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# Sustained attention in attention-deficit subjects and the impact of binaural beat stimulation evaluated by behavior and EEG

Gabriel Alves Castro, Anne Bonnefond, Bich-Thuy Pham, Axel Hutt

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Gabriel Alves Castro, Anne Bonnefond, Bich-Thuy Pham, Axel Hutt. Sustained attention in attention-deficit subjects and the impact of binaural beat stimulation evaluated by behavior and EEG. Experimental Brain Research, 2025, pp.211. 10.1007/s00221-025-07154-0. hal-05012299

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https://inria.hal.science/hal-05012299v1

Submitted on 31 Mar 2025

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# Sustained attention in attention-deficit subjects and the impact of binaural beat stimulation evaluated by behavior and EEG

Gabriel Alves-Castro<sup>a,b,c</sup>, Anne Bonnefond<sup>c</sup>, Bich-Thuy Pham<sup>c</sup> and Axel Hutt<sup>a,b,*</sup>

<sup>a</sup>MLMS, ICube laboratory, University of Strasbourg – CNRS – Inria, NextMed Building, 2 rue Marie Hemm, 67000 Strasbourg, France

<sup>b</sup>MIMESIS, INRIA Center at University of Lorraine, NextMed Building, 2 rue Marie Hemm, 67000 Strasbourg, France

<sup>c</sup>INSERM UMR-S 1329 (Strasbourg Translational Neuroscience and Psychiatry), University of Strasbourg, 1 place de l'Hôpital, 67091 Strasbourg Cedex, France

\*: Corresponding author. Email: [axel.hutt@inria.fr](mailto:axel.hutt@inria.fr)

**Abstract:**

Recent research on binaural beat stimulation has raised the question whether it can improve sustained attention. Neurotypicals and subjects with attention deficits of single gender performed a visual attention task under auditory noise, monoaural and binaural beat stimulation, while recording electroencephalographic activity. We found that subjects with attention deficits perform with longer reaction times than neurotypical subjects. To explore EEG activity, two periods of interest were distinguished: before a correct detection and before a miss, supposed to reflect respectively moments of engagement versus disengagement of attention. Under noise stimulation, neurotypicals have larger frontal P300 and $\alpha$-power and lower parietal $\theta/\beta$ power ratio in correct trials than in missed trials, whereas subjects with attention deficits show the inverse relation. Moreover, neurotypicals exhibit a negative relation of frontal $\delta$-power and $\theta/\beta$ ratio in a time window of 6s before targets, whereas subjects with attention deficits show positively related $\delta$- and $\alpha$-power in this time window.

Binaural beats diversify these results. Neurotypical subjects respond with a longer reaction time compared to noise stimulation, while attention-deficit subjects respond equally. Moreover, frontal P300 and $\alpha$-power and parietal $\theta/\beta$ ratio resemble corresponding results under noise stimulation, whereas brain activity in subjects with attention deficits is rather heterogeneous. In addition, in attention-deficit subjects frontal and parietal $\delta$- and $\alpha$-power are positively related in a 6s time window before targets.

In sum, under noise stimulation we found behavioral and electrophysiological biomarkers, which were inverse in neurotypicals and subjects with attention deficits. Binaural beats break up these relations in both subject groups and they have not been found to be beneficial, neither in behavior nor in electrophysiological biomarkers.

**Keywords:**

EEG, sustained attention, binaural beats, attention deficit, continuous temporal expectancy task

**Highlights:**

* Under noise stimulation neurotypical and attention deficit subjects show inverse relationships in behavior and electrophysiological biomarkers

* Under binaural beats, attention-deficit subjects exhibit positively related $\delta$- and $\alpha$-power in a time window of 6s duration before targets.
* The parietal θ/β power ratio in neurotypicals is larger in missed trials than in correct trials and the inverse holds in attention-deficit subjects. This relation is robust to auditory stimulations.

# 1. Introduction

Attention deficits harm human's everyday life, e.g., yielding educational underachievement or diminished social interactions with psychiatric comorbidities such as eating disorders, anxiety or sleep disorders (French et al., 2024). Visual sustained attention refers to long-term visual focus and is related to vigilance, i.e. the ability to maintain a consistent behavioral response to task-related stimuli during continuous and repetitive activity (Huang et al., 2023). The frontal brain lobe plays an important role in visual sustained attention control, while it establishes strong functional connections to posterior brain areas. Since various brain functions are controlled in the frontal or posterior lobe and pathologies in these structures may yield deficits in sustained attention (DSA), these deficits also affect other brain functions. For instance, visual sustained attention has been found to affect motor control (Yuan et al., 2019; Karampela et al., 2020) and its deficit emerges in various mental disorders (Grant and Chamberlain, 2023), such as ADHD (Segal, 2023), schizophrenia (Hoonakker et al., 2017) and bipolar disorders (Harmell et al., 2014).

Today a broad range of possible medical treatments promise to remedy DSA. More and more the conventional treatment like pharmacological medication and psychotherapy is complemented by alternative techniques like electromagnetic neurostimulation or neurofeedback (Rubia et al., 2021). These latter techniques request a large technological effort and typically are offered to patients by specialized clinical institutions. In addition to these treatments recommended by professional medical doctors, in the internet publicly available sound and video files promote auditory beat stimulation (ABS) as beneficial do-it-yourself utilities to improve cognition and attention. Such ABS sounds may be binaural beats (BB), whose auditory tones have a single frequency presented on each ear with a frequency difference (called beat frequency) and a basic (carrier) frequency (Chaieb et al., 2015; Oster, 1973; Orozco Perez et al., 2020). As an alternative, auditory stimulation by monoaural beats (MB) have identical tones played on both ears, where the each tone superimposes a tone with the carrier frequency and a tone, whose frequency is the sum of carrier and beat frequency. In spite of its public prominence, the beneficial impact of ABS is still under discussion in the scientific literature due to its resulting diverse experimental performance in former studies (Klichowski et al., 2023; Melnichuk et al., 2025; Liu et al., 2022 ; Garcia-Argibay et al., 2019). Presumably the diverse results originate from non-standardized experimental parameters (Melnichuk et al., 2025). In the present work, we consider previous research studies indicating how to improve the choice of such experimental parameters. For instance, we optimized the combination of beat and carrier frequency to achieve a maximum sensitivity according to Perrot and Nelson (1969). There are also very few studies specifying the ABS sound volume (see e.g. Galvez et al., 2018), which however choose the sound pressure level (SPL) identical for each participant. Since each subject has her/his own auditory sensitivity and hearing threshold, we adapted the SPL of the ABS to each individual participant. Moreover, most studies performed experiments with gender-heterogenous groups to avoid a gender bias. Since the perception of BB has been reported to depend on the participant gender (Tobias et al., 1965; Oster, 1973), we decided to choose participants of a single gender to mitigate a possible heterogeneity in the subject groups.

The presented work aims to explore whether BB improves sustained attention in participants with and without attention deficits compared to a noise stimulation as control condition. To this end, the study identified the ABS impact on motor behavior and electrophysiological activity. In detail, we analyzed ABS impact on event-related components and the spectral power in different frequency bands in resting state. We found that the modification of the ratio of parietal θ/β spectral power with respect to participant groups and transitory attention level is negatively correlated to the frontal P300 component amplitude and α-spectral power under noise stimulation. Moreover, the modifications of
the θ/β ratio with respect to participant groups and transitory attention level were rather robust to ABS. Conversely, binaural beats heavily affect α-spectral power in participants with attention deficits compared to participants without attention deficits.

The subsequent section provides details on the participating subjects, the experimental paradigm and the statistical analysis applied. In the Results section, motor behavior and electrophysiological biomarkers are presented with respect to diverse experimental conditions under noise stimulation, monoaural and binaural beat stimulation. The major results are put into context and current literature in the following Discussion section also pointing out limits of the study and research perspectives. The final conclusion summarizes briefly the study's major insights and closes the work.

## 2. Material and Methods

### 2.1. Participants

Originally, the study comprised 22 male students of the University of Strasbourg (France). We have focused on male participants since own preliminary psychophysical studies before the experiment indicated dramatic differences in reaction times and errors between male and female participants in accordance to previous studies (Solianik et al., 2016; Riley et al., 2016; Alavi et al.; Efrat and Orna, 2022). This choice of subjects renders the participant group and consequently the statistical results more homogeneous. Participants were recruited by means of an online survey and, after acceptance, were rewarded by an allowance of 15 Euros / hour. All subjects provided informed written consent. For all subjects, exclusion criteria comprised the presence of neurological and/or psychiatric disorders, regular cannabis consumption, as well as the use of antidepressant and/or antipsychotic medications. Finally, after rejection of some subjects 14 subjects were considered between 19 and 29 years (mean age 24.2 years). By virtue of their age, the participants could be assumed to represent the population of young adults.

Selected participants were grouped according to the scores obtained from the Adult Self-Report Scale (ASR) (Kessler et al, 2005). The ASRS is a self-assessment scale for symptoms of Attention Deficit Hyperactivity Disorder (ADHD). It includes 18 items assessing the frequency of occurrence of inattention symptoms (9 items) and hyperactivity/impulsivity symptoms (9 items) over the past 6 months. For each item, the subject had to choose from five possible responses (never, rarely, sometimes, often, very often), scored from 0 to 4, respectively. Two scores are obtained, one for inattention and the other for hyperactivity/impulsivity. A high score (> 23/36) indicates a strong likelihood of presenting the symptom. The control group in the present study consisted of subjects with a score of 16 or lower on the 9 items evaluating inattention symptom (reflecting a low probability of presenting this symptom) and a score of 16 or lower on the 9 items evaluating hyperactivity/impulsivity symptoms (reflecting a low probability of presenting these symptoms). The inattention group consisted of subjects with attention deficits (or an inattentive trait), as evidenced by a score of 24 or higher for inattention symptom (reflecting a high probability of presenting this symptom) and a score of 16 or lower for hyperactivity/impulsivity symptoms. This led to 7 subjects in the control (mean age 24.4 between 19 and 29 years) and 7 subjects in the inattention group (mean age 24.3 between 21 and 28 years).

All the personal data was encrypted with a code prepared in Python3 and the Cypher package by the authors before they were shared with collaboration partners. The key was maintained in security in a proper place, and was not registered at the same repository as the encrypted data.

### 2.2 Attention task
Attention was measured by means of the continuous temporal expectancy task (CTET) (O'Connell et al., 2009), a sustained visual attention task which included a patterned stimulus presented in the center of a screen with gray background (Fig. 1(A)). This stimulus underwent a change of patterns at regular intervals, resulting in a continuous stream of images. The key task was to monitor the temporal duration of each presented image and to detect rare target images. The standard images were presented for a duration of 800ms and the target images for 1120ms.

<figure><img src="image_3.png" /><figcaption>Figure 1: Visual attention task. (A) Subjects performed the continuous temporal expectancy task (CTET) presenting changing patterns of duration 800ms in standard trials and 1120ms in target trials. (B) Before the main experiment, subjects passed a training phase with a short 5min period of CTET to get to know the experiment, a test phase to determine the optimal loudness level of auditory stimulation and an adaption phase to noise stimulation of 4 minutes.</figcaption></figure>

The pattern stimulus consisted of a single square divided into a grid of identical square tiles, each one diagonally split into black and white halves. The tile orientation shifted by 90° randomly clockwise or counter-clockwise yielding four distinct patterns. Stimuli were pseudo-randomly presented such that there were between 4 and 10 standard images presented after each target image. Participants were asked to press a response key (character 't' on a French keyboard) as quickly as possible when they detected a frame of longer duration (target image).

## 2.3 Auditory stimulation

In general, music affects the cognitive function of humans (Gupta et al., 2018) and, played in the background, has an effect on sustained attention (Kiss and Linnell, 2021). Specifically, white noise (Egeland et al., 2023) and colored noise (Nigg et al., 2024) has been shown to improve behavioral performance in attention-deficit subjects. In our experiment, we chose pink noise as auditive stimulation in the control condition termed *noise condition* in the following. This noise type is a specific colored noise with a comfortable sound (like light rain).

Moreover, *binaural beats* (BB) have been found to affect the mental state of human subjects (Atwater, 1997). They are stereo signals, which represent mono-frequency sinusoidal signals with a different frequency on each hearing side (Ingendoh et al., 2023). In detail, the frequency on one side represents the so-called carrier frequency and the frequency on the other side is the sum of the carrier frequency and a small so-called beat frequency. According to (Perrot and Nelson, 1969), there is an optimal combination of carrier and beat frequency. We chose the carrier frequency to 500Hz and the beat-frequency in the *β*-frequency range to 15Hz. This lead to a stereo-signal with frequency 500Hz on one side and 515Hz on the other. Since it is known that oscillatory auditory stimulation signals entrain brain rhythms (Orozco Perez et al., 2020), it was interesting to distinguish the binaural effect with the effect by two superimposed oscillatory signals of different frequencies. Such a signal was presented on both hearing sides synchronously. This signal provided a so-called *monoaural beat* (MB) stimulation (Becher et al., 2015) and represented a control variant to the binaural signal.

Then the final binaural and monoaural stimulation was the scaled sum of both pink noise and beat signal and pink noise and monoaural signal, respectively. Before summing up, both signals were normalized to identical variance.
For each subject, the personal hearing threshold and the most comfortable loudness level was estimated by step-wise increase (step size 5dB) of a test signal's amplitude. This test signal was pink noise. The signal's amplitude has an important impact on the subject's response to binaural beats (Oster, 1973) and hence was controlled by computer software (Audacity v3.2). The sound loudness was estimated by the signal's sound level pressure estimates (SPL) controlled by the software (see Appendix A). The subject-individual most comfortable SPL was chosen as the loudness level during the experiment for all auditory stimulation types, i.e., noise, superposition of pink noise and MB (called monoaural or MB in the following) and superposition of pink noise and BB (called binaural or BB in the following). These values were found between 45dB and 75 dB (mean 60.0dB, standard deviation 9.8dB) in the control group and between 45dB and 80dB (mean 64.2dB with standard deviation 12.9dB) in the inattention group.

We mention that, in a survey after the experimental sessions, participants reported the BB as disturbing and stressful.

## 2.4 Experimental paradigm

Each subject started an experimental session with a learning phase of the paradigm of 45 trials lasting 5 minutes, while no auditory stimulation was present (Fig.1(B)). The subject could continue with the session only if he detected all trials. All subjects considered in the subsequent analysis passed this test. This phase was followed by an estimation of the optimal loudness during the next 3 minutes while hearing pink noise.

Then, the subject was asked to just listen to noise to allow to reach a possible steady-state brain entrainment (Hunag and Charyton, 2008). In the subsequent experimental phase, the subjects were asked to perform the task in 3 sequences of 225 trials each, i.e., the presentation of 3x225 images, under auditory noise stimulation. This phase was followed by an experimental phase of 4 sequences, i.e. 4x225 trials, while hearing MB or BB sounds. Extended offline data analysis based on behavioral data could not detect any transient performance, which indicated stationary behavior and stationary brain responses.

To distinguish the impact of MB and BB stimulation, each subject performed two sessions. Only the first session included the task learning phase and the loudness test each as described before, together with the noise and oscillatory (monoaural or binaural) stimulation. In the second session, the subjects performed the noise learning phase and interchanged the oscillatory stimulation type. These two sessions were performed with a delay of 2 weeks to minimize any possible learning effects in the first session. The sequence of MB and BB stimulation in both sessions was chosen randomly for each subject.

## 2.5 Behavioral data and statistical analysis

The subjects were asked to press a button, when they detected the target image which was presented for a longer time than the standard image. The reaction time (RT) is the time between button press for target images and the screen occurrence of the image reduced by 800ms (the presentation time of a standard image). It is called a *correct* trial if the subjected detected correctly the target image with a reaction time shorter than 2s. If the subjects waited longer than 2s after the image screen occurrence, the presentation trial is counted as *missed* trial. Other button presses are called *false* trial.

Visual attention is a high-dimensional phenomena and its degree may be quantified by several statistical measures or biomarkers. A prominent biomarker is the average RT of correct trials of a subject. Another biomarker was the sum of the number of missed and false trials relative to the number of correct trials. This relative error is high for a large number of errors or a low number of correct trials compared to the number of errors. The relative error is low when subjects performed well with large number of correct trials and relatively low number of errors.

RTs are known to obey a non-Gaussian gamma function-like distribution and histograms of relative errors are also non-Gaussian (test not shown). Consequently, we deployed non-parametric statistics
computing medians of RTs and relative errors and applied non-parametric Mann-Whitney U-tests (MWU) to test on statistical differences between two distributions of RT and of relative errors. Non-parametric ANOVAs (np-ANOVA) were performed by deploying the Kruskall-Wallis test (KW), which provided a corresponding *H-value*. Significance level of all tests was α=0.05 and all statistical tests were performed by utilizing the Python3 module `scipy`.

## 2.6 EEG recording and statistical analysis

Electroencephalogram (EEG) recordings were collected using the *BioSemi ActiveTwo System* (Amsterdam, Netherlands) with 64 Ag/AgCl electrodes mounted according to the standard 10–20 system. The reference electrodes were the subject’s left and right ear and the average of the electrode signal’s difference to these electrodes represented the EEG signal under study. The sampling rate was 2048Hz, a band-pass forward-backward IIR-filter of 0.01 to 30 Hz and a notch filter at 50Hz was applied offline before the analysis with proprietary software based on Python3 modules such as ` numpy` and `mne`. Blinks and horizontal eye movements were removed using semi-automatic ICA ocular correction complimented by a linear detrending.

Event-related potentials (ERP) represented averages over EEG time series temporally aligned at image onset with a pre-stimulus baseline of 200ms. Since the present study focused on the preparatory phase of target presentation and not on how targets are detected or missed, the analysis considered a time window of 800ms after target presentation. A well-known signal feature reflecting the brain activity during preparation and thus the state of the brain is the trial-averaged amplitude of the P300 (or short P3) component. These ERPs were computed from about 240 trials for the given time window and chosen parameters of artifact rejection. Since the trial distribution of EEG time series may not be normal-distributed, we also computed ERPs as medians and applied MWU and KW to detect significant differences. Essentially, we computed the P3 amplitude as averages of trial medians over the time window [200s,320s] at the frontal and parietal electrode Fpz and Pz, respectively.

Investigating the spectral power, it was estimated in the windows of 4s duration before target presentation. The Fourier Transform of single-trial EEG time series provided single-trial Periodograms and their median over trials led to the trial-averaged power spectrum. The number of trials considered depended on the experimental condition and the subject group and was in the range between 240 and 5300 trials. Since the spectral power distribution of EEG time series is known to be non-normal, the statistical evaluation applied MWU and KW to detect significant differences. The power in the different frequency bands in each trial was defined as the mean in the frequency interval [0.25Hz;4.0Hz] (δ-band), [4.0Hz;8.0Hz] (θ-band), [8.0Hz;12.0Hz] (α-band) and [12.0Hz,25.0Hz] (β-band). The statistical analysis considered the spectral power in the frontal and parietal electrode Fpz and Pz, respectively. Besides the statistical evaluation in the δ-band and the α-band, which are known biomarkers in sustained attention (Da Silva Junior et al., 2019; Ko et al., 2017), in addition we estimated the θ/β-ratio as another well-known indicator of sustained attention (Putman et al., 2014). The statistical analysis of this ratio was based on medians over trials and applied MWU and KW for significant tests (α=0.05).

Statistical tests on differences between experimental conditions in the δ-and the α-band power and the θ/β-ratio separately does not permit to reveal how δ-and the α-band power and the θ/β-ratio depend on each other. Typical parametric correlation measures may not be applicable to estimate relations between these quantities since their distribution may be non-Gaussian or their correlation may be nonlinear. To this end, we chose the non-parametric Spearman rank-order correlation ρ, which evaluates the monotonicity between two distributions. It takes values between ρ = -1 and ρ = 1, where -1 (+1) indicates a maximum negative (positive) monotonic relationship. Negative (positive) monotonicity states that large values of one variable indicates small (large) values of the other variable. The closer ρ is to zero, the less monotone is the relationship and thus ρ = 0 indicates a non-monotonous relation between two variables. To ensure the significance of the estimated correlation
coefficient ρ, we performed a permutation test utilizing all sample pairs of both variables to gain a solid estimation of the null hypothesis of a missing monotonicity. The resulting p-value provides insights whether the estimated value of ρ is significantly different from zero (α=0.05). To perform this test, we employed the Python3 module scipy. Moreover, we plotted samples from one variable with respect to the other variable together with a linear function fit to the data. This linear function just illustrates positive (negative) correlation values by its positive (negative) slope. Only data with significant monotonic relation are visualized. In this correlation analysis, we analyzed spectral power distributions in the windows [-6s;-2s] and [-4s;0s] before target presentation. onset. These different time windows permit to address the question how long in advance of the target presentation the power spectrum correlation is present.
# 3. Results

## 3.1 Behavioral data

The np-ANOVA performed on response time (RT) for noise and BB stimulation revealed a significant main effect of group (H=68.9, *p* < 0.005). Subjects of the inattention group exhibited longer RT than subjects of the control group (Figure 1A). Distinguishing effects of the auditory stimulation, a np-ANOVA in the noise condition revealed that RT were significantly larger in the inattention group than in the control group (H=74.6, *p*<0.005), whereas RTs were undistinguishable in both groups under BB stimulation (H=3.3, *p*=0.06), see Figure 1B. This difference between both conditions indicated an interaction between the group and condition. Moreover, subjects of the control group exhibited longer RT during BB stimulation than during noise stimulation (H=15.2, *p*<0.005), whereas no difference was observed in subjects of the inattention group (H=0.6, *p*=0.66).

The np-ANOVA performed on relative errors for noise and BB stimulations revealed significant higher relative errors in the inattention group compared to the control group (H=7.9, *p*<0.005), see Figure 1C. Taking a closer look, this increase in relative errors could be found under BB stimulation (H=4.0, *p*<0.05), whereas noise stimulation yielded statistically indistinguishable relative errors in both groups (H=2.35, *p*=0.12), see Figure 1D.

<figure><img src="image_4.png" /><figcaption>Figure 2: Behavioral statistics. Subjects in the inattention group show a significantly larger RT (panel A) and more errors (panel C) compared to control subjects. Detailed analysis indicates an interaction between group and condition, where different stimulations impact RT (panel B) and relative errors (panel D) differently.</figcaption></figure>

## 3.2 ERP data

At first, we considered the frontal P3 amplitude under noise stimulation, cf. Fig.3. Subjects in the control group exhibited a reduced amplitude before a missed target compared to a correct detection (H=362, *p*<0.005). Conversely, the inattention group responded by larger amplitudes (H=75, *p*<0.005). Moreover, before a correct detection, subjects of the inattention group responded with lower P3 amplitudes than control group subjects (H=359, *p*<.05). However, before a missed target, amplitudes were increased in the inattention group compared to the control group (H=136, *p*<0.005), see Figure 3 B(a). These results indicated that there is a strong interaction between group and detection type (correct/missed).

Under BB stimulation, in both the control and inattention group missed targets exhibited lower amplitudes compared to a correct detection (H<sub>ctrl</sub>=356, *p*<0.005; H<sub>inatt</sub>=15.8, *p*<0.005). Moreover, before a correct detection, amplitudes were reduced in inattention subjects compared to control group subjects (H=4.9, *p*<0.05). However, before a missed target, amplitudes in the inattention group
were larger than in the control group (H=334, p<0.005), see Figure 3 B(b). As for the noise stimulation, the results indicated a strong interaction between group and detection type.

In the parietal electrode Pz, the EEG-activity in the P3-time window resembles qualitatively the frontal electrode and their modification in groups, conditions and detection types. The only prominent difference occurs in the BB condition, where correct trials have a larger P3 amplitude in the inattention group than in the control group (H=225, p<0.005).

<figure><img src="image_5.png" /><figcaption>Figure 3: Event-Related Potentials (ERP) in target trials in the time window [0ms;800ms] after target presentation. (A) Time series of medians of subjects in the control group (black) and the inattention group (red). Panels in the top and low row show ERPs from correct and missed trials, respectively. (B) Box plots of trials distributions of P3 amplitudes and markers of significant differences (horizontal brackets) with p<0.05.</figcaption></figure>

## 3.3 Spectral power

Attention is known to modulate α-power (Misselhorn et al., 2019) and δ-power (Guich et al., 1989) in frontal electrodes. At first, let us consider the power spectrum at the frontal electrode, cf. Fig.4. Under noise stimulation, we found that missed targets exhibited reduced α - power compared to detected targets in control subjects (H=87, p<0.005), whereas they showed increased α - power in inattention subjects (H=17.7, p<0.005). Moreover, missed targets lead to reduced α-power in the control group compared to subjects of the inattention group (H=99, p<0.005), whereas correctly detected targets yield the inverse relation (H=9.7, p<0.005). The parietal electrode showed similar spectral power differences for missed targets, whereas its α-power before correctly detected target tasks were statistically indistinguishable in the control and inattention group (H=3.5, p=0.06), but showed the same tendency.

Regarding the frontal δ-power, in the control group the statistical differences between correctly detected and missed trials resemble well the differences in α-power. Moreover, differences between control and inattention subjects also resembled well to differences in α-power. The exception was the δ-power in missed trials, which is statistically indistinguishable in both subject groups (H=2.1, p=0.14).
At the parietal electrode, under noise stimulation α- and δ-power behave similarly. In correctly detected trials, the control and inattention group is statistically indistinguishable (H=0.11, p=0.73 (α-power); H=3.53, p=0.06 (δ-power)), while missed trials exhibit larger δ- and α-power in the inattention group as in the control group (H=15.5, p<0.001 (α-power); H=158.3, p<0.001 (δ-power)). Moreover, missed trials exhibit lower power (H=122.5 (α-power), H=121.0 (δ-power), p<0.001) than correct trials in the control group. Different power relations occurred in the inattention group, where α-power was higher (H=10.0, p<0.05) and δ-power was lower (H=16.4, p<0.001) in missed trials compared to correct trials.

During BB stimulation, the frontal α- and δ-power was reduced before missed trials compared to correct trials in both the control (H=14.0, p<0.005) and the inattention group (H=23.9, p<0.005). Moreover, the inattention group exhibited larger α- (H=31.0, p<0.005 for correct targets and H=12.9, p<0.005 for missed targets) and δ-power (H=12.4, p<0.005 for correct targets and H=1.3, p<0.005 for missed targets) than the control group in both detection types.

In the parietal electrode, both α- and δ-power dropped before missed trials (H=18.4, p<0.05 and H=6.3, p=0.01, respectively) compared to correct trials in the control group, whereas subjects in the inattention group did not exhibit α-power (H=0.18, p=0.66) and δ-power differences (H=0.09, p=0.76) between correct and missed trials. Moreover, α-power was not significantly different before correct targets (H=1.3, p=0.3) in the control and inattention group, but was larger in the inattention group before missed targets (H=10.1, p<0.005). Conversely, the δ-power before correct targets in the inattention group was smaller than in the control group (H=17.4, p<0.005), whereas subjects in the control and inattention group exhibited statistically indistinguishable δ-power (H=0.09, p=0.9) before missed targets.
<figure><img src="image_6.png" /><figcaption>Figure 4: Spectral power in the 4s-interval before target presentation. (A) Spectral power distribution of trial medians of subjects in the control group (black) and the inattention group (red). Panels in the top and low row show power distributions of correct and missed trials, respectively. (B) Box plots of spectral power in the α-band (top row) and the δ-band (bottom row). In each panel, box plots on the left (right) hand side give results from correctly detected (missed) trials. Markers of significant differences are visualized by horizontal brackets (p<0.05).</figcaption></figure>

## 3.4 θ-β ratio

The θ/β ratio is supposed to reflect cognitive processing in attention tasks (Picken et al., 2020) and we analyzed how this ratio depends on subject groups, detection and auditory stimulation types, see Fig.5. During noise stimulation before a correctly detected trials, both frontal and parietal θ/β ratios were reduced in the control group compared to subjects of the inattention group (frontal: H=23.4, p<0.005; parietal: H=36.0, p<0.005). Before missed trials, only the parietal θ/β ratio differed between the two groups: it was reduced in the inattentive group compared to subjects of control group (H=7.2, p<0.05). Moreover, in the inattention group both the frontal and parietal θ/β decreased before missed targets (frontal: H=10.9, p<0.005; parietal: H=13.7, p<0.005). In the control group, the parietal θ/β before missed targets were larger than before correct targets (H=14.1, p<0.005), frontal θ/β is statistically indistinguishable in both detection types (H=2.3, p=0.13).

During BB stimulation, only the parietal θ/β differed between the two subject groups: before correctly detected trials, the ratio was reduced in the control group compared to the inattentive group (H=5.4, p<0.05), but increased in the control group compared to the inattentive group before missed trials
(H=3.9, p<0.05). Moreover, in the attention group the θ/β ratio decreased before missed targets (H=8.4, p<0.05).

<figure><img src="image_7.png" /><figcaption>Figure 5: θ/β power ratio in the time window 4s before target presentation. The box plots in the panels provide the statistical trial distributions under noise (left) and BB (right) stimulation. Markers of significant differences are visualized by horizontal brackets (p<0.05).</figcaption></figure>

## 3.4 Prediction of spectral relations

After analyzing spectral features separately, we investigate relations between the α- and δ-power values and the ratio θ/β and whether such relations may evolve over time. To this end, we analyzed correlations in the time interval [-6s;-2s] and [-4s;0s] before target presentations. Significant Spearman coefficients (see Methods) indicated a monotonic relationship between spectral features, while this relationship may be linear or non-linear. Figure 6(A) demonstrates that δ- power and the ratio θ/β in the frontal region had a significant negative relationship (p<0.05) to each other in the control group in both time intervals before correct and missed targets during noise stimulation. Since this negative relationship was present in both time windows, it was present for a duration of 6s before target presentation.

In the inattention group, this inverse correlation between δ- power and the θ/β-ratio is not present anymore. Instead, a positive Spearman coefficient between α- and δ- power in both time windows before correct targets indicates a monotonical positive relationship between both frequency band power values (Fig.6(B)). Such a correlation is found both in the frontal and parietal region during noise stimulation. Moreover, this relationship shows qualitative accordance to the frontal region during BB stimulation. However under BB stimulation this relationship was not found in the same time windows before correct targets in the parietal region. There, the negative relationship of δ- power and θ/β-
ratio 6s before correct targets (Spearman coefficient of -0.2, p<0.05) switched to a positive relationship in the time window 4s before target presentation (Spearman coefficient of +0.2, p<0.05). Moreover, in both time windows before missed targets BB stimulation induced a positive relationship between α- and δ- power both in the frontal and parietal region.

<figure><img src="image_8.png" /><figcaption>Figure 6: **Statistically significant monotonicity relations between spectral features.** (A) Relations in the control group. (B) Relations in the inattention group. All results shown exhibited statistically significant relations with corresponding Spearman coefficient (numbers next to lines) for the pre-stimulus time interval [-4s;0s] (black) and [-6s;-2s] (red) before target presentations. The lines result from linear regression and just serve as illustration for the corresponding feature relations. More statistically significant correlations have been found, but the shown relations are the only to be present in both pre-stimulus time intervals.</figcaption></figure>

## 3.5 Monoaural stimulation

In the previous paragraphs we showed how BB stimulation impacted on behavior and brain activity. This raised the question whether this impact just resulted from the fact that the stimulation is oscillatory (in contrast to noise stimulation) or whether the specific choice of oscillatory stimulation affects the brain activity. To this end, we compared the gained results on behavior and brain activity under BB stimulation with results gained under MB stimulation. Figure 7(A) demonstrates that MB
stimulation yielded significantly shorter RT than for BB in the control group (H=10.8, p<0.005), but larger RT in the inattention group (H=6.8, p<0.05). Relative errors were statistically indistinguishable between BB and MB stimulation in both subject groups (control group: H=0.03, p=0.85; inattention group: H=2.2, p=0.14).

Taking a closer look at the brain activity, the P3-amplitude was significantly lower under MB than BB stimulation (H=33.3, p<0.005) in the inattention group. This held in both frontal and parietal activity. Conversely, the control group did not exhibit any statistically significant differences in P3 amplitudes between BB and MB stimulation and this held true in frontal and parietal activity (H=0.11, p=0.73 in frontal region; H=3.67, p=0.055 in parietal region).

Moreover, α- and δ- power were significantly lower under MB stimulation compared to BB stimulation in frontal activity in both subject groups (α-power: H=212, p<0.001 in control subjects and H=250, p<0.001 in inattention subject; δ-power: H=22.2, p<0.001 in control subjects and H=82, p<0.001). In parietal activity, α-power under MB stimulation was lower than under BB stimulation in the control group (H=5.2, p=0.02), whereas in this subject group δ- power was statistically indistinguishable under both stimulation types (H=1.9, p=0.17). In the inattention group, parietal α-power was statistically indistinguishable under both stimulation types (H=2.9, p=0.09), whereas δ-power under MB stimulation was higher than under BB stimulation (H=41.0, p<0.001).

The power ratio θ/β is supposed to be informative on cognitive processing during attention. We found that this ratio in frontal activity was statistically indistinguishable under MB and BB stimulation (H=3.6, p=0.06 in the control group; H=2.9, p=0.08 in the inattention group). In the parietal activity, the ratio θ/β was also statistically indistinguishable under both stimulation types in the inattention group (H=1.23, p=0.26). Conversely, in the control group the ratio θ/β was lower under the MB than BB stimulation (H=18.1, p<0.001).

<figure><img src="image_9.png" /><figcaption>Figure 7: Comparison of binaural and monoaural stimulation impact. Results are shown in correct trials only and the statistical comparison between the control and inattention group is not shown. Corresponding differences under BB stimulation may be read off previous figures.</figcaption></figure>
## 4. Discussion

The most prominent finding in our statistical analysis of behavioral and EEG data is the strong interaction between most experimental conditions. Rarely, there were effects which held for several experimental conditions. Consequently, statistical results were heterogenous, fundamental insights not very obvious and difficult to identify, although they exist. In the subsequent paragraphs we state clearly the homogenous effects holding for several different experimental conditions. Moreover, we point out few heterogeneous effects, which held under some experimental conditions only but which we considered to be insightful. Other findings, although observed and presented in the Results section, received less attention in the following.

### The attention state under noise stimulation

By considering the differences in performance between the two subject groups, i.e. without taking into account the experimental conditions, our results revealed that subjects in the inattention group behaved significantly different to subjects in the control group. They performed poorer than control subjects in terms of both RT and errors, which is in accordance to previous studies (Mazor-Karsenty et al., 2019). Under noise condition, only the effect on RT is prominent. As longer RTs are often interpreted, in detection tasks, as a behavioral consequence of attentional disengagement, these results suggest a tendency towards a greater frequency of transient moments of attentional disengagement during the performance of CTET under noise stimulation, in subjects with attention deficits.

Besides behavioral performance, the analysis of electrophysiological biomarkers first allowed to investigate the correlates of attentional processes involved during a temporal discrimination task at the nearest error (i.e. the frontal and parietal P3 in correct and missed trials). In the control group, under noise stimulation, our results are in line with previous studies using the same task, in which the frontal and parietal P3 amplitude was also found to be reduced in missed trials compared to correct trials (O'Connell et al., 2009; Chidharom et al., 2021; Jonkmann et al., 1997; Smart et al., 2014). There is some evidence that missed trials reflect lapses of attention (Pinggal et al., 2022). Assuming that ERP-component P3 reflects neural mechanisms underlying the continuous deployment of attentional resources to the time domain, i.e., the sustained attention to stimulus duration, in sum our results indicate a brief disengagement of these mechanisms immediately before a behavioral lapse. More surprisingly, in subjects of the inattention group, the results profile is reversed, i.e., missed trials under noise stimulation exhibited larger P3 amplitudes than correct trials in both frontal and parietal electrodes. This affirms findings in pre-school children with ADHD (Tao et al., 2024) but contrasts to previous studies indicating that the older adults with ADHD have a smaller P3 amplitude in parietal electrodes (Szuromi et al., 2011). For illustration, Fig. 8A summarizes these results pointing out that the combinations (correct trials/control group) and (missed trials/inattention group) yield large P3 activity and the combinations (correct trials/inattention group) and (missed trials/control group) yields low P3 activity. To our best knowledge, no previous experimental study has reported this inversion before. A possible reason may be that no study has employed the CTET with subjects with attention deficits yet. While they should be treated with caution, P3 amplitude differences being relatively small, our results in this group of subjects could suggest that missed trials might take place at an earlier stage of processing, like the reduced attention allocated to the visual stimulus (as reflected by reduced P1 and N1 components, see Luck et al., 1990; Di Russo et al., 2003).
<figure><img src="image_10.png" /><figcaption>Figure 8: Illustration of the relative power of biomarkers in different brain states and subject. The biomarkers are the frontal P3-amplitude (left column), α-power (center column) and the parietal θ/β ratio (right column) for each combination of brain state ('correct' and 'missed' trial) and subject type ('control' or 'inattention' group). Arrows from one state/subject combination to another denotes an increase of the corresponding biomarker value. The circled '-' sign at a state/subject combination indicates a state, whose biomarker value is minimum compared to the value of a neighbor combination. Similarly, circled '+' sign describes a state maximum biomarker value compared to its neighbors. All black biomarker changes are statistically significant (p<0.05), whereas the grey arrow reflects a tendency (0.05<p<0.1).</figcaption></figure>

Results regarding α-power are comparable in every respect to those obtained on P3. In the control group, under noise stimulation, α-power is reduced in missed trials compared to correct trials, while the results profile is reverse in subjects of the inattention group. They therefore confirm, in both groups, the strong relation between P3 components and pre-stimulus resting state α-power (Studenova et al., 2023; Polich, 1997). More interestingly, the more direct comparison of the two groups reveals that brain activity in correct trials exhibit lower α-power in the inattention group than in the control group in accordance to previous studies (Deiber et al., 2021; Woltering et al., 2012). The inverse holds true for missed trials, whose resting α-power in the inattention group is larger than in the control group. Figure 8B summarizes these results for frontal activity and reveals the similarity of P3 and α-power. We observe that the combinations (correct/control) and (missed/inattention) yield large α-power activity and (correct/inattention) and (missed/control) yields low α-activity. High alpha power has been associated with reduced perception of sensory stimuli and a state of internal orientation favoring mind wandering and loss of attention (Mathewson et al., 2009; Ros et al., 2013; Sigala et al., 2014; van Dijk et al., 2008). Hence, we conclude that all these results could suggest the involvement of different neural mechanisms in the occurrence of lapses in control and inattentive subjects.

The role of the power ratio θ/β in attention is still under discussion (Barry et al., 2003; Barry et al., 2004) and recent evidence indicates a relation to cognitive processing during attention (Barry et al., 2009; Picken et al., 2020). We found in correct trials a decreased ratio in the control group compared to the inattention group in accordance to literature (Woltering et al., 2012; Luo et al., 2023). Moreover, in the inattention group missed trials exhibit a lower θ/β ratio than correct trials. These findings hold in both frontal and parietal activity. There is also a tendency in parietal activity that missed trials in control groups have larger θ/β ratios than in correct trials and in the inattention group. In sum, the combination (correct/control) and (missed/inattention) yielded low θ/β ratios, whereas the combinations (correct/inattention) and (missed/control) exhibit high θ/β ratios, see Fig.8C. Comparing to Fig.8A and B, effects highlighted on the θ/β ratio are completely opposite to those obtained on α-power and P3 in all states and subject groups.
In sum, a high level of attention can be assumed in control subjects (due to short RT) during correct trials. The corresponding neurophysiological activity exhibited high P3 amplitude, high α-power and low θ/β ratios. As clearly visible in Fig. 8A-C, however, these biomarker values also occured in missed trials of inattention subjects. Consequently, these biomarkers are not sufficient to reflect the level of attention. Hence, it is necessary to consider additional biomarkers to describe the attention level, e.g. the δ-power. The modification of δ-power in different trial types and subject groups was rather heterogenous and did not fit to the picture based on frontal P3 amplitude, α-power and parietal θ/β ratios. We found a statistically significant negative correlation between frontal δ-power and θ/β ratios in control subjects up to 6s before target presentation, while no such correlation between δ-power, P3 amplitude and α-power was statistically significant. Moreover, inattention subjects exhibited a significant positive relationship between frontal δ- and α-power in correct trials in a 6s time window before target presentation, while no such relationship was significant in missed trials. In agreement, such a coupling between δ- and α-activity has also been found in and between several regions (Lukarski et al, 2023). The δ-α relationship emerges in inattention subjects in correct trials only and resembles previous results in visual memory tasks in neurotypicals (Aliramezani et al., 2024). This let us conclude that the correlations of frontal δ-power with frontal θ/β ratio and with α-power, together with frontal P3 amplitude, frontal α-power and parietal θ/β ratios, are important biomarkers to distinguish levels of attention under noise stimulation.

## Binaural beat stimulation

After identification of biomarkers under noise stimulation, the question rises how findings change under auditory beat stimulation. Under BB stimulation, RT and relative errors in the inattention group had the tendency to be larger than in the control group in accordance to the behavior under noise stimulation. Moreover, BB stimulation slowed down the response times in the control group compared to noise stimulation in accordance to previous findings (Robison et al., 2022). Interestingly, BB did not affect the error rate in the control group, which however contrasted to previous studies showing lower error rates (Engelbregt et al., 2021).

The frontal P3 amplitude under BB stimulation decreased in missed trials compared to correct trials in the control group, which is similar to the frontal P3 amplitude under noise stimulation and in agreement with previous studies (Deiber et al., 2021; Woltering et al., 2012), cf. Fig. 8D. In inattention subjects we also found correct trials with larger P3 amplitude than in missed trials, which contrasts to findings under noise stimulation. Comparing frontal α-power under BB stimulation (Fig. 8E) and under noise stimulation (Fig. 8B), we observed that both exhibit minimum α-power in missed trials in control subjects. This minimum was the only equivalent α-power feature when comparing both stimulation types.

Interestingly, the modifications of parietal θ/β ratios under BB stimulation resembled very much the modifications under noise stimulation (cf. Fig. 8F) revealing its robustness under noise and BB stimulation. This different impact of BB stimulation compared to P3 and α-power indicate, that θ- and β-activity obeys different underlying neural processes compared to P3 responses and α-activity.
These results are accompanied by a statistically significant frontal and parietal δ-α relationship in correct and missed trials observed in inattention subjects. This contrasts to noise stimulation, which does not show such a δ-α relationship in missed trials.

BB combine two frequencies in a rather specific way. Previous studies indicate that the BB's effect goes beyond the sole presence of a beat frequency, e.g., as present in MB stimulation. For a MB stimulation, we observe a slightly different impact compared to BB stimulation. The RT in control subjects improved under MB stimulation compared to BB stimulation, but responses slowed down in inattention subjects. Moreover, no statistically significant differences in the relative errors were observed in our study. These results contrast to a previous study (Engelbregt et al., 2021), where no statistically significant modifications in response times but larger errors were found under MB stimulation. Moreover, the
frontal P3 amplitude and frontal α-power were lower under MB stimulation in correct trials in both subject groups. Finally, MB stimulation decreased the parietal θ/β ratio in control subjects during correct trials in comparison to BB stimulation, the parietal θ/β ratio in inattention subjects did not change.

In sum, BB and MB stimulation poorly influenced RT and behavioral errors, but affected heavily the frontal P3 amplitude and several spectral features. This strong impact is heterogeneous in control and inattention subjects. Moreover, participants reported a disturbing impression by BB. At a first glance, this was surprising to us, since we optimized the stimulation sound level to an individual comfortable level. However, it is known that uncomfortable sounds compared to comfortable sounds induce stronger variations of attention at lower sound levels (Liu et al., 2020). This might explain the neutral or partially negative impact of BB and the consequent lower attention level.

## Limits and perspectives

The obvious limit of the present study to mention is the low number of control and inattention subjects. Under some conditions, these low numbers led to statistically insignificant results however close to the significance threshold, i.e. with a certain tendency. The comparison of experimental conditions with such tendencies makes an interpretation difficult, larger numbers of subjects may render inference tests more clear.

We also mention the gender-based bias of the gained results by only male participants. This choice was taken by purpose to reduce a possible gender-based heterogeneity of results. Future experimental studies will perform an identical experimental paradigm with female participants and a gender-balanced group of subjects to evaluate the gained results in the present work.

Moreover, some subjects reported the BB stimulation to be unpleasant after some time. This may have diminished the individual subject's attention and may thus explain the larger RT in control subjects under binaural stimulation. Although we controlled the subject-specific sound intensity by an initial experimental check of the pleasant sound pressure level, the subjects' feedback on disturbances by BB stimulation points out that the sound intensity represents an important stimulation parameter. To our knowledge, previous experimental studies rarely reported an optimal sound pressure level adaption, which however should be performed. In future work, this sound pressure level will be chosen much lower or, alternatively, the sound level of BB relative to the stimulation's noise intensity will be chosen to lower values. In addition, future work will cover the low BB stimulation by prominent comfortable sounds or music as performed in commercial BB products.

## 5. Conclusion

The effects of sound on humans have been studied for about a century. In recent years, publicly available sound and video files have been commercially promoted as beneficial, easy-to-use tools to enhance cognition. Conversely, the beneficial effects of auditory beats are still under debate. The diversity of experimental results to date is due to the non-standardized experimental parameters, such as the combination of beat and carrier frequency and the sound level volume of the auditory beats. In addition, most studies conducted experiments with gender-heterogeneous groups. In the present study, we aimed at a detailed investigation of sustained attention under different auditory stimulation tones, taking into account what appear to be optimal stimulation parameters. Such parameters were the optimal combination of beat and carrier frequency, control of the individual sound volume, and a gender-homogeneous group of participants.

We found that, contrary to our initial hypothesis, binaural beats do not have a beneficial effect on attention compared to noise stimulation. This neutral effect is supported by motor behavior and
electrophysiological activity. Furthermore, all subjects show a similar response to binaural beats in their parietal θ/β ratio, which was confirmed to be a prominent biomarker of attention. Healthy subjects also showed no significant effect of binaural BB stimulation on their α-power compared to noise stimulation. Subjects with attentional deficits, however, showed a strong effect by binaural beat stimulation, although heterogeneous across different frequency bands.

**Funding support**

This work was supported by the Interdisciplinary Thematic Institute HealthTech, as part of the ITI 2021-2028 program of the University of Strasbourg, CNRS and Inserm.

**Author contributions**

Conceptualization: A.B. and A.H. contributed equally; Methodology: G.A.-C., B-T.P. and A.B. directed the experiments; Software: G.A.-C. and A.H. developed the data analysis scripts. Writing: G.A.-C. started a manuscript draft and A.B. and A.H. finalized it by equal contributions.

**Declaration of conflicts of interests**

The authors have nothing to declare.

**Declaration of generative AI and AI-assisted technologies in the writing process**

During the preparation of this work, the authors used DeepL in order to improve English language. After using this tool, the authors reviewed and edited the content as needed and takes full responsibility for the content of the published article.

**Declaration of data availability**

The data under study may be provided on request from the corresponding author.
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## Appendix A

The software Audacity (version 3.3.3) provides the signal amplitude as the root mean squared error (RMSE) in decibel (dB) with respect to an internal reference value $p_0$. We call this amplitude value (in dB) as amplitude $p_{Au}$, which then relates to the real RMSE of the output by

$$p_{Au}^{1} = 20\log\left(\frac{rmse^{1}}{p_{0}}\right), p_{Au}^{ref} = 20\log\left(\frac{rmse^{ref}}{p_{0}}\right)$$

Here $rmse^1$ is the RMSE of the signal under study and $rmse^{ref}$ is the RMSE of the signal at the audition threshold, i.e., the audible signal with the lowest intensity.

The sound pressure level $p_{ear}$ generated in the ear phones can be supposed (in a good approximation) to be proportional to the amplitude in the generated signal, i.e., the RMSE, and hence (Bies et al., 2024)

$$p_{ear}^{1} = a \cdot rmse^{1}, p_{ear}^{ref} = a \cdot rmse^{ref}$$

where $a \neq 0$ is any proportionality factor reflecting the properties of the devices and cables between the software output signal and the ear-phone signal. In addition, the Sound Pressure Level (SPL) is defined as

$$SPL = 20 \cdot \log\left(\frac{p_{ear}^{1}}{p_{ear}^{ref}}\right) dB$$

Then taking all equations together yields

$$SPL = (p_{Au}^{1} - p_{Au}^{ref}) dB.$$