Induction and stabilization of delta frequency brain oscillations by phase-synchronized rTMS and tACS

Background: Brain oscillations in the delta frequency band have been linked with deep sleep and consolidation of declarative memory during sleep. However, the causal relationship of these associations remains not competely clarified, primarily due to constraints by technical limitations of brain stimulation approaches suited to induce and stabilize respective oscillatory activity in the human brain. The objective of this study was to establish a non-invasive brain stimulation protocol capable of reliably inducing, and stabilizing respective oscillatory activity in the delta frequency range. Hypothesis: We aimed to develop an efficient non-invasive brain stimulation (NIBS) protocol for delta frequency induction and stabilization via concurrent, phase-locked repetitive transcranial magnetic stimulation (rTMS) and transcranial alternating current stimulation (tACS). We hypothesized that rTMS induces oscillatory resting-state activity in the delta frequency and that tACS stabilizes this effect, as has been shown before for alpha and theta frequencies. Methods: 19 healthy participants took part in a repeated-measures experimental protocol. We applied rTMS pulses synchronized with the peak or trough phase of 0.75Hz tACS over the bilateral prefrontal cortex. Resting state EEG in eyes-open (EO) and eyes-closed (EC) conditions was recorded before, immediately after and every 10 min for up to 1 h after intervention. Results: rTMS phase-synchronized to the trough of the tACS waveform significantly increased delta frequency activity for up to 60 min in both EO and EC conditions after stimulation. The effects extended from frontal to temporal regions and this enhancement of oscillatory activity was shown to be specific for the delta frequency range. Conclusion: Concurrent, trough-synchronized 0.75 Hz rTMS combined with tACS may be a reliable protocol to induce long-lasting oscillatory activity in the delta frequency range. The results of the current study might perspectively be relevant for clinical treatment of sleep disturbances which are accompanied by pathologically altered brain oscillations, and enhancement of memory consolidation.


Introduction
Brain oscillations are known to be involved in diverse cognitive functions and correlate with states of consciousness.The delta frequency (<4 Hz), originating from thalamic neurons and spreading through thalamocortical connections, is the predominant oscillation during slowwave, non-rapid-eye-movement (NREM) sleep.It is an indicator of Stage 3 NREM sleep, and its activity patterns are correlated with cycles of NREM and REM sleep [1,2].A disturbance of this oscillatory sleep architecture is associated with sleep disorders, such as insomnia, which is specifically accompanied by reduced delta activity in NREM sleep [3,4].
The deep sleep stage, characterized by predominant cortical activity in the delta frequency band, is moreover relevant for cognitive processes, particularly declarative memory consolidation.It is assumed that this sleep stage promotes the consolidation of declarative memory [5,6].In accordance, it was shown that patients with insomnia show diminished consolidation of declarative memory, suggesting a significant role of the delta frequency in memory formation [7].Furthermore, it is assumed that spindle activity during the NREM (Non-Rapid Eye Movement) sleep stage plays also a pivotal role in memory consolidation [8,9].Binder et al. (2012) created an animal model to explore the significance of delta activity during NREM sleep for declarative memory encoding [10], and showed an association between memory performance and high delta power during NREM sleep in rats via EEG recordings.However, findings from animal studies may not directly translate to humans, and associations do not prove a causal involvement.Therefore, direct causal evidence for the role of delta activity in humans is still required, and here non-invasive brain stimulation might play a pivotal role.
NIBS methods were developed to investigate the causal role of delta activity for memory consolidation in humans by directly modulating neuronal activity.For instance, Marshall and coworkers (2006) applied slow oscillatory anodal transcranial direct current stimulation (tDCS), targeting frontal cortical areas, which mimic oscillatory activity within the thalamocortical network, during deep sleep [11].They observed an increase of slow oscillatory activity and spindle activity, as well as facilitated declarative memory performance as a result of this intervention.This improvement of declarative memory consolidation following slow oscillatory tDCS was replicated by some studies in children with attention deficit disorder and older adults [12,13], and also in animals [14].However, these studies still do not unequivocally clarify the causal role of delta oscillations for memory consolidation, since beyond its modulating effects on oscillations, tDCS also induces long term potentiation-like neuroplasticity, which is relevant for memory formation [15,16].Moreover, some follow-up studies showed no effects of stimulation on declarative memory performance with a comparable stimulation protocol and task, in contrast to the findings of Marshall et al. (2006), and the outcomes are therefore not completely consistent between studies [17,18].Beyond its effects on cognitive functions, one study showed that slow oscillatory tDCS prolonged the duration of the deep sleep stage in patients with insomnia, but these results are preliminary due to its small sample size [19].Hence, in order to examine the causal relationship between delta frequency, memory consolidation and deep sleep to a larger degree, a stimulation protocol that can specifically induce and stabilize neuronal oscillations in the delta frequency range is warranted.
TMS delivers a brief and high-intensity magnetic pulse to the scalp through a coil, inducing an electrical field in brain tissue which leads to activation of neurons [20,21].By repeatedly delivering pulses at a specific frequency, rTMS is able to induce neuronal oscillations at the induced frequency [20,22].However, this effect is stable only for a short duration [23].In contrast, tACS delivers a weak electrical current to the scalp via electrodes, which modulates the frequency of spontaneous neuronal activity without directly inducing neuronal activation.This results in entrainment of neuronal oscillations and has been shown to affect cognitive and perceptual processes [24,25].Compared to rTMS, tACS exerts long-lasting physiological after-effects [26,27].However, tACS only entrains pre-existing oscillations, which means that relevant activity in the targeted frequency band is necessary for the stimulation to be efficient [28,29].
Previous studies, which used a combination of repetitive transcranial magnetic stimulation (rTMS) and transcranial alternating current stimulation (tACS) have shown long-lasting effects on alpha and theta oscillatory activity and functional connectivity in these frequency bands [30,31].In addition, the combined theta rTMS and tACS protocol improved working memory performance, in which neuronal theta oscillations are involved [30].It thus has been shown that by stabilizing rTMS-induced oscillatory activity, tACS can prolong and strengthen rTMS effects, overcoming the limitations of each technique.However, this particular stimulation protocol has not yet been tested in the delta frequency band.
We hypothesized that combined rTMS and tACS, specifically, the peak-synchronized protocol which induced and stabilized respective neuronal activities most effectively in previous studies [30,31], enhances delta oscillatory activity and that respective effects should be sustained.The current study tested this hypothesis by using 1) peak-synchronized rTMS + tACS, 2) trough-synchronized rTMS + tACS, 3) rTMS combined with sham tACS, 4) tACS combined with sham rTMS, 5) sham rTMS + sham tACS, and evaluated changes in delta power and functional connectivity in the delta frequency band in the EEG before and after this intervention administered to healthy adults in a state of relaxed wakefulness.

Participants
19 healthy individuals were recruited (7 males, mean age 29.21, SD 9.43).Exclusion criteria were age less than 18 or older than 65 years, tobacco smokers, pregnancy, history of neurological or psychiatric disorders, including epilepsy or head trauma, intake of CNS-acting medication, and having metal implants.Prior to the beginning of the experimental sessions, all participants were screened by a medical professional.All participants provided written informed consent and were compensated for participation.The experiment conformed to the principles of the Declaration of Helsinki and was approved by the Institutional Review Board of the Leibniz Research Centre for Working Environment and Human Factors (Dortmund, Germany).The datasets generated in the current study are available from the corresponding author upon reasonable request.

Stimulation
Five stimulation protocols were designed to assess whether the concurrent application of rTMS + tACS was more effective than each stimulation protocol alone, and sham stimulation for induction, and stabilization of delta activity: 1) rTMS at the peak of the tACS wave; 2) rTMS at the trough of the tACS wave; 3) rTMS alone (with sham tACS); 4) tACS alone (with sham rTMS); 5) sham rTMS with sham tACS.The order of the stimulation conditions was randomized.Stimulation intensity and duration were chosen in a manner compliant with technical and safety limits [32].
We employed a custom-made circuit to align transcranial magnetic stimulation (TMS) pulses within specific phases of the tACS waveform, which was described in detail in previous studies [30,31].Fig. 1 shows an overview of the circuit, and depicts the waveform and the timing of the stimulation in each condition.Biphasic TMS pulses were delivered using two figure-of-eight shaped coils (diameter of each winding 70 mm, PMD coil type; Mag and More GmbH, Munich, Germany).In peak-synchronized rTMS + tACS, TMS pulses were delivered at the peak of the tACS wave, and in trough-synchronized rTMS + tACS, TMS pulses were delivered at the trough of the tACS wave.For sham TMS conditions, two separate sham coils were used (double 70 mm pCool-SHAM coil; Mag and More GmbH, Munich, Germany) which elicited audible clicks at the same decibel intensity as the active/real stimulation coil, but without inducing electromagnetic pulses.In order to deliver TMS pulses through two coils with no latency between pulses, the TMS devices were connected in series with TTL signals triggering the TMS.The two pulses were verified to have near-zero latency via measurements obtained by an oscilloscope.With regard to tACS, we used a Starstim 8-channel constant-current, battery-powered electric stimulator (Neuroelectrics, Barcelona, Spain).Stimulation electrodes were circular (2 cm radius, 12.57 cm 2 area) and made of carbonated rubber, with the connector located at the center of the electrode.Conductive Ten20 paste (Weaver and Company, USA) was applied to the bottom of the electrodes.Care was taken to ensure that the electrodes had full contact with the scalp, with hair moved to the side.Stimulation electrodes were positioned over the F3, F4, TP9 and TP10 EEG electrode positions (10 20 International System).
The multichannel Starstim device allows external programming of customized stimulation waveforms at fixed latencies and current amplitudes through the eight available channels.As such, two channels were used to program pulses at precise timepoints for delivering rTMS pulses in predefined relation to four other channels that were used to deliver sinusoidal alternating currents to the head.
For triggering TMS, pulses (0.1 mA peak, 0.5 % duty cycle) were delivered from the electric stimulator to a separate circuit containing an optocoupler (developed in-house) in order to shield the stimulation from main power.Current-to-voltage conversion resulted in a 5 V signal which was used as a TTL signal to communicate with the TRIGGER-IN of the TMS machine.Latencies of the waveform generated by the electric stimulator and the TMS stimulator were measured and verified to be aligned ( ± 1 ms resolution) via an oscilloscope.
As mentioned above, tACS included four electrodes, with two channels delivering alternating current in the same phase to the left and right prefrontal cortex, and antiphase to the respective ipsilateral mastoid region.Stimulation electrodes were positioned at the F3, F4, TP9 and TP10 EEG positions, which resulted in an electric field distribution spanning from dorsal to deeper ventral regions of the frontal cortex, including also portions of the thalamus, according to finite-element modeling using software SimNIBS v3.0 [33] described in previous studies with comparable experimental protocols (Fig. S1) [30,31].Two TMS coils were positioned directly over each tACS electrode at F3 and F4, and received signals from the tACS device through the circuit which triggered pulses at precise timepoints relative to the tACS sinusoid.Both, TMS and tACS were delivered with the frequency of 0.75 Hz for 30 min continuously.rTMS was applied at 80 % of each individual's active motor threshold, while tACS was applied at 1 mA peak-to-peak intensity, with the time of ramping up and ramping down of tACS at 15 s each.The coils were held and maintained by the coil holders over the F3 and F4 stimulation sites.Electrode cables were only connected during the course of stimulation, and then detached for the remainder of the recording.

Electroencephalography
EEG was recorded with a NeurOne Tesla EEG amplifier (Bittium, NeurOne, Bittium Corporation, Finland).We measured neural activity from 62 Ag/AgCI EEG electrodes.The sampling frequency was 2000 Hz, and the 62 electrodes were mounted on the head with a cap (EASYCAP GmbH, Herrsching, Germany).The reference electrode was positioned on FCz, and the ground electrode was placed at the CPz position.To establish a connection with the head, we used a high-viscosity electrolyte gel (SuperVisc, Easycap, Herrsching, Germany).EEG impedance maintained at values less than 10 kOhms.During recording, digital TTL triggers transmitted to the EEG system by a presentation PC were used to demarcate the start and end of all experimental conditions.

Experimental procedure
Each participant attended all experimental sessions at the same time of day (either 9 a.m. or 1pm) to control for daytime-dependent interindividual differences of arousal due to chronotype [34].In every session, the experiment started at the same time of day for each participant.Participants returned on five separate days, each session corresponding to one of the five different stimulation conditions.Sessions were separated by at least seven days to avoid carry-over effects.The experimental laboratory was illuminated with artificial lighting, and sound-shielded.Participants were seated comfortably in a reclined chair, with an adjustable vacuum pillow placed behind the neck to support and maintain the position of the head throughout stimulation and Fig. 2. Experimental design.The baseline resting-state EEG was recorded in eyes open (EO) and eyes closed (EC) conditions for 2 min per block each before and after intervention.Stimulation was applied for 30 min rTMS was applied at 80 % intensity of the individual active motor threshold (AMT).tACS was applied continuously for 30 min at 1 mA peak-to-peak intensity between the pairs of tACS electrodes.recordings.A 62-channel EEG cap was prepared on the participant's head according to the 10-10 convention, and connected directly with the recording system.In each session, active motor threshold (AMT) was determined by applying single pulses of TMS over the left primary motor cortex in order to elicit motor-evoked potentials (MEP) from the right abductor digiti minimi (ADM) muscle.The lowest TMS pulse intensity required to elicit MEP response of ~200-300 μV during moderate tonic contraction of the right ADM muscle (~20 % of the maximum muscle strength) in at least three out of six consecutive trials was defined as AMT [35].For each individual, 80 % of the stimulation intensity required to produce the AMT was used as rTMS intensity for the main experimental sessions.Fig. 2 depicts the procedure of the EEG measurements.Baseline EEG recordings in eyes open (EO) and eyes closed (EC) conditions were conducted for 2 min each.In the EO condition, participants were instructed to fixate a cross on the wall (positioned at precisely 1 m eye distance).Following these baseline recordings, stimulation of one of the predefined rTMS/tACS combinations was delivered for 30 min in randomized order.During stimulation, neuronavigation was performed with the Localite TMS Nagivator software (LOCALITE Biomedical Visualization Systems GmbH, Sankt Augustin, Germany) to monitor a stable coil position.Following stimulation, 2 min eyes open and eyes closed resting state recordings were collected (timepoint "0 min"), and again 10, 20, 30, 40, 50 and 60 min after the end of the intervention.After each session, participants were asked to fill in a questionnaire.This questionnaire contained rating scales to measure the strength and frequency of different sensations felt during the stimulation.These sensations encompassed visual phenomena, itching, tingling, burning, and pain.Furthermore, participants were requested to assess the presence and degree of skin redness, and symptoms like headache, fatigue, difficulties in concentration, nervousness, and sleep disturbances after stimulation.These assessments were made on a numerical scale spanning from zero (representing the absence of the sensation) to five (indicating an exceptionally intense sensation) [36,37].

EEG power analysis
Offline EEG analysis was performed using MNE-Python [38].Raw data were down-sampled to 512 Hz.Artifactual electrodes contaminated by noise were identified using Random Sample Consensus (RANSAC) implemented in the Python package autoreject [39].The data were re-referenced to the average of the EEG, excluding artifactual electrodes, and the F3, F4, TP9 and TP10 electrodes, which were located in areas covered by the tACS electrodes.An offline high-pass filter at 0.1 Hz and an offline low-pass filter at 45 Hz were then applied.For further artifact rejection, the independent component analysis "fastica [40]" was applied and EEG components identifying eye-blinks were automatically selected and removed based on the Pearson correlation between an Independent component and the EOG channel.This method employs an adaptive z-scoring technique, where components with a z-score threshold of 3 or higher are identified as being related to eye movements or blinks.These blink-associated components were masked and the process iterated until no further blink-related components were found.After this procedure, F3, F4, TP9, TP10 and other artifactual electrodes were interpolated per subject using the cleaned data.To examine

Table 1
The presence and intensity of stimulation-related side effects was analyzed by one-way repeated-measures ANOVAs.Detailed ratings of the presence and intensity of side effects are documented in Table S1   changes in delta band oscillatory activity, the power spectral density (PSD) of predefined frontal, central and temporal channels (spanning the region of stimulation; F5, F3, F4, F6, FC3, FC4, FC5, FC6, C5, C6, C3, C4, F7, F8, FT7, FT8, T7, T8, TP7, TP8, CP5, CP6, CP3, CP4) at 0.75 Hz as well as for the entire delta band (0.5-3.9 Hz) was computed on the preprocessed data using multitapers [41] with the default window half-bandwidth of 4 Hz.In addition, to examine whether the stimulation protocol exerted a delta frequency-specific effect, average changes in frontotemporal activity across the power spectrum between 0.5 and 45 Hz were calculated.Outliers in raw power values were identified as data points falling below the first quartile (Q1, -1.5 times of the interquartile range (IQR)) or above the third quartile (Q3, +1.5 times of the IQR), and excluded from further analysis.Recently, it has been suggested to discern periodic and aperiodic EEG activity via a new analysis approach, the Fitting Oscillations & One Over F (fooof) method [42].This algorithm parameterizes both, the putative periodic oscillatory component and the aperiodic component of the EEG.Results using the fooof method are shown in the Supplementary Figure, S3.

Whole brain functional connectivity analyses
We captured connectivity information between all pairwise combinations of the 62 EEG channels by the weighted phase lag index (wPLI) by using the Python package MNE-Connectivity [38].
In these equations, X ij is the cross-spectral density (CSD) between two signals S i (t) from channel i and S j (t) from channel j.I refers to the imaginary component, and E[] is the expectation [43].In these equations, X ij is the cross-spectral density (CSD) between two signals S i (t) from channel i and S j (t) from channel j.I refers to the imaginary component, and E[] is the expectation [43].
The CSD X ij of channel i and j is defined as ] Where f j (ω) is the finite Fourier transform of signal S j (t) at frequency ω.
is the complex conjugate of f i (ω) at frequency ω.
At the whole-brain level, we adopted global efficiency E global as a measure of global information integration.Resting state EEG was used to compute global efficiency, a metric that quantifies the capacity of the brain to integrate information.A previous study has shown that this metric accurately measures information integration capacity and is associated with improvements of working memory performance [30].
E global is defined as Where N is the number of nodes in the network G. d j,k is the shortest path between nodes i and j.We used wPLIs as weights of edges to construct the graph without thresholding the weights.Global efficiency is a scaled measure ranging from 0 to 1, with a value of 1 indicating maximum global efficiency of a network.This measure was computed by the network graph contructed by the wPLIs using the Brain Connectivity Toolbox [44].Outliers in raw global efficiency values were identified as data points falling below the first quartile (Q1, -1.5 times the Interquartile range (IQR)) or above the third quartile (Q3, +1.5 times the IQR), and excluded from further analysis.

Statistical analyses
The data were analyzed via R and Python programming language.To evaluate the impact of brain stimulation on delta frequency activity, we conducted a statistical analysis on EEG data obtained from frontotemporal channels (F5, F3, F4, F6, FC3, FC4, FC5, FC6, C5, C6, C3, C4, F7, F8, FT7, FT8, T7, T8, TP7, TP8, CP5, CP6, CP3, CP4) across both the target stimulation frequency (0.75 Hz) and the entire delta frequency band (0.5-3.9 Hz).The absolute delta frequency power was calculated separately for each frontotemporal channel.To evaluate the effects of the intervention on oscillatory activity, baseline normalization of the data was initially conducted (note that baseline delta power (0.5-3.9 Hz) was assessed for differences between stimulation conditions.No significant differences were observed (Supplementary Table S3)).This normalization involved dividing post-stimulation power by prestimulation power for each electrode at each measurement timepoint (Pre, Post 0, 10, 20, 30, 40, 50, 60 min).Subsequently, in order to account for any between-timepoint variance, baseline-normalized data were epoched, averaging the data from timepoints between 0 min and 20 min (Post 0-20 min) and between 30 min and 60 min (Post 30-60 min).The baseline-normalized, epoched data were analyzed using linear mixed-effect models, fitted with the lmer function from the lme4 R package [45].Fixed effects included the sitmulation protocol (Protocol, 5 levels), EEG measurement timepoint (Timepoint, 3 levels), EEG channel (Electrode, 24 levels) and their interactions.A by-participant random intercept term was included to account for the non-independence of observations within subjects.The significance levels for the model's fixed effects were computed using Satterthwaite's approximation for degrees of freedom and assessed using F-tests from the ANOVA function in the in the lmer Test R package [46].The critical significance level (alpha error) for all tests was set to 0.05.In case of significant effects of the factors, we conducted post-hoc pairwise comparisons using the estimated marginal means obtained from the model via the emmeans R package [47].These means account for both the random effects and main factors of the model.The false discovery rate (FDR) controlled for multiple comparisons.The choice of estimated marginal means instead of pairwise t-tests for post hoc testing was motivated by its capacity to account for covariates and address dependencies within the data.
Furthermore, we conducted a whole-brain analysis of resting state EEG at the sensor level.This analysis contrasted the session-wise change in delta, theta, alpha, beta and gamma frequency activity between active stimulation protocols and the sham condition using permutation paired t-tests (averaging timepoints between 0 and 20 min).The analysis involved 5000 permutations, and correction for multiple comparisons was applied using the FDR method.The analysis was performed separately for each active stimulation protocol.
Moreover, a statistical analysis was performed on global efficiency over all channels.Similar to the power analysis, post-stimulation global efficiency was divided by pre-stimulation global efficiency for baseline correction at each measurement timepoint for each participant.Baseline-normalized global efficiency data were then epoched, averaging the data from timepoints between 0 min and 20 min (Post 0-20 min) and between 30 min and 60 min (Post 30-60 min).The baselinenormalized, epoched data were entered into a linear mixed model with the fixed effects sitmulation protocol (Protocol, 5 levels), EEG measurement timepoint (Timepoint, 3 levels) and their interactions.In case of significant effects of the factors, we conducted post-hoc pairwise Fig. 4. Whole-brain, sensor level t-contrasts are shown to compare the baseline-corrected changes of delta activity (0.75 Hz and 0.5-3.9Hz) within 0-20 min after active stimulation with sham stimulation.Asterisks denote EEG sensors that remained significant after correcting for multiple comparisons (p < 0.05, corrected).The maps visualize the differential distribution of changes in delta power in each paired comparison, revealing a broader distribution of enhanced delta power in the EC condition compared to the EO condition.A broader enhancement of delta power, along with the significant channels, was consistently observed for both delta bands.comparisons using the estimated marginal means obtained from the linear mixed-effects model, correcting for multiple comparisons using the FDR correction method.All analyses were conducted separately for EO and EC conditions.
Additionally, to assess potential side effects during and after stimulation, we performed one-way repeated-measures ANOVAs using the AnovaRM function from the statsmodels Python package [48], with stimulation protocol (5 levels) as the within-subject factor and rating scores as the dependent variable.

Tolerability of stimulation protocols
We conducted one-way repeated-measures ANOVAs to assess potential side effects resulting from the stimulation protocols.Our analysis showed mild side effects associated with the stimulation protocols.A significant effect was noted for reports of pain during stimulation (F (4, 72) = 3.09, p = 0.021), with the most pronounced pain scores corresponding to the peak-synchronized rTMS + tACS protocol (Table 1 and Table S1).To assess possible effects of pain on delta frequency activity in the peak-synchronized rTMS + tACS condition, we performed Spearman's rank correlation analyses.Specifically, the correlation between the delta frequency activity (0.75 Hz and 0.5-3.9Hz) during the period from 0 to 20 min after stimulation and pain ratings was tested.The analyses showed no significant correlation between the intensity of pain and delta frequency activity (Supplementary Table S2).
No other side effects showed significant differences across stimulation protocols, as outlined in Table 1.Severe adverse side effects were not observed.Detailed information regarding ratings of the presence and intensity of side effects can be found in the supplementary materials (Table S1).

Delta activity
No significant differences at baseline between stimulation conditions in delta power (0.5-3.9 Hz) were found in either EO or EC conditions at the group level, as indicated by linear mixed model analyses (Supplementary Table S3).
Subsequent post-hoc comparisons revealed significantly higher 0.75 Hz activity following trough-synchronized rTMS + tACS administration in the EO condition, compared to sham, peak-synchronized rTMS + tACS, rTMS alone, and tACS alone.These effects persisted for a duration of 60 min.
Additionally, in the EC condition, there was significantly higher 0.75 Hz activity following trough-synchronized rTMS + tACS administration compared to sham, peak-synchronized rTMS + tACS, rTMS alone and tACS alone within the Post 0-20 min time window.
(Supplementary Table S4).A whole-brain analysis indicated a significant increase in 0.75 Hz power with its maximum over frontal and temporal regions after trough-synchronized rTMS + tACS in the EC condition, when contrasted against sham (Fig. 4; p < 0.05, corrected).

Overall power spectrum
We furthermore conducted a confirmatory analysis by examining the effect of the intervention on baseline-normalized brain oscillations within the range of 0.5-45 Hz.This analysis focused on the period from 0 to 20 min after stimulation, during which changes in delta activity were evident.We aimed to investigate whether alterations of oscillations across different stimulation protocols and frequencies were present.
Subsequent post-hoc comparisons demonstrated a consistent increase specifically within the delta frequency range (0.5-3.9 Hz) for the trough-synchronized rTMS + tACS condition compared to frequencies outside this range and the sham condition in both EO and EC conditions (Fig. 5).This finding underscores the low-frequency specific effect of the stimulation protocol.Suppressed power after the trough-synchronized rTMS + tACS was observed in the alpha frequency range (8-12 Hz) in both EO and EC conditions.Furthermore, in the EC condition, rTMS alone and tACS alone also induced an enhancement of oscillatory power in the delta frequency range.In contrast, compared to sham, a significant suppression of alpha, beta (12-30 Hz) and gamma (30-45 Hz) power after administration of peak-synchronized rTMS + tACS, rTMS alone, and tACS alone was observed (Fig. 5).
Power changes across all frequency bands are depicted in the topographic plots in Fig. S2 in the supplementary materials.Except for the delta band, no EEG channels were identified that showed a significant power increase following the stimulation intervention when compared to the sham condition.

Global efficiency
We employed linear mixed model analyses to examine changes in functional connectivity at two different frequency ranges: 0.75 Hz and within the 0.5-3.9Hz band, similar to our approach applied for delta power analysis.
For 0.75 Hz connectivity, we found no significant effects of stimulation protocols on global efficiency in either EO or EC conditions, with the exception of a significant main effect of time in the EC condition (Protocol, EO: F( 4 4).
Post-hoc comparisons revealed a significant higher global efficiency for the 0.5-3.9Hz frequency range in the EO condition following the administration of trough-synchronized rTMS + tACS compared to sham, as well as compared to rTMS alone and tACS alone.These effects remained significant for up to 60 min (summarized in Fig. 6 and detailed in Supplementary Table S7).

Discussion
In sum, our findings showed that trough-synchronized rTMS and tACS effectively induced and stabilized resting-state delta activity compared to other stimulation protocols, and the frequency-specificity of this effect.More specifically, at a stimulation frequency of 0.75 Hz, for that frequency and across the entire delta frequency range (0.5-3.9 Hz), under both EO and EC conditions, the trough-synchronized rTMS and tACS induced significantly higher power in the frontotemporal region compared to the sham stimulation condition.Notably, the observed power increase across the entire delta range in the EC condition persisted for up to 60 min following intervention.Moreover, while we observed a prominent increase of oscillatory power within the delta frequency range, but suppressed or unchanged power in other frequencies such as alpha and gamma were observed, suggesting frequency-specific effects of the trough-synchronized rTMS and tACS protocol to enhance the delta power.Furthermore, trough-synchronized rTMS and tACS resulted in an increased global efficiency within the entire delta frequency range in the EO condition for up to 60 min.
In contrast, peak-synchronized rTMS and tACS did not have a robust effect on delta oscillations, which differs from findings from Hosseinian et al. (2021a,b), who reported a significant increase in alpha (10 Hz) as well as theta (6 Hz) power with peak-synchronized rTMS and tACS, but no alpha power changes with trough-synchronized rTMS and tACS.Although the peak-synchronized rTMS and tACS had the strongest impact on stimulation-related pain, an association between pain intensity, and the impact of stimulation on delta power was however excluded by a non-significant correlations.
Furthermore, while previous research [30] demonstrated an increase of global efficiency with peak-synchronized theta (6 Hz) rTMS and tACS, our results did not observe respective global efficiency alterations with peak-synchronized delta rTMS and tACS.These findings suggest that the impact of synchronized rTMS and tACS depends on both, stimulation frequency and phase of association.The results of the present study align with previous studies, which demonstrated phase-dependent modulation of TMS effects associated with specific phases of natural oscillations, revealing that TMS applied at the ongoing trough of the μ frequency over the motor cortex produced larger MEP amplitudes as well as higher amplitudes of the evoked EEG potential compared to its application at the μ frequency peak [49][50][51].Conversely, in the beta frequency, TMS applied at the positive peak of ongoing beta oscillations   To support this mechanistic explanation, employing methods such as direct recordings of neuronal responses in animal studies would be relevant [52].While our study added insights into the effects of synchronized delta rTMS and tACS on cerebral oscillations, it is important to acknowledge some limitations.Recently, the fooof approach has been introduced for its ability to decompose neural power spectra into aperiodic and periodic components.To further validate our findings, we performed an additional analysis using the fooof method, which resulted in outcomes which differed relevantly between eyes open and closed conditions, and between calculations including the specific stimulated frequency, and the whole delta frequency band.The results were only partially consistent with those of the primary analysis method we used (Supplementary Fig. S3).For the fooof protocol, there was a significant increase in delta power following peak-synchronized rTMS + tACS in the EO condition, although trough-synchronized rTMS + tACS was found to be more effective at inducing and stabilizing delta activity in the main analysis.A detailed discussion about the results can be found in the supplementary information.Given the discrepancies between the main findings and those using the fooof approach, future studies should explore the effects of both peak-and trough-synchronized rTMS + tACS to establish periodic delta activity in a sleep medicine context, and be able to identify the most efficient protocol.
In this study, the order of the stimulation conditions of the current study was randomized, but not counterbalanced.To ensure that the main findings were not influenced by the order of conditions, particularly the trough-synchronized rTMS and tACS condition and the sham conditions, we conducted additional analyses, which show no significant dysbalance in the order of these conditions (Supplementary Table S8).Therefore, the main findings should not be relevantly affected by this experimental design aspect.
EEG measurements were limited to a duration of 60 min after intervention, restricting our ability to determine the precise duration of the observed effects.For instance, in the EC condition, we observed an increase of whole delta range power for up to 60 min, but the persistence of this effect beyond this timeframe remains uncertain.Furthermore, the mechanistic explanations for the effectiveness of the synchronized rTMS and tACS protocol are still largely speculative and need to be revealed in future studies.Further detailed exploration of the specific mechanisms underlying the effects of trough-synchronized rTMS and tACS is thus required, and reproducibility of these findings has to be shown.Future studies should test the generalizability of the current findings to sleep states and investigate the applicability of the delta stimulation protocol in a sleep medicine context.Nevertheless, we observed in the current study that increased delta power persisted for up to 60 min after the application of rTMS synchronized to the trough of tACS.These findings imply that long-lasting delta activity induced by this stimulation protocol during wakefulness potentially extends to subsequent sleep.Moreover, a stimulation protocol that can induce long-lasting specific frequency activity during wakefulness should offer flexibility for various experimental designs.Fig. 7 illustrates the application concept of the stimulation protocol.For instance, insomnia patients are known to exhibit lower delta power during the sleep onset period compared to healthy subjects [53].Inducing delta power through stimulation in wakefulness could facilitate sleep onset in patients.Furthermore, given the evidence that delta oscillations play a role in cognitive functions also during wakefulness, our study results might contribute to enhancing understanding of the role of delta oscillations in various cognitive domains by enabling delta activity induction during wakefulness [54,55].Thus, our study provides an application-relevant foundation for future studies of delta stimulation protocols in awake volunteers.
To our knowledge, this study presents the first results of the impact of synchronized rTMS and tACS at the delta frequency range on brain oscillations, extending application features of concurrent rTMS and tACS.Our study showed a robust, and specific effect of rTMS and tACS on oscillatory activity within the targeted frequency range.The efficacy of this stimulation protocol suggests the potential of phase-synchronized rTMS and tACS to directly modulate neuronal oscillations in humans.This approach might be useful for exploring the causal role of delta activity for cognitive functions such as declarative memory consolidation, and to restore pathologically altered brain oscillations.Moreover, it might contribute to the development of therapeutic interventions for the treatment of sleep disorders associated with decreased delta activity.In our study, the use of either rTMS or tACS alone did not result in a robust increase of delta power as well as global efficiency, indicating the critical role of phase-dependent interaction between rTMS and tACS.Future studies employing direct recordings in animal experiments may be able to offer an understanding of these dynamic interactions between rTMS and tACS to a larger degree.

Fig. 1 .
Fig. 1.The multi-modal rTMS and tACS stimulation montage and timing of stimulation application in each protocol are shown.Orange bars indicate TMS pulses, gray dotted bars indicate audible clicks of sham coils, and blue waveforms represent a single tACS channel with a peak-to-peak amplitude of 1 mA.The montage consisted of two TMS coils and four tACS electrodes.TMS coils were positioned at an angle of 45 • to the midline, aligned with each target tACS electrode during stimulation.Two tACS electrodes applied sinusoidal current in the same phase over F3 and F4 EEG positions, while the remaining two electrodes applied currents in the opposite phase over the left and right mastoid positions (TP9 and TP10).In the rTMS + tACS Peak stimulation protocol, rTMS was administered at the positive peak of the tACS waveform, while in the rTMS + tACS Trough protocol, rTMS was delivered at the negative peak of the tACS waveform.For the rTMS + sham tACS protocol, only rTMS pulses were administered, whereas in the sham rTMS + tACS protocol, tACS was applied along with audible clicks from sham TMS coils.In the sham condition, only audible clicks from sham TMS coils were applied (The figure was adapted from Hosseinian et al. (2021a,b) and modified with permission).(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 3 .
Fig. 3. Time-course of baseline-normalized power changes of frontotemporal 0.75 Hz and the entire delta frequency band (0.75 Hz and 0.5-3.9Hz) activity as a function of stimulation protocol and timepoint.Asterisks indicate significant pair-wise differences relative to sham (p < 0.05).Error bars represent the standard error of means.

Fig. 5 .
Fig. 5. Line plot of the changes (0-20 min after the stimulation) of frontotemporal oscillatory activity across the power spectrum between 0.5 and 45 Hz in EO and EC conditions.Asterisks indicate pairwise differences relative to sham (p < 0.05).Error bars represent the standard error of means.

Fig. 6 .
Fig. 6.Time-course of baseline-normalized changes of global functional network efficacy in the delta frequency range (0.75 Hz and 0.5-3.9Hz) as a function of stimulation protocol and timepoint.Asterisks indicate pairwise differences relative to sham (p < 0.05).Error bars represent the standard error of means.

Table 2
Results of the effect analysis performed by linear mixed models conducted for baseline-normalized 0.75 Hz activity.EO indicates Eyes Open and EC indicates Eyes Closed conditions.d.f.= degrees of freedom.Asterisks indicate significant differences (*p < 0.05, **p < 0.001).

Table 4
Results of the effect analysis performed by linear mixed models for baselinenormalized global efficiency at 0.75 Hz.EO indicates Eyes Open and EC indicates Eyes Closed conditions.d.f.= degrees of freedom.Asterisks indicate significant differences (*p < 0.05, **p < 0.001).

Table 5
[51]lts of the effect analysis performed by linear mixed models conducted for baseline-normalized global efficiency between 0.5 and 3.9 Hz.EO indicates Eyes Open and EC indicates Eyes Closed conditions.d.f.= degrees of freedom.Especially, the enhanced motor cortex excitability state after the application of TMS at the μ frequency trough indicates that the phase-dependency of TMS effects can be attributed to the sensitivity of cortical neurons to brain oscillation-determined excitability fluctuations[51].This may indicate that the neuronal populations responsible for generating delta frequency activity may exhibit heightened spiking probabilities at the trough of delta frequency oscillations.Wischnewski  et al. (2014)suggest that differences of axonal orientations of neurons, which serve as sources for distinct frequency activities, could underlie this phase-dependency, potentially yielding heterogeneous outcomes.