Добавил:
Sekretar
kiopkiopkiop18@yandex.ru
t.me/Prokururor I Вовсе не секретарь, но почту проверяю
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Предмет:
Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_6027_Библиотеки_им_академика_М_И_Перельмана.pdf
462 H. I. Stecher et al.
31.5 Differentiation Between Aperiodic and Periodic
Activity
31.5.1 Rationale
Researchers familiar with EEG recognize that the spectral representation of brain
activity does not only display periodic activity (such as the classical brain rhythms
alpha, beta, gamma, delta, and theta) as distinct peaks in the spect rum but also
consistently includes additional activity whose power follows a 1/f distribution
(Buzsaki, 2006; Pritchard, 1992).
This “1/f-noise floor” (also referred to as “pink noise,” “scale-invariant activity,”
or
“fractal component”) represents aperiodic (or “arrhythmic”) brain activity.
Endogenous brain rhythms, such as alpha, beta, gamma, delta, and theta, are
considered truly periodic, characterized by a sinusoidal pattern with a continuous
sequence of positive and negative deflections of equal amplitude and duration. In
contrast, aperiodic activity encompasses all other types of neuronal activity that do
not follow a continuous sine-wave pattern, such as unipolar voltage deflections.
However, spectral analysis methods, like, for example, the Fourier transformation,
primarily measure how closely a given signal resembles cosines of various frequencies. But even non-cosine-shaped signals (e.g., a Gaussian peak) partially resemble
cosines across multiple frequencies, resulting in their representation in the spectral
domain as 1/f-acti vity.
Recent evidence suggests that regarding 1/f-activity as mere “noise” is inadequate
et al., 2010; He, 2014). Multiple studies have demonstrated that the level of 1/f-
(He
activity
Ouya
lead
the
between excitatory and inhibitory neuronal activity (Gao et al.,
total
attenuate, or exaggerate intervent ion effects. Moreover, the intervention itself could
modify the shape of aperiodic activity, potentially indicating changes in the overall
ratio between excitation and inhibition. Therefore, it is essential to decompose the
spectral outcomes of neuromodulation studies into periodic and aperiodic components and asses each separately for intervention effects (Keil et al.,
et
et
is functionally relevant for various cognitive processes (Miller et al., 2014;
ng et al., 2020). Moreover, failing to account for changes in 1/f-activity can
to distorted effects (Gyurkovics et al., 2021). Additional research suggests that
specific exponent of the power spectrum is closely related to the current balance
2017).
In the context of neuromodulation research, this means that solely analyzing the
spectral activity without accounting for changes in aperiodic activity may mask,
2022; Donoghue
al.,
2022), as demonstrated in several recent studies (Kasten et al., 2024; Masina
al.,
2025; Venugopal et al., 2025; Davis et al., 2023).
31.5.2 Procedure
To separate aperiodic and periodic activity from the total spectrum, the aperiodic
activity must first be estimated as a fractal component. This component is then
31 Combining EEG and Transcranial Electric Brain Stimulation 463
Fig. 31.3 Basic principle of dividing spectral data into periodic and aperiodic components. (a)
Original total spectrum composed of aperiodic activity (1/f-floor) and two oscillatory signals
(visible as peaks in the spectrum). The magnitude of the peaks represents the magnitude of the
periodic activity plus the underlying noise floor. (b) The same spectrum as viewed on a doublelogarithmic scale (blue line). On this scale the aperiodic noise floor resembles a straight line.
Through iterative fitting procedures, the total spectrum is divided into an aperiodic fit (red) and an
oscillatory fit (yellow). (c) Subtracting the aperiodic fit from the total spectrum (transparent blue
curve) yields the corrected purely periodic spectrum (solid blue), from which we can now extract
the corrected peak-frequency and peak-power values for further analysis of periodic activity. (d)
The aperiodic fit (red) can be used for the characterization of the pink-noise activity: We can extract
the offset ( log
pink-noise activity
of the intercept in log-log space) and the exponent (-slope in log-log space) of the
10
“subtracted” from the full spectrum, isolating the “truly” periodic activity. Note that
a subtraction in logarithmic space is mathematically a division in linear space,
rendering the term ambivalent. Some studies (e.g., Kasten et al.,
correct
ion as a subtraction in linear space, while others perform it in log space
(Donoghue et al.,
2020). Which approach is the “correct” one is currently debated
(Gyurkovics et al., 2021) and depends on the specific research question. Figure
depicts the basic thought proces
s behind the general approach.
2024) perform the
31.3
Seven distinct approaches have been proposed, each addressing the problem from
a different perspective:
1. SPECPARAM
(Spectral Parameterization; Donoghue et al., 2020) works by
iteratively modeling periodic activity as Gaussian peaks and the fractal component as a line in log-log space. Note that this approach was formerly called
FOOOF (Fitting Oscillations and One-Over-F).
464 H. I. Stecher et al.
2. IRASA (Irregular Resampling Auto-Spectral Analysis; Wen and Liu, 2016)
separates oscillatory and fractal (1/f) components by resampling the signal at
non-integer rates and computing the geometric mean of the power spectra at these
rates to isolate the fractal component. Subtracting this fractal component from the
total spectrum isolates the oscillatory signals.
3. eBOSC (extended Better Oscillation Detection; Kosciessa et al., 2020) identifies
ions by setting thres holds based on a statistical model of the background
oscillat
(1/f) noise, enabling differentiation of oscillations from noise. It refines the
traditional BOSC approach (Whitten et al., 2011; Caplan et al., 2001) by incorporat
ing longer time windows and enhancements to improve the detection of
oscillations in the presence of 1/f noise.
4. PAWNextra (Pink and White Noise Extraction; Barry and De
Blasio, 2021)
employs a traditional Welch periodogram to estimate the power spectrum,
followed by techniques to distinguish the oscillatory peaks from the background
1/f slope and white noise. It utilizes model fitting to extract the power of
oscillations relative to the 1/f baseline.
5. MODAL (Multiple Oscillations Detection Algorithm; Watrous et al., 2018)
s oscillatory frequency bands by fitting an aperiodic component using
detect
robust linear regression. Frequencies that deviate by more than one standard
deviation from this fit are classified as periodic activity.
6. BSD (Bayesian Spectral Decomposition; Medrano et al., 2025) models neural
powe
r spectra as a composite of Gaussian peaks and aperiodic activity with added
noise. The parameters of these components are estimated by employing a Bayesian framework that accounts for uncertainty.
7. SPRiNT (Spectral Parameterization Resolved in Time; Wilson et al., 2022) is an
extension to the SPECPARAM approach that works on time-frequency data.
SPECPARAM is built into the Brainstorm (Tadel et al., 2011) and Fieldtrip
(Oosten
implem
veld et al., 2011) toolboxes and also available as Python code. IRASA is
ented in Fieldtrip as well and also available for Python. EBOSC and SPRiNT
have MATLAB code available on GITHUB, and BSD is stated to be made available
as a toolbox as part of the SPM software package.
SPECPARAM
and IRASA are currently the most widely used methods
(SPECPARAM: 1223 citations, IRASA: 307 citations). For both methods, Gerster
et al. (2022) conducted a detailed analysis using artificial spectra with known ground
truth
to identify common challenges. SPECPARAM performs well, when there are
no plateaus (disrupting the power-law distribution) within the fitting range. Oscillatory peaks at the border of the fitting range cannot be accurately modeled, and
oscillations lacking distinct peaks are indistinguishable from the noise floor. For
IRASA, the resampling procedure extends the evaluated frequency range beyond the
fitted range, which can introduce biases toward lower slopes if the evaluated range
encounters high-pass filter edges or high-frequency noise. To mitigate this, small
resampling factors should be used. However, broad oscillatory peaks require high
resampling factors for accurate detection by the algorithm, necessitating a trade-off
31 Combining EEG and Transcranial Electric Brain Stimulation 465
between these challenges. Additionally, as with SPECPARAM, IRASA struggles to
detect oscillations that do not manifest as a clear peak.
For all methods, there is no universal set of parameters that fits every recording,
and relying solely on goodness-of-fit metrics might not prevent overfitting as was
pointed out for SPECPARAM by Ostlund et al. (2022). Recently, Wilson et al.
(
2024) proposed an algorithm in a preprint to assist with model selection for
SPECPA
(ms-SPECPARAM and ms-SPRinT). Generally, the most effective approach for
all methods involves starting with the recommended default parameters, followed by
visual inspection before adjusting the parameters to better align with the specific
experimental data.
RAM and SPRiNT, with code available for MATLAB
31.6 Closed-Loop Systems
Most stimulation studies employ a predetermined set of parameters to elicit their
effects. Ideally, individual anatomy and individual brain activity features like individual peak-frequencies are taken into account, but once the stimulation has started,
it usually follows a fixed waveform.
It has been established in several studies, however, that the effects of stimulation
are
dependent on the brain’s current state (Neuling et al., 2013; Ruhnau et al., 2016;
et al., 2013; Wei et al., 2024), with only certain states actually being affected
Feurra
(Kasten
tions
with time on task (Benwell et al., 2019). Consequently, parameters that were fitting
at
Concurrent EEG recording during stimulation provides an opportunity to adapt to
these changes in brain activity by applying stimulation selectively during certain
states or adjusting the phase and frequency to align with a targeted endogenous
oscillation. Such setups are commonly referred to as “closed-loop system” or “brain
state-dependent NTBS” (Bergmann et al.,
Figure 31.4 illustrates the general schematic of such a system. A control computer is
connected to both a neuroimaging device (e.g., EEG, MEG, and fMRI) and a
stimulator (e.g., TMS, tDCS, tACS, and transcranial ultrasound stimulator), which
are both connected to a participant. The control computer receives neuro-imaging
data in (near) real time, extracts relevant brain activity features, and adjusts or
triggers stimulation based on these features. Due to its relatively low cost and
practicality, EEG is a prime-candidate for the neuroimaging component of such a
system.
close
Towns
Shirin
& Herrmann, 2022; Luo et al., 2025). Moreover, endogenous brain oscilla-
can change over time, for instance, the peak alpha frequency tends to decrease
the onset of stimulation might become ineffective as an experiment progresses.
2016; Bergmann, 2018; Thut et al., 2017).
Numerous studies have highlighted the need for and outlined the principles of
d-loop brain stimulation systems (Soleimani et al., 2023; Frohlich &
end, 2021; Zarubin et al., 2018; Iturrate et al., 2018; Kohli et al., 2017;
pour et al., 2025; Schestatsky et al., 2013; Xiong et al., 2025). However,
466 H. I. Stecher et al.
Fig. 31.4 Schematic of a closed-loop brain stimulation system: A participant or patient receives
ongoing brain stimulation. Neuroimaging data (e.g., EEG) is concurrently recorded and fed to a
control computer via remote data access, Lab Streaming Layer (LSL), or a similar protocol. The
control computer performs a rapid analysis of brain activity, like current state, or power, frequency
or phase of a brain rhythm. Based on the extracted features, the control computer either triggers the
application of a predefined waveform or updates a waveform and feeds it to the attached stimulator
via a digital-to-analog converter
only a limited number of studies have implemented this concept. This scarcity may
stem from two primary technical challenges in EEG/TES closed-loo p designs. The
first challenge is the requirement for rapid computational processing to acquire EEG
data, performing data-processing routines, feature extraction, and the generation of
waveforms. All system latencies must be minimal or at least predictable to ensure
stimulation aligns precisely with the specific brain ac
tivity features. In pract ice, this
demands dedicated real-time systems, such as the Real-Time eXperiment Interface
(RTXI) (Patel et al.,
2017) or field programmable gate array (FPGA) (Wilde et al.,
2015). The second challenge in EEG/TES closed-loop systems is the artifact induce d
by electrical stimulation in the EEG signal (see Sect. 31.3). To address this, many
studies have adopted an intermittent closed-loop approach rather than true real-time
processing. In such a system stimulation is delivered in short blocks of limited
length, with feature extraction performed on EEG segments recorded between
these blocks. For example, in a proof-of-principle study, Leite et al. (
2017) devel-
oped a protocol that triggered a continuous block of tDCS when the EEG exhibited a
certain alpha-to-beta ratio. Similarly, in tACS studies, stimulation is delivered in
short blocks, interleaved with stimulation-free EEG intervals, during which new
stimulation features are extracted. Schwippel et al. (
2024) implemented 120-s of
tACS at individual alpha frequency when the alpha power within a 10-s observation
window exceeded a predefined threshold as a treatment for Major Depressive
Disorder. To selectively enhance sleep spindles, Lustenberger et al. (
2016)
31 Combining EEG and Transcranial Electric Brain Stimulation 467
employed an RTXI system to deliver 1-s bursts of 12 Hz tACS followed by a 6.5-s
timeout, triggered when ongoing band-pass-filtered brain activity exhibited five
rectified sigma peaks exceeding an individual threshold. Stecher et al. (
implem
recordings, continuously adjusting the stimulation frequency to match the current
prevalent alpha peak-frequency. Zarubin et al. (2020) employed an intermittent
desig
upcoming block using a Hilbert-transformed 250-ms window before each stimulation block, allowing tACS to be applied either in-phase or antiphase with the
endogenous alpha rhythm. Similarly, Ketz et al. (
utilized
a sine-wave matched in frequency and phase, and applying it for five cycles. Both
setups rely on accurate estimates of system latencies, including the time required to
receive EEG data, process it, and initiate stimulation.
feature extraction occurring simultaneously with ongoing stimulation, each
employing distinct methods to obtain usable EEG data despite stimulation artifacts.
For tDCS, as long as the EEG data does not clip, the artifact primarily causes a
spectral offset at 0 Hz without affecting the spectrum of typical brain oscillations.
Employing a combination of standard low-pass and high-pass filters along with basic
artifact rejection, Caravati et al. (2024) adjusted ongoing tDCS amplitude—either
incre
window of EEG data to improve performance in a continuous performance task. In
tACS studies, when the stimulated frequency band and the evaluated band of interest
do not overlap, a narrow band-pass filter around the band of interest can yield artifact
free EEG recordings. Boyle and Fröhlich (
system, continuously applying 40 Hz tACS while monitoring alpha activity in the
EEG. To obtain stimulation artifact-free EEG data, they applied a narrow band-pass
filter in the alpha range and delivered 2-s bursts of 1 mA tACS when alpha power
exceeded a predefined threshold. Otherwise, the system constantly applied 0.1 mA
tACS. Lastly, tTIS and AM-tACS theoretically produce artifact-free data in the band
of interest, even during stimulation, as only the carrier signal should appear in the
spectrum. In practice, however, residual artifacts may still occur at the envelope
frequency (see Sect.
source
restored phase-estimates of the ongoing alpha activity, enabling stimulation at six
different phases by continuously adjusting the envelope-phase and frequency of the
AM-tACS.
ented a design using 8-s tACS blocks, alternating with 8-s epochs of EEG
n with 1-s stimula tion blocks, predicting the alpha rhythm phase for the
2018) and Jones et al. (2018)
a setup with a running 5-s buffer to detect slow-waves in the EEG, fitting
Three studies have implemented true real-time closed-loop approaches, with
asing or decreasing it—based on statistical metrics d erived from a sliding 3-s
2013) utilized this approach with an RTXI
31.3.3.2). By combining AM-tACS and stimulation artifact
separation in a real-time computer, Haslacher et al. (2021) successfully
2021)
31.7 Technical Requirements
The technical requirements for combining EEG and tES depend primarily on the
research objective: Whether the focus is on offline or online effects. For offline
effects, the stimulation component imposes minimal constrains on the EEG setup.
468 H. I. Stecher et al.
Most EEG systems feature high input impedance in the range of Mega-Ω s which
safeguards the amplifier from the applied current. However, the placement of
stimulation electrodes might overlap with standard EEG electrode sites, limiting
the spatial resolution of the recordings. Using a “high definition” stimulation setup
(hd-tDCS or hd-tACS), composed of multiple smaller electrodes in favor of few
large electrodes can not only increase focality of stimulation but can al
placement of more EEG electrodes (Roy et al.,
prevent
bridging between closely positioned electrodes. Additional requirements are
2014). Care must also be taken to
so allow the
determined by the frequency and amplitude of the brain activity under study. The
EEG sampling rate should adhere to the Nyquist-Shannon sampling theorem to
accurately capture the oscillation of interest, with the general recommendation to
over-sample by at least 3–5 times the target frequency (Luck, 2014). For example, to
high gamma activity up to 150 Hz, a minimum sampling rate of at least 450 Hz
study
is required. Given that brain oscillations follow a power-law distribution, high
frequency bands like gamma typically produce small amplitudes of less than 1 μV
in the EEG (Busch et al.,
resolu
tion, typically 0.1 μV per bit, is essential for accurate measurem ent (see
2006). Therefore, a system with a sufficient voltage
Chap. 12: Hardware for Recording EEG and Peripheral Physiology).
When the focus is on physiological online effects in the EEG during active
stimulation, two primary challenges must be addressed to accurately recover true
brain activity: 1. EEG saturation and 2. distortion caused by the stimulation artifact.
Saturation occurs when the EEG amplitude exceeds the dynamic range of the
amplifier’s analog-to-digital (A/D) converter. As illustrated in Fig. 31.5, the tACSartifact
can reach amplitudes in the millivolt range, depending on factors such as
impedance, the proximity of recording electrode to stimulation site, and the stimulation amplitude. This huge artifact can drive the EEG signal into saturation if the
amplifier’s A/D range is insufficient. Saturation is characterized by blocking
(or clipping) of the signal, where the amplifier continuously records the maximum
or minimum value upon reaching the A/D limit, effectively obliterating any recoverable information about brain activity (see Fig.
ting an EEG system with a wide A/D range is critical. For example, the
selec
24-bit actiCHamp device from Brain Products offers an A/D range of
31.6). To mitigate saturation,
400 mV,
significantly broader than their 16-bit BrainAmp system, which is limited to 16
mV. Additio nally, maintaining low impedances for both stimulation and recording
electrodes is essential to minimize the artifact and ensure accurate EEG recordings.
The distort
ions of waveforms in EEG recordings during brain stimulation stem
from various sources, primarily rooted in the nonlinear response characteristics of
the involved systems. Nonlinear response functions, inherent to all electrical equipment, result in a nonproportional mapping of the ideal input signal (the digital
stimulation signal) to the output (the stimulation waveform in the EEG, see
Fig.
31.7). Kasten et al. (2018) explored these nonlinear properties in an
CS setup, demonstrating that nonlinearities are introduced by the stimulation
AM-tA
device, the EEG hardware, and, to a lesser extent, the digital-to-analog converter
driving the stimulation, all of which impact the accuracy of the recorded stimulation
signal. Nonlinearities pose significant challenges when analyzing EEG data during
31 Combining EEG and Transcranial Electric Brain Stimulation 469
Fig. 31.5 Example of a tACS-artifact size in an EEG recoding. (a) A 110 seconds EEG recording
during onset of tACS at 2 mA and 10 Hz, recorded from electrode Pz, with stimulation applied over
Cz and Oz. The normal EEG signal is situated in the μV range, while the tACS-artifact reaches a
peak-to-peak amplitude of 10mV. The gray regions depict 10 second windows for the FFT-spectra
below. (b) Semi-logarithmic plot of a normal EEG spectrum with a visible alpha peak at 10.9 Hz. (c)
Semi-logarithmic plot of an EEG containing tACS. Notice the peak at the stimulation frequency that
is 3 orders of magnitude above any physiological activity. Harmonics are visible at 20 and 30 Hz
concurrent stimulation, affecting both artifact removal strategies (such as template
subtraction or spatial filtering) and approaches that focus on uncontaminated frequency bands (e.g., tTIS, AM-tACS). Distortions of the ideal waveform by nonlinear
transfer effects can introduce (sub)harmonic components or the envelope frequency
of tTIS or AM-tACS stimulation into the EEG spectrum, complicating accurate
analysis of brain activity. To minimize nonlineariti
es, in transcranial electrical
stimulation, the choice of electrode type is critical. Typically, three different types
of electrodes are used: carbonized rubber electrodes enveloped in saline-soaked
sponges, bar rubber electrodes affixed with adhesive conductive paste, or Ag/AgCl
electrodes applied to the scalp with an appropriate electrolyte. Carbonized rubber
electrodes, however, are polarizable (Agrebi et al.,
Stecher et al., 2025),
leading to charge accumulation on their own that risks amplifier
2017; Zhu & Deegan, 2024;
saturation and inherently causes nonlinear response functions (Fig. 31.7). Therefore,
it might be preferable to use Ag/AgCl electrodes for stimulation, which are
470 H. I. Stecher et al.
Fig. 31.6 Example of EEG
signal drifting (naturally or
by applied stimulation into
the limit of the amplifiers
A/D range). In the clipped
region, all recorded samples
have the same value. Any
physiological information is
lost from this time period
Fig. 31.7 Example of
nonlinear component
response in a stimulation +
EEG setup. The gray line
shows the perfect digital
square-wave, before passing
through the digital/analog
converter, the stimulation
device, rubber electrodes,
EEG electrodes, and the
EEG amplifier. The black
line shows how this square
was recorded in the EEG.
Note the distortions at both
rising and falling edges of
the square
nonpolarizable. However, it should be considered that Ag/AgCl electrodes have a
comparatively higher price and limited lifespan (Langenbach et al., 2020).
On the stimulator side, the sampling rate of the generated signal must be sufficient
to avoid aliasing of the waveform in the EEG. If the stimulator’s sampling rate is
lower than that of the EEG, the recorded waveform will appear as a staircase,
introducing subharmonic components into the EEG spectrum. For optimal results,
especially when employing template subtraction for artifact correction (Vosskuhl
et al.,
2020), the recording and stimulation devices should be synchronized using a
shared clock-channel. Otherwise, even minor clock drifts between the systems can
cause phase divergence and distortions of the recorded waveform.
31 Combining EEG and Transcranial Electric Brain Stimulation 471
31.8 Conclusion
In conclusion, we strongly advocate for verifying that brain stimulation methods
effectively modulate brain activity by demonstrating changes in EEG recordings,
whether online or offline. As discu ssed, this necessitates specific recording hardware
and careful measures to eliminate or min imize artifacts.
As an EEG amplifier that can definitely cope with the voltages of tES without
into saturation, we can recommend the 24-bit actiCHamp by Brain Products.
going
We hope that readers find our suggestions helpful.
The website Combining EEG and tACS that is also linked from the Brain
Product
Conflicts of Interest
CSH
interest.
Funding
CSH was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research
Foundat
390895286. CSH was also funded by the research training group on
Neuromodulation of Motor and Cognitive Function in Brain Health and Disease
(RTG 2783).
s website lists some of our key papers on the topic:
https://uol.de/allgemeine-psychologie/combining-eeg-and-tacs.
holds a patent on brain stimulation. All other authors declare no conflicts of
ion) under Germany’s Excellence Strategy—EXC 2177/1—Projec t ID
References
Agrebi, F., Ghorbel, N., Ladhar, A., Bresson, S., & Kallel, A. (2017). Enhanced dielectric properties
induced by loading cellulosic nanowhiskers in natural rubber: Modeling and analysis of
electrode polarization. Materials Chemistry and Physics, 200, 155–163.
Aktürk, T., de Graaf, T. A., Güntekin, B., Hanoğlu, L., & Sack, A. T. (2022). Enhancing memory
capacity
Scienti c Reports, 12(1), 14199.
Antal, A., & Herrmann, C. S. (2016). Transcranial alternating current and random noise stimulation:
Possible
Antal, A., Kincses, T. Z., Nitsche, M. A., Bartfai, O., & Paulus, W. (2004). Excitability changes
induced
electrophysiological evidence. Investigative Ophthalmology & Visual Science, 45(2), 702–707.
Barry, R. J., & De Blasio, F. M. (2021). Characterizing pink and white noise in the human
electroencephalogram.
Benwell, C. S., London, R. E., Tagliabue, C. F., Veniero, D., Gross, J., Keitel, C., & Thut,
G.
on-task. Neuroimage, 192, 101–114.
Bergmann, T. O. (2018). Brain state-dependent brain stimulation. Frontiers in Psychology, 9, 2108.
Bergmann, T. O., Karabanov,
Combining non-invasive transcranial brain stimulation with neuroimaging and electrophysiol-
ogy: Current approaches and future perspectives. Neuroimage, 140, 4–19.
by experimentally slowing theta frequency oscillations using combined EEG-tACS.
mechanisms. Neural Plasticity, 2016(1), 3616807.
in the human primary visual cortex by transcranial direct current stimulation: Direct
Journal of Neural Engineering, 18(3), 034001.
(2019). Frequency and power of human alpha oscillations drift systematically with time-
A., Hartwigsen, G., Thielscher, A., & Siebner, H. R. (2016).