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Research Article| Volume 15, ISSUE 5, P1093-1100, September 2022

The phase of sensorimotor mu and beta oscillations has the opposite effect on corticospinal excitability

Open AccessPublished:August 11, 2022DOI:https://doi.org/10.1016/j.brs.2022.08.005

      Highlights

      • Real-time EEG-TMS-induced MEPs show an opposing relationship for ongoing sensorimotor beta and mu oscillations.
      • MEP amplitudes are maximal at the peak-to-falling phase of the sensorimotor beta rhythm.
      • MEP amplitudes are maximal at the trough-to-rising phase of the sensorimotor mu rhythm.
      • Independent of phase, pre-TMS mu power, but not beta power, is positively correlated with MEP size.

      Abstract

      Background

      Neural oscillations in the primary motor cortex (M1) shape corticospinal excitability. Power and phase of ongoing mu (8–13 Hz) and beta (14–30 Hz) activity may mediate motor cortical output. However, the functional dynamics of both mu and beta phase and power relationships and their interaction, are largely unknown.

      Objective

      Here, we employ recently developed real-time targeting of the mu and beta rhythm, to apply phase-specific brain stimulation and probe motor corticospinal excitability non-invasively. For this, we used instantaneous read-out and analysis of ongoing oscillations, targeting four different phases (0°, 90°, 180°, and 270°) of mu and beta rhythms with suprathreshold single-pulse transcranial magnetic stimulation (TMS) to M1. Ensuing motor evoked potentials (MEPs) in the right first dorsal interossei muscle were recorded. Twenty healthy adults took part in this double-blind randomized crossover study.

      Results

      Mixed model regression analyses showed significant phase-dependent modulation of corticospinal output by both mu and beta rhythm. Strikingly, these modulations exhibit a double dissociation. MEPs are larger at the mu trough and rising phase and smaller at the peak and falling phase. For the beta rhythm we found the opposite behavior. Also, mu power, but not beta power, was positively correlated with corticospinal output. Power and phase effects did not interact for either rhythm, suggesting independence between these aspects of oscillations.

      Conclusion

      Our results provide insights into real-time motor cortical oscillation dynamics, which offers the opportunity to improve the effectiveness of TMS by specifically targeting different frequency bands.

      Keywords

      1. Introduction

      Neocortical activity in the motor cortex is characterized by neural oscillations, foremost in the mu (8–13 Hz) and beta (14–30 Hz) rhythms. On the one hand, changes in their power correlate with motor functions such as preparation and execution of voluntary movement [
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      Oscillatory interactions between sensorimotor cortex and the periphery.
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      Synchronization in monkey motor cortex during a precision grip task. II. effect of oscillatory activity on corticospinal output.
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      Human motor cortical activity is selectively phase-entrained on underlying rhythms.
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      Synchrony drives motor cortex beta bursting, waveform dynamics, and phase-amplitude coupling in Parkinson's disease.
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      ].
      Although the coupling between cortical oscillation phase and spiking activity is well-established. However, the relationship between functional cortical excitability and phase of mu and particularly beta oscillations in the motor cortex remains to be fully understood. To provide causal evidence for a relation between oscillatory phase and cortical excitability, one needs to synchronize the electrocortical read-outs and causal probing of excitability with millisecond precision. Recent advances in real-time tracking of cortical oscillations and non-invasive modulation of motor cortex activity in healthy human participants have provided new insights [
      • Bergmann T.O.
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      Pulsed facilitation of corticospinal excitability by the sensorimotor μ-alpha rhythm.
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      • Tomasevic L.
      • Siebner H.R.
      No trace of phase: corticomotor excitability is not tuned by phase of pericentral mu-rhythm.
      ,
      • Sasaki K.
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      • Odagaki M.
      A transcranial magnetic stimulation trigger system for suppressing motor-evoked potential fluctuation using electroencephalogram coherence analysis: algorithm development and validation study.
      ,
      • Schaworonkow N.
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      • Belardinelli P.
      • Ziemann U.
      • Bergmann T.O.
      • Zrenner C.
      Μ-rhythm extracted with personalized EEG filters correlates with corticospinal excitability in real-time phase-triggered EEG-TMS.
      ,
      • Schaworonkow N.
      • Triesch J.
      • Ziemann U.
      • Zrenner C.
      EEG-triggered TMS reveals stronger brain state-dependent modulation of motor evoked potentials at weaker stimulation intensities.
      ,
      • Karabanov A.N.
      • Madsen K.H.
      • Krohne L.G.
      • Siebner H.R.
      Does pericentral mu-rhythm “power” corticomotor excitability? – a matter of EEG perspective.
      ,
      • Shirinpour S.
      • Alekseichuk I.
      • Mantell K.
      • Opitz A.
      Experimental evaluation of methods for real-time EEG phase-specific transcranial magnetic stimulation.
      ,
      • Zrenner C.
      • Belardinelli P.
      • Müller-Dahlhaus F.
      • Ziemann U.
      Closed-loop neuroscience and non-invasive brain stimulation: a tale of two loops.
      ,
      • Zrenner C.
      • Desideri D.
      • Belardinelli P.
      • Ziemann U.
      Real-time EEG-defined excitability states determine efficacy of TMS-induced plasticity in human motor cortex.
      ,
      • Zrenner B.
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      • Gordon P.C.
      • Belardinelli P.
      • McDermott E.J.
      • Soekadar S.R.
      • et al.
      Brain oscillation-synchronized stimulation of the left dorsolateral prefrontal cortex in depression using real-time EEG-triggered TMS.
      ,
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      • Norato G.
      • Zrenner C.
      • Ziemann U.
      • et al.
      Phase-dependent offline enhancement of human motor memory.
      ]. Such real-time systems, combining electroencephalography (EEG) and transcranial magnetic stimulation (TMS), have provided evidence for a modulation of corticospinal excitability by motor cortical oscillatory phase and power [
      • Bergmann T.O.
      • Lieb A.
      • Zrenner C.
      • Ziemann U.
      Pulsed facilitation of corticospinal excitability by the sensorimotor μ-alpha rhythm.
      ,
      • Madsen K.H.
      • Karabanov A.N.
      • Krohne L.G.
      • Safeldt M.G.
      • Tomasevic L.
      • Siebner H.R.
      No trace of phase: corticomotor excitability is not tuned by phase of pericentral mu-rhythm.
      ,
      • Karabanov A.N.
      • Madsen K.H.
      • Krohne L.G.
      • Siebner H.R.
      Does pericentral mu-rhythm “power” corticomotor excitability? – a matter of EEG perspective.
      ,
      • Zrenner C.
      • Desideri D.
      • Belardinelli P.
      • Ziemann U.
      Real-time EEG-defined excitability states determine efficacy of TMS-induced plasticity in human motor cortex.
      ].
      Reports in non-human primates and patients with neurosurgical implants suggest that motor functioning is phase-dependent on oscillations in the motor cortical mu rhythm [
      • Yanagisawa T.
      • Yamashita O.
      • Hirata M.
      • Kishima H.
      • Saitoh Y.
      • Goto T.
      • et al.
      Regulation of motor representation by phase–amplitude coupling in the sensorimotor cortex.
      ,
      • Haegens S.
      • Nácher V.
      • Luna R.
      • Romo R.
      • Jensen O.
      α-Oscillations in the monkey sensorimotor network influence discrimination performance by rhythmical inhibition of neuronal spiking.
      ] Based on this, first pursuits on real-time detection of motor oscillation phase relationships in healthy volunteers have focused on the mu rhythm [
      • Bergmann T.O.
      • Lieb A.
      • Zrenner C.
      • Ziemann U.
      Pulsed facilitation of corticospinal excitability by the sensorimotor μ-alpha rhythm.
      ,
      • Madsen K.H.
      • Karabanov A.N.
      • Krohne L.G.
      • Safeldt M.G.
      • Tomasevic L.
      • Siebner H.R.
      No trace of phase: corticomotor excitability is not tuned by phase of pericentral mu-rhythm.
      ,
      • Schaworonkow N.
      • Caldana Gordon P.
      • Belardinelli P.
      • Ziemann U.
      • Bergmann T.O.
      • Zrenner C.
      Μ-rhythm extracted with personalized EEG filters correlates with corticospinal excitability in real-time phase-triggered EEG-TMS.
      ,
      • Schaworonkow N.
      • Triesch J.
      • Ziemann U.
      • Zrenner C.
      EEG-triggered TMS reveals stronger brain state-dependent modulation of motor evoked potentials at weaker stimulation intensities.
      ,
      • Zrenner C.
      • Desideri D.
      • Belardinelli P.
      • Ziemann U.
      Real-time EEG-defined excitability states determine efficacy of TMS-induced plasticity in human motor cortex.
      ], Various studies suggest that motor evoked potential (MEP) amplitude is larger at the trough of the mu rhythm and smaller at the peak [
      • Bergmann T.O.
      • Lieb A.
      • Zrenner C.
      • Ziemann U.
      Pulsed facilitation of corticospinal excitability by the sensorimotor μ-alpha rhythm.
      ,
      • Schaworonkow N.
      • Caldana Gordon P.
      • Belardinelli P.
      • Ziemann U.
      • Bergmann T.O.
      • Zrenner C.
      Μ-rhythm extracted with personalized EEG filters correlates with corticospinal excitability in real-time phase-triggered EEG-TMS.
      ,
      • Schaworonkow N.
      • Triesch J.
      • Ziemann U.
      • Zrenner C.
      EEG-triggered TMS reveals stronger brain state-dependent modulation of motor evoked potentials at weaker stimulation intensities.
      ,
      • Zrenner C.
      • Desideri D.
      • Belardinelli P.
      • Ziemann U.
      Real-time EEG-defined excitability states determine efficacy of TMS-induced plasticity in human motor cortex.
      ,
      • Desideri D.
      • Zrenner C.
      • Ziemann U.
      • Belardinelli P.
      Phase of sensorimotor μ-oscillation modulates cortical responses to transcranial magnetic stimulation of the human motor cortex.
      ]. However, others have provided evidence that ongoing mu phase does not significantly predict corticospinal excitation [
      • Madsen K.H.
      • Karabanov A.N.
      • Krohne L.G.
      • Safeldt M.G.
      • Tomasevic L.
      • Siebner H.R.
      No trace of phase: corticomotor excitability is not tuned by phase of pericentral mu-rhythm.
      ,
      • Karabanov A.N.
      • Madsen K.H.
      • Krohne L.G.
      • Siebner H.R.
      Does pericentral mu-rhythm “power” corticomotor excitability? – a matter of EEG perspective.
      ]. Rather, pre-stimulation mu power is suggested to determine MEP amplitude [
      • Bergmann T.O.
      • Lieb A.
      • Zrenner C.
      • Ziemann U.
      Pulsed facilitation of corticospinal excitability by the sensorimotor μ-alpha rhythm.
      ,
      • Madsen K.H.
      • Karabanov A.N.
      • Krohne L.G.
      • Safeldt M.G.
      • Tomasevic L.
      • Siebner H.R.
      No trace of phase: corticomotor excitability is not tuned by phase of pericentral mu-rhythm.
      ,
      • Karabanov A.N.
      • Madsen K.H.
      • Krohne L.G.
      • Siebner H.R.
      Does pericentral mu-rhythm “power” corticomotor excitability? – a matter of EEG perspective.
      ,
      • Thies M.
      • Zrenner C.
      • Ziemann U.
      • Bergmann T.O.
      Sensorimotor mu-alpha power is positively related to corticospinal excitability.
      ].
      Whereas findings on associations between corticospinal excitability and mu phase are mixed, to the best of our knowledge, no result on real-time non-invasive neuromodulation of the beta rhythm has been published. Despite superficial similarities between mu and beta oscillations they reflect distinct functional sensorimotor networks and may have different anatomical origins [
      • Gaetz W.
      • Cheyne D.
      Localization of sensorimotor cortical rhythms induced by tactile stimulation using spatially filtered MEG.
      ,
      • Jones S.R.
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      • Sikora M.A.
      • Stufflebeam S.M.
      • Hämäläinen M.
      • Moore C.I.
      Quantitative analysis and biophysically realistic neural modeling of the MEG mu rhythm: rhythmogenesis and modulation of sensory-evoked responses.
      ,
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      • et al.
      The impact of GABAergic drugs on TMS-induced brain oscillations in human motor cortex.
      ,
      • Ronnqvist K.
      • McAllister C.
      • Woodhall G.
      • Stanford I.
      • Hall S.
      A multimodal perspective on the composition of cortical oscillations.
      ,
      • Salmelin R.
      • Hari R.
      Spatiotemporal characteristics of sensorimotor neuromagnetic rhythms related to thumb movement.
      ,
      • Salmelin R.
      • Hámáaláinen M.
      • Kajola M.
      • Hari R.
      Functional segregation of movement-related rhythmic activity in the human brain.
      ]. As such, it is likely that phase-modulation of cortical excitability would reflect distinct patterns for mu and beta rhythms. Human and non-human primate studies have suggested a potential coupling of motor responses and motor cortical beta-phase [
      • Miller K.J.
      • Hermes D.
      • Honey C.J.
      • Hebb A.O.
      • Ramsey N.F.
      • Knight R.T.
      • et al.
      Human motor cortical activity is selectively phase-entrained on underlying rhythms.
      ,
      • Murthy V.N.
      • Fetz E.E.
      Synchronization of neurons during local field potential oscillations in sensorimotor cortex of awake monkeys.
      ,
      • Reimer J.
      • Hatsopoulos N.G.
      Periodicity and evoked responses in motor cortex.
      ,
      • Peles O.
      • Werner-Reiss U.
      • Bergman H.
      • Israel Z.
      • Vaadia E.
      Phase-specific microstimulation differentially modulates beta oscillations and affects behavior.
      ]. Electrocorticography (ECoG) has shown phase-dependency of motor network beta-rhythm activity in Parkinson's disease patients [
      • Miller K.J.
      • Hermes D.
      • Honey C.J.
      • Hebb A.O.
      • Ramsey N.F.
      • Knight R.T.
      • et al.
      Human motor cortical activity is selectively phase-entrained on underlying rhythms.
      ,
      • O'Keeffe A.B.
      • Malekmohammadi M.
      • Sparks H.
      • Pouratian N.
      Synchrony drives motor cortex beta bursting, waveform dynamics, and phase-amplitude coupling in Parkinson's disease.
      ,
      • Bouthour W.
      • Mégevand P.
      • Donoghue J.
      • Lüscher C.
      • Birbaumer N.
      • Krack P.
      Biomarkers for closed-loop deep brain stimulation in Parkinson disease and beyond.
      ,
      • de Hemptinne C.
      • Ryapolova-Webb E.S.
      • Air E.L.
      • Garcia P.A.
      • Miller K.J.
      • Ojemann J.G.
      • et al.
      Exaggerated phase–amplitude coupling in the primary motor cortex in Parkinson disease.
      ]. Furthermore, beta phase-dependent stimulation in these patients has been shown to ameliorate motor deficits [
      • Cagnan H.
      • Pedrosa D.
      • Little S.
      • Pogosyan A.
      • Cheeran B.
      • Aziz T.
      • et al.
      Stimulating at the right time: phase-specific deep brain stimulation.
      ,
      • Holt A.B.
      • Kormann E.
      • Gulberti A.
      • Pötter-Nerger M.
      • McNamara C.G.
      • Cagnan H.
      • et al.
      Phase-dependent suppression of beta oscillations in Parkinson's disease patients.
      ,
      • Salimpour Y.
      • Mills K.A.
      • Hwang B.Y.
      • Anderson W.S.
      Phase- targeted stimulation modulates phase-amplitude coupling in the motor cortex of the human brain.
      ].
      The absence of real-time TMS-EEG studies on beta rhythm may stem from the intrinsically lower signal-to-noise ratio, faster pace, and broader frequency band compared to mu oscillations. Additionally, it has been proposed that motor cortical beta oscillations partially reflect a harmonic of the mu rhythm (mu-beta), as it follows an arch-shape, rather than being sinusoidal [
      • Cole S.R.
      • Voytek B.
      Brain oscillations and the importance of waveform shape.
      ,
      • Triggiani A.I.
      • Valenzano A.
      • Del Percio C.
      • Marzano N.
      • Soricelli A.
      • Petito A.
      • et al.
      Resting state Rolandic mu rhythms are related to activity of sympathetic component of autonomic nervous system in healthy humans.
      ]. To reliably target the beta phase in real-time, we optimized a cutting-edge real-time algorithm - Educated Temporal Prediction (ETP) - to perform accurate forward predictions during real-time phase targeting [
      • Shirinpour S.
      • Alekseichuk I.
      • Mantell K.
      • Opitz A.
      Experimental evaluation of methods for real-time EEG phase-specific transcranial magnetic stimulation.
      ]. Due to its robustness to noise and fast processing time, ETP can accurately track and stimulate both mu and beta oscillations. Using our approach, we targeted mu and beta phase in the motor cortex in real-time. Our results show a double dissociation in the relationship between mu and beta phase on corticospinal excitability. That is, phases of mu oscillation that resulted in larger than average motor cortex output generate smaller than average motor cortex output for the same phases of beta, and vice versa. Our data provide the first evidence for distinct phase-dependency of mu- and beta-mediated functional sensorimotor networks that modulate corticospinal excitability. Optimizing TMS-targeting to mu or beta phase can increase robustness of TMS with clear implications for improving the efficacy of TMS in clinical use.

      2. Methods

      2.1 Participants

      We recruited 20 healthy volunteers (11 female, mean ± std age: 22.7 y ± 2.9) in this double-blinded randomized crossover study. Each participant visited for two sessions (targeting mu and beta oscillations). Participants were right-handed, between 18 and 45 years of age, without a history of neurological or psychiatric disorders, head injuries, or metal or electric implants in the head, neck, or chest area. Participants were not pre-selected on the basis of electrophysiological characteristics, such as motor threshold or sensorimotor oscillatory power. The study was approved by the institutional review board of the University of Minnesota and all volunteers gave written informed consent prior to participation.

      2.2 Transcranial magnetic stimulation

      We applied single-pulse biphasic TMS using the Magstim Rapid2 with a figure-of-eight shaped D702 coil (Magstim Inc., Plymouth, MN, USA). The coil was placed over the left motor cortex, corresponding to the hotspot of the right first dorsal interossei (FDI) muscle, and oriented approximately at a 45° angle relative to the midline. Electromyography (EMG) was used to record motor-evoked potentials (MEP) from the FDI using self-adhesive, disposable electrodes. EMG sampling rate was set to 10 kHz using a BIOPAC ERS100C amplifier (BIOPAC systems, Inc., Goleta, CA, USA). Initially, the motor hotspot, i.e. the location and orientation that leads to the largest MEP, was determined. Hotspot coordinates were stored and coil location and orientation in reference to the hotspot were continuously tracked using a Brainsight neuronavigation system (Rogue Research Inc., Montreal, Canada). At the hotspot, the resting motor threshold (RMT) was determined using an adaptive threshold-hunting algorithm [
      • Julkunen P.
      Mobile application for adaptive threshold hunting in transcranial magnetic stimulation.
      ]. The test intensity during the experimental session was set to 120% of RMT.

      2.3 EEG processing for real-time TMS triggering

      Throughout the experiment, EEG was recorded using a 10–20 system, 64 active channel, TMS-compatible EEG system (actiCAP slim EEG cap, actiCHamp amplifier; Brain Products GmbH, Gilching, Germany). EEG data was streamed using Lab Streaming Layer (LSL) software to Matlab 2020b, where we used custom scripts to apply the ETP algorithm (Shirinpour et al., 2020). A sampling rate of 10 kHz with a 24-bits resolution per channel was used, and impedances were kept below 20 kΩ. Data was downsampled to 1 kHz. The electrode of interest for this experiment was C3, located over the hand knob of the left sensorimotor area. To extract mu and beta oscillations unique to the electrode of interest, a Laplacian reference method was used, where the mean of the 8 surrounding electrodes was subtracted from the signal measured at C3 (Fig. 1). This Laplacian C3 signal was used for real-time stimulation, as well as for offline analysis of mu and beta power.
      Fig. 1
      Fig. 1Overview of the educated temporal prediction (ETP) algorithm. Left: The algorithm is first trained using the resting state data from the sensorimotor cortex. Signals at sensorimotor cortex channel C3 are re-referenced using a center-surround Laplacian montage using 8 channels (Fc1, Fc3, Fc5, C1, C5, Cp1, Cp3, and Cp5). Depending on the experimental condition, we stimulated while tracking the phase of mu (8–13 Hz, blue) or beta (14–30 Hz, orange) range. From the resting-state data, the typical cycle length is extracted and used during the real-time stimulation. Right: During real-time application, EEG preprocessing follows the same pipeline as the training step. TMS is triggered at four different phases, namely peak (0°), rising phase (90°), trough (180°), or falling phase (270°). For each phase and oscillatory rhythm, we recorded MEPs from the FDI muscle. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
      The EEG-TMS setup for real-time stimulation used here follows our previously validated implementation [
      • Shirinpour S.
      • Alekseichuk I.
      • Mantell K.
      • Opitz A.
      Experimental evaluation of methods for real-time EEG phase-specific transcranial magnetic stimulation.
      ]. In short, the ETP algorithm uses resting-state data from a training step before the real-time application, which provides an initial estimate of individual temporal dynamics of cortical oscillations. For this, we record resting-state data for 3 min perform a C3 Laplacian spatial filtering, and clean the signal using a zero-phase FIR (Finite Impulse Response) filter in the mu (8–13 Hz) or beta (14–30 Hz) range, as implemented in the Fieldtrip toolbox [
      • Oostenveld R.
      • Fries P.
      • Maris E.
      • Schoffelen J.-M.
      FieldTrip: open source software for advanced analysis of meg, eeg, and invasive electrophysiological data.
      ]. To obtain an undistorted ground truth, phase was based on the whole resting-state data (3 min). During the training, 500 ms sliding windows of the recorded data are used and signal edges after bandpass filtering (brick-wall filter) are removed. In doing so, we avoid ripples that can distort the data during filtering. Then, the algorithm estimates the typical cycle length (peak to peak interval) and validates its accuracy by simulating the accuracy of peak projection using the training data (Fig. 1).
      During real-time estimation, the calculated cycle length is adjusted to inform the forecasting algorithm that predicts upcoming peak, falling phase, trough, or rising phase (throughout this paper phase angles will be expressed in relation to a cosine, e.g. 0° is peak) of oscillation of interest and triggers TMS at the correct time. The EEG preprocessing pipeline during real-time measurements was the same as during the validation phase. Accuracy of ETP in targeting peak, falling, trough and rising phases for mu and beta is shown in Supplementary Fig. 1. Overall processing delay of our system, i.e. the time between sending trigger and actual pulse delivery was accounted for in our algorithm to accurately deliver the TMS at the desired phases [
      • Shirinpour S.
      • Alekseichuk I.
      • Mantell K.
      • Opitz A.
      Experimental evaluation of methods for real-time EEG phase-specific transcranial magnetic stimulation.
      ]. Real-time TMS-EEG was performed in four blocks of 150 pulses. Within each block, phases were applied pseudorandomly. The experimenter and the participant were blinded to the phase order. A jittered interval between 2 and 3 s between consecutive triggers was introduced to minimize the direct effects of previous trials. After this interval our algorithm targets the subsequent phase. Time between pulses was generally below 5 s (Supplementary Fig. 2). Mu and beta oscillations were targeted in two different sessions, which were separated by at least 48 h. The order of sessions was randomized. The sessions were performed at the same time of the day.

      2.4 Data processing and analysis

      2.4.1 MEP analysis

      We calculated peak-to-peak MEP amplitude using a custom Matlab script. MEPs were identified in a window between 20 and 60 ms after the TMS pulse. Noise in the pre-TMS EMG can influence MEP amplitude and thus we excluded MEPs if average absolute EMG activity in a window from −100 to 0 ms before the TMS pulse was above 0.02 mV and larger than absolute average EMG activity +2.5 times standard deviation of the resting state. For this resting state we used a window of −500 to −400 ms before the TMS pulse and at least 1500 ms after the previous pulse, which is most likely captures a state of rest with no effects of the previous pulse [
      • Wischnewski M.
      • Kowalski G.M.
      • Rink F.
      • Belagaje S.R.
      • Haut M.W.
      • Hobbs G.
      • et al.
      Demand on skillfulness modulates interhemispheric inhibition of motor cortices.
      ]. All MEPs were visually inspected. Altogether, 3.3% of trials were removed (3.5% for targeting mu phases and 3.0% for targeting beta phases). For analysis, a participant's individual MEPs were normalized to the overall average of that participant. .

      2.4.2 Offline EEG analysis

      Pre-TMS power was analyzed offline for inclusion in the main analysis. Raw EEG data were re-referenced to the Laplacian C3 montage as was used for online analyses (Fig. 1). Data were epoched in a window between −1000 and 0 ms with respect to TMS trigger and a bandpass filter (2–50 Hz) was applied. Pre-TMS power was calculated by applying a fast Fourier transform with Hanning taper at a resolution of 1 Hz Furthermore, periodic and aperiodic signals were separated by using an Irregular Resampling Auto-Spectral Analysis (IRASA) [
      • Wen H.
      • Liu Z.
      Separating fractal and oscillatory components in the power spectrum of neurophysiological signal.
      ] as implemented in FieldTrip [
      • Oostenveld R.
      • Fries P.
      • Maris E.
      • Schoffelen J.-M.
      FieldTrip: open source software for advanced analysis of meg, eeg, and invasive electrophysiological data.
      ]. Subsequently, we averaged power values between 8 and 13 Hz (mu power, periodic), 14 and 30 Hz (beta power, periodic), and broadband aperiodic signals (2–50 Hz) at the single-trial level.
      To investigate potential differences in mu and beta oscillation topography, sensor-level distributions were examined. Resting-state EEG data were re-referenced to a common average and filtered in the mu (8–13 Hz) and beta (14–30 Hz) bands, respectively. We estimated the pairwise correlations between the electrode of interest C3 to all other electrodes. Topographic plots were used to depict the spatial distribution of the correlations for mu and beta separately, as well as the difference between both conditions.
      Since the mu-rhythm has been shown to follow an arch shape rather than a sinusoidal shape, power in the beta range may partially reflect harmonic activity of the mu rhythm [
      • Cole S.R.
      • Voytek B.
      Brain oscillations and the importance of waveform shape.
      ,
      • Triggiani A.I.
      • Valenzano A.
      • Del Percio C.
      • Marzano N.
      • Soricelli A.
      • Petito A.
      • et al.
      Resting state Rolandic mu rhythms are related to activity of sympathetic component of autonomic nervous system in healthy humans.
      ]. Importantly, a priori our real-time algorithm is agnostic to whether activity in the beta frequency range results from a mu harmonic or from independent beta oscillations. To test for harmonicity, we calculated the ratio between the periods of bandpassed mu and beta oscillations.

      2.4.3 Statistical analysis

      In a trial level analysis, a general linear mixed-effects model (GLMM) was used on trial data with target phase (peak, falling, trough, rising) and target rhythm (mu, beta) as fixed effects variable and participant number as random effects variable. MEP amplitude was the dependent variable. Independently, after averaging MEPs per phase for each participant, Rayleigh's z-test of non-uniformity was performed for phase modulation at mu and beta oscillations.
      As a follow up, to test the effects of pre-TMS power, two additional GLMMs were run on mu and beta conditions separately with pre-TMS power and phase as fixed effects variables. These analyses were followed up by post hoc subject-level simple linear regression models. Additionally, we performed a group-level repeated-measures ANOVA on phase and target rhythm, followed by paired-samples t-tests. Subsequently, Spearman rank correlation between pre-TMS power and MEP amplitude for each subject and session were calculated.
      Finally, a linear correlation was performed on the topographic distribution of mu and beta oscillations. This was followed by one-sample t-tests (test value = 0) on the Fisher z-transformed correlation data to test if the average deviates significantly from zero. For all analyses, significance level was set at α = 0.05.

      3. Results

      Real-time TMS of ongoing cortical oscillations resulted in a double dissociation of phase relationships for mu and beta oscillations (Fig. 2A). Accordingly, GLMM regression showed a significant interaction between target phase and target rhythm on MEP amplitude (F = 16.42, p < 0.001). Distinct phase relation patterns were confirmed by Rayleigh's test for non-uniformity of circular group level data. Normalized MEP amplitudes at phases of the mu rhythm were non-uniformly distributed (Z = 3.02, p = 0.048), with a mean direction of the circular distribution of θ = 225.00° and circular dispersion of κ = 29.27°. Thus, MEP amplitudes were maximal when mu oscillations are at trough and rising phase (Fig. 2B) and lower than average at the opposing phases. Normalized MEP amplitudes at phases of the beta rhythm were also non-uniformly distributed (Z = 3.27, p = 0.037), with circular mean of θ = 29.05° and dispersion of κ = 30.53°. This means that MEP amplitudes were maximal when beta oscillations are at peak or falling phase (Fig. 2B) and again lower than average at the opposing phases.
      Fig. 2
      Fig. 2A) Group average (n = 20) ± standard error of mean of normalized MEPs for targeted phases in the mu and beta frequency. B) Circular representation of the data with smooth interpolation between conditions.
      The results of phase on MEPs were confirmed on the group level. A repeated-measures ANOVA showed a significant phase∗target rhythm interaction (F = 11.24, p < 0.001), with no main effects for phase (F = 0.16, p = 0.923), or target rhythm (F = 0.62, p = 0.440). Post hoc t-tests showed differences between mu and beta peak falling phase (t = 3.96, p < 0.001), trough (t = 4.37, p < 0.001), and rising phase (t = 3.10, p = 0.006). The difference between mu and beta peak showed a non-significant trend (t = 2.09, p = 0.051).
      The results are largely consistent at the individual level. The observed pattern of larger MEP amplitudes at the beta peak compared to the mu peak were observed in 13 out of 20 participants. Larger MEP amplitudes at beta falling compared to mu falling were observed in 14 out of 20 participants. Larger MEP amplitudes at mu trough compared to beta trough were observed in 18 out of 20 participants. Larger MEP amplitudes at mu rising compared to beta rising were observed in 14 out of 20 participants (Fig. 3). Phase responses for both mu and beta per participant are shown in Supplementary Fig. 3.
      Fig. 3
      Fig. 3Individual phase-dependent modulation of MEP amplitude for mu and beta oscillations. Error bars represent standard error of mean.
      In analyses of each target rhythm condition separately, we added pre-TMS power of the targeted rhythm and the aperiodic component. MEP amplitude during targeting of the mu rhythm was affected by both target phase (F = 3.75, p = 0.011) and pre-TMS periodic mu power (F = 15.30, p < 0.001). Crucially, however, no significant phase∗power interaction was observed (F = 1.77, p = 0.151), suggesting that both power and phase affect MEP amplitude independently. At an individual level, correlation between mu power and MEP amplitude ranged between ρ = −0.102 and ρ = 0.250 (median ρ = 0.055). A one-sample t-test on the Fisher z-transformed correlation values confirmed that on average pre-TMS mu power shows a significant positive relationship with MEP amplitude (t = 4.74, p < 0.001). A significant positive relationship was observed in 15 out of 40 sessions, whereas a significant negative relationship was observed in 1 session (Fig. 4A). MEP amplitude while targeting beta rhythm was affected by target phase alone (F = 4.26, p = 0.005). No effect of pre-TMS periodic beta power (F = 0.24, p = 0.622), nor a phase∗power interaction (F = 2.50, p = 0.058) was observed on MEP amplitude. At an individual level, correlation between beta power and MEP amplitude ranged between ρ = −0.168 and ρ = 0.151 (median ρ = −0.008). A one-sample t-test on the Fisher z-transformed correlation values confirmed that on average pre-TMS beta power does not significantly relate to MEP amplitude (t = 0.90, p = 0.375). A significant positive relationship was observed in 12 out of 40 sessions, whereas a significant negative relationship was observed in 4 out of 40 sessions (Fig. 4B). Finally, MEP amplitude was not significantly affected by the aperiodic component of the power signal (F = 0.05, p = 0.821), nor a phase∗power interaction (F = 0.02, p = 0.996).
      Fig. 4
      Fig. 4Histogram of individual Spearman correlations between MEP amplitude and A) pre-TMS mu power, and B) pre-TMS beta power after extracting the periodic components of each frequency band.
      One possible confound could arise where channels in the Laplacian reference montage contribute differently to the target electrode between conditions. Therefore, we performed a sensor-level analysis of mu and beta distributions, by looking at the channel-to-channel correlations. Resulting topographic plots showed highly similar distributions for both mu and beta rhythms at sensor level (Fig. 5). Distributions were highly correlated (ρ = 0.92, p < 0.001), suggesting that our main results cannot be explained by differences in mu and beta signal arrangement.
      Fig. 5
      Fig. 5Spatial topographies for the recorded mu rhythm, beta rhythm, and the difference between both. Color map represents correlational values of electrode pairings between target electrode C3 and all other electrodes. The black electrode corresponds to C3. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
      Finally, the typical arch-shape of the mu signal results in harmonics in the beta frequency range (referred to as mu-beta). To test whether our algorithm picked up a mu-harmonic or independent beta activity, we made a strict mathematical estimation of harmonicity between the signals and inspected individual power spectra (Supplementary Fig. 4). By definition, the harmonic signals should have a period ratio that is an integer number. However, no integer values were observed with an average ratio of 2.148 and values for all participants and sessions ranging between 2.051 and 2.248. As such, we observed no indication for beta signals resulting from a mu harmonic. Furthermore, the phase relationship between mu and beta rhythms was generally weak, suggesting little dependence between phases of both signals (Supplementary Fig. 5).

      4. Discussion

      In this study, we demonstrate for the first time that mu and beta oscillation phase differentially modulate MEP amplitude. In summary, we found that I) phase of mu and beta oscillations picked up at sensorimotor channels modulate corticospinal excitation; II) this phase-dependent MEP modulation follows an opposing pattern for mu and beta; III) mu power, but not beta power, significantly modulates MEP amplitude; IV) modulation of MEP amplitudes by phase and power do not interact.
      To our knowledge, we provide the first direct evidence for MEP amplitude modulation by beta phase, in addition to mu phase, measured with real-time TMS-EEG. Beta-phase dependency has been hinted at by previous offline TMS studies using post-hoc analyses [
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      Motor cortex inputs at the optimum phase of beta cortical oscillations undergo more rapid and less variable corticospinal propagation.
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      Corticospinal beta-band synchronization entails rhythmic gain modulation.
      ]. Also, human subdural electrocorticographic (ECoG) recordings have shown that motor cortical beta activity is phase-locked to neural population activity during movement [
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      ]. Furthermore, motor cortical spiking activity has been shown to be dependent on local field potential beta-phase in non-human primates [
      • Reimer J.
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      Periodicity and evoked responses in motor cortex.
      ,
      • Witham C.L.
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      Cells in somatosensory areas show synchrony with beta oscillations in monkey motor cortex.
      ]. Sensorimotor beta oscillations have been suggested to arise from alternating de- and hyper-polarization of layer V pyramidal cells, mediated by phase-locked gamma-aminobutyric acid (GABA) mediated interneuron inputs [
      • Baker S.N.
      Oscillatory interactions between sensorimotor cortex and the periphery.
      ,
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      ,
      • Rossiter H.E.
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      • Boudrias M.-H.
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      Beta oscillations reflect changes in motor cortex inhibition in healthy ageing.
      ,
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      • Hall S.D.
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      Spike firing and IPSPs in layer v pyramidal neurons during beta oscillations in rat primary motor cortex (M1) in vitro.
      ]. Here we show that beta phase-dependency can be probed non-invasively in real-time. Our data showed largest MEP amplitudes during beta peak and falling phase (Fig. 2). Salimpour et al. [
      • Salimpour Y.
      • Mills K.A.
      • Hwang B.Y.
      • Anderson W.S.
      Phase- targeted stimulation modulates phase-amplitude coupling in the motor cortex of the human brain.
      ] applied real-time electrical motor cortex stimulation in Parkinson's disease patients during surgery. Although direct comparison of results from electrical stimulation and ECoG data to ours may be challenging, it is interesting to point out that phase-dependency was similar, with beta peak and falling phase leading to the largest motor output.
      We found no dependency of beta power on MEP amplitude, nor was there an interaction between beta phase and power, in line with previous findings [
      • Hussain S.J.
      • Claudino L.
      • Bönstrup M.
      • Norato G.
      • Cruciani G.
      • Thompson R.
      • et al.
      Sensorimotor oscillatory phase–power interaction gates resting human corticospinal output.
      ,
      • Schilberg L.
      • Oever S.T.
      • Schuhmann T.
      • Sack A.T.
      Phase and power modulations on the amplitude of TMS-induced motor evoked potentials.
      ,
      • Mitchell W.K.
      • Baker M.R.
      • Baker S.N.
      Muscle responses to transcranial stimulation in man depend on background oscillatory activity.
      ,
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      • Tobimatsu S.
      Prestimulus cortical EEG oscillations can predict the excitability of the primary motor cortex.
      ,
      • Peters J.C.
      • Reithler J.
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      • Schuhmann T.
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      • Sack A.T.
      Concurrent human TMS-EEG-fMRI enables monitoring of oscillatory brain state-dependent gating of cortico-subcortical network activity.
      ]. This should not imply that beta oscillations are not related to motor output and evidence from previous research suggests that the relationship between beta oscillations and motor activation is complex. Pre-movement reduction of beta power has been associated with faster voluntary movement [
      • Khanna P.
      • Carmena J.M.
      Beta band oscillations in motor cortex reflect neural population signals that delay movement onset.
      ]. Chronic elevation of beta power, observed in Parkinson's disease has been related to difficulty initiating and controlling movements [
      • Brown P.
      Bad oscillations in Parkinson's disease.
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      ]. Furthermore, in addition to low-amplitude ongoing beta activity, high-amplitude beta bursts are suggested to be positively correlated to movement control [
      • O'Keeffe A.B.
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      • Sparks H.
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      Synchrony drives motor cortex beta bursting, waveform dynamics, and phase-amplitude coupling in Parkinson's disease.
      ,
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      ,
      • Bonaiuto J.J.
      • Little S.
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      Laminar dynamics of high amplitude beta bursts in human motor cortex.
      ,
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      ,
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      Bursts of beta oscillation differentiate postperformance activity in the striatum and motor cortex of monkeys performing movement tasks.
      ]. Although these behavioral studies imply that beta power and beta bursts are crucial for endogenous control of voluntary movement, our and previous studies suggest that they are not related to exogenously probed cortico-spinal excitability [
      • Hussain S.J.
      • Claudino L.
      • Bönstrup M.
      • Norato G.
      • Cruciani G.
      • Thompson R.
      • et al.
      Sensorimotor oscillatory phase–power interaction gates resting human corticospinal output.
      ,
      • Ogata K.
      • Nakazono H.
      • Uehara T.
      • Tobimatsu S.
      Prestimulus cortical EEG oscillations can predict the excitability of the primary motor cortex.
      ,
      • Peters J.C.
      • Reithler J.
      • Graaf TA de
      • Schuhmann T.
      • Goebel R.
      • Sack A.T.
      Concurrent human TMS-EEG-fMRI enables monitoring of oscillatory brain state-dependent gating of cortico-subcortical network activity.
      ]. Furthermore, Peters and colleagues [
      • Peters J.C.
      • Reithler J.
      • Graaf TA de
      • Schuhmann T.
      • Goebel R.
      • Sack A.T.
      Concurrent human TMS-EEG-fMRI enables monitoring of oscillatory brain state-dependent gating of cortico-subcortical network activity.
      ] found that pre-TMS resting beta power does not affect the propagation of TMS excitations throughout the cortical-subcortical motor network. Therefore, it seems that beta power may be a predictor for corticospinal activation during voluntary or task-related motor control, but not during resting-state motor excitability per se.
      Additionally, we found that corticospinal excitation was modulated by the mu rhythm with an opposite phase relationship compared to beta oscillations. Various studies previously indicated mu phase-dependent modulation of MEP amplitudes, with larger responses at the mu trough compared to mu peak [
      • Bergmann T.O.
      • Lieb A.
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      Pulsed facilitation of corticospinal excitability by the sensorimotor μ-alpha rhythm.
      ,
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      Μ-rhythm extracted with personalized EEG filters correlates with corticospinal excitability in real-time phase-triggered EEG-TMS.
      ,
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      EEG-triggered TMS reveals stronger brain state-dependent modulation of motor evoked potentials at weaker stimulation intensities.
      ,
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      ,
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      ]. Our results confirm these findings on mu peak and trough, but the phase effects extended towards the subsequent falling and rising phase respectively. That is, we show that trough and rising phase yield largest corticospinal excitation, whereas mu peak and falling yield the smallest motor cortex activation (Fig. 2).
      Pre-stimulus mu power was a significant predictor for corticospinal excitability, but did not interact with mu phase, suggesting independence between mu power and phase. Subject-level positive correlations were observed in majority of subjects. Although the observed relationship was relatively weak - correlations varying between −0.1 and 0.25 - it is in line with previous observations [
      • Bergmann T.O.
      • Lieb A.
      • Zrenner C.
      • Ziemann U.
      Pulsed facilitation of corticospinal excitability by the sensorimotor μ-alpha rhythm.
      ,
      • Karabanov A.N.
      • Madsen K.H.
      • Krohne L.G.
      • Siebner H.R.
      Does pericentral mu-rhythm “power” corticomotor excitability? – a matter of EEG perspective.
      ,
      • Thies M.
      • Zrenner C.
      • Ziemann U.
      • Bergmann T.O.
      Sensorimotor mu-alpha power is positively related to corticospinal excitability.
      ,
      • Schilberg L.
      • Oever S.T.
      • Schuhmann T.
      • Sack A.T.
      Phase and power modulations on the amplitude of TMS-induced motor evoked potentials.
      ]. However, others have found no relationship between mu power and MEP amplitude [
      • Berger B.
      • Minarik T.
      • Liuzzi G.
      • Hummel F.C.
      • Sauseng P.
      EEG oscillatory phase-dependent markers of corticospinal excitability in the resting brain.
      ,
      • Zrenner C.
      • Desideri D.
      • Belardinelli P.
      • Ziemann U.
      Real-time EEG-defined excitability states determine efficacy of TMS-induced plasticity in human motor cortex.
      ], or even a negative association [
      • Madsen K.H.
      • Karabanov A.N.
      • Krohne L.G.
      • Safeldt M.G.
      • Tomasevic L.
      • Siebner H.R.
      No trace of phase: corticomotor excitability is not tuned by phase of pericentral mu-rhythm.
      ,
      • Sauseng P.
      • Klimesch W.
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      • Hummel F.C.
      Spontaneous locally restricted EEG alpha activity determines cortical excitability in the motor cortex.
      ,
      • Zarkowski P.
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      • Dang T.
      • Russo J.
      • Avery D.
      EEG and the variance of motor evoked potential amplitude.
      ]. At a first glance, a positive relationship between mu power and corticospinal activity seems counterintuitive since sensorimotor mu oscillations are related to GABAa-mediated inhibitory activity [
      • Bergmann T.O.
      • Lieb A.
      • Zrenner C.
      • Ziemann U.
      Pulsed facilitation of corticospinal excitability by the sensorimotor μ-alpha rhythm.
      ]. Also, higher mu power has been shown to reduce TMS-induced blood oxygenation level-dependent (BOLD) responses throughout the cortical-subcortical motor network [
      • Peters J.C.
      • Reithler J.
      • Graaf TA de
      • Schuhmann T.
      • Goebel R.
      • Sack A.T.
      Concurrent human TMS-EEG-fMRI enables monitoring of oscillatory brain state-dependent gating of cortico-subcortical network activity.
      ]. However, mu oscillations are thought to predominantly originate from the somatosensory cortex [
      • Gaetz W.
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      Localization of sensorimotor cortical rhythms induced by tactile stimulation using spatially filtered MEG.
      ,
      • Jones S.R.
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      ,
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      The impact of GABAergic drugs on TMS-induced brain oscillations in human motor cortex.
      ,
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      A multimodal perspective on the composition of cortical oscillations.
      ,
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      ,
      • Salmelin R.
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      Functional segregation of movement-related rhythmic activity in the human brain.
      ]. Interconnections between somatosensory and primary motor cortex comprise of an intricate network of excitatory and inhibitory reciprocal connections. Increased mu power may reflect feedforward inhibition to primary motor cortex resulting in local disinhibition, which could explain a positive relationship between mu power and MEP amplitudes. Although our findings do agree with previous reports [
      • Bergmann T.O.
      • Lieb A.
      • Zrenner C.
      • Ziemann U.
      Pulsed facilitation of corticospinal excitability by the sensorimotor μ-alpha rhythm.
      ,
      • Karabanov A.N.
      • Madsen K.H.
      • Krohne L.G.
      • Siebner H.R.
      Does pericentral mu-rhythm “power” corticomotor excitability? – a matter of EEG perspective.
      ,
      • Thies M.
      • Zrenner C.
      • Ziemann U.
      • Bergmann T.O.
      Sensorimotor mu-alpha power is positively related to corticospinal excitability.
      ,
      • Schilberg L.
      • Oever S.T.
      • Schuhmann T.
      • Sack A.T.
      Phase and power modulations on the amplitude of TMS-induced motor evoked potentials.
      ]. One important aspect may be to extract the periodic components of the power spectra [
      • Wen H.
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      Separating fractal and oscillatory components in the power spectrum of neurophysiological signal.
      ,
      • Donoghue T.
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      Parameterizing neural power spectra into periodic and aperiodic components.
      ], which may explain why this positive relationship was not found by others.
      Sensorimotor mu and beta oscillations have been suggested to stem from distinct neural origins [
      • Gaetz W.
      • Cheyne D.
      Localization of sensorimotor cortical rhythms induced by tactile stimulation using spatially filtered MEG.
      ,
      • Jones S.R.
      • Pritchett D.L.
      • Sikora M.A.
      • Stufflebeam S.M.
      • Hämäläinen M.
      • Moore C.I.
      Quantitative analysis and biophysically realistic neural modeling of the MEG mu rhythm: rhythmogenesis and modulation of sensory-evoked responses.
      ,
      • Premoli I.
      • Bergmann T.O.
      • Fecchio M.
      • Rosanova M.
      • Biondi A.
      • Belardinelli P.
      • et al.
      The impact of GABAergic drugs on TMS-induced brain oscillations in human motor cortex.
      ,
      • Ronnqvist K.
      • McAllister C.
      • Woodhall G.
      • Stanford I.
      • Hall S.
      A multimodal perspective on the composition of cortical oscillations.
      ,
      • Salmelin R.
      • Hari R.
      Spatiotemporal characteristics of sensorimotor neuromagnetic rhythms related to thumb movement.
      ,
      • Salmelin R.
      • Hámáaláinen M.
      • Kajola M.
      • Hari R.
      Functional segregation of movement-related rhythmic activity in the human brain.
      ]. Specifically, mu oscillations are proposed to originate pre-dominantly from the post-central gyrus [
      • Salmelin R.
      • Hari R.
      Spatiotemporal characteristics of sensorimotor neuromagnetic rhythms related to thumb movement.
      ,
      • Salmelin R.
      • Hámáaláinen M.
      • Kajola M.
      • Hari R.
      Functional segregation of movement-related rhythmic activity in the human brain.
      ], although pre-central origins of mu have been reported as well [
      • Ronnqvist K.
      • McAllister C.
      • Woodhall G.
      • Stanford I.
      • Hall S.
      A multimodal perspective on the composition of cortical oscillations.
      ,
      • Smit D.J.A.
      • Linkenkaer-Hansen K.
      • Geus EJC de
      Long-range temporal correlations in resting-state alpha oscillations predict human timing-error dynamics.
      ,
      • Szurhaj W.
      • Derambure P.
      • Labyt E.
      • Cassim F.
      • Bourriez J.-L.
      • Isnard J.
      • et al.
      Basic mechanisms of central rhythms reactivity to preparation and execution of a voluntary movement: a stereoelectroencephalographic study.
      ]. In contrast, beta oscillations are thought to stem from pre-central primary motor cortex [
      • Jurkiewicz M.T.
      • Gaetz W.C.
      • Bostan A.C.
      • Cheyne D.
      Post-movement beta rebound is generated in motor cortex: evidence from neuromagnetic recordings.
      ,
      • Salmelin R.
      • Hari R.
      Spatiotemporal characteristics of sensorimotor neuromagnetic rhythms related to thumb movement.
      ,
      • Salmelin R.
      • Hámáaláinen M.
      • Kajola M.
      • Hari R.
      Functional segregation of movement-related rhythmic activity in the human brain.
      ,
      • Donoghue J.P.
      • Sanes J.N.
      • Hatsopoulos N.G.
      • Gaál G.
      Neural discharge and local field potential oscillations in primate motor cortex during voluntary movements.
      ], but are also observed in post-central somatosensory cortex [
      • Jurkiewicz M.T.
      • Gaetz W.C.
      • Bostan A.C.
      • Cheyne D.
      Post-movement beta rebound is generated in motor cortex: evidence from neuromagnetic recordings.
      ,
      • Szurhaj W.
      • Derambure P.
      • Labyt E.
      • Cassim F.
      • Bourriez J.-L.
      • Isnard J.
      • et al.
      Basic mechanisms of central rhythms reactivity to preparation and execution of a voluntary movement: a stereoelectroencephalographic study.
      ,
      • Brovelli A.
      • Ding M.
      • Ledberg A.
      • Chen Y.
      • Nakamura R.
      • Bressler S.L.
      Beta oscillations in a large-scale sensorimotor cortical network: directional influences revealed by Granger causality.
      ]. Although our study cannot make inferences on the source of mu and beta oscillations, sensor-level signal distributions were highly similar (Fig. 5). Similar scalp-level topographies suggest that potential differences in neural origin did not influence phase detection during real-time stimulation. A potential explanation for the opposing phase-relationship we observed results from differences in axonal orientation within mu and beta sources. This possibility could be investigated in future studies.
      The sensorimotor mu-signal tends to resemble an arch-shape, rather than a sinusoid [
      • Salmelin R.
      • Hari R.
      Spatiotemporal characteristics of sensorimotor neuromagnetic rhythms related to thumb movement.
      ,
      • Cole S.R.
      • Voytek B.
      Brain oscillations and the importance of waveform shape.
      ,
      • Triggiani A.I.
      • Valenzano A.
      • Del Percio C.
      • Marzano N.
      • Soricelli A.
      • Petito A.
      • et al.
      Resting state Rolandic mu rhythms are related to activity of sympathetic component of autonomic nervous system in healthy humans.
      ,
      • Pfurtscheller G.
      • Brunner C.
      • Schlögl A.
      • Lopes da Silva F.H.
      Mu rhythm (de)synchronization and EEG single-trial classification of different motor imagery tasks.
      ]. As a result of this higher-frequency harmonics can be observed in the frequency spectra. Particularly first-order harmonics would appear in the beta frequency range (referred to as mu-beta). It is worth nothing that our ETP algorithm used here is agnostic to the origin of beta oscillations. However, the opposing results in MEP amplitudes between mu and beta phase would be unexpected since mu harmonics reflect similar functional properties [
      • Pfurtscheller G.
      • Brunner C.
      • Schlögl A.
      • Lopes da Silva F.H.
      Mu rhythm (de)synchronization and EEG single-trial classification of different motor imagery tasks.
      ]. Additionally, we formally tested for harmonicity and found no evidence for it (Supplementary Figs. 4 and 5). Thus, we believe that the modulation of MEPs when targeting at frequencies between 14 and 30 Hz results from independent beta oscillations. A further limitation of this study is that phase accuracy was only established in the beginning of a session. Although we previously have shown that phase targeting with ETP is stable on average of a single session [
      • Shirinpour S.
      • Alekseichuk I.
      • Mantell K.
      • Opitz A.
      Experimental evaluation of methods for real-time EEG phase-specific transcranial magnetic stimulation.
      ], individual fluctuations in oscillatory activity over time may affect targeting accuracy.
      Our findings are crucial for the improvement of TMS effectiveness for treatment of neurological and psychiatric disorders. Targeting optimal rhythms with repetitive TMS could decrease variability of TMS outcomes [
      • Zrenner C.
      • Desideri D.
      • Belardinelli P.
      • Ziemann U.
      Real-time EEG-defined excitability states determine efficacy of TMS-induced plasticity in human motor cortex.
      ,
      • Baur D.
      • Galevska D.
      • Hussain S.
      • Cohen L.G.
      • Ziemann U.
      • Zrenner C.
      Induction of LTD-like corticospinal plasticity by low-frequency rTMS depends on pre-stimulus phase of sensorimotor μ-rhythm.
      ]. For instance, targeting optimal oscillation phase could improve efficacy of TMS in the recovery of stroke [
      • Hussain S.J.
      • Hayward W.
      • Fourcand F.
      • Zrenner C.
      • Ziemann U.
      • Buch E.R.
      • et al.
      Phase-dependent transcranial magnetic stimulation of the lesioned hemisphere is accurate after stroke.
      ] and treatment of major depressive disorder [
      • Zrenner B.
      • Zrenner C.
      • Gordon P.C.
      • Belardinelli P.
      • McDermott E.J.
      • Soekadar S.R.
      • et al.
      Brain oscillation-synchronized stimulation of the left dorsolateral prefrontal cortex in depression using real-time EEG-triggered TMS.
      ]. In this study, to our knowledge, we were able to non-invasively target the beta rhythm in real-time reliably for the first time. In future work it will be crucial to further optimize real-time and closed-loop systems, in order to target different oscillatory rhythms, and different spatial locations [81–83]. Eventually, this will allow for adaptive non-invasive neuromodulation that can provide personalized decoding of on-going brain states. This individualization can greatly benefit clinical application of TMS, by reducing variability between and within patients.

      Funding

      Research presented here was supported by the University of Minnesota’s MnDRIVE Initiative; and NSF Career Grant 2143852.

      CRediT authorship contribution statement

      Miles Wischnewski: Conceptualization, Investigation, Formal analysis, Writing – original draft, Visualization, Funding acquisition. Zachary J. Haigh: Investigation, Writing- Reviewing and Editing. Sina Shirinpour: Conceptualization, Methodology, Software, Validation, Formal analysis, Writing- Reviewing and Editing. Ivan Alekseichuk: Conceptualization, Methodology, Software, Validation, Formal analysis, Writing- Reviewing and Editing. Alexander Opitz: Supervision, Writing- Reviewing and Editing, Funding acquisition.

      Declaration of competing interest

      Authors declare no conflict of interest.

      Appendix A. Supplementary data

      The following is the Supplementary data to this article:

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