Improving SSVEP-BCI Performance Through Repetitive Anodal tDCS-Based Neuromodulation: Insights From Fractal EEG and Brain Functional Connectivity

This study embarks on a comprehensive investigation of the effectiveness of repetitive transcranial direct current stimulation (tDCS)-based neuromodulation in augmenting steady-state visual evoked potential (SSVEP) brain-computer interfaces (BCIs), alongside exploring pertinent electroencephalography (EEG) biomarkers for assessing brain states and evaluating tDCS efficacy. EEG data were garnered across three distinct task modes (eyes open, eyes closed, and SSVEP stimulation) and two neuromodulation patterns (sham-tDCS and anodal-tDCS). Brain arousal and brain functional connectivity were measured by extracting features of fractal EEG and information flow gain, respectively. Anodal-tDCS led to diminished offsets and enhanced information flow gains, indicating improvements in both brain arousal and brain information transmission capacity. Additionally, anodal-tDCS markedly enhanced SSVEP-BCIs performance as evidenced by increased amplitudes and accuracies, whereas sham-tDCS exhibited lesser efficacy. This study proffers invaluable insights into the application of neuromodulation methods for bolstering BCI performance, and concurrently authenticates two potent electrophysiological markers for multifaceted characterization of brain states.


I. INTRODUCTION
T HE brain-computer interface (BCI) stands as a bur- geoning technology facilitating direct interaction between the brain and external apparatus, sidestepping traditional physiological movements [1], [2].BCI's performance intrinsically hinges on brain states, referring to the various activity and functional conditions within the brain.The diversity in brain states manifests distinct activity patterns, potentially impacting BCI's recognition accuracy [3], [4].Consequently, delving into brain state estimation and intervention techniques emerges as a crucial avenue for amplifying BCI performance.
Brain state intervention techniques bear substantial potential to enhance BCI operations.Their physiological foundation is rooted in the brain's plasticity, allowing adjustments in neural connections, functionality, and activity levels to influence brain states [5].These interventions, encompassing attention training, neurofeedback, and brain stimulation techniques [6], [7], [8], aim to augment or fine-tune brain functionality.Among these, transcranial direct current stimulation (tDCS) emerges as a non-invasive brain stimulation method, modulating brain neuron excitability with weak direct currents [9].This method bears the potential for substantial enhancement in BCI performance.For instance, tDCS applied to the prefrontal lobe cortex can enhance participants' attention levels [10].
During BCI training, tDCS stimulation of motor-related brain areas can promote neuron excitability and cortical plasticity, thus improving patients' control over motor functions and rehabilitation outcomes [11].Additionally, tDCS targeting specific brain regions like the prefrontal cortex lobe has been shown to enhance working memory functions [12].Although the pioneering exploration into tDCS for optimizing BCI performance has shown promise, tDCS technology remains in its infancy.It necessitates extensive research to unravel its intricate mechanisms, optimal parameter settings, and prolonged effects.Despite its validated enhancement in P300-BCI and motor imagery-based BCI systems performance [12], [13], [14], its integration in steady-state visual evoked potential (SSVEP)-BCI research remains relatively confined and yields underwhelming results.
In light of these research gaps, this study aspires to employ repetitive tDCS-based neuromodulation to bolster SSVEP-BCI performance.A long-term experimental design comprising two five-day rounds is proposed.To meticulously explore tDCS stimulation efficacy under diverse brain states, we will amass and contrast EEG data from three task modes (eyes open, eyes closed, and SSVEP stimulation), and employ anodal and sham tDCS patterns for comprehensive comparison and validation.
Moreover, this study is committed to uncovering EEG biomarkers for characterizing diverse brain states, bolstering the evaluation of tDCS efficacy.Prevailing brain state assessments frequently rely on narrow-band energy spectral analysis [15], [16], which has evident limitations, including potential information loss and inapplicability to evoked EEG scenarios (e.g., SSVEP), where evoked oscillations may obscure the extraction of underlying EEG spectral features.To transcend these, this research introduces a technique for segregating EEG fractal components from oscillatory components and constructs associations between these elements and brain states.Additionally, mathematical modeling is deployed to quantitatively delineate EEG fractal features.
This research also embarks on characterizing brain state features using brain functional connectivity methods, an essential tool for comprehending the transmission of information and interactions within various brain regions [17].In different brain states, connectivity patterns in the brain may change to adapt to various cognitive and behavioral demands [18].During cognitive tasks, connectivity between task-related brain regions may strengthen or weaken to support specific cognitive processes [19], [20].Comprehending the influence of brain states on brain functional connectivity holds substantial significance for understanding both brain functionality and behavior, offering critical insights for BCIs and attention cognition [21], [22].Given the complexity of brain networks, this study will use information flow gain to quantitatively outline brain functional connectivity and probe the modulation effects of diverse brain states on brain networks.
In summation, this research is poised to explore effective neuromodulation methods for enhancing BCI performance and unearth electrophysiological biomarkers for proficient brain state assessment.The contributions of this study are manifold.It delves into tDCS-based neuromodulation techniques to modulate brain states and impact EEG characteristics, thereby enhancing cognitive activity and SSVEP-BCI performance.Furthermore, it unveils two novel brain state estimation methods, offering diverse angles for evaluating cognitive state alterations induced by neuromodulation and task modes.Lastly, it investigates the employment of parameter-based brain state quantification for evaluating brain awakening and EEG modeling.

A. Subjects
Thirteen healthy subjects (7 females; aged 21-28 years, mean age 23.8 years), with normal or corrected-to-normal vision participated in this study.All subjects were righthanded in this study.Participants must possess either normal or corrected-to-normal vision, be free of any mental health disorders, and previous experience with brain-computer interface experiments or neuromodulation is not required.All subjects provided informed consent prior to the experiment and received monetary compensation for their participation.The Research Ethics Committee of Tsinghua University approved this study.The study was approved by the Institutional Review Board of Tsinghua University (application number: 20180041, Jan. 3, 2019).

B. tDCS Settings
A commercial tDCS stimulator (neuroConn DC Stimulator Plus, Germany) was employed for the experiment.The dimensions of the tDCS electrodes were 7 × 5 cm2.Cathodal and anodal tDCS electrodes were strategically positioned at the Cz and Oz locations, consistent with the international 10-20 EEG system [23].The electrodes were considered comfortable to wear, and all participants amicably tolerated the tDCS, with no reports of adverse effects.
This study utilized two tDCS patterns: anodal-tDCS and sham-tDCS.For sham-tDCS, the stimulation current progressively increased from 0 to 2 mA over 30 seconds, maintained at 2 mA for an additional 30 seconds, and then regressed to 0 mA over the following 30 seconds.The tDCS remained inactive for the remaining 19.5 minutes.Conversely, for anodal-tDCS, the stimulation current rose from 0 to 2 mA over 30 seconds, sustained at 2 mA for 20 minutes, and then diminished to 0 within the final 30 seconds.During receiving tDCS stimulation, subjects did not need to perform specific tasks, but only need to keep relaxed.

C. SSVEP Stimulation
For visual stimuli presentation, a 23.6-inch liquid-crystal display (LCD) screen, with a resolution of 1920 × 1080 pixels and a refresh rate of 60 Hz, was employed.Participants observed the screen from an approximate distance of 70 cm.
The visual stimulus phase was rigorously regulated using the sampled sinusoidal stimulation method [24].Nine targets were encoded with an initial phase of 0, and frequencies ranging from 9 Hz to 11 Hz (see Figure 1).To mark the commencement of each SSVEP-stimulus period, an event trigger was dispatched to the data acquisition system by the stimulus program.The SSVEP stimulation protocol unfolded as follows: each block encompassed 72 trials, amalgamating 9 frequencies with 8 repetitions, presented in a randomized sequence.Each trial spanned 5 seconds, culminating in a 6-minute block duration.Within each trial, a visual cue, embodied as a red rectangle, enveloped the target stimulus for the initial 0.5 seconds.Then, the nine targets began flashing for 4 seconds, during which subjects focused on the target's black cross.A half-second interval, wherein the screen ceased to flash, interlaced the trials.

D. Experimental Process
The experimental procedure, illustrated in Figure 2, was divided into two sessions based on the tDCS patterns: anodal-tDCS and sham-tDCS.Each session extended for five days, separated by a minimum one-week interval.The tDCS patterns remained consistent within each session and varied between the two sessions, with their sequence randomized for equitable comparison.The sequences of anodal-tDCS and sham-tDCS stimulations were randomized and the number of anodal -tDCS performed first was roughly balanced with the number of sham -tDCS performed first.
On the first day, participants sequentially underwent eyesopen (120 s), eyes-closed (120 s), SSVEP stimulation (6 minutes ×2 blocks), and tDCS (21 minutes) tasks, with EEG data collection at each stage.Subjects received tDCS stimulation for 21 minutes, and this setting had similarities to a previous research [31].Initially, participants focused on a central white fixation cross on a black screen.Following a 120-second rest period to mitigate visual fatigue, the eyesclosed task required participants to close their eyes while staying alert.Subsequently, two blocks of SSVEP stimulation tasks were administered.
Following the SSVEP tasks, subjects were exposed to either anodal-tDCS or sham-tDCS stimulation, employing the settings delineated in a prior study [25].The subsequent three days entailed tDCS stimulation, maintaining the initial day's parameters, and ensuring the start time was within two hours of the first day.The fifth day replicated tDCS, eyes open, eyes closed and SSVEPs tasks sequentially with the parameter settings same with the first day.There was a roughly 2 minutes time gap between tDCS stimulation and the onset of the follow experiments.

E. Data Acquisition
EEG data were acquired using a Synamps2 system (Neuroscan, Inc.) with a sampling rate of 1000 Hz.The data were band-pass filtered between 1 and 100 Hz and captured from 64 electrodes, excluding CB1, CB2, M1, and M2 during data analysis.Initially referenced to the vertex electrode, the data were subsequently re-referenced to a common average, adhering to the international 10-20 system standards.Electrode impedances were maintained below 10 k .

F. IRASA Method
Irregular-Resampling Auto-Spectral Analysis (IRASA) was utilized to segregate fractal and oscillatory activities from raw EEG data.The IRASA approach, exploiting the self-affine property of fractal time series and the frequency-specific property of oscillatory time series [26], first extracted the spectral component related to fractal activity from the original neural signal spectrum.The difference between the original and the extracted fractal spectra approximated the spectral component induced by oscillatory activity.IRASA was employed to separate oscillatory x(t) and fractal activities f(t) from original EEG y(t), as shown in equation ( 1): The estimated fractal power spectrum, fitted in log scale using least squares estimation, yielded a linear function with designated 'exponent' and 'offset' as the slope and intercept, respectively.
In the IRASA algorithm parameter setting, the curve fitting frequency range was 1-50 Hz, and the EEG epoch input data lengths for eyes open, eyes closed, and SSVEP stimulation conditions were set to 120s, 120s, and 4s, respectively.This study analyzing the frequency band of 1-50 Hz aligned with the settings in our prior publication [4].

G. Brain Functional Connectivity
Information flow gain ρ was employed to evaluate the brain functional network under different experimental conditions [27].Assume X is the EEG signal, expressed as: where t is time and n is the number of channels.A Multi-Variate Auto Regressive Model (MVAR) is used to fit X with the formula [28]: In this equation (2), A(k), E(t) and q represent the MVAR model parameter, zero-mean white noise and the fitting order, respectively.This formular is converted to the frequency domain as: Here, H ( f ) is connective matrix and H i j is signal connection strength from channel j to i. Define the Directed Transfer Function (DTF) connection matrix θ 2 i j and normalize it as y 2 m j : Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
For channel m, the inflow information (information received by m from other channels) and outflow information (information transmitted from m to other channels), are denoted as: The information flow gain is then defined as: H. SSVEP Analysis SSVEP envelopes in diverse neuromodulation patterns were extracted using the Hilbert transform, applying a band-pass filter from f -1 to f +1, wherein ' f ' corresponds to the stimulus frequency.
The comparison of SSVEP classification accuracies under distinct tDCS patterns incorporated a 140 ms delay in the classification algorithms to offset visual pathway delays [29].SSVEP frequency detection utilized the training-free method of Filter Bank Canonical Correlation Analysis (FBCCA) [29] and the training-required method of Task-Related Component Analysis (TRCA) [30].

I. Statistical Analysis
Statistical analyses were conducted using SPSS software (IBM SPSS Statistics, IBM Corporation), employing the t-test to test the differences of offset, information flow gain, amplitudes, accuracies and information transfer rates between different task modes and tDCS patterns, with a statistical significance threshold set at p <0.05.

A. The Effect of tDCS on Fractal EEG
Figure 3(a) illustrates the application of the IRASA method to EEG data.Power Spectral Density (PSD) is presented in logarithmic coordinates.The raw, fractal, and oscillatory curves depict the distribution of PSD for raw, fractal, and oscillatory EEG, respectively.The fractal curve is extracted using the IRASA method, linearly fitted by the power-law curve, and further characterized by its exponent and offset.These terms reflect the slope of the power-law curve and the ordinate of its intersection with the vertical axis, respectively.The oscillatory curve is derived by subtracting the fractal curve from the raw curve.Figure 4(a) presents topographic maps of offset under diverse experimental conditions.The lowest offset values are found in central and parietal regions, while the highest values are noted in the prefrontal region, aligning with previous findings [4].This figure also outlines the impact of tDCS on offset values, displaying differences (Diff) in offset values post-(Before) and pre-tDCS (After).Channels showcasing statistically significant differences post-and pre-tDCS, mainly located in the central and parietal regions, and some in the occipital region, are highlighted.
Figure 4(b) displays the influence of task modes on offsets.It exhibits the differences in offsets and channels with significant disparities for eyes closed, eyes open, and SSVEP stimulation.In most scalp channels, eyes closed and SSVEP stimulation correspond to the largest and smallest offsets, respectively, with distinctions primarily located in the temporal, central, and some occipital and parietal regions.Anodal-tDCS, compared to sham-tDCS, induces more substantial offset differences among the three task modes.

B. The Effects of tDCS Patterns and Task Modes on Brain Functional Connectivity
Figure 5(a) delineates the process of applying the brain function connectivity method on EEG data in the alpha band (8-12Hz), using an example of SSVEP stimulation postanodal-tDCS.Initially, the DTF) was computed to obtain the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.connectivity matrix, representing the entire network's information transfer characteristics.Each matrix column and row signify the intensity of information flow from this channel to other channels and from other channels to this channel, respectively.This data is visualized on a spherical model, with colored arrows representing the intensity of information transmission.Utilizing the connectivity matrix data, we calculated both the information flow out and in, and their quotient provided the information flow gain.Figure 5(a) also displays the topographic map of information flow gain, highlighting the largest values primarily in the occipital and parietal regions.This finding aligns with previous research asserting that during SSVEP visual stimulation, the occipito-parietal lobe acts as a connective cortex for pooling brain information [27].
Figure 5(b) illustrates the effects of various task modes on information flow gains.The analysis reveals that different task modes yield notable differences in information flow gains.These differences are color-coded, with channels showing statistically significant differences highlighted in each Diff topographic map's right square.The smallest information flow gain values are evident in the eyes-closed state, escalating in the eyes-open state, and peaking during SSVEP stimulation.Primarily in central and parietal regions, the findings underscore a more pronounced disparity between SSVEP stimulation and the other two task modes.Anodal-tDCS is also shown to evoke larger differences in information flow gains between task modes compared to sham-tDCS.
Pairwise comparisons unveil that anodal-tDCS engenders larger information flow gains compared to sham-tDCS, evident in both occipital and parietal regions.For instance, the mean information flow gains significantly escalated from before to after anodal-tDCS application in both regions ( p = 0.004 in the parietal region; p <0.001 in the occipital region).Conversely, sham-tDCS effects were found negligible compared to anodal-tDCS, substantiating anodal-tDCS's superior efficacy in enhancing brain functional connectivity.The accuracies and information transfer rates (ITRs) for both FBCCA and TRCA methods are depicted in Figure 8. Analysis demonstrates enhanced accuracies and ITRs postanodal-tDCS at data lengths of [1200:1600 2400:4000] ms ( p <0.05) for FBCCA, and at data lengths of 3400 ms ( p = 0.0415), 3500 ms ( p = 0.389), and 3600 ms ( p = 0.0499) for TRCA results.No notable differences in accuracies and ITRs are observed post-sham-tDCS for either method.

A. Impact of tDCS and Task Modes on Fractal EEG
In this study, tDCS-induced neural modulation led to a reduction in both offset and exponent, suggesting enhanced brain arousal.Initially, a positive linear relationship was observed between the exponent and intercept.Figure 3(b) illustrates a nearly positive linear correlation between the exponent and offset across various task modes and tDCS stimulations, consistent with previous research [26], [31].Subsequently, the study provided evidence of an increase in brain state arousals due to tDCS-based neural modulation.Figures 3(b   Averaged envelopes of SSVEPs over the nine stimulation frequencies and the nine occipital channels (Pz, PO5, PO3, POz, PO4, PO6, O1, Oz, O2).across all conditions.This shift in parameters, associated with frequency energies, indicates a decrease in low-frequency energy and an increase in high-frequency energy, suggesting enhanced brain arousal.Additionally, compared to sham tDCS, anodal tDCS more significantly reduced fractal parameter values, highlighting its superior effectiveness as a neural modulation pattern, in line with earlier research [31].
Fractal EEG features demonstrate potential as reliable indicators of various brain states.Generally, a decline in brain arousal level is associated with an increase in low-frequency energy and a decrease in high-frequency energy.Power-law characteristics have emerged as effective metrics for evaluating these states [16], [32], [33].This study, by comparing different task conditions, further validates the assertion that fractal EEG parameters serve as efficient physiological markers for estimating brain states.Figure 4(b) showcases significant differences in offset among various conditions, and Figure 4(a) highlights the offset's ability to distinguish different brain states induced by tDCS, suggesting the potential for characterizing distinct brain states using fractal EEG features.
Despite our initial assumption that sham tDCS would have a negligible effect, its outcomes surpassed our expectations.For example, as demonstrated in Figure 3(c), sham tDCS managed to decrease the power law slope, albeit to a lesser extent compared to anodal tDCS.This finding implies that the sham tDCS mode might possess unexpected application potential.We have added the related information in the article.

B. Impact of tDCS and Task Modes on Brain Functional Connectivity
The concept of flow gain, defined as the ratio of outflow to inflow, effectively illuminates the intensity of output.By simultaneously integrating input and output data, flow gain offers a more straightforward and transparent representation than that of functional connectivity patterns.Unlike phase coherence which captures the relationship between regions, flow gain's value not only highlights the intensity of the output but also subtly includes directional data.The higher the flow gain, the greater the contribution of a region to others.Through mapping methods, flow gain can also provide localized insights, identifying potential hubs.Fundamentally, flow gain presents distinct information from phase coherence, enhancing the visualization and quantification of connectivity patterns.This study augments power spectral density (PSD) analysis by incorporating brain network techniques rooted in functional connectivity analysis, offering a comprehensive assessment of neural modulation efficacy and brain state characteristics.Unlike the PSD method that provides amplitude activity information for specific brain regions alone, the brain network approach unearths correlated information across different brain regions, bolstering both the visualization and quantification of connectivity patterns.Functional connectivity holds paramount importance for discerning organized behaviors of cortical regions, transcending mere activity mapping [34].The exploration of the effect of tDCS-based neural modulation on brain networks, being largely uncharted territory, underscores the significance of this study.
Moreover, this research employs information flow gain to parameterize brain functional connectivity, enabling the quantitative comparison of information transmission processes under varied tDCS-induced brain states.Information flow gain amalgamates input and output information, presenting results more directly and transparently than functional connectivity patterns.It not only mirrors the output strength but also embeds implicit directional information, supplying local information and identifying hubs through mapping.This multi-faceted attribute positions information flow gain as a prospective physiological marker for brain state assessment, with higher values signifying a region's amplified contribution to others.
In this exploration, the tDCS's modulatory effects on brain functional connectivity were probed by measuring information flow gain values.The research substantiated the location of the information flow control center in the parietal region.The topographic map in figures 5(a) depict the parietal region's paramount information flow gain, underscoring its significant contribution to brain information transmission and its unique role as an information exchange hub, a finding corroborated by prior research [35], [36].
Furthermore, the study illuminates the enhancement of information flow in the parietal and occipital regions post anodal-tDCS, bolstering the parietal lobe's commanding capacity as a brain information exchange hub, as evinced in Figure 6.This enhancement, not mirrored by sham-tDCS stimulation, signifies a heightened information transaction capacity.
Additionally, the alpha band was harnessed to appraise brain functional connectivity.alpha oscillations, pivotal for characterizing cognitive and memory states, and playing a vital inhibitory role in information processing, underscore the augmentation of functional connectivity in the alpha band by tDCS.This enhancement reflects the amplified ability of the brain to stifle task-irrelevant information and bolster attention regulation [37].
Conclusively, this study ratifies information flow gain as a promising physiological marker for estimating brain states.Figures 5(b) and 6 exhibit notable differences in information flow gain across various conditions and demonstrate its utility in characterizing diverse brain states pre and post anodal-tDCS stimulation, especially in the parietal lobe, reinforcing the potential of characterizing brain states using information flow gain.

C. Effect of Neuromodulation on the Characteristics of SSVEP
The enhancement of SSVEP responses by anodal-tDCS can be attributed to the operational principles of tDCS, a method Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
known for modulating the activity of neurons within the cerebral cortex [13].Neurophysiological studies have shown that exposure to static electric fields, or direct current, results in alterations in the firing frequencies of neurons [23].It has been observed that the spontaneous firing rates of neurons either increase with the application of anodal-tDCS or decrease under cathodic-tDCS, depending on the polarity of the stimulation applied near the neuronal cells [25].Consequently, anodal stimulation leads to an increase in neuronal excitability, whereas cathodic stimulation results in a decrease.These changes in excitability are directly manifested through either the amplification or attenuation of triggered neural responses, respectively.

D. Expected Applications
Figures 7 and 8 underline the impact of tDCS on the characteristics of oscillatory components, demonstrating an increase in amplitudes, accuracies, and ITRs of SSVEP following anodal-tDCS treatment.This finding aligns with the theory of attentional resource allocation.Previous studies have affirmed the relationship between brain states and visual attention, suggesting that an elevated arousal state allocates more attentional resources towards visual stimuli, producing a more robust SSVEP response [38], [39].In the present study, evidence from fractal EEG established that anodal-tDCS induced a higher level of arousal (Figure 4), thus enhancing the performance of SSVEP-BCIs [40], [41].
This inference is also consistent with the findings from brain functional connectivity studies.Past research has underscored the crucial role of the parietal cortex in autonomously directing attention towards a location of interest, establishing a close connection with attention to visual stimuli [8].In this study, anodal-tDCS improved information flow gain in the parietal region, consequently augmenting the performance of SSVEP-BCIs.In contrast, sham-tDCS had a minimal effect on accuracies and ITRs compared to anodal-tDCS, highlighting the distinct impacts of anodal tDCS and sham-tDCS on inducing changes in brain states.
We also conduct a comparison of single versus repetitive anodal-tDCS sessions, analyzing EEG data from six participants.This data are gathered prior to anodal-tDCS application on the first day and following consecutive stimulations on both the first and fifth days.Our research demonstrates a notably larger improvement in SSVEP performance with repetitive anodal-tDCS compared to its single-session counterpart.For context, FBCCA accuracies, before the application of anodal-tDCS, are recorded at 81.0%, 83.0%, 85.2%, and 86.5% for EEG durations of 1200 ms, 1300 ms, 1400 ms, and 1500 ms, respectively.Following a single anodal-tDCS session, these accuracies undergo moderate increases, achieving 83.3%, 85.9%, 86.1%, and 87.8% correspondingly for the aforementioned durations.Notably, the application of repetitive anodal-tDCS sessions catalyze further enhancements, propelling the accuracies to 85.2%, 87.8%, 89.5%, and 90.2%.This pattern of consistent growth not only highlights but also reinforces the superior efficacy of employing repetitive anodal-tDCS protocols in amplifying SSVEP results.
V. CONCLUSION This study endeavored to modulate brain states using tDCS and explore electroencephalographic markers capable of delineating brain state characteristics based on both local and global features.The efficacy of these markers was further confirmed through SSVEP performance.Anodal tDCS contributed to an enhancement in SSVEP classification performance, a reduction in offset, and an increase in information flow gain.These results suggest a negative relationship between SSVEP performance and offset, along with a positive relationship between SSVEP performance and information flow gain.Additionally, a negative association between offset and information flow gain was noted.
These findings are plausible and may encompass underlying attentional and cognitive mechanisms.On the one hand, offset denotes power spectral density characteristics and mirrors the level of brain arousal, exhibiting a negative correlation with it.The use of anodal-tDCS led to a diminution in offset, signifying an amplification of brain arousal.In accordance with the theory of attentional resource allocation, a heightened level of brain arousal results in the allocation of more attentional resources for processing SSVEP visual stimuli, thus leading to an enhancement in the quality of SSVEP signals.
On the other hand, information flow gain epitomizes the brain's information interaction capabilities, particularly highlighting the control ability of the parietal cortex.The application of tDCS augmented information flow gain, enhancing the interaction between the parietal cortex and other brain regions, notably with the occipital region.This enhancement boosted the brain's perception of stimuli, such as visual and auditory cues, in turn augmenting the signal-to-noise ratio of SSVEP.Moreover, the negative relationship between offset and information flow gain reflects a positive correlation between brain arousal levels and information control capabilities.Essentially, an elevation in brain arousal level signifies an enhancement in the brain's information processing and control capabilities, further contributing to the improvement of SSVEP-BCI performance.

Figure 3 (
Figure 3(b) depicts scatter plots of the exponent and offset,showing an almost positive linear relationship between these two variables.Moreover, the spatial distribution of scatter plots varies among the three task modes (as seen in the left map), with the eyes-closed and SSVEP stimulation corresponding to the largest and smallest values, respectively.Post-anodal-tDCS, both offsets and exponents show a reduction compared to their pre-anodal-tDCS values.This observed positive linear relationship between exponent and offset corroborates earlier research[26],[31].Figure 3(c) demonstrates the power-law curves under varying task modes and tDCS patterns.Anodal-tDCS induces smaller exponent and offset values compared to sham-tDCS.Relative to SSVEP stimulation, static brain states (eyes closed, eyes open) are more sensitive to tDCS treatment, as seen in the comparison among the left (eyes closed), middle (eyes open), and right maps.Figure4(a) presents topographic maps of offset under diverse experimental conditions.The lowest offset values are found in central and parietal regions, while the highest values are noted in the prefrontal region, aligning with previous findings[4].This figure also outlines the impact of tDCS on offset values, displaying differences (Diff) in offset values post-(Before) and pre-tDCS (After).Channels showcasing statistically significant differences post-and pre-tDCS, mainly located in the central and parietal regions, and some in the occipital region, are highlighted.In contrast to sham-tDCS, anodal-tDCS leads to larger offset differences between the Before and After states.For example, the differences at Oz are −0.50, −0.44, and −0.41 (sham), and −0.77, −0.71, and −0.67 (anodal) for eyes closed, eyes open, and SSVEP stimulation, respectively.Figure4(b) displays the influence of task modes on offsets.It exhibits the differences in offsets and channels with significant disparities for eyes closed, eyes open, and SSVEP stimulation.In most scalp channels, eyes closed and SSVEP stimulation correspond to the largest and smallest offsets, respectively, with distinctions primarily located in the temporal, central, and some occipital and parietal regions.Anodal-tDCS, compared to sham-tDCS, induces more substantial offset differences among the three task modes.

Figure 3 (
Figure 3(b) depicts scatter plots of the exponent and offset,showing an almost positive linear relationship between these two variables.Moreover, the spatial distribution of scatter plots varies among the three task modes (as seen in the left map), with the eyes-closed and SSVEP stimulation corresponding to the largest and smallest values, respectively.Post-anodal-tDCS, both offsets and exponents show a reduction compared to their pre-anodal-tDCS values.This observed positive linear relationship between exponent and offset corroborates earlier research[26],[31].Figure 3(c) demonstrates the power-law curves under varying task modes and tDCS patterns.Anodal-tDCS induces smaller exponent and offset values compared to sham-tDCS.Relative to SSVEP stimulation, static brain states (eyes closed, eyes open) are more sensitive to tDCS treatment, as seen in the comparison among the left (eyes closed), middle (eyes open), and right maps.Figure4(a) presents topographic maps of offset under diverse experimental conditions.The lowest offset values are found in central and parietal regions, while the highest values are noted in the prefrontal region, aligning with previous findings[4].This figure also outlines the impact of tDCS on offset values, displaying differences (Diff) in offset values post-(Before) and pre-tDCS (After).Channels showcasing statistically significant differences post-and pre-tDCS, mainly located in the central and parietal regions, and some in the occipital region, are highlighted.In contrast to sham-tDCS, anodal-tDCS leads to larger offset differences between the Before and After states.For example, the differences at Oz are −0.50, −0.44, and −0.41 (sham), and −0.77, −0.71, and −0.67 (anodal) for eyes closed, eyes open, and SSVEP stimulation, respectively.Figure4(b) displays the influence of task modes on offsets.It exhibits the differences in offsets and channels with significant disparities for eyes closed, eyes open, and SSVEP stimulation.In most scalp channels, eyes closed and SSVEP stimulation correspond to the largest and smallest offsets, respectively, with distinctions primarily located in the temporal, central, and some occipital and parietal regions.Anodal-tDCS, compared to sham-tDCS, induces more substantial offset differences among the three task modes.

Fig. 3 .
Fig. 3. Averaged envelopes of the nine fundamental-frequency SSVEPs.Time ranges with significant differences are marked with gray shading.

Fig. 4 .
Fig. 4. Effects of experimental conditions on offset.(a) Effects of tDCS on offset.(b) Effects of task modes on offset.

Fig. 5 .
Fig. 5.The results of brain functional connectivity.(a).Details the processing of the brain functional connectivity method on EEG data.(b).The effects of various task modes on information flow gains.
) and 3(c) highlight the sensitivity of fractal features to tDCS-based neural modulation.Notably, anodal-tDCS results in lower exponents and offsets compared to pre-tDCS Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

Fig. 6 .
Fig. 6.Effects of tDCS on information flow gains.(a) Results in parietal region.(b) Results in occipital region.