{"paper_id":"a60e5fb8-08ac-44b5-907b-201f5804ebf7","body_text":"1 \n \nLocal modulation of sleep slow waves depends on timing between auditory stimuli \n(Sven Leach †,A, Sara Fattinger†,A), Elena Krugliakova A,B, Jelena Skorucak A, Georgia Sousouri A,C,D, Sophia Snipes A,E, \nSelina SchühleA, Maria Laura FersterD, Giulia Da PoianF, Walter KarlenG, Reto HuberA,H \n†Joint first authorship \nA) Child Development Centre and Children’s Research Centre, University Children’s Hospital Zurich, University of Zurich, Zurich, Switzerland \nB) Donders Institute for Brain, Cognition and Behaviour, Radboud University Medical Center, Nijmegen, the Netherlands \nC) Institute of Pharmacology & Toxicology, University of Zurich, Zurich, Switzerland \nD) Mobile Health Systems Lab, Department of Health Sciences and Technology, Institute of Robotics and Intelligent Systems, ETH Zurich, Zurich, Switzerland \nE) Sorbonne Université, Institut du Cerveau - Paris Brain Institute - ICM, Inserm, CNRS, APHP , Hôpital de la Pitié Salpêtrière, Paris, France \nF) Sensory-Motor Systems Lab, Department of Health Sciences and Technology, ETH Zurich, Zurich, Switzerland \nG) Institute of Biomedical Engineering, Faculty of Engineering, Computer Science and Psychology, Ulm University, Ulm, Germany \nH) Department of Child and Adolescent Psychiatry and Psychotherapy, Psychiatric Hospital, University of Zurich, Zurich, Switzerland \nAbstract \nConflicting evidence exists regarding the role of the targeted slow-wave phase in determining the direction and spatial \nspecificity of slow -wave activity (SWA) modulation via phase -targeted auditory stimulation (PTAS) during sleep. To \nreconcile these discrepancies, we re -analyzed high-density electroencephalography (hd-EEG) data from previous \nstudies, focusing on SWA responses to auditory stimuli presented with varying inter -stimulus intervals (ISIs). Our \nanalysis reveals that ISI is a primary determinant of PTAS-induced SWA modulation, exceeding the influence of targeted \nphase alone. Specifically, auditory stimulation with longer ISIs evoked a global increase in SWA, consistent with a \nstereotypical auditory-evoked K-complex (KC), independent of targeted phase. Conversely, longer stimulus trains with \nrapid successive stimulus presentation resulted in spatially localized, phase-dependent SWA modulation, with up-\nPTAS enhancing and down-PTAS reducing SWA locally around the targeted area . This distinction resolve s \ninconsistencies in prior PTAS studies by demonstrating that  phase alone in insuUicient in predicting slow -wave \nresponses. Rather, it was the ISI which determined whether PTAS resulted in a global, KC-mediated response or a local, \nphase-specific modulation of SWA. Consequently, our findings refine the mechanistic understanding of PTAS, \nsuggesting that ISI regulates the engagement of distinct neural circuits and thereby potentially enables the targeted \nmanipulation of specific slow-wave subtypes and their associated functions. \nIntroduction \nNeural oscillations—rhythmic brain activity patterns evident in the electroencephalogram (EEG) —underlie various \naspects of human behavior. Their study is primarily motivated by the desire to understand the computational principles \ngoverning core neural processes (Cohen, 2017). Neuromodulation techniques seek to experimentally manipulate such \noscillations to study  concurrent behavioral consequences, oUering a promising approach to  establishing causal \nrelationships between the two (Herrmann et al., 2016). Neuromodulation during sleep has placed particular emphasis  \non slow waves (0.5 –4 Hz) and sleep spindles (1 2–16 Hz) , two prominent EEG oscillations during non -rapid eye \nmovement (NREM) sleep which are thought vital for sustaining a wide range of physiological functions (Fernandez & \nLüthi, 2020; Léger et al., 2018). \nGiven its simplicity and non -invasiveness, the modulation of slow waves with non -arousing auditory stimuli has \nreceived substantial attention over the last decade. At its core, phase-targeted auditory stimulation (PTAS), also known \nas phase -locked (PLAS) o r closed -loop auditory stimulation (CLAS), involves the presentation of auditory stimuli \nlocked to a specific phase of ongoing slow waves (Ngo et al., 2013). Using PTAS, several studies have suggested causal \nrelationships between slow waves and memory consolidation (Clark et al., 2024; Diep et al., 2020; Leminen et al., \n2017; Moreira et al., 2021; Ngo et al., 2013; Ong et al., 2016, 2018; Papalambros et al., 2017; Prehn-Kristensen et al., \n2020; Salfi et al., 2025) , immune functions (Besedovsky et al., 2017) , cardiovascular health (Grimaldi et al., 2019; \nHuwiler et al., 2023, 2024) , learning capacity (Fattinger et al., 2017) , and general sleep -related recovery processes \n(Krugliakova et al., 2022). \nThe central premise of a conceptual framework that describes how PTAS is thought to modulate neural oscillations \nduring sleep is that the phase of targeted slow waves directly relates to neuronal firing (or silence) of cortical neurons \n(Nir et al., 2011; Steriade et al., 1993; Vyazovskiy et al., 2009). An auditory stimulus delivered during the up-phase of \nslow waves (up-PTAS), a depolarized state as active as during wake, is thought to contribute to the existing neuronal \nactivity and therefore further enhance neuronal synchrony . Conversely, targeting the down -phase (down-PTAS), a \nhyperpolarized state where neurons are completely silenced for a few hundred milliseconds, is proposed to disrupt \nneural synchrony by perturbing this silenced state (Bellesi et al., 2014) . The second central aspect is the locality of \nPTAS eUects. Most slow waves do not occur synchronously across the scalp but originate in one location and travel \nacross the cortex (Massimini et al., 2004; Sousouri et al., 2022). Phase-locked stimuli are delivered based on the EEG \nsignal from a single detection electrode. As a result, systematic phase targeting occurs primarily near the detection \nelectrode, with precision diminishing as the distance from this electrode increases.  This explains how an auditory \nstimulus, despite reaching a large portion of the cortex, could interact systematically with only a circumscribed region. \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.05.641406doi: bioRxiv preprint \n\n2 \n \nThe current landscape of data, however, partly conflicts with this framework : (1) While up -PTAS has consistently \nresulted in enhancements of slow waves, this eUect has never been demonstrated to be local (Huwiler et al., 2022; \nKrugliakova et al., 2022); (2) while down-PTAS should exclusively result in the local suppression of slow waves (Fattinger \net al., 2017; Moreira et al., 2021; Ngo et al., 2013), also global enhancements thereof have been observed (Huwiler et \nal., 2022; Leach et al., 2024). These incongruent results seriously question the current conceptual framework of PTAS \nand therewith the derived conclusions from studies that applied PTAS.  \nThis work aims to reconcile these conflicting results by introducing a critical new ingredient to the framework : inter-\nstimulus intervals (ISIs). In our previous work, we observed that PTAS induces a K -complex-like (KC-like) response, \nregardless of the targeted phase, particularly when stimuli were spaced apart (Leach et al., 2024). Since KC induction \nhabituates with repeated stimulus presentation , potentially due to inherent refractory periods (Colrain, 2005), a \nstimulation protocol which presents stimuli irregularly and infrequently would facilitate KC induction by periodically \ninterrupting habituation processes or resetting refractory periods. Indeed, the only study which reported a local \nmodulation of slow-wave activity (SWA; spectral power between 1 and 4 Hz) presented stimuli continuously throughout \nsleep (Fattinger et al., 2017), facilitating stimulus habituation and suppressing KC induction. In contrast, studies which \nreported global SWA increases restricted stimulus presentation to periodically occurring ON windows with durations \nof a few seconds (Huwiler et al., 2022; Krugliakova et al., 2022; Leach et al., 2024), allowing the regular interruption of \nstimulus habituation and facilitating KC induction. In these studies, the largest increase in SWA was observed with the \nfirst stimulus within an ON window, supporting the idea that habituation was lost during intermittent stimulation \nbreaks. Consequently, we hypothesized that a local, phase-specific response could only occur when stimuli bypass \nKC induction, for instance, when being presented regularly and in rapid succession. To test this, we reanalyzed two \npreviously published datasets (see Methods) in which participants underwent at least two separate laboratory nights: \none with up- or down-PTAS, and another without any stimulation (SHAM). We indeed found that PTAS induces local, \nphase-dependent modulations of slow waves only when stimuli were presented in rapid succession within trains. \nResults \nTo test whether PTAS responses depend on the timing between stimuli, we reanalyzed high-density EEG (hd-EEG) data \nrecorded from 128 channels in ten participants during a night with and without up-PTAS, and from fourteen participants \nduring a night with and without down-PTAS (see Methods). In these studies, stimuli (50 ms pink noise) were presented \nduring ON windows (6 s and 16 s for up- and down-PTAS, respectively), allowing stimulation, which alternated with OFF \nwindows (6 s and 8s), withholding stimulatio n. Phase-targeting was achieved using EEG from a detection electrode \nnear FP2 (up -PTAS) or C3 (down -PTAS). We previously observed that spectral responses following PTAS closely \nresembled those of auditory evoked KCs when stimuli followed a long stimulation -free period (Leach et al., 2024). \nAnalogously, we here compare the event-related spectral perturbation (ERSP) following stimuli which were preceded \nby either long (≥ 5 seconds) or short (≤ 1 second) stimulation-free periods after both up- and down-PTAS. \nK-complex response \nReplicating previous findings (Leach et al., 2024) , both up- and down-PTAS resulted in a stereotypical KC-response \nprofile when considering isolated stimuli with long prior stimulation-free periods (Fig. 1A & Fig. 2A). This response was \ncharacterized by a global enhancement of SWA in an early, pre-defined time window (1 – 4 Hz; 300 – 700 ms) following \nboth up-PTAS (max. g = 1.17; mean g = 0.66;  cluster of 100 channels; see Methods) and down-PTAS (max. g = 1.66; \nmean g = 1.10; cluster of 110 channels), compared to SHAM (p <. 05, cluster corrected; Fig. 1A). As anticipated for KC \nresponses, SWA increases were accompanied by a global enhancement in theta activity (4 – 8 Hz; 300 – 700 ms) \nfollowing both up-PTAS (max. g = 1.12; mean g = 0.81; cluster of 103 channels) and down-PTAS (max. g = 1.65; mean g \n= 1.29; cluster of 110 channels), compared to SHAM (p < .05, cluster corrected;  Supplementary Fig. 3), as well as  \nsigma activity (12 – 16 Hz; 0.9 – 1.5 s) following both up-PTAS (max. g = 0.90; mean g = 0.66; cluster of 106 channels) \nand down-PTAS (max. g = 0.80; mean g = 0.59; cluster of 110 channels), compared to SHAM (p < .05, cluster corrected; \nSupplementary Fig. 4A). \nPhase-specific response \nConversely, when stimuli were presented in rapid succession, we observed diverging and localized PTAS eUects which \ndepended on the targeted phase after the fifth stimulus in a train of such stimuli ( Fig. 1B & Fig. 2B). Topographic \nanalyses of SWA responses during a later time window (1 – 4 Hz; 1.2 – 2.6 s; minimizing potential interference from co-\noccurring KC responses) revealed locally enhanced SWA following up-PTAS in a cluster of 19 frontal channels (max. g = \n0.98; mean g = 0.33), and locally reduced SWA following down-PTAS in a cluster of 19 centro-parietal channels (min. g = \n-0.34; mean g = -0.22), compared to SHAM (p <. 05, cluster corrected; Fig. 1B).  \nNotably, following up-PTAS, an increase in SWA was already detectable after the second tone (max. g = 0.75; mean g = \n0.28; cluster of 68 channels) and became progressively more localized with each subsequent stimulus (3rd stimulus: \ncluster of 34 channels; max. g = 0.96; mean g = 0.33; 4th stimulus: cluster of 30 channels; max. g = 0.90; mean g = 0.31). \nIn contrast, with down-PTAS, the phase-dependent response was first evident after the fifth stimulus. Consistent with \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.05.641406doi: bioRxiv preprint \n\n3 \n \nthe reported refractory period of thalamocortical cells underlying spindle generation (Fernandez & Lüthi, 2020), this \nglobal increase in sigma activity was observed specifically for stimuli that followed long stimulation-free periods (all \np > .05, cluster corrected; Supplementary Fig. 4B). \nDiscussion \nThe precision with which auditory stimuli align with the targeted phase of slow waves has traditionally been considered \nthe single most important factor in determining the outcome of PTAS (Navarrete et al., 2020; Ngo et al., 2013). However, \nconflicting results in PTAS studies already suggest that the targeted phase is insuUicient to fully explain its outcomes. \nThis work introduces another factor which appears to be at least equally important for predicting PTAS outcomes: inter-\nstimulus intervals.  \nSpecifically, our findings indicate a dual-response to PTAS, where stimuli can both (1) lead to a global enhancement of \nSWA, irrespective of the targeted phase, likely through the induction of KCs and (2) locally modulate SWA, with up- and \ndown-PTAS either increasing or reducing SWA, respectively. Importantly, the nature of these responses was \ndetermined by the length of the  stimulation-free period prior to a  given stimulus, with longer intervals promoting a \nglobal enhancement of SWA and shorter intervals allowing the local modulation of SWA. \nAs early as the 1930s, researchers observed that sensory stimuli, particularly auditory stimuli (Davis et al., 1939), could \nevoke KCs during sleep (Loomis et al., 1938). The term \"K-complex\" itself likely derives from the \"knock\" stimuli used \nin those early studies (Halász, 2016). It is therefore only logical that auditory stimuli, even when timed to specific slow-\nwave phases, can still evoke KCs. The observation of either a global increase in SWA following PTAS (Huwiler et al., \n2022; Krugliakova et al., 2022), or a stereotypical KC spectral response profile, encompassing increases in SWA, theta, \nand sigma activity (Krugliakova et al., 2020, 2022; Leach et al., 2024; Ong et al., 2016, 2018), would therefore strongly \nimplicate KCs as at least a partial contributor to the observed modulation of SWA in these studies. \nConversely, rapid stimulus presentation has been shown to diminish the likelihood of eliciting subsequent KCs (Davis \net al., 1939; Roth et al., 1956). Consistent with this, here, both up- and down-PTAS were capable of modulating SWA \nlocally when stimuli were presented in rapid succession within trains, thereby essentially bypassing KCs, with up-PTAS \nincreasing and down-PTAS reducing SWA, respectively. Thus, these findings serve as first evidence suggesting that \na phase-specific response, spatially confined to areas around and posterior to the detection electrode, likely due to \nslow-wave traveling (Massimini et al., 2004; Sousouri et al., 2022), unfolds once stimuli are presented consecutively \nwithin trains. Our findings indicate weaker phase-specific SWA modulations compared to KC responses, as reflected \nin the smaller eUect sizes for both up-PTAS (max. g = 1. 17 vs. 0.98) and down-PTAS (max. g = 1. 66 vs. -0.34).  \nCrucially, this insight reconciles conflicting results from prior studies, where down-PTAS was reported to either reduce \n(Fattinger et al., 2017; Moreira et al., 2021; Ngo et al., 2013) or enhance SWA (Huwiler et al., 2022; Leach et al., 2024). \nThese discrepancies may be attributed to diUerences in the applied stimulation protocols, with some favoring and \nsome bypassing KCs. Viewing KCs as a probabilistic phenomenon, specific stimulation parameters related to \nirregularity and novelty detection, such as long ISIs, fast rise-and-fall times, and high stimulus intensities, all together \nmodulate its probability of occurrence (Bastien & Campbell, 1992). Also, the phase within a sleep cycle (Halász, 2005) \nand other brain-state fluctuations (Dimitriades et al., 2024) may play a role. Studies reporting global SWA enhancement \nemployed long stimulation breaks (OFF windows) of 8 to 10 seconds, significantly increasing the likelihood of evoking \nsubsequent KCs. Such evoked KCs can also explain why, in these studies, the largest SWA increase was observed \nimmediately after stimulation breaks, at the onset of ON windows (Huwiler et al., 2022; Krugliakova et al., 2022; Leach \net al., 2024). In contrast, studies which observed a reduction in SWA with down-PTAS employed continuous stimulation \nprotocols (Fattinger et al., 2017; Moreira et al., 2021)  or implemented much shorter and regular stimulation breaks \n(Ngo et al., 2013). Such short ISIs may have led to sustained stimulus habituation, likely ideal for preventing evoked KC \nand allowing phase-specific eUects to emerge.  \nThe probabilistic nature of evoked KC may also explain the occasional observation of KCs following the second or third \nstimulus within a train (Davis et al., 1939; Roth et al., 1956) , oUering an explanation as to why the reduction of SWA \nfollowing down-PTAS only started with the 5th stimulus within the train. Given the shared directionality of the KC and \nphase-specific response for up -PTAS, pinpointing the specific stimulus within a train where the phase -specific \noutweighs the KC response is rather challenging (see Fig. 1B). It appears, however, that with each successive stimulus \nwithin a train, the probability of KC occurrence decreases, while phase-specific eUects increasingly dominate.     \nGiven the diverging electrophysiological response patterns following  isolated stimuli and those presented \nconsecutively within trains, it seems likely that the underlying neuronal mechanisms are also fundamentally distinct, \nakin to how diUerent types of slow waves are thought to arise from diUerent sources (Bernardi et al., 2018; Siclari et al., \n2014). With this in mind, it seems possible that the KC and phase-specific response impact distinct sleep functions, \nwith phase-specific responses particularly influencing functions associated with the targeted area (Fattinger et al., \n2017; Sousouri et al., 2022). By disentangling PTAS responses, researchers may be able to establish causal links with \nbehavioral outcomes and specific slow -wave subtypes, potentially represented by the distinct PTAS responses. \nBeyond a better understanding of basic sleep mechanisms, these insights could be essential for translating PTAS into \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.05.641406doi: bioRxiv preprint \n\n4 \n \nclinical applications. Depending on the specific neuronal networks aUected in a given  clinical population, targeting \none system over the other may lead to more eUective outcomes—a distinction that could be particularly relevant in \nhome or long-term settings (e.g., Kasties et al., 2024). \nConclusion \nAuditory stimuli are highly eUective at evoking K-complexes (KCs). This property persists when stimuli are presented \nphase-locked to ongoing slow waves. Here, it was the timing between stimuli which determined whether a phase-\nspecific or a KC-mediated response would unfold. These two distinct electrophysiological outcomes of PTAS, likely \nreflecting the engagement of diUerent neural circuits associated with specific sleep-related functions, underscore the \nnecessity of a nuanced mechanistic understanding of sleep neuromodulation, particularly PTAS. Such understanding \nis essential for establishing robust causal links between neural oscillations and behavior, advancing both fundamental \nneuroscience and clinical applications.  \nLimitations \nThis study encompasses certain limitations that warrant acknowledgment. While the used datasets allowed the \nassessment of phase-specific eUects following both up- and down-PTAS, the respective studies were originally not \ndesigned to investigate the impact of diUerent ISIs. For instance, the employed ON|OFF window design, with a window \nduration of 6 s for up-PTAS, artificially interrupted continuous stimulus trains, resulting in borderline trial numbers for \nlonger train lengths. This limitation prevented us from analyzing the responses to specific stimuli within a train, as doing \nso would have further reduced trial numbers. Additionally, stimuli were grouped post-hoc based on their stimulation-\nfree periods prior to that stimulus. Consequently, the presentation of stimuli with shorter or longer stimulation -free \nperiods was not experimentally controlled, potentially confounding this variable with other factors, such as variations \nin sleep depth. This is also why the interpretation of chosen ISI cutoUs (1 and 5 s) should be approached with caution. \nThese cutoUs represent a trade -oU between ensuring suUicient separation between stimuli to observe distinct \nresponses and maintaining an adequate number of stimuli for robust statistical analysis. Lastly, the two studies \nrecruited a rather small number of diUerent individuals and diUered in certain stimulation protocol settings, including \ndiUerent ON|OFF window durations, diUerent detection electrode location, and diUerent stimulation opportunity \nperiods (see Methods). These diUerences most notably limited our ability to directly contrast responses between up- \nand down-PTAS. Although initial evidence suggests that the observed locality of the phase-specific response indeed \ndepends on the location of the detection electrode (Fattinger et al., 2017) , a systematic investigation of this \nrelationship is needed to definitively resolve this question . Thus, while this study presents the very first compelling \nargument that ISIs are indeed a key factor for predicting PTAS responses, these findings should be validated in a study \nthat is specifically designed to test this hypothesis. \nAcknowledgements \nWe are deeply grateful to the members of Prof. Reto Huber's lab and the SleepLoop consortium for their invaluable \nconstructive feedback and stimulating discussions.  Their collaborative spirit significantly contributed to the \ndevelopment of this work. This research was supported by the Swiss National Science Foundation (SNF) under grant \nnumber 320030_179443 and is part of the HMZ Flagship grant  SleepLoop under the umbrella of  Hochschulmedizin \nZürich, Switzerland. \nMethods \nDatasets \nFor the presented reanalysis, hd-EEG recordings (128 channels) from previously conducted studies were reanalyzed \n(Krugliakova et al., 2022; Leach et al., 2024; Sousouri et al., 2022) . In the first dataset, N=18 participants underwent \nthree nights: a night with up-PTAS, down-PTAS, and a night without stimulation as described in Sousouri et al. (2022). \nDuring the first 2.5 h of NREM sleep, 50 ms pink noise stimuli were presented (ISI ≥ 0.5 s) in an ON|OFF window design. \nUsing that design, ON windows (6 s), allowing stimulation, took turns with OFF windows (6 s), withholding stimulation. \nThe detection electrode, used for real-time PTAS during NREM sleep, was placed next to channel Fp2. This dataset was \nused previously (Krugliakova et al., 2022; Leach et al., 2024; Sousouri et al., 2022). For this reanalysis, we included hd-\nEEG data with and without up-PTAS from N=10 participants as reported in Sousouri et al. (2022) (mean±sd: 23.70±1.70 \nyears old; all right -handed; 6 females, 4 males).  Nights with down-PTAS were not considered due to an insuUicient \nnumber of trials containing long stimulation trains.  Instead, down-PTAS data were obtained from a second dataset , \ncomprising N=14 participants (mean±sd = 23.25±2.53 years old; all right-handed; 10 females, 4 males) who underwent \ntwo nights: one night with and another without down-PTAS (Leach et al., 2024). The stimulation protocol was identical \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.05.641406doi: bioRxiv preprint \n\n5 \n \napart from longer ON (16 s) and OFF windows (8 s), as well as a longer stimulation opportunity (whole night), resulting \nin more trials with extended stimulus trains. The detection electrode was placed next to channel C3. \nSoftware \nEEG analyses and statistics were performed in Matlab (R20 22a & R2024b; The Math -Works, Inc., Natick, \nMassachusetts) implementing functions from the  EEGLAB toolbox (v2023.1; Delorme & Makeig, 2004) . Circular \noutcome measures (e.g., mean phase) were computed with functions from the toolbox for circular statistics (Berens, \n2009). \nPreprocessing \nHd-EEG data was sleep -scored, artefact-corrected, and preprocessed as previously reported (Leach et al., 2024; \nSousouri et al., 2022). To ensure consistent preprocessing across both datasets, filter settings were adapted to match \nthose reported in Leach et al., 2024.  \nReferencing \nFor time-frequency analyses, hd-EEG data was referenced to the mean of all channels located above the ear (up to 109 \nchannels for up -PTAS; 110 channels for down -PTAS). Only those channels located above the ear were included in \nfurther analyses to minimize artifact contamination. For the phase estimation  of auditory stimuli, hd-EEG data was \nreferenced to linked mastoids. \nTime-frequency analysis \nTime-frequency analyses for both up- and down-PTAS were performed as reported in Leach et al., 2024, separate for \nstimuli with short and long  ISIs. To eliminate participant and frequency biases  irrespective of the duration of the \nanalyzed time window, spectral power values were normalized by dividing each value by the average spectral power \nvalue of both nights (sample- and frequency-wise). An automated outlier detection routine removed trials with clearly \nbad data. Specifically, trials where the maximum spectral power value across channels, samples, and frequencies, or \nthe mean EEG signal amplitude across channels and samples exceeded six standard deviations from their respective \nmean across trials were excluded. \nInter-stimulus interval (ISI) \nStimuli with long ISIs followed the previous stimulus with a distance of at least 5 seconds. Time-frequency responses \nof stimuli with long ISIs are depicted in Fig. 1A and Fig. 2A. Those with short ISIs followed the previous stimulus at a \ndistance of 1 second or less. Whenever subsequent stimuli fulfilled this condition, they were considered to belong to \nthe same train. For instance, a train of five stimuli consisted of five stimuli with an ISI of no longer than 1 second. The \nstimulation-free period prior to the first stimulus was not of interest. Fig. 1B and Fig. 2B depict the average response \nto a stimulus and all subsequent stimuli within the train rather than the response to a stimulus at a particular train \nposition. With the assumption that a phase -specific response would persist with subsequent stimuli, such an \napproach increases trial numbers. The number of trains containing the respective number of stimuli is summarized in \nSupplementary Fig. 2A. \nPhase estimation of auditory stimuli  \nPhase estimations for stimuli of both up- and down-PTAS were computed as reported in Leach et al., 2024.  Phase \ndistributions are reported in Supplementary Fig. 1. \nTopographies \nAbsolute spectral power values were averaged across reported time- and frequency ranges, specific to the respective \nanalysis. \nStatistics \nFor topographical comparisons between conditions (STIM−SHAM), paired Student’s t-tests (α = .05, two-tailed) were \nperformed (channel-wise). To account for multiple comparisons, non -parametric cluster-based statistical mapping \nwas applied. EUect sizes are reported by reporting the mean and maximum Hedge’s g value of significant channels.  \nNon-parametric cluster-based statistical mapping \nIn short, the condition label (STIM or SHAM) was pseudorandomly assigned to participants, resulting in a random \nswitch between conditions. The number of permutations is restricted by the number of participants (2 N − 1). Hence, \nthe data was permuted 5000 times for down-PTAS and 1000 times for up-PTAS. Each permutation resulted in mutually \nexclusive condition labels. Paired Student’s t-tests were performed in each permutation, and the maximum cluster \nsize of significant neighboring electrodes was computed separately for positive and negative t-values. This resulted in \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.05.641406doi: bioRxiv preprint \n\n6 \n \ntwo distributions of cluster sizes, one for positive and one for negative t-values, with as many values as permutations \nperformed. For topographical comparisons, the 97.5th percentile in each distribution was defined as the critical \ncluster size threshold. When the original data showed a cluster of significant electrodes equal to  or larger than the \ncritical cluster size threshold, this cluster of electrodes was considered significant. Multiple clusters could coexist and \nwere reported as such when observed. \nBibliography \nBastien, C., & Campbell, K. (1992). The evoked K -complex: \nAll-or-none phenomenon? 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The form, voltage \ndistribution and physiological significance of the K -complex. \nElectroencephalography and Clinical Neurophysiology , 8(3), \n385–402. \nSalfi, F ., D’Atri, A., Arnone, B., Corigliano, D., Amicucci, G., \nViselli, L., Naccarato, F ., Festucci, F ., Tempesta, D., & Ferrara, \nM. (2025). Promoting vocabulary learning during sleep at \nhome using closed -loop targeted memory reactivation. \nJournal of Sleep Research, e70000. \nSiclari, F ., Bernardi, G., Riedner, B. A., LaRocque, J. J., Benca, \nR. M., & Tononi, G. (2014). Two distinct synchronization \nprocesses in the transition to sleep: A high -density \nelectroencephalographic study. Sleep, 37(10), 1621–1637. \nSousouri, G., Krugliakova, E., Skorucak, J., Leach, S., Snipes, \nS., Ferster, M. L., Da Poian, G., Karlen, W., & Huber, R. (2022). \nNeuromodulation by means of phase -locked auditory \nstimulation adects key marker of excitability and connectivity \nduring sleep. Sleep, 45(1), zsab204. \nSteriade, M., Nunez, A., & Amzica, F . (1993). A novel slow (< 1 \nHz) oscillation of neocortical neurons in vivo: Depolarizing \nand hyperpolarizing components. Journal of Neuroscience , \n13(8), 3252–3265. \nVyazovskiy, V. V., Olcese, U., Lazimy, Y . M., Faraguna, U., \nEsser, S. K., Williams, J. C., Cirelli, C., & Tononi, G. (2009). \nCortical firing and sleep homeostasis. Neuron, 63(6), 865 –\n878. \n \n  \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.05.641406doi: bioRxiv preprint \n\n8 \n \nFigures \n \n \nFig. 1: Slow-wave activity response to isolated stimuli and those presented consecutively within trains. (A) Topography of absolute slow-wave activity (SWA; 1 – 4 Hz; 300 – \n700 ms following stimulus onset) in response to isolated stimuli, that is, stimuli following a stimulation -free period of ≥ 5 s. Responses are displayed either for stimuli targeting \nthe up-phase (top) or down-phase (bottom) of slow waves. (B) Topography of absolute SWA (1.2 – 2.6 s) in response to stimuli within a train of consecutive stimuli, that is, stimuli \nwith an inter-stimulus interval (ISI) ≤ 1 s. The average response to a stimulus and all subsequent stimuli within the train rather than the response to a stimulus at a particular train \nposition is shown (indicated by the ellipsis, the three dots; see Supplementary Fig. 2A for trial numbers). Symbols: The black cross indicates the detection electrode. White dots \nrepresent electrodes with significant diTerences between conditions (STIM vs. SHAM, paired t-test, cluster corrected). Take-away: The local, phase-specific response becomes \nmore local over time and occurs faster when targeting the up - compared to the down -phase of slow waves, potentially as both the K -complex and phase -specific response \nfollowing up-PTAS share the same direction of eTect.  \n \n \nFig. 2: Time-frequency response to isolated stimuli and those within later train positions.  Normalized (see methods) event -related spectral perturbation (ERSP) following \nstimuli targeting either the up - (top) or down -phase (bottom) of slow waves. (A) The ERSP of the average of all channels following isolated stimuli, that is, stimuli following a \nstimulation-free period of ≥ 5 s, is shown. K-Complex (KC) characteristics, encompassing increases in SWA, theta, and sigma activity, are clearly visible after both up- and down-\nphase stimulation. The topography of the global slow-wave activity (SWA) response (300 – 700 ms; 1 – 4 Hz, indicated by the white dashed box) is depicted in Fig. 1A. (B) ERSP in \nresponse to stimuli following a train of stimuli with an inter-stimulus interval (ISI) ≤ 1 s. The response to the 5th and all subsequent stimuli within a given train was averaged. The \ntopography of the localized SWA response (1.2 – 2.6 s; 1 – 4 Hz, indicated by the white dashed box) is depicted in Fig. 1B. This later time period was chosen to minimize potential \ninterference from KC responses as observed in Fig. 1A. To account for the locality of this response, the ERSP depicted here represents an average across channels showing a \nsignificant diTerence in SWA between conditions in Fig. 1B. Takeaway: Isolated stimuli elicit a global, stereotypical KC response, regardless of the targeted slow-wave phase. In \ncontrast, following a train of stimuli presented in rapid succession, a local, phase-specific response occurs: targeting the up-phase of slow waves locally enhances, while targeting \ndown-phase of slow waves locally decreases SWA. \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.05.641406doi: bioRxiv preprint \n\n9 \n \nSupplementary figures \n \nSupplementary Fig. 1: Phase precision of delivered stimuli . (A) Proportion of stimuli falling within specific phase bins (30° increments). The x -axis marks the boundaries of \neach phase bin. Proportions were calculated individually for each participant, and scatter-box plots show the distribution across participants. The color of the box plots reflects \nthe targeted phase (red: up -phase targeting; blue: down -phase targeting), while the dot colors represent the stimulation condition (red and blue: STIM; grey: SHAM). (B) \nTopographic phase precision, expressed as the circular standard deviation of phase values at the times of stimulation. For each electr ode, the circular standard deviation was \ncomputed per participant, then averaged across participants. Topographic maps of phase precision are shown separately for up- and down-phase targeting, as well as for STIM \nand SHAM nights. The black cross marks the detection electrode, where phase precision is highest. \n \n \nSupplementary Fig. 2: Number of trials. (A) Scatter-box plots illustrate the number of isolated stimuli per night, defined as stimuli following a stimulation-free period of ≥ 5 s, \nalongside the number of stimulus trains of varying lengths (2–6 consecutive stimuli) with an inter-stimulus interval (ISI) of ≤ 1 s. The availability of trials diminished with \nincreasing train length. Number of trials is presented separately for nights with up-phase-targeted (red) and down-phase-targeted (blue) auditory stimulation (PTAS). Notably, \nthe number of trials was generally higher in nights with down- compared to up-PTAS, attributed to longer ON windows (16 s vs. 6 s), higher ON/OFF window ratios (16/8 vs. 6/6), \nand longer overall stimulation periods (entire night vs. first 2.5 hours). Colored dots indicate the number of trials per stimulation night, while grey dots represent SHAM nights. \nThe inset plot in the top right provides a zoomed-in view of the number of trains for the longest stimulus trains. The grey shaded area indicates participants with less than 5 trials \nper night. (B) Bar plot displaying the number of participants with ≥ 5 trials per night for trains with varying numbers of stimuli. The longest train length which was analyzed was 5 \nconsecutive stimuli. \n \n \nSupplementary Fig. 3: Theta activity following isolated stimuli. Topography of absolute theta activity (4 – 8 Hz; 300 – 700 ms following stimulus onset) in response to isolated \nstimuli, that is, stimuli following a stimulation -free period of ≥ 5 s. Responses are displayed either for stimuli targeting the up -phase (left) or down-phase (right) of slow waves. \nSymbols: The black cross indicates the detection electrode. White dots represent electrodes with significant diTerences between conditions (STIM vs. SHAM, paired t-test, cluster \ncorrected).  \n \n \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.05.641406doi: bioRxiv preprint \n\n10 \n \n \nSupplementary Fig. 4: Sigma activity response over time. (A) Topography of absolute sigma activity (12 – 16 Hz; 0.9 – 1.5 s following stimulus onset) in response to isolated \nstimuli, that is, stimuli following a stimulation-free period of ≥ 5 s. Responses are displayed either for stimuli targeting the up-phase (top) or down-phase (bottom) of slow \nwaves. (B) Topography of absolute sigma activity (0.9 – 1.5 s) in response to stimuli within a train of consecutive stimuli, that is, stimuli with an inter-stimulus interval (ISI) ≤ 1 s. \nThe average response to a stimulus and all subsequent stimuli within the train rather than the response to a stimulus at a particular train position is shown (indicated by the \nellipsis, the three dots). Note that the sigma response is only present following isolated stimuli. Symbols: The black cross indicates the detection electrode. White dots \nrepresent electrodes with significant diTerences between conditions (STIM vs. SHAM, paired t-test, cluster corrected). \n.CC-BY 4.0 International licensemade available under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is \nThe copyright holder for this preprintthis version posted March 10, 2025. ; https://doi.org/10.1101/2025.03.05.641406doi: bioRxiv preprint","source_license":"CC-BY-4.0","license_restricted":false}