TI^1 Hz, N = 7 TES^15 kHz) from the first five cohorts of the STRENGTHEN study were included in the current study (Fig. 1C). All participants were medically healthy, with no acute illness at the time of participation and no diagnosed chronic illness, including sleep disorders, or medications that may have influenced the outcome of the study. Participants had a baseline magnetic resonance imaging (MRI) scan and a sleep night in the lab. The baseline sleep night did not include overnight stimulation. Participants were to be excluded if they had any neuroradiologist-identified structural abnormalities of the brain; no participants in the current work were excluded for this reason. Participant recruitment began with an online survey. Potential participants were then further screened by phone call to see if they met eligibility criteria. They then underwent additional screening and an informed consent discussion in person prior to potential enrollment in the study. In general, screening consisted of questions regarding demographics, availability, medical and mental health, medications, and sleep. Participants with responses meeting exclusion criteria were not included in the study. As part of screening, for example, participants were asked about current or prior diagnoses of obstructive sleep apnea (OSA); if yes, the participant was excluded. Full eligibility criteria can be found on the ClinicalTrials.gov website. As part of the pre-intervention baseline sleep visit, sleep technicians monitored for sleep quality. During the baseline sleep visit, two participants had loud snoring, breath holding and gasping accompanied by periods of wake. Given concern for OSA and overall poor sleep that would preclude experiment completion, these two participants were withdrawn after their baseline visit (Fig. 1C). All participants gave written informed consent in accordance with the University of Wisconsin-Madison Institutional Review Board.

Datasets included

Baseline, first, and last intervention nights were utilized here; a future publication will report on all the intervention nights. In total, twenty-two first nights and twenty-seven last nights were included in subsequent analyses that evaluated the effects of stimulation. Four first nights were excluded due to technical issues, and two first nights were excluded due to poor sleep that precluded experiment completion (e.g., fewer than five out of ten intended stimulation protocols were completed). One last night was excluded due to technical issues. Analyses comparing baseline, first, and/or last intervention nights were restricted to participants with usable data across all nights. Further details about which datasets were included in the analyses can be found in Supplementary Fig. 1.

Daytime meditation training

Meditation and sham meditation interventions were delivered via the Healthy Minds Program smartphone app, which provides a comprehensive curriculum for well-being training based upon four pillars of well-being: awareness, connection, insight, and purpose^42,43. The program includes didactic mini-podcasts that provide the background science underlying each of the four well-being pillars, along with specific mental exercises—forms of procedural learning—that complement the declarative scientific content^42,43. Participants assigned to the meditation intervention were guided through brief, daily meditation practice (5–30 min) and provided regular reminders of key practice goals several times each day. Each week focused on one of the four pillars of well-being. Participants assigned to the sham meditation intervention listened to didactic material only, without meditation instruction.

Nighttime stimulation procedure

Participants spent overnights in the sleep lab at the Wisconsin Sleep Center, where they were outfitted with a 256-channel hd-EEG net for recording brain activity and additional channels for recording polysomnography (PSG) data (electrooculography adjacent to lateral canthi, submental electromyography, and electrocardiography). Channels for performing TES-TI were embedded in the hd-EEG net, placed in lieu of recording channels. While the participant was awake, short stimulation protocols (15-s with 15-s ramping up/down periods) were performed with increasing current amplitudes (up to 5 mA zero-to-peak) to determine if the participant began to feel sensation on their scalp. The current amplitude was then lowered systematically and checked again, such that the final current value of 5 mA chosen was confirmed to not elicit any sensation. Then, the participant went to sleep, and a sleep technician performed stimulation protocols based on sleep features visible on the hd-EEG and PSG recordings (data visualization parameters in accordance with staging parameters found in the “Sleep staging” section). Specifically, when NREM sleep was identified and stable (≥3 min), stimulation was delivered in 3-min protocols with 15-s ramping up/down periods. Each protocol was separated by at least 6 min and repeated approximately ten times, in most cases confined to NREM sleep episodes during the first four hours after sleep onset. Participants were monitored throughout the night from a control room, and a sleep technician was available for communication at any time.

Sleep quality surveys

After each overnight in the sleep lab, participants completed the 9-question restorative sleep questionnaire (REST-Q) survey, which was designed by a panel of expert sleep specialists to define and measure restorative sleep^44,45 and chosen here for its potential to link the perceived restorative effects of sleep with the SWA that may underlie these restorative effects. They rated to what extent they felt tired, sleepy, in a good mood, rested, refreshed, ready to start the day, energetic, mentally alert, and grouchy on scales of 1–5 (1 = not at all, 2 = a little bit, 3 = some, 4 = very much, 5 = completely). An overall REST-Q score was calculated in line with⁴⁴. Overall scores from after the first and last intervention nights were included in the analyses.

TES-TI targeting

A standardized channel montage was used for all participants (channel 1: E20–E34, channel 2: E70–E95 of the hd-EEG net) targeting left ventromedial prefrontal cortical regions. Channel placement was first approximated using the Temporal Interference Planning Tool (TIP v1.0, IT’IS Foundation, Switzerland), in which an optimal channel configuration was chosen from the 10:10 system to target the left ventromedial prefrontal cortex with maximal intensity and minimal off-target stimulation^46,47. TIP simulations were performed using the comprehensive MIDA head model, which details the electrical properties for different tissues in a 29-year-old healthy female volunteer⁴⁸. For further confirmation, targeting was then verified using SimNIBS software (v4.1.0) that provided tools for electric field modeling with additional details including: an individual’s MRI, and channel material, geometry, and position in the 256 hd-EEG system^49–51. Modeling began with the segmentation of an individual participant’s T1 and T2 scans to extract the electrical properties of different tissues. Segmentation and meshing were performed using the charm function. The participant’s head model was then aligned to a template 256-channel hd-EEG net⁵¹. Next, electric fields were simulated, accounting for channel properties (see “TES-TI” section), a current value of 5 mA, and location in the 256-channel hd-EEG net extrapolated from the 10:10 system locations used in TIP simulations. Simulation of the temporal interference field (V/m) was implemented using the function get_maxTI that calculates the maximal modulation amplitude of the difference frequency using the equation described in refs. ^22,51. The interference field values obtained in grey matter were then extracted and plotted over the individual’s T1 scan as well as over a standardized atlas (MNI152) for visualization using SimNIBS and Analysis of Functional NeuroImages software^52,53.

Overall, simulations performed in SimNIBS with individualized head models agreed with those performed in TIP using the standardized MIDA head model. Based on these simulations using individualized head models, across all TES^15 kHz-TI^1 Hz participants (N = 21), maximal intensity values in left ventromedial prefrontal cortex grey matter were 0.82 ± 0.09 V/m, ranging 0.62–0.99 V/m, and average intensity values were 0.46 ± 0.05 V/m, ranging 0.36–0.52 V/m. Of note, the channel configuration used for two TES^15 kHz-TI^1 Hz participants differed by one channel (E94 instead of E95); however, their data was included given that electric field simulations for both configurations were highly similar.

TES-TI

Four silver-silver chloride stimulating channels (12.6 mm outer diameter, 8.0 mm inner diameter, 2.2 mm width) with 1.5-m cable length were embedded into the hd-EEG net, attached to the participant’s scalp with conductive paste (Ten20), and then connected to the TI Brain Stimulator for Research (TIBS-R v3.0, TI Solutions AG, Switzerland). Electrode impedances were monitored throughout the experiment and served as an indicator for the need to adjust electrodes; substantial increases in impedance (to greater than 6500 Ohm) indicated poor positioning and a need for adjustment. Adjustments were targeted for when a participant entered a light stage of sleep (i.e., N1) or was awake. Adjustments consisted of applying additional Ten20 conductive paste and/or measures to improve electrode adherence to the scalp. Overall, adjustments were infrequent, as out of the 49 stimulation nights analyzed, only 4 nights had adjustments, which occurred one or two times during periods of wake. Average impedances were 4590 ± 110 Ohm for channel 1 and 5020 ± 600 Ohm for channel 2. TES-TI protocols during NREM sleep had the following parameters: 15,000 Hz carrier frequency, 1 Hz difference frequency, sinusoidal waveform, 5 mA zero-to-peak, 3-min duration with 15-s ramping up/down periods. Channel 1 used a 15,000 Hz frequency and channel 2 used a 15,001 Hz frequency. As a higher carrier frequency lowered impedance at the electrode-scalp interface, a 15,000 Hz carrier frequency was chosen to mitigate the possibility of sensations being felt by participants during sleep. Actual, average current delivered was 5.21 ± 0.21 mA for channel 1 and 5.06 ± 0.19 mA for channel 2 as reported by the TIBS-R device. Programming of the TIBS-R device was performed using its Python software.

hd-EEG data acquisition

The hd-EEG system from MagStim Electrical Geodesics, Inc. (EGI) consisted of a hd-EEG net, an amplifier (NA 400), and a physiological input box. Each net had 256 silver-silver chloride electrodes and was appropriately sized to each individual participant. In cases where the stimulating electrodes were very close to the hd-EEG recording electrodes, e.g., small net sizes, surrounding recording electrodes were not gelled to avoid the possibility of bridging between stimulating and recording electrodes. Nets were then connected to EGI amplifiers that interface with EGI’s Net Station Acquisition software (v5.4.2) for real-time data visualization. All recording electrode impedances were kept below 50,000 Ohm, with the reference electrode below 5,000 Ohm, as measured at the start of the recording. The physiological input box was used to collect polysomnography data (electrooculography, electromyography, and electrocardiography). In addition, data from the TIBS-R trigger was input into the physiological input box. The optical trigger box output a 5 V square wave signal with the onset and offset of stimulation and, when synchronized to hd-EEG recordings, allowed for offline identification of stimulation intervals. All data were collected at a 500 Hz sampling rate. The total number of hours of EEG data acquired across the baseline, first, and last nights utilized in these analyses was 7.99 ± 0.75 hours per night per participant.

Hardware filters specifically designed for the TIBS-R device allowed for simultaneous TES-TI and hd-EEG recording. A low-pass filter (7th order, 100 Hz cutoff) was placed in the path of the hd-EEG amplifier input such that signals from the hd-EEG net were filtered before they reached the amplifier. A high-pass filter (4th order, 250 Hz cutoff) was placed in the path of the TIBS-R output such that intermodulation products and low-frequency noise generated by the TIBS-R were filtered before they reached the stimulating electrodes. Both hardware filters were used to allow for simultaneous TES-TI stimulation and hd-EEG recording.

MRI data acquisition

MRI data were collected using a 3 Tesla MAGNUS (Microstructure Anatomy Gradient for Neuroimaging with Ultrafast Scanning, GE Healthcare) head-only MRI scanner. The head coil used was a 32-channel head radio frequency (RF) array (Nova Medical, Wakefield, MA). Structural images were acquired using T1- and T2-weighted images, with 0.8 mm isotropic voxels, and the following parameters. T1-weighted: sequence =  MP-RAGE (magnetization-prepared rapid gradient-echo), repetition time (TR) = 2000 ms, echo time (TE) = 3 ms, inverse time (TI) = 1100 ms, flip angle = 8 degrees, field of view (FOV) = 256 × 256 mm², matrix size = 320 × 320 pixels, resolution = 0.8 mm × 0.8 mm × 0.8 mm, number of slices = 240, acquisition time = 4 min. T2-weighted: sequence = CUBE-T2, TR = 2500 ms, TE = 90 ms, echo train length (ETL) = 120, FOV = 256 × 256 mm², matrix size = 320 × 320 pixels, resolution = 0.8 mm × 0.8 mm × 0.8 mm, number of slices = 240, acquisition time = 4 min. The structural MRI data were converted into NIfTI format using the open-source tool dcm2niix. Both T1- and T2-weighted images were defaced for all participants using the open-source Python-based defacing utility tool, pydeface.

Sleep staging

Sleep staging was performed manually in accordance with the American Academy of Sleep Medicine guidelines and as follows by a registered polysomnographic technician⁵⁴. Electrooculography, electromyography, and 6 hd-EEG channels that approximate 10:20 locations F3, F4, C3, C4, O1, O2, were used for staging. Hd-EEG data were filtered using MATLAB’s filtfilt function with a design: 4th order infinite impulse response filter band-passed 1–30 Hz. Electromyography data were filtered using MATLAB’s filtfilt function with design: 4th order infinite impulse response filter band-passed 1–100 Hz followed by a notch filter: 4th order infinite impulse response filter stop band 59–61 Hz. CountingSheepPSG (v1.4.5) MATLAB software was then used to perform staging in 30-s epochs and calculate sleep metrics, such as total sleep time, sleep onset latency (to Stage 1), wake after sleep onset, and others. The number of arousals and arousal index (number of arousals per hour) were quantified in line with AASM guidelines⁵⁴. Number of awakenings was also included and refers to the number of times the stage transitioned from sleep to wake. Nonparametric statistical tests were used to evaluate for potential changes in these metrics across participant groups (Wilcoxon rank sum) and within participants, across intervention nights (Friedman test).

hd-EEG preprocessing

hd-EEG data preprocessing was performed using MATLAB (v2023b) and EEGLAB (v2025.0.0)⁵⁵. hd-EEG data were band-pass filtered 0.5–40 Hz using EEGLAB’s finite impulse response filter function, pop_eegfiltnew. Only 30-s NREM epochs staged 2 or 3 were included in spectral power analyses.

hd-EEG artifact rejection

Semi-automated artifact rejection was performed to remove channels and epochs containing artifactual activity (e.g., high-frequency noise, interrupted contact with the scalp)^56–58. Specifically, a fast Fourier transform was used to calculate spectral power in low (0.5–4 Hz) and high (20–30 Hz) frequency ranges for 6-s NREM epochs. For each channel, automatic thresholds were calculated at the 99th percentile and then plotted and visually inspected. If epochs with substantially greater low- or high-frequency power did not exceed the automatic threshold, the threshold was lowered. All epochs exceeding the threshold were then removed. Removed epochs (due to artifact or a sleep stage that was not NREM 2 or 3) were replaced with NaN values to maintain the temporal structure of the data, but were not included in the spectral power calculations.

Channels in which artifacts affected most of the recording were removed. Additional spectral- and topographic-based procedures were used to identify and remove channels with distinctly greater power relative to neighboring channels. On average, 74% (189 ± 23) of the 256-hd EEG channels remained on intervention nights. A final visual review of the hd-EEG data was performed to remove any remaining channels and epochs with artifactual activity.

To increase the signal-to-noise ratio, analyses were restricted to 185 scalp channels (excluding neck and face channels). Any removed channels, including channels that were not gelled, within the scalp 185 channels were interpolated using spherical spline interpolation via the eeg_interp function. All channel data was then re-referenced to the average of the final 185 channels. For visualization only, topographies were plotted using EEGLAB’s topoplot function with a decreased radius (plotrad = 0.51); all 185 channels were included in analyses.

hd-EEG alignment

Timing of TES-TI throughout the night was determined based on hardware trigger signals in agreement with timestamps recorded at the start and end of individual stimulation protocols. Time periods included a baseline PRE stimulation period, 3-min prior to the start of stimulation, a STIM period including a 15-s ramp up, 3-min stimulation and 15-s ramp down and a POST stimulation period, 3-min after the ramp down. Analyses comparing STIM and PRE or POST intervals excluded the ramping interval to allow for equal 3-min comparisons.

hd-EEG spectral power analyses

For each hd-EEG channel, the power spectral density (PSD) was calculated with Welch’s method using 6-s windows with 90% overlap for a 0.167 Hz step size. PSD values were then averaged over frequencies to calculate band power (e.g., SWA, 0.5–4 Hz). Band power was normalized to account for differences between participants and night-to-night variability within participants⁵⁹. For each participant and each night, the band power of interest (e.g., SWA) for each channel in PRE, STIM, and POST periods was divided by the average band power (e.g., SWA) during NREM sleep throughout the entire night to obtain a relative change (shown as a percent) from the mean overnight band power⁵⁹. Canonical frequency bands were defined as follows: SWA: 0.5–4 Hz, theta: 4–8 Hz, alpha: 8–12 Hz, low sigma: 9–12 Hz, high sigma: 12–16 Hz, beta: 16–25 Hz, and gamma: 25–40 Hz. The main analyses were also repeated using a narrower frequency band surrounding SWA, 0.5–2 Hz, and the results were qualitatively similar to the broader 0.5–4 Hz band.

Statistics and reproducibility

Summary statistics for the main figures, including sample sizes and effect sizes (Cohen’s d), can be found in Supplementary Table 4.

TES^15 kHz-TI^1 Hz preserves sleep architecture

We compared sleep architecture metrics across baseline, first, and last intervention nights for those TES^15 kHz-TI^1 Hz participants with usable data on all nights (Table 3, TES^15 kHz-TI^1 Hz N = 16, Friedman tests, X², df = 2). There is a weak main effect of night on total sleep time; however, it is not significant after correction for multiple comparisons (X² = 6.12, unadjusted p = 0.047, adjusted p > 0.999). There are no significant differences in any other sleep characteristics. Notably, there are no differences in metrics related to wake, including the number of arousals, arousal index, number of awakenings, or time spent awake after sleep onset. In addition, participants did not report feeling the stimulation during the night.

SWA (power spectral density, PSD in 0.5–4 Hz range) was quantified throughout each entire night, then averaged across channels for each participant. There is no main effect of night (baseline, first, or last) on whole-night SWA (Table 3, TES^15 kHz-TI^1 Hz: N = 16, one-way repeated measures ANOVA, F, df = 2). Similar results were found when SWA was measured during the first four hours after sleep onset; this early SWA did not differ between baseline, first, or last nights (Table 3). Additionally, the number of stimulation protocols completed during NREM sleep did not differ between first and last nights (first = 10 ± 2, last = 9 ± 1, W = 29.0, p = 0.910; two-sided Wilcoxon signed rank test). These comparisons were also repeated for the TES^15 kHz group, but given the small sample size, results should be considered exploratory and hypothesis-generating (Supplementary Table 1).

SWA increases during and after TES^15 kHz-TI^1 Hz

We measured SWA in the immediate 3-min before (PRE), during (STIM), and after (POST) TES^15 kHz-TI^1 Hz stimulation and calculated the differences between time periods (Fig. 3A). SWA was normalized (%SWA) to account for SWA differences between participants and night-to-night variability within participants (see “Methods,” hd-EEG spectral power analyses). Since SWA changes were consistent on the first and last intervention nights (Supplementary Fig. 2), we averaged $\mathrm{\Delta }\%$SWA across the two nights for each participant (Supplementary Fig. 1). We also included participants (N = 5) with only one intervention night of usable data to increase statistical power.

Overall, we find a significant difference in the all-channel average SWA across PRE, STIM, and POST periods (N = 21, df = 2, F = 30.95, p = 7.54 × 10^‒9, one-way repeated measures ANOVA). We find a global (across all channels) increase in SWA during the stimulation as compared to before stimulation (Fig. 3A, STIM-PRE, N = 21, t = 6.64, p = 4.97 × 10^‒6, d = 1.45; two-sided paired samples t-test). A global increase in SWA is also present after stimulation compared to before stimulation (Fig. 3A, POST-PRE, N = 21, t = 7.46, p = 1.86 × 10^‒6, d = 1.63; two-sided paired samples t-test). There are no significant differences between the periods after (POST) stimulation and those during (STIM) stimulation in the average across all channels (Fig. 3A, POST-STIM, N = 21, t = 0.63, p = 0.982, d = 0.14, two-sided paired samples t-test). To identify statistically significant topographic changes at the level of individual channels, we implemented a nonparametric cluster-based statistical approach using a suprathreshold cluster analysis to control for multiple comparisons. The results of this topographical analysis confirm the results at the global level, i.e., SWA increases across all channels during stimulation and the increase persists to a similar degree after, with no significant differences between the STIM and POST periods, despite a higher T-statistic in frontal regions in the POST period (Fig. 2B, STIM-PRE: 1 positive cluster, 185 significant electrodes, $\overline{\mathrm{p}}$ = 1.92 × 10^‒5; POST-PRE: 1 positive cluster, 185 significant electrodes, $\overline{\mathrm{p}}$ = 6.98 × 10^‒6; POST-STIM: 0 clusters, 0 significant electrodes, $\overline{\mathrm{p}}$ = 0.538). A similar pattern of increases during and after stimulation are found when using a narrower frequency band surrounding SWA, 0.5–2 Hz (Supplementary Fig. 3A). Analyses were also repeated for the TES^15 kHz group, but given the small sample size, results should be considered exploratory and hypothesis-generating (Supplementary Fig. 4).

To investigate potential differences across subgroups that received the TES^15 kHz-TI^1 Hz intervention (Groups 2, 3, and 4), a linear mixed effects model (LME) was applied for the first and last nights separately. SWA was the response variable, TES^15 kHz-TI^1 Hz subgroup, and period (PRE, STIM, and POST) were fixed effects. We find no significant interaction between subgroup and period (First: f ² = 0.16, p = 0.079; Last: f ² = 0.07, p = 0.571) and find no main effect of subgroup (first: f ² = 0.23, p = 0.482; last: f ² = 0.11, p = 0.709). Importantly, effects are moderate and nonsignificant on the last night, when subgroup assignment may have theoretically had the greatest impact. Overall, these results indicate that changes in SWA during and after stimulation are similar across subgroups and support the decision to pool their data. Further supporting this approach is that a main effect of period was found for both first and last nights (first: f ² = 0.90, p = 1.42 × 10^‒5; last: f ² = 0.84, p = 2.66 × 10^‒6). Thus, the qualitative conclusions are the same—that SWA increases during and after TES^15 kHz-TI^1 Hz stimulation—whether the subgroups are factored in with the LME or whether the subgroups are aggregated.

TES^15 kHz-TI^1 Hz effects on SWA during stimulation

We then performed a comparison of the effects on SWA of TES with amplitude modulation (TES^15 kHz-TI^1 Hz, 1 Hz difference) and without (TES^15 kHz, 0 Hz difference) during stimulation (Fig. 4A). To do so, we directly compared normalized SWA (%SWA) in the STIM period between TES^15 kHz-TI^1 Hz and TES^15 kHz. Using nonparametric cluster-based statistics, we find a broad set of channels with SWA that is significantly greater in TES^15 kHz-TI^1 Hz as compared to TES^15 kHz (Fig. 4B, left, 1 positive cluster, 116 significant electrodes, $\overline{\mathrm{p}}$ = 0.028). In the average across these channels, SWA during TES^15 kHz-TI^1 Hz is greater than SWA during TES^15 kHz (Fig. 4B, right, TES^15 kHz-TI^1 Hz N = 21, TES^15 kHz N = 7, t = 2.47, p = 0.020, d = 1.08, two-sided independent samples t-test).

We also tested whether the effects on SWA changed throughout the STIM period during TES^15 kHz-TI^1 Hz. For this analysis, we compared the last 45 seconds (LATE) of the STIM period with the first 45 seconds (EARLY), including the 15-second ramping interval (Fig. 4C). During TES^15 kHz-TI^1 Hz, SWA is higher in LATE compared to EARLY, and these increases in LATE SWA are global and strongest in the frontal region (Fig. 4C, left, 1 positive cluster, 168 significant electrodes, $\overline{\mathrm{p}}$ = 9.31 × 10^‒3; Fig. 4C, right, N = 21, t = 3.47, p = 2.41 × 10^‒3, d = 0.76; two-sided paired samples t-test). Similar patterns suggesting increased SWA during TES^15 kHz-TI^1 Hz as compared to TES^15 kHz, and during LATE TES^15 kHz-TI^1 Hz as compared to EARLY, are found when using a narrower frequency band surrounding SWA, 0.5–2 Hz (Supplementary Fig. 3B, C).

TES^15 kHz-TI^1 Hz effects on other frequency bands

Next, we tested whether TES^15 kHz-TI^1 Hz had additional effects on the EEG power spectrum. PSD values were averaged for each PRE, STIM, and POST period, then across electrodes, then across first and last intervention night, to yield one spectrum per participant (N = 21). Spectra were then averaged across participants (Fig. 5). For each frequency bin (N = 240, 0.167 Hz steps), the STIM-PRE difference, as well as the POST-PRE difference, were calculated. For statistical comparisons, for each canonical band (e.g., theta, alpha), PSD values were averaged across the frequencies in that band for each participant, then STIM-PRE and POST-PRE comparisons were performed using paired samples t-tests with correction for multiple comparisons (Supplementary Table 2). For selected significant topographical analyses, as was done with SWA, band power was normalized (% band power) by the average band power during NREM sleep throughout the entire night to give a relative change from the mean overnight band power. Then, the difference between time periods (STIM-PRE, POST-PRE) was evaluated with nonparametric cluster-based statistics.

We find that, as compared to before, during stimulation, TES^15 kHz-TI^1 Hz increases power in the theta (4–8 Hz) range and decreases power in the beta (16–25 Hz) range (Fig. 5A, STIM-PRE, N = 21, theta: t = 4.28, p = 0.011, d = 0.93; beta: t = −3.30, p = 0.034, d = −0.72; two-sided paired samples t-tests). Both changes are global (Fig. 5B, theta: 1 positive cluster, 185 significant electrodes, $\overline{\mathrm{p}}$ = 8.97 × 10^‒4; beta: 1 negative cluster, 173 significant electrodes, $\overline{\mathrm{p}}$ = 7.67 × 10^‒3). As compared to before stimulation, after TES^15 kHz-TI^1 Hz, we find an increase in power in the theta range and a decrease in the sigma (12–16 Hz) range (Fig. 5C, POST-PRE, N = 21, theta: t = 3.90, p = 8.92 × 10^‒4, d = 0.85; sigma: t = −3.95, p = 7.95 × 10^‒4, d = −0.86; two-tailed paired samples t-tests). All these changes are also global (Fig. 5D, theta: 1 positive cluster, 185 significant electrodes, p = 1.35 × 10^‒3; sigma: 1 negative cluster, 185 significant electrodes, $\overline{\mathrm{p}}$ = 4.44 × 10^‒3). Analyses were also repeated for the TES^15 kHz group, but given the small sample size, results should be considered exploratory and hypothesis-generating (Supplementary Table 3).

Changes in SWA during TES^15 kHz-TI^1 Hz are associated with improved sleep quality ratings following the TES^15 kHz-TI^1 Hz intervention

Finally, we examined potential relationships between stimulation-related changes in normalized SWA (%SWA) and participants’ perceptions of how they slept. For each participant in the TES^15 kHz-TI^1 Hz group, we compared the difference in SWA during (STIM-PRE) and after (POST-PRE) TES^15 kHz-TI^1 Hz with subjective sleep quality ratings from the restorative sleep questionnaire (REST-Q)^44,45, assessed the morning after each intervention night. In line with Robbins and colleagues⁴⁴, an overall REST-Q score was calculated for each participant and each intervention night.

To identify potential factors associated with overall REST-Q scores, we used a predictive modeling approach, specifically, LASSO estimation with 5-fold cross-validation. Power across all channels in SWA, theta, beta, low sigma, and high sigma bands during STIM-PRE and POST-PRE periods (independent variables) were used as predictors for overall REST-Q ratings (dependent variable). The model was fit on first and last night data as well as the difference between last and first nights to assess for longitudinal changes over the course of the intervention in the context of inter-individual variability.

For first and last night data (λ_min = 2.98, cross-validated MSE = 313.0), no factors improve predictive performance. For the difference between last and first nights (λ_min = 9.44, cross-validated MSE = 298.6), only one factor improves predictive performance: the change in SWA during the STIM-PRE period. Specifically, this factor has a positive regression coefficient, indicating that greater increases in SWA during TES^15 kHz-TI^1 Hz (STIM-PRE) on the last night compared to the first night are associated with higher overall REST-Q scores on the last night compared to the first night. To visualize the predictive model, we fit a simple linear regression model and extracted the line of best fit and R² values (Fig. 6A, Left, β₁ = 2.20, R² = 0.38). To further investigate whether the predictive power in the observed data was spatially localized, R² values are plotted topographically (Fig. 6A, right). We find relatively high R² values globally, with the greatest values in the left frontal region. However, we note that these topographies are purely descriptive. Changes in sigma power (STIM-PRE) are shown as an example of a factor that does not improve predictive performance of the model (Fig. 6B, high sigma: 12–16 Hz, N = 16, β₁ = −0.43, R² = 0.05).

Peer review information

Communications Medicine thanks Tamir Avigdor, Heta Helakari, and the other anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.